cracked black powder grains were screened to 1 / 16 to 3 / 32 inch size such that the grain size distribution was relatively narrow -- i . e ., a size distribution to within 50 %. the grains were then coated with a glue that also functions as a propellant . the glue was made by dissolving a high nitrogen nitrocellulose , i . e ., 12 to 12 . 5 % nitrogen , in a solvent such as acetone , ether , or ether alcohol . in initial trials , the mass fraction of combustible glue was roughly 5 to 10 % although other percentages will give different burn rates . the coated grains were then packed in an open end tube -- a rocket casing 10 cm long -- and allowed to dry ( i . e . the solvent of the glue was allowed to evaporate ). when the dried and cured propellant was ignited , it burned stably in about a tenth of a second . this gives a burn rate of 100 cm sec - 1 . a smaller mass fraction of glue -- say 1 %-- increases this burn rate by another factor of 10 . if a heterogeneous propellant like nh 4 clo 4 or kclo 4 plus aluminum is used , the glue can take the form of a combustible hydrocarbon such as epoxy or urethane . the ratio of glue to aluminum to oxidizer should be such as to create a stoichiometric balance for highest performance although a slower burn rate may require a compromise of performance . it will also be appreciated by one skilled in the art that other common oxidizers may be used according to the invention such as the compounds having na , k , and nh 4 as the cation and no 3 , clo 3 and clo 4 as the anion . in another embodiment the monobase or double base powders ( nitrocellulose or nitrocellulose plus nitroglycerine ) may be pre - formed into balls all accurately the same size , or more complicated shapes , grains , as is well known in military cannon technology . the simplest shape , called ball powder , is ideally suited to the present concept of a controlled fast - burning propellant . a ball powder can be made of a predetermined cut of different size balls so that different packing fractions are achieved , i . e . different ratios of void space to propellant space . in addition the maximum ball size determines the burn rate as an additional delay time to the glue melting time . in this case the glueing of such a matrix is relatively simple . in one case the prepacked powder can be wetted with a solvent like ether or acetone or other well known solvent for nitrocellulose and the solvent allowed to partially dissolve the grains , e . g . balls , for a predetermined length of time . the solvent is then allowed to drain out and the dissolved surfaces of the grains then act as their own glue . the subsequent evaporation of the solvent from within the volume of the propellant is facilitated by the fact that the void space interconnects the whole volume and hence air transport of the solvent can readily take place . alternately , for slower burning of the same propellant at a high chamber pressure , for example greater than 1000 psi , it may be desirable to use a thicker glue layer filling 1 / 2 the void space . then the balls should be precoated with glue before packing . the glue in this case preferably is a propellant also so that it adds to the reactive mass . again nitrocellulose dissolved in solvent is an advantageous choice . however there may be circumstances where high specific impulse may not be the only consideration , but instead a high volume of gas may be desired . then a glue that gives a high volume of inert gas when heated such as polycarbonates or ureas could be advantageously used . the particular advantage of heterogeneous propellants where oxidizer and fuel are physically separated in the matrix -- such as nh 4 no 3 , thiokol rubber , and aluminum -- is that they are much safer to handle and transport and are considered practically immune to detonation . accidental ignition is however possible and , while not necessarily as catastrophic as a detonation , is nonetheless serious . hence , there is a need to make safer very fast burning heterogeneous propellants . again the heterogeneous propellant can be preformed into grains and then the grains glued to one another in a fashion entirely analagous to the homogeneous propellants . the standard heterogeneous propellant that uses a polymerized rubber , for example thiokol , is not as easily dissolved in place as nitrocellulose , and so the preferred embodiment in this case requires that a glue be added to the grains before casting . again the pre - polymerized rubber combined with fuel ( aluminum ) is one choice but many self - polymerizing glues with oxidizers added like epoxy and kclo 4 or urethane and kclo 4 are feasible . in this example the propellant is considered to be a heterogeneous mixture that is fluidized with a viscosity η . the scale of the heterogenity is the grain size δ of oxidizer or oxidizer - fuel grains . the instability growth is already initiated at large amplitude by the different properties of density and temperature of the burning grain boundaries and the viscous fluid . if the burn pressure is p , then the differential acceleration , δa , will be of the order ## equ5 ## where ρ is the average density and δρ the density difference between grains and fluid . the differential acceleration will be balanced by a shear stress from the velocity gradient , ( δv / δ ) in the viscous fluid of viscosity η . the viscosity shear stress is approximately 2η ( δv / δ ) so that balancing of forces yields or ## equ6 ## choosing typical values , the typical grain size of the cheapest commercial oxidizer , nano 3 , is δ ≃ 1 mm . the density contrast between the cheapest viscous fluid fuel , i . e . petroleum oils and tars , and nano 3 is δρ / ρ ≃ 1 / 3 . the typical pressure required for fracturing a well 1 km deep would be 300 atmospheres . then the intergrain or instability flow velocity would be this formula of course does not