Continuous analysis of produced gases from a small packed bed reactor, at both isothermal and linearly increasing temperatures, has shown that combustion of crude oil in porous media follows several consecutive reactions. Molar carbon dioxide/carbon monoxide (CO2/CO) and apparent hydrogen/carbon (H/C) ratios were used to observe the transition between these reactions at different temperature levels. A new kinetic model for oxidation of crude oil in porous media is presented in Part 2 of this paper (Page 408) Introduction The quantity of fuel consumed and the reaction rate within the burning zone have been studied intensively for two reasons. First, the maximum oil recovery is the difference of the original oil in place (OOIP) at the start of the operation and the oil consumed as fuel. Second, one of the most important factors in the economic evaluation of any in-situ combustion project is the cost of air compression. Excessive fuel deposition causes a slow rate of advance of the burning front and large air compression costs. However, if the fuel concentration is too low, the heat of combustion will not be sufficient to raise the temperature of the rock and the contained fluids to a level of self-sustained combustion. This may lead to combustion failure. Thus, it is necessary to understand the reactions occurring at different temperatures as the combustion front moves in the porous medium. The most crucial and yet least understood zone of insitu combustion oil recovery is the burning front, where temperature reaches a maximum value. The velocity of the burning front is controlled by the chemical reactions involved. However, since crude oil is a mixture of hydrocarbons, it is necessary to consider a global description of the reaction mechanism. Reaction Mechanism The reaction between fuel and oxygen in a forward combustion process is a heterogeneous flow reaction. Injected oxidant gas must pass through the burning zone to make the burning front move. Within the burning zone, four known transport processes occur:oxygen diffuses from the bulk gas stream to the fuel interface; then, perhaps,the oxygen absorbs and reacts with the fuel;then combustion products desorb; andproducts finally transfer into the bulk gas stream. If any of these steps is inherently much slower than the remaining ones, the overall rate will be controlled by that step. Also, the rate of each series of steps must be equal in the steadystate condition. However, there are no useful correlations for computing absorption and desorption of oxygen in a porous medium. Consequently, consideration of these phenomena becomes extremely difficult for even simple reactions. Theoretical expressions for postulated mechanisms often contain 10 or more arbitrary constants. Because of the large number of arbitrary constants, sever-al expressions developed for widely different mechanisms often will match experimental data equally well. In general, the combustion rate, Rc, of crude oil in a porous medium can be described as dCm m nRc = - ------ = kpo2 Cm,............................(1)dt whereCm = instantaneous concentration of fuel, k = rate constant, Po2 = partial pressure of oxygen, andm, n = reaction orders. The reaction constant, k, is often a function of temperature, T, as expressed by k=w exp(– E/RT).......................................(2) where E is the activation energy, w is the Arrhenius constant, and R is the universal gas constant. For heterogeneous reactions, the constant w is a function of the surface area of the rock. Early studies of crude oil oxidation in a porous medium were mostly qualitative. Differential thermal analysis (DTA) was performed on samples of crude oil, and the resulting thermograms represented the thermal history of each sample as it was heated at a uniform rate (usually 18 degrees F/min [10 degrees C/min]) in a constant air flow (usually 277 mL/min [277 cm3/min]). These thermograms indicated the presence of a number of exothermic reactions. Another method of analysis is thermogravimetric analysis (TGA). Here, a sample of crude oil is weighed continuously as it is heated at a constant rate. The resulting curve of weight change vs. time or temperature indicates the occurrence of at least two reactions at different temperatures. SPEJ P. 399^

