7 research outputs found
A space-time adaptive method for flows in oil reservoirs
No full textThesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2015.Cataloged from PDF version of thesis.Includes bibliographical references (pages 133-137).This work presents a space-time adaptive framework for simulating multi-phase flows through porous media, with specific applications to flows in oil reservoirs. A fully unstructured discretization of space and time is used instead of a conventional time-marching approach. For d-dimensional spatial problems, this requires the generation of (d+1)-dimensional meshes, where time is treated as an additional spatial dimension. Anisotropic mesh adaptation is performed based on a posteriori error estimation to reduce the error of a specified output of interest. This work makes use of the DWR method for error estimation and the MOESS algorithm for metric-based mesh optimization. A discontinuous Galerkin finite element discretization is used to solve on simplex meshes with arbitrary anisotropy, and thereby obtain solutions of higher order accuracy in both space and time. The adaptive framework has been applied to single-phase and two-phase flow test problems in a one-dimensional reservoir, and the results were compared to those obtained from a time-marching finite volume method that is representative of a typical industrial simulator.by Yashod Savithru Jayasinghe.S.M
An adaptive space-time discontinuous Galerkin method for reservoir flows
No full textThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 205-216).Numerical simulation has become a vital tool for predicting engineering quantities of interest in reservoir flows. However, the general lack of autonomy and reliability prevents most numerical methods from being used to their full potential in engineering analysis. This thesis presents work towards the development of an efficient and robust numerical framework for solving reservoir flow problems in a fully-automated manner. In particular, a space-time discontinuous Galerkin (DG) finite element method is used to achieve a high-order discretization on a fully unstructured space-time mesh, instead of a conventional time-marching approach. 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.An analysis of the adjoint equations, boundary conditions and solutions of the Buckley-Leverett and two-phase flow equations is presented, with the objective of developing a theoretical understanding of the adjoint behaviors of porous media models. The intuition developed from this analysis is useful for understanding mesh adaptation behaviors in more complex flow problems. This work also presents a new bottom-hole pressure well model for reservoir simulation, which relates the volumetric flow rate of the well to the reservoir pressure through a distributed source term that is independent of the discretization. Unlike Peaceman-type models which require the definition of an equivalent well-bore radius dependent on local grid length scales, this distributed well model is directly applicable to general discretizations on unstructured meshes.We show that a standard DG diffusive flux discretization of the two-phase flow equations in mass conservation form results in an unstable semi-discrete system in the advection-dominant limit, and hence propose modifications to linearly stabilize the discretization. Further, an artificial viscosity method is presented for the Buckley-Leverett and two-phase flow equations, as a means of mitigating Gibbs oscillations in high-order discretizations and ensuring convergence to physical solutions. Finally, the proposed adaptive solution framework is demonstrated on compressible two-phase flow problems in homogeneous and heterogeneous reservoirs. Comparisons with conventional time-marching methods show that the adaptive space-time DG method is significantly more efficient at predicting output quantities of interest, in terms of degrees-of-freedom required, execution time and parallel scalability.by Yashod Savithru Jayasinghe.Ph. D.Ph.D. Massachusetts Institute of Technology, Department of Aeronautics and Astronautic
Adjoint analysis of Buckley-Leverett and two-phase flow equations
No full textThis 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 two-phase flow adjoints to the Buckley-Leverett adjoint. Adjoint solutions from space-time discontinuous Galerkin finite element approximations of the two-phase flow equations are observed to obey this relationship. Keywords: Adjoint solutions; Buckley-Leverett; Two-phase flow; Conservation law; Continuous analysis; Shockwave
A space-time adaptive method for reservoir flows: formulation and one-dimensional application
No full textThis 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 space-time 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 first-order time-marching finite volume method and the space-time discontinuous Galerkin method on structured meshes. Keywords:
Unstructured space-time methods, Anisotropic mesh adaptation, Discontinuous Galerkin, High-order, Two-phase flowSaudi Aramc
A space-time adaptive method for reservoir flows: formulation and one-dimensional application
No full text
Upwinding and artificial viscosity for robust discontinuous Galerkin schemes of two-phase flow in mass conservation form
No full textAbstract
High-order discretizations have become increasingly popular across a wide range of applications, including reservoir simulation. However, the lack of stability and robustness of these discretizations for advection-dominant problems prevent them from being widely adopted. This paper presents work towards improving the stability and robustness of the discontinuous Galerkin (DG) finite element scheme, for advection-dominant two-phase flow problems in particular. A linearized analysis of the two-phase flow equations is used to show that a standard DG discretization of the two-phase flow equations in mass conservation form results in a neutrally stable semi-discrete system in the advection-dominant limit. Furthermore, the analysis is also used to propose additional terms to the DG method which linearly stabilize the discretization. These additional terms are derived by comparing the linearized equations in mass conservation form against an upwinded pressure-saturation form of the equations. Next, a partial differential equation-based artificial viscosity method is proposed for the Buckley-Leverett and two-phase flow equations, as a means of mitigating Gibbs oscillations in high-order discretizations and ensuring convergence to physical solutions. The modified DG method with artificial viscosity 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
