Bibliographic Details
| Title: |
Mathematical modeling of a pH swing precipitation process and optimal model design. |
| Authors: |
Hiremath, Sandesh Athni, Hegde, Chinmay, Voigt, Andreas |
| Source: |
Applied Mathematics for Modern Challenges; Jun2026, Vol. 8, p1-53, 53p |
| Subject Terms: |
Precipitation (Chemistry), Calcium carbonate, Stochastic partial differential equations, Stochastic differential equations, Particle size distribution, Artificial neural networks, Chemical kinetics, Mathematical models |
| Abstract: |
In this work we consider the semi-batch process of precipitation of calcium carbonate solids from a solution containing calcium ions by adjusting the pH of the solution. The change in pH is induced either by the addition of an alkaline solution such as sodium hydroxide (NaOH) or by the addition of carbon dioxide gas (CO2) to the given ionic solution. Under this setup we propose a system of degenerate stochastic partial differential equations that is able to explain the dynamical behavior of the key components of precipitation process. In particular, we propose a semi-linear advection equation for the dynamics of particle size distribution (PSD) of the precipitated particles. This is in turn coupled with a system of stochastic differential equations (SDEs) that is able to explain the chemical kinetics between calcium ions (Ca2+), calcium carbonate (CaCO3) in aqueous state, and pH of the solution. The resulting coupled system is first mathematically studied, in particular conditions for the existence of a mild-solution is established and also the long time behavior of the system is established. Following this we consider the validation of the model using experimentally obtained lab-scale data. To this end, we propose three methods to fit the model with the data which also validates the suitability of the proposed model. The three methods include manual intuitive tuning, the classical forward backward SDE (FBSDE) method, and finally a DNN based method. The FBSDE method is based on the stochastic optimal control formulation for which we provide the necessary and sufficient condition for the existence of an optimal solution. Lastly, we compare the three methods and show that DNN method is the best in terms of the lowest error and as the most economical in terms of computational resources necessary during online use. [ABSTRACT FROM AUTHOR] |
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| Database: |
Complementary Index |