This application is a divisional of co-pending U.S. application Ser. No. 11/417,976, filed on May 4, 2006, which is a continuation of International Application No. PCT/EP2003/050794, filed on Nov. 5, 2003, all of which are incorporated by reference herein in their entirety. 
    
    
     FIELD OF THE INVENTION 
     Chromatography systems perform a broad range of analysis methods to separate and/or analyze complex mixtures. There are a number of different types of chromatography systems, such as gas chromatography systems, Ion exchange chromatography systems, affinity chromatography systems, liquid chromatography systems, etc. In each type of chromatography system, components of a mixture are separated and distributed between two phases known as a mobile phase and a stationary phase. 
     DISCUSSION OF THE BACKGROUND ART 
     During operation, a mixture of various components is processed through a chromatography system at different rates. The different rates of migration through the chromatography system facilitate the separation of the mixture. Once the separation is accomplished, the different components of the mixture may be analyzed. 
     One conventional type of chromatography system is a High Pressure Liquid Chromatography system (HPLC). HPLC is a form of liquid chromatography used to separate compounds that are dissolved in a liquid. A conventional HPLC system is shown in  FIG. 1 . A reservoir  100  stores a liquid. The liquid in the reservoir  100  is considered as the mobile phase. The liquid is drawn (i.e., pumped) out of the reservoir  100  using a pump  102 . A variety of pumps may be implemented, such as syringe pumps, reciprocating pumps, etc. A sample is introduced by an injector  104 . The mixture of the initial liquid held in the reservoir  100  and the sample is then pushed through a column  106  packed with material. The column  106  is known in the art as the stationary phase. Different components of the mixture move through the column  106  at different rates and as a result, may be analyzed by a detector  108 . Final analysis of the mixture is then performed using a computer  110 . The mixture ultimately is deposited as waste  112 . 
     A significant component of a chromatography system is the pumping system. A conventional pumping system includes at least one pump. The pump includes a chamber with a reciprocating piston disposed in the chamber. Each pump typically includes an input valve positioned at an input side of the chamber and an output valve positioned at an output side of the chamber. The input valve throttles the flow of liquid into the pump (i.e., chamber) and the outlet valve throttles the flow of liquid out of the pump (i.e., chamber). 
     One substantial feature that distinguishes the pumping systems is whether they are low-pressure gradient pumping systems or high-pressure gradient pumping systems. In a low-pressure gradient pumping system, liquid mixing (i.e., mixing of the mobile phase if more than one solvent is used) occurs before the pump. In a high-pressure gradient pumping system, liquid mixing occurs after the liquid is processed through the pump. 
     Since a chromatography system separates and quantifies a sample (i.e., mixtures of compounds) based on the rate a liquid is processed through a column, controlling and managing the flow of liquid through the chromatography system is critical to performing the proper analysis of the sample (i.e., mixtures). A central component used to manage the flow of liquid through a chromatography system is the pumping system. In addition, since the liquid (i.e., flow rate, volume) that is processed through a chromatography system is extremely small, an incredible amount of precision and control must be applied to properly manage the flow of liquid through the chromatography system. 
     However, there are a number of problems that arise when processing liquid through the chromatography system. The problems impact the flow of liquid through the chromatography system and as a result, impact the analysis of the sample (i.e., mixtures of components). For example, varying the flow of liquid through a pump affects the analysis of the sample in a chromatography system; leaks may affect the flow of liquid through a chromatography system; incorrectly calibrated devices, such as sensor(s), may affect the flow of liquid through a chromatography system; cross over of liquids in a pumping system with multiple channels may affect the flow of liquid through a chromatography system; discontinuities in a liquid may affect the flow of liquid through a chromatography system; the intake operation of the pump may affect the flow of liquid through a chromatography system; and the piston timing of a pump may affect the flow of liquid through a chromatography system. 
     Thus, there is a need for a method and apparatus for managing the flow of liquids in a chromatography system. There is a need for a method and apparatus for managing the flow rate of liquids processed through a pumping system deployed in a chromatography system. There is a need for a method and apparatus for detecting and compensating for leaks within a pump. There is a need for a method and apparatus for attaining and retaining desired flow rates. There is a need for a method and apparatus for calibrating flow sensors. There is a need for a method and apparatus for avoiding channel cross over in multiple channel pumping systems. There is a need for a method and apparatus for optimizing delay volume in a pumping system. There is a need for a method and apparatus for optimizing the intake stroke in a pumping system. Lastly, there is a need for a pumping system with improved piston timing. 
     SUMMARY OF THE INVENTION 
     It is an object of the invention to provide an improved chromatography system. A variety of methods and apparatus for operating a pumping system are presented. Among these methods and apparatus are a pumping apparatus with a variable concept for flow generation dependent on a required flow rate; a method for determining and compensating for leaks in piston pumps; a method for calibrating a mass flow sensor; a method for avoiding channel cross flow in multiple channel pumping systems; a pumping method and apparatus with optimized delay volume; a pumping method and apparatus with optimized intake stroke; and a pumping method and apparatus with improved piston timing. 
     Embodiments of the invention can be partly or entirely embodied or supported by one or more suitable software programs, which can be stored on or otherwise provided by any kind of data carrier, and which might be executed in or by any suitable data processing unit. 
     One embodiment of a pumping system may comprise: means for configuring the pumping system with at least one sensor means; means for sensing a flow rate of fluid in the pumping system in response to configuring the pumping system with at least one sensor means; and means for determining leaks in the pumping system in response to sensing the flow rate of the fluid. 
     One embodiment of a pumping system may comprise: means for configuring the pumping system with at least one flow sensor; means for reconfiguring the at least one flow sensor within the pumping system; and means for determining leaks in the pumping system in response to reconfiguring the pumping system with the at least one flow sensor. 
     One embodiment of a pumping system may comprise: means for characterizing the pumping system to determine leaks in the pumping system; means for metering fluid through the flow sensor; and means for determining a calibration factor in response to characterizing the pumping system to determine leaks and in response to metering fluid through the flow sensor. 
     One embodiment of a pumping system may comprise: a pumping unit means; a flow sensor means positioned after the pumping unit means; means for characterizing the pumping unit means; means for metering fluid from the pumping unit means through the flow sensor means; and means for determining a calibration factor in response to metering fluid from the pumping unit means through the flow sensor means. 
     One embodiment of a pumping system may comprise: a channel; an output; means for pumping fluid at a flow rate in the pumping system; means for determining if the flow rate is below a predefined threshold; means for operating at least one first flow sensor at the output of the pumping system if the flow rate is below a predefined threshold; and means for determining if the flow rate is above the predefined threshold; and means for operating at least one second flow sensor within the channel if the flow rate is above the predefined threshold. 
     One embodiment of a pumping system may comprise: at least one channel, the channel including pumping units and an output; means for pumping fluid at a flow rate in the channel; means for determining if the flow rate is below a predefined threshold; means for operating at least one first flow sensor at the output of the channel if the flow rate is below a predefined threshold; and means for determining if the flow rate is above the predefined threshold; means for operating at least one second sensor within the channel if the flow rate is above the predefined threshold, wherein the at least one second flow sensor is positioned between the pumping units. 
     One embodiment of a pumping system may comprise: a conveyance; a pressure sensor coupled to the conveyance; a chamber coupled to the conveyance; means for compressing fluid in the chamber; means for monitoring pressure on the conveyance in response to compressing the fluid in the chamber; and means for determining a leak in response to monitoring the pressure on the conveyance. 
     One embodiment of a pumping system may comprise: a conveyance; a flow sensor coupled to the conveyance and to a valve, the valve further coupled to a chamber including a piston disposed therein, the chamber coupled to the conveyance; means for closing the valve; means for performing an intake stroke with the piston; means for monitoring for flow of fluid with the flow sensor in response to closing the valve and in response to performing an intake stroke with the piston; and means for determining a leak in response to monitoring for the flow of the fluid. 
     One embodiment of a pumping system may comprise: a pumping unit, the pumping unit comprising a chamber, and a pressure sensor coupled to the chamber; means for pressurizing the chamber; means for testing pressure in the chamber in response to pressurizing the chamber; means for determining a leak in response to testing the pressure in the chamber; and means for compensating for the leak in response to determining the leak. 
     One embodiment of a pumping system may comprise: an intake tube; a pressure sensor coupled to the intake tube and a chamber coupled to the intake tube; means for filling the chamber with fluid by conveying fluid through the intake tube; means for monitoring pressure on the intake tube in response to conveying fluid on the intake tube; and means for determining if the pressure has dropped below a predefined level in response to monitoring pressure on the intake tube. 
     One embodiment of a pumping system may comprise: an intake tube; a conveyance; a switching valve coupling the intake tube to the conveyance; a flow sensor coupled to the conveyance and a chamber, the chamber including a piston disposed therein; means for closing the switching valve; means for attempting to convey fluid on the conveyance subsequent to closing the switching valve; means for measuring fluid flow with the flow sensor in response to attempting to convey the fluid on the conveyance; and means for determining a leak in response to measuring the fluid flow with the flow sensor. 
     One embodiment of a pumping system may comprise: a chamber including an outlet and a piston disposed therein; an outlet valve coupled to the outlet of the chamber; a flow sensor coupled to the outlet valve; means for closing the outlet valve; means for moving the piston upward in the chamber; means for measuring fluid flow with the flow sensor in response to moving the piston upward in the chamber; and means for determining a leak in response to measuring the fluid flow with the flow sensor. 
     One embodiment of a pumping system may comprise: a conveyance coupled to a pumping unit; means for conveying fluid on the conveyance, the fluid including discontinuities; and means for operating the pumping unit to limit the discontinuities in the fluid. 
     One embodiment of a pumping system may comprise: means for metering at a flow rate; means for determining a leak in response to metering at the flow rate; and means for compensating for the leak by metering at a new flow rate. 
     One embodiment of a pumping system may comprise: means for monitoring the pumping system with a flow sensor; means for determining a change in flow rate in response to monitoring the pumping system with the flow sensor; and means for identifying a leak in response to determining a change in the flow rate. 
     One embodiment of a pumping system may comprise: means for monitoring a flow rate; means for determining a leak rate in response to monitoring the flow rate; and means for compensating for the leak rate in response to determining the leak rate. 
     One embodiment of a pumping system may comprise: means for monitoring a flow rate; means for determining a leak rate in response to monitoring the flow rate; and means for adjusting the flow rate in response to determining the leak rate. 
     One embodiment of a pumping system may comprise: a first pumping unit capable of generating a first volume of fluid and a second pumping unit capable of generating a second volume of fluid, wherein the first volume of fluid has a relationship with the second volume of fluid; means for operating the first pumping unit; means for operating the second pumping unit; means for identifying a change in the relationship between the first volume of fluid and the second volume of fluid in response to operating the first pumping unit and in response to operating the second pumping unit; and means for identifying a leak in response to identifying the change in the relationship between the first volume of fluid and the second volume of fluid. 
     One embodiment of a pumping system may comprise: first and second pumping units coupled together and a flow sensor located between the first and second pumping units; means for metering a flow rate; means for measuring a flow rate; means for comparing the measured flow rate to the metered flow rate; and means for determining a leak in response to comparing the measured flow rate to the metered flow rate. 
     One embodiment of a pumping system may comprise: a first pumping unit comprising a first chamber, a pressure sensor coupled to the first chamber; a second pumping unit including a second chamber, the second pumping unit in series with the first pumping unit; a valve positioned between the first pumping unit and the second pumping unit; means for delivering solvent with the second pumping unit; means for intaking solvent into the first chamber; means for compressing the solvent in the first chamber; means for opening the outlet valve in response to compressing the solvent in the first chamber while the second pumping unit is delivering solvent; means for delivering a small amount of solvent with the first pumping unit until the second pumping unit must be refilled; and means for measuring system pressure in response to delivering solvent with the first pumping unit and opening the outlet valve. 
     One embodiment of a pumping system may comprise: a first channel transporting first fluid; a second channel transporting second fluid; a waste output having a valve coupled to the first channel and coupled to the second channel via a conveyance, the waste output adapted for transporting waste, a system output coupled to the first channel via the conveyance and coupled to the second channel, the system output adapted for transporting system fluid; means for opening the valve; means for flushing the second channel in response to opening the valve; means for flushing the first channel in response to flushing the second channel; means for closing the valve in response to flushing the first channel; and means for pumping solvent from the first channel through the conveyance. 
     One embodiment of a pumping system may comprise: a first channel pumping first fluid; a second channel pumping second fluid; a system output coupled to the first channel and coupled to the second channel, the system output transporting system fluid in response to the first fluid and in response to the second fluid and a flow sensor coupled to the output of the first channel to measure the flow of the first fluid; means for stopping the first channel pumping the first fluid; means for sensing backflow with the flow sensor in response to stopping the first channel pumping the first fluid; and means for determine a leak in response to sensing the backflow. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of a prior art chromatography system. 
         FIG. 2  is a schematic diagram of an embodiment of an isocratic pumping system with additional liquid selection. 
         FIG. 3  is a block diagram of an embodiment of a pump control chip. 
         FIG. 4  is a block diagram of an embodiment of a computer. 
         FIG. 5  is a schematic diagram of an embodiment of a high-pressure gradient pumping system. 
         FIG. 6  is a schematic diagram of an embodiment of a low-pressure gradient pumping system. 
         FIG. 7  is a schematic diagram of an embodiment of a high-pressure gradient pumping system. 
         FIG. 8  is a schematic diagram of an embodiment of a high-pressure gradient pumping system. 
         FIG. 9A  is a schematic diagram of a pumping system, such as a single-channel pumping system, where the pumping units are positioned in series. 
         FIG. 9B  is a schematic diagram of a channel of a pumping system with pumping units configured in parallel. 
         FIG. 10  is a schematic diagram of a high-pressure gradient pumping system, such as a dual-channel pumping system. 
         FIG. 11A  is a flowchart of a method of determining leaks in a pumping system. 
         FIG. 11B  is a flowchart of a method of reconfiguring sensors in a pumping system. 
         FIG. 11C  is a flowchart of a method of calibrating sensors. 
         FIG. 11D  is a graph of voltage versus flow rate. 
         FIG. 11E  is a flowchart of a method of producing a variable flow rate. 
         FIG. 12  is a schematic of a pumping unit including a flow sensor and a pressure sensor(s). 
         FIG. 12A  is a flowchart of a method of identifying and compensating for leaks using a pressure sensor. 
         FIG. 12B  is a flowchart of a method of identifying and compensating for leaks using a flow sensor. 
         FIG. 12C  is a flowchart of a method of identifying and compensating for leaks using a pressure sensor. 
         FIG. 12D  is a flowchart of a method of identifying a blocked inlet tube. 
         FIG. 12E  is a flowchart of a method of identifying and compensating for leaks using a pressure sensor. 
         FIG. 12F  is a flowchart of a method of detecting a leak in a proportioning valve. 
         FIG. 13  is a schematic diagram of a single-channel pumping system including flow sensors. 
         FIG. 13A  is a flowchart of a method of detecting a leak in a gradient valve. 
         FIG. 13B  is a flowchart of a method of detecting a leak in an inlet valve. 
         FIG. 13C  is a flowchart of a method of performing a smooth intake stroke. 
         FIG. 13D  is a graph relating to a method of metering the intake flow to adjust for discontinuities in the intake flow. 
         FIG. 14  is a schematic diagram of a dual-channel pumping system including flow sensors. 
         FIG. 14A  is a flowchart of a method of operating a pumping system. 
         FIG. 15A  is a flowchart of a method of determining a leak in a piston. 
         FIG. 15B  is a graph depicting flow variations within a channel. 
         FIG. 15C  is a flowchart of a method of determining the piston velocity required to produce the nominal (desired) flow rate. 
         FIG. 15D  is a flowchart of a method of monitoring compression phases in a pumping chamber and monitoring the system pressure of a chromatography system. 
         FIG. 16  is a schematic diagram of a dual-channel pumping system including a flow sensor and a pressure sensor. 
         FIG. 16A  is a flowchart of a method of flushing a multi-channel pumping system. 
         FIG. 16B  is a flowchart of a method of eliminating cross-channel flow in a multi-channel pumping system. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     While the present invention is described herein with reference to illustrative embodiments for particular applications, it should be understood that the invention is not limited thereto. Those having ordinary skill in the art and access to the teachings provided herein will recognize additional modifications, applications, and embodiments within the scope thereof and additional fields in which the present invention would be of significant utility. 
       FIG. 2  is a schematic diagram of an embodiment of an isocratic pumping system with additional liquid selection at a pump inlet. It should be appreciated that the methods presented in the instant application may be implemented on a pumping system, such as a pumping system  200  displayed in  FIG. 2 . Pumping system  200  displays two pumping units  218  and  232  positioned in series. Pumping unit  218  includes an inlet valve  216  on an input side of pumping unit  218  and an outlet valve  220  on an output side of the pumping unit  218 . Pumping unit  232  includes a purge valve  242  on an output side of pumping unit  232 . 
     A liquid reservoir  202  stores liquids denoted as A, B, C, and D. Input conveyances  204 ,  206 ,  208 , and  210  provide pathways and convey liquids A, B, C and D, respectively, from liquid reservoir  202  to a liquid selection valve  212 . A selector  214  selects which input conveyance ( 204 ,  206 ,  208 ,  210 ) is connected to inlet valve  216 . Liquid selection valve  212  is controlled by a liquid selection unit  294 . It should be appreciated that in another embodiment of the present invention, a low-pressure gradient pumping system may be implemented by implementing liquid selection valve  212  as a proportioning valve and implementing liquid selection unit  294  as a gradient control unit. 
     Pumping unit  218  includes a chamber  222 , a piston  224 , a seal  226 , and a piston holder  228 . Liquid A, B, C, or D is drawn through inlet valve  216  into chamber  222  by a downward motion (i.e., intake stroke) of piston  224 . Outlet valve  220  throttles a pathway to a damper unit  230 . It should be appreciated that whilee damper unit  230  and a pressure transducer  284  are shown in pumping system  200 , either damper unit  230  and/or pressure transducer  284  may be removed. 
     Liquid A, B, C, or D flows through damper unit  230  to pumping unit  232 . Pumping unit  232  includes a chamber  234 , a piston  236 , a seal  238 , and a piston holder  240 . Piston  236  performs an intake stroke and draws liquid A, B, C, or D into chamber  234 . On a delivery stroke (i.e., upward movement) of piston  236 , liquid A, B, C, or D leaves chamber  234  and is pushed through a valve, such as purge valve  242 . Purge valve  242  provides a pathway  244  to a downstream system (not shown in  FIG. 2 ) or a pathway  246  to waste. It should be appreciated that throughout the disclosure, while a specific pumping unit (i.e.,  218 ,  232 ) may be described and discussed, various modifications of the pumping unit (i.e.,  218 ,  232 ) may be performed and still remain within the scope of the present invention. In addition, while pumping units with chambers and pistons are implemented, other types of pumping units, such as pumping units with impellers, etc., are anticipated and are within the scope of the present invention. In addition, valves, such as inlet valves  216 , outlet valve  220 , or purge valve  242 , may be implemented as active valves or passive valves. 
     In one embodiment, a gear system  248  includes a ball  250 , an actuator  252 , a shaft  254 , a gear  256 , and a gear  258 . Ball  250  is housed in actuator  252  and is in contact with piston holder  228 . Shaft  254  causes ball  250  and piston  224  to move upward (i.e., delivery stroke) and downward (i.e., intake stroke), as gear  256  is rotated clockwise and then counterclockwise. In one embodiment, gear  256  is a toothed gear, which is interlocked with gear  258 , which is connected to a motor/encoder unit  260 . In one embodiment, motor/encoder unit  260  includes a combined motor and encoder coupled to the motor. A position-servo unit  299  communicates information to motor/encoder unit  260  through a position-servo interface  264  and receives feedback via feedback line  262 . 
