Supersaturation with respect to an active compound triggers several precipitation-related processes that may proceed (essentially concurrently) along the flow path. The interaction between fluid dynamics and physicochemical processes (i.e., nucleation, particle growth, and coagulation) leads to an axial variation of bulk properties (species concentration and particle size distribution) and of ionic and particulate deposition rates at the pipe wall. To simulate this complicated system, very simple hydrodynamics (plug flow) is combined with rather comprehensive modeling of physicochemical phenomena. Considerable effort is devoted to the optimization of computational requirements, thus developing a numerical algorithm efficient and flexible enough to cope with even more demanding future tasks such as the inclusion of mixing. The performance of the model is examined using, as a test case, the precipitation of a sparingly soluble salt under conditions typical for geothermal installations. An extensive study of the effects of the initial saturation ratio and of the tendency for particle coagulation on the deposition rate and on the particle size distribution along the pipe is carried out.