Use of the generalized integral transform method for solving equations of solute transport in porous media

The generalized integral transform technique (GITT) is applied to solve the one-dimensional advection±dispersion equation (ADE) in heterogeneous porous media coupled with either linear or nonlinear sorption and decay. When both sorption and decay are linear, analytical solutions are obtained using the GITT for one-dimensional ADEs with spatially and temporally variable ̄ow and dispersion coecient and arbitrary initial and boundary conditions. When either sorption or decay is nonlinear the solutions to ADEs with the GITT are hybrid analytical±numerical. In both linear and nonlinear cases, the forward and inverse integral transforms for the problems described in the paper are apparent and straightforward. Some illustrative examples with linear sorption and decay are presented to demonstrate the application and check the accuracy of the derived analytical solutions. The derived hybrid analytical±numerical solutions are checked against a numerical approach and demonstratively applied to a nonlinear transport example, which simulates a simpli®ed system of iron oxide bioreduction with nonlinear sorption and nonlinear reaction kinetics. Ó 2000 Elsevier Science Ltd. All rights reserved.