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Coarse-Scale Modeling of Multicomponent Diffusive Mass Transfer in Dual-Porosity Models


 Numerical simulation of flow and mass transfer in fractured reservoir is challenging due to the complexity of the fracture networks. To handle the geological complexity, dual-porosity models are often used to approximate such reservoir settings. In dual-porosity models, it is assumed that two domains, a high permeability flowing domain (fracture) and a low permeability stagnant domain (matrix) are in communication and that viscous flow is marginal in the stagnant domain.
 In commercial reservoir simulation tools, transfer rates between the flowing and the stagnant domains are commonly modeled using the Warren and Root approach, where no attempt is made to a solve diffusion equation within each matrix block and a quasi-steady state transfer is assumed between the two domains. Previous research has demonstrated that such a simplification does not correctly represent the mass transfer between the domains. A more accurate approach to modeling transfer rates in such settings is to discretize the matrix blocks. However, this approach reduces the computational efficiency of large scale implicit reservoir simulation, due to the associated significant increase in the number computational cells.
 In this work, we present a semi-analytical approach to model multicomponent molecular diffusion within each matrix block in a coarse-scale simulation model and develop equations for time-dependent transfer functions between the flowing and stagnant domains. The time-dependency of the transfer functions are formulated based on initial and average compositions of the domains. Generalized Fick's law is used to describe the diffusive fluxes to account for dragging effects between components. Analytical and semi-analytical solutions to the multicomponent mass transfer equations are obtained through linearization and eigenvalue decomposition of the diffusion coefficient matrix.
 To demonstrate the accuracy of the proposed semi-analytical approach, various examples are presented. In these examples the results of the suggested approach are compared to the Warren-root model, analytical solutions and high-resolution fine-scale results for different of fluid compositions and geometries. We demonstrate that the proposed approach (coarse-scale modeling with time-dependent transfer functions) accurately represents the analytical solution, at a significantly lower CPU time requirement relative to high-resolution fine-scale models. Furthermore, we compare the proposed approach to experimental observations of mass transfer in a binary (CO2-Brine) system to further validate the precision of the proposed model.
 A novel and consistent matrix-fracture transfer function for coarse-scale models is introduced in this paper using semi-analytical solutions to multicomponent diffusive mass transfer. In the proposed approach, the inaccuracies of the conventional representation of diffusive mass transfer in dual-porosity models are resolved, while eliminating the need for further discretization of the matrix blocks. This allows for accurate, yet efficient simulation of diffusive mass transfer in fractured reservoirs.