In this paper, we study the properties of a geochemical model involving aqueous and precipitation-dissolution reactions at a local equilibrium. By reformulating the model as an equivalent optimization problem, we prove existence and uniqueness of a solution. It is classical in thermodynamic to compute diagrams representing the phases of the system. We introduce here the new precipitation diagram that describes the mineral speciation in function of the parameters of the system. Using the polynomial structure of the problem, we provide characterizations and an algorithm to compute the precipitation diagram. Numerical computations on some examples illustrate this approach.