Modified sequential fully implicit scheme for compositional flow simulation

Moncorgé, Arthur; Jenny, Patrick

doi:10.1016/j.jcp.2017.02.032

Cited by 32 publications

(20 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…But for compositional systems, flow and transport usually cannot be decoupled, and it is thus necessary to perform several outer iterations to reduce to an acceptable tolerance. Recently, this second class of methods has been abandoned, that is, the first class of methods is preferred [19,23].…”

Section: Compositional Systemmentioning

confidence: 99%

“…For strongly coupled flow and transport, even a tolerance of 0.01 may take many outer iterations, or no convergence may be achieved at all. This strategy is not practical, as it requires too many iterations in order to be competitive with methods like mSFI [20]. The second strategy consists of relaxing the tolerances of |R thermo | ∞ and |R ut | ∞ in order to achieve convergence with less outer iterations.…”

Section: Compositional Systemmentioning

confidence: 99%

“…Moncorgé et al [20] enriched the pressure equation with Fully-Implicit (FI) coupling in regions that experience phase appearance to ensure convergence of the full system to any given tolerance. This approach is efficient as long as the fraction of cells that have both liquid and vapor phases is relatively small.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sequential fully implicit formulation for compositional simulation using natural variables

Moncorgé

Tchelepi

Jenny

2018

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

The Sequential Fully Implicit (SFI) method was proposed (Jenny et al., JCP 2006), in the context of a Multiscale Finite Volume (MSFV) formulation, to simulate coupled immiscible multiphase fluid flow in porous media. Later, Lee et al. (Comp. Geosci. 2008) extended the SFI formulation to the black-oil model, whereby the gas component is allowed to dissolve in the oil phase. Most recently, the SFI approach was extended to fully compositional isothermal displacements by Moncorgé et al., (JCP 2017). SFI schemes solve the fully coupled system in two steps: (1) Construct and solve the pressure equation (flow problem). (2) Solve the coupled species transport equations for the phase saturations and phase compositions. In SFI, each outer iteration involves this two-step sequence. Experience indicates that complex interphase mass transfer behaviors often lead to large numbers of SFI outer iterations compared with the Fully Implicit (FI) method. Here, we demonstrate that the convergence difficulties are directly related to the treatment of the coupling between the flow and transport problems, and we propose a new SFI variant based on a nonlinear overall-volume balance equation. The first step consists of forming and solving a nonlinear pressure equation, which is a weighted sum of all the component mass conservation equations. A Newton-based scheme is used to iterate out all the pressure dependent nonlinearities in both the accumulation and flux terms of the overall-volume balance equation. The resulting pressure field is used to compute the Darcy phase velocities and the total-velocity. The second step of the new SFI scheme entails introducing the overall-mass density as a degree-of- freedom, and solving the full set of component conservation equations cast in the natural-variables form (i.e., saturations and phase compositions). During the second step, the pressure and the total-velocity fields are fixed. The SFI scheme with a nonlinear pressure extends the SFI approach of Jenny et al. (JCP 2006) to multi-component compositional processes with interphase mass transfer. The proposed compositional SFI approach employs an overall balance for the pressure equation; however, unlike existing volume-balance Sequential Implicit (SI) schemes (Acs et al.and Doster et al., CRC 2014), which use overall compositions, this SFI formulation is well suited for the natural variables (saturations and phase compositions). We analyze the 'splitting errors' associated with the compositional SFI scheme, and we show how to control these errors in order to converge to the same solution as the Fully Implicit (FI) method. We then demonstrate that the compositional SFI has convergence properties that are very comparable to those of the FI approach. This robust sequential-implicit solution scheme allows for designing numerical methods and linear solvers that are optimized for the sub-problems of flow and transport. The SFI scheme with a nonlinear pressure formulation is well suited for multiscale formulations, and it promises to replace the widely...

show abstract

Section: Compositional Systemmentioning

confidence: 99%

Section: Compositional Systemmentioning

confidence: 99%

See 1 more Smart Citation

Sequential fully implicit formulation for compositional simulation using natural variables

Moncorgé

Tchelepi

Jenny

2018

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…This has been successful in the sense that state-of-the-art multiscale methods (Møyner andLie 2016a, 2016b) today largely can handle model sizes, flow physics, grid geometries, and petrophysical heterogeneity seen in contemporary asset models (Lie et al 2017b). As a result, the research underpinning the development of next-generation multiscale reservoir simulators is shifting its focus from multiscale methods to more efficient and robust transport solvers and sequential solution algorithms (Moncorgé et al 2017(Moncorgé et al , 2018Møyner and Tchelepi 2018;Møyner and Moncorgé 2019).…”

Section: Introductionmentioning

confidence: 99%

Dynamic Coarsening and Local Reordered Nonlinear Solvers for Simulating Transport in Porous Media

Klemetsdal

Lie

2020

SPE Journal

View full text Add to dashboard Cite

Summary We present a robust and flexible sequential solution approach in which the flow equation is solved on the original grid, whereas the transport equations are solved with a new dynamic coarsening method that adapts the grid resolution locally to reduce the number of cells as much as possible. The resulting grid is formed by combining precomputed coarse partitions of an underlying fine model. Our approach is flexible and makes very few assumptions on cell geometries and the topology of the grid. To further accelerate the transport step, we combine dynamic coarsening with a local nonlinear solver that permutes the discrete transport equations into an optimal block-triangular form so that these can be solved very efficiently using a nonlinear back-substitution method. Efficiency and utility of the overall approach are assessed through a number of conceptual test cases, including the Olympus field model.

show abstract

“…The SI methods still exhibit conditional stability due to the semi-implicit treatment of the velocity. In addition, material balance errors of SI may accumulate with time (Moncorg et al 2017). To resolve these issues, Jenny et al (2006) proposed the sequential fully implicit (SFI) method, which iterates on implicitly solving the pressure and transport equations before advancing to the next time-step.…”

Section: Introductionmentioning

confidence: 99%

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

View full text Add to dashboard Cite

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.

show abstract

Modified sequential fully implicit scheme for compositional flow simulation

Cited by 32 publications

References 29 publications

Sequential fully implicit formulation for compositional simulation using natural variables

Sequential fully implicit formulation for compositional simulation using natural variables

Dynamic Coarsening and Local Reordered Nonlinear Solvers for Simulating Transport in Porous Media

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

Contact Info

Product

Resources

About