MONTE-CARLO SIMULATION AND EFFECTIVE-MEDIUM APPROXIMATION IN SUBSURFACE FLOW MODELING

A refined Monte Carlo (MC) simulation procedure an an Effective Medium Approximation (EMA) are presented for solving the stochastic subsurfa ce flow problem. The refined MC simulation procedure uses analytical m eans to estimate the sample size by controlling the error incurred in using the sample average in place of its population mean at a chosen c onfidence level for the pressure head. Also, an unbiased estimator of the pressure head that takes advantage of its correlation with the sat urated conductivity to reduce its variance is proposed. This reduced v ariance results in a smaller width of uncertainty about the predicted pressure head thereby improving the precision. The EMA permits one to solve the stochastic subsurface flow problem in a single run to genera te the expected pressure head field with the aid of a field-scale effe ctive hydraulic conductivity that has a form similar to the Gardner eq uation. Both the MC and the EMA approaches perform well when applied t o example problems taken from the literature.