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[1] We propose a new physical interpretation of the diffusion process for the piezometric head h(x, t) in heterogeneous aquifers based on the continuous time random walk (CTRW) theory. For the typical heterogeneities considered in this work, we find that a CTRW based diffusion equation for h(x, t) provides better fits to the transient flow simulations than the classical diffusion equation (DE). The DE is found to be a special case of the CTRW diffusion equation. The results of this work have clear implications for the interpretation of pumping tests and what information can be extracted from them.

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