     A gear system  266  includes a ball  268  positioned within an actuator  270 . Ball  268  makes contact with piston holder  240 . A shaft  272  causes ball  268  and piston  236  to reciprocate in an upward and downward motion as a gear  274  is rotated clockwise and then counterclockwise. Gear  274  is interlocked with a gear  276 , which is connected to a motor/encoder unit  278 . A position-servo unit  297  communicates information to motor/encoder unit  278  through a position-servo interface  282  and receives feedback via a feedback line  280 . 
     In one embodiment, a pump control chip  288  is implemented to control pumping system  200 . A pump drive control unit  298  controls position-servo unit  299 . Position-servo unit  299  controls motor/encoder unit  260  through position-servo interface  264  and receives feedback through feedback line  262 . A pump drive control unit  296  controls position-servo unit  297 . Position-servo unit  297  controls motor/encoder unit  278  through position-servo interface  282  and receives feedback on the position and movement of motor/encoder unit  278  through feedback line  280 . 
     Pump drive control unit  296  and pump drive control unit  298  interface with an analog-to-digital converter (ADC)  290 , an inlet control unit  292 , and liquid selection unit  294  through a system controller  295 . In addition, users may use a user interface  286  to interface with pumping system  200  through system controller  295 . 
     ADC  290  interfaces with and receives a signal from pressure transducer  284 . Inlet control unit  292  interfaces with and controls inlet valve  216 , and liquid selection unit  294  interfaces with and controls liquid selection valve  212 . A more thorough explanation of the operation of a pumping system such as pumping system  200  may be found in European Patent EP0309596, entitled “Pumping apparatus for delivering liquid at high pressure,” published Apr. 5, 1989, which is herein incorporated by reference. 
     During operation, one of the liquid containers for liquids A, B, C, or D, shown collectively as liquid reservoir  202 , is connected to inlet valve  216  so that liquid A, B, C, or D can be delivered. This can be accomplished by either holding selector  214  in a fixed position so that liquid selection valve  212  is connected to one of the liquid containers for liquids A, B, C, or D in liquid reservoir  202 . Alternatively, liquid selection valve  212  may be operated as a proportioning valve by moving selector  214  across each input conveyance  204 ,  206 ,  208 , and  210  so that one of the liquid containers for liquids A, B, C, or D proportions the amount of liquid A, B, C, or D drawn in from liquid reservoir  202 . 
     During a start-up period, piston  224  is moved to a predefined distance referred to as the upper dead center (UDC). Under the control of pump control chip  288 , piston  224  moves upward into chamber  222  until piston holder  228  abuts the lower end of chamber  222 . Once this end position has been reached, piston  224  moves back downward a predefined distance. In addition, a corresponding angular setting of motor/encoder unit  260  is registered and stored to recreate the movement of piston  224  to the UDC position. In one embodiment, moving a piston, such as piston  224 , to a predefined position based on the corresponding angular setting of motor/encoder unit  260  is referred to as metering. In another embodiment of the present invention, any change of piston position or rate of motion, which results in a change in a flow rate of liquid entering and exiting a chamber, such as chamber  222 , is considered metering. Metering may be performed by operating piston  224  in combination with motor/encoder unit  260  and pump control chip  288 . A similar procedure may be performed to record a piston position where piston  224  moves to a lowest point in the chamber  222  required to draw liquid A, B, C, or D into chamber  222 . The lowest point is known as the lower dead center (LDC). 
     After identifying and setting the UDC position and the LDC position in both pumping units  218  and  232 , pumping system  200  begins nominal operation. Inlet valve  216  is opened under the control of inlet control unit  292 , and piston  224  moves down from the UDC position to the LDC position. As piston  224  moves from the UDC position to the LDC position, liquid A, B, C, or D is drawn into chamber  222 . 
     In one embodiment, user operates position-servo interface  282  to specify a flow rate for pumping system  200 . A corresponding stroke length, which is defined as the distance piston  224  travels between the UDC position and the LDC position, is then implemented in both pumping units  218  and  232  to accomplish the flow rate. Based on the flow rate input by the user, pump control chip  288  computes a corresponding stroke length using a predetermined mathematical relationship between flow rate and stroke length (or stroke volume, which is proportional to the stroke length). In an alternate embodiment of the present invention, pump control chip  288  may be modified to permit a variable or changing selection of the stroke length or volume. 
     Once piston  224  has traveled the stroke length determined by pump control chip  288  from the UDC position to the LDC position, motor/encoder unit  260  stops movement to stop the flow of liquid into chamber  222  and inlet valve  216  is closed. Motor/encoder unit  260  is restarted, moving in the opposite direction as before until it again reaches the UDC position. Once this is completed, the sequence repeats with piston  224  reciprocating in chamber  222  (i.e., moving down from the UDC position to the LDC position and back again). Piston  236  performs a similar sequence of motions and delivers liquid A, B, C, or D to other parts of the chromatography system (i.e., column) via pathway  244 . In one embodiment of the present invention, the movement of piston  224  and piston  236  is synchronized in such a way that the flow through the system is constant over time. 
       FIG. 3  is a block diagram of a pump control chip. In one embodiment, pump control chip  300  represents an implementation of pump control chip  288 , shown in  FIG. 2 . In another embodiment, pump control chip  300  is implemented in a pumping system. In another embodiment, pump control chip  300  may be implemented in a computer that interfaces with a pumping system. Input signaling, such as control signals  302 , address signals  304 , and range detector signals  306 , are received by a bi-directional bus interface  308 . Bi-directional bus interface  308  provides an interface between the input signaling (i.e.,  302 ,  304 , and  306 ) and a frequency synthesizer unit  310 , a compensation position unit  312 , and a range detector unit  314 . Frequency synthesizer unit  310  provides frequency and counting direction information based on the movement of a piston. Compensation position unit  312  calculates an amount of piston movement necessary in a pre-compression phase of piston operation. Range detector unit  314  defines the upper dead center (UDC) and lower dead center (LDC) of a piston and is responsible for defining the total stroke length of the piston. A set point position counter  316  maintains the position of the piston. For example, if a piston reaches the UDC or LDC, a signal is sent to set point position counter  316 , the number of steps for pre-compression are transferred to set point position counter  316  as soon as the piston begins to move upwards, etc. 
     Range detector unit  314  provides an input to an inlet valve control unit  318 , which controls an active valve  324 . Range detector unit  314  and set point position counter  316  provide input to a position-servo system  320 , which interfaces with a motor  328  through a position-servo interface  326 . Motor  328  is coupled to an encoder  330 , which provides feedback to position-servo system  320 . Lastly, set point position counter  316 , range detector unit  314 , and bi-directional bus interface  308  provide input to a gradient valve timer  322 , which provides an output  332  to a gradient valve (not shown in  FIG. 3 ). It should be appreciated that while a specific embodiment of pump control chip  300  is presented in  FIG. 3  and discussed herein, a variety of embodiments may be implemented and still remain within the scope of the present invention. 
       FIG. 4  is a block diagram of a computer  400  implemented in accordance with the teachings of the present invention. A central processing unit (CPU)  402  functions as a brain of computer  400 . An internal memory  404  includes a short-term memory and a long-term memory. The short-term memory may be implemented as a Random Access Memory (RAM)  406  or a memory cache used for staging information. The long-term memory may be implemented as a Read Only Memory (ROM)  408  or an alternative form of memory used for storing information. In one embodiment of the present invention, a short-term memory, such as RAM  406 , may be a display memory and used for storing a GUI for display on a monitor. 
     Computer  400  includes a storage memory  410 , such as a hard drive. Computer  400  also includes a pump control system  415 , such as pump control chip  288  of  FIG. 2  or pump control chip  300  of  FIG. 3 . In another embodiment, pump control system  415  may be implemented using the other components of computer  400 , such as CPU  402 , storage memory  410 , internal memory  404 , a communication pathway  412 , an input interface  414 , an output interface  416 , etc. For example, the logic implementing the functionality of pump control system  415  may be implemented in RAM  406  or in ROM  408 . In yet another embodiment, input devices  418  and output devices  420  may be combined in a pump control system, such as pump control system  415 . In this configuration, pump control system  415  may be implemented in a pump system and controlled by computer  400 . Communication pathway  412  is used to communicate information between RAM  406 , ROM  408 , storage memory  410 , input interface  414 , output interface  416 , CPU  402 , and pump control system  415 . 
     Input devices  418  may include devices such as a joystick, a keyboard, a microphone, a communication connection, servo motor inputs, inlet control inputs, outlet control inputs, gradient control inputs, ADC inputs, a mouse, etc. Input devices  418  interface with the system through input interface  414 . Output devices  420  may include devices such as a monitor, speakers, communication connections, servo motor outputs, inlet control outputs, outlet control outputs, gradient control outputs, ADC outputs, etc. Output devices  420  communicate with computer  400  through output interface  416 . 
     In one embodiment of the present invention, routines used to operate a pumping system, such as pumping system  200  of  FIG. 2 , may be stored in internal memory  404 , storage memory  410 , or in pump control system  415 . CPU  402  may operate under the control of these routines and control pumping system  200  of  FIG. 2  by communicating with input devices  418  and output devices  420 . 
       FIG. 5  is a schematic diagram of an embodiment of a high-pressure gradient pumping system, such as a binary pumping system. A pumping system  500  includes two channels. The first channel includes a pumping unit  506  positioned in series (i.e., coupled to/in liquid communication) with a pumping unit  516 . The second channel includes a pumping unit  526  positioned in series (i.e., coupled to/in liquid communication) with a pumping unit  536 . Pumping unit  506  receives liquid through an inlet valve  504  and outputs liquid through an outlet valve  508 . Pumping unit  536  receives liquid through an inlet valve  538  and outputs liquid through an outlet valve  534 . Each pumping unit  506 ,  516 ,  526 , and  536 , interfaces with a gear system  510 ,  520 ,  530 , and  540 , respectively. Further, each gear system  510 ,  520 ,  530 , and  540  interfaces with a motor/encoder unit  514 ,  522 ,  532 , and  544 , respectively. Lastly, each motor/encoder unit  514 ,  522 ,  532 , and  544  is in communication with a computer  524 . It should be appreciated that throughout the disclosure a gear system, such as gear system  510 , and a motor/encoder unit, such as motor/encoder unit  514 , may be considered a drive system used to drive a pumping unit, such as pumping unit  506 . It should also be appreciated that alternative forms of pumping units, such as syringe pumping units, etc., and alternative forms of drive systems may be implemented in each of the disclosed embodiments and may still remain within the scope of the present invention. For example, any conventional system (i.e., drive system) used to drive a pumping apparatus is within the scope of the present invention. 
     The first channel and the second channel are in parallel with each other, and liquid flows from pumping unit  516  and pumping unit  526  into a mixing chamber  548 . Mixing chamber  548  is connected to a damper  550 . Damper  550  is connected to a mixer  552 , which in turn is connected to a purge valve  554 . Liquid flows from purge valve  554  out as waste  556  or as output  588  to a remainder of the chromatography system (not shown in  FIG. 5 ). 
     Each motor/encoder unit  514 ,  522 ,  532 , and  544  is connected to computer  524 . As a result, each pumping unit  506 ,  516 ,  526 , and  536  may be controlled. In one embodiment of the present invention, metering of liquid and delivery of the liquid to the chromatography system are performed by individually controlling the operation of pumping units  506 ,  516 ,  526 , and  536  with the motor/encoder units  514 ,  522 ,  532 , and  544  in conjunction with the computer  524 . 
     During operation, liquid flows from liquid reservoirs through inlet valve  504  and inlet valve  538 , as shown by arrows  502  and  546 , respectively. Motor encoder unit  514  interfaces with gear system  510  to individually control pumping unit  506 . Motor/encoder unit  522  interfaces with gear system  520  to individually control pumping unit  516 . Motor/encoder unit  532  interfaces with gear system  530  to individually control pumping unit  526 . Lastly, motor/encoder unit  544  interfaces with gear system  540  to individually control pumping unit  536 . 
     Pumping unit  506  includes a piston  512 . Pumping unit  516  includes a piston  518 . Pumping unit  526  includes a piston  528 . Pumping unit  536  includes a piston  542 . 
     In one embodiment, motor/encoder unit  514  and motor/encoder unit  522  are synchronized via computer  524  to enable and piston  518  to operate at variable speeds relative to each other. In one embodiment, piston  512  may operate at some multiple of piston  518 . For example, piston  512  may operate at a continuous multiple of 2×, 4×, 7×, etc. of piston  518 . In an alternative embodiment, piston  512  may operate at a varying multiple of piston  518 . It should also be appreciated that the piston (i.e.,  512 ,  518 ,  528 , and  542 ) in each pumping unit (i.e.,  506 ,  516 ,  526 ,  536 ) may operate at an equal speed, a speed that is a continuous multiple or varying multiple relative to another piston. Operating a pumping unit relative to another pumping unit controls and/or manages the metering of liquid into and out of each pumping unit (i.e.,  506 ,  516 ,  526 ,  536 ). 
     In one embodiment, during operation, liquid enters the pumping unit (i.e.,  506 ,  516 ,  526 ,  536 ) in the bottom of a chamber and leaves the unit close to the top of a chamber. However, it should be appreciated that in alternate embodiments, liquid may enter and exit the chamber at different locations. In one embodiment, each chamber includes a piston, which has an outer diameter, which is smaller than the inner diameter of the chamber. As a result, liquid can fill the gap in between the outer diameter of the piston and the inner diameter of the chamber. In one embodiment, a piston has a stroke volume in the range of 20-100 ul as a function of the flow rate. A pump chip located in computer  524  controls the flow rates in a range of nano-liters to milliliters. However, it should be appreciated that a wide range of stroke volumes and flow rates may be implemented and remain within the range of the present invention. 
     During operation, pumping system  500  performs an initialization procedure to determine the upper dead center (UDC) and the lower dead center (LDC) for each of pistons  512 ,  518 ,  528 , and  542 . In addition, during initialization, motor/encoder units  514 ,  522 ,  532  and  544  are monitored to determine feedback movements, reference position signals are monitored, and assemblies are tested and monitored. Each piston  512 ,  518 ,  528 , and  542  moves upward slowly into a mechanical stop of a chamber and from there it moves back a defined path length. Computer  524  stores these piston positions in memory. After this initialization, pumping system  500  starts operation with a set parameters for each pumping unit. 
     Inlet valves  504  and  538 , are opened. Piston  512  and piston  542  each perform an intake stroke to draw liquid into pumping units  506  and  536 , respectively. At the same time, pistons  518  and  528  move upward delivering liquid to mixing chamber  548 . After a controller-defined stroke length (depending on the flow rate), each motor/encoder unit  514 ,  522 ,  532 , and  544  is stopped and inlet valves  504  and  538  are closed. The direction of each motor/encoder unit  514 ,  522 ,  532 , and  544  is reversed and pistons  512  and  542  move upward until they reach the stored upper limit (i.e., UDC), and at the same time, pistons  518  and  528  move downward. 
     The sequence repeats itself moving pistons  512 ,  518 ,  528 , and  542  up and down between the two limits (i.e., UDC and LDC). During the upward movement of pistons  512  and  542 , the liquid in pumping units  506  and  536  is pressed through outlet valves  508  and  534 , respectively, into pumping units  516  and  526 , respectively. Pistons  518  and  528  each draw in a portion of a volume displaced by pistons  512  and  542 , and a remaining volume is directly delivered to the system. During the drawing stroke of pistons  512  and  542 , pistons  518  and  528  deliver the drawn volume into the system. 
       FIG. 6  is a schematic diagram of an embodiment of a low-pressure gradient pumping system, such as a quaternary pumping system. A pumping system  600  includes two pumping units ( 616 ,  632 ) positioned in series. Liquids  602 ,  604 ,  606 , and  608  are processed through a vacuum chamber  610  and through a proportioning valve  612 . Proportioning valve  612  is in series with pumping unit  616 , which is in series with a damper unit  630 , which is further in series with pumping unit  632 . A purge valve  638  provides an outlet via a path  640  to the system (not shown in  FIG. 6 ) and to waste  642 . A gear system  620 ,  634  and a motor/encoder unit  624 ,  636  are connected to each pumping unit  616 ,  632 , respectively. Each motor/encoder unit  624 ,  636  is coupled to a computer  628 , which controls pumping units  616  and  632 . 
     Pumping system  600  is based on a dual-pump configuration. Metering of liquid and delivery are regulated by operating (a) pumping unit  616  individually using gear system  620 , motor/encoder unit  624 , and computer  628 , and (b) pumping unit  632  individually using gear system  634 , motor/encoder unit  636 , and computer  628 . Degassing of liquids is performed in vacuum chamber  610 , and liquid compositions are generated by proportioning valve  612 . In one embodiment, the pumping unit  616  includes an active inlet valve  614  and an outlet valve  618 . Damper unit  630  is connected between pumping units  616  and  632 . 
     When turned on, the pumping system  600  runs through an initialization procedure to determine the upper dead center (UDC) of piston  622 . Piston  622  moves slowly upward into a mechanical stop of the chamber and from there it moves back a predetermined path length. Computer  628  stores the position of piston  622  in memory. The lower dead center (LDC) varies as a function of the flow rate, stroke length, etc. After initialization, pumping system  600  starts operation with the parameters acquired during the initialization procedure. Active inlet valve  614  is opened and piston  622 , while moving down, draws liquid into the chamber. At the same time, piston  626  is moving upward delivering liquid into the system. After a controller-defined stroke length (depending on the flow rate), motor/encoder unit  624  is stopped and active inlet valve  614  is closed. Motor/encoder unit  624  is reversed and moves piston  622  up until it reaches the stored upper limit and at the same time, motor/encoder unit  636 , which controls piston  626 , moves piston  626  downward. The sequence then repeats itself with pistons  622  and  626  moving up and down between the two limits (i.e., reciprocating). During the up movement of piston  622 , the liquid in the chamber of pumping unit  616  is delivered through outlet valve  618  into damper unit  630 . Piston  626  draws in, from damper unit  630 , a portion of the volume displaced by piston  622 , and the remaining amount of the volume is delivered to the system. During the intake stroke (i.e., drawing stroke) of piston  622 , piston  626  delivers the drawn volume to the system via path  640 . For liquid compositions that require percentages of liquids  602 ,  604 ,  606 , and  608 , computer  628  controls and divides the length of the intake stroke into fractions and coordinates with proportioning valve  612  to connect the specified liquid channel to pumping units  616  and  632  to acquire the liquid in the proper percentages. 
       FIG. 7  is a schematic diagram of a pumping system, such as a capillary pumping system. In  FIG. 7 , liquid flows into a pumping system  700  through a conveyance or inlet tubes  702 ,  704 ,  706 , and  708 . The liquid flows through a vacuum chamber  710 . The liquid then flows through a solvent selection valve (SSV)  712  and a solvent selection valve (SSV)  732 . SSV  712  is in series with a pumping unit  716 , which includes an inlet valve  714  and an outlet valve  718 . Pumping unit  716  is controlled by a gear system  720 , which is connected to a motor/encoder unit  724 . Pumping unit  716  is in series with a pumping unit  722 , which is controlled by a gear system  726  that is connected to a motor/encoder unit  728 . 
     SSV  732  is connected to a pumping unit  734 , which is connected to a gear system  736 , which interfaces with a motor/encoder unit  738 . A pumping unit  740  is connected to a gear system  742 , which is connected to motor/encoder unit  744 . Each motor/encoder unit  724 ,  728 ,  744  and  738  is in communication with a computer  730 . Pumping unit  722  and pumping unit  740  are connected to a mixing chamber  746 . Mixing chamber  746  is in series with a damper  748 , which is in series with a mixer  750 . A variable nozzle  752  is positioned in series with mixer  750 . Variable nozzle  752  controls a split ratio of a total flow between the flow of a flow sensor  756  and the flow to a waste  754 . Flow sensor  756  is positioned on an output of pumping system  700 . 
