Calcium carbonate scale formation is a well known problem for water producing wells. Although there are several types of scale forming processes, we investigate the case of calcium carbonate precipitation when the degassing of CO₂ causes the calcium equilibrium concentration to decrease towards a production well. We study a simplified system of carbonate chemistry, which allows for analytical expressions for the porosity loss as a function of time. The precipitation process normally goes from flow-limited away from the well to precipitation-limited close to the well. We derive an expression that estimates the transition zone between these two regimes. Furthermore, we present analytical estimates for the porosity reduction at a given radius as a function of time, including an estimate for each of these precipitation regimes. These analytical results are tested against numerical solutions for the porosity loss, which account for the full set of equations of the model. The analytical models give an accurate estimate of the linear porosity reduction with time, until at least half the porosity is lost. Examples of scale formation are given for the two regimes. Reasonable values for the precipitation kinetics indicate that most production operations have a kinetics-limited regime close to the well. The models also show that this type of scale formation takes place very close to the wells, typically within a few well radii from the walls of the well.