Stochastic and Deterministic Controls on Pore Size Evolution During Cementation in Porous Geological Media: A Population Dynamics Approach

Abstract The distribution of pore sizes in a rock evolves continuously throughout its diagenetic history, strongly affecting flow and storage properties. One of the most important drivers of this evolution is mineral cementation, although existing models have not simultaneously represented the distinct effects of both carbonate and quartz cement within a single framework. Here we develop a modified population dynamics model that represents cementation as a combination of deterministic, size-dependent pore closure and stochastic, size-independent porosity reduction. We test the model against pore size distributions derived from digital rock image analysis of three sandstone samples with contrasting cementation histories, and demonstrate that the hybrid approach outperforms both purely deterministic and purely stochastic models. Carbonate cement preferentially occludes large pores, truncating the tail of the pore size distribution and disproportionately reducing permeability relative to the volume of porosity lost. Quartz cement, by contrast, preferentially reduces the abundance of smaller pores through uniform grain-surface overgrowth, leaving the largest flow pathways largely intact. Analysis of the optimized model parameters reveals that the deterministic component is only well-constrained where carbonate cementation is sufficiently abundant to impose a detectable size-selective signature. Our results demonstrate that the framework provides a computationally efficient basis for connecting cementation history to pore structure evolution in porous media.