       FIG. 8  is a schematic diagram of an embodiment of a pumping system  800  being employed as a high-pressure gradient pumping system, such as a preparative pumping system. To reduce the complexity of the description of pumping system  800 , a single channel is depicted in  FIG. 8 . A liquid  802  is input into a pumping unit  808 , which is coupled to an inlet valve  806  and an outlet valve  810 . In addition, a liquid  804  is input into a pumping unit  820 , which is coupled to an inlet valve  818  and outlet valve  822 . Pumping unit  808  interfaces with a gear system  812 , which is controlled by a motor/encoder unit  814 . 
     In one embodiment of the high-pressure gradient pumping system  800 , pumping unit  820  interfaces with a gear system  824 , which is controlled by a motor/encoder unit  826 . Pumping unit  808  includes a piston  809 , and produces an output  828 . Pumping unit  820  produces an output  830 . Output  828  and output  830  combine in a mixer  832 . Mixer  832  is in series with a purge valve  834 . Purge valve  834  is in series with, and provides a liquid output  836  to, a T-junction  838 . T-junction  838  also receives liquid  840  from a second channel (not shown) of pumping system  800 . It should be appreciated that  FIG. 8  displays one channel of pumping system  800 . A second channel of pumping system  800 , which is not shown, replicates the first channel shown in  FIG. 8 . The output of the second channel, i.e., liquid  840 , is shown. A mixer  842  is in series with T-junction  838 , and mixes liquid  840  and provides an output  844 . 
     In another embodiment, pumping system  800  is implemented without gear systems  812  and  824 . In an alternative configuration, the pistons (e.g., piston  809 ) are coupled and driven by an encoder controlled motor. 
       FIG. 9A  is a schematic diagram of a pumping system  900 , such as a single-channel pumping system, where the pumping units are positioned in series. In one embodiment, pumping system  900  is a low-pressure gradient pumping system, where mixing occurs prior to a routing of the liquid through a pumping unit. In one embodiment, a switch  912  may represent a selection switch. In another embodiment, switch  912  may represent a proportioning valve. It should be appreciated that the schematic diagram shown in  FIG. 9A  may be used to represent an isocratic pump as shown in  FIG. 2 , a single channel of a binary pump as shown in  FIG. 5 , a quaternary pump as shown in  FIG. 6 , a single channel of a capillary pump as shown in  FIG. 7 , or a preparative pump as shown in  FIG. 8 . It should also be appreciated that the methods presented in this application may be implemented on each of these pumping system configurations and, therefore, implementing any one of the methods presented in the instant application on any one of the pumping system configurations is within the scope of the present invention. 
     A variety of conventions have been employed in presenting the instant application. Throughout the instant application many figures include components that are outlined with dashed lines. Components outlined with dashed lines are used to display where the components may be positioned within the pumping system. However, each component may not be used in every configuration. For example, the pumping system  900  includes a flow sensor  918 , a flow sensor  932 , and a flow sensor  942 . Each flow sensor  918 ,  932  and  942  is outlined with dashed lines. Therefore, some of the methods presented below may utilize one of the flow sensors (i.e.,  918 ,  932 ,  942 ) or a combination of the flow sensors (i.e.,  918 ,  932 ,  942 ). For example, a method may utilize an individual flow sensor  918 ,  932 , or  942 . In the alternative, a method may utilize a combination of flow sensors, for example,  918  and  932 ,  932  and  942 ,  918  and  942 , or  918 ,  932 , and  942 . Flow sensors  918 ,  932 , and  942 , when implemented, detect liquid flow within pumping system  900 , and are coupled to a computer  928 , to provide to computer  928 , an indication of the detected liquid flow. Below, to identify which components are configured and/or implemented in pumping system  900  during a discussion of a method being employed in pumping system  900 , referencing text explaining the method will identify the components that are configured and operating in pumping system  900  during the performance of the method. 
     Pumping units, such as pumping units  920  and  934 , are also outlined with dashed lines. The dashed lines presented around the pumping units (i.e.,  920 ,  934 ) are provided to refer to the pumping units (i.e.,  920 ,  934 ) with a single label (i.e., pumping unit). Although the methods presented in the instant application operate with at least two pumping units, variations and modifications of the methods may be performed to work with a single pumping unit, and are still within the scope of the present invention. Any discussion of methods that utilize pumping units will identify the pumping unit configuration. 
       FIG. 9A  shows two pumping units (i.e.,  920 ,  934 ) in series. In one embodiment, pumping units  920  and  934  comprise a channel. An inlet valve  916  is in series with flow sensor  918 , which is in series with pumping unit  920 . An outlet valve  930  is in series with flow sensor  932 , which is in series with pumping unit  934 . Lastly, flow sensor  942  is in series with pumping unit  934 . Liquid flows from pumping unit  934 , through sensor  942 , to produce an output  944 . 
     As mentioned previously, flow sensors  918 ,  932 , and  942  are represented in dashed lines, which depicts that different combinations of flow sensors  918 ,  932  and  942  may be implemented when performing the methods presented in the instant applications. Therefore, a specific flow sensor (i.e.,  918 ,  932 , and  942 ) will be discussed and described when the flow sensor is configured and operating during the performance of the method. 
     Pumping system  900  includes a variety of liquids (i.e., A, B, C, D) stored in a liquid reservoir  902 . Each liquid (i.e., A, B, C, D) is conveyed through a conveyance  904 ,  906 ,  908  or  910 , respectively, to switch  912 . When switch  912  is implemented as a proportioning valve, the liquids (i.e., A, B, C, D) are mixed. The liquids (i.e., A, B, C, D) are then drawn through a conveyance  914  and inlet valve  916  into pumping unit  920 . Pumping unit  920  includes a chamber  922  and a piston  924 , which performs a reciprocating motion (i.e., performs a piston stroke which consist of an intake stroke and a delivery stroke). Outlet valve  930  is in series with pumping unit  920 . Flow sensor  932  is in series with outlet valve  930 . Pumping unit  934  is in series with flow sensor  932 , which is in series with outlet valve  930 . Pumping unit  934  includes a chamber  936  and a piston  938 . Throughout the discussion of the figures in the present invention, inlet valves and outlet valves will be described and discussed. It should be appreciated that the inlet valves, such as inlet valve  916 , and the outlet valves, such as outlet valve  930 , may be implemented as active valves or passive valves. In addition, the flow sensors, such as flow sensor  918 , may be positioned before inlet valve  916  or after inlet valve  916 , and flow sensor  932  may be positioned before outlet valve  930  or after outlet valve  930 . A wide variety of flow sensors may be implemented in accordance with the teachings of the present invention. One specific flow sensor that may be implemented in the present invention is flow sensor model SLG 1430 implemented by Sensirion, Switzerland. 
     A motor/encoder system  926  and a motor/encoder system  940  each includes gears (i.e., gear system), a motor, and encoders required to individually operate pumping unit  920  and pumping unit  934 , respectively. Computer  928  is coupled to both of motor/encoder system  926  and motor/encoder system  940 . 
     During initialization, procedures are performed to identify a upper dead center (UDC) and a lower dead center (LDC) of piston  924  and piston  938  using motor/encoder systems  926  and  940 , respectively. Additional activities, such as opening and closing inlet valve  916  and outlet valve  930 , may also be performed during initialization. 
     During operation, inlet valve  916  is opened. An intake stroke of piston  924  draws liquid (i.e., A, B, C, D) through switch  912  and fills chamber  922 . In one embodiment, liquids  922 A,  922 B,  922 C, and  922 D are drawn into chamber  922 . Liquids  922 A,  922 B,  922 C, and  922 D correspond to the liquids A, B, C and D, respectively, that are stored in liquid reservoir  902 . Various percentages of liquids A, B, C and D are mixed together when switch  912  is implemented as a proportioning valve. On the delivery stroke of piston  924 , liquid (i.e.,  922 A,  922 B,  922 C,  922 D) is compressed and forced out of chamber  922  through outlet valve  930 . Motor/encoder system  926  and computer  928  are used to adjust the intake and delivery stroke of piston  924  to adjust the metering (i.e., intake and expulsion) of liquid (i.e.,  922 A,  922 B,  922 C,  922 D) from chamber  922 . In a similar manner, motor/encoder system  940  and computer  928  are used to adjust the intake and delivery stroke of piston  938  to meter (i.e., adjust the intake and expulsion) of liquid from chamber  936 . 
     Metering is implemented using a number of alternative mechanisms. In one embodiment, metering is performed by individually controlling pumping unit  920  with motor/encoder system  926  and computer  928 . In another embodiment, metering is accomplished by individually controlling pumping unit  934  with motor/encoder system  940  and computer  928 . In another embodiment, metering is performed by integrating and controlling the operation of pumping units  920  and  934  with motor/encoder systems  926  and  940 , respectively, and computer  928 . Lastly, metering may involve an integrated system operation controlling the flow rate of liquid throughout the entire pumping system  900  (i.e., single-channel pump). Metering in this context may include using various components in addition to pumping unit  920  or pumping unit  934 . Therefore, metering using an integrated system may include using inlet valve  916 , flow sensor  918 , pumping unit  920 , outlet valve  930 , flow sensor  932 , pumping unit  934 , and flow sensor  942 , selectively or in combination, to meter the flow of liquid through pumping system  900 . 
       FIG. 9B  is a schematic diagram of a pumping system, such as a single channel of a pumping system with pumping units configured in parallel.  FIG. 9B  displays two pumping units (i.e.,  958 ,  978 ) in parallel. In one embodiment, the two pumping units (i.e.,  958 ,  978 ) are positioned in parallel and are implemented in a channel of a pumping system  950 . An inlet valve  954 , a flow sensor  956 , a pumping unit  958 , an outlet valve  966 , and a flow sensor  968  are positioned in series. An inlet valve  974 , a flow sensor  976 , a pumping unit  978 , an outlet valve  986 , and a flow sensor  988  are positioned in series. A flow sensor  994  is positioned in parallel with flow sensor  968 . In addition, flow sensor  994  is positioned in parallel with flow sensor  988 . 
     A liquid is conveyed from a reservoir  952  through inlet valve  954  and through flow sensor  956  to pumping unit  958 . Pumping unit  958  is in series with flow sensor  956 . It should be appreciated that flow sensor  956  may be configured before inlet valve  954  or after inlet valve  954 . Liquid is drawn from reservoir  952  into pumping unit  958  during an intake stroke. Pumping unit  958  includes a chamber  960  and a piston  962 , which performs a reciprocating motion (i.e., performs a piston motion which consists of a delivery stroke and an intake stroke) Outlet valve  966  is positioned in series with pumping unit  958 . Flow sensor  968  is in series with outlet valve  966 . It should be appreciated that flow sensor  968  may be configured before outlet valve  966  or after outlet valve  966 . An output  970  is also shown. 
     Liquid is conveyed from reservoir  972  through inlet valve  974  and through flow sensor  976  to pumping unit  978 , which is in series with flow sensor  976 . It should be appreciated that flow sensor  976  may be configured before inlet valve  974  or after inlet valve  974 . Liquid is drawn from reservoir  972  into pumping unit  978  during an intake stroke. Pumping unit  978  includes a chamber  980  and a piston  982 , which performs a reciprocating motion (i.e., performs a piston motion which consists of a delivery stroke and an intake stroke). Outlet valve  986  is positioned in series with pumping unit  978 . Flow sensor  988  is in series with outlet valve  986 . It should be appreciated that flow sensor  988  may be configured before outlet valve  986  or after outlet valve  986 . An output  992  is also shown. Both output  970  and output  992  connect to a channel output  996 . Flow sensor  994  is positioned in channel output  996 . 
     Flow sensors  956 ,  968 ,  976 ,  988  and  994  are coupled to a computer  990 . Flow sensors  956 ,  968 ,  976 ,  988  and  994  detect a flow of liquid, and report the detected flow to computer  990 . A motor/encoder system  964  is connected to pumping unit  958 . Motor/encoder system  964  is controlled by computer  990 . A motor/encoder system  984  is connected to pumping unit  978 . The Motor/encoder system  984  is controlled by computer  990 . 
     During initialization, procedures are performed to identify an upper dead center (UDC) and a lower dead center (LDC) of piston  962  and of piston  982 , using motor/encoder systems  964  and  984 , respectively. Additional activities, such as opening and closing inlet valves  954  and  974 , and outlet valves  966  and  986 , may also be performed during initialization. 
     During operation, an inlet valve, such as inlet valve  954  and/or inlet valve  974 , is opened. An intake stroke of a piston, such as piston  962  and/or piston  982 , draws liquid from reservoir  952  and/or reservoir  972 . The liquid is drawn through an inlet valve, such as inlet valve  954  and/or inlet valve  974 , and through a flow sensor, such as flow sensor  956  and/or flow sensor  976 , respectively. The liquid fills a chamber, such as chamber  960  and/or chamber  980 , on the intake stroke. Piston  962  and/or piston  982  perform(s) a delivery stroke and, accordingly, liquid stored in chambers  960  and  980  is compressed and forced out of chambers  960  and  980  and through outlet valves  966  and  986 , respectively. The liquid flows through flow sensors  968  and  988  to outputs  970  and  992 . Outputs  970  and  992  combine at channel output  996 . The liquid flows through flow sensor  994 . Motor/encoder systems  964  and  984 , in conjunction with computer  990 , are used to adjust the intake and delivery stroke of pistons  962  and  982 , respectively, to adjust the metering (i.e., intake and delivery) of liquid from chambers  960  and  980 . 
       FIG. 10  is a schematic diagram of a pumping system, such as a dual-channel pumping system. In one embodiment, a pumping system  1000  may represent a high-pressure gradient pumping system, such as the pumping systems represented in  FIG. 5  and  FIG. 7 . In a first channel, an inlet valve  1004 , a flow sensor  1005 , a pumping unit  1006 , an outlet valve  1016 , a flow sensor  1018 , a pumping unit  1020 , and a flow sensor  1030  are positioned in series. In a second channel, an inlet valve  1042 , a flow sensor  1043 , a pumping unit  1044 , an outlet valve  1052 , a flow sensor  1054 , a pumping unit  1056 , and a flow sensor  1038  are positioned in series. The first channel and the second channel are parallel to each other. The first channel and the second channel combined and routed through a flow sensor  1032  to an output  1034 . Flow sensors  1005 ,  1018 ,  1030 ,  1043 ,  1054 ,  1038  and  1032  are coupled to a computer  1014 . Flow sensors  1005 ,  1018 ,  1030 ,  1043 ,  1054 ,  1038  and  1032  detect a flow of liquid, and report the detected flow to computer  1014 . It should be appreciated that although  FIG. 10  displays a dual-channel pumping system with pumping units configured in series, the methods presented in the instant application may also be implemented in a dual-channel pumping system where the pumping units are positioned in parallel. 
     Pumping system  1000  includes a liquid stored in a liquid reservoir  1002 . The liquid stored in liquid reservoir  1002  is drawn through flow sensor  1005  and through inlet valve  1004  into pumping unit  1006 . Pumping unit  1006  includes a chamber  1008  and a piston  1010 , which reciprocates upward and downward within chamber  1008 . On an intake stroke of piston  1010 , liquid is drawn into chamber  1008  and on a delivery stroke of piston  1010 , liquid is compressed and forced out of chamber  1008 . A motor/encoder system  1012  and a computer  1014  are used to meter an intake and an expulsion (i.e., flow) of liquid into and out of chamber  1008  by adjusting (i.e., position, such as stroke length and/or timing) the upward and intake strokes of piston  1010 . 
     Outlet valve  1016  is positioned in series with pumping unit  1006 . Flow sensor  1018  is positioned in series with outlet valve  1016  (note: flow sensor  1018  can be located either before or after outlet valve  1016 ) and detects the flow of liquid between pumping unit  1006  and pumping unit  1020 . A piston  1024  operates within a chamber  1022 . During an intake stroke of piston  1024 , liquid flows from pumping unit  1006  to pumping unit  1020 , into chamber  1022 . On the delivery stroke of piston  1024 , liquid is forced out of chamber  1022  to a channel output  1028 . In an alternate embodiment, liquid from chamber  1008  flows through chamber  1022  directly to channel output  1028  if piston  1024  is stationary or moving upwards. It should be appreciated that a variety of embodiments may be implemented and still remain within the scope of the present invention. A motor/encoder system  1026  and computer  1014  are used to meter (i.e., adjust the upward and intake stroke) the flow of liquid from chamber  1022 . 
     Pumping system  1000  includes a liquid reservoir  1040 . Liquid is drawn through flow sensor  1043  and through inlet valve  1042 . The liquid is then drawn into pumping unit  1044 . Pumping unit  1044  includes a chamber  1046  and a piston  1048 , which reciprocates upward and downward within chamber  1046 . On an intake stroke of piston  1048 , liquid is drawn into chamber  1046  and on a delivery stroke of piston  1048 , liquid is compressed and forced out of chamber  1046 . A motor/encoder system  1050  and computer  1014  are used to meter the flow of liquid into and out of chamber  1046  by adjusting (i.e., position, such as stroke length and/or timing) the upward and intake stroke of piston  1048  to adjust the intake of liquid into, and the expulsion of liquid from, chamber  1046 . 
     Outlet valve  1052  is positioned in series with pumping unit  1044 . Flow sensor  1054  is positioned in series with outlet valve  1052  and detects a flow of liquid between pumping unit  1044  and pumping unit  1056 , which is in series with pumping unit  1044 . Pumping unit  1056  includes a chamber  1058  having a piston  1060  therein. Liquid flows from pumping unit  1044  to pumping unit  1056 . Liquid is drawn into chamber  1058  on an intake stroke of piston  1060 , and on a delivery stroke of piston  1060 , liquid is compressed and forced out of chamber  1058  to a channel output  1036 . In an alternate embodiment, liquid from chamber  1046  flows through chamber  1058  directly to channel output  1036  if piston  1060  is stationary or moving upwards. As previously stated, it should be appreciated that a variety of embodiments may be implemented and still remain within the scope of the present invention. A motor/encoder system  1062  and computer  1014  are used to meter (i.e., adjust the intake and delivery stroke) the flow of liquid from chamber  1058  and to adjust the intake and expulsion of liquid from chamber  1058 . 
     In one embodiment, pumping unit  1006  and pumping unit  1020  combine to form a first channel, which outputs liquid to channel output  1028 . In another embodiment, pumping unit  1044  and pumping unit  1056  combine to form a second channel, which outputs liquid to channel output  1036 . Both of channel output  1028  and channel output  1036  are coupled to output  1034 . Therefore, a combination of liquid conveyed on channel output  1028  and liquid conveyed on channel output  1036  is conveyed on output  1034 . 
     In one embodiment, flow sensor  1030  is positioned on channel output  1028  and detects the flow of liquid conveyed via channel output  1028 . In another embodiment, flow sensor  1038  is positioned on channel output  1036  and detects the flow of liquid conveyed via channel output  1036 . In another embodiment, flow sensor  1032  is positioned on output  1034  and detects the flow of liquid conveyed via output  1034 . 
       FIG. 11A  is a flowchart of a method of configuring sensors in a pumping system.  FIGS. 9A ,  9 B, and  10  will be discussed in conjunction with  FIG. 11A . The method commences with step  1100 . 
     At step  1100 , a pumping system, such as the pumping systems represented by the schematic diagrams depicted in  FIGS. 9A ,  9 B, and  10 , are configured with flow sensors. Configuring may include manufacturing the pumping system with a specific configuration of flow sensors or implementing (i.e., operating) a specific configuration of flow sensors in the pumping system during operation of the pumping system. Implementing a specific configuration of flow sensors may include real-time operation of flow sensors connected to the pumping system, non-real time implementation of flow sensors between testing, etc. 
