Spatial Markov Model for the Prediction of Travel‐Time‐Based Solute Dispersion in Three‐Dimensional Heterogeneous Media

In recent years, Spatial Markov Models have gained popularity in simulating solute transport heterogeneous formations. They describe the transition times of particles between equidistant observation planes by statistical distributions, assuming correlation transit individual subsequent steps. By this, approach naturally captures preasymptotic dispersion. this study, we analyze bivariate log-normal distributions particle slowness (i.e. inverse velocity) transitions. The model is fully parameterized mean Eulerian velocity, variance log-slowness, and coefficient log-slowness We derive closed-form expressions for distance-dependent ensemble dispersion, which defined terms second-central moments breakthrough curves. relate coefficients to properties underlying log-hydraulic conductivity field second-order stationarity. results are consistent with linear stochastic theory limit small log-conductivity variances, while extends high-variance cases. demonstrate validity comparison three-dimensional particle-tracking simulations advective media isotropic, exponential structure variances up five. This study contributes relating dispersion metrics porous-medium cases strong heterogeneity. article protected copyright. All rights reserved.