TY - JOUR

T1 - Upscaling relative permeabilities in a structured porous medium

AU - Gasda, S. E.

AU - Celia, Michael Anthony

N1 - Funding Information:
This work was sponsored in part by a grant from BP and Ford Motor Company through funding of the Carbon Mitigation Initiative at Princeton, and by the National Science Foundation through a graduate fellowship to S. Gasda. We also thank Helge Dahle for his important contributions to this work.

PY - 2005/5

Y1 - 2005/5

N2 - Upscaling of multi-phase flow problems for a heterogeneous porous medium requires modification of constitutive functions at the grid-block scale. A particular type of heterogeneity that has important environmental consequences involves thin, continuous streaks of high permeability through lower-permeability background rocks. These streaks, which may correspond to features like abandoned wells in mature sedimentary basins, can become preferential flow paths for an invading fluid. Quantification of flow through these types of heterogeneities in deep, geological formations is necessary for estimates of migration and possible leakage of injected fluids such as hazardous liquid wastes, municipal liquid wastes, and, possibly, carbon dioxide. One of the important constitutive functions for proper estimation of flow through these flow paths is the relative permeability function. In the simple case of a single high-permeability streak in a uniform rock matrix, with both materials having identical (local) relative permeability functions, the upscaled relative permeability must be changed significantly to capture the proper leakage. Standard petroleum reservoir pseudo-functions for relative permeability capture the general features of the upscaled function, but they still produce errors of several hundred percent in the leakage estimation. Detailed three-dimensional numerical simulations and associated upscaled calculations demonstrate the proper form for the upscaled relative permeability, and provide a modified derivation of pseudo-functions to capture the leakage behavior in upscaled models.

AB - Upscaling of multi-phase flow problems for a heterogeneous porous medium requires modification of constitutive functions at the grid-block scale. A particular type of heterogeneity that has important environmental consequences involves thin, continuous streaks of high permeability through lower-permeability background rocks. These streaks, which may correspond to features like abandoned wells in mature sedimentary basins, can become preferential flow paths for an invading fluid. Quantification of flow through these types of heterogeneities in deep, geological formations is necessary for estimates of migration and possible leakage of injected fluids such as hazardous liquid wastes, municipal liquid wastes, and, possibly, carbon dioxide. One of the important constitutive functions for proper estimation of flow through these flow paths is the relative permeability function. In the simple case of a single high-permeability streak in a uniform rock matrix, with both materials having identical (local) relative permeability functions, the upscaled relative permeability must be changed significantly to capture the proper leakage. Standard petroleum reservoir pseudo-functions for relative permeability capture the general features of the upscaled function, but they still produce errors of several hundred percent in the leakage estimation. Detailed three-dimensional numerical simulations and associated upscaled calculations demonstrate the proper form for the upscaled relative permeability, and provide a modified derivation of pseudo-functions to capture the leakage behavior in upscaled models.

KW - Abandoned well leakage

KW - Relative permeability function

KW - Structured heterogeneity

KW - Two-phase flow

KW - Upscaling

KW - Waste disposal

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U2 - 10.1016/j.advwatres.2004.11.009

DO - 10.1016/j.advwatres.2004.11.009

M3 - Article

AN - SCOPUS:14844343995

VL - 28

SP - 493

EP - 506

JO - Advances in Water Resources

JF - Advances in Water Resources

SN - 0309-1708

IS - 5

ER -