Diffusion coefficients in binary dense fluid systems are measured and used along with data available in the literature to obtain a generalized correlation for predicting binary molecular diffusion coefficients in dense gases over a broad range of conditions. Introduction ATTEMPTS to quantify mixing phenomenal in porous media are often, encountered in design studies of processes(@ related to petroleum recovery. Dispersion, an important part of mixing phenomena, can be related to the distribution in travel times that results when a fluid passes through a porous media"1. On a micro-scopic scale, the two most important mechanisms con-tributing to dispersion are variations in velocity be-tween fluid elements flowing in neighbouring pores or groups of pores (often referred to as convective mixing) and molecular diffusion",', ". Although there is some controversy over the magnitude of convective effects, it has been thought that in vertical gravity-stabilized miscible floods, such as those carried out in the carbonate pinnacle reefs of Alberta, molecular diffusion played an important role in the mixing of the solvent bank with drive gas and oil('-,In other pro-cesses, such@h -as gas, solvent or C02 horizontal 'miscible floods, the effects of molecular diffusion are difficult to quantify, but are thought to be important in the recovery of non-flowing oil by mass transfer", ', "'. The estimation of molecular diffusion coefficients in low-pressure gases using .'the Chapman @@sk ?g Theory"." is adequate for a wide variety oi singie-Phillip M. Sigmund graduated from the University of Waterloo with a B.A.Sc. (c emical engineering) in 1963 and a M.A.Sc. (chemical en-gineering) in 1964. After obtaining his Pb.D. (chemical engineering) from the University of Texas in 1969, he joined the Petroleum Recovery Re-search Institute, where he is cur-rently employed as a senior research engineer.He has been involved in Institute research projects dealing _ with retrograde phenomena in porous media, diffusion and dispersion phenomena, hydrocarbon recovery from car-bonate reservoirs, and the use of CO, and SO, for en-hanc4@d oil recovery. Dr. Sigmund is a member of CIM, CIC, AIME and the Association of Professional Engineers of Alberta. 4a@ component and binary gases ... .... In liquids, the success of theoreticil models has been more limited, perhaps because of ilhe complex nature of molecular interac-tions in the liquid state. Nevertheless, except in the critical region, liquid diffusion coefficients can at present be predicted by empirical correlations, with sufficient accuracy for many engineering pur-poses"@ In the critical or dense fluid state, there are few exp@@rimental studies of diffusion coefficients inbinary mixtures. This has made it difficult t.o assess predictive t(@chniques, which have so far been tested largely on l-,he basis of self-diffusion data and are generally considered unreliable(',").The pres(@nt two-part paper describes Petroleum Re(!overy Institute work that was directed toward de-veloping improved predictive me...

With typical heterogeneous carbonate core samples, large uncertainties of unknown magnitude can occur in the relative permeabilities derived using different methods. This situation can be improved by analyzing the recovery and pressure response to two-phase laboratory displacement tests by a nonlinear least-squares procedure. The suggested technique fits the finite-difference solution of the Buckley-Leverett two-phase flow equations (which include capillary pressure) to the observed recovery and pressure data. The procedure is used to determine relative-permeability curves characterized by two parameters and their standard errors for heterogeneous cores from two Alberta carbonate reservoirs.

SIGMUND, P.M., PETROLEUM RECOVERY RESEARCH INSTITUTE, CALGARY, ALTA., CANADA PETROLEUM RECOVERY RESEARCH INSTITUTE, CALGARY, ALTA., CANADA DRANCHUK, P.M., MEMBER SPE-AIME, U. OF ALBERTA EDMONTON, ALTA., CANADA MORROW, N.R., MEMBER SPE-AIME, PETROLEUM RECOVERY RESEARCH INSTITUTE, CALGARY, ALTA., CANADA PETROLEUM RECOVERY RESEARCH INSTITUTE, CALGARY, ALTA., CANADA PURVIS, R.A., MEMBERS SPE-AIME, PURVIS, R.A., MEMBERS SPE-AIME, ENERGY RESOURCES CONSERVATION BOARD, CALGARY, ALTA., CANADA Abstract The effect of porous media on the phase behavior of hydrocarbon binaries was investigated both experimentally and theoretically. When liquid and vapor coexist in a porous medium, the interlace between them will be curved. Calculations of the effect of curvature on phase behavior show that equilibrium composition and Pressures would not be disturbed significantly except at very high surface curvatures. Such curvatures are unlikely in hydrocarbon reservoirs even where clay-size particles are present because the finest pores will particles are present because the finest pores will be occupied by connate water. Measured dewpoint or bubblepoint pressures were found to be independent of the presence of porous media. Liquid saturations calculated from previous conventional phase behavior studies were compared with saturations calculated from the dimensions of a limited number of capillary structures which could be observed through the sight glass of a Jerguson cell. Saturations calculated from conventional phase-equilibrium data fell between saturations phase-equilibrium data fell between saturations calculated with The assumption that all capillary structures had equal curvature and those calculated with the assumption that they bad equal volumes. Introduction Reservoir engineering frequently involves the use of pressure-volume-temperature (PVT) relationships for hydrocarbon mixtures. Examples arise in reservoirs, and gas-drive miscible displacements, condensation and revaporization in gas condensate reservoirs, and gas-drive miscible displacements. The PVT relationships used in such engineering calculations are usually based on measurements on equilibrium behavior of hydrocarbon mixtures contained in PVT cells. For some time there has been question as to whether phase - behavior calculations made on data measured in such cells would correctly represent the behavior of hydrocarbon mixtures held within the interstices of porous reservoir rocks. The results of several recently reported experimental studies indicate that the presence of a porous medium has a significant influence presence of a porous medium has a significant influence on the equilibrium behavior of hydrocarbon mixtures. Trebin and Zadora contend that the initial condensation pressures (dew points) of gas condensate mixtures in pressures (dew points) of gas condensate mixtures in porous media can be 10 to 15 percent higher than those porous media can be 10 to 15 percent higher than those observed in conventional PVT cells. Tindy and Raynal reported that saturation pressures of crude oil in porous media were several percent higher than those porous media were several percent higher than those measured in conventional test cells. On the other hand, earlier results reported by Weinaug and Cordell indicated that vapor-liquid equilibrium relationships of the system methane-n-butane and methane-n-pentane were not affected by the presence of dry sand. Oxford and Huntington studied the revaporization of n-hexane by nitrogen and found that withdrawal rate and the presence of brine in the porous medium had little effect on the revaporization process. In a study of the effects of wettability change, process. In a study of the effects of wettability change, Smith and Yarborough concluded that the detailed form of the capillary structures of retrograde liquid held in a porous medium had no effect on the revaporization process. porous medium had no effect on the revaporization process. Clark studied the adsorption and desorption of light paraffinic hydrocarbons in clay and partially water-saturated paraffinic hydrocarbons in clay and partially water-saturated sand and sand-clay packs to determine their effect on equilibrium behavior. Compressibility factors for propane at 100 degrees F in the presence of dry sand-clay propane at 100 degrees F in the presence of dry sand-clay packs were lowered by 13 percent. However, in sand-clay packs were lowered by 13 percent. However, in sand-clay mixtures containing water, the compressibilities differed by less than 1 percent from those obtained in the absence of the porous media. Clark also studied effect of a dry sand-clay media on the PVT properties of mixtures of methane and propane. Only small changes were observed, and these were considered to be inconclusive - partly because the fluid was not recirculated through the porous media to ensure homogeneity. In summary, porous media to ensure homogeneity. In summary, evidence for the effect of porous media on equilibrium behavior is somewhat contradictory. SPEJ P. 93

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.

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