Probability density function of steady-state concentration in two-dimensional heterogeneous porous media

摘要: [1] Spatial variability of hydraulic aquifer parameters causes meandering, squeezing, stretching, and enhanced mixing steady state plumes in concentrated hot-spots mixing. Because the exact spatial distribution is uncertain, rates also uncertain. We discuss how relevant resulting uncertainty for predicting concentrations. develop analytical solutions full statistical concentration two-dimensional, statistically uniform domains with log-hydraulic conductivity following an isotropic exponential model. In particular, we analyze statistics at fringes wide plumes, conceptually represented by a solute introduced over half width domain. Our framework explicitly accounts streamline meandering effective transverse (defined Darcy scale). make use existing low-order closed-form expressions that lead to local values. Along expected position plume fringe, strongly clusters its extreme This behavior extends travel distances up tens integral scales tested our study. this regime, substantial enough have noticeable effects on probability density function. At significantly larger distances, intermediate values become most likely, becomes negligible. A comparison numerical Monte Carlo simulations flow transport show excellent agreement theoretically derived expressions.