Whereas most previous studies of biomass growth and biological clogging consider continuous biofilms, we investigate how the growth of biomass in the form of aggregates affects the permeability and the transport properties of porous media. This paper presents modeling of processes in a single pore, and a companion paper [Dupin et al., this issue] describes modeling over a network of pores. Each pore (channel) is seeded with initial biomass that consumes an electron donor and an electron acceptor according to dual Monod kinetics. Biomass is modeled as a continuous uniform isotropic hyperelastic material, whose expansion and deformation are governed by material mechanics stress-strain relations, unlike traditional approaches that use ad hoc empirical schemes. The Stokes flow, the advection-diffusion-reaction mass transport, and the biomass deformation partial differential equations are solved using finite elements. The solute transport problem is made more computationally efficient by controlling the time step discretization. Results from a simulation illustrate the methodology.