Natural organic matter (NOM) interferes with the adsorption of trace organic compounds on porous adsorbents such as powdered activated carbon (PAC) by pore blockage and direct competition for adsorption sites. The competitive effect of NOM in flow-through systems in which the retention time of the PAC is greater than the hydraulic retention time of the system can be magnified because NOM from the influent water can continue to adsorb on the PAC retained in the system. As a result, the adsorption capacity and the diffusion coefficient of trace compounds can decrease as NOM from the influent water accumulates. In this study, a dynamic three-component adsorption model was developed to quantitatively describe the removal of a trace compound from water in flow-through PAC processes. The system was simplified by using p-dichlorobenzene (p-DCB) to represent the NOM fraction that competes directly with the target trace organic atrazine for adsorption sites and by using poly(styrene sulfonate) (PSS-1.8k) to represent large, pore-blocking NOM. The model was based on the homogeneous surface diffusion assumption with the adsorption capacity of atrazine being gradually adjusted using a simplified version of the ideal adsorbed solution theory model developed in this study. The surface diffusion coefficients of atrazine and p-DCB were modeled as a function of the surface concentration of the pore-blocking compound, PSS-1.8k. The model was verified experimentally with a PAC/microfiltration (MF) system. The use of single-solute adsorption parameters obtained from batch isotherm and kinetic tests resulted in good model predictions for the adsorption of atrazine and the two model compounds under operating conditions typical of PAC/MF systems. The model will be applied to study various operating conditions and other system parameters of PAC/membrane systems in part 2 of this study.