Modeling Multicomponent Diffusion and Convection in Porous Media
- Kassem Ghorayeb (Reservoir Engineering Research Inst.) | Abbas Firoozabadi (Reservoir Engineering Research Inst.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2000
- Document Type
- Journal Paper
- 158 - 171
- 2000. Society of Petroleum Engineers
- 5.8.8 Gas-condensate reservoirs, 5.2.2 Fluid Modeling, Equations of State, 5.3.2 Multiphase Flow, 4.3.3 Aspaltenes, 5.2 Reservoir Fluid Dynamics, 5.2.1 Phase Behavior and PVT Measurements, 4.1.5 Processing Equipment, 5.5 Reservoir Simulation, 4.1.2 Separation and Treating
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Numerical investigations of diffusion and convection in multicomponenthydrocarbon mixtures in two-dimensional (2D) cross-sectional ( x,z)porous media are performed using the finite-volume method. Spatialdiscretization is performed by a second-order centered scheme. It is shown thatmethane, unlike in binary hydrocarbons where it often segregates towards thebottom-hot side of the porous media, may be at higher concentration at thecold-top side in ternary mixtures and in multicomponent reservoir fluids. Thisbehavior, which is consistent with oilfield data, is due to competing diffusionmechanisms which have not been properly accounted for in the past. It is alsodemonstrated that convection may significantly affect the compositionalvariation in some hydrocarbon reservoirs. Depending on fluid mixtures, a weakconvection may drastically change compositional variation.
Field observations show a wide range of compositional variation; there isgenerally vertical compositional variation of the components in somereservoirs.1 In other reservoirs, a pronounced horizontalcompositional variation is seen.2 In yet others, there is verylittle compositional variation with depth.3 One may even observe adecrease of heavy components such as C 7+ with depth.4 Itis believed that multicomponent diffusion and convection affect thedistribution of various components in hydrocarbon reservoirs.5,6 Ina multicomponent fluid, the total molar flux of a given component consists oftwo parts: (1) the convective flux from the velocity of the bulk fluid, and (2)the diffusive flux as a result of the difference between component velocity andbulk velocity. The molecular diffusive flux of a given component depends notonly on its composition gradient (mutual diffusion), but also on thecomposition gradient of all the other components in the mixture(cross-molecular diffusion). The diffusive flux also depends on pressure andthermal gradients—the so-called thermal diffusion (Soret effect) and pressurediffusion (gravitational segregation), respectively.7 All theseeffects can be modeled using thermodynamics of irreversible processes.
The compositional variation of a component in multicomponent mixtures (morethan two components) in a porous medium may radically differ from that inbinary mixtures. The cross effects (cross-molecular diffusion and thermaldiffusion) are the main processes contributing to this behavior. The primarygoal of this work is to model the compositional variation of multicomponentmixtures in porous media, taking various cross effects into account, and toshow that all the trends in field data (from Refs. 1 through 4) can bepredicted.
Methane in binary mixtures of C1/C2, C1/C3, and C1/ nC4, where experimental dataare available, segregates to the hot side of a differentially heated apparatus.8-10 On the other hand, in hydrocarbon reservoirs, there isgenerally more methane on the cold side (top of the reservoir).4,5These facts imply that one may not use effective thermal diffusion factors tostudy the segregation of methane in mixtures with more than two components in anonisothermal medium. Cross-molecular diffusion has also been shown to beimportant in some ternary and higher mixtures. There is no reference in theliterature to studies of the combined effect of thermal diffusion, moleculardiffusion, and convection in ternary and higher mixtures. Larre etal.11 investigated the stability of a horizontal layer heatedfrom below filled with a water-isopropanol-ethanol mixture. The authorsneglected the cross-molecular diffusion coefficients and assumed that thethermal diffusion factor of a component could be expressed as the sum of thethermal diffusion factors of the binaries consisting of the given component andthe two others, respectively. The model results do not, however, agree with theexperimental data. A similar conclusion is drawn by Krupiczka andRotkegel12 who investigated mass transfer in ternary mixtures ofisopropanol-water-air and isopropanol-water-helium. Considerable discrepanciesbetween experimental data and theoretical predictions were observed whencross-diffusion terms were neglected. 12
There is a vast body of literature on molecular diffusion coefficients inbinary systems.13 A sizable amount of binary data on hydrocarbons isalso available.14-16 However, molecular diffusion data for mixturesconsisting of three or more components, especially for hydrocarbon mixtures atreservoir conditions, are scarce. Reviews of the available data in ternarymixtures with summaries of the measurement methods are presented byCussler13 and Tyrell and Harris.17 Kooijman andTaylor18 summarized the existing models for predicting the moleculardiffusion coefficients in multicomponent mixtures and presented a correlationbased on the Vignes correlation19 for binary systems. Compared withexperimental data for ternary systems, Kooijman and Taylor'scorrelation18 provides better results than do the other availablecorrelations. In this work, we adopt Kooijman and Taylor's correlation tocalculate the molecular diffusion coefficients.
Surprisingly, no experimental data for ternary and higher mixtures exist inthe literature for thermal diffusion factors, a necessary requirement for thecalculation of thermal diffusion in a multicomponent mixture. Firoozabadi etal.20 have recently developed a theoretical model to estimatethermal diffusion factors for ternary and higher mixtures. The new modelaccurately predicts the thermal diffusion factors of binary mixtures.Furthermore, using the thermal diffusion factors obtained by this model, we areable to successfully simulate the compositional variation in athermogravitational porous column containing a ternary mixture reported by ElMaataoui.21 The agreement between compositional data fromexperiments and the model provides indirect validation for multicomponentmixtures.
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