A mathematical model for predicting porosity histories due to quartz overgrowth in quartz-rich sandstone reservoirs has been developed. The model neglects secondary dissolution porosity and other diagenetic processes such as compaction and precipitation of carbonate and clay minerals. Nevertheless, the model is straightforward and easy to use to calculate porosity. The calculated porosity corresponds to measured porosity of simple quartz-cemented sandstones in 27 wells in North and South America.

The model is based on fluid flow through initially porous, unlithified sands in which the fluid phase is saturated with Si(OH)₄ and is always in equilibrium with quartz. As the continuously circulating fluid migrates updip toward the basin edge, it cools, and quartz precipitates into the pore spaces causing a loss of porosity. Basinal fluid velocities may be calculated assuming (1) thermal convection and (2) hydrostatic pressure due to recharge at the edge of the basin. Porosity diagrams relating porosity to geothermal gradient, burial rate, and depth of burial are compared to thermal maturation models of source rocks, fluid flow history, and grain-size distribution. The rate of porosity reduction depends on the following variables in decreasing order of significance: buria rate, age, initial porosity, basin size (dip angle), fluid dynamics, initial permeability, and geothermal gradient.