Abstract
Describing matrix–fracture interaction is one of the most important factors for modeling natural fractured reservoirs. A common approach for simulation of naturally fractured reservoirs is dual-porosity modeling where the degree of communication between the low-permeability medium (matrix) and high-permeability medium (fracture) is usually determined by a transfer function. Most of the proposed matrix–fracture functions depend on the geometry of the matrix and fractures that are lumped to a factor called shape factor. Unfortunately, there is no unique solution for calculating the shape factor even for symmetric cases. Conducting fine-scale modeling is a tool for calculating the shape factor and validating the current solutions in the literature. In this study, the shape factor is calculated based on the numerical simulation of fine-grid simulations for single-phase flow using finite element method. To the best of the author’s knowledge, this is the first study to calculate the shape factors for multidimensional irregular bodies in a systematic approach. Several models were used, and shape factors were calculated for both transient and pseudo-steady-state (PSS) cases, although in some cases they were not clarified and assumptions were not clear. The boundary condition dependency of the shape factor was also investigated, and the obtained results were compared with the results of other studies. Results show that some of the most popular formulas cannot capture the exact physics of matrix–fracture interaction. The obtained results also show that both PSS and transient approaches for describing matrix–fracture transfer lead to constant shape factors that are not unique and depend on the fracture pressure (boundary condition) and how it changes with time.
Highlights
The most relevant feature in a dual-porosity model is the flow between the matrix and the fracture. It is described using a transfer term. This transfer term is influenced by the shape of the matrix block, flow regime [e.g., pseudo-steady state (PSS) or transient], depletion scheme of fracture pressure and physical recovery mechanism
As most of the studies in the literature are based on single-phase flow, this study focuses on this type of flow to compare the observed trend with other studies in terms of shape factor calculation
For modeling naturally fractured reservoirs, an accurate value of the shape factor is required for both the transient and PSS behavior and the geometry of the matrix–fracture system
Summary
The most relevant feature in a dual-porosity model is the flow between the matrix and the fracture. Saboorian-Jooybari et al (2012) developed a new time-dependent matrix–fracture shape factor to diagnose different states of the imbibition process They obtained an analytical solution for fluid saturation distribution within a matrix block by solving capillary-diffusion equation under different boundary conditions. They used the single-porosity fine-grid simulations and the previous experimental data presented by other authors to verify their solutions and concluded that the shape factor is completely phase sensitive that is the important parameter in diagnosing different states of imbibition process. A time-dependent matrix–fracture shape factor formulation is analytically derived for two-phase flow in a three-dimensional matrix block in the imbibition process which considers both capillary and gravity forces on matrix–fracture coupling They verified their results by a fine-grid simulation model (Saboorian-Jooybari et al 2015).
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