7 research outputs found
A phase-field model for hydraulic fracture nucleation and propagation in porous media
Many geo-engineering applications, e.g., enhanced geothermal systems, rely on
hydraulic fracturing to enhance the permeability of natural formations and
allow for sufficient fluid circulation. Over the past few decades, the
phase-field method has grown in popularity as a valid approach to modeling
hydraulic fracturing because of the ease of handling complex fracture
propagation geometries. However, existing phase-field methods cannot
appropriately capture nucleation of hydraulic fractures because their
formulations are solely energy-based and do not explicitly take into account
the strength of the material. Thus, in this work, we propose a novel
phase-field formulation for hydraulic fracturing with the main goal of modeling
fracture nucleation in porous media, e.g., rocks. Built on the variational
formulation of previous phase-field methods, the proposed model incorporates
the material strength envelope for hydraulic fracture nucleation through two
important steps: (i) an external driving force term, included in the damage
evolution equation, that accounts for the material strength; (ii) a properly
designed damage function that defines the fluid pressure contribution on the
crack driving force. The comparison of numerical results for two-dimensional
(2D) test cases with existing analytical solutions demonstrates that the
proposed phase-field model can accurately model both nucleation and propagation
of hydraulic fractures. Additionally, we present the simulation of hydraulic
fracturing in a three-dimensional (3D) domain with various stress conditions to
demonstrate the applicability of the method to realistic scenarios
Adaptive multilevel space-time-stepping scheme for transport in heterogeneous porous media (ADM-LTS)
We present ADM-LTS, an adaptive multilevel space-time-stepping scheme for transport in heterogeneous porous media. At each time step, firstly, the flow (pressure) solution is obtained. Then, the transport equation is solved using the ADM-LTS method, which consists of two stages. In the first stage, an initial solution is obtained by imposing the coarsest space-time grid. This initial solution is then improved, in the second stage, by imposing a space-time adaptive grid on the cells where the solution does not satisfy the desired quality. The quality control is based on error estimators with user-defined threshold values. The time-integration procedure, in which the coarsest-scale solution provides local flux boundary conditions for sub-domains with local time refinement, is strictly mass conservative. In addition, the method employs space-time fine grid cells only at the moving saturation fronts. In order to ensure local mass conservation at all levels, finite-volume restriction operators and unity prolongation operators are developed. Several numerical experiments have been performed to analyze the efficiency and accuracy of the proposed ADM-LTS method for both homogeneous and heterogeneous permeability fields on two and three dimensional domains. The results show that the method provides accurate solutions, at the same time it maintains the computational efficiency. The ADM-LTS implementation is publicly available at https://gitlab.com/darsim2simulator
Algebraic dynamic multilevel (ADM) method for fully implicit simulations of multiphase flow in porous media
Incomplete mixing in porous media: Todd-Longstaff upscaling approach versus a dynamic local grid refinement method
Field-scale simulation of flow in porous media in presence of incomplete mixing demands for high-resolution computational grids, much beyond the scope of state-of-the-art simulators. Hence, the upscaling-based Todd and Longstaff (TL) approach is typically used, where coarse grid cells are employed with effective mixing fluid properties and parameters found by matching results obtained with fully resolved reference simulations. Dynamic local grid refinement (DLGR) techniques, on the other hand, only employ fine-scale grid resolution where the fully mixed assumption is not valid. The rest of the domain is then solved at coarser resolutions, where the fully mixed assumption is valid. Here, we assess the accuracy and the robustness of DLGR- and TL-based simulations of miscible displacements in homogeneous and heterogeneous porous media. Due to the intrinsic uncertainty within the unstable displacement nature of the studied incomplete mixing processes, the performance of the methods is also investigated based on a range of acceptable solutions rather than relying only on a single reference one. Systematic numerical results illustrate that the DLGR method is much more robust and accurate than the upscaling-based TL approach, and employs only a small fraction of fine-scale reference grids. Especially, the TL upscaling results (though history matched with computationally expensive fine-scale results) are very sensitive to the change of the simulation parameters. Based on this study, we propose a dynamic multilevel simulation strategy for efficient and reliable large-scale simulation of the complex incomplete mixing processes.Petroleum Engineerin