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Remarks on ``Some Criteria for the In Situ Combustion of Crude Oil''

H. R. Baileyand B. K. Larkin

Citation: Journal of Applied Physics 31, 1123 (1960); doi: 10.1063/1.1735760

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L E T T E R S TO T H E E D I T O R 1123filled by injected gas which does not cross the boundary, the rateat which gas does cross the boundary representing the heat frontis given by Vol-tpV/. Assume the same temperature To at bothinlet and outlet ends of the system, and .::\.'>0 to satisfy Cooperman's second criterion; with Po and y having the same meaning asin footnote reference 1, the expression

H = (Vgl- tpvj)ypgTo::\ 4)represents the excess heat per unit time carried into the systemby the reactants over and above the heat carried away by thereaction products, because of the difference in heat capacities.The change in heat capacity being caused by the chemical reaction,it occurs at the zone boundary. But Eq. (4) is equivalent to Eq.(60), footnote reference 1, in the adiabatic case; thus, Cooperman'swork must assume implicitly that the change in heat capacity atthe boundary is the only mechanism of heat release, and that theheat generated by the combustion reaction itself is zero ornegligible. This is also apparent from the fact that Eq. (57),footnote reference 1, which Cooperman claims to connect the heatgenerated with the flux of air, contains only specific heats and inletand outlet temperatures, but not the heat of combustion eithe r forfuel or for oxygen. Note also that according to Cooperman, if hissecond condition is not satisfied and n/m=3.05, there would be noheat flux and no release of heat although the reaction Eq. (50),footnote reference 1, would still be going on. The magnitude ofthe error involved is readily seen from a numerical example:with n/m=6, y=0.21 (injection of air, complete oxygen utilization), To=600oR= 140F. and the same specific heats as in theforegoing, Eq. (4) yields only 0.6 Btu/std cu ft of air passingthrough the combustion zone, while the heat of combustion forair, with petroleum fuels, is on the order of 100 Btu/std cu ft.4. Consider a segment extending, both upstream and downstream of the front, f ar enough so that the temperature is substantially equal to To and the temperature gradient is negligible. Thissegment has, in steady state, a constant heat conten't and anyheat generated must be removed by the sensible heat of the flowingfluids. This is possible in Cooperman's theor y because he assumesa rate of heat generation based on the heat carrying capacity ofthe flowing fluids; but if we are to take into account the muchlarger amounts of heat generated by the combustion reaction in areal system, the heat capacities of the flowing fluids becomegrossly inadequate to remove all the heat generated at anyreasonable temperature level. Hence, the assumption of steadystate in a linear system with real combustion cannot be justified.

1 P. Cooperman, J. App . Phys. 30, 1376 (1959).2 A. L Benham and F. H. Poettmann, Trans. A.I.M.E. 213, 406 (1958).'W. L. Martin, J. D. Alexander, and J. N Dew, Trans. A.I.M.E. 213, 28(1958).

Remarks on Some Criteria for the n ituCombustion of Crude Oil

H. R. BAILEY AND B. K LARKINThe Ohio Oil Research Center, Littleton, Colorado(Received October 12, 1959; revised manuscriptreceived February 1, 1960)I N a recent paperl by P. Cooperman, the following three criteriafor in situ combustion of crude oil are obtained: (i) A hydrodynamic condition-that the oil saturation So must be greater

than a certain constant times the water saturation (Inequality38, footnote reference 1); (ii) A condition based on thermal andchemical considerations-that the carbon-hydrogen mole ratio ofthe burning hydrocarbon must exceed 3.05 (Inequality 51; footnote reference 1); and (iii) A thermal condition-that the gasvelocity behind the moving combustion front must exceed a certainminimum (Inequalit y 60, footnote reference 1.)As pointed out in footnote reference 1, the in situ combustionprocess consists of a combination of thermal, hydrodynamic , andchemical processes, Any model of these processes must include

many simplifications in order that the resulting equations beamenable to solution.Criteria (ii) and (iii) are not in agreement with experimentalresults and it is the purpose of this letter to show where the modelconsidered in footnote reference 1 is not realistic and to indicatecriteria which can be obtained from a more realistic model.In particular, the steady-state temperature behind the movingcombustion front is of the form

T l = A l e - ~ l ~ + B "and from Eqs. (18) and (22) of footnote reference 1 we have

{31 = (1-q,)PrCrVt+q,V/Po,COI-VgIPgICgl'The notation used in this letter is the same as footnote reference1 and, where needed, the units are lb, ft, hr, btu, and OF. t can beshown2 ,3 that for typical combustion conditions

' V g I P O l ~ 1 4 . 7 w ~ .This result is based on material balance considerations and is ingood agreement with laboratory results. W is the amount offuel on a unit volume of rock (fuel density). Typical values forthe foregoing parameters are (1-q,)p rcr=28, W,0, it is clear that Al =0 since otherwise Tl would beunbounded as - 00 Thus the solution behind the front is ofthe form Tl =B l , a constant. f vertical losses are considered thenthe temperature does fall behind the combustion front; however,the adiabatic case is a good first approximation.