     In one embodiment, selected flow sensors are implemented in the pumping system to individually detect the flow of liquid in the pumping system. In another embodiment, flow sensors are implemented in the pumping system and simultaneously operate to detect and compare the flow of liquid throughout the pumping system. For example, referring to  FIG. 9A , flow sensors  918 ,  932 , and  942  may each individually be implemented within the pumping system and work individually to detect liquid flow within the pumping system. In another embodiment, flow sensors  918 ,  932 , and  942  may all be implemented within the pumping system and work collaboratively to detect and determine the flow of liquid throughout the pumping system. Lastly, any combination of flow sensors may be implemented and operate collectively within the pumping system. 
     Referring to  FIG. 9B , flow sensors  956 ,  968 ,  976 ,  988 , and  994  may each individually be implemented within the pumping system and work individually to detect liquid flow within the pumping system. In another embodiment, flow sensors  956 ,  968 ,  976 ,  988 , and  994  may all be implemented within the pumping system and work collaboratively to detect and determine the flow of liquid throughout the pumping system. Lastly, any combination of flow sensors  956 ,  968 ,  976 ,  988 , and  994  may be implemented and operate collectively within the pumping system. 
     A similar methodology may be implemented using  FIG. 10  as a reference. Flow sensors  1005 ,  1018 ,  1030 ,  1032 ,  1038 ,  1043 , and  1054  may each be implemented individually or collectively in the pumping system  1000 . Further, any combination or permutation of the flow sensors  1005 ,  1018 ,  1030 ,  1032 ,  1038 ,  1043 , and  1054  may be implemented in the pumping system  1000 . 
     From step  1100 , the method progresses to step  1102 . 
     In step  1102 , the pumping system performs normal operations as shown by  1102 . From step  1102 , the method progresses to step  1104 . 
     At step  1104 , leaks may be determined by using the flow sensors. A variety of techniques may be used to determine leaks using the flow sensors. For example, 1) a change in the flow rate recorded by a flow sensor over time may suggest a leak in a pumping system; 2) a comparison between the flow rate metered by the motor/encoder system and the flow rate measured by a flow sensor may identify a leak; 3) a comparison in flow rates measured by different flow sensors within the channel or between channels may suggest a leak in a pumping system; and 4) a comparison of flow rates metered by different pumping units within the channel or between the channels may suggest a leak in a pumping system. While specific examples of determining a leak with a flow sensor are provided, numerous examples for determining leaks with a flow sensor are presented in the instant application and are within the scope of the present invention. From step  1104 , the method progresses to step  1106 . 
     At step  1106 , compensation is made for the leaks in the pumping system. For example, each pumping unit may be controlled to compensate for the leaks by varying the metering of liquid flowing through each pumping unit. 
       FIG. 11B  is a flowchart of a method of reconfiguring sensors in a pumping system.  FIGS. 9A ,  9 B, and  10  will be discussed in conjunction with  FIG. 11B . The method commences with step  1120 . 
     At step  1120 , a pumping system, such as the pumping systems represented by the schematic diagram depicted in  FIGS. 9A ,  9 B, and  10 , is configured with flow sensors. The flow sensors are configured into a first configuration. Configuring may include manufacturing the pumping system with a specific configuration of flow sensors or implementing/operating (i.e., turning on and off) a specific configuration of flow sensors in the pumping system during operation of the pumping system. 
     In one embodiment, selected flow sensors are implemented in the pumping system individually to detect the flow of liquid in the pumping system. In another embodiment, flow sensors are implemented in the pumping system and simultaneously operate to detect and compare the flow of liquid throughout a pumping system. For example, referring to  FIG. 9A , flow sensors  918 ,  932 , and  942  may each be individually implemented within the pumping system and work individually to detect flow within the pumping system. In another embodiment, flow sensors  918 ,  932 , and  942  may all be implemented within the pumping system and/or work collaboratively to detect and determine the flow of liquid throughout the pumping system. Referring to  FIG. 9B , flow sensors  956 ,  968 ,  976 ,  988 , and  994  may each individually be implemented within the pumping system and work individually to detect liquid flow within the pumping system. In another embodiment, flow sensors  956 ,  968 ,  976 ,  988 , and  994  may all be implemented within the pumping system and work collaboratively to detect and determine the flow of liquid throughout the pumping system. Lastly, any combination of flow sensors  956 ,  968 ,  976 ,  988 , and  994  may be implemented and operate collectively within the pumping system. 
     A similar methodology may be implemented using  FIG. 10  as a reference. Flow sensors  1005 ,  1018 ,  1030 ,  1032 ,  1038 ,  1043  and  1054  may each be implemented individually or collectively in the pumping system  1000 . Further, any combination or permutation of the flow sensors  1005 ,  1018 ,  1030 ,  1032 ,  1038 ,  1043 , and  1054  may be implemented in the pumping system  1000 . It should also be appreciated that any combination of the foregoing methods or configurations may be implemented and still remain within the scope of the present invention. 
     From step  1120 , the method progresses to step  1122 . 
     At step  1122 , the pumping system performs normal operations. From step  1122 , the method progresses to step  1124 . 
     At step  1124 , leaks may be determined by using the flow sensors. A variety of techniques may be used to determine leaks using the flow sensors. For example, a change in the flow rate, such as a decrease in the flow rate indicated by the flow sensor over time, may suggest a leak. While a specific example of determining a leak with a flow sensor is provided in this example, numerous examples for determining leaks with a flow sensor are presented in the instant application and are within the scope of the present invention. From step  1124 , the method progresses to step  1126 . 
     At step  1126 , techniques, such as metering, are used to compensate for the leaks determined while operating the pumping systems. From step  1126 , the method progresses to step  1128 . 
     At step  1128 , the flow sensors are reconfigured into a second configuration. In one embodiment, reconfiguring the flow sensors may occur in real time during testing operations. In another embodiment, reconfiguring the flow sensors may occur in non-real time. In one embodiment, reconfiguration includes implementing a different configuration of flow sensors in the pumping system. From step  1128 , the method progresses to step  1130 . 
     At step  1130 , leaks are determined using the new configuration (i.e., reconfiguration) of flow sensors. For example, 1) a change in the flow rate recorded by a flow sensor over time may suggest a leak in a pumping system; 2) a comparison between the flow rate metered by the motor/encoder system and the flow rate measured by a flow sensor may identify a leak; 3) a comparison in flow rates measured by different flow sensors within the channel or between channels may identify a leak; and 4) a comparison of flow rates metered by different pumping units within the channel or between the channels may identify a leak. Further, each of these methods of determining leaks when the flow sensors are configured in the second configuration (i.e., at step  1128 ) may be compared against the methods of determining leaks when the flow sensors are configured in the first configuration (i.e., at step  1120 ). The comparison may then be used to determine leaks. From step  1130 , the method progresses to step  1132 . 
     At step  1132 , compensation is made for the leaks in the pumping system. For example, each pumping unit may be controlled to compensate for the leaks by varying the metering of liquid from each pumping unit. 
     A number of alternative embodiments may be implemented using  FIG. 11B . For example, after operating the pumping system as stated at step  1122 , the step of reconfiguring the sensors as stated at step  1128  may be performed. Once the step of re-configuring the flow sensors as stated at step  1128  is performed, then the step of determining leaks is performed as stated at step  1130 , and the step of compensating for the leaks may be performed as stated at step  1132 . In alternate embodiments, the step of reconfiguring the sensors at step  1128  may be performed after the step of operating the pumping system as stated at step  1122  or after the step of determining leaks as stated at step  1124 . Once the step of reconfiguring the sensors as stated at step  1128  is performed, then the step of determining leaks is performed as stated at step  1130 , and the step of compensating for the leaks may be performed as stated at step  1132 . It should be appreciated that a variety of permutations and combinations of the various methods depicted by the flow diagram shown in  FIG. 11B  may be performed without departing from the spirit or scope of the invention. 
       FIG. 11C  is a flowchart of a method of calibrating flow sensors.  FIGS. 9A ,  9 B, and  10  will be discussed in conjunction with  FIG. 11C . The method commences with step  1133 . 
     At step  1133 , the operation of a pumping system is characterized to determine leaks or the tightness of each pumping unit. In one embodiment, the pumping unit is characterized by determining the tightness of the pumping unit. To determine the tightness of the pumping unit, each pumping unit 1) is blocked (i.e., the inlet valve and the outlet valve surrounding the pumping unit is closed, the pumping unit is manually blocked online or offline, etc.); 2) the pressure in the pumping unit (i.e., in the chamber) is increased; and then 3) the pressure in the pumping unit (i.e., in the chamber) is monitored for a decrease in pressure. For example, using  FIG. 9A  as an example, piston  924  performs an intake stroke to draw liquid into chamber  922 . Inlet valve  916  and outlet&#39;valve  930  are then closed. Piston  924  moves through part of a delivery stroke to pressurize chamber  922 . Lastly, chamber  922  is monitored for a decrease in pressure. If there is a decrease in pressure, this signals a leak in the pumping unit. If there is no pressure decrease, then there are no leaks (i.e., the pumping unit is tight). This process may be performed for each pumping unit in the pumping systems shown in  FIGS. 9A ,  9 B, and  10  to determine the tightness of each pumping unit. From step  1133 , the method progresses to step  1134 . 
     At step  1134  of  FIG. 11C , the liquid is then metered out of the pumping unit. Metering the liquid involves individually controlling and recording the movement of an encoder found in the motor/encoder system to determine the exact amount of liquid that is being delivered out of a chamber in a pumping unit. For example, metering the liquid may involve recording the movement of an encoder found in motor/encoder system  926  to determine the amount of liquid output from chamber  922 . In an alternate embodiment, the liquid may be metered out of chamber  922  at different flow rates and then measured by a flow sensor that we are attempting to calibrate. From step  1134 , the method progresses to step  1135 . 
     At step  1135 , a calibration factor is determined. To determine the calibration factor, a graph, such as the graph shown in  FIG. 11D , may be used. The graph shown in  FIG. 11D  presents voltage on the y-axis and flow rate on the x-axis. The graph also includes a calibration curve  1136 , a voltage  1140 , and a voltage  1138 . Calibration curve  1136  is a calibration curve for a know solvent, and is provided (e.g., by the manufacturer). 
     Voltage  1138  is a voltage of the known solvent at a known flow rate, i.e., a flow rate  1142 . An unknown solvent (i.e., a solvent in a chamber) is then processed through a flow sensor at flow rate  1142 . Voltage  1140  is a voltage of the unknown solvent at flow rate  1142 . A calibration factor  1144  is then defined by a relation between the voltage of the unknown solvent, i.e., voltage  1140 , and the voltage of the known solvent, i.e., voltage  1138 . In one embodiment, the calibration factor  1144  is equivalent to the voltage of the unknown solvent, i.e., voltage  1140 , divided by the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     An alternate method of calibrating a flow sensor is presented using the flowchart depicted in  FIG. 11C , the graph presented in  FIG. 11D , and the pumping unit depicted in  FIG. 9A . In the alternate embodiment, a method of calibrating solvents in a low-pressure gradient pump is presented. The method commences with step  1133 . 
     At step  1133  of  FIG. 11C , the operation of a pumping system is characterized to determine leaks or the tightness of each pumping unit. For example, using  FIG. 9A  as an example, piston  924  performs an intake stroke to draw liquid into chamber  922 . In the alternate embodiment of the present invention, switch  912  is switched to allow liquids conveyed on conveyances  904 ,  906 ,  908 , and  910  to be accessed from reservoir  902  and transported via conveyance  914 . The liquid is then stacked in chamber  922  as shown by liquid  922 A, liquid  922 B, liquid  922 C, and liquid  922 D. Inlet valve  916  and outlet valve  930  are then closed. Piston  924  moves through part of a delivery stroke to pressurize chamber  922 . Lastly, chamber  922  is monitored for a decrease in pressure. In one embodiment, the decrease in pressure may be measured using a pressure sensor (not shown) positioned to measure the pressure in chamber  922 . It should be appreciated that a pressure sensor may be deployed in each chamber of the pumping units presented in  FIGS. 9A ,  9 B, and  10 . The pressure for the chamber in each of the pumping units may then be measured by the pressure sensor using methods presented in the instant application. Lastly, additional methods of determining a decrease in the pressure of the chamber may be implemented and are within the scope of the present invention. If there is a decrease in pressure, this signals a leak in the pumping unit. If there is no pressure decrease, then there are no leaks (i.e., the pumping unit is tight). This process may be performed for each pumping unit in the pumping systems shown in  FIGS. 9A ,  9 B, and  10  to determine the tightness of each pumping unit. From step  1133 , the method progresses to step  1134 . 
     At step  1134  of  FIG. 11C , the liquid is then metered out of the pumping unit. Metering the liquid involves individually controlling and recording the movement of an encoder found in the motor/encoder system to determine the exact amount of liquid that is being delivered out of a chamber in a pumping unit. For example, metering the liquid may involve recording the movement of an encoder found in motor/encoder system  926  to determine the amount of liquid output from chamber  922 . In an alternate embodiment, the liquid may be metered out of chamber  922  at different flow rates and then measured by a flow sensor that we are attempting to calibrate. 
     In one embodiment, metering is performed to deliver each liquid, and then calibration is performed relative to each liquid. For example, liquid  922 A, liquid  922 B, liquid  922 C, and liquid  922 D are each metered out of the chamber and used to calibrate flow sensor  918  and/or flow sensor  932 . 
     From step  1134 , the method progresses to step  1135 . 
     At step  1135 , a calibration factor is determined. To determine the calibration factor, a graph, such as the graph shown in  FIG. 11D , may be used. As mentioned above, in  FIG. 11D , calibration curve  1136  is a calibration curve for a known solvent, and voltage  1138  is a voltage of the known solvent at a known flow rate  1142 . An unknown solvent, such as liquid  922 A, liquid  922 B, liquid  922 C, and liquid  922 D, is then processed through the flow sensor at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     In the following, the method of calibrating a flow sensor depicted in  FIG. 11B  will be described with respect to several configurations in  FIG. 9A . For example, a method of calibrating flow sensor  918  is presented. A method of calibrating flow sensor  932  is presented, and a method of calibrating flow sensor  942  is presented. 
     To calibrate flow sensor  918 , a test as described above is performed to determine the tightness of pumping unit  920 . Inlet valve  916  is then opened and outlet valve  930  is closed, and the liquid stored in chamber  922  is metered out of chamber  922  and through flow sensor  918 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid  922 A, liquid  922 B, liquid  922 C, and liquid  922 D, is then processed through flow sensor  918  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     To calibrate flow sensor  932 , a test as described above is performed to determine the tightness of pumping unit  920 . Outlet valve  930  is then opened, inlet valve  916  is closed, and the liquid (i.e., unknown solvent) stored in chamber  922  is metered out of chamber  922  and through flow sensor  932 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid  922 A, liquid  922 B, liquid  922 C, and liquid  922 D, is then processed through flow sensor  932  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     To calibrate flow sensor  942 , a test as described above is performed to determine the tightness of pumping unit  920  and pumping unit  934 . A variety of testing methods may be used to calibrate a flow sensor placed on an output of a low-pressure gradient pumping system. In one embodiment, pumping unit  920  is used to calibrate flow sensor  942 . In a second embodiment, pumping unit  934  is used to calibrate flow sensor  942 . In a third embodiment, a combination of pumping unit  920  and pumping unit  934  are used to test flow sensor  942 . 
     In one embodiment, to calibrate flow sensor  942 , a test is made to determine the tightness of pumping unit  920  and pumping unit  934 . Liquid stored in pumping unit  920  is metered out of chamber  922 , through flow sensor  932 , through chamber  936 , and through flow sensor  942 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid  922 A, liquid  922 B, liquid  922 C, and liquid  922 D, is then processed through flow sensor  942  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     In a second embodiment, to calibrate flow sensor  942 , a test is made to determine the tightness of pumping unit  934 . The liquid stored in pumping unit  934  is metered out of chamber  936  and through flow sensor  942 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid  922 A, liquid  922 B, liquid  922 C, and liquid  922 D, is then processed through flow sensor  942  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     In a third embodiment, to calibrate flow sensor  942 , a test is made to determine the tightness of pumping unit  920  and pumping unit  934 . The liquid stored in pumping unit  920  is metered out of chamber  922  and through flow sensor  932 , through chamber  936 , and through flow sensor  942 . The liquid stored in pumping unit  934  is metered out of the chamber  936  and through flow sensor  942 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid  922 A, liquid  922 B, liquid  922 C, and liquid  922 D, is then processed through flow sensor  942  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
       FIG. 9B  will be discussed in conjunction with  FIG. 11C . The method commences with step  1133 . 
     At step  1133  of  FIG. 11C , the operation of a pumping system is characterized to determine leaks or the tightness of each pumping unit. For example, using  FIG. 9B  as an example, piston  962  and/or piston  982  perform(s) an intake stroke to draw liquid into chamber  960  and/or chamber  980 . Inlet valve  954  and/or inlet valve  974 , and outlet valve  966  and/or outlet valve  986  are then closed. Piston  962  and/or piston  982  may each move through part of a delivery stroke to pressurize chamber  960  and/or chamber  980 . Lastly, chamber  960  and/or chamber  980  is/are monitored for a decrease in pressure. If there is a decrease in pressure, this signals a leak in the pumping unit (i.e.,  958 ,  978 ). If there is no pressure decrease, then there are no leaks (i.e., the pumping unit is tight). This process may be performed for each pumping unit (i.e.,  958 ,  978 ) in pumping system  950  shown in  FIG. 9B  to determine the tightness of each pumping unit (i.e.,  958 ,  978 ). From step  1133 , the method progresses to step  1134 . 
     At step  1134  of  FIG. 11C , the liquid is then metered out of the pumping unit. Metering the liquid involves individually controlling and recording the movement of an encoder found in the motor/encoder system to determine the exact amount of liquid that is being delivered out of a chamber in a pumping unit. For example, metering the liquid may involve recording movement of an encoder found in the motor/encoder system  964  and/or motor/encoder system  984  to determine the amount of liquid output from the chamber  960  and/or chamber  980 . In an alternate embodiment, the liquid may be metered out of chamber  960  and/or chamber  980  at different flow rates and then measured by a flow sensor that we are attempting to calibrate. From step  1134 , the method progresses to step  1135 . 
     At step  1135 , a calibration factor is determined. To determine the calibration factor, a graph, such as the graph shown in  FIG. 11D , may be used. The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  952  or reservoir  972 , is then processed through a flow sensor (i.e.,  956 ,  968 ,  976 ,  988 ,  994 ) at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     The method of calibrating a sensor depicted in  FIG. 11C  will be described with respect to several configurations in  FIG. 9B . For example, a method of calibrating flow sensor  956  is presented, a method of calibrating flow sensor  968  is presented, a method of calibrating flow sensor  976  is presented, a method of calibrating flow sensor  988  is presented, and a method of calibrating flow sensor  994  is presented. 
     To calibrate flow sensor  956 , pumping system  950  is characterized to determine leaks in pumping system  950 . Inlet valve  954  is then opened and outlet valve  966  is closed, and the liquid stored in chamber  960  is metered out of chamber  960  and through flow sensor  956 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  952 , is then processed through a flow sensor  956  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     To calibrate flow sensor  968 , pumping system  950  is characterized to determine the tightness of pumping units  958  and  978 . Outlet valve  966  is then opened, inlet valve  954  is closed, and the liquid stored in chamber  960  is metered out of chamber  960  and through flow sensor  968 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  952 , is then processed through flow sensor  968  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. In one embodiment of the present invention, the foregoing methods may also be used to calibrate flow sensors  976  and  988 . 
