Examples of subsurface solute spreading driven by inhomogeneous velocity fields

Most of solutions of flow and transport problems available in literature are obtained under assumptions of stationarity of flow field and/or ergodicity of transport, even though in real-world analyses these hypotheses cannot be always verified. For instance, into problems that are met in practical applications, the statistics of flow are often location dependent and the stationarity of flow is violated. The nonstationarity of velocity field may originate from finite domain boundaries, complex flow configurations (pumping and injecting), nonstationarity of medium properties or conditioning of the log conductivity field to measurements of head or conductivity. Moreover the lack of ergodicity related to the finite size of solute sources makes difficult transport analyses that are often carried out by rough schematizations. Some examples of solute dispersion of nonergodic passive solute plume in heterogeneous formations with nonstationary flow conditions are here considered and solved by a new approach. By this method the spatial moments of finite initial volume of solute are obtained from the statistics of velocity field evaluated by first-order perturbation expansion of steady state flow equation in Taylor series combined with a finite element discretization. The approach allows to handle nonstationarity due to several causes and is here applied to some test cases in bounded domains. A comparison of numerical results in terms of particle displacements moments with known solutions available in literature and with Monte Carlo simulations gives a measure of the effect related to the lack of plume ergodicity and of flow spatial stationarity in real-world transport analyses.