Both criteria (ii) and (iii) of footnote reference 1 are based on thepremise that Al? O. This is explicitly stated in the derivation ofcriterion (ii) and it is implicitly used in deriving criterion (iii) byassuming that the constant Bl is determined by the boundarytemperature at - 00 Since Al =0, the constant Bl is determined by the heat flux supplied at the source. This problem is considered by Jakob4 for the case of heat flow by conduction from amoving source.

The conch sion that Bl is determined by a boundary conditionresults in a formula, crite ria (iii) (Ine qual ity 60, footnote reference 1), for minimum gas velocity which becomes infinite forthe case of zero-boundary conditions and this result does not seemreasonable.Criterion (ii)-that the carbon-hydrogen mole ratio n/mmust exceed 3.05-is violated by all published experimental resultswhich we have seen. Some known results6- 7 are given below inTable I.

TABLE1. Experimental values for fuel composition.

Type of experimentLaboratoryFieldLaboratory field

n/m1.4--2.01.20.69-1.1

Reference number567

Transient solutions including vertiral losses have beenobtained 8 ,9 for a conduction model of heat flow. A model includingconvection effects has also been considered2 and the steady-stateadiabatic (no vertical losses) temperature is given byT 1; /Tm -T.=vj/v/- J, ~ OT T; /Tm-T,=v//v/- J exp[ - ( v j - ( J ) ~ a - l J , ~ > O

where(J=VgIPglCgI/PmCm, a=k/Pmcm,

PmCm = PrCr 1-q,) +PalCalq T, = ambient temperature, T m = .::\.HW/PmC tJ.H =heat of combustion of the fuel in btu/lb and W-thefuel density in lb/eu ft. The assumption that W is a constant ina particular in situ combustion process is bask in our model. W isthe fuel dens ity of a coke that is deposited ahead of the combustionfront, and it has been shown6 in tube-run experiments that W ispractically a constant for any given experiment.

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1124 L E T T E R S TO T H E E I T O RA criterion for the Illllllmum air injection rate required tosustain combustion is given in footnote 2 and 9. These resultsare based on a transient solution of a radial heat flow model,assuming that a minimum ignition temperature for the fuel isknown. Copies of various reports and papers describing thiswork can be obtained by writing the authors.1 P. Cooperman, J. App . Phys. 30, 1376 (1959).2 H. R. Bailey and B. K. Larkin IIConduction-convection. n n e r ~ r o u ~

combustion." Presented to an A.I.Ch.E.-S.P.E. SymposIUm on n SttuCombustion, San Francisco, December, 1959. A. L. Benham and F. H. Poetmann, Trans. AIME 213, 46 (1958). M. Jacob, Heat Transfer (John Wiley Sons, Inc., New York, 1949),Vo ' 1. W. L. Martin, J. D. Alexander, and J. N. Dew, Trans. AIME 213, 28(1958). C. F. Gates and H. J. Ramey, J. Petro . Techno . 10,236-244 (1958).7 J. T. Moss, P. D. White, and J. S. McNiel, J. Petro ' Techno . 11,55-64 (1959).8 H. J. Ramey, Trans. AIME 216 (1959); AIME paper 1133-G (1958). H. R. Bailey and B. K. Larkin, Trans. AIME 216 (1959); AIMEpaper 1134-G (1958).

