homework2_f10_sol

homework2_f10_sol - University of California, Davis...

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University of California, Davis Department of Chemical Engineering and Materials Science ECH 157 Process Dynamics and Control Ahmet Palazoglu HOMEWORK 2 / SOLUTION Fall 2010 1. (10 pts) An agitated batch tank is used to dissolve a solid component from a solid matrix into a liquid solvent medium. For this system, develop the modeling equation(s), stating all assumptions clearly. Obtain an analytical solution of this model that expresses the evolution of the concentration of the liquid solvent as a function of time. Solution: The agitated tank operates in the batch mode, i.e., no inlet or outlet flows. With no inflow or outflow, the total mass stays constant. The solution will then involve a liquid-phase component balance for the soluble material, combined with an expression for the rate of mass transfer of the solid into the liquid. The component material balance is expressed as: = solvent the to solid the of transfer of Rate solvent the in material the of on accumulati of Rate We make the assumption that the tank is well stirred so no spatial gradients exist. We can also assume that the liquid volume and the solid volume remain approximately constant during the process. For this system, the component balance would be written as () ) ( ) ( * * L L L L L L L L L L C C A k dt dC V C C A k C V dt d = = 1
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Here, V L denotes the liquid volume and C L is the concentration. k L is the mass transfer coefficient and A refers to the total interfacial area for mass transfer with C L * being the equilibrium value. We can obtain an analytical solution also considering that k L , A and C L * are constants as well: L L V At k L L L L e C C C C / 0 * * = For the case where the soluble component is leaching from an inert solid matrix, a separate solid phase component balance would be required to establish the solute
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homework2_f10_sol - University of California, Davis...

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