Most existing stochastic models assume that the porous medium being studied can be characterized by one single correlation scale. However, hydraulic properties exhibit spatial variations at various scales, thus stochastic models developed for unimodal media may not be applicable to flow and transport in a bimodal heterogeneous medium. The aim of this study is to investigate under what circumstances the second-order moment-based stochastic models are applicable to the bimodal porous medium. We assume that two materials (categories) in the porous medium may have a different mean, variance, and correlation scale. The distribution of materials in the domain is characterized by indicator random variables and that of the composite field in terms of categorical proportions and transition probability. We solved the second-order flow moment equations for the 'equivalent' unimodal field with an exponential covariance of a single correlation scale computed for the composite field. On the other hand, we conduct two sets of Monte Carlo simulations: one with bimodal random fields and the other with equivalent unimodal fields. Numerical experiments show that a bimodal InK field may be well approximated with an equivalent unimodal field when the bimodal distribution is highly asymmetric, under which condition the applicability of the second-order moment-based stochastic model is subject to the same limitation of relatively small variances as that for unimodal fields. When the bimodal distribution is symmetric, although it cannot be adequately represented by an equivalent unimodal distribution the second-order moment-based stochastic model seems to be applicable to larger composite variance systems than it does for an asymmetric distribution.
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