Implementation of a Flux-Continuous Finite Difference Method for Stratigraphic, Hexahedron Grids

Lee, S.H.; DeChant, L.F.

doi:10.2118/51901-ms

Cited by 37 publications

(39 citation statements)

References 9 publications

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“…Multipoint flux approximation (MPFA) has been introduced in the late nineties by Edwards and Rogers [1998], Aavatsmark et al [1998], and Aavatsmark [2002]. There are several types of MPFA such O, L, U, and Z-methods, which the details of the them could be found in Aavatsmark et al [1998] and Lee et al [2002] for MPFA O-method, Aavatsmark et al [2008] and Cao et al [2009] for MPFA L-method, Aavatsmark and Eigestad [2006] for MPFA U-method, and Nordbotten and Eigestad for MPFA Z-method [2005]. In this work, we only implement the MPFA O-method.…”

Section: Multipoint Flux Approximation and Its Numerical Discretizationmentioning

confidence: 99%

Density-Driven Flow Simulation in Anisotropic Porous Media: Application to CO2 Geological Sequestration

2014

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Carbon dioxide (CO 2 ) sequestration in saline aquifers is considered as one of the most viable and promising ways to reduce CO 2 concentration in the atmosphere. CO 2 is injected into deep saline formations at supercritical state where its density is smaller than the hosting brine. This motivates an upward motion and eventually CO 2 is trapped beneath the cap rock. The trapped CO 2 slowly dissolves into the brine causing the density of the mixture to become larger than the host brine. This causes gravitational instabilities that is propagated and magnified with time. In this kind of density-driven flows, the CO 2 -rich brines migrate downward while the brines with low CO 2 concentration move upward. With respect to the properties of the subsurface aquifers, there are instances where saline formations can possess anisotropy with respect to their hydraulic properties. Such anisotropy can have significant effect on the onset and propagation of flow instabilities. Anisotropy is predicted to be more influential in dictating the direction of the convective flow. To account for permeability anisotropy, the method of multipoint flux approximation (MPFA) in the framework of finite differences schemes is used. The MPFA method requires more point stencil than the traditional two-point flux approximation (TPFA). For example, calculation of one flux component requires 6-point stencil and 18-point stencil in 2-D and 3-D cases, respectively. As consequence, the matrix of coefficient for obtaining the pressure fields will be quite complex. Therefore, we combine the MPFA method with the experimenting pressure field technique in which the problem is reduced to solving multitude of local problems and the global matrix of coefficients is constructed automatically, which significantly reduces the complexity. We present several numerical scenarios of density-driven flow simulation in homogeneous, layered, and heterogeneous anisotropic porous media. The numerical results emphasize the significant effects of anisotropy in driving the migration of dissolved CO 2 along the principal direction of anisotropy even if the porous medium is highly heterogeneous. Furthermore, the impacts of the increase of density difference between the brine and the CO 2 -saturated brine with respect to the onset time of convection, the CO 2 flux, and the CO 2 total dissolved mass are also discussed in this paper. Motivation and backgroundNowadays, global warming issue has become the world-widely discussed topic due to the change of climate on the Earth. One of the causes of the global warming is the greenhouse gasses emission, i.e., the release of CO 2 into the atmosphere due to the use of fossil fuels in the industry activities such as power plant, refineries, petrochemical industries, oil and gas processing, etc. The amount of CO 2 concentration in the atmosphere has steadily increased particularly in the last century, from 280 ppm (prior to the industrial revolution) to 390 ppm (at the current time) with annual increase of 1 to 2 ppm [Firoozabadi ...

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Section: Multipoint Flux Approximation and Its Numerical Discretizationmentioning

confidence: 99%

Density-Driven Flow Simulation in Anisotropic Porous Media: Application to CO2 Geological Sequestration

2014

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“…The method was further refined by [15]. Lee et al [52] developed a flux-continuous scheme for 2D models and extended the method [53] to 3D models. Further improvement of the method was suggested by [44].…”

Section: Introductionmentioning

confidence: 99%

“…In 3D structured grids, for example, the MPFA method developed by [1] results in a 27-point stencil for the cellcentered pressure equations, compared with the sevenpoint stencils used in the TPFA methods. The approach has been studied by others as well [30,53].…”

