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prosess model for series of isothermal constant holdup CSTR.
- 1. CSTR with variable hold up Active Learning Assignment on Prepared By: Patel Meet J. (150490105035) Guided By: Prof. Darshan Sarang Asst. Professor Chemical Engg. Dept. S. N. Patel Institute of Technology and Research Centre Chemical Engineering Department SEMESTER – VIII SUBJECT – PMSO (2180503)
- 2. 2 Process model for series of isothermal constant hold up CSTR:- F0 F1 CA1 F2 CA2 F3 CA3 V1 K1 T1 V2 K2 T2 V3 K3 T3 • Basis and Assumptions A → B (first order reaction) Compositions are molar and flow rates are volumetric Constant V, ρ, T • Overall Mass Balance 𝑑ρ𝑉 𝑑𝑡 = ρ𝐹0 − ρ𝐹1 = 0 i.e. at constant V, F3 =F2 =F1 =F0 ≡ F So overall mass balance is not required!
- 3. 3 • F0 = Volumatric flow rate to tank-1 • CA0 = Inlet concentration • V1 = Volume of CSTR-1 • K1 = Rate constant • ρ = Constant Density • Changes from previous case: V of reactors (and F) varies with time, Reaction is nth order(Where n=1) • Parameters to be known: k1, k2, k3, n • Disturbances to be specified: CA0, F0 • Unknown variables: CA1, CA2, CA3, V1, V2, V3, F1, F2, F3
- 4. 4 • Component A mass balance on each tank :- 𝑑𝐶 𝐴1 𝑑𝑡 = 𝐹 𝑉1 𝐶 𝐴0 − 𝐶 𝐴1 − 𝑘1 𝐶 𝐴1 𝑑𝐶 𝐴2 𝑑𝑡 = 𝐹 𝑉2 𝐶 𝐴1 − 𝐶𝐴2 − 𝑘2 𝐶 𝐴2 𝑑𝐶 𝐴3 𝑑𝑡 = 𝐹 𝑉3 𝐶 𝐴2 − 𝐶𝐴3 − 𝑘3 𝐶 𝐴3 kn depends upon temperature kn = k0 e-E/RTn where n = 1, 2, 3 Specified variables F and CA0 known but not constant. Simplify the above constant V, T and putting τ = V/F
- 5. 5 • If throughput F, temperature T and holdup V are same in all tanks, then for τ = V/F . 𝑑𝐶 𝐴1 𝑑𝑡 + 𝐶 𝐴1 𝑘 + 1 τ = 1 τ 𝐶 𝐴0 𝑑𝐶 𝐴2 𝑑𝑡 + 𝐶𝐴2 𝑘 + 1 τ = 1 τ 𝐶 𝐴1 𝑑𝐶 𝐴3 𝑑𝑡 + 𝐶𝐴3 𝑘 + 1 τ = 1 τ 𝐶 𝐴2 • In this way, only forcing function variable to be specified is CA0.
- 6. 6 • Mass Balances (Reactor 1) :- 𝑑𝑉1 𝑑𝑡 = 𝐹0 − 𝐹1 𝑉1 𝑑(𝐶𝐴1 ) 𝑑𝑡 = 𝐹0 𝐶 𝐴0 − 𝐹1 𝐶 𝐴1 −𝑉1 𝑘1(𝐶𝐴1 ) • Mass Balances (Reactor 2) :- 𝑑𝑉2 𝑑𝑡 = 𝐹1 − 𝐹2 𝑉2 𝑑(𝐶𝐴2 ) 𝑑𝑡 = 𝐹1 𝐶 𝐴1 − 𝐹2 𝐶 𝐴2 −𝑉2 𝑘2(𝐶 𝐴2) • Mass Balances (Reactor 3) :- 𝑑𝑉3 𝑑𝑡 = 𝐹2 − 𝐹3 𝑉3 𝑑(𝐶𝐴3 ) 𝑑𝑡 = 𝐹2 𝐶 𝐴2 − 𝐹3 𝐶 𝐴3 −𝑉3 𝑘3(𝐶 𝐴3)
- 7. 7 THANK YOU