lec06_correction

# lec06_correction - output solution is vanishingly small lim...

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Consider the unconstrained optimization of a CSTR with volume V. A B r = k [ A ] q [A] 0 [A] [B] V The goal is to maximize F B with respect to changes in the volumetric flow rate, q. F B = q [ B ] Steady state material balances on species A and B give: 0 = F A 0 F A rV = q ( [ A ] 0 [ A ] ) kV [ A ] 0 = F B 0 F B + rV = − q [ B ] + kV [ A ] Hence, [ B ] = k [ A ] ( V / q ) and F B = rV = k [ A ] V ; thus production of B is maximized when [A] takes its maximum value, which is [A] 0 . Continuing with the material balances, we find: [ A ] = [ A ] 0 = [ A ] 0 1 + ( kV / q ) 1 + k τ When Da = k τ << 1, [A] goes to [A] 0 . F B = rV = kV [ A ] = kV [ A ] o = kV [ A ] o 1 + k τ 1 + kV / q o lim F B = lim kV [ A ] = kV [ A ] 0 q →∞ q →∞ 1 + kV / q Unfortunately, in the limiting case of infinite flow rate, the concentration of B in the
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Unformatted text preview: output solution is vanishingly small: lim[ B ] = lim ( k [ A ] ( V / q )) = lim ⎜ ⎜ ⎛ k [ A ] 0 ( V / q ) ⎟ ⎞ ⎟ = 0 . q →∞ q →∞ q →∞ ⎝ 1 + ( kV / q ) ⎠ Cite as: William Green, Jr., and K. Dane Wittrup, 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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