the invention serves to more nearly eliminate the irreversibilities in the cryogenic distillation system of the lower pressure column of a double column system . this reduces the system energy requirements to a greater degree than is possible with conventional practice . by partially condensing a lower pressure feed air stream in an intermediate heat exchanger in the lower pressure column against partially reboiling column liquid , the operating line of this section of the column is brought closer to the equilibrium line thus reducing the energy requirements of the system . phase separation of the partially condensed lower pressure feed air provides the opportunity for the incorporation of a second intermediate heat exchanger at a higher level in the lower pressure column . in this second intermediate heat exchanger the separated vapor from the first intermediate heat exchanger is preferably totally condensed against partially reboiled column liquid . the liquid leaving the intermediate heat exchanger does not mix with the entering liquid on the vaporizing side . the liquids produced in each stage of intermediate heat exchange are transferred to the proper levels in the column thus supplementing the normally available reflux . the use of the second intermediate stage of heat exchange further reduces the irreversibilities in the column and thus reduces the energy requirements for the system . refrigeration requirements for the system are met by turboexpansion of a portion of the air fed to the plant which has been boosted in pressure above that used for partial condensation in the intermediate heat exchangers . a further reduction in energy requirements may be obtained by adding a second pair of intermediate heat exchangers located at a level higher in the column operating in much the same fashion as the first pair . the second pair of intermediate heat exchangers is fed with near saturated lower pressure air from the primary heat exchanger . the first pair of intermediate heat exchangers is fed with near saturated air at a pressure somewhat above the second pair . refrigeration for the cycle is balanced by turboexpansion of a portion of the air to the plant which has been boosted above that of the first pair of intermediate heat exchangers . the invention will be described in greater detail with reference to the drawings . referring now to fig1 feed air 100 is compressed to a pressure generally within the range of from 20 to 50 pounds per square inch absolute ( psia ) by passage through base load compressor 31 and resulting feed air stream 60 is cleaned of high boiling impurities such as water vapor and carbon dioxide by passage through purifier 50 . a portion 63 of cleaned , compressed feed air 61 , generally comprising from about 20 to 50 percent of the feed air 100 , is withdrawn from the feed air for use with the intermediate heat exchangers as will be more fully described later . remaining feed air stream 62 is compressed by passage through booster compressor 32 to a pressure within the range of from 40 to 100 psia and resulting feed air stream 79 is passed into main heat exchanger 1 wherein it is cooled by indirect heat exchange with return streams . a portion 80 of feed air stream 79 , generally comprising from about 5 to 15 percent of feed air 100 , is withdrawn after partial traverse of main heat exchanger 1 , turboexpanded by passage through turboexpander 30 to generate refrigeration , and passed as stream 81 into lower pressure column 11 . remaining feed air stream 64 , preferably comprising the major portion of the feed air and generally comprising from about 35 to 75 percent of feed air 100 , is passed from main heat exchanger 1 to product boiler 23 wherein it is at least partially condensed by indirect heat exchange with boiling product oxygen . resulting feed air stream 65 is passed as the first feed air portion into first or higher pressure column 10 . first column 10 is the higher pressure column of a double column system which also includes second or lower pressure column 11 . higher pressure column 10 is operating at a pressure within the range of from 40 to 100 psia . within higher pressure column 10 the first feed air portion is separated by cryogenic rectification into nitrogen - enriched vapor and oxygen - enriched liquid . nitrogen - enriched vapor is withdrawn from column 10 as stream 82 and passed into main condenser 20 wherein it is condensed by indirect heat exchange with boiling lower pressure column bottom liquid . resulting nitrogen - enriched liquid 83 is divided into stream 84 which is returned to higher pressure column 10 as reflux , and into stream 85 which is cooled by passage through heat exchanger 101 and passed through valve 87 into lower pressure column 11 as reflux . oxygen - enriched liquid is withdrawn from higher pressure column 10 as stream 71 , cooled by passage through heat exchanger 102 and passed through valve 73 into lower pressure column 11 . in the embodiment illustrated in fig1 stream 71 is combined with stream 68 from the first intermediate exchange and this combined stream 75 is passed into the lower pressure column . second or lower pressure column 11 is operating at a pressure less than that of higher pressure column 10 and within the range of from 15 to 30 psia . feed air stream 63 is cooled by passage through main heat exchanger 1 by indirect heat exchange with return streams . resulting cooled lower pressure feed air stream 66 is passed as a second feed air portion into first intermediate heat exchanger 21 which is located within lower pressure column 11 generally about 2 to 15 equilibrium stages above the heat exchange of bottom reboiler 20 . within first intermediate heat exchanger 21 , second feed air portion 66 is partially condensed by indirect heat exchange with vaporizing , preferably partially vaporizing , liquid flowing down column 11 thereby generating upflow vapor for column 11 and producing a first liquid air portion and a first vapor air portion in two phase stream 67 which is passed from first intermediate heat exchanger 21 into phase separator 40 . first vapor air portion 99 , which has a nitrogen concentration which exceeds that of stream 66 , is passed out from phase separator 40 into second intermediate heat exchanger 22 which is located within lower pressure column 11 above , generally about 1 to 10 equilibrium stages above , first intermediate heat exchanger 21 . within second intermediate heat exchanger 22 , first vapor air portion 99 is at least partially and preferably is totally condensed by indirect heat exchange with vaporizing , preferably partially vaporizing , liquid flowing down column 11 thereby generating additional upflow vapor for column 11 and producing a second liquid air portion . first liquid air portion 68 , which has an oxygen concentration which exceeds that of stream 66 , is passed out from phase separator 40 , through valve 69 and into lower pressure column 11 at a point at or above , generally up to 10 equilibrium stages above , second