Modeling Problem: Consider a CSTR reactor with flash product separation as shown in the schematic below. Fresh feed enters the reactor with a volumetric flow rate q [L/min] and a constant feed concentration Cao [mol/L]. The reaction A→B occurring only in the reactor is a 1st order reaction with rate constant k [1/min]. The reaction mixture containing A and B is removed from the reactor at a volumetric flow rate 2 q, i.e., twice as fast as fresh feed is added. The reactor outlet is then separated in a flash unit forming 2 phases. The lighter phase has a concentration equal to 1.5 Ca(t) of species A and 0.5 CB(t) of species B. This reactant-rich phase is recycled back to the reactor with the volumetric flow rate q. The remainder is in the heavier phase, which is the final product and removed with the flow rate q from the flash separation unit. Assumptions: • Uniform concentration of A and B in reactor. The reaction occurs only in the reactor, rate of production of B = r = kCa Constant volume and density in reactor and flash separator. • All flow rates are volumetric flow rates [L/min] and all concentrations are in [mol/L]. Schematic: Fresh Feed: q, Cao CA(t), Ga(t) 1.5 C,(t) 0.5 C,(t) 29 0.5 CA(t) Product: q 1.5 C,(t) Formulate material balances for species A and B in the reactor and give your (Ca(t) (Ca'(t)` sult in matrix notation, ie, () = 4E8) +9(). For certain values of q, V, and k the problem takes the form: r() - (? )r+) Y' (t) Ive this nonhomogeneous system of equations.
Modeling Problem: Consider a CSTR reactor with flash product separation as shown in the schematic below. Fresh feed enters the reactor with a volumetric flow rate q [L/min] and a constant feed concentration Cao [mol/L]. The reaction A→B occurring only in the reactor is a 1st order reaction with rate constant k [1/min]. The reaction mixture containing A and B is removed from the reactor at a volumetric flow rate 2 q, i.e., twice as fast as fresh feed is added. The reactor outlet is then separated in a flash unit forming 2 phases. The lighter phase has a concentration equal to 1.5 Ca(t) of species A and 0.5 CB(t) of species B. This reactant-rich phase is recycled back to the reactor with the volumetric flow rate q. The remainder is in the heavier phase, which is the final product and removed with the flow rate q from the flash separation unit. Assumptions: • Uniform concentration of A and B in reactor. The reaction occurs only in the reactor, rate of production of B = r = kCa Constant volume and density in reactor and flash separator. • All flow rates are volumetric flow rates [L/min] and all concentrations are in [mol/L]. Schematic: Fresh Feed: q, Cao CA(t), Ga(t) 1.5 C,(t) 0.5 C,(t) 29 0.5 CA(t) Product: q 1.5 C,(t) Formulate material balances for species A and B in the reactor and give your (Ca(t) (Ca'(t)` sult in matrix notation, ie, () = 4E8) +9(). For certain values of q, V, and k the problem takes the form: r() - (? )r+) Y' (t) Ive this nonhomogeneous system of equations.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Modeling Problem: Consider a CSTR reactor with flash product separation as
shown in the schematic below. Fresh feed enters the reactor with a volumetric
flow rate q [L/min] and a constant feed concentration Ca0 [mol/L]. The reaction
A→B occurring only in the reactor is a 1st order reaction with rate constant k
[1/min]. The reaction mixture containing A and B is removed from the reactor at
a volumetric flow rate 2 q, i.e., twice as fast as fresh feed is added. The reactor
outlet is then separated in a flash unit forming 2 phases. The lighter phase has a
concentration equal to 1.5 CA(t) of species A and 0.5 CB(t) of species B. This
reactant-rich phase is recycled back to the reactor with the volumetric flow rate
q. The remainder is in the heavier phase, which is the final product and removed
with the flow rate q from the flash separation unit.
Assumptions:
Uniform concentration of A and B in reactor.
• The reaction occurs only in the reactor, rate of production of B =r = kCA
Constant volume and density in reactor and flash separator.
• All flow rates are volumetric flow rates [L/min] and all concentrations are
in [mol/L].
Schematic:
Fresh Feed: q, CA.o
C,(t), Ca(t)
|1.5 Ca(t)
29
0.5 C,(t)
0.5 Calt) Product: q
1.5 G,(t)
Formulate material balances for species A and B in the reactor and give your
sult in matrix notation, i.e.,
(CA'(t)
\Cg'(t).
8) + 94).
For certain values of q, V, and k the problem takes the form:
r'(1) = (} )r) +G)
-2
-3
Ive this nonhomogeneous system of equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2140facb-0981-40cd-bf23-81e224855fc4%2F2fae95c1-4a1a-45ba-9f8a-04c99e5586df%2Fcs1vwxf_processed.png&w=3840&q=75)
Transcribed Image Text:Modeling Problem: Consider a CSTR reactor with flash product separation as
shown in the schematic below. Fresh feed enters the reactor with a volumetric
flow rate q [L/min] and a constant feed concentration Ca0 [mol/L]. The reaction
A→B occurring only in the reactor is a 1st order reaction with rate constant k
[1/min]. The reaction mixture containing A and B is removed from the reactor at
a volumetric flow rate 2 q, i.e., twice as fast as fresh feed is added. The reactor
outlet is then separated in a flash unit forming 2 phases. The lighter phase has a
concentration equal to 1.5 CA(t) of species A and 0.5 CB(t) of species B. This
reactant-rich phase is recycled back to the reactor with the volumetric flow rate
q. The remainder is in the heavier phase, which is the final product and removed
with the flow rate q from the flash separation unit.
Assumptions:
Uniform concentration of A and B in reactor.
• The reaction occurs only in the reactor, rate of production of B =r = kCA
Constant volume and density in reactor and flash separator.
• All flow rates are volumetric flow rates [L/min] and all concentrations are
in [mol/L].
Schematic:
Fresh Feed: q, CA.o
C,(t), Ca(t)
|1.5 Ca(t)
29
0.5 C,(t)
0.5 Calt) Product: q
1.5 G,(t)
Formulate material balances for species A and B in the reactor and give your
sult in matrix notation, i.e.,
(CA'(t)
\Cg'(t).
8) + 94).
For certain values of q, V, and k the problem takes the form:
r'(1) = (} )r) +G)
-2
-3
Ive this nonhomogeneous system of equations.
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