@MISC{Dean_stochasticdifferential, author = {D. W. Dean}, title = {Stochastic Differential Equations In Transport}, year = {} }

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Abstract

This report is intended to explain our use of stochastic differential equations as mathematical models of contaminant transport in highly heterogeneous environments. The two major components in the stochastic model are a drift term and a dispersion term. The drift term is the expected velocity of the fluid particle along its streamline and the dispersion term is derived from the velocity field. The details of the development the dispersion term are found in Dean[14], Dean and Russell[15]. This report focuses on the connection between the model stochastic differential equations and their associated partial differential equations. Ito's formula is used to explain the relationship between the stochastic differential equation and the advection-dispersion equation. By solving the stochastic differential equation via the Monte Carlo method, contaminant plumes are produced. The effectiveness of a remediation well is tested with this approach using actual data from flow tank experiments conduc...