This paper investigates mixing in short cores where the mixed zone is large compared with the core length. In such systems the boundary conditions used affect the resulting solutions. Two models, the diffusion equation and the dead-end pare equation, are commonly used to match such displacements. Although the solutions using the diffusion equations differ considerably in form, this paper shows that, if the boundary conditions are interpreted correctly, and proper allowance is made for the difference between in-situ concentration and flowing concentration, the predicted results from these equations are nearly identical. The simplest way to analyze effluent data is to use the volume modifying junction, U, and to plot the data on probability paper. probability paper. The dead-end pore model has been used incorrectly in the past. It must be adjusted at the effluent boundary to account for the difference between in-situ concentration and flowing concentration. In addition, one must check the experimental data to make sure a material balance is preserved. The data and calculations in the paper show the disastrous predictions that can result if these corrections are not made. Introduction When miscible displacement occurs in short cores with a large dispersion coefficient, the effluent mixed zone is large compared with the length of the core. The effluent concentration curve may extend over more than 2 PV. Under this experimental condition it is prudent to worry about be validity of the various equations used to describe mixing in the core. For instance, if the displacement follows the diffusion equation, there are several solutions that differ, depending on the boundary conditions one imposes. The question arises, "How do these boundary conditions differ, and which is the correct solution to use?" A more complex mixing equation, the dead-end pore model, is also available to describe the pore model, is also available to describe the displacement process. This model also will produce differing results when differing boundary conditions are applied. Thus these same questions should arise. The practical significance of this problem is that native-state core displacements must nearly always be run in short cores. If a displacement model is used incorrectly in such a system, it will seriously affect the mixed-zone volume predicted for long distances. In turn, the predicted size of the solvent slug for vertical miscible floods will be wrong. DIFFUSION EQUATIONS When one fluid is miscibly displacing another in a linear porous medium and when the displacement is stable so that viscous fingers do not form, the diffusion equation is often used to describe the displacement. This equation is(1) Generally, for convenience, the concentration limits are shown from 0 to 1. I will use 0 for the concentration of the fluid originally in place, and 1 for the concentration of the displacing fluid. Several solutions to Eq. 1 can be found in the literature. In general, they are various combinations of the error function, differing according to the boundary conditions imposed. Ordinarily, when the porous medium is long compared with the length of porous medium is long compared with the length of the mixed zone, it makes little difference which solution one uses, for they all give virtually identical results. On the other hand, when the mixed zone is about the same length as the porous medium, the boundary conditions can have a noticeable effect on the results, and we need to worry about which of the several solutions to use. The dimensionless grouping that characterizes this worry is the dimensionless dispersion, uL/K, called gamma by Coats and Smith. Smaller gamma's show greater dispersion, and greater boundary condition effects. In this paper we will look at various solutions in some detail for a particular case in which the dimensionless group, gamma, is equal to 14.0. This is a particularly small value of gamma, where the boundary conditions will be quite important. Breakthrough occurs at about 0.4 PV injection. PV injection. SPEJ P. 91

The paper describes experiments on miscible displacement in various porous media and the results of these experiments. Both glass bead packs and natural cores were used. Bead diameters varied from 0.044 to 0.47 mm, and pack lengths varied from 83 to 678 cm. Natural cores used were Berea and Torpedo sandstone.By taking samples as small as 0.5 cc and using refractive index for analysis, the data on breakthrough curves could be plotted to within ± 0.5 per cent. To plot the data correctly on error function paper, a parameter (Vp -V)/y'V was used which allowed for the predicted growth of the front as it moved past the observer.The change in the amount of mixing (length of mixed zone) was studied by varying velocity, length of travel, bead size, viscosity ratio and pack diameter. When the displaced material was less viscous than the displacing material (favorable viscosity ratio), these changes were adequately predicted by theory. When natural cores were used, rath'er than glass beads, the amount of mixing was greatly increased -also qualitatively predicted by theory.In experiments with favorable viscosity ratios in which the ratio was varied from 0.175 to 0.998, it was found that the rate of mixing was changed by a factor of 5.7. Thus, the rate of mixing is strongly affected by viscosity ratio, even when the theoretical error function relationship for mixing is valid.Experiments using. fluids with viscosity ratios near 1.0 showed that the instability effects of even a slightly unfavorable viscosity ratio (1.002) caused disproportionately m 0 r e elongated breakthrough curves than found with a favorable viscosity ratio (.998). When the viscosity ratio was as high as 5.71 these instability effects were much more pronounced, as evidenced by the shape of the breakthrough curve. The displacements at viscosity ratios above 1.0 no Original manuscript received in Society of Petroleum Engi~ neers Office Nov. 30, 1959. Revised manuscript received Oct.

This study presents analytical solutions to elliptical flow problems that are applicable to infiniteconductivity vertically fractured wells, elliptically shaped reservoirs, and anisotropic reservoirs producing at a constant rate or pressure. Type curves and tables are presented for the dimensionless flow rate and the dimensionless wellbore pressure for various inner boundary conditions ranging from K = 1, which corresponds to a circle, to K = 00, which corresponds to a vertical fracture. For elliptical reservoirs, K is the ratio of the major to minor axes of the inner boundary ellipse; for anisotropic reservoirs, it is the square root of the ratio of maximum to minimum permeabilities.

No abstract