Dual Mesh Method for Multiphase Flows in Heterogeneous Porous Media

Verdiere, Sophie; Guérillot, Dominique; Thomas, J. M.

doi:10.3997/2214-4609.201406903

Cited by 15 publications

(8 citation statements)

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“…This is contrast with the claim that the homogenized relative permeabilities are tensorial quantities [e.g., Quintard and Whitaker, 1999;Verdière et al, 1996]. This remark is supported by the work of Bear et al [1987] on 3-D orthogonal network of capillary tubes.…”

Section: Discussioncontrasting

confidence: 49%

“…[20] The tensorial property applies to the macroscale permeability K e a , and then to the macroscale intrinsic permeability, as for example K se = K e w (p c0 = 0), but does not apply to macroscale relative permeabilities (k re a ) ij , (a = w, n), as defined (component by component) by (45). This is contrast with the claim that the homogenized relative permeabilities are tensorial quantities [e.g., Quintard and Whitaker, 1999;Verdière et al, 1996]. This remark is supported by the work of Bear et al [1987] on 3-D orthogonal network of capillary tubes.…”

Section: Discussionmentioning

confidence: 83%

“…These solutions have shed light on the macroscale effect of heterogeneity, and on the correct averaging of key hydrodynamic parameters such as permeability. However, in spite of numerous studies, the homogenization of multiphase flow systems remains a difficult problem which has not been fully analyzed nor resolved, except with stringent constraining assumptions and/or auxiliary numerical calculations [Bourgeat, 1984;Quintard and Whitaker, 1988;Gelhar, 1987, 1989;Bear et al, 1987;Chang et al, 1995;Abdin et al, 1995;Verdière et al, 1996;Guzman et al, 1994]. A more complete review of the literature is given by Fadili [2001] and Farmer [2002].…”

Section: Introductionmentioning

confidence: 99%

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Dual homogenization of immiscible steady two‐phase flows in random porous media

Fadili

Ababou

2004

Water Resources Research

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[1] We develop a dual conductivity-resistivity homogenization for immiscible steady two-phase flow in heterogeneous, spatially correlated, random porous media. The objective is to obtain macroscale equations for an equivalent homogeneous medium. We assume that the flow is governed locally by the generalized Darcy equations. Two formulations are developed, one in terms of capillary pressure p c and the other in terms of saturation s. In each case the perturbation approach is used to express average and fluctuation equations, and the closure problems are solved using the Wiener-Kinchine spectral theory. The macroscale permeability K e a and resistivity R e a tensors are determined for each fluid a, which also yield the relative permeabilities. These dual results provide a physically consistent correction of the perturbation-based tensors. The corrected macroscale tensors are then always positive, symmetric, and reciprocal to each other. We also develop, similarly, the homogenization of the capillary pressure curve p c (x, q) and of its reciprocal q(x, p c ), where q is the wetting fluid content. Finally, these general analytical results are applied to the special case where hrp c i % 0 and/or hrqi % 0, which can be interpreted as a mean capillary equilibrium.

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Section: Discussioncontrasting

confidence: 49%

Section: Discussionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

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Dual homogenization of immiscible steady two‐phase flows in random porous media

Fadili

Ababou

2004

Water Resources Research

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“…From a mathematical point of view, the DMM approach is justified by the parabolical (or elliptical) nature of the pressure equation (long range forces) compared with the hyperbolical nature of the saturation equation. It makes the pressure profiles to be smoother than the saturation profiles (Verdière et al, 1996).…”

Section: Pressure Based Approachmentioning

confidence: 99%

A New Experimental Method To Determine Interval of Confidence for Capillary Pressure and Relative-Permeability Curves

Egermann

Lombard

Fichen

et al. 2005

Proceedings of SPE Annual Technical Conference and Exhibition

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe saturation profiles are routinely measured during Special Core Analysis (SCAL experiments). Several ways exist to use this information in the inversion procedure of the relative permeability data. To date, the local saturation profiles are either included in a global objective function that is minimized during the inversion process, or smoothed and used as input data in the simulation, which leads to non smoothed simulated pressure drop. None of these methods permit to reproduce the local saturation fluctuations that are measured during coreflooding experiments. Our approach has the advantage to take benefit from these fluctuations to characterize the petrophysical properties for a given rock-type. In this paper, the methodology is first recalled and illustrated on a synthetic case. It is based on upscaling techniques applied in reservoir simulation. Both the stabilized and transient saturation profiles are analyzed to evaluate the local properties. The quality of the history matching is significantly improved. In addition, both kr and Pc-curves are obtained from only one experiment and the variability of these parameters with the heterogeneity is also investigated. This estimated interval of confidence for kr and Pc can be very useful to perform uncertainty studies at the reservoir scale. The Pc-curve interval of confidence determined with this method on a carbonate sample, is in good agreement with the variability observed with several centrifuge experiments performed on sister plugs. Finally an alternative approach derived of the heterogeneous method is proposed, which allows a very quick acquisition of all the information relative to kr and Pc during a multi-rate flow experiments.

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“…An accurate alternative to pseudo-functions, known as the dual-mesh (DM) method [33,95], solves for the pressure distribution in the upscaled grid and includes the fine-scale heterogeneities in the computation of the phase saturations. Arbogast and Bryant [4] introduced a version of the DM method that upscales the transmissivities.…”

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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Dual Mesh Method for Multiphase Flows in Heterogeneous Porous Media

Cited by 15 publications

References 0 publications

Dual homogenization of immiscible steady two‐phase flows in random porous media

Dual homogenization of immiscible steady two‐phase flows in random porous media

A New Experimental Method To Determine Interval of Confidence for Capillary Pressure and Relative-Permeability Curves

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

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