Modeling groundwater in multimodal porous media with localized decompositions

In the present paper, a new stochastic framework is introduced to decompose random variables. This decomposition method is shown to better capture and reflect the medium heterogeneity for multimodal porous media than the classical Reynolds decomposition does. In particular, with this decomposition method, the variance of log conductivity is decomposed into two parts. The first one measures the mean differences of log conductivity across different units having high contrasting conductivity. The second part measures the variation of log conductivity arisen within individual units. Based on this localized decomposition, a new stochastic model is proposed for flow in a highly heterogeneous porous media. This stochastic model shall produce much sharper approximations under the assumption that only the second part of the variance of log conductivity is small. Therefore, the proposed model can partially overcome the assumption of small composite variance for log conductivity in current theory for both flow and transport.