     A variety of testing methods may be used to calibrate a flow sensor placed on an output, such as flow sensor  994 , which is positioned on the output of pumping system  950 . In one embodiment, pumping unit  958  is used to calibrate flow sensor  994 . In a second embodiment, pumping unit  978  is used to calibrate flow sensor  994 . In a third embodiment, a combination of pumping unit  958  and pumping unit  978  is used to calibrate flow sensor  994 . 
     To calibrate flow sensor  994 , pumping system  950  is characterized to determine the tightness of pumping unit  958  and pumping unit  978 . Liquid stored in pumping unit  958  is metered out of chamber  960 , through flow sensor  968 , and through flow sensor  994 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  952 , is then processed through flow sensor  994  at a known flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. It should be appreciated that flow sensors  968  and  994  may both be calibrated using the foregoing methods and then compared to provide a more accurate calibration factor  1144  for each flow sensor (i.e.,  968 ,  994 ). 
     In a second embodiment, to calibrate flow sensor  994 , pumping system  950  is characterized to determine the tightness of pumping unit  958  and the pumping unit  978 . Liquid stored in pumping unit  978  is metered out of chamber  980  through flow sensor  988  and through flow sensor  994 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  972 , is then processed through flow sensor  994  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. It should be appreciated that flow sensors  988  and  994  may both be calibrated using the foregoing methods and then compared to provide a more accurate calibration factor  1144  for each flow sensor (i.e.,  988 ,  994 ). 
     In a third embodiment, to calibrate flow sensor  994 , pumping system  950  is characterized to determine the tightness of pumping unit  958  and pumping unit  978 . The liquid stored in pumping unit  958  is metered out of chamber  960  through flow sensor  968  and through flow sensor  994 . The liquid stored in pumping unit  978  is metered out of chamber  980  through flow sensor  988  and through flow sensor  994 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  952 , is then processed through flow sensor  994  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     The method of calibrating a flow sensor depicted in  FIG. 11C  will be described with respect to several configurations in  FIG. 10 . The calibration method depicted in  FIG. 11C  is applied to each configuration to calibrate one of the flow sensors. In the following discussion, methods are presented for calibrating flow sensors  1005 ,  1018 ,  1030 ,  1032 ,  1038 ,  1043 , and  1054 . 
     To calibrate flow sensor  1005 , pumping system  1000  is characterized to determine the tightness of pumping units  1006 ,  1020 ,  1044 , and  1056 . Outlet valve  1016  is closed and inlet valve  1004  is opened. Flow sensor  1005  may be positioned before or after inlet valve  1004 . Liquid stored in pumping unit  1006  is metered out of chamber  1008  through flow sensor  1005 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in liquid reservoir  1002 , is then processed through flow sensor  1005  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     To calibrate flow sensor  1018 , pumping system  1000  is characterized to determine the tightness of pumping units  1006 ,  1020 ,  1044 , and  1056 . Inlet valve  1004  is closed and outlet valve  1016  is opened. Flow sensor  1018  may be positioned before or after outlet valve  1016 . Liquid stored in pumping unit  1006  is metered out of chamber  1008  through flow sensor  1018 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  1002 , is then processed through flow sensor  1018  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     To calibrate flow sensor  1043 , pumping system  1000  is characterized to determine the tightness of pumping units  1006 ,  1020 ,  1044 , and  1056 . Outlet valve  1052  is closed and inlet valve  1042  is opened. Flow sensor  1043  may be positioned before or after inlet valve  1042 . Liquid stored in pumping unit  1044  is metered out of chamber  1046  through flow sensor  1043 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  1040 , is then processed through flow sensor  1043  at a known flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     To calibrate flow sensor  1054 , pumping system  1000  is characterized to determine the tightness of pumping units  1006 ,  1020 ,  1044 , and  1056 . Inlet valve  1042  is closed and outlet valve  1052  is opened. Liquid stored in pumping unit  1044  is metered out of chamber  1046  through flow sensor  1054 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  1040 , is then processed through flow sensor  1054  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. 
     To calibrate flow sensors  1030 ,  1032 , or  1038 , pumping system  1000  is characterized to determine the tightness of pumping units  1006 ,  1020 ,  1044 , and  1056 . A variety of testing methods may be used to test a flow sensor placed on an output of pumping system  1000 . In one embodiment, pumping unit  1006  is used to test flow sensors  1030 ,  1032 , or  1038 . In a second embodiment, pumping unit  1020  is used to test the flow sensors  1018 ,  1030 , or  1032 . In a third embodiment, a combination of the pumping unit  1006  and the pumping unit  1020  is used to test flow sensors  1030 ,  1032 , or  1038 . 
     In one embodiment, a pumping unit in a second channel may be used to calibrate a flow sensor positioned on the output of the second channel. In another embodiment, a pumping unit in a first channel in combination with a pumping unit in the second channel may be used to calibrate a flow sensor positioned on the output of the second channel. For example, when calibrating flow sensor  1038 , piston  1024  may be used in combination with piston  1060  or piston  1060  may be used individually to calibrate flow sensor  1038 . When using piston  1024  in combination with piston  1060 , piston  1024  performs a delivery stroke and piston  1060  performs an intake stroke to calibrate flow sensor  1038 . When using piston  1060  individually to calibrate flow sensor  1038 , piston  1060  performs an intake stroke for backward calibration or piston  1060  performs a delivery stroke for forward calibration. It should be appreciated that a similar approach may be used to calibrate flow sensor  1030  using piston  1060  in combination with piston  1024  or piston  1024  individually. 
     In one embodiment, pumping unit  1006  is used to test flow sensors  1030 ,  1032 , and  1038 . A test is made to determine the tightness of the pumping unit  1006 , pumping unit  1020 , and pumping unit  1056 . The liquid stored in pumping unit  1006  is metered out of chamber  1008  through flow sensor  1018 , through chamber  1022 , and through flow sensors  1030 ,  1032 , and/or  1038 . The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  1002 , is then processed through a flow sensor(s)  1030 ,  1032 , and/or  1038  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. It should be appreciated that a similar approach may be performed to test flow sensors  1030 ,  1038 , and  1032  using pumping unit  1044 . 
     In a second embodiment, pumping unit  1020  is used to test flow sensors  1030 ,  1032 , and  1038 . A test is made to determine the tightness of pumping unit  1020  and pumping unit  1056 . The liquid stored in the pumping unit  1020  is metered out of chamber  1022  and through flow sensors  1030 ,  1032 , and/or  1038 . It should be appreciated that in the case of flow sensor  1038 , piston  1060  moves through an intake stroke to draw in solvent as piston  1024  performs a delivery stroke. The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  1002 , is then processed through a flow sensor  1030 ,  1032 , and/or  1038  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. It should be appreciated that a similar method may be used to test flow sensors  1030 ,  1038 , and  1032  using pumping unit  1056 . 
     In a third embodiment, pumping unit  1006  and pumping unit  1020 , in combination, are used to test flow sensors  1030 ,  1032 , and  1038 . A test is made to determine the tightness of pumping unit  1006  and pumping unit  1020 . The liquid stored in pumping unit  1006  is metered out of chamber  1008  and through flow sensor  1018 , through chamber  1022 , and through flow sensors  1030 ,  1032 , or  1038 . The liquid stored in pumping unit  1020  is metered out of chamber  1022  and through flow sensors  1030 ,  1032 , or  1038 . Any combination of pumped solvent from pumping unit  1006  and  1020  is possible. It should be appreciated that in the case of flow sensor  1038 , piston  1060  moves through an intake stroke to draw in solvent as piston  1024  performs a delivery stroke. 
     The voltage of a known solvent at a known flow rate is identified, i.e., voltage  1138  is identified for flow rate  1142 . An unknown solvent, such as liquid stored in reservoir  1002 , is then processed through flow sensors  1030 ,  1032 , and/or  1038  at flow rate  1142 . Voltage  1140  is the voltage of the unknown solvent at flow rate  1142 . Calibration factor  1144  is then defined as a ratio of the voltage of the unknown solvent, i.e., voltage  1140 , to the voltage of the known solvent, i.e., voltage  1138 . This method may be performed at different flow rates. It should be appreciated that a similar method may be used to test flow sensors  1030 ,  1038 , and  1032  using pumping unit  1044  in combination with pumping unit  1056 . 
       FIG. 11E  is a flowchart depicting a method of producing a variable flow rate.  FIG. 11E  will be discussed in conjunction with  FIG. 9A ,  9 B, and  FIG. 10 . In the method of producing a variable flow rate, flow sensors are positioned at various locations within a pumping system depending on the required flow rate of the pumping system. In one embodiment, the total flow rate of the pumping system is measured at low flow rates. In another embodiment, a portion of the total flow rate is measured at high flow rates. In both cases, leaks in the pumping system are identified and compensated for. For a channel having a high flow rate, the flow sensors are connected within the channel. For a channel having a low flow rate, the flow sensors are connected at the output of the channel. The method commences with step  1150 . 
     At step  1150 , a flow rate is identified. The flow rate may be identified by reading a flow sensor, or may be identified based on a metering system, or may be identified by inputting a predefined flow rate into a computer for operations. From step  1150 , the method progresses to step  1151 . 
     At step  1151 , a test is performed to determine whether the flow rate is above or below a predefined level. In one embodiment, the predefined level corresponds to the maximum measuring capability of the flow sensor. If the flow rate is above the predefined level, then the method progresses to step  1152 . If the flow rate is below the predefined level, then the method progresses to step  1154 . 
     In step  1152 , the flow sensor is implemented within the channel. From step  1152 , the method progresses to step  1153 . 
     In step  1153 , the flow sensor is used to perform flow measurement, determine leaks, and compensate for leaks. 
     In step  1154 , the flow sensor is implemented at the output of the channel as stated at step  1154 . From step  1154 , the method progresses to step  1155 . 
     In step  1155 , the flow sensor at the output of the channel is used to characterize the total flow measurement of the pumping system. 
     Step  1152  and  1154  each involve implementing a flow sensor. In one embodiment, implementing the flow sensor may include configuring or implementing a flow sensor into a pumping system during operations. For example, when the pumping system is operating with a low flow rate, the flow sensors at the output of the channel may be turned on and operating, and when the pumping system is operating to produce a high flow rate, the flow sensors positioned within the channel of the pumping system may be turned on and operating. It should be appreciated that the same flow sensor can be used for both positions. 
     The method of producing a variable flow rate presented in  FIG. 11E  will be discussed with respect to  FIGS. 9A ,  9 B, and  10 . In  FIG. 9A , flow sensor  918  and/or flow sensor  932  may be implemented in pumping system  900  when pumping system  900  is operating to produce a high flow rate, and flow sensor  918  and/or flow sensor  942  may be implemented when the pumping system  900  is operating at a low flow rate. Further, at a high flow rate, flow sensor  918  and/or flow sensor  932  may indicate a portion of a total flow rate of the pumping system, where the total flow rate is measured at output  944 . At a low flow rate, flow sensor  942  is implemented and used to operate pumping system  900 . Using a method presented in the present application, leaks are detected and compensated for by metering the flow of liquid out of chamber  922 , chamber  936 , or chamber  922  in combination with chamber  936 . 
     The method of producing a variable flow rate presented in  FIG. 11E  will be discussed with respect to  FIG. 9B . In  FIG. 9B , flow sensors  956 ,  968 ,  976 , and  988  may be implemented when pumping system  950  is operating to produce a high flow rate, and sensors  956 ,  976 , and  994  may be implemented when the pumping system  900  is operating to produce a low flow rate. Further, at a high flow rate, flow sensors  956 ,  968 ,  976 , and  988  may indicate a portion of the total flow rate of pumping system  950 , where the total flow rate is measured at channel output  996 . At a low flow rate, flow sensor  994  is implemented and used to operate pumping system  950 . Using a method presented in the present application, leaks are detected and compensated for by metering the flow of liquid out of chamber  960 , chamber  980 , or chamber  960  in combination with chamber  980 . 
     In  FIG. 10 , flow sensors  1005 ,  1018 ,  1043 , and/or  1054  may be implemented in pumping system  1000  to measure a high flow rate, and flow sensors  1030 ,  1032 , and  1038  may be implemented when pumping system  1000  is operating to measure a low flow rate. Further, at a high flow rate, flow sensors  1018  and  1054  may represent a portion of the total flow rate of pumping system  1000 , where the total flow rate is the flow rate of liquid at output  1034 . At a low flow rate, flow sensors  1030 ,  1032 , and/or  1038  are implemented and used to operate pumping system  1000 . Using methods presented in the instant application, leaks are detected and compensated for by metering the flow of liquid out of chamber  1008 , chamber  1022 , chamber  1046 , chamber  1058 , or any combination of chambers  1008 ,  1022 ,  1046 , and/or  1058 . 
       FIG. 12  is a schematic of a pumping system that includes pressure sensors. A pumping system  1200  includes a variety of liquids A, B, C, and D. Liquids A, B, C, and D are stored in a reservoir  1202 . Each liquid A, B, C and D is conveyed on a conveyance  1202 A,  1202 B,  1202 C, and  1202 D, respectively. Liquids A, B, C and D are mixed using a proportioning valve  1204 . The liquid (i.e., A, B, C, D) is drawn through an inlet valve  1208  via a conveyance  1205 . A pressure sensor  1206  is positioned on conveyance  1205  to sense the pressure between proportioning valve  1204  and inlet valve  1208 . A pumping unit  1210  is positioned in series with inlet valve  1208 . Pumping unit  1210  includes a chamber  1212 , a piston  1214 , and a seal  1213 . On an intake stroke of piston  1214 , liquid fills chamber  1212 , and on a delivery stroke of piston  1214 , liquid is compressed and forced out of chamber  1212 , through an outlet valve  1220 . A pressure sensor  1209  is positioned to measure the pressure in the chamber  1212 . 
     A motor/encoder system  1218  and a computer  1224  are used to adjust the intake stroke and the delivery stroke of piston  1214 , which meters the flow of liquid through chamber  1212  by adjusting the intake and expulsion of liquid from the chamber  1212 . A flow sensor  1222  is positioned in series with outlet valve  1220 . Flow sensor  1222  is capable of measuring the flow of liquid out of pumping unit  1210 . Flow sensor  1222  reports the measured flow to computer  1224 . 
     A variety of methods for determining and compensating for leaks are presented and implemented with pumping system  1200 . In one embodiment, a method of determining leaks in an inlet valve is presented. In a second embodiment, a method of detecting leaks in an outlet valve is presented. In a third embodiment, a method of determining leaks in a seal/piston combination is presented. In a fourth embodiment, a method of determining leaks in a gradient valve is presented. 
       FIG. 12A  is a flowchart of a method of identifying and compensating for leaks using pressure sensors.  FIG. 12A  will be discussed in conjunction with  FIG. 12 . The method commences with step  1230 . 
     At step  1230 , a chamber is filled with liquid. For example, chamber  1212  is filled with liquid. To fill chamber  1212  with liquid, outlet valve  1220  is closed, proportioning valve  1204  is opened, and inlet valve  1208  is opened. Liquid is drawn into chamber  1212  as piston  1214  performs an intake stroke. After step  1230 , the method progresses to perform each of steps  1231 ,  1232  and  1233 , generally, in parallel with one another. 
     In step  1231 , proportioning valve  1204  is closed. From step  1231  (after the completion of steps  1232  and  1233 ), the method progresses to step  1234 . 
     In step  1232 , inlet valve  1208  is closed. From step  1232  (after the completion of steps  1231  and  1233 ), the method progresses to step  1234 . 
     In step  1233 , outlet valve  1220  is closed. From step  1233  (after the completion of steps  1231  and  1232 ), the method progresses to step  1234 . 
     In step  1234 , with each of proportioning valve  1204 , inlet valve  1208 , and outlet valve  1220  being closed, compression is performed. During compression, piston  1214  moves upward (i.e., delivery stroke) to compress the liquid in the chamber  1212 . Compressing liquid in chamber  1212  increases the pressure in chamber  1212 . From step  1234 , the method progresses to step  1235 . 
     In step  1235 , after pumping system  1200  reaches steady state (i.e., all the components have settled), the pressure is measured. Pressure sensor  1206  is monitored for a change in pressure. If an increase in pressure is determined, the increase in pressure signals a flow of liquid back through inlet valve  1208  as a result of a leak in inlet valve  1208 . From step  1235 , the method progresses to step  1236 . 
     In step  1236 , based on the amount of pressure increase in pressure sensor  1206 , the amount of the leak in inlet valve  1208  is calculated. In one embodiment of the present invention, the amount of leak in inlet valve  1206  is calculated using the volume between proportioning valve  1204  and inlet valve  1206 , the compressibility factor of the liquid and the pressure increase. From step  1236 , the method progresses to step  1237 . 
     In step  1237 , once the amount of the leak has been determined, adjustments are made in pumping system  1200  to compensate for the leak. For example, using piston  1214 , motor/encoder system  1218 , and computer  1224 , metering may be performed to compensate for the leak. 
       FIG. 12B  is a flowchart of a method of identifying and compensating for leaks using flow sensors. The method commences with steps  1240 ,  1241  and  1242  being performed, generally, in parallel with one another. 
     In step  1240 , a proportioning valve is opened. From step  1240  (after the completion of steps  1241  and  1242 ), the method progresses to step  1243 . 
     In step  1241 , an inlet valve is opened. From step  1241  (after the completion of steps  1240  and  1242 ), the method progresses to step  1243 . 
     In step  1242 , an outlet valve is closed. From step  1242  (after the completion of steps  1240  and  1241 ), the method progresses to step  1243 . 
     In step  1243 , a first piston in a first pumping unit performs an intake stroke. It should be appreciated that in a second embodiment, the method depicted in  FIG. 12B  may be performed without performing the intake stroke as stated at step  1243 . Opening the proportioning valve as stated at step  1240 , opening the inlet valve as stated at step  1241 , and closing the outlet valve as stated at step  1242  will result in a backflow of liquid provided that the pressure after the outlet valve is higher than the pressure within the chamber. From step  1243 , the method progresses to step  1244 . 
     In step  1244 , a flow sensor is used to monitor the backflow. From step  1244 , the method progresses to step  1245 . 
     In step  1245 , the backflow is used to calculate the amount of a leak. From step  1245 , the method progresses to step  1246 . 
     In step  1246 , leaks are compensated for, for example, by metering, e.g., with a second piston. 
     The method depicted in the flow diagram of  FIG. 12B  will now be discussed with respect to the pumping system depicted in  FIG. 12 . The method commences with steps  1240 ,  1241  and  1242  being performed, generally, in parallel with one another. 
     At steps  1240 ,  1241 , and  1242 , proportioning valve  1204  is opened, inlet valve  1208  is opened, and outlet valve  1220  is closed. After the completion of steps  1240 ,  1241 , and  1242 , the method progresses to step  1243 . 
     At step  1243 , piston  1214  performs an intake stroke. From step  1243 , the method progresses to step  1244 . 
     At step  1244 , flow sensor  1222  is monitored to detect a backflow  1226 . If backflow  1226  is detected by flow sensor  1222 , there is a leak in outlet valve  1220 . From step  1244 , the method progresses to step  1245 . 
     In step  1245 , once the leak has been determined, the amount of liquid flowing through flow sensor  1222  may be used to calculate the amount of the leak. In one embodiment, it should be appreciated that the flow sensor is measuring the amount of the leak directly. If a leak occurs, the new-metered flow rate with a piston after the flow sensor (not shown in  FIG. 12 ) is equivalent to the metered flow, which is equal to the nominal flow plus the leak. From step  1245 , the method progresses to step  1246 . 
     In step  1246 , once the amount of the leak is calculated, metering may be performed to compensate for the leak. Metering may include operating, e.g., a second piston of a serial pumping system, a motor/encoder unit responsible for moving that second pumping piston, and a corresponding computer (not shown in  FIG. 12 ) to compensate for the amount of the leak. 
