A mathematical model has been developed for simulating the one-dimensional transport of solutes in a saturated porous medium. The numerical model, GCHEMFLOW (geochemistry and fluid flow), considers dispersion/diffusion, convection, ion exchange, the formation of complexes in the aqueous phase, the dissociation of water, competitive adsorption of organics, and the biodegradation of selected organics. This model was developed to predict the extent of process liabilities of in situ energy extraction. The geochemical equilibrium equations are solved simultaneously with the partial differential equations (PDEs) describing the convection/diffusion behavior of the solutes and the PDE for saturated flow of water through porous media. The resulting system of algebraic and differential equations are discretized with respect to space and integrated across time using Newton-Raphson iteration with variable time stepping. The discretization is done implicitly so that the unknown variables - pressure, velocity, and species concentrations - are determined simultaneously throughout the reservoir at a future time. A consistent set of model compounds consisting of both organic and inorganic species is selected for debugging and evaluating numerical solution technique characteristics. This report details the mathematical representations of the models fundamental equations, the numerical techniques used for obtaining solutions, the necessary model input data, and the output from the model. 33 refs.