Exploration of behaviour of a stochastic transport model using computational experiments

Abstract

Fickian assumptions are used in deriving the advection-dispersion equation which models the solute transport in porous media. The hydrodynamic dispersion coefficient defined as a result of these assumptions has been found to be scale dependent. Kulasiri and Verwoerd [1999] developed a stochastic computational model for solute transport in saturated porous media without using Fickian assumptions. The model consists of two main parameters; correlation length and variance, and the velocity of solute was assumed as a fundamental stochastic variable. In this paper, the stochastic model was investigated to understand its behaviour. As the statistical nature of the model changes with the parameters, the computational solution of the model was explored in relation to the parameters. The variance is found to be the dominant parameter, however, there is a correlation between two parameters and they influence the stochasticity of the flow in a complex manner. We hypothesised that the variance is inversely proportional to the pore size and the correlation length represents the geometry of flow. The computational results of different scales show that the hypotheses are reasonable. The model illustrates that it could capture the scale dependence of dispersivity and mimic the advection-dispersion equation in more deterministic situations.