Consistent upwinding for sequential fully implicit multiscale compositional simulation

Moncorgé, Arthur; Møyner, Olav; Jenny, Patrick

doi:10.1007/s10596-019-09835-6

Cited by 15 publications

(19 citation statements)

References 29 publications

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“…Fully implicit discretizations are the most common formulation used in commercial simulators and allow for a concise and clear presentation. Note that HU schemes have shown significant efficiency benefits in sequential implicit schemes as well [19]. Future work will investigate the benefits of the presented scheme for sequential formulations.…”

Section: Numerical Discretization Of Mass Balance Equationsmentioning

confidence: 92%

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Smooth Implicit Hybrid Upwinding for Compositional Multiphase Flow in Porous Media

Bosma,

Hamon,

Mallison

et al. 2021

Preprint

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In subsurface multiphase flow simulations, poor nonlinear solver performance is a significant runtime sink. The system of fully implicit mass balance equations is highly nonlinear and often difficult to solve for the nonlinear solver, generally Newton(-Raphson). Although the physical problem is inherently nonlinear, discretization schemes introduce several strong nonlinearities that can cause Newton iterations to diverge or converge very slowly. This frequently results in time step cuts, leading to wasted iterations and computationally expensive simulations. Much literature has looked into how to improve the nonlinear solver through enhancements or safeguarding updates. In this work, we take a different approach; we aim to improve convergence with a smoother finite volume discretization scheme which is more suitable for the Newton solver.Building on recent work, we propose a novel total velocity hybrid upwinding scheme with weighted average flow mobilities (WA-HU TV) that is unconditionally monotone and extends to compositional multiphase simulations. Analyzing the solution space of a one-cell problem, we demonstrate the improved properties of the scheme and explain how it leverages the advantages of both phase potential upwinding and arithmetic averaging. This results in a flow subproblem that is smooth with respect to changes in the sign of phase fluxes, and is well-behaved when phase velocities are large or when co-current viscous forces dominate. Additionally, we propose a WA-HU scheme with a total mass (WA-HU TM) formulation that includes phase densities in the weighted averaging.The proposed WA-HU TV consistently outperforms existing schemes, yielding benefits from 5% to over 50% reduction in nonlinear iterations. The WA-HU TM scheme also shows promising results; in some cases leading to even more efficiency. However, WA-HU TM can occasionally also lead to convergence issues. Overall, based on the current results, we recommend the adoption of the WA-HU TV scheme as it is highly efficient and robust.

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Section: Numerical Discretization Of Mass Balance Equationsmentioning

confidence: 92%

“…and q t is a total mass source term constructed similarly to the total mass flux in (19). Note that as the phase compositions sum up to unity, they are not explicitly present in the flow problem, eq.…”

Section: Total Mass Flux Formulationmentioning

confidence: 99%

Smooth Implicit Hybrid Upwinding for Compositional Multiphase Flow in Porous Media

Bosma,

Hamon,

Mallison

et al. 2021

Preprint

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“…Specifically, when the approximation is based on PPU, convergence difficulties may arise when a small change in the primary variables -pressure and saturation -causes an abrupt change from cocurrent flow to countercurrent flow, and vice versa. This issue, referred to as the "flip-flopping" of the phase fluxes, was recently addressed with Implicit Hybrid Upwinding (IHU) in Lee et al (2015); Efendiev (2016, 2018); ; Hamon et al ( , 2018; Moncorgé et al (2019). The IHU strategy is based on a separate evaluation of the viscous, buoyancy, and capillary parts to achieve a differentiable flux in the highly nonlinear transport problem.…”

Section: Introductionmentioning

confidence: 99%

Fully Implicit multidimensional Hybrid Upwind scheme for coupled flow and transport

Hamon

Mallison

2020

Computer Methods in Applied Mechanics and Engineering

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Robust and accurate fully implicit finite-volume schemes applied to Darcy-scale multiphase flow and transport in porous media are highly desirable. Recently, a smooth approximation of the saturationdependent flux coefficients based on Implicit Hybrid Upwinding (IHU) has been proposed to improve the nonlinear convergence in fully implicit simulations with buoyancy. Here, we design a truly multidimensional extension of this approach that retains the simplicity and robustness of IHU while reducing the sensitivity of the results to the orientation of the computational (Cartesian) grid. This is achieved with the introduction of an adaptive, local coupling between the fluxes that takes the flow pattern into account. We analyze the mathematical properties of the proposed methodology to show that the scheme is monotone in the presence of competing viscous and buoyancy forces and yields saturations remaining between physical bounds. Finally, we demonstrate the efficiency and accuracy of the scheme on challenging two-dimensional two-phase examples with buoyancy, with an emphasis on the reduction of the grid orientation effect.

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“…Domain decomposition is also very appealing as a nonlinear solution strategy in reservoir simulation: The system of nonlinear equations tends to be strongly coupled, highly nonlinear, and unbalanced (i.e., a safe step length for Newton's method is determined by a small subset of the full variable set [3]), so that unless we take very short timesteps, the initial guess is typically far from the solution. A particularly popular nonlinear variable-decomposition approach is sequential splitting of the full problem into a pressure subproblem and a set of transport subproblems [33,34,38,47,50], which also facilitates using efficient multiscale methods for the pressure subproblem [13,27,36].…”

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confidence: 99%

A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow

et al. 2021

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Domain decomposition methods are widely used as preconditioners for Krylov subspace linear solvers. In the simulation of porous media flow there has recently been a growing interest in nonlinear preconditioning methods for Newton’s method. In this work, we perform a numerical study of a spatial additive Schwarz preconditioned exact Newton (ASPEN) method as a nonlinear preconditioner for Newton’s method applied to both fully implicit or sequential implicit schemes for simulating immiscible and compositional multiphase flow. We first review the ASPEN method and discuss how the resulting linearized global equations can be recast so that one can use standard preconditioners developed for the underlying model equations. We observe that the local fully implicit or sequential implicit updates efficiently handle the local nonlinearities, whereas long-range interactions are resolved by the global ASPEN update. The combination of the two updates leads to a very competitive algorithm. We illustrate the behavior of the algorithm for conceptual one and two-dimensional cases, as well as realistic three dimensional models. A complexity analysis demonstrates that Newton’s method with a fully implicit scheme preconditioned by ASPEN is a very robust and scalable alternative to the well-established Newton’s method for fully implicit schemes.

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Consistent upwinding for sequential fully implicit multiscale compositional simulation

Cited by 15 publications

References 29 publications

Smooth Implicit Hybrid Upwinding for Compositional Multiphase Flow in Porous Media

Smooth Implicit Hybrid Upwinding for Compositional Multiphase Flow in Porous Media

Fully Implicit multidimensional Hybrid Upwind scheme for coupled flow and transport

A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow

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