Consider a constant volume and isothermal continuous-stirred-tank-reactor (CSTR). One feed stream containing only reactant A enters the CSTR at a volumetric flow rate q, and one product stream leaves the reactor at the same flow rate containing reactant A and products B and C. A series reaction given by the following scheme occurs in the CSTR: 1₁ 12 A→B→C where r₁ and r2 are molar reaction rates per unit volume given by r₁ = k₁CA and r₂ = k₂CB. The volumetric flow rate to the reactor is constant, but the feed concentration CAo can vary. The CSTR design conditions follow: V = 1.0 m³, q=0.10 m³/min, k₁ = 0.10 min-¹, k₂ = 0.025 min-¹ CAO = 1.0 kgmol/m³, ¯Ã = 0.5 kgmol/m³, Ñ = 0.4kgmol/m³ Ao 'A Cc = 0.1kgmol/m³ (a) Derive the mathematical model for the CSTR and the transfer functions relating the concentrations of A, B and C in the product stream to the concentration of A in the feed stream. Obtain numerical values for all the time constants and steady- state gains. (b) Suppose the feed stream concentration of A suddenly decreases to CAO = 0.8 kgmole/m³ and remains at that value indefinitely. Determine the new steady-state concentrations of A, B and C in the product stream.
Consider a constant volume and isothermal continuous-stirred-tank-reactor (CSTR). One feed stream containing only reactant A enters the CSTR at a volumetric flow rate q, and one product stream leaves the reactor at the same flow rate containing reactant A and products B and C. A series reaction given by the following scheme occurs in the CSTR: 1₁ 12 A→B→C where r₁ and r2 are molar reaction rates per unit volume given by r₁ = k₁CA and r₂ = k₂CB. The volumetric flow rate to the reactor is constant, but the feed concentration CAo can vary. The CSTR design conditions follow: V = 1.0 m³, q=0.10 m³/min, k₁ = 0.10 min-¹, k₂ = 0.025 min-¹ CAO = 1.0 kgmol/m³, ¯Ã = 0.5 kgmol/m³, Ñ = 0.4kgmol/m³ Ao 'A Cc = 0.1kgmol/m³ (a) Derive the mathematical model for the CSTR and the transfer functions relating the concentrations of A, B and C in the product stream to the concentration of A in the feed stream. Obtain numerical values for all the time constants and steady- state gains. (b) Suppose the feed stream concentration of A suddenly decreases to CAO = 0.8 kgmole/m³ and remains at that value indefinitely. Determine the new steady-state concentrations of A, B and C in the product stream.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:Consider a constant volume and isothermal continuous-stirred-tank-reactor (CSTR).
One feed stream containing only reactant A enters the CSTR at a volumetric flow rate
q, and one product stream leaves the reactor at the same flow rate containing reactant
A and products B and C. A series reaction given by the following scheme occurs in
the CSTR:
A→B→C
where ri and r2 are molar reaction rates per unit volume given by ri = kıCA and r2 =
K2CB. The volumetric flow rate to the reactor is constant, but the feed concentration
CAo can vary. The CSTR design conditions follow:
V= 1.0 m³, q = 0.10 m³/min, kı
0.10 min-l, k2 = 0.025 min-!
CAo =1.0 kgmol/m', Ca = 0.5 kgmol /m', Cg = 0.4 kgmol /m
Cc = 0.1 kgmol/m³
3
´Ao
(a) Derive the mathematical model for the CSTR and the transfer functions relating
the concentrations of A, B and C in the product stream to the concentration of A
in the feed stream. Obtain numerical values for all the time constants and steady-
state gains.
(b) Suppose the feed stream concentration of A suddenly decreases to CAo = 0.8
kgmole/m3 and remains at that value indefinitely. Determine the new steady-state
concentrations of A, B and C in the product stream.
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