Multidimensional upstream weighting for multiphase transport in porous media

Kozdon, Jeremy E.; Mallison, Bradley T.; Gerritsen, Margot

doi:10.1007/s10596-010-9211-5

Cited by 16 publications

(23 citation statements)

References 36 publications

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“…Kozdon et al (2011) prove the monotonicity of this scheme for time-dependent problems. A straightforward extension of this proof is sufficient to show that when proper well conditions are applied, DQA MDU is an M-matrix.…”

Section: Finite-volume Discretizationmentioning

confidence: 80%

“…Our simplest discretization is based on SPU weighting, which corresponds to the lowest-order DG scheme. We also investigate a truly MDU weighting scheme that is monotonic and reduces transverse numerical diffusion (Kozdon et al 2009;Kozdon et al 2011;Keilegavlen 2010). The resulting discrete systems can be solved efficiently using the approach of Natvig et al (2007).…”

Section: Introductionmentioning

confidence: 99%

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An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids

et al. 2012

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Streamline-based methods can be used as effective post-processing tools for assessing flow patterns and well allocation factors in reservoir simulation. This type of diagnostic information can be useful for a number of applications, including visualization, model ranking, upscaling validation, and optimization of well placement or injection allocation. In this paper, we investigate finite-volume methods as an alternative to streamlines for obtaining flow diagnostic information. Given a computed flux field, we solve the stationary transport equations for tracer and time of flight by use of either single-point upstream (SPU) weighting or a truly multidimensional upstream (MDU) weighting scheme. We use tracer solutions to partition the reservoir into volumes associated with injector/producer pairs and to calculate fluxes (well allocation factors) associated with each volume. The heterogeneity of the reservoir is assessed with time of flight to construct flowcapacity/storage-capacity (F-vs.-U) diagrams that can be used to estimate sweep efficiency. We compare the results of our approach with streamline-based calculations for several numerical examples, and we demonstrate that finite-volume methods are a viable alternative. The primary advantages of finite-volume methods are the applicability to unstructured grids and the ease of implementation for general-purpose simulation formulations. The main disadvantage is numerical diffusion, but we show that a MDU weighting scheme is able to reduce these errors.

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Section: Finite-volume Discretizationmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids

et al. 2012

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show abstract

“…Hence, the interpolation operator a is sparse and can be constructed efficiently. Kozdon et al (2011) prove the monotonicity of this scheme for time-dependent problems. A straightforward extension of this proof is sufficient to show that when proper well conditions are applied, is an M-matrix.…”

mentioning

confidence: 80%

“…Our simplest discretization is based on single-point upstream weighting (SPU) which corresponds to the lowest order DG scheme. We also investigate a truly multi-dimensional (multi-D) upstream weighting (MDU) scheme that is monotone and reduces transverse numerical diffusion (Kozdon et al (2009), Kozdon et al (2011), Keilegavlen (2010). The methods of Lamine and Edwards (2010) are similar and could also be used in this context.…”

Section: Introductionmentioning

confidence: 99%

An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids

et al. 2011

View full text Add to dashboard Cite

Streamline-based methods can be used as effective post-processing tools for assessing flow patterns and well allocation factors in reservoir simulation. This type of diagnostic information can be useful for a number of applications including visualization, model ranking, upscaling validation and optimization of well placement or injection allocation. In this paper, we investigate finite volume methods as an alternative to streamlines for obtaining flow diagnostic information. Given a computed flux field, we solve the stationary transport equations for tracer and time of flight using either single-point upstream weighting or a truly multi-dimensional upstream weighting scheme. We use tracer solutions to partition the reservoir into volumes associated with injector-producer pairs and to calculate fluxes (well allocation factors) associated with each volume. The heterogeneity of the reservoir is assessed by using time of flight to construct flow capacity-storage capacity (F-Ф) diagrams which can be used to estimate sweep efficiency. We compare the results of our approach with streamlinebased calculations for several numerical examples and we demonstrate that finite volume methods are a viable alternative. The primary advantages of finite volume methods are applicability to unstructured grids and ease of implementation for general purpose simulation formulations. The main disadvantage is numerical diffusion, but we show that a multidimensional upstream weighting scheme is able to reduce these errors.

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“…The weights given to the upwind volumes are chosen to improve accuracy by accounting for characteristic information while also honoring monotonicity. To define this stencil, we adapt the approach previously used in Kozdon et al (2011a); Keilegavlen et al (2012) and use a dual grid made of the union of interaction regions as illustrated in Fig. 1.…”

Section: Integration Region Frameworkmentioning

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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Multidimensional upstream weighting for multiphase transport in porous media

Cited by 16 publications

References 36 publications

An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids

An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids

An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids

Fully Implicit multidimensional Hybrid Upwind scheme for coupled flow and transport

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