On the Use of a Mixed Multiscale Finite Element Method for GreaterFlexibility and Increased Speed or Improved Accuracy in Reservoir Simulation

Aarnes, Jørg E.

doi:10.1137/030600655

Cited by 281 publications

(243 citation statements)

References 19 publications

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“…Different definitions of the multiscale basis functions exist [16,1,2], and in this work we have adopted the recent one proposed by [28], where the multiscale basis function is the solution to a flow problem restricted to a pair of adjacent coarse elements with source terms specified in such a way that the flow through the interface is identically one (see Figure 2-1). More precisely, the multiscale basis functions (N Hh, f'H,h) for interface Fa (common to coarse elements Ei and Ej) are the solution to the following local problem:…”

Section: Proposed Subgrid Communicationmentioning

confidence: 99%

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A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source terms

Juanes

Dub

2008

Comput Geosci

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Multiscale phenomena are ubiquitous to flow and transport in porous media. They manifest themselves through at least the following three facets: (1) effective parameters in the governing equations are scale dependent; (2) some features of the flow (especially sharp fronts and boundary layers) cannot be resolved on practical computational grids; and (3) dominant physical processes may be different at different scales. Numerical methods should therefore reflect the multiscale character of the solution. We concentrate on the development of simulation techniques that account for the heterogeneity present in realistic reservoirs, and have the ability to solve for coupled pressure-saturation problems (on coarse grids). We present a variational multiscale mixed finite element method for the solution of Darcy flow in porous media, in which both the permeability field and the source term display a multiscale character. The formulation is based on a multiscale split of the solution into coarse and subgrid scales. This decomposition is invoked in a variational setting that leads to a rigorous definition of a (global) coarse problem and a set of (local) subgrid problems. One of the key issues for the success of the method is the proper definition of the boundary conditions for the localization of the subgrid problems. We identify a weak compatibility condition that allows for subgrid communication across element interfaces, something that turns out to be essential for obtaining high-quality solutions. We also remove the singularities due to concentrated sources from the coarse-scale problem by introducing additional multiscale basis functions, based on a decomposition of fine-scale source terms into coarse and deviatoric components. The method is locally conservative and employs a low-order approximation of pressure and velocity at both scales. We illustrate the performance of the method on several synthetic cases, and conclude that the method is able to capture the global and local flow patterns accurately.

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Section: Proposed Subgrid Communicationmentioning

confidence: 99%

“…A mixed finite element version that guarantees local mass conservation at the element level was proposed in [16]. This work was recently extended in a number of important ways by the Norwegian school [1,2]. Inspired in the multiscale finite element method, a multiscale finite volume method was proposed in [24].…”

Section: Introductionmentioning

confidence: 99%

A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source terms

Juanes

Dub

2008

Comput Geosci

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“…In the previous studies [1,7,11], it was found that the use of global information can improve the multiscale finite element method. In particular, the solution of the pressure equation at initial time is used to construct the boundary conditions for the basis functions.…”

Section: Multiscale Finite Element Methods For Upscaling Of Pressure mentioning

confidence: 99%

“…When considering two-phase flow upscaling, we use multiscale basis functions to compute the macrodispersion. Recently, a limited global information has been used [1,11] in constructing multiscale basis functions. It is interesting to note that, in the flow-based coordinate system, these multiscale methods reduce to a standard multiscale finite element method [16].…”

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confidence: 99%

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Multiscale simulations of porous media flows in flow-based coordinate system

2008

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In this paper, we propose a multiscale technique for the simulation of porous media flows in a flow-based coordinate system. A flow-based coordinate system allows us to simplify the scale interaction and derive the upscaled equations for purely hyperbolic transport equations. We discuss the applications of the method to two-phase flows in heterogeneous porous media. For two-phase flow simulations, the use of a flow-based coordinate system requires limited global information, such as the solution of single-phase flow. Numerical results show that one can achieve accurate upscaling results using a flow-based coordinate system.

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Sequential approach to joint flow‐seismic inversion for improved characterization of fractured media

Kang

Zheng

Fang

et al. 2016

Water Resources Research

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Seismic interpretation of subsurface structures is traditionally performed without any account of flow behavior. Here we present a methodology for characterizing fractured geologic reservoirs by integrating flow and seismic data. The key element of the proposed approach is the identification-within the inversion-of the intimate relation between fracture compliance and fracture transmissivity, which determine the acoustic and flow responses of a fractured reservoir, respectively. Owing to the strong (but highly uncertain) dependence of fracture transmissivity on fracture compliance, the modeled flow response in a fractured reservoir is highly sensitive to the geophysical interpretation. By means of synthetic models, we show that by incorporating flow data (well pressures and tracer breakthrough curves) into the inversion workflow, we can simultaneously reduce the error in the seismic interpretation and improve predictions of the reservoir flow dynamics. While the inversion results are robust with respect to noise in the data for this synthetic example, the applicability of the methodology remains to be tested for more complex synthetic models and field cases.

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On the Use of a Mixed Multiscale Finite Element Method for GreaterFlexibility and Increased Speed or Improved Accuracy in Reservoir Simulation

Cited by 281 publications

References 19 publications

A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source terms

A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source terms

Multiscale simulations of porous media flows in flow-based coordinate system

Sequential approach to joint flow‐seismic inversion for improved characterization of fractured media

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