Modeling CSTRs in Series constant holdup, isothermal

1. CHE412 Process Dynamics and ControlBSc (Engg) Chemical Engineering (7th Semester)Week 3 (contd.)Mathematical Modeling (Contd.)Luyben (1996) Chapter 3 Stephanopoulos (1984) Chapter 5DrWaheedAfzal Associate Professor of Chemical Engineering Institute of Chemical Engineering and TechnologyUniversity of the Punjab, Lahorewa.icet@pu.edu.pk

2. Modeling CSTRs in Seriesconstant holdup, isothermal Basis and Assumptions A → B (first order reaction) Compositions are molar and flow rates are volumetric Constant V, ρ, T Overall Mass Balance i.e. at constant V, F3 =F2 =F1 =F0 ≡ F So overall mass balance is not required! F0 F1 CA1 V2 K2 T2 V1 K1 T1 F2 CA2 V3 K3 T3 F3 CA3 Luyben (1996)

3. Modeling CSTRs in Seriesconstant holdup, isothermal Component A mass balance on each tank (A is chosen arbitrarily) kndepends upon temperature kn = k0 e-E/RTn where n = 1, 2, 3 Apply degree of freedom analysis! Parameters/ Constants (to be known): V1, V2, V3, k1, k2, k3 Specified variables (or forcing functions): F and CA0 (known but not constant) . Unknown variables are 3 (CA1, CA2, CA3) for 3 ODEs Simplify the above ODEs for constant V, T and putting τ = V/F

4. Modeling CSTRs in Seriesconstant holdup, isothermal If throughput F, temperature T and holdup V are same in all tanks, then for τ= V/F (note its dimension is time) In this way, only forcing function (variable to be specified) is CA0.

5. Modeling CSTRs in Series Variable Holdups, nth order Changes from previous case: V of reactors (and F) varies with time, reaction is nth order 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 Mass Balances (Reactor 1) n Mass Balances (Reactor 2) n Mass Balances (Reactor 1) )n

6. Modeling a Mixing Process H2 H1 Basis and Assumptions F (volumetric), CA (molar); Well Stirred Feed (1, 2) consists of components A and B Enthalpy of mixing is significant Process includes heating/ cooling ρ is constant Stephanopoulos (1984) H3 Q in or out Overall Mass Balance Component Mass Balance 3

7. Modeling a Mixing Process Conservation of energy (recall first law of thermodynamics) (for constant ρ/ liquid systems is zero) Energy Balance enthalpy balance (h is energy/mass) We were familiar with energy ; how to characterize h(specific enthalpy) into familiar quantities (T, CA, parameters, …) H is enthalpy, h is specific enthalpy; CP is heat capacity, cP is specific heat capacity …. H2 H1 H3

8. Modeling a Mixing Process Since enthalpy depends upon temperature so lets replace h with h(T) enthalpy associated with ΔT was easy to obtain, how to obtain h(T0) and are molar enthalpy of component A and B and is heat of solution for stream i at T0. Put values of h in overall energy balance

9. Modeling a Mixing Process Re-arranging (and using component mass balance equations) If we assume cP1 =cP2 = cP3 =cP cp • If heats of solutions are strong functions of concentrations then and are significant • Mixing process is generally kept isothermal (how?)

10. Tips For Assessment (Exam)Introduction + Modeling (week 1-3) • Consult your class notes, board proofs, discussions • Stephanopoulos (1984) chapters 1-5, examples and end-chapter problems • Luyben (1996) chapter 3 page 40 to 74. Practice examples and end-chapter problems for chapter 3. In exam, you may be asked short descriptive questions to check your understanding of process control and to prepare a mathematical model for a chemical process or processes and to make the system exactly specified (i.e. Nf = 0)

11. Week 3Weekly Take-Home Assignment • Follow all the example modeling exercises in Luyben (1996) chapter 3 page 40 to 74. Practice these example processes. • Solve at least 10 end-chapter problems from Luyben(1996) chapter 3 (Compulsory) Submit before Friday (Feb 7) Curriculum and handouts are posted at: http://faculty.waheed-afzal1.pu.edu.pk/