Dual-Porosity Modeling of Multicomponent Diffusion in Tight Fractured Systems

In recent years, modeling studies of carbon dioxide (CO2) injection in tight fractured reservoirs have employed an advective/diffusion model coupled with either a single-porosity model (SPM) or an embedded discrete fracture model (EDFM). A key feature of these gridding approaches is their reliance on a large number of gridblocks to represent fracture segments and capture the transient behavior observed in such reservoirs. Incorporating diffusive fluxes into conventional advective-only reservoir simulators adds significant computational complexity, making these approaches particularly demanding. In this paper, we address the application of the dual-porosity model (DPM) to study diffusive mass transfer in tight fractured reservoirs. The implicit and coarse representation of the fractures in a DPM offers higher computational efficiency compared to the SPM or EDFM. To address the inaccuracies that may result from conventional transfer functions of DPM's, we propose an improved matrix/fracture representation that accounts for both advective and diffusive mass transfer. Both mechanisms follow the functional form of the Warren and Root (1963) model and incorporate a time-dependent correction factor derived from the generalized Vermeulen transfer function (Zhang et al., 2022). However, the representation of molecular diffusion in the DPM includes nc independent correction factors, as opposed to a scalar quantity for advective transport. Moreover, to identify relevant matrix/fracture interaction parameters (σ and V), we show that the values for diffusion are equivalent to those for the viscous flow expression. We first demonstrate, using numerical examples, the validity of the DP compositional model by comparing calculation results with an analytical solution and fine-grid SPM results. These examples serve as a benchmark for the new model in diffusion-dominated problems involving binary and multicomponent fluid systems. Subsequently, we present our efforts to model CO2 HnP conducted on an Eagle Ford shale core. In all calculations, the DPM approach employs a single-block representation, which outperforms other modeling approaches (SPM and EDFM) that require a larger number of gridblocks. We demonstrate that the proposed DPM, incorporating an advanced transfer function, provides for an accurate and efficient representation of multicomponent diffusive mass transfer in tight fractured systems. Consequently, this approach serves as a practical and reliable platform for modeling EOR in large-scale applications by overcoming the limitations of conventional DPM's and avoiding the need for fine gridding required in SPM or EDFM.