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Q: Calculate the production rate of crystals (in mass per unit time) and the dominant length of the crystal obtained at steady-state operation for
Q: Calculate the production rate of crystals (in mass per unit time) and the dominant length of the crystal obtained at steady-state operation for the following process. A water desalination company is crystallising the solution obtained from the retentate of the reverse osmosis unit. The highly concentrated solution is fed into a cooling crystallizer to precipitate the salt present in the solution. The crystallizer used operates continuously and is modelled as a Mixed Suspension Mixed Product Removal (MSMPR) unit. The feed of the crystallizer unit is at a temperature (T_in) of 24 degrees Celsius. Assume the crystallizer unit is at steady state and operates at 12 degrees Celsius. Also, the crystals have a cubic shape. Solubility of salt at 12C = 12 wt% Density of water = 1 103 kg m-, Density of salt = 1998 kg m-3 and Data to be used: Estimated kinetic parameters and system's temperature (T): Nucleation: Wnucl = 6 107 mh-1 Vnucl = 1.875 K Growth: W growth 7 10-4 m h1 V growth = 3.145 K Rate equations for the kinetics of nucleation and growth of the salt respectively: Vnucl T(lns) J = Wnucl S e\] G = Wgrowth (S 1) e Vgrowth T(S-1) [row], 'S' is the supersaturation of the mother phase where S=c/ceq) and T is the temperature of the system.
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