Section: Introductionmentioning

confidence: 99%

Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

Rasaei

Sahimi

2008

Comput Geosci

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We describe a new approach for simulation of multiphase flows through heterogeneous porous media, such as oil reservoirs. The method, which is based on the wavelet transformation of the spatial distribution of the single-phase permeabilities, incorporates in the upscaled computational grid all the relevant data on the permeability, porosity, and other important properties of a porous medium at all the length scales. The upscaling method generates a nonuniform computational grid which preserves the resolved structure of the geological model in the near-well zones as well as in the high-permeability sectors and upscales the rest of the geological model. As such, the method is a multiscale one that preserves all the important information across all the relevant length scales. Using a robust front-detection method which eliminates the numerical dispersion by a high-order total variation diminishing method (suitable for the type of nonuniform upscaled grid that we generate), we obtain highly accurate results with a greatly reduced computational cost. The speedup in the computations is up to over three orders of magnitude, depending on the degree of heterogeneity of the model. To demonstrate the accuracy and efficiency of our methods, five distinct models (including one with fractures) of heterogeneous porous media are considered, and two-phase flows in the models are studied, with and without the capillary pressure.

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“…It is generally agreed that when strong full-tensor effects are present, MPFA methods are preferable. Many authors have investigated MPFA approaches for solving single-phase flow problems with full-tensor permeability that is assumed constant over grid cells [1,12,22]. Naturally, MPFA methods lead to larger stencils than TPFA.…”

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confidence: 99%

Integration of local–global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations

Gerritsen

Lambers

2008

Comput Geosci

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Abstract. We propose a methodology, called multi-level local-global (MLLG) upscaling, for generating accurate upscaled models of permeabilities or transmissibilities for flow simulation on adapted grids in heterogeneous subsurface formations. The method generates an initial adapted grid based on the given fine-scale reservoir heterogeneity and potential flow paths. It then applies local-global (LG) upscaling for permeability or transmissibility [7], along with adaptivity, in an iterative manner. In each iteration of MLLG, the grid can be adapted where needed to reduce flow solver and upscaling errors. The adaptivity is controlled with a flow-based indicator. The iterative process is continued until consistency between the global solve on the adapted grid and the local solves is obtained. While each application of local-global upscaling is also an iterative process, this inner iteration generally takes only one or two iterations to converge. Furthermore, the number of outer iterations is bounded above, and hence the computational costs of this approach are low. We design a new flow-based weighting of transmissibility values in local-global upscaling that significantly improves the accuracy of LG and MLLG over traditional local transmissibility calculations.For highly heterogeneous (e.g., channelized) systems the integration of grid adaptivity and localglobal upscaling is shown to consistently provide more accurate coarse-scale models for global flow, relative to reference fine-scale results, than do existing upscaling techniques applied to uniform grids of similar densities. Another attractive property of the integration of upscaling and adaptivity is that process dependency is strongly reduced, that is, the approach computes accurate global flow results also for flows driven by boundary conditions different from the generic boundary conditions used to compute the upscaled parameters.The method is demonstrated on Cartesian Cell-based Anisotropic Refinement (CCAR) grids, but can be applied to other adaptation strategies for structured grids, and extended to unstructured grids.1. Introduction. The permeability of reservoir rocks is often highly variable and uncertain. However, it can greatly affect flow and transport in subsurface formations, and must therefore be adequately modeled. The effects of uncertain reservoir heterogeneity can be included either through stochastic modeling or by simulating a number of deterministic geostatistical realizations of the reservoir [9], which is the underlying assumption in this paper. Because the computational costs of solving for a large number of realizations are high, simulations are generally performed on grids that are coarse compared to the given geological models. The grid size is typically determined by computational considerations. These coarsened flow models should adequately represent key behaviors, such as the overall flow rate for given boundary conditions or critical connected flow paths.In this paper, we focus on single-phase upscaling to test the effectiveness o...

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Implementation of a Flux-Continuous Finite Difference Method for Stratigraphic, Hexahedron Grids

Abstract: This paper was prepared for presentation at the 1999 SPE Reservoir Simulation Symposium held in Houston, Texas, 14-17 February.

Cited by 37 publications

References 9 publications

Density-Driven Flow Simulation in Anisotropic Porous Media: Application to CO2 Geological Sequestration

Density-Driven Flow Simulation in Anisotropic Porous Media: Application to CO2 Geological Sequestration

Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

Integration of local–global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations

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