A Petrov-Galerkin Dual-Porosity Framework for Thermal Analysis of Fractured Porous Media

Thermal analysis of fractured porous media is of interest in environmental and reservoir engineering. The dual-porosity method is a common and cost-efficient approach for modeling fractured domain. In the case of thermal analysis, this method encounters two challenges; the high dependence on the matrix to fracture transfer parameter, “shape factor,” and numerical oscillations produced in the conventional Galerkin finite element formulation for convection dominant problems. To overcome these issues a Petrov-Galerkin dual porosity (PGDP) algorithm is presented for the analysis of 2D transient heat flow in fractured porous media. In the computational algorithm, an appropriate unit cell is selected from the primary domain and the corresponding thermal shape factor is evaluated with a time-varying function. Unlike conventional constant shape factor models, this shape factor accounts for not only the geometry of the blocks, but also the thermal properties of the domain and existing boundary conditions. Several case studies are simulated to investigate the validity and sensitivity of the time-dependent thermal shape factor to different parameters for square and non-square blocks. Moreover, the Petrov-Galerkin formulation is applied to effectively achieve the accurate spatial results for highly convective heat flows. Numerical simulations are performed to study the efficiency and accuracy of the proposed PGDP algorithm for different range of convection and conduction regimes. This study illustrates that the PGDP algorithm efficiently enhances the accuracy of the simulation in modeling of fractured domains, particularly in transient stages. Moreover, the capability of the proposed computational algorithm is demonstrated in modeling square and non-square matrix formations.