A semianalytical approach to spatial averaging of hydraulic conductivity in heterogeneous aquifers
- Moscow State Univ. (Russian Federation)
- Lawrence Berkeley National Lab., CA (United States). Earth Sciences Div.
Numerical models of groundwater flow require hydraulic conductivity values to be assigned to the grid blocks covering the flow domain. However, field-measured conductivities tend to be measured at a different scale (usually smaller) than that of the grid blocks. The present paper describes a novel approach for upscaling field values to block-scale, which combines the rigorous result of small-value perturbation analysis with a plausible generalization of the first-order results to large variance. Also the correlation lengths are assumed to be comparable to block size. Steady-state flow through a block of stochastically heterogeneous medium with constant hydraulic head values at the two opposite sides is analyzed. An upscaling rule and relationship is obtained between the local-scale hydraulic conductivity and the expected mean and variance of block-scale conductivity, where the block size is comparable with the correlation scale of the local conductivity field. The rather simple expressions obtained are validated using data from numerical experiments. Furthermore, a generalized spatial power-averaging method to calculate the block-scale conductivity from values of local-scale conductivity is developed, in which the exponent value is given as a function of the ratios of flow domain dimensions to the respective correlation lengths.
- Research Organization:
- Lawrence Berkeley National Lab., CA (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 578616
- Report Number(s):
- LBNL--40839; ON: DE98051531
- Country of Publication:
- United States
- Language:
- English
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