This paper, the first of two parts [see Abrams and Loague, this issue], takes the compartmentalized approach for the geochemical evolution of redox zones presented by Abrams et al.  and embeds it within a solute transport framework. In this paper the compartmentalized approach is generalized to facilitate the description of its incorporation into a solute transport simulator. An equivalent formulation is developed which removes any discontinuities that may occur when switching compartments. Rate-limited redox reactions are modeled with a modified Monod relationship that allows either the organic substrate or the electron acceptor to be the rate-limiting reactant. Thermodynamic constraints are used to inhibit lower-energy redox reactions from occurring under infeasible geochemical conditions without imposing equilibrium on the lower-energy reactions. The procedure used allows any redox reaction to be simulated as being kinetically limited or thermodynamically limited, depending on local geochemical conditions. Empirical reaction inhibition methods are not needed. The sequential iteration approach (SIA), a technique which allows the number of solute transport equations to be reduced, is adopted to solve the coupled geochemical/solute transport problem. When the compartmentalized approach is embedded within the SIA, with the total analytical concentration of each component as the dependent variable in the transport equation, it is possible to reduce the number of transport equations even further than with the unmodified SIA. A one-dimensional, coupled geochemical/solute transport simulation is presented in which redox zones evolve dynamically in time and space. The compartmentalized solute transport (COMPTRAN) model described in this paper enables the development of redox zones to be simulated under both kinetic and thermodynamic constraints. The modular design of COMPTRAN facilitates the use of many different, preexisting solute transport and geochemical codes. The companion paper [Abrams and Loague, this issue] presents examples of the application of COMPTRAN to field-scale problems.