intermediate heat exchanger 22 . as mentioned previously , fig1 illustrates an embodiment wherein stream 68 is combined with stream 71 to form stream 75 which is then passed into column 11 . second liquid air portion 76 , which has a nitrogen concentration which exceeds that of stream 66 , is passed out from second intermediate heat exchanger 22 , through valve 77 and into lower pressure column 11 at a point above , generally from 5 to 20 equilibrium stages above , second intermediate heat exchanger 22 . the first and second liquid air portions serve to provide additional reflux liquid into lower pressure column 11 to improve the cryogenic separation within that column . within second or lower pressure column 11 the various fluids passed into that column are separated by cryogenic rectification into nitrogen - rich fluid and oxygen - rich fluid . nitrogen - rich fluid is withdrawn from column 11 as vapor stream 89 , warmed by passage through heat exchangers 101 , 102 and 1 and passed out of the system as nitrogen stream 1 which may be recovered , in whole or in part , as nitrogen product . oxygen - rich fluid is withdrawn from column 11 and recovered , in whole or in part , as product lower purity oxygen . in the embodiment illustrated in fig1 oxygen - rich fluid is withdrawn from column 11 as liquid stream 92 which is passed into product boiler 23 wherein it is vaporized by indirect heat exchange with condensing first feed air portion 64 . resulting oxygen - rich vapor stream 93 is warmed by passage through main heat exchanger 1 and recovered as product lower purity oxygen stream 94 . if desired , a portion of stream 92 may be recovered directly as product lower purity liquid oxygen . fig2 illustrates another embodiment of the invention wherein a second pair of intermediate heat exchangers is employed within the lower pressure column . the numerals of fig2 correspond to those of fig1 for the common elements and these common elements will not be described again in detail . referring now to fig2 a third portion 103 of feed air stream 61 , generally comprising from about 5 to 20 percent of feed air 100 , is taken from stream 61 for processing in the second pair of intermediate heat exchangers . stream 61 is then compressed to a higher pressure by passage through compressor 33 before being processed as described in accordance with the embodiment illustrated in fig1 . feed air stream 103 is warmed by passage through main heat exchanger 1 and resulting stream 104 is partially condensed in third intermediate heat exchanger 24 which is located within lower pressure column 11 generally about 1 to 10 equilibrium stages above second intermediate heat exchanger 22 . within third intermediate heat exchanger 24 , feed air stream 104 is partially condensed by indirect heat exchange with vaporizing , preferably partially vaporizing , liquid flowing down column 11 thereby generating upflow vapor for column 11 and producing a third liquid air portion and a further vapor air portion in two phase stream 105 which is passed from third intermediate heat exchanger 24 into phase separator 41 . further vapor air portion 106 , which has a nitrogen concentration exceeding that of stream 103 , is passed out from phase separator 41 into fourth intermediate heat exchanger 25 which is located within lower pressure column 11 above , generally about 1 to 10 equilibrium stages above , third intermediate heat exchanger 24 . within fourth intermediate heat exchanger 25 , further vapor air portion 106 is at least partially and preferably is totally condensed by indirect heat exchange with vaporizing liquid flowing down column 11 thereby generating additional upflow vapor for column 11 and producing a fourth liquid air portion . third liquid air portion 107 , which has an oxygen concentration exceeding that of stream 103 , is passed through valve 108 and combined with stream 68 to form stream 109 which then is combined with stream 71 to form stream 75 which is processed as described above . fourth liquid air portion 110 , which has a nitrogen concentration exceeding that of stream 103 , is passed out from fourth intermediate heat exchanger 25 , through valve 111 , and combined with stream 77 which is processed as described above . while fig1 and 2 illustrate the heat exchange associated with heat exchangers 21 , 22 , 24 and 25 as occurring physically within the shell of the column , this is done to simplify the illustration of the method of the invention . in many instances it is expected that one or more such heat exchangers will be located physically outside the shell of the column , i . e . functionally within the column . fig3 illustrates one arrangement in generalized form of such a heat exchanger functionally within the column . referring now to fig3 liquid descending within column 200 is collected and withdrawn from the column as stream 204 . means for collection and withdrawal of the liquid are well known to those knowledgeable in the design of distillation equipment . liquid stream 204 is introduced to heat exchanger 201 which may be a brazed aluminum heat exchanger . as liquid 204 traverses heat exchanger 201 , it is at least partially vaporized by indirect heat exchange with a fluid 202 which is at least partially condensed . fluid 202 represents the vapor flow into the heat exchanger , e . g . stream 66 or stream 99 of fig1 . streams 202 and 204 flow in a counter - current fashion within heat exchanger 201 . partially vaporized liquid 205 exits heat exchanger 201 and is delivered back to column 200 . preferably the partially vaporized liquid is returned to the column in such a fashion that the vapor portion 206 is able to mix with vapor 209 rising within the column from below the point where liquid 204 was originally withdrawn . the means for accomplishing this are commonly employed in distillation column design when a two - phase stream is introduced to an intermediate location within the column . the liquid portion 207 of stream 205 is disengaged from the vapor portion and is preferably distributed to those mass transfer elements such as packing or trays immediately below the level from where liquid 204 was originally withdrawn . the means for disengaging the liquid from the vapor and for distributing the liquid as described are commonly employed in distillation column design . although from a functional viewpoint it is preferred to employ all of the column downflowing liquid for stream 204 , some design circumstances may dictate using only a portion of the downflowing liquid for this purpose . as mentioned , stream 202 is at least partially condensed by the heat exchange within heat exchanger 201 . fluid in stream 203 is passed into the column . stream 203 corresponds , for example , to stream 67 or stream 76 of fig1 . although the invention has been described in detail with reference to certain preferred embodiments , those skilled in the art will recognize that there are other embodiments of the invention within the spirit ad the scope of the claims .