Inexact methods for sequential fully implicit (SFI) reservoir simulation

Jiang, Jiamin; Tomin, Pavel; Zhou, Yifan

doi:10.1007/s10596-021-10072-z

Cited by 12 publications

(4 citation statements)

References 45 publications

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“…The nodal values of the pressure allow to compute the velocity at FV cell interfaces, applying Darcy's law. Once the velocities are obtained, their values are introduced in the water saturation equation, (18), which is solved by the FV technique, where v w,x and v w,y are the components of water velocity in x and y directions, respectively. The forcing term appearing in (18), F s , is readily obtained using some software of symbolic computation (Fig.…”

Section: Two-dimensional (2d) Extensionmentioning

confidence: 99%

“…We refer the reader to the seminal work [27] for a strong background in reservoir simulation, comprising physical principles, mathematical models, and numerical resolution by finite-difference formulations. There is also some literature on the application of finitevolume numerical methods in the field of reservoir simulation, see for instance [6,11,14,18,20,23].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Luna

Hidalgo

2022

Commun. Appl. Math. Comput.

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Two-phase flow in porous media is a very active field of research, due to its important applications in groundwater pollution, $${\text {CO}}_2$$ CO 2 sequestration, or oil and gas production from petroleum reservoirs, just to name a few of them. Fractional flow equations, which make use of Darcy’s law, for describing the movement of two immiscible fluids in a porous medium, are among the most relevant mathematical models in reservoir simulation. This work aims to solve a fractional flow model formed by an elliptic equation, representing the spatial distribution of the pressure, and a hyperbolic equation describing the space-time evolution of water saturation. The numerical solution of the elliptic part is obtained using a finite-element (FE) scheme, while the hyperbolic equation is solved by means of two different numerical approaches, both in the finite-volume (FV) framework. One is based on a monotonic upstream-centered scheme for conservation laws (MUSCL)-Hancock scheme, whereas the other makes use of a weighted essentially non-oscillatory (ENO) reconstruction. In both cases, a first-order centered (FORCE)-$$\alpha$$ α numerical scheme is applied for intercell flux reconstruction, which constitutes a new contribution in the field of fractional flow models describing oil-water movement. A relevant feature of this work is the study of the effect of the parameter $$\alpha$$ α on the numerical solution of the models considered. We also show that, in the FORCE-$$\alpha$$ α method, when the parameter $$\alpha$$ α increases, the errors diminish and the order of accuracy is more properly attained, as verified using a manufactured solution technique.

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Section: Two-dimensional (2d) Extensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Luna

Hidalgo

2022

Commun. Appl. Math. Comput.

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“…The comparison takes into account the role of the upwinding scheme-Phase Potential Upwinding [40,41] or Implicit Hybrid Upwinding [11,[42][43][44][45][46][47][48]-as well as the role of the nonlinear tolerance used in the subproblems. To do so, we propose an adaptive method to compute the subproblem nonlinear tolerance at each preconditioning step, as typically done in inexact Newton methods [49][50][51][52][53][54]. We demonstrate that the two-step nonlinear preconditioners and, in particular, FSMSN, are successful at accelerating nonlinear convergence and are worth being explored as viable options to reduce the computational cost of reservoir simulation-which will be addressed in a future publication.…”

Section: Introductionmentioning

confidence: 99%

Comparison of nonlinear field-split preconditioners for two-phase flow in heterogeneous porous media

Ndiaye¹,

Hamon²

2022

Preprint

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This work focuses on the development of a two-step field-split nonlinear preconditioner to accelerate the convergence of two-phase flow and transport in heterogeneous porous media. We propose a field-split algorithm named Field-Split Multiplicative Schwarz Newton (FSMSN), consisting in two steps: first, we apply a preconditioning step to update pressure and saturations nonlinearly by solving approximately two subproblems in a sequential fashion; then, we apply a global step relying on a Newton update obtained by linearizing the system at the preconditioned state. Using challenging test cases, FSMSN is compared to an existing field-split preconditioner, Multiplicative Schwarz Preconditioned for Inexact Newton (MSPIN), and to standard solution strategies such as the Sequential Fully Implicit (SFI) method or the Fully Implicit Method (FIM). The comparison highlights the impact of the upwinding scheme in the algorithmic performance of the preconditioners and the importance of the dynamic adaptation of the subproblem tolerance in the preconditioning step. Our results demonstrate that the two-step nonlinear preconditioning approachand in particular, FSMSN-results in a faster outer-loop convergence than with the SFI and FIM methods. The impact of the preconditioners on computational performance-i.e., measured by wall-clock time-will be studied in a subsequent publication.

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“…Zhang proposed the queued competition algorithm to calculate shale-gas production reserves and established a shale-gas production reserve optimization model [5]. Jiang proposed the sequential fully implicit (SFI) scheme for solving coupled flow and transport problems [6]. Zhou proposed a new method for evaluating favorable shale-gas exploration areas based on multi-linear regression analysis [7].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Uncertain Causality Graph Applied to the Intelligent Evaluation of a Shale-Gas Sweet Spot

2021

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Shale-gas sweet-spot evaluation as a critical part of shale-gas exploration and development has always been the focus of experts and scholars in the unconventional oil and gas field. After comprehensively considering geological, engineering, and economic factors affecting the evaluation of shale-gas sweet spots, a dynamic uncertainty causality graph (DUCG) is applied for the first time to shale-gas sweet-spot evaluation. A graphical modeling scheme is presented to reduce the difficulty in model construction. The evaluation model is based on expert knowledge and does not depend on data. Through rigorous and efficient reasoning, it guarantees exact and efficient diagnostic reasoning in the case of incomplete information. Multiple conditional events and weighted graphs are proposed for specific problems in shale-gas sweet-spot evaluation, which is an extension of the DUCG that defines only one conditional event for different weighted function events and relies only on the experience of a single expert. These solutions make the reasoning process and results more objective, credible, and interpretable. The model is verified with both complete data and incomplete data. The results show that compared with other methods, this methodology achieves encouraging diagnostic accuracy and effectiveness. This study provides a promising auxiliary tool for shale-gas sweet spot evaluation.

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Inexact methods for sequential fully implicit (SFI) reservoir simulation

Cited by 12 publications

References 45 publications

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Comparison of nonlinear field-split preconditioners for two-phase flow in heterogeneous porous media

Dynamic Uncertain Causality Graph Applied to the Intelligent Evaluation of a Shale-Gas Sweet Spot

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