batch_reactor - − kN A H A dH A N A = Q& − kN A H B...

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HW6 Batch Reactor Balances It is not legitimate to simply take the CSTR enthalpy balance and set the flow terms to zero. This is an incorrect enthalpy balance on the reactor in batch mode. See below for a review of how to use thermodynamics in this situation. Given that there is negligible gas holdup in the reactor: N B ( t ) = N C ( t ) = 0 hence, dN B dN C = = 0 dt dt Enthalpy balance: dH d ( N A H A + N B H B + N C H C ) d ( N A H A ) dN A dH A = = = H A + N A dt dt dt dt dt dH = Q F B H B F C H C dt dN dH dt A H A + dt A N A = Q F B H B F C H C Batch Reactor mole balances: dN A dt = − kN A dN B = 0 = − F B , out + kN A dt F B , out = kN A dN C = 0 = − F C , out + 2 kN A dt F C , out = 2 kN A Plugging in the three mole balance relationships into the enthalpy balance we find:
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Unformatted text preview: − kN A H A + dH A N A = Q & − kN A H B − 2 kN A H C dt dH A N A = Q & − kN A ( H B + 2 H C − H A ) = Q & − kN A ∆ H rxn ( T ) dt dH A dT = c dt p , a dt dT = Q & − kN A ∆ H rxn ( T ) = Q & − km A ∆ H ˆ rxn ( T ) dt N A c p , a m A c ˆ p , a Cite as: David Adrian, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]....
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