       FIG. 12C  is a flowchart of a method of detecting a leak in a chamber, such as chamber  1212  of  FIG. 12 .  FIG. 12C  will be discussed in conjunction with  FIG. 12 . The method depicted in the flowchart of  FIG. 12C  may be used to detect leaks in a piston/seal  1214 / 1213  combination, the leak in an inlet valve  1208 , the leak in an outlet valve  1220 , a leaky fitting, etc. The method commences with step  1251 . 
     At step  1251 , pressure in chamber  1212  is increased to a level above atmospheric pressure. In one embodiment, piston  1214  is moved through a portion of a delivery stroke to pressurize liquid in chamber  1212 . From step  1251 , the method progresses to step  1252 . 
     At step  1252 , stopping the movement of piston  1214  stops the pressurization. From step  1252 , the method progresses to step  1253 . 
     At step  1253 , time is allotted to wait for the settling effects and pressure is monitored over a period of time. For example, time is allotted to wait for the settling effects of pumping unit  1210 . After settling is completed, pressure sensor  1209  is used to monitor the pressure in chamber  1212  over a period of time. Since, in step  1251  pressure in chamber  1212  was increased to a level above atmospheric pressure, if the pressure decreases during step  1253 , such a decrease would be indicative of a leak. From step  1253 , the method progresses to step  1254 . 
     At step  1254 , a determination is made as to whether the pressure has decreased to a value below a predefined value. If the pressure has not decreased to a value below the predefined value, then there is no leak, and the method progresses to step  1255 . If the pressure has decreased to a value below the predefined value, then there is a leak, and the method progresses to step  1256 . 
     In step  1255 , since the pressure has not decreased to a value below the predetermined value, there is no leak. 
     At step  1254 , since the pressure has decreased to a value below the predefined value, there is a leak. The leak may be determined using two methods. Accordingly, from step  1254 , the method progresses to either of step  1257  or step  1258 . 
     In step  1257 , a leak is determined by a pressure decrease over time. As a result, the leak equals the internal volume times solvent compressibility times the pressure decrease, where the internal volume is the volume of the liquid in chamber  1212 , the solvent compressibility is the compression of liquid in chamber  1212 , and the pressure decrease is given by a change in the pressure reading on pressure sensor  1209 . 
     In step  1258 , the leak is determined by moving piston  1214  upward until the pressure is stable. Using  FIG. 12 , this would include moving piston  1214  upward through a portion of a delivery stroke until the pressure registered by pressure sensor  1209  is stable. During the partial delivery stroke, the metered liquid or solvent may be determined using motor/encoder system  1218  and computer  1224 . From step  1258 , the method progresses to step  1259 . 
     In step  1259 , the leak will then equal the metered solvent. 
       FIG. 12D  is a flowchart of a method of detecting a blocked conveyance (i.e., a blocked filter at a conveyance inlet).  FIG. 12D  will be discussed in conjunction with  FIG. 12 . The method commences with step  1260 . 
     At step  1260 , a pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is determined during an intake of liquid through each conveyance  1202 A,  1202 B,  1202 C and  1202 D. From step  1260 , the method progresses to step  1261 . 
     At step  1261 , the limits of the pressure drop are defined for each conveyance. The pressure drop for the individual channels  1202 A,  1202 B,  1202 C and  1202 D can be defined individually. From step  1261 , the method progresses to step  1262 . 
     At step  1262 , the pressure drop is monitored as liquid is conveyed through each conveyance  1202 A,  1202 B,  1202 C and  1202 D. From step  1262 , the method progresses to step  1263 . 
     In step  1263 , the method determines whether the pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is below a predefined value. If the pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is below the predefined value, then there is no blockage, and the method progresses to step  1264 . If the pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is not below the predefined value, that is the pressure is greater than the predefined value for one or more of conveyances  1202 A,  1202 B,  1202 C or  1202 D, then the method progresses to step  1265 . 
     In step  1264 , since the pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is below the predefined level, no blockage is detected. 
     In step  1265 , since the pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is not below the predefined level, that is the pressure is greater than the predefined value for one or more of conveyances  1202 A,  1202 B,  1202 C or  1202 D, blockage is detected. From step  1265 , the method progresses to step  1266 . 
     In step  1266 , in one embodiment, an adjustment is made to compensate for the blockage. For example, in the case of a partial blockage, the intake stroke of piston  1214  may be adjusted to draw in liquid with lower speed to compensate for the blockage (e.g., avoid generation of gas bubbles). 
     The flowchart of  FIG. 12D  will be discussed in conjunction with pumping system  1200  depicted in  FIG. 12 . In  FIG. 12 , pressure sensor  1206  may be used to calibrate the inlet pressure for conveyances  1202 A,  1202 B,  1202 C, and  1202 D. To calibrate the inlet pressure for each conveyance  1202 A,  1202 B,  1202 C, and  1202 D, as inlet valve  1208  is opened and piston  1214  intakes liquid (i.e., A, B, C, D), pressure is measured as the liquid (i.e., A, B, C, D) is conveyed past pressure sensor  1206 . For example, when liquid A flows through conveyance  1202 A, via conveyance  1205 , to inlet valve  1208 , the pressure is measured. When liquid B flows through conveyance  1202 B, via conveyance  1205 , to inlet valve  1208 , the pressure is measured. When liquid C flows through conveyance  1202 C, via conveyance  1205 , to inlet valve  1208 , the pressure is measured. When liquid D flows through conveyance  1202 D, via conveyance  1205 , to inlet valve  1208 , the pressure is measured. 
     In step  1260 , using the aforementioned techniques, a pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is determined. From step  1260 , the method progresses to step  1261 . 
     In step  1261 , the limits of the pressure drop are defined. From step  1261 , the method progresses to step  1262 . 
     At step  1262 , the pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is monitored during the intake phase of the solvent using pressure sensor  1206 . From step  1262 , the method progresses to step  1263 . 
     In step  1263 , during operation, a test is made to determine if the pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is below a predefined value (i.e., level). If the pressure drop across each conveyance  1202 A,  1202 B,  1202 C and  1202 D is below the predefined value (i.e., Yes), then the method progresses to step  1264 . If the pressure drop across at least one conveyance  1202 A,  1202 B,  1202 C or  1202 D is not below the predefined value (i.e., No), then the method progresses to step  1265 . 
     In step  1264 , since the pressure drop is below the predefined level, no blockage is detected. 
     In step  1265 , since the pressure drop is not below the predefined level, blockage is detected. In one embodiment, the blockage may occur in conveyances  1202 A,  1202 B,  1202 C and/or  1202 D. From step  1265 , the method progresses to step  1266 . 
     In step  1266 , once blockage has been detected, activities may be performed to compensate for a partial blockage. For example, piston  1214  may perform an adjusted intake stroke to ensure the correct volume of liquid is brought in across the conveyance. For example, in one embodiment, the intake stroke speed is reduced to avoid the generation of gas bubbles. 
     In one embodiment of detecting a leak in a proportioning valve, an on/off valve, such as a proportioning valve  1204 , is closed. If more channels or conveyances are connected (e.g., for liquids A, B, C, D), all the channels or conveyance are closed. A piston, such as piston  1214 , is moved to intake liquid into chamber  1212 . Pressure is measured. For example, pressure sensor  1206  may measure the pressure on conveyance  1205 . In one embodiment, when performing an intake stroke with piston  1214  (i.e., inlet valve  1208  opened, and outlet valve  1220  closed), the pressure on conveyance  1205  decreases to a level below atmospheric pressure. Piston  1214  stops and the pressure is monitored. After waiting a time for settling effects, the pressure is constant. In the case of a leak in proportioning valve  1204 , the pressure will increase to atmospheric pressure. It should be appreciated that the pumping unit must be tested for tightness before the test described above is performed. 
     In another embodiment, the tightness of the proportioning valve is tested. First, the pumping unit (i.e., piston/chamber) is tested for tightness as described above. Afterwards, all of the channels (i.e., each conveyance) of the proportioning valve are closed, the inlet valve is opened and the outlet valve is closed. The piston moves upward to increase the pressure in conveyance  1205  to a level above atmospheric pressure. The piston stops, waiting a time for settling effects and monitoring the pressure. If proportioning valve  1204  is tight, the pressure is constant and remains above a predefined level. If leaky, the pressure decreases to atmospheric pressure over time. 
     In both embodiments presented above, the amount of leak is calculated by the volume of liquid between proportioning valve  1204  and inlet valve  1208 , the compressibility factor of the liquid, and the pressure change over time. For example, in one embodiment, the leak is equal to the volume times the compressibility of liquid times the pressure change. 
     In another embodiment, chamber  1212  is checked for tightness using a pressure sensor  1206  on a conveyance, such as conveyance  1205 . Inlet valve  1208  is opened, outlet valve  1220  is closed, proportioning valve  1204  is closed completely (all channels), and conveyance  1205  is pressurized by moving piston  1214  upwards. The pressure is monitored. A pressure level is predefined. Adapting the speed of piston  1214  to keep the pressure constant controls the pressure. The pumped liquid required to keep that pressure constant on conveyance  1205  is equivalent to the amount of the leak. 
       FIG. 12E  is a flowchart of a method of detecting a leak in a piston chamber including an adapted valve such as an outlet valve or a proportioning valve.  FIG. 12E  will be discussed in conjunction with  FIG. 12 . The method depicted in  FIG. 12E  commences with step  1271 . 
     At step  1271 , an outlet valve, such as outlet valve  1220 , is closed; an inlet valve, such as inlet valve  1208 , is opened; and a valve, such as proportioning valve  1204 , is closed. From step  1271 , the method progresses to step  1272 . 
     At step  1272 , pressure in chamber  1212  is decreased. In one embodiment, decreasing the pressure in chamber  1212  includes moving piston  1214  downward through a partial intake stroke. When piston  1214  moves downward through the partial intake stroke, the pressure on conveyance  1205  decreases to a level below atmospheric pressure. 
     At step  1273 , the piston  1214  is stopped to discontinue the decrease in pressure on the conveyance  1205 . 
     At step  1274 , time is allowed to wait for settling effects. 
     At step  1275 , the pressure is monitored on conveyance  1205  using pressure sensor  1206 . Since, in step  1272  pressure in chamber  1212  was decreased to a level below atmospheric pressure, if the pressure increases during step  1275 , such an increase would be indicative of a leak. 
     At step  1276 , a test is made to determine if the pressure has increased above a predefined value. If the pressure has not increased above the predefined value, then there is no leak, and the method progresses to step  1278 . If the pressure has increased above the predefined value, i.e., toward atmospheric pressure, then there is a leak, and the method progresses to step  1278 . 
     In step  1277 , since the pressure has not increased above the predefined value, there is no leak. 
     In step  1278 , since the pressure has increased above the predefined value, i.e., toward atmospheric pressure, then a leak in the piston chamber or in an adapted valve such as an outlet valve or a proportioning valve may be determined. The leak may be determined in two ways. Accordingly, from step  1278 , the method may progress to either of step  1279  or step  1280 . 
     In step  1279 , the leak is calculated by the increase in pressure over time. In this case, the calculated leak equals the internal volume times the solvent compressibility times the pressure increase. 
     In step  1280 , the leak is determined by moving piston  1214  downward until the pressure measured by pressure sensor  1206  is stable. From step  1280 , the method progresses to step  1281 . 
     In step  1281 , motor/encoder system  1218  and computer  1224  are then used to determine the metered solvent from the downward movement of piston  1214 , and the leak is equal to the metered solvent. 
       FIG. 12F  is a flowchart of a method of testing for a leak in the piston chamber or an adapted valve such as an outlet valve or a proportioning valve.  FIG. 12F  will be discussed in conjunction with  FIG. 12 . The method depicted in  FIG. 12F  commences with step  1286 . 
     At step  1286 , an outlet valve, such as outlet valve  1220 , is closed; an inlet valve, such as inlet valve  1208 , is opened; and a proportioning valve, such as proportioning valve  1204 , is closed. From step  1286 , the method progresses to step  1287 . 
     At step  1287 , pressure in chamber  1212  is increased to a level greater than atmospheric pressure. In addition, since inlet valve  1208  is opened, conveyance  1205  is also pressurized. In one embodiment, increasing pressure in chamber  1212  includes moving piston  1214  upward through a partial delivery stroke. When piston  1214  moves upward through the partial intake stroke, the pressure on conveyance  1205  is increased to a level above atmospheric pressure. From step  1287 , the method progresses to step  1288 . 
     At step  1288 , piston  1214  is stopped to stop the pressurization of chamber  1212  and conveyance  1205 . From step  1288 , the method progresses to step  1289 . 
     At step  1289 , time is allowed to wait for settling effects. From step  1289 , the method progresses to step  1290 . 
     At step  1290 , the pressure is monitored on conveyance  1205  using pressure sensor  1206 . Since, in step  1287  pressure in chamber  1212  was increased to a level above atmospheric pressure, if the pressure decreases during step  1290 , such a decrease would be indicative of a leak. From step  1290 , the method progresses to step  1291 . 
     At step  1291 , a test is made to determine whether the pressure has decreased to a value below a predefined value. If the pressure has not decreased to a value below the predefined value, then there is no leak, and the method progresses to step  1292 . If the pressure has decreased to a value below the predefined value, then there is a leak, and the method progresses to step  1294 . 
     In step  1292 , since the pressure has not decreased to a value below the predefined value, there is no leak. 
     In step  1294 , since the pressure has decreased to a value below the predefined value, there is a leak. The leak may be determined in two ways. Accordingly, from step  1294 , the method may progress to either of step  1293  of step  1295 . 
     In step  1293 , the leak is calculated by the decrease in pressure over time. In this case, the calculated leak equals the internal volume times the solvent compressibility times the pressure decrease. 
     In step  1295 , the leak is determined by moving piston  1214  upward until the pressure measured by pressure sensor  1206  is stable. From step  1295 , the method progresses to step  1296 . 
     In step  1296 , motor/encoder system  1218  and computer  1224  are then used to determine the metered solvent from the upward movement of piston  1214 , and the leak equals the metered solvent. 
       FIG. 13  is a schematic diagram of a single-channel pumping system, i.e., a pumping system  1300 , including flow sensors. Pumping system  1300  includes a reservoir  1302  storing a variety of liquids as shown by liquids A, B, C, and D. A switch, such as a proportioning valve  1304 , is connected in series with a flow sensor  1306 . Flow sensor  1306  is connected in series with an inlet valve  1308 . Inlet valve  1308  is in series with a pumping unit  1311 . Pumping unit  1311  includes a chamber  1312  and a piston  1314 . Pumping unit  1311  is further in series with a pumping unit  1319  that includes a piston  1320  and a chamber  1318 . In one embodiment, a flow sensor  1313  is positioned between pumping unit  1311  and pumping unit  1319 . Pumping unit  1311  is connected to a motor/encoder system  1316 , and pumping unit  1319  is connected and controlled by a motor/encoder system  1322 . Both of motor/encoder system  1316  and motor/encoder system  1322  are connected to, and controlled by, a computer  1324 . 
     The liquids (i.e., A, B, C, D) are mixed in proportioning valve  1304  and conveyed through flow sensor  1306  to inlet valve  1308 . On the intake stroke of piston  1314 , liquid (i.e., A, B, C, D) fills chamber  1312 , and on the delivery stroke of piston  1314 , liquid (i.e., A, B, C, D) is compressed and forced out of chamber  1312 , through outlet valve  1310 . Motor/encoder system  1316  and computer  1324  are used to meter the flow of liquid (i.e., A, B, C, D) through pumping unit  1311  by adjusting the upward and intake stroke of piston  1314  to adjust the intake and expulsion of liquid (i.e., A, B, C, D) from chamber  1312 . Outlet valve  1310  is positioned to allow liquid (i.e., A, B, C, D) to flow between pumping unit  1311  and pumping unit  1319 . Liquid (i.e., A, B, C, D) is received from chamber  1312  into chamber  1318 . The flow of liquid (i.e., A, B, C, D) between pumping unit  1311  and pumping unit  1319  is measured by flow sensor  1313 . Liquid (i.e., A, B, C, D) fills chamber  1318 , and on the delivery stroke of piston  1320 , liquid (i.e., A, B, C, D) is forced out of chamber  1318 . Motor/encoder system  1322  and computer  1324  are used to adjust the upward and intake stroke of piston  1320  to adjust the intake and expulsion of liquid (i.e., A, B, C, D) from chamber  1318 . Lastly, liquid (i.e., A, B, C, D) is delivered, as represented by arrow  1326 , to the remainder of the chromatography system (not shown in  FIG. 13 ). 
       FIG. 13A  is a flowchart of a method of detecting a leak in a gradient valve.  FIG. 13A  will be discussed in conjunction with  FIG. 13 . The method depicted in  FIG. 13A  commences with step  1340 . 
     At step  1340 , a flow sensor positioned between proportioning valve  1304  and inlet valve  1308  is calibrated for each liquid (i.e., A, B, C, D) stored in reservoir  1302 . For example, flow sensor  1306  is calibrated for each liquid (i.e., A, B, C, D) stored in reservoir  1302 . 
     At step  1341 , proportioning valve  1304  is closed, inlet valve  1308  is opened, and outlet valve  1310  is closed. 
     At step  1342 , piston  1314  performs a portion of an intake stroke to attempt to intake liquid (i.e., A, B, C, D) from proportioning valve  1304 . If there is no leak, then no fluid should flow. 
     At  1343 , flow sensor  1306  is used to measure the flow of liquid (i.e., A, B, C, D). 
     In step  1344 , if there is a leak in proportioning valve  1304 , liquid (i.e., A, B, C, D) flows through flow sensor  1306  (as measured in step  1343 ), and a leak is determined. 
       FIG. 13B  is a flowchart of a method of detecting a leak in an inlet valve.  FIG. 13B  will be discussed in conjunction with  FIG. 13 . The method depicted in  FIG. 13B  commences with step  1346 . 
     At step  1346 , flow sensor  1306  is calibrated for each liquid (i.e., A, B, C, D) stored in reservoir  1302 . 
     At step  1347 , chamber  1312  is filled with liquid (i.e., A, B, C, D). To fill chamber  1312  with liquid (i.e., A, B, C, D), proportioning valve  1304  is opened, inlet valve  1308  is opened, and outlet valve  1310  is closed. Piston  1314  then performs an intake stroke to fill chamber  1312 . Once chamber  1312  is filled, inlet valve  1308  is closed. 
     In step  1348 , piston  1314  then moves through a delivery stroke to compress the liquid (i.e., A, B, C, D) and pressurize chamber  1312 . 
     At step  1349 , an attempt is then made to measure a flow of liquid (i.e., A, B, C, D) in flow sensor  1306 . If there is no leak, then no fluid should flow. If a flow of liquid (i.e., A, B, C, D) is measured in flow sensor  1306 , the flow of liquid (i.e., A, B, C, D) is an indication that inlet valve  1308  has a leak. 
     In step  1350 , the leak is determined. 
     In step  1351 , after the leak is determined, metering may be performed to compensate for the leak. 
     In an alternate embodiment, the method depicted in  FIG. 13B  may be used to determine a leak in outlet valve  1310 .  FIG. 13B  will now be discussed in conjunction with  FIG. 13 . 
     At step  1346 , flow sensor  1313  is calibrated for each liquid (i.e., A, B, C, D) stored in liquid reservoir  1302 . It should be appreciated that flow sensor  1313  may be positioned either before or after outlet valve  1310 . 
     At step  1347 , chamber  1318  is filled with liquid (i.e., A, B, C, D). To fill chamber  1318  with liquid (i.e., A, B, C, D), while inlet valve  1308  is closed and outlet valve  1310  is opened, piston  1314  moves upward through a delivery stroke and piston  1320  moves downward through an intake stroke. Performing the intake stroke fills chamber  1318 . Once chamber  1318  is filled, outlet valve  1310  is closed. Piston  1320  then moves through a delivery (i.e., upward) stroke. 
