C1-Continuous relative permeability and hybrid upwind discretization of three phase flow in porous media

Lee, S.H.; Efendiev, Yalchin

doi:10.1016/j.advwatres.2016.07.017

Cited by 26 publications

(16 citation statements)

References 18 publications

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“…An interpolation method is usually used to compute k ro from two-phase oil-gas k rog (s o ) and oil-water k row (s o ) data, see for example the works by Stone (1973) and Baker (1988). As discussed in Lee and Efendiev (2016), the method choice can affect the nonlinear convergence of the underlying discretization scheme.…”

Section: Resultsmentioning

confidence: 99%

“…which is the default setting of the commercial simulator Eclipse (Schlumberger 2013). This choice ensures positive values and continuous derivatives provided that k row , k rog fulfill the same criterion (Baker 1988;Lee and Efendiev 2016). We consider simple relative permeabilities given by Corey functions for a pair of wetting and non-wetting fluids,…”

Section: Resultsmentioning

confidence: 99%

“…In addition, detailed geological models with heterogeneous coefficients are usually constructed as input to reservoir simulators. These properties make the development of robust, efficient, and accurate discretization and solution schemes quite challenging (Lee et al 2015;Jiang and Younis 2017).…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear acceleration of sequential fully implicit (SFI) method for coupled flow and transport in porous media

Jiang

2019

Computer Methods in Applied Mechanics and Engineering

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The sequential fully implicit (SFI) method was introduced along with the development of the multiscale finite volume (MSFV) framework, and has received considerable attention in recent years. Each time step for SFI consists of an outer loop to solve the coupled system, in which there is one inner Newton loop to implicitly solve the pressure equation and another loop to implicitly solve the transport equations. Limited research has been conducted that deals with the outer coupling level to investigate the convergence performance. In this paper we extend the basic SFI method with several nonlinear acceleration techniques for improving the outer-loop convergence. Specifically, we consider numerical relaxation, quasi-Newton (QN) and Anderson acceleration (AA) methods. The acceleration techniques are adapted and studied for the first time within the context of SFI for coupled flow and transport in porous media. We reveal that the iterative form of SFI is equivalent to a nonlinear block Gauss-Seidel (BGS) process.The effectiveness of the acceleration techniques is demonstrated using several challenging examples. The results show that the basic SFI method is quite inefficient, suffering from slow convergence or even convergence failure. In order to better understand the behaviors of SFI, we carry out detailed analysis on the coupling mechanisms between the sub-problems. Compared with the basic SFI method, superior convergence performance is achieved by the acceleration techniques, which can resolve the convergence difficulties associated with various types of coupling effects. We show across a wide range of flow conditions that the acceleration techniques can stabilize the iterative process, and largely reduce the outer iteration count.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Nonlinear acceleration of sequential fully implicit (SFI) method for coupled flow and transport in porous media

Jiang

2019

Computer Methods in Applied Mechanics and Engineering

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“…In practice, reservoir simulators often suffer from serious difficulties in obtaining converged numerical solutions for the preselected timestep size. This is because even though FIM is unconditionally stable, the nonlinear Newton-based solver will not be unconditionally convergent (Lee and Efendiev 2016). When convergence failures are encountered, the most commonly used remedy is to restart the nonlinear solver with a smaller timestep size (Younis et al 2010).…”

Section: Introductionmentioning

confidence: 99%

“…Lee et al (2015) proposed a continuously differentiable numerical flux scheme called Hybrid Upwinding (HU) to address the discontinuous behavior due to flow reversal. In HU, the upwinding of the viscous term of the numerical flux is based on the sign of the total velocity, whereas the directionality of the gravitational term is determined by phase densities, such that the heaviest fluid goes down and the lightest fluid goes up (Lee and Efendiev 2016). extended the work of Lee et al (2015) to an arbitrary number of fluid phases.…”

Section: Introductionmentioning

confidence: 99%

Dissipation-based continuation method for multiphase flow in heterogeneous porous media

Jiang

2018

Journal of Computational Physics

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In reservoir simulation, solution of the coupled systems of nonlinear algebraic equations that are associated with fully-implicit (backward Euler) discretization is challenging. Having a robust and efficient nonlinear solver is necessary in order for reservoir simulation to serve as the primary tool for managing the recovery processes of large-scale reservoirs. However, there are several outstanding challenges that are intimately connected to the nature of the problem. Given a set of sources and sinks, the variation in the total velocity can span many orders of magnitude due to the extreme levels of permeability heterogeneity in large-scale subsurface porous formations. Moreover, multiple and complex saturation fronts need to be properly resolved throughout the three-dimensional reservoir model of interest. Add to that the fact that the numerical simulations need to predict the field-scale recovery performance over many decades, and the challenge of developing robust and efficient nonlinear solvers across a very wide parameter space becomes quite clear. Here, we develop a continuation method based on the use of a dissipation operator to simulate nonlinear two-phase flow and transport in heterogeneous porous media in the presence of viscous, gravitational, and capillary forces. The homotopy is constructed by adding numerical dissipation to the discrete conservation equations. A continuation parameter is introduced to control the amount of dissipation. Numerical evidence of multi-dimensional models and detailed analysis of single-cell problems are used to explain how the dissipation operator improves the nonlinear convergence of the coupled system of equations. An adaptive strategy to determine the optimum dissipation coefficient is proposed. The adaptive dissipation is computed locally for each cell interface, and is applicable to coupled flow and transport. We demonstrate the efficacy of the new nonlinear solver using several examples, including 1D scalar transport and 2D heterogeneous problems with fully-coupled flow and transport. The new solver exhibits superior convergence properties compared with the standard Newton solver used in reservoir simulation. We show that the new solver works robustly for a wide range of flow conditions without parameter tuning of the dissipation operator.

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Nonlinear solver for three-phase transport problems based on approximate trust regions

Møyner

2017

Comput Geosci

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C1-Continuous relative permeability and hybrid upwind discretization of three phase flow in porous media

Cited by 26 publications

References 18 publications

Nonlinear acceleration of sequential fully implicit (SFI) method for coupled flow and transport in porous media

Nonlinear acceleration of sequential fully implicit (SFI) method for coupled flow and transport in porous media

Dissipation-based continuation method for multiphase flow in heterogeneous porous media

Nonlinear solver for three-phase transport problems based on approximate trust regions

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