Exploration of the Behaviour of a Stochastic Transport Model Using Computational Experiments

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