Reaction Kinetics of In-Situ Combustion: Part 2--Modeling

Abstract

Abstract A model is proposed to analyze and differentiate between crude oil/oxygen reactions at different temperatures. The results of this analysis along with correlations of apparent hydrogen/carbon (H/C) ratio and molar carbon dioxide/carbon monoxide (CO2/CO) ratio indicated three major reactions at different temperatures. Low-temperature oxidation (LTO) appears to occur between the gas and liquid phases. Middle-temperature fuel deposition reactions appear to be homogeneous. The latter was found to be the rate-determining step in clean sands. Natural cores from the reservoirs were found to have different kinetic behavior than the clean sand matrices for these reasons:metallic additives lower the activation energy of the combustion reaction and hence shift the rate-determining steps, andclay and finer sands adsorb more fuel. The proposed kinetic model was found to be applicable to the five oils tested and hence may be generalized for application to any oil. Introduction Several experiments were conducted to study the oxidation reactions of crude oil in porous media. The results of these tests were reported in Part 1 of this study (see Page 399). A kinetic model is proposed here that is useful in analyzing and differentiating between the oxidation reactions occurring in in-situ combustion. Modeling of the Reactions Appendix A presents development of a model based on Weijdema's kinetic equation. The temperature can be increased linearly with time, and, by proper graphing of the variables, a semilog straight line should result. The variable temperature runs were made to test this model. Fig. 1 shows the gases produced and the oxygen consumed as the sand mix is heated uniformly in Run 110. From the data in this graph, the relative reaction rate, was calculated and is graphed in Fig. 2. The reaction order, n, was assumed to be unity. Later on, n was obtained through the curve fit optimization. Note that the high-temperature data fall on a straight line as predicted by Weijdema's model, but at lower temperatures (increasing values of 1/T) a departure from the straight line is observed. It is clear from these data that a single-reaction model does not adequately describe the reaction kinetics observed. A straight line was drawn through the high-temperature data. From the slope of that line an activation energy, E = 135 kJ/mol, is obtained (Fig. 3a, Curve 1). It was assumed that this reaction also occurs at lower temperatures according to an extrapolation of the high-temperature data. The method used is described in Appendix B. Fig. 4a shows the original delta CO2 data for Run 110 (similar to Fig. 1). If Curve I is subtracted from this curve, Curve II (Fig, 4a) is obtained, which describes the oxidation behavior at the medium temperature range. Following the same procedure, the produced carbon oxides in the medium temperature range (Curve III, Fig. 4a) can be obtained by subtracting Curve I from the total produced carbon oxides. From Curve II of Fig. 4a, a calculation of the relative reaction rate, as a function of 1/T leads to the Curve II in Fig. 3b (open triangles). The data are not linear. However, a computation of an equivalent term for the carbon oxides formed, where, from Curve III, Fig. 4b, shows a definite straight line (Curve III, Fig. 3b). An activation energy of E = 84 kJ/g mol is calculated from the slope of this line. In this figure, although the data scatter considerably, it appears reasonable to assume that the oxygen consumption curve in the medium temperature range follows the same slope as the carbon oxides curve. Using this assumption, the oxygen consumption can be calculated and subtracted from Curve II of Fig. 4a and the remainder is represented in Curve V (Fig. 4c). When the data from Curve V, Fig. 4c are evaluated by using the Weijdema integral, and the result is graphed on Fig. 3c, a straight line (Curve V) is formed, which describes the LTO reaction. The activation energy calculated from the slope of this line is E = 93 kJ/g mol. By using the computer interactively, this same analysis was applied to other experiments. The results always fit straight lines. However, for different crude oils, the order of the reaction with respect to fuel concentration, n, was different. SPEJ P. 408^