hold unless η is quite large such that δv is much less than sound speed , e . g . δv & lt ;& lt ; 2 × 10 3 meter sec - 1 . otherwise the assumption of neglecting inertial forces in favor of viscous forces would not apply . however , because a relatively slow speed ( compared to sound speed ) of δv ≃ 10 to 20 meter sec - 1 is desired , a viscous fluid binder or fuel of η ≃ 3000 poise will be necessary . since sae 50 automotive oil has a viscosity at 100 ° f . of roughly 1 / 10 this value ( 260 poise ) it can be seen that the viscous fluid should have a viscosity between a typical road tar and bunker c fuel oil . this is fortunate because for the proposed use these residual oils are the least expensive . therefore a typical embodiment of a viscous solid propellant for oil well fracturing or underground bulking could combine the cheapest oxidizer nano 3 blended with a residual oil such as to form the products nao + n 2 + h 2 o + co 2 . in addition , in order to ensure burning of the relatively refractory oxidizer nano 3 , one can increase the flame temperature by the addition of powdered aluminum or a similar high energy fuel . in this case , depending upon the stoichiometric fraction , some of the heavy oil will be just vaporized rather than burned . the effectiveness of this vaporized oil as a fracturing gas is comparable to the combustion product gases . this then becomes a preferred mixture . if the heavy oil has a low value of h to c of ≅ 1 , then an excess of fuel may yield less oxygen and the products co , co 2 and h 2 . this is slightly preferred in fracturing because the steam ( h 2 o ) will give up its heat to fractures and liquefy to water , thereby reducing the useful gas volume for fracturing . the limiting viscosity of a viscous binder is a solid . coal will not re - form with heat , but as a pulverized solid it can give a fast burning rate as a powder depending on particle size . the natural bitumen &# 34 ; gilsonite &# 34 ; has the peculiar properties that it can be ground as a solid , but then partially reformed as a plastic and so a variable degree of binding can be achieved between oxidizer and fuel particles . this also can lead to medium to fast burning rate propellant just as the glued grain example . a typical embodiment of well fracturing with a fast burning propellant starts with the completion of a well , for example 8 &# 34 ; in diameter although larger or smaller diameters are entirely feasible . the volume of propellant to be burned is determined by the desired fracture system . typically volumes of very large fracture or stimulation operations are of the order of 10 , 000 barrels or 2000 cubic meters . a gasified solid propellant expands to a volume of roughly 100 times the propellant volume to a typical formation pressure of 200 atmospheres ( 3000 psi ). the energy content of the propellant is roughly 5 × 10 10 ergs / gm giving rise to a pressure of ≃ 10 11 dynes cm - 2 . the adiabatic expansion of the propellant gases from 10 11 dynes to 200 atmospheres , or 2 × 10 8 dynes cm - 2 , results in a volume change of ( 10 11 / 2 × 10 8 ) 1 / γ ≃ 85 fold . since the density of the propellant is somewhat greater than unity , the volume of gases should be roughly 100 times the volume of propellant . the expansion of the gases may not be entirely adiabatic depending upon the back pressure in the burning region . however , if the expansion is at constant enthalpy , the volume of gas will be greater up to the ratio v 1 / v 2 = p 1 / p 2 ≃ 500 . hence the adiabatic approximation is the lower limit of available fracture volume . in the above circumstances , the initial propellant charge of 10 m 3 should be the equivalent of 1000 m 3 or 5000 barrels of pumped fracture fluid . next a string is set with an igniter at the base ( preferably thermite or other high temperature burning igniter ) and with the maximum diameter that will go down the hole -- e . g . 8 &# 34 ; in the present example . the strength of the string must be great enough to contain the propellant in place . in this example l = vol / area ≃ 300 meters assuming a pipe string wall thickness of 1 / 4 &# 34 ;, enough to hold the added fracture pressure during the transient burn period and assuming a competent formation as backup of the well liner . the top of the string can be closed off with a packer or stemmed with a weak cement or sand if later drill back is expected . the advantage of the weak cement or sand stem is that in the event of a blow - out from unforeseen reasons the propellant and cement particles could vent to the surface with lessened danger to personnel in the immediate vicinity . the propellant is mixed down hole with preheated viscous oil and oxidizer . in this regard , nano 3 is preferred as it is the cheapest oxidizer . by mixing down hole , one avoids the danger of preignition and possible danger to personnel . in a less preferred embodiment , one might consider pumping the propellant slurry through a nozzle down hole during burning at a velocity sufficiently great so that the burn front does not climb up the injection string . in this way one could avoid the difficulty of setting a casing string , and instead use cheaper , smaller diameter tubing . however , certain difficulties can be foreseen with this approach . first , by the previous analysis the viscosity of the oil must be low for rapid pumping , yet high in order to control the burning rate of the propellant . the high viscosity of 3000 poise essentially precludes rapid pumping because of viscous pipe losses . a lower viscosity will give too high a burn rate . finally if a slurry of pre - mixed fuel and oxidizer is pumped at a high pressure , there is always the danger of ignition by friction in the pump valves and piping . this could lead to an explosion . hence the propellant is preferably mixed in the relative safety of down hole and burned in situ .