     At step  1349 , an attempt is then made to measure liquid (i.e., A, B, C, D) in flow sensor  1313 . If there is no leak, then no fluid should flow. If flow is measured in flow sensor  1313 , such flow is backflow from chamber  1318 , and is an indication that outlet valve  1310  has a leak 
     In step  1350 , the leak is determined. It should be appreciated that the leak may be determined using any of the methods presented for determining leaks. 
     In step  1351 , once the leak is determined, metering may be performed to compensate for the leak as stated at step  1351 .  FIG. 13C  is a flowchart of a method of performing a smooth intake stroke.  FIG. 13C  will be discussed in conjunction with  FIG. 13 . The method depicted by  FIG. 13C  commences with step  1352 . 
     At step  1352 , pumping system  1300  is operating. During operation, proportioning valve  1304  allows liquid (i.e., A, B, C, D) from reservoir  1302  to be delivered to pumping unit  1311 . 
     At step  1353 , a flow sensor, such as flow sensor  1306 , positioned between proportioning valve  1304  and pumping unit  1311 , is used to measure the intake flow. In another embodiment, the flow sensor is not configured in the system. In one embodiment, the intake flow of liquid is not a continuous flow, and has discontinuities or increases and decreases in volume or flow. 
     At step  1354 , motor/encoder system  1316  is used to meter the intake flow to adjust for any discontinuities in the intake flow. Metering the intake flow includes adjusting the speed and/or timing of piston  1314  using motor/encoder system  1316  in conjunction with computer  1324 . 
       FIG. 13D  is a graph relating to a method of metering the intake flow to adjust for discontinuities in the intake flow. As a result of metering, a smooth and highly precise intake flow may be accomplished. The individual liquids (A, B, C, and D) accelerate and facilitate smooth transitions when proportioning valve  1304  is switched.  FIG. 13D  will be discussed in conjunction with  FIG. 13 . 
       FIG. 13D  presents a graph of the position of piston  1314  as a function of time. The upper limit of piston movement known as the upper dead center (UDC), and the lower limit of piston movement known as the lower dead center (LDC), are shown on the Y-axis of the graph. The liquid intake period is shown as  1360  and the liquid delivery period is shown as  1362  (i.e., for part of the delivery cycle). The portion of the graph associated with the intake of liquid A is shown as  1364 , the portion of the graph associated with the intake of liquid B is shown as  1366 , the portion of the graph associated with intake of liquid C is shown as  1368 , and the portion of the graph associated with the intake of liquid D is shown as  1370 . In addition, the initial compression and the final delivery of liquid, which occurs during the liquid delivery period  1362  is shown as  1372  and  1374 , respectively. 
     As shown in  FIG. 13D , piston  1314  is moving in a non-uniform manner to vary intake speed and the position of piston  1314  as shown by the portion of the graph associated with the intake of liquid A shown as  1364 , the portion of the graph associated with the intake of liquid B shown as  1366 , the portion of the graph associated with the intake of liquid C shown as  1368 , and the portion of the graph associated with the intake of liquid D shown as  1370 . As a result, no discontinuities in the intake of the liquid (i.e., A, B, C, D) are seen by pumping system  1300  when proportioning valve  1304  switches between liquids in reservoir  1302 . Further, more precise metering is accomplished when no liquid or less liquid is drawn by piston  1314  while activating proportioning valve  1304 . The corresponding liquids (i.e., A, B, C, D) are accelerated and decelerated very smoothly. 
       FIG. 14  is a schematic diagram of a dual-channel pumping system, i.e., a pumping system  1400 . A channel  1401  and a channel  1402  are shown in the pumping system  1400 . A liquid may be stored in a reservoir  1403 . An inlet valve  1404  is positioned in series with a pumping unit  1405 . Pumping unit  1405  includes a chamber  1406  and a piston  1408  capable of reciprocating motion within chamber  1406 . Pumping unit  1405  may be configured with a pressure sensor  1407 , which is positioned in chamber  1406 , to detect the pressure in chamber  1406 . An outlet valve  1424  is positioned in series with pumping unit  1405  and is positioned on an oppositely disposed side of chamber  1406  from inlet valve  1404 . A motor/encoder system  1414  is connected to pumping unit  1405  and controls the reciprocating motion of piston  1408 . A computer  1417  controls motor/encoder system  1414 . 
     A pumping unit  1427  is in series with pumping unit  1405 . Pumping unit  1427  includes a chamber  1428 , and a piston  1420 , with a seal  1421 , capable of reciprocating motion within chamber  1428 . Pumping system  1400  may be configured with a flow sensor  1425  positioned between pumping unit  1405  and pumping unit  1427 . It should be appreciated that flow sensor  1425  may be positioned before or after outlet valve  1424 . Pumping system  1400  may be configured with a flow sensor  1429  positioned on an output  1423  of channel  1401 . A motor/encoder system  1415  is connected to pumping unit  1427  and controls the reciprocating motion of piston  1420 . Computer  1417  controls motor/encoder system  1415 . 
     A liquid may be stored in a reservoir  1432 . An inlet valve  1434  is positioned in series with a pumping unit  1435 . Pumping unit  1435  includes a chamber  1436  and a piston  1438  capable of reciprocating motion within chamber  1436 . Pumping system  1400  may be configured with a pressure sensor  1431  positioned in chamber  1436 . An outlet valve  1442  is in series with pumping unit  1435  and is positioned on an oppositely disposed side of chamber  1436  from inlet valve  1434 . A motor/encoder system  1440  is connected to the pumping unit  1435  and controls the reciprocating motion of piston  1438 . Computer  1417  controls motor/encoder system  1440 . 
     A pumping unit  1447  is in series with pumping unit  1435 . Pumping system  1400  may include a flow sensor  1430  positioned between pumping unit  1435  and pumping unit  1447 . Pumping unit  1447  includes a chamber  1446 , and a piston  1448 , with a seal  1449 , capable of reciprocating motion within chamber  1446 . Pumping system  1400  may include a flow sensor  1433  positioned on an output  1443  of channel  1402 . A motor/encoder system  1450  is connected to pumping unit  1447  and controls the reciprocating motion of piston  1448 . Computer  1417  controls motor/encoder system  1450 . Lastly, a pressure sensor  1445  is positioned on an output  1455  of the pumping system  1400 . 
       FIG. 14A  is a flowchart of a method of operating a pumping channel. In addition, alternate embodiments of the method of operating a pumping channel are presented. For example, a method of detecting a leak in a first piston in a channel is presented. A method of detecting a leak in a second piston in a channel is presented. A method of detecting a leak when pumping system  1400  is operating at low flow rates (i.e., within the range of the flow sensor) is presented. A method of detecting a leak when pumping system  1400  is operating outside of the range of the flow sensor (i.e., high flow rates) is presented.  FIG. 14A  will be discussed in conjunction with  FIG. 14 . 
     In addition to the various embodiments, several parameters are defined for discussion purposes. In one embodiment, a nominal flow rate may be defined as a flow rate requested at output  1455 . The nominal flow rate may be input by a user into computer  1417 , and pumping system  1400  may coordinate between the various pumping units (i.e.,  1407 ,  1427 ,  1435 , and  1447 ) within pumping system  1400  to produce the nominal flow rate. In one embodiment, the measured flow rate may be defined as the flow rate measured by a flow sensor, such as flow sensors  1425 ,  1429 ,  1430 , and  1433 . Lastly, in one embodiment, a metered flow rate may be defined as a flow rate produced or recorded by motor/encoder system  1414 , motor/encoder system  1415 , motor/encoder system  1440 , or motor/encoder system  1450 . In one embodiment of the present invention, a leak is equivalent to the metered flow rate minus the measured flow rate (i.e., leak=metered flow rate−measured flow rate). 
     A method of determining leaks is presented in  FIG. 14A . The method commences with step  1460 . 
     At step  1460 , the flow rate of a pumping unit (i.e.,  1405 ,  1427 ,  1435 ,  1447 ) is determined. The flow rate may be determined by measuring, metering, etc. Further, the flow rate may be determined at various positions within pumping system  1400 . 
     At step  1461 , a change in the flow rate is determined. In one embodiment, a change in the flow rate is determined by measuring the change with a flow sensor (i.e.,  1425 ,  1429 ,  1430 ,  1433 ). 
     At step  1462 , a leak is identified and calculated in the channel. 
     At step  1463 , compensation is made for the leak. 
     A method of determining a leak in a pumping unit in a channel when the pumping unit is operating within the range of a flow sensor is presented. The method will be discussed using  FIG. 14  in combination with the flow diagram presented in  FIG. 14A . First, a constant flow rate is metered (i.e., used) for as the nominal flow rate. 
     At step  1460  of  FIG. 14A , the flow rate is determined. For example, flow sensor  1425  or flow sensor  1430  is used to determine the measured flow rate of pumping unit  1405  or pumping unit  1435 , respectively. Since flow sensor  1425  and flow sensor  1430  are connected to computer  1417 , computer  1417  is capable of recording the flow rate detected by each flow sensor (i.e.,  1425 ,  1430 ) over time. 
     At step  1461 , each flow sensor (i.e.,  1425 ,  1430 ) is monitored to identify a change in the flow rate. 
     At step  1462 , a change in the flow rate signifies a leak in a pumping unit. In one embodiment, this assumes a constant metered flow rate. 
     At step  1463 , compensation is made for the leak in the channel. 
     In a second embodiment, at step  1460  of  FIG. 14A , the flow rate is determined. For example, flow sensor  1425  or flow sensor  1430  is used to determine the measured flow rate of pumping unit  1405  or pumping unit  1435 , respectively. 
     At step  1461 , the metered flow rate is determined. For example, motor/encoder system  1414  and motor/encoder system  1440  are each used in combination with computer  1417  to determine a metered flow rate for each pumping unit (i.e.,  1405  and  1435 , respectively). 
     At step  1462 , a leak is identified and calculated. In one embodiment, the leak equals the metered flow rate minus the measured flow rate (i.e., leak=metered−measured). 
     At step  1463 , once the leak has been calculated, compensation is made for the leak. Compensation for the leak may include operating pumping units  1405  and  1435  to deliver additional liquid, which is equivalent to the amount of the leak. 
     In another embodiment of the present invention, a method of determining a leak in a channel when the output of the channel is within the operating range of a flow sensor is presented. The method will be discussed using  FIG. 14  in combination with the flow diagram presented in  FIG. 14A . 
     At step  1460  of  FIG. 14A , the flow rate is determined. For example, flow sensor  1429  and flow sensor  1433  is used to determine the measured flow rate of channels  1401  and  1402 , respectively. Since flow sensor  1429  and flow sensor  1433  are connected to computer  1417 , computer  1417  is capable of recording the flow rate detected by each flow sensor (i.e.,  1429 ,  1433 ) over time. 
     At step  1461 , each flow sensor (i.e.,  1429 ,  1433 ) is monitored to identify a change in the flow rate. In one embodiment, this assumes a constant metered flow rate. 
     At step  1462 , a change in the flow rate signifies a leak in the channel (i.e.,  1401 ,  1402 ). 
     At step  1463 , compensation is made for the leak in the channel (i.e.,  1401 ,  1402 ). In one embodiment, compensating for the leak in the channel (i.e.,  1401 ,  1402 ) may include operating a pumping unit ( 1405 ,  1435 ) in the channel (i.e.,  1401 ,  1402 )) to output liquid equal to the amount of the leak. In a second embodiment, compensating for the leak in the channel may include operating a pumping unit (i.e.,  1427 ,  1447 ) in the channel to output liquid equal to the amount of the leak. In a third embodiment, compensating for the leak in the channel may include operating pumping units ( 1405 ,  1435 ) in the channel in combination with a pumping unit ( 1427 ,  1447 ) in a channel to output liquid equal to the amount of the leak. It should be appreciated that the foregoing method may be extended to any amount of pumping units configured in a channel. 
     At step  1460  of  FIG. 14A , in a second embodiment of determining a leak in a channel when the output of the channel is within the operating range of a flow sensor, the flow rate is determined. For example, flow sensor  1429  or flow sensor  1433  may be used to determine the measured flow rate of channel  1401 . 
     At step  1461 , the metered flow rate is determined for each pumping unit (i.e.,  1405 ,  1427 ,  1435 ,  1447 ). For example, motor/encoder system  1414 , motor/encoder system  1440 , motor/encoder system  1415 , and motor/encoder system  1450  are each used in combination with computer  1417  to determine a metered flow rate for each pumping unit (i.e.,  1405 ,  1435 ,  1427 ,  1447 , respectively). 
     At step  1462 , a leak is identified and calculated. In one embodiment, the leak equals the metered flow rate minus the measured flow rate (i.e., leak=metered−measured). 
     At step  1463 , once the leak has been calculated, compensation is made for the leak. Compensation for the leak may include operating pumping units  1405 ,  1427 ,  1435 , and  1447  to deliver additional liquid, which is equivalent to the amount of the leak calculated for each channel (i.e.,  1401 ,  1402 ). 
     In a number of alternate embodiments, once a leak has been determined, a number of methods are presented for compensating for the leak in pumping system  1400  as stated in step  1463 . For example, individual metering methods may be implemented or integrated metering methods may be implemented. With an individual metering method, the flow of liquid through a single pumping unit (i.e.,  1405 ,  1427 ,  1435 ,  1447 ) may be metered to compensate for the leak in the channel (i.e.,  1401 ,  1402 ). Each pumping unit (i.e.,  1405 ,  1427 ,  1435 ,  1447 ) in a channel (i.e.,  1401 ,  1402 ) may be individually adjusted to compensate for a leak in the channel (i.e.,  1401 ,  1402 ). For example, pumping units  1405  and  1427  may be individually adjusted to meter liquid through the pumping unit (i.e.,  1405 ,  1427 ) and consequently compensate for the leak in channel  1401 . In a similar manner, pumping units  1435  and  1447  may be individually adjusted to meter liquid through the pumping unit (i.e.,  1435 ,  1447 ) and consequently compensate for the leak in channel  1402 . In the alternative, integrated metering methods may be implemented. For example, if there is a leak in channel  1401 , pumping unit  1405  and pumping unit  1427  may operate in a coordinated fashion to compensate for the leak. 
       FIG. 15A  is a flowchart of a method of determining a leak in a piston seal with a flow sensor positioned between two pumping units in a channel of a pumping system.  FIG. 15A  will be discussed in conjunction with  FIG. 14  and  FIG. 15B . 
     The flow diagram of  FIG. 15A  depicts a method of determining a leak in seal  1421  using sensor  1425 , and/or determining a leak in seal  1449  using sensor  1430 . The method commences with step  1560 . 
     At step  1560 , each pumping unit (i.e.,  1405 ,  1427 ,  1435 ,  1447 ) within each channel (i.e.,  1401 ,  1402 ) is operating. 
     At step  1561 , the flow variations of channel  1401  and channel  1402  are monitored. 
     In one embodiment, monitoring the flow variations in each channel (i.e.,  1401 ,  1402 ) includes plotting the flow variations between each pumping unit (i.e.,  1405 ,  1427 ,  1435 ,  1447 ) in a channel (i.e.,  1401 ,  1402 ). For example, monitoring the flow variation in each channel (i.e.,  1401 ,  1402 ) includes plotting the flow rate of one pumping unit (i.e.,  1405 ,  1427 ,  1435 ,  1447 ) relative to another pumping unit (i.e.,  1405 ,  1427 ,  1435 ,  1447 ) in the channel (i.e.,  1401 ,  1402 ). In another embodiment, monitoring the flow variations may include plotting the metering variations of each pumping unit (i.e.,  1405 ,  1427 ,  1435 ,  1447 ) in each channel (i.e.,  1401 ,  1402 ). 
     Using  FIG. 15B , graphs of the flow variations within a channel (i.e.,  1401 ,  1402 ) are schematically presented. In one embodiment, the pumping units  1405  and  1427  are positioned in series and pumping units  1435  and  1447  are positioned in series. A graph  1570  represents a piston that is deployed in a pumping unit  1405 ,  1435 , positioned in a channel, and a graph  1571  represents a piston that is deployed in a pumping unit  1427 ,  1447  positioned in the channel. Both graphs (i.e.,  1570  and  1571 ) display movement of piston versus time as the channel operates. A graph  1572  displays the velocity of a piston (i.e., in a pumping unit  1405 ,  1435 ) in a channel versus time. A graph  1573  displays the velocity of a piston in a pumping unit  1427 ,  1447  in the same channel versus time. 
     During an interval  1574 , there is a liquid intake period into pumping unit  1405 ,  1435 . Interval  1574  is bounded by the vertical axes on each graph and the dashed lines to the right of the vertical axes. 
     During an interval  1575 , there is a fast pre-compression jump of the piston chamber  1406 ,  1436 . Interval  1575  is bounded by vertical dashed lines. 
     During an interval  1576 , there is a final compression of chambers  1406  and  1436 . 
     During an interval  1577 , there is a delivering of liquid with the pumping units (i.e.,  1405 ,  1435 ;  1427 ,  1447 ) within a channel. Interval  1577  is bounded by vertical dashed lines. 
     During an interval  1578 , pumping units  1405  and  1435  deliver the liquid into the pumping system, and pumping units  1427  and  1447  are filled by pumping units  1405  and  1435 , respectively. 
     Graph  1570  represents the movement of a piston positioned in a pumping unit in a channel. For example, graph  1570  may represent the movement of piston  1408  or piston  1438 . 
     Graph  1571  represents the movement of a piston positioned in a pumping unit in a channel. For example, graph  1571  may represent the movement of piston  1420  or piston  1448 . During the liquid intake period, i.e., interval  1574 , the piston (i.e.,  1408  or  1438 ) in the channel moves from upper dead center (UDC) to lower dead center (LDC). In addition, the velocity of the pistons (i.e.,  1408  and  1420  or  1438  and  1448 ) may be shown schematically by graphs  1572  and  1573 . The velocity of the piston (i.e.,  1408 ,  1438 ) within a channel is chosen so that pumping unit  1405  and/or pumping unit  1435  is/are outputting liquid within the operating range of flow sensor  1425  and/or flow sensor  1430 . Therefore, flow sensors  1425  and/or  1430  will be able to measure the flow rate. The piston within the channel, such as piston  1420  and/or piston  1448 , is then used to deliver the remainder of the requested flow rate (i.e., nominal flow rate). Pressure sensor  1445  is used to measure the pressure drop of pumping system  1400 . In addition, pressure sensor  1445  is used to correlate the flow rate on output  1455 . 
     At step  1562  of  FIG. 15A , the frequently changing relationship between the pumped volume between two pistons (i.e.,  1408  and  1420  and/or  1438  and  1448 ) within the same channel is identified. In  FIG. 15B , this frequently changing relationship is shown as detail  1579 . The frequently changing relationship of the pump volume between two pumping units within the same channel in combination with different pressure levels corresponding to the frequently changing piston speeds at the output of the pumping system is an indication of a leak. For example, the changing relationship depicted in detail  1579  is indicative of a dynamic leak in seal  1421  and/or seal  1449 , if pressure sensor  1445  indicates a lower pressure on output  1455  when the volume of liquid output from the piston(s) (i.e.,  1420  and/or  1448 ) in the channel is higher than the volume of liquid output by piston  1408  and/or piston  1438  in channel  1401  and/or channel  1402 . It should be appreciated that dynamic leaks in piston/seal combinations can be detected. In a second embodiment, only one channel is connected to output  1455 . 
     It should be appreciated that a number of different pumping scenarios may be implemented and still remain in accordance with the teachings of the present invention. It should also be appreciated that individual pumping units may operate at specific times. For example, operating the piston (e.g.  1408  and  1438 ) within the channel without operating piston  1420  and/or piston  1448  within channel  1401  and/or channel  1402 , respectively, is within the scope of the present invention. 
