Prediction of Molecular Diffusion At Reservoir Conditions. Part II - Estimating the Effects Of Molecular Diffusion And Convective Mixing In Multicomponent Systems

Abstract

It is shown how multicomponent diffusion theory and the empirical corelation for binary diffusion described previously in Part I of this study may be used for predicting diffusion coefficients in multicomponent systems at reservoir conditions. It is also demonstrated how the effects of convection and diffusion may be combined to calculate concentration profiles for fluid mixtures flowing in a porous media. Theory of Diffusion in Multicomponent Systems The Continuity and Flux Equations The fundamental equation used to express the composition change of each component in a diffusing mixture with respect to time and space is the continuity equation. In an n + 1 component mixture, this equation may be written for each of the independent components as (1, 2, 3). Equation (1) Available In Full Paper. At constant temperature and pressure, in a system in which all components have a constant partial molar volume, the flux equations which express diffusion rates with respect to a coordinate moving at the reference velocity u may written as(4, 5) Equation (2) Available In Full Paper. The reference velocity u may be taken as mass, molar or volume average(2, 5). For an n + 1 component system, equation (2) defines a (n × n) matrix of diffusion coefficients [D] of the type developed by Onsager(2, 10). The n2 elements Dlk of the matrix [D] are termed the multi component diffusion coefficients. The off-diagonal diffusion coefficients Dlk (i ≠k) have been termed the "cross diffusion coefficients" and the diagonal values (Dll) the "main diffusion coefficients"(2). The magnitudes of the cross coefficients, Dlk, are a measure of the coupling or interaction that takes place between the n + 1 diffusing species. It has been suggested(1, 17) that the effects of coupling can e conveniently taken into account, for some calculations, by defining an effective diffusion coefficient Dlm for each component such that Equation (3) Available In Full Paper. Methods of estimating the multicomponent diffusion coefficents Dlk and the effective diffusion coefficients Dlm are considered in subsequent discussions. Concentration Distributions Resulting From Diffusion In Multicomponent Systems If the values of Dlk can be estimated either by measurement or by theory, then equations (1) and (2) can be solved(2, 3). Analytic solutions can be obtained by assuming concentration independence of [D]. An examination of the errors which result from not accounting for concentration dependence has been made previously(1, 7). A thorough discussion of the linearized treatment of equations (1) and (2) used to calculate multicomponent concentration profiles appears elsewhere(2, 3). The solution for a ternary system in one dimension can be written as(3, 3, 8) Equation (4a) Available In Full Paper. Equation (4b) Available In Full Paper. where Equation (4c) Available In Full Paper. and where Dk are the eigenvalues of the matrix [D]. For the ternary case they are given by(2, 8) Equation (5a) Available In Full Paper.

Numerical Modeling of Diffusion in Fractured Media for Gas-Injection and -Recycling Schemes

“…Most of the experimental data on diffusion coefficients are limited to binary or ternary mixtures (Cullinan and Toor 1965;Sigmund 1976aSigmund , 1976bRenner 1988;Leahy-Dios et al 2005). There are no measured diffusion coefficients for reservoir fluids.…”

“…In the past, attempts to measure multicomponent diffusion coefficients have been limited. Most correlations for multicomponent diffusion coefficients are mainly based on data for binary diffusion coefficients (Mathur and Thodos 1965;Dawson et al 1970;Takahashi 1975;Sigmund 1976aSigmund , 1976bRiazi and Whitson 1993). These correlations may not apply to reservoir fluids and may not be consistent with the thermodynamic stability considerations (Ghorayeb and Firoozabadi 2000a).…”

CO2 injection for enhanced oil recovery in Bakken tight oil reservoirs

“…CO 2 and trapped oil will become completely miscible and 107 CO 2 will extract light and intermediate hydrocarbons from the oil 108 phase, and the interfacial tension will become zero and capillary 109 pressure disappears, resulting in the oil phase and CO 2 phase, 110 which contains some extracted hydrocarbon components, flow 111 together more easily through the porous media [16][17][18]. 112 Fai-Yengo et al [9] presented that the effect of capillary pressure 190 where / is matrix porosity, q s is matrix density, q ' is density of which is defined as 199 199 200 where k is the formation permeability tensor, k r' is the relative per-201 meability of phase, ', p ' is pressure of phase ' and l ' is viscosity of Sigmund correlation [31] is often used to calculate the oil and gas 211 diffusion coefficients (unit is cm 2 /s) since it is valid for both oil 212 and gas phases [32]. The binary diffusion coefficient between com-213 ponent i and j is calculated by [31,32] 214…”

“…112 Fai-Yengo et al [9] presented that the effect of capillary pressure 190 where / is matrix porosity, q s is matrix density, q ' is density of which is defined as 199 199 200 where k is the formation permeability tensor, k r' is the relative per-201 meability of phase, ', p ' is pressure of phase ' and l ' is viscosity of Sigmund correlation [31] is often used to calculate the oil and gas 211 diffusion coefficients (unit is cm 2 /s) since it is valid for both oil 212 and gas phases [32]. The binary diffusion coefficient between com-213 ponent i and j is calculated by [31,32] 214…”

The Role of Diffusion and Dispersion in Miscible CO2Injection in an Iranian Naturally Fractured Reservoir

“…Simulating a miscible CO2 injection in an oil field reservoir with different dispersivities was done to distinguish those zones (Sigmund, 1976b).…”