A Class of Viscosity Profiles for Oil Displacement in Porous Media or Hele-Shaw Cell

Paşa, Gelu; Titaud, Olivier

doi:10.1007/s11242-004-0773-3

Cited by 8 publications

(7 citation statements)

References 13 publications

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“…In the absence of diffusion, some principles have been formed for determining the optimal viscous profile without an exhaustive search. 8,7,10,22 In Refs. 8 and 10, selection principles for optimal viscous profiles are determined through a numerical study for three and four layer flows, respectively.…”

Section: A the Case Of Fixed Concentration On The Interfaces (Permeamentioning

confidence: 99%

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Studies on dispersive stabilization of porous media flows

Daripa

Gin

2016

Physics of Fluids

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Motivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of three-layer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of capillary number, Peclet number, longitudinal and transverse dispersion, and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Key results obtained are (i) three-layer porous media flows with permeable interfaces can be almost completely stabilized by diffusion if the optimal viscous profile is chosen, (ii) flows with impermeable interfaces can also be almost completely stabilized for short time, but become more unstable at later times because diffusion flattens out the basic viscous profile, (iii) diffusion stabilizes short waves more than long waves which leads to a "turning point" Peclet number at which short and long waves have the same growth rate, and (iv) mechanical dispersion further stabilizes flows with permeable interfaces but in some cases has a destabilizing effect for flows with impermeable interfaces, which is a surprising result. These results are then used to give a comparison of the two types of interfaces. It is found that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces. Published by AIP Publishing.

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Section: A the Case Of Fixed Concentration On The Interfaces (Permeamentioning

confidence: 99%

“…In Ref. 22, a class of optimal viscous profiles is determined analytically under some additional assumptions. No similar results exist for determining the optimal viscous profile a priori in the present case.…”

Section: A the Case Of Fixed Concentration On The Interfaces (Permeamentioning

confidence: 99%

Studies on dispersive stabilization of porous media flows

Daripa

Gin

2016

Physics of Fluids

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“…Thus, the results reported by Guo and Zhao (2005) cannot be considered definitive, and the status of this problem as a benchmark can only be considered preliminary. While there have been some studies on temperature-dependent viscosity of water and oil in porous media (Horne, 1975;Weber, 1975;Gary and others, 1982;Pasa and Titaud, 2005;Afify, 2007), there is not a specific benchmark problem simulating natural convection and variations in viscosity of single phase oil from changes in temperature in a porous medium, except for the work by Guo and Zhao (2005). More tests will need to be done to establish Guo and Zhao's work as a standard benchmark problem.…”

Section: Problem 2: Two-dimensional Oil Convection In Aluminum Foammentioning

confidence: 99%

Application of SEAWAT to select variable-density and viscosity problems

Dausman¹,

Langevin²,

Thorne³

et al. 2010

Scientific Investigations Report

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SEAWAT is a combined version of MODFLOW and MT3DMS, designed to simulate three-dimensional, variable-density, saturated groundwater flow. The most recent version of the SEAWAT program, SEAWAT Version 4 (or SEAWAT_V4), supports equations of state for fluid density and viscosity. In SEAWAT_V4, fluid density can be calculated as a function of one or more MT3DMS species, and optionally, fluid pressure. Fluid viscosity is calculated as a function of one or more MT3DMS species, and the program also includes additional functions for representing the dependence of fluid viscosity on temperature. This report documents testing of and experimentation with SEAWAT_V4 with six previously published problems that include various combinations of density-dependent flow due to temperature variations and/or concentration variations of one or more species. Some of the problems also include variations in viscosity that result from temperature differences in water and oil. Comparisons between the results of SEAWAT_V4 and other published results are generally consistent with one another, with minor differences considered acceptable.

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“…A class of optimal viscosity in M.L. was obtained by Paşa and Titaud (2005), including exponential profiles:…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Diffusive Displacement in Three-Layer Hele-Shaw Cell or Porous Medium

Paşa

2010

Transp Porous Med

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We study the linear stability of three-layer Hele-Shaw flow, which models the secondary oil recovery by polymer flooding, in the presence of a diffusion process and a variable viscosity in the middle layer (denoted by M.L.). Then the hydrodynamic stability of the flow is related with the advection-diffusion equation of the species. The diffusion coefficient and the viscosity in M.L. are used as parameters for minimizing the Saffman-Taylor instability. This model was studied also by Daripa and Paşa (Transp Porous Med 70(1):11-23, 2007). A particular basic solution was considered. The stabilizing effect of diffusion was proved, by using a variational formulation of the stability system. However, this analytical method was not giving sufficient conditions for improving the stability; the obtained upper bound of the growth constant (in time) of the perturbations was depending on the eigenfunctions of the stability system. In this paper, we improve the above result. We use a discretization method and obtain a classical algebraic eigenvalue problem, equivalent with the Sturm-Liouville system which governs the flow stability. A generalization of the Gerschgorin's localization theorem is given and two estimates of the growth constant are obtained, not depending on the eigenfunctions. The new estimates are used to obtain sufficient conditions for improving the stability. These conditions are given in terms of the viscosity profile, the diffusion coefficient, the injection velocity, and the M.L. length. We conclude that a strong diffusion process improves the stability in the range of large wavenumbers. In the range of small wavenumbers, a stability improvement is obtained if the viscosity jump on the M.L.-oil interface is small enough and the length of M.L. is large enough.

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A Class of Viscosity Profiles for Oil Displacement in Porous Media or Hele-Shaw Cell

Cited by 8 publications

References 13 publications

Studies on dispersive stabilization of porous media flows

Studies on dispersive stabilization of porous media flows

Application of SEAWAT to select variable-density and viscosity problems

Stability Analysis of Diffusive Displacement in Three-Layer Hele-Shaw Cell or Porous Medium

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