       FIG. 15C  is a flowchart of a method of determining a piston velocity required to produce a nominal (desired) flow rate. In one embodiment, a flow sensor is used to determine a leak rate. A nominal flow rate is determined by performing metering as defined by a metered flow rate, determining the delivered flow rate (i.e., measured flow rate), calculating the leak by comparing metered flow rate and measured flow rate, and calculating correction and/or compensation factors. Metering is then performed to operate the pumping system at the nominal rate. For example, using pumping unit  1405 , metering is performed using motor/encoder system  1414 . The metering outputs liquid from pumping unit  1405  at a metered flow rate. Flow sensor  1425  is then used to measure the flow rate. The measurement produces a measured flow rate. The difference between the metered flow rate and the measured flow rate is then referred to as the leak rate. Motor/encoder system  1414  then adjusts the operation of piston  1408  to compensate for the leak rate. In one embodiment, compensating for the leak rate includes adjusting the operation of piston  1408  to produce an additional amount of liquid from pumping unit  1405  to compensate for the liquid lost as a result of the leak. 
       FIG. 15C  will be discussed in conjunction with  FIG. 14 . The method depicted in  FIG. 15C  commences with step  1580 . 
     At step  1580 , a flow sensor is implemented between pumping units within a channel. For example, flow sensor  1425  is positioned between pumping unit  1405  and pumping unit  1427 . In another embodiment, flow sensor  1430  is positioned between pumping unit  1435  and pumping unit  1447 . From step  1580 , the method progresses to step  1582 . 
     At step  1582 , liquid is taken into chamber  1406  and/or chamber  1436 . This requires a downward stroke of piston  1408  and/or piston  1438 . In one embodiment of the present invention, the downward stroke is a quick downward stroke. Typically, it is possible to draw in 100 μl liquid within less than 1 second. 
     At step  1583 , after filling chamber  1406  and/or chamber  1436 , liquid in chamber  1406  and/or chamber  1436  is compressed. In one embodiment, the liquid is compressed rapidly. For example, in one embodiment compress chamber  1406  and/or chamber  1436  rapidly. In one embodiment, the initial upward stroke of piston  1408  and piston  1438  is performed quickly, within 100 ms. 
     At step  1584 , when the liquid in the chamber is fully compressed, open the outlet valve. For example, after the liquid stored in chamber  1406  and/or chamber  1436  is fully compressed, open outlet valve  1424  and/or outlet valve  1442 . 
     At step  1585 , a flow sensor, such as flow sensor  1425  and/or flow sensor  1430  is/are used to detect the measured rate. Once the outlet valve  1424  and/or outlet valve  1442  is/are opened, flow sensor  1425  and/or flow sensor  1430  will detect the flow rate delivered by piston  1408  and/or piston  1438 . Since flow sensor  1425  and/or flow sensor  1430  is/are calibrated, the reading attained from flow sensor  1425  and/or flow sensor  1430  is the actual (i.e., measured) flow rate and can be determined by reading flow sensor. 
     At step  1586 , the encoder located in the motor/encoder system is read. The number of steps produced by the motor/encoder system is equal the metered flow rate. 
     At step  1587 , compare the actual flow rate with the metered flow rate. 
     At step  1588 , a comparison of the actual (i.e., measured) flow rate and the metered flow rate is performed to calculate the leak. 
     In step  1589 , once the leak has been calculated, the leak can be compensated for by metering at a new calculated piston velocity, etc. 
     A second method of determining the piston velocity required to produce the nominal (desired) flow rate is presented. In the second method, a leak is determined in an outlet valve when a second piston is pumping. In one embodiment, the method depicted in the flow diagram of  13 B is implemented. 
     At step  1347 , chamber  1428  and/or chamber  1446  is filled. Outlet valve  1424  and/or outlet valve  1442  is closed. 
     At step  1348 , piston  1421  and/or piston  1449  performs a delivery stroke. 
     At step  1349 , flow sensor  1425  and/or flow sensor  1430  is/are used to measure backflow. 
     At step  1350 , since the backflow is equivalent to the amount of the leak; the backflow is used to determine the leak. 
     At step  1351 , piston  1421  and/or piston  1449  is/are adjusted to compensate for the leak. In one embodiment, compensating for the leak includes calculating a new piston velocity required to produce the nominal or desired flow rate at the output. 
     Using  FIG. 14  to discuss the method, chamber  1427  and/or chamber  1447  is/are filled with liquid. Outlet valve  1424  and/or outlet valve  1442  is/are closed. Piston  1421  and/or piston  1448  perform(s) a delivery stroke. Flow sensor  1425  and/or flow sensor  1430  is/are used to measure any flow of liquid. A flow of liquid indicates a leak in outlet valve  1424  and/or outlet valve  1442 . The leak is equivalent to the flow of liquid. A new piston velocity may then be determined to compensate for the leak. The new piston velocity may be calculated by computer  1417  and implemented by motor/encoder system  1415  and/or motor/encoder system  1450 , respectively. Once the compensation is made, a nominal flow rate will be produced at output  1455 . 
     It should be appreciated that once outlet valve  1424  and/or outlet valve  1442  is/are opened, and chamber  1428  and/or chamber  1446  is/are fully compressed, the creeping effect of pumping system  1400  must be considered when calculating the leak rate. Creeping is a natural function of pumping system  1400 , in which the components of pumping system  1400  settle. During creeping, some leakage may occur. However, once creeping effects have terminated, pumping system  1400  should operate in steady state (i.e., with or without leakage). 
     In one embodiment, a method of determining leaks when the flow rate is higher than the range of the flow sensor is presented. A chamber in a first pumping unit is filled with fluid. At the same time that the chamber in the first pumping unit is being filled with fluid, the second pumping unit is delivering the desired flow rate. After filling the first pumping unit, the piston in the first pumping unit moves upward to compress the liquid in the first chamber at the same time the second piston is delivering the desired flow rate. Once the compression is complete, the outlet valve associated with the first pumping unit is opened. Afterwards, the first pumping unit delivers a portion of total flow rate into the system. The portion of the total flow rate is selected within the range of the flow sensor. A leak is then determined. The difference between the metered flow rate and the measured flow rate defines the leak. At the same time, the second piston delivers the remainder (nominal flow rate−measured flow rate) of the desired flow rate into the system. In the case where the first piston is delivering the total flow rate into the system, the metered flow rate is equivalent to the nominal flow rate plus the leak (i.e., nominal flow rate+the leak). 
     Using  FIG. 14 , chamber  1406  and/or chamber  1436  is/are filled with liquid. At the same time, pumping unit  1427  and/or pumping unit  1449  is/are delivering the desired flow rate. After filling chamber  1406  and/or chamber  1436 , piston  1408  and/or piston  1438 , respectively, move upward to compress the solvent in chamber  1406  and/or chamber  1436  at the same time that piston  1420  and/or piston  1448  is/are delivering the desired flow rate. Once the compression is complete, outlet valve  1424  and/or outlet valve  1442  is/are opened. Afterwards, pumping unit  1405  and/or pumping unit  1435  deliver(s) a portion of total flow rate into the system. The portion of the total flow rate is selected within the range of flow sensor  1425  and/or flow sensor  1430 . A leak is then determined. The difference of metered flow rate and measured flow rate defines the leak. At the same time, piston  1420  and/or piston  1448  deliver(s) the remainder (nominal flow rate−measured flow rate) of the desired flow rate into the system. In the case where piston  1408  and/or piston  1438  is/are delivering the total flow rate into the system, the metered flow rate is equivalent to the nominal flow rate plus the leak (i.e., nominal flow rate+the leak). 
       FIG. 15D  is a flowchart of a method of monitoring compression phases in a pumping chamber and monitoring the system pressure of a chromatographic system. In one embodiment, a single pressure sensor, such as pressure sensor  1407  and/or pressure sensor  1431  is/are required to monitor a compression phase of chamber  1406  and/or chamber  1436 , and to monitor system pressure of the chromatographic system.  FIG. 15D  will be described in conjunction with  FIG. 14 . The method depicted in  FIG. 15D  commences with step  1590 . 
     At step  1590 , solvent (i.e., liquid) is delivered into a pumping system using a second pumping unit. 
     At step  1591 , the first piston is used to rapidly intake liquid into the chamber in the first pumping unit (i.e., first pumping chamber). 
     At step  1592 , pressure is measured within the chamber of the first pumping unit. 
     At step  1593 , the liquid in the first pumping chamber is immediately compressed. 
     At step  1594 , the pressure in the first pumping chamber is measured during the compression phase with the pressure sensor in the first pumping chamber. 
     At step  1595 , the outlet valve associated with the first pumping chamber is immediately opened. 
     At step  1596 , the pressure in the first pumping chamber may be used to measure the system pressure of pumping system  1400 . 
     At step  1597 , the outlet valve is kept opened by pumping a small amount of liquid until the second chamber must be refilled. 
     At step  1598 , monitor the system pressure and blockages with the pressure sensor in the first pumping chamber. 
     At step  1599 , delivery of liquid into the system is stopped if a system blockage is detected. 
       FIG. 14  will be used to demonstrate the method detailed in the flow diagram in  FIG. 15D . 
     At step  1590 , solvent (i.e., liquid) is delivered into the system using a second pumping unit. Therefore, pumping unit  1427  and/or pumping unit  1447  is/are used to deliver liquid into the system. 
     At step  1591 , piston  1408  and/or piston  1438  rapidly intake solvent into chamber  1406  and/or chamber  1436 . Pumping unit  1405  and/or pumping unit  1435  rapidly intake liquid into chamber  1406  and/or chamber  1436 , respectively. 
     At step  1592 , pressure is measured within chamber  1406  and/or chamber  1436 . Pressure sensor  1407  is used to measure the pressure of chamber  1406 , and/or pressure sensor  1431  is used to measure the pressure of chamber  1436 . 
     At step  1593 , the liquid in chamber  1406  and/or chamber  1436  is immediately compressed. Piston  1408  is used to compress liquid such as solvent stored in chamber  1406 , and/or piston  1438  is used to compress liquid such as solvent stored in chamber  1436 . 
     At step  1594 , the pressure in chamber  1406  and/or chamber  1436  is measured during the compression phase with pressure sensor  1406  and/or pressure sensor  1431 . As piston  1408  is compressing the liquid in chamber  1406 , pressure sensor  1407  is used to measure the pressure in chamber  1406 . As piston  1438  compresses liquid in chamber  1436 , pressure sensor  1431  is used to measure the pressure in chamber  1436 . 
     At step  1595 , the outlet valve associated with the first pumping chamber is immediately opened. Outlet valve  1424  and/or outlet valve  1442  is/are immediately opened. 
     At step  1596 , the pressure in the first pumping chamber may be used to measure the system pressure of pumping system  1400 . After opening outlet valve  1424  and/or outlet valve  1442 , pressure sensor  1407  and/or pressure sensor  1431  may be used to measure the system pressure. 
     At step  1597 , the outlet valve is kept opened by pumping a small amount of liquid until the second piston must be refilled. Outlet valve  1424  and/or outlet valve  1442  remain(s) open, and piston  1408  and/or piston  1438  deliver(s) a small amount of liquid until the second pumping unit, i.e.,  1427  and/or pumping unit  1447 , must be refilled. 
     At step  1598 , monitor the system pressure and blockages with the pressure sensor in the first pumping chamber. Pressure sensor  1407  and/or pressure sensor  1431  is/are used to measure system pressure to detect blockage in pumping system  1400 . Changes in pressure measured by pressure sensor  1407  and/or pressure sensor  1431  when pressure sensor  1407  and/or pressure sensor  1431  is/are used to measure system pressure, will signal a blockage in the pumping system. 
     At step  1599 , delivery of liquid into the system is stopped if a system blockage is detected. If a blockage is detected, delivery of solvent with pumping unit  1427  and/or pumping unit  1447  is terminated. 
       FIG. 16 . is a schematic diagram of a dual-channel pumping system, i.e., a pumping system  1600 . Pumping system  1600  includes a channel  1610  and a channel  1620 . Channel  1610  includes a pumping unit  1612  in series with a pumping unit  1614 . Channel  1620  includes a pumping unit  1622  in series with a pumping unit  1624 . A reservoir  1602  stores a first liquid. A reservoir  1604  stores a second liquid. A channel output  1630  is connected to channel  1610 . A channel output  1642  is connected to channel  1620 . A pressure sensor  1632  is positioned on channel output  1630 . Channel output  1630  is connected to a waste output  1633  through a T-junction  1637 . A purge valve  1634  is positioned on waste output  1633 . A waste exhaust  1636  provides an output for liquid conveyed on waste output  1633 . 
     A T-junction  1640  provides a connection between channel output  1642  and a system output  1641 . System output  1641  provides a pathway to a chromatography system (not shown in  FIG. 16 ). A conveyance  1639  is shown between T-junction  1637  and T-junction  1640 . In one embodiment, a flow sensor  1638  is positioned along conveyance  1639 . In another embodiment, flow sensor  1638  is not included in pumping system  1600 . It should also be appreciated that in an alternate embodiment, T-junction  1637 , purge valve  1634 , waste output  1633 , and waste exhaust  1636  may be positioned in channel output  1642 . 
     During operation, a liquid is pumped through channel  1610  to channel output  1630 , and a liquid is pumped through channel  1620  to the channel output  1642 . A mixture of channel output  1630  and channel output  1642  is combined at T-junction  1640  and conveyed on system output  1641 , as represented by arrow  1645 . It should be appreciated that while an embodiment of a specific pumping unit is detailed in each channel (i.e.,  1610 ,  1620 ), the present invention may be directed to pumping systems with different channel components (i.e., pumping units, valves, etc.). It should also be appreciated that more than two channels may be connected at T-junction  1640 . In addition, waste from channel output  1630  and channel output  1642  may travel along waste output  1633 , through purge valve  1634 , and through waste exhaust  1636 . 
       FIG. 16A  is a flowchart of a method of flushing a pumping system completely.  FIG. 16A  will be discussed in conjunction with  FIG. 16 . The method commences with step  1650 . 
     At step  1650 , a purge valve, such as purge valve  1634 , is opened. 
     At step  1652 , the channel in which purge valve  1634  is positioned is flushed. For example, in system  1600 , channel  1610  is flushed. Flushing channel  1610  includes conveying liquid on channel output  1630 , through T-junction  1637 , through waste output  1633 , through purge valve  1634 , and through waste exhaust  1636 . 
     At step  1654 , a channel that purge valve  1634  is not positioned in is flushed. For example, channel  1620  is flushed. Flushing channel  1620  includes conveying liquid on channel output  1642 , through T-junction  1640 , through conveyance  1639 , through T-junction  1637 , through waste output  1633 , through purge valve  1634 , and through waste exhaust  1636 . 
     Step  1656  is an optional step where both channels  1610  and  1620  may be flushed together. 
     At step  1658 , the channel in which purge valve  1634  is positioned is flushed one more time. For example, channel  1610  is flushed again. 
     At step  1660 , purge valve  1634  is closed. 
     At step  1662 , a decision is made regarding how to flush conveyance  1639 , i.e., the conveyance between the two T-junctions (i.e.,  1637  and  1640 ), with liquid from the channel the purge valve  1634  is positioned. For example, this would include flushing conveyance  1639  with liquid flowing through channel output  1630 . If the decision is made to flush conveyance  1639  via system output  1641 , then the method progresses to step  1664 . If the decision is made to not flush conveyance  1639  via pump system outlet  1641 , then the method progresses to step  1668 . 
     In step  1664 , solvent is pumped from the channel in which purge valve  1639  is positioned until liquid is at the mixing point. This has the effect of cleaning the conveyance between the two T-junctions, of liquid from the second channel. Using  FIG. 16  as an example, this would include pumping liquid from channel  1610 , through channel output  1630 , across T-junction  1637 , across conveyance  1639  to a mixing point defined by the location where channel output  1630 , channel output  1642 , and pumping system output  1641  meet in T-junction  1640 . From step  1664 , the method progresses to step  1666 . 
     In step  1666 , normal operation is continued. 
     At step  1668 , solvent is pumped from the channel in which the purge valve is positioned, backwards to the channel in which the purge valve is not positioned, until the correct solvents occur at a defined mixing point. Using  FIG. 16 , this would mean pumping liquid from channel  1610  along channel output  1630 , past T-junction  1637 , along conveyance  1639 , past T-junction  1640  backwards into channel output  1642 . From step  1668 , the method progresses to step  1669 . 
     In step  1669 , normal operation is continued. 
       FIG. 16B  displays a flowchart depicting a method of compensating for a leak in a multi-channel pumping system.  FIG. 16B  will be discussed in conjunction with  FIG. 16 . The method commences with step  1670 . 
     At step  1670 , a pumping system, such as pumping system  1600 , is operating. 
     At step  1672 , the pumping in one channel is stopped. 
     At step  1674 , the backflow into the stopped channel is detected. 
     At step  1676 , the backflow into the stopped channel is used to calculate the amount of the leak. 
     At step  1678 , a technique for compensating for the leak is selected from a first technique and a second technique. If the first technique is selected, the method progresses to step  1680 . If the second technique is selected, the method progresses to step  1682 . 
     In step  1680 , the first technique for compensating for the leak is employed. In accordance with this first technique, a small amount of flow is delivered to maintain zero flow at the channel output. 
     In step  1682 , the second technique for compensating for the leak is employed. In accordance with this second technique, the leak is stored in the stopped channel output. The channel output itself is cleaned from time to time by delivering the stored leak. 
     The method depicted by the flowchart of  FIG. 16B  will now be discussed in conjunction with the pumping system  1600  of  FIG. 16 . 
     At step  1670 , pumping system  1600  is operating. 
     At step  1672  one channel, such as channel  1610 , is stopped. 
     At step  1674 , the backflow into channel  1610  is sensed. In one embodiment, the backflow into channel  1610  is sensed in flow sensor  1638 . 
     At step  1676 , the amount of leak in channel  1610  is calculated. The leak may be calculated using a number of the foregoing techniques presented in the instant application. For example, in one embodiment, the leak equals the measured flow minus the metered flow determined by pumping units  1612  and  1614 . 
     At step  1678 , a technique for compensating for the leak is selected from a first technique and a second technique. If the first technique is selected, the method progresses to step  1680 . If the second technique is selected, the method progresses to step  1682 . 
     At step  1680 , the first technique is employed. A small amount of flow is delivered to maintain a zero flow at the mixing point. For example, an amount of flow equal to the leak may be generated dynamically to maintain a zero flow at the mixing point defined by T-junction  1640 . Delivering the flow equal to the leak will include operating channel  1610  to generate an amount equivalent to the leak and a zero flow at T-junction  1640 . 
     At step  1682 , the second technique is employed. An amount of liquid equivalent to the amount of leak is stored in channel output  1630 . The channel is cleaned from time to time, preferably when the chromatography is not influenced. 
     Thus, the present invention has been described herein with reference to a particular embodiment for a particular application. Those having ordinary skill in the art and access to the present teachings will recognize additional modifications, applications, and embodiments within the scope thereof. 
     It is, therefore, intended by the appended claims to cover any and all such applications, modifications, and embodiments within the scope of the present invention.
A liquid chromatograph includes a mobile phase supplying apparatus including liquid-feeding pumps to feed mobile phases, liquid-feeding flow paths, a mixer to mix the mobile phases, at least one control device to control each liquid-feeding pump, flow rate measuring sections provided downstream in each liquid-feeding flow path configured to measure an actual flow rate and to detect a back-flow, and actual flow rate computing sections configured to compute an actual flow rate in the corresponding liquid feeding flow path. Also included are a sample injecting section downstream of the mobile phase supplying apparatus, a separating column for separating an injected sample into its constituents, and a detector for detecting each of the separated constituents. When one of the actual flow rate measuring sections detects a back-flow, the corresponding actual flow-rate computing section computes an actual back-flow rate and outputs a signal to the corresponding control device to cancel the back-flow.