A mathematical model for the polymerization of ethylene using silica-supported chromium catalysts is presented, The fundamentals for the physical and chemical representation of the phenomenon are detailed. The emerging mathematical problem is attached and solved using a multiple, moving-boundary numerical scheme, Predictions are made using the model for the cases of low and high activity catalysts tested by experiments, and the results used to evaluate the model. ?The main feature of the model is its structural nature : catalyst characterization and morphology data are used to create a physical scheme that does not require tile assumptions concerning particle geometry, usually made In models. The initial catalyst fragmentation process is modeled using a pore-structure scheme based upon porosimetry data. The whole fragmentation sequence is treated as a set of steps that follow the actual rupture process of the initial solid into fragments with irregular shapes. Parameters are evaluated from data for the initial support, and time evolution is followed using a realistic interpretation of the pore filling process. A novel application of moving-boundary solution techniques permits a relatively simple mathematical scheme to handle the transport and reaction processes that take place in the polymerizing particle. Only the results obtained for the experimental laboratory conditions are analyzed. In subsequent parts, the case of thermal effects typical of industrial conditions will be discussed. The results obtained are in excellent agreement with the experimental data.