Reply t the Letters of Szasz andBailey and LarkinPHILIP COOPERMANUniversity of Pittsburgh Pittsburgh Pennsylvania

(Received January 12, 1960; revised manuscriptreceived March 7, 1960)

BECAUSE of a lack of reliable evidence on the nature ofmany of the processes of in situ combustion, theoreticaldevelopments must be limited to qualitative rather than quantitative results. The two-zone version of my theory had only thisrestricted goal, as was clearly indicated at the beginning and endof my paper. t would, therefore, be no surprise to learn that someof the criteria (e.g., carbon-hydrogen mole ratio for combusion)had to be modified. However, the po int of the paper was not thatthe G/H ratio had to exceed 3.05, but that it had to exceed someminimum value. Similar statements could be made for the othercriteria.There is no point, however, in changing or discarding thesecriteria unless a sufficient reason is given. In my opinion, no suchreason has been presented in the above letters. For example,Szasz's first criticism of the theory is that the criterion specifyinga minimum oil saturation for nonzero oil mobility is also satisfiedfor saturations for which the oil mobility vanishes. Subsequently,he remarks that if oil is to be produced from the reservoir, themobility must be different from zero, and that this requirementwould forestall his criticism. Since the produCtion of oil is thepoint of in situ combustion, Szasz has answered himself.Secondly, Szasz claims that the experiments of Martin et al.as interpreted by Benham and Poettmann, indicate that the G/Hratio can be smaller than 3.05. This would be no surprise even ifthe data from these experiments could be accepted, but when theexperimental conditions are considered, it is clear that the data

must be viewed with great suspicion. The apparatus used consistedof materials of extremely low thermal conductivities (sand, oil)encased in a tube of high-conductivity material (steel). Elementary calculations show that, under these circumstances, the largerpart of the heat flux bypasses the sand-oil mixture and travelsthrough the steel tube. Because of this, the temperature profileand thermal history of the oil differs from what it would otherwisebe, and the deviations are in such a direction as to make t appearthat successful combustion can be attained at a lower G/Hratio. t should be emphasized that the magnitu.de of the deviations from ideal is not reasonably small; under ideal conditions,none of the heat would travel through the tube, but in practice,60-80% of the total does.

The third question raised by Szasz is based on a misinterpretation of Eq. 4) of his letter. Szasz understands this equation asthe definition of a heat flux density H which is the difference inthe convected upstream and downstream heat flux densities.

However, this is not the case. is defined in my paper as theheat flux density resu.lting from the combustion itself. By virtueof the first law of thermodynamics, is the difference (or vectorsum) of the total flux densities conveyed by conduction andconvection. At the ends of an infinitely long tube, the temperaturegradient vanishes, and hence, there is no conducted heat there.Thus the heat of combustion must be equal to the convectedheat at the tube ends. Tbis is the significance of Eq. (4), and inobjecting to it, Szasz is opposing the first law. His numericalexample stems from the same misconception in that is givenas the heat of combustion, and cannot be calculated by Eq. (4).What is to be calculated is the requisite air flux and the contradiction means that Szasz has not used correct values in the right-handside of Eq. (4). Since his last point also is connected with hismisinterpretation, there is no need to discuss it separately.

The remarks of Bailey and Larkin are mostly concerned withthe discrepancy between the theoretical criteria for combustionand experimental data obtained in tube experiments. In particular,they question the validity of the criterion for the C/H ratio, andcite field and labora tory data in support of their argument. It hasalready been shown that laboratory data are insufficient for thispurpose; field data are even more unsatisfactory because of themany disturbing factors (e.g., inhomogeneities and gravitysegregation of fluids), and because of poor instrumentation causedby limited access to t he reservoir. Hence, these data do not forceany modification of the crite ria in question.These writers also make use of the equation

P a v a I ~ 1 4 . WVIto show that the quantity {3, must be positive, whereas the G/Hcriterion depends on it's being negative. However, W which isthe weight of coke per unit volume of rock has been determinedby steel tube experiments. Since the formation of coke is obviouslydependent'on the thermal history of oil, the values of W used byBailey and Larkin have not been established, and their argumentconcerning the other constants of the theory is left resting on aninfirm foundation.

The temperature equations advanced by Bailey and Larkinoffer a clue to the reason for their rejection of the G/H criterion.Their equation for the temperature upstream from the combustionfront states that it is constant. This is impossible unless there is asource of heat at the upstream end. In tube experiments, there isusually a heater placed at this end for the purpose of initiatingthe combustion, but I have seen no paper in which it has beenspecifically sta ted that these end heaters are turned off after theinitial period. The temperature equation for the region ~ ~given by Bailey and Larkin is consistent with the experimentalcondition in which end heaters are permitted to operate afterignition. Under these circumstances, the combustion is notself-sustaining and, as shown in my paper [under Eq. (43)J, theG/H criterion need not be obeyed. From a practical viewpoint,in situ combustion may become commercially practicable only ifa supplemental source of heat is used since most crude oils do nothave a sufficiently high C/H ratio.

The downstream temperature of Bailey and Larkin is identicalwith the one appearing in the original paper for the upstreamtemperature. t is clearly invalid if {J