Mathematical analysis to optimize crystal growth

For the production of sodium sulfate, a brine is crystallized and crystals of glauber salt are generated by this process. The phase data related to the most common sodium sulfate minerals are as follows: mirabilite (Na2SO4 ⋅ 10H2O), tenardite (Na2SO4), glauberite (Na2SO4 ⋅ CaSO4), astrakanite (Na2SO4 ⋅ MgSO4 ⋅ 4H2O). The units commonly used to express the phases are moles of salt per 1000 moles of water. These latter units simplify the construction of the commonly employed four-sided Janecke phase diagrams. The cooling temperature or the speed with which the solution is cooled has an effect on the size and purity, as well as the amount of crystals produced. We seek to establish, through the population balance equations (PBE), which process variables can be modified to obtain a specific crystal size, as well as to validate the mathematical model that best predicts the amount of crystals precipitated as a function of temperature. The adjustment by least squares, cubic splines, pitzer equations and Lagrange interpolation is tested. The experimental results agree with the characteristics of the proposed models.