pset10_soln - 10.37 Spring 2007 Problem Set 10 Solutions 1...

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10.37 Spring 2007 Problem Set 10 Solutions 1. a) Yes, the reaction is limited by external diffusion. b) Table 12-1 shows that external diffusion-limited ra varies with U 1/2 and nearly linearly with T. This is the case for: F T0 = 10 mol/hr, all T F T0 = 100 mol/hr, about 362K < T < 375K c) Yes, the reaction is “reaction-rate-limited”. d) According to Fogler, r A varies exponentially with both reaction-rate-limitations and internal- diffusion-limitations, and is nearly independent of F T0 . However, rA varies more with T more strongly in the reaction-rate limited regime. So, the reaction-rate-limitation is overcome before the internal-diffusion-limitation as T is increased. This is the case for: T < 362K, F T0 = 100 mol/hr T < 365K, F T0 > 1000 mol/hr e) Yes, the reaction is limited by internal diffusion. f) Internal-diffusion limitations are seen at: 367K < T > 377K, F T0 > 1000 mol/hr ' mol actual _ rate ( external _ lim ) r A 10 hr ,360 K .25 g) Ω = ideal _ rate ( rxn _ lim ) = r A ' 5000 mol ,360 K .70 = 0.36 hr ' mol actual_rate ( internal_lim ) r A 5000 hr ,367 K h) η = ideal_rate ( rxn_lim ) = ' mol r A 5000 ,367 K hr Extrapolate the reaction-rate limited portion of the F T0 = 5000 mol/hr curve up to 367 K. 1.2 η = 0.8 1.5 i) Fort a first order reaction with spherical pellets: η = φ 3 2 ( φ 1 coth φ 1 1 ) = 0.8 1 Solve: φ 1 = 2.0 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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C sinh ( ) 1 φ λ Ψ = C A A , S = λ sinh φ 1 1 with λ = r / R = 1/ 2 1 sinh ( ) mol ( ) φ λ sinh 1 mol A C A , S λ sinh φ = 1 L ( ) sinh ( ) 2  = 0.65 L C = 1 2 1 j) For a given F T0 , the reaction rate will increase either exponentially or linearly with T (meaning the needed pipe length to achieve a certain conversion will decrease either exponentially or linearly with T). external diffusion limited L rnal diffusion limited Rxn limited ex inte int ternal diffusion limited L ernal diffusion limited Rxn limited T For a given T, increasing the flowrate will increase the pipe length needed for a given conversion. However, while in the external diffusion limited region, an increase in F T0 also increases the reaction rate (i.e. decreases the pipe length). The higher r A will offset somewhat the effect of the higher flow rate, and therefore the needed pipe length will increase slowly with F T0 while in the external-diffusion limited region. When the process is internal-diffusion or rxn- rate limited, r A no longer increases with F T0 , so the pipe length needed for a given conversion will increase sharply. L external diffusion limited no external limitations L external diffusion limited limitations F T0 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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