We present the unified multi-component cellular automaton (UMCCA) model, which predicts quantitatively the development of the biofilm's composite density for three biofilm components: active bacteria, inert or dead biomass, and extracellular polymeric substances. The model also describes the concentrations of three soluble organic components (soluble substrate and two types of soluble microbial products) and oxygen. The UMCCA model is a hybrid discrete-differential mathematical model and introduces the novel feature of biofilm consolidation. Our hypothesis is that the fluid over the biofilm creates pressures and vibrations that cause the biofilm to consolidate, or pack itself to a higher density over time. Each biofilm compartment in the model output consolidates to a different degree that depends on the age of its biomass. The UMCCA model also adds a cellular automaton algorithm that identifies the path of least resistance and directly moves excess biomass along that path, thereby ensuring that the excess biomass is distributed efficiently. A companion paper illustrates the trends that the UMCCA model is able to represent and shows a comparison with experimental results.