Code No: 37063/37064

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IV B.Tech I Semester Regular Examinations,Nov/Dec 2009 PROCESS MODELING AND SIMULATION Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. Solve yn+1 - 2yn cos α+ yn−1 = 0.

[16]

2. Solve the following: y 0 (t) + y (t − 1) = t, if y(t)=0 for t ≤ 0.

ld .

[16]

3. Derive the mass balance equations for interacting and non-interacting tanks and also write the computer program for simulation. [16] 4. (a) Describe the ideal binary distillation with a neat sketch

or

(b) Write the Model questions for “Top tray” and “next to top tray” in an ideal binary distillation column. [8+8] 5. Consider a CSTR in which consecutive 1st order reactions A00 → B → C occur k1 k2 with exothermic heats of reaction A −→ B −→ C with exothermic heats of reaction λ1

λ2

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λ1 and λ2 . Write the energy equation.

[16]

6. A cup of coffee has an initial temperature of 74o C, but cools to 68o C in one minute when placed in a room with a temperature of 21o C. Let Tn be the temperature of the coffee after ‘n’ minutes (a) Write a difference equation which describes the change in temperature of the coffee from minute to minute (b) Solve the resulting difference equation.

nt

(c) Find the temperature of the coffee after 25 minutes.

[16]

7. Write short notes on the following: (a) Indcidence matrix

[8+8]

Aj

(b) Adjacency matrix.

8. A perfectly mixed, isothermal CSTR has an outlet weir. The flow rate over othe weir is proportional to the height of liquid over the weir, how to the 2.5 power. The weir height is hw . The cross sectional area of the tank is A. Assume constant k density. A 1st order reaction takes place in the tank. A → − B, Derive the model equations describing the system. [16] ?????

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Code No: 37063/37064

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IV B.Tech I Semester Regular Examinations,Nov/Dec 2009 PROCESS MODELING AND SIMULATION Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. Write the component continuity equations for a perfectly mixed batch reactor (no inflow or outflow) with first-order isothermal reactions.

ld .

(a) Simultaneous (b) Consecutive.

[8+8]

2. Solve: yn+1 - 4yn =3n

[16]

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3. Explain about Sequential modular approach with a neat flow chart in process plant simulation. [16] 4. Develop a mathematical model for ideal binary distillation column.

[16]

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5. An irreversible exothermic reaction is carried out in a single perfectly mixed nonisothermal CSTR. The reaction is A→ B The reaction is nth order in reactant A and has heat of react λ (energy units/mole of A reacted). Negligible heat losses and constant densities are assumed. To remove the heat of reaction, a cooling jacket surrounds the reactor. Cooling water is added to the jacket at a constant volumetric flow rate. Develop a mathematical model for the system assuming that the CSTR has a perfectly mixed cooling jacket. State all the assumptions made and explain the notations scheme used clearly. [16] 2 6. Solve yx+1 − 3yx+1 yx + 2y 2x = 0

[16]

Aj

nt

7. 8000 kg/h of a 5% by weight solution of acetaldehyde in toluene is to be treated with 5000 kg/h of water in a 6 theoretical stage extraction column operating under counter flow conditions. If the concentration of the feed conditions is suddenly changed to a 3% by weight solution, how long will it take for the extractor to settle down to steady state operation under the new condition? The equilibrium relation is Y = 2.2 X Where, Y = Kg of Acetaldehyde per Kg of water X = Kg of Acetaldehyde per Kg of toluene, The holdup per stage can be assumed to be constant at 750 Kg toluene; 300 Kg water. [16] 8. Write down a computer simulation program to carry out dew point calculations. [16] ?????

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Code No: 37063/37064

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IV B.Tech I Semester Regular Examinations,Nov/Dec 2009 PROCESS MODELING AND SIMULATION Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

(a) Continuity equation

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2. Write short note on:

ld .

1. An irreversible exothermic reaction is carried out in a single perfectly mixed nonisothermal CSTR. The reaction is A→B The reaction is nth order in reactant A and has heat of react λ (energy units/mole of A reacted). Negligible heat losses and constant densities are assumed. To remove the heat of reaction, a cooling jacket surrounds the reactor. Cooling water is added to the jacket at a constant volumetric flow rate. Develop a mathematical model for the system assuming that the CSTR has a lumped cooling jacket. State all the assumptions made and explain the notations scheme used clearly. [16]

(b) Component continuity equation

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(c) Energy equation (d) Equation of motion.

[4+4+4+4]

3. Solve the following differential difference equation : Y0 (t) + Y(t − 1) = t2 ifY(t) = 0fort ≤ 0

[16]

4. Solve yn+2 - 5yn+1 - 6yn = 2n.

[16]

nt

5. Develop finite difference approximation for multi stage distillation column and explain the method of solving is under various boundary conditions. [16] 6. (a) Distinguish between design mode and analysis mode in process simulation (b) What is tearing a system equations ? Discuss any one algorithm for this purpose. [16]

Aj

7. Write down a computer simulation program to carry out bubble point calculations. [16]

8. Write the model equations involved in a Batch reactor when it is in the cooling phase with a neat diagram. [16] ?????

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Code No: 37063/37064

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IV B.Tech I Semester Regular Examinations,Nov/Dec 2009 PROCESS MODELING AND SIMULATION Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Write down the uses of ‘batch reactor’.

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(b) Write the mathematical model of a batch reactor in which the reaction K1 K2 A −→ B, −→ C is taking place. [4+12]

2. Give the examples of chemical process applications described by the differential difference equations. Discuss about the solution options. [16]

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3. Write the component continuity equation for a CSTR in which a “simultaneous K2 K reaction” (first - order, isothermal) takes place A − → B, A −→ C. [16] 4. A chemical process is represented by the following set of equations : f1(x3,x4)=0 ; f2(x5,x2) =0 ; f3(x6) = 0 ; f4(x6,x1) = 0 ; f5(x3,x2) = 0 & f6 (x4,x5,x1) =0 Determine the following

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(a) Associated incidence matrix (b) Digraph of the process

(c) Associated adjacency matrix.

[16]

5. Derive the dynamic model for an ideal binary distillation column. State all the assumptions made. [16] 6. Solve yx+1 - yx + xyx+1 yx = 0, given y1 =2.

[16]

nt

7. An ice cube is dropped into a hot, perfectly mixed, insulated cup of coffee. List all assumption and define all terms. Develop the equations describing the dynamics of the system. [16]

Aj

8. Benzoic acid is continuously extracted from toluene using water as solvent in a cascade of stages in series. Each stage consists of (a) a mixture where vigorous stirring of the contents takes place and

(b) a settler where the mixture pumped from the mixer is allowed to settle into layers. The upper toluene layer and the lower water layer are removed separately. Develop a mathematical model to find the final fraction of benzoic acid extracted for the case of counter current operation. [16] ?????

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