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Effects of core‐scale heterogeneity on steady state and transient fluid flow in porous media: Numerical analysis
Author(s) -
Bachu Stefan,
Cuthiell David
Publication year - 1990
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr026i005p00863
Subject(s) - hydraulic conductivity , isotropy , porous medium , anisotropy , clastic rock , steady state (chemistry) , mechanics , conductivity , materials science , geotechnical engineering , geology , porosity , soil science , physics , sedimentary rock , chemistry , paleontology , quantum mechanics , soil water
Numerical simulations are used in an inverse approach to study the effects of actual core‐scale heterogeneity on the steady state and transient fluid flow in aquifers and reservoirs. The heterogeneous porous medium consists of homogeneous and isotropic shale clasts of variable size, geometry, orientation, and distribution, embedded in a homogeneous and isotropic sand matrix. The data was obtained by digitizing shale clasts from cores in a heavy oil reservoir. The presence of the clasts in the sand matrix creates anisotropy at larger scales, due mainly to the predominantly flat shape and subhorizontal orientation of the clasts. The steady state effective hydraulic conductivity generally has values between the geometric and arithmetic averages of the two component values, averages weighted by heterogeneity fraction. The dependence of the effective hydraulic conductivity on the heterogeneity fraction and conductivity contrast between the clasts and the matrix can be described empirically by a power‐average model. The reduction in the effective conductivity exhibits an asymptotic behaviour for conductivity contrasts greater than 2 orders of magnitude. When multiple heterogeneity scales are present, a sequential approach can be used by which heterogeneous media at smaller scales are replaced successively by homogeneous media characterized by corresponding effective hydraulic conductivities. For transient flow, the effective values of hydraulic conductivity and specific storage are time and flow dependent, with asymptotic behaviour toward the steady state effective value for hydraulic conductivity and toward the space‐average value for specific storage. The error in using steady state effective hydraulic conductivity and space‐average specific storage is relatively large for rapidly varying flows but is probably acceptable for slowly varying flows. Generally, the results of the numerical simulations show that the effective values of hydraulic parameters are dependent on both the intrinsic structure of the heterogeneous porous medium and on the flow process.