A MODEL FOR POROSITY REDUCTION IN QUARTZITE RESERVOIRS BY QUARTZ CEMENTATION

Abstract

Quartz cementation is an important process of porosity reduction in sandstones. A mathematical model is presented for predicting the distribution and amount of quartz cement in a sandstone reservoir as a function of time and space. The approach combines kinetics and transport mechanism and incorporates the following assumptions: (1) no compaction during cementation, (2) transport of dissolved silica by advection, (3) surface-controlled growth, (4) sands simplified to a framework of spheres, and (5) isothermal system. The model predicts that low flow rates, small grain size, and higher temperatures favor limited volume of quartz cement because the pores are rapidly obstructed. Pervasive cementations are predicted in the presence of coarse-grain sands, high fluid flows, and low temperatures. Substantial volumes of quartz may occur within 250,000 years under conditions of shallow burial (T = 20°C, u = 10 m/y). During conditions of deeper burial and higher temperatures (T = 80°C), quartz cement should form during geologically rapid events rather than during the entire history of burial.SYMBOLSA0 initial interfacial area (m2)A interfacial area (m2)c concentration of silica in solution (kg per kg of fluid)ceq solubility of quartz (kg per kg of fluid)cin concentration of silica of the supersaturated solution entering the sands (kg per kg of fluid)k- precipitation rate constant (y-1)K apparent precipitation rate constant (y-1)M mass of solution (kg)N number of grains per m3r radius of the grains (m)dr increase of radius of the grains (m)Sg surface of one grain (m2)t time (y)T temperature (K)V representative elementary volume of rock (m3)Vf volume of fluid in V (m3)Vg volume of one grain (m3)Vq volume of quartz grains in V (m3)x distance from fluid entrance (m3)φ0 initial porosityφ porosityρw density of the solution (1000 kg/m3)ρq density of quartz (2650 kg/m3)u fluid flow (m/y)