This paper presents a space-time adaptive framework for solving porous media flow problems, with specific application to reservoir simulation. A fully unstructured mesh discretization of space and time is used instead of a conventional time-marching approach. A space-time discontinuous Galerkin finite element method is employed to achieve a high-order discretization on the anisotropic, unstructured meshes. Anisotropic mesh adaptation is performed to reduce the error of a specified output of interest, by using a posteriori error estimates from the dual weighted residual method to drive a metric-based mesh optimization algorithm. The spacetime adaptive method is tested on a one-dimensional two-phase flow problem, and is found to be more efficient in terms of computational cost (degrees-of-freedom and total runtime) required to achieve a specified output error level, when compared to a conventional firstorder time-marching finite volume method and the spacetime discontinuous Galerkin method on structured meshes. Keywords unstructured space-time methods • anisotropic mesh adaptation • discontinuous Galerkin • high-order • two-phase flow This research was supported through a Research Agreement with Saudi Aramco, a Founding Member of the MIT Energy Initiative (http://mitei.mit.edu/), with technical monitors Dr. Ali Dogru and Dr. Nicholas Burgess.
Summary In this paper, we present a new well model for reservoir simulation. The proposed well model relates the volumetric flow rate and the bottomhole pressure (BHP) of the well to the reservoir pressure through a spatially distributed source term that is independent of the numerical method and the discrete mesh used to solve the flow problem. This is in contrast to the widely used Peaceman–type well models, which are inherently tied to a particular numerical discretization by the definition of an equivalent well radius. The proposed distributed well model does not require the calculation of an equivalent well radius. Hence, it can be readily applied to finite–difference, finite–volume (FV), or finite–element discretizations on arbitrarily unstructured meshes, which also makes it an attractive option for mesh–adaptation schemes. The new well model is demonstrated on a steady-state single-phase flow problem and an unsteady two-phase flow problem, using a conventional FV method and a high–order discontinuous Galerkin (DG) method. The distributed well model produces error–convergence behaviors that are very similar to the Peaceman well model on uniform structured meshes, but its applicability to high–order discretizations and mesh–adaptation schemes allows for higher convergence rates and more cost-efficient solutions, especially on adapted unstructured meshes.
This paper analyzes the adjoint equations and boundary conditions for porous media flow models, specifically the Buckley-Leverett equation, and the compressible two-phase flow equations in mass conservation form. An adjoint analysis of a general scalar hyperbolic conservation law whose primal solutions include a shock jump is initially presented, and the results are later specialized to the Buckley-Leverett equation. The non-convexity of the Buckley-Leverett flux function results in adjoint characteristics that are parallel to the shock front upstream of the shock, and emerge from the shock front downstream of the shock. Thus, in contrast to the behavior of Burgers' equation where the adjoint is continuous at a shock, the Buckley-Leverett adjoint, in general, contains a discontinuous jump across the shock. Discrete adjoint solutions from space-time discontinuous Galerkin finite element approximations of the Buckley-Leverett equation are shown to be consistent with the derived closed-form analytical solutions. Furthermore, a general result relating the adjoint equations for different (though equivalent) primal equations is used to relate the compressible two-phase flow adjoints to the Buckley-Leverett adjoint. Adjoint solu
is demonstrated on a two-phase flow problem with heterogeneous rock permeabilities, where the high-order discretizations significantly outperform a conventional first-order approach in terms of computational cost required to achieve a given level of error in an output of interest.Keywords two-phase flow • discontinuous Galerkin • linear stability • upwinding • artificial viscosity • high-order
This paper introduces two new approaches for modeling reservoirs with tilted fluid contacts. We first introduce a method based on local capillary pressure adjustments, which uses adjustments of the capillary pressure near the oil-water contact to ensure that the contact surface does not move during production. The second approach uses hydrodynamic aquifer flow to support the oil-water tilt. A non-linear inverse problem is solved to determine the parameters that control the aquifer flow. Both approaches are implemented in a parallel reservoir simulator and applied to a synthetic reservoir case.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.