Probabilistic simulation of advection-reaction-dispersion equation using random lattice Boltzmann method

Mass transfer is subject to numerous sources of uncertainties due to scarcity of observational data. In this research, a numerical procedure was developed for the probabilistic study of a two-dimensional advection-dispersion problem, while considering chemical reactions. Innovatively, the lattice Boltzmann method was coupled with the concept of random field theory for the probabilistic simulations. The effects of various coefficients of variations (COV) and a number of autocorrelation distances were considered for the stochastic parameters, including dispersion coefficient, pore velocity, and the reaction term. The results indicated that the introduced probabilistic framework can be employed to effectively describe the effects of uncertainties in parameters related to the advection-dispersion equation. Moreover, it was deduced that the mass travel time and the time-concentration curves were influenced significantly by the variations of COV and autocorrelation distance for pore velocity. Interestingly, the mass transfer in the transverse direction increased (through the dispersion phenomenon) with a rise in the values of COV for longitudinal pore velocity. However, different values of COV and autocorrelation distances for the dispersion coefficient and the reaction term caused small alterations in the mass travel time and time-concentration curve. (C) 2019 Elsevier Ltd. All rights reserved.