Process description Consider a jacketed continuous stirred tank reactor (CSTR) shown below: Fo, CAO, TO Fjo. Tio Fjo. T

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Process Description Consider A Jacketed Continuous Stirred Tank Reactor Cstr Shown Below Fo Cao To Fjo Tio Fjo T 1 (60.33 KiB) Viewed 42 times

Process description Consider a jacketed continuous stirred tank reactor (CSTR) shown below: Fo, CAO, TO Fjo. Tio Fjo. T A B-C Fo, CAT The following series of reactions take place in the reactor: A "1, B2C where A + B is a highly exothermic, first-order reaction, and B + C is a first-order reaction that generates a negligible amount of heat. The reactions follow an Arrhenius rate law: r = kloe-Es/RTCA r2 = k20e-E/RTCB where k10 and k20 are the pre-exponential factors (given in units of per time), E, and E, are the activation energies, and R is the gas constant.
The reactor is fed by species A in an inert solvent at temperature To, concentration CAO and volumetric flow rate Fo. The effluent stream leaves the reactor at concentrations CA, CB, Cc, and temperature T. The liquid contents of the reactor are well-mixed (tem- perature and composition are uniform) and have a constant density (p), liquid hold-up volume (V), heat of reactions (AHand AH, for reactions 1 and 2, respectively) and heat capacity (Cp). The jacket is fed by cooling water at temperature T;o and flow rate Fjo. The overall heat transfer coefficient and heat transfer area of the jacket are U and A, respectively. The effluent stream leaves the jacket at temperature T;. The jacket water is assumed to have a uniform temperature. The material and energy balances that describe the dynamic behavior of the process have the following dimensionless variable form: dr =1 - 11 - Da exp(-Ēj/13).11 de d.x2 -22 + Da exp(-Ē1/13).11 - Da exp(-Ē2/13).12 de d.13 = 130 13+ Da exp(-Ē/13)?ı + Da'exp(-Ē2/13).22 - Ū(E3 – ) de dre = €162(140 – 14) + Ū€163(13 – 14) de (1) where: I1 = CA/CA: dimensionless concentration of species A in the reactor 22 = CB/CAo: dimensionless concentration of species B in the reactor 13 = T/Tref: dimensionless temperature of the reactor 14 = Tj/Tref: dimensionless temperature of the jacket 130 = To/Tref: dimensionless temperature of the reactor inlet stream 140 = T;0/Tref: dimensionless temperature of the jacket inlet stream 0 = Fot/V: dimensionless time Tref is the reference temperature and the remaining parameters (Dan, Daz, Daí, Dan, Ē, Ē2, Ū, €1, 62 and €3) are dimensionless process parameters. Use the temperature of the reactor as the controlled and measured output (i.e., y = 13 – 73 where i3 is the steady state value), the temperature of the jacket inlet stream as the manipulated input (i.e., u = 140 - 740 where 740 is the steady state value), and the temperature of the reactor inlet stream as the disturbance (i.e., d= I30 – 530 where T30 is the steady state value).
2. (30 pts.) For the model of (1) and for the following set of parameters: Da; = 10, Da, = 107, Da = 1.5 x 10®, Da', = 0 (i.e., B C generates a negligible amount of heat), Ēj = 1.0066, Ē, = 1.0532, Ū = 8, €1 12.5, €2 = 40 and 63 = 1, and for the following steady state values of 730 0.025, 140 0.025, compute the three steady states of the nonlinear dynamic system. = =