Lumped models of convective solute transport in one-dimensional porous media are derived from the mass balance and the law of mass action. These models predict cumulative leaching from cumulative solute application and cumulative irrigation or rainfall. The solutes can be subject to adsorption or exchange governed by a nonlinear isotherm. The most important feature of the models is that although the properties of the medium and the liquid phase are allowed to be nonuniform, application requires only knowledge of the integrated moisture storage and adsorption isotherm over the medium section under consideration. Sufficient conditions are derived for the validity of lumped models and convenient expressions for evaluation of the model output are given. The results will be applied in part 2 of this paper, forthcoming, which will deal with convective solute transport along fixed streamlines in three-dimensional porous media.