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>A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations
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A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations
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机译：A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations
A general problem in groundwater modeling is how to assign conductivity values to blocks of a numerical model. In this study, a method is proposed to upscale the conductivity measurements observed at a given scale to block conductivity values for arbitrary block size. Assuming a multilognormal distribution for the point conductivities, the block conductivity appears as a random function whose distribution, conditional to point measurements, can be derived. This conditional distribution allows filling the flow simulator blocks with equiprobable realizations of block conductivities locally conditioned to actual data. These realizations could also be conditioned to conductivity values measured at any scale if the size of the measurement support is known. The analytical results are compared to results obtained through a Monte Carlo analysis, and a good agreement was found even for variances of ln (T) larger than 1.
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