Stochastic Simulation of Solute Transport in Heterogeneous Formations: A Comparison of Parametric and Nonparametric Geostatistical Approaches

The Monte Carlo simulation of solute transport in heterogeneous formations generates equally likely realizations of hydraulic conductivity using geostatistical approaches. The available field data on hydraulic conductivity can be classified as hard data (i.e., measurements with a low degree of uncertainty) and soft data (i.e., measurements with a greater degree of uncertainty). Information on hydraulic conductivity should be honored in the generated realizations in order to reduce uncertainty in the simulation. The traditional parametric approaches, such as the Turning Bands (TUBA) method, are multi-Gaussian and make it difficult (if not impossible) to include the use of soft data. A recently developed nonparametric geostatistical approach, the Sequential Indicator Simulation (SIS) method, can incorporate soft data easily and generate any distribution functions not limited by multi-Gaussian. The main goal of this paper is to investigate the effects of incorporating soft data on solute transport simulations by using SIS. Two synthetic 2-D heterogeneous reference hydraulic conductivity fields, one with an isotropic multi-Gaussian underlying model and the other with an anisotropic non-Gaussian model, are sampled to obtain limited hard hydraulic conductivity data and a relatively large number of soft data. Based on the sampled data, realizations of simulated hydraulic conductivity fields are generated by using SIS for different cases depending on whether or not the soft data are used. TUBA is also used to generate realizations when only the hard data are used for the comparisons. Solute transport results are calculated by the Monte Carlo method. It is shown that when only limited hard data are available, SIS and TUBA provide similar simulation results which in these cases deviate from the results of the reference fields. The main conclusion of this study is that, by adding a relatively large number of soft data, the statistical features of the reference hydraulic conductivity fields are better characterized and transport simulation results are improved significantly. The uncertainties in predictions of both solute arrival time and arrival position are reduced when soft data are included. More investigations are needed to study the effects on solute transport of high continuity at extreme hydraulic conductivity values and the effects of incorporating large amounts of soft data with larger degrees of uncertainty, e.g., the soft data interpreted from seismic lines.