The application of photocatalysis for wastewater treatment on an industrial scale has been partially impeded by the lack of simple mathematical models and optimisation studies. In this paper, a mathematical model (LSSE-LSPP model) for a laminar falling him slurry (LFFS) photocatalytic reactor is presented. The model is expressed in terms of five dimensionless parameters and can be solved with a minimal number of simple integrations. Model predictions are presented for different reaction kinetics and model parameters. As the parameters used in the model can be readily estimated from real systems, the model may be used for scale-up. A study of the sensitivity of the model to variations of the model parameters and validation of the model with experimental results of the oxidation of salicylic acid in a pilot-scale LEES photocatalytic reactor are presented in Part II of this paper.