PROGRAM ELECTIVE I
MODELLING AND SIMULATION IN FOOD PROCESSING
Max. Marks: 100 Duration: 3 hours
PART A
(Answer all questions; each question carries 3 marks) 1. Distinguish between probabilistic model and deterministic model.
2. Define degrees of freedom for a process model.
3. Distinguish between basic information flow diagram and basic integration block
diagrams.
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4. Develop the Component continuity equation for pseudo first order reaction which
takes place in CSTR.
5. Define radical kinetics with suitable examples.
6. Develop the general modeling scheme for any fluid flow problems.
7. Distinguish between distributed parameter model and lumped parameter model.
8. With simple example show that staged operations are modeled by difference
equations.
9. List any iterative convergence methods used in numerical simulations.
10. Compare and contrast between Euler’s explicit and Euler’s implicit methods.
PART B
(Answer one full question from each module, each question carries 14 marks) 11. a) Consider a plug flow reactor in which a first order reaction takes according to the
following stoichiometry A B. Concentration of A CA decreases in axial direction as A is consumed in the reaction. Density ρ, Velocity v and concentration CA can all vary with time and axial direction. Plug flow condition is assumed, it means that there is no velocity, density and concentration gradients in radial directions. Develop component continuity equation for component A and B for this reactor. (9) b) Explain in detail about principles of formulation of mathematical model (5)
[OR]
12. Explain in detail about the classification of models. (14) 13. a) Develop the mathematical model for a continuous, jacketed flow boiling system in
which the feed is supplied as a liquid and product is withdrawn as vapour. List out the assumptions made while developing model and represent the model using basic integration block diagrams. (9) b) Prove that the following Ordinary differential equation is stiff, when step size h ≥
2/a (5)
[OR]
14. A semi batch reactor is run at constant temperature by varying the rate of addition of one of the reactants, A. The irreversible, exothermic reaction is first order in reactants A and B.
A+B C
The tank is initially filled to its 40 percent level with pure reactant B at a concentration CPQ. Maximum cooling water flow is begun, and reactant A is slowly added to the perfectly stirred vessel. Develop the equations describing the system.
Without solving the equations, sketch the profiles of FA, CA and CB with time during the batch cycle. (14)
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15. a) Develop the reaction kinetics model for the following reaction that takes place in isothermal liquid phase CSTR. The input molar flow rate of the reactant is Fi(mol/min) and the molar flow rate of product is F0 (mol/min). The reaction stochiometry is given below (8)
A+ B C +D C+ B E A + E F
b) Develop a mathematical model for gas flowing through three tanks interconnected through valves. State all the assumptions made and make a pictorial representation of the model. (6)
[OR]
16. a) An open reservoir feed the water through a long pipe to an enclosed vessel compressing the gas space. Because the feed line has a large diameter, the momentum of water is significant level to compress the gas space. Construct the mathematical model that defines the transient pressure surge in the enclosed vessel.
State clearly all the assumptions made and sketch the information flow diagram. (12) b) State the significance rate limiting step in reaction kinetics models. (2) 17. Develop the mathematical model 15 stage binary distillation column for dynamic
simulation such that terminal compositions of the column can be controlled and state all the assumptions made in the formulation of model. (14)
[OR]
18. a) Develop the mathematical model for the Counter current double heat exchanger at transient conditions and give a pictorial representation of the model. State your assumptions. (8) b) Develop the mathematical model for multistage counter-current extraction unit with reaction for dynamic simulation and state all the assumptions. (6) 19. a) Consider a reaction A B carried out in a plug flow reactor. The differential
equation for species A is
u =-kCA
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The initial condition is: at z=0, CA=1 mol/m3. The rate constant of the reaction is 0.1 s
-1. Using Runge-Kutta fourth order method, determine the concentration of A at 5 m from entrance. Take u=1 m/s. (10) b) Distinguish between the truncation errors and round off errors of any numerical
scheme. (4)
[OR]
20. Consider a stirred vessel which initially contains 760 kg of solvent at 250C. 12 kg/min of solvent flows into the stirred vessel at 250C and exits out also at the same rate. At t=0 the flow of steam is started in a coil in the stirred vessel. The heat supplied by steam to the solvent is given by Q=UA(TS-T), where UA is the overall heat transfer coefficient multiplied by coil area through which heat exchange takes place and TS is the temperature of steam and is 1500. UA=11.5 kJ/min-K. The specific heat of the solvent is CP=2.3 kJ/kg-K. Show that
(0C/s)=0.023-0.000373T
i. Determine the solvent temperature after 50 min.
ii. Also determine the maximum temperature that can be reached in the tank.
(14) Syllabus
Module 1
Introduction to mathematical modelling: uses, principles of formulation, Classification of models –Simple vs. dynamic, Transport phenomena based vs statistical; fundamental laws of modelling, model building, modelling difficulties. Population balance models and applications; Empirical models; Model parameters estimation
Module 2
Mathematical models for simple operations: simple hydraulic tank, continuous flow tank, enclosed vessel, mixing vessel with and without reaction, steam jacketed vessel, steam jacketed vessel with mixing, continuous flow boiling system
Module 3
Modelling of Staged operations: Extraction, Distillation column, Modelling of Distributed systems- tubular reactor, heat exchangers, membrane separation process
Module 4
Basics of simulation: Introduction to flow sheet simulation; Sequential modular approach;
Equation oriented approach; Partitioning and tearing; recycle convergence methods, Simulation examples of fluid flow processes; Monte Carlo simulation. Inventory and queuing problem
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Module 5
Simulation of food process system: simple hydraulic tank, continuous flow tank, mixing vessel with and without reaction, Distillation column, heat exchangers
Text Books
1. Roger G.E Franks, Mathematical modelling in chemical engineering, John Wiley and sons, 1972
2. Luyben W.L, Process modelling, simulation and control for chemical engineers, McGraw Hill (ISE) 1990.
Reference Books
1. M.M. Denn, “Process Modelling”, Wiley, New York, (1990)
2. C.D. Holland and A.L. Liapis, “Computer Methods for solving Dynamic Separation Problems”, McGraw Hill, (1983)
3. C.D. Holland, “Fundamentals of Modelling Separation Processes “, Prentice Hall, (1975).
Course Contents and Lecture Schedule
No Topic No. of Lectures
1 Introduction to mathematical modelling 7 1.1 Uses, principles of formulation, Classification of models –Simple
vs. dynamic, Transport phenomena-based vs statistical;
3 1.2 Fundamental laws of modelling, model building, modelling
difficulties.
2 1.3 Population balance models and applications; Empirical models;
Model parameters estimation
2 2 Mathematical models for simple operations 7 2.1 Simple hydraulic tank, continuous flow tank, enclosed vessel,
mixing vessel with and without reaction
3 2.2 steam jacketed vessel, steam jacketed vessel with mixing,
continuous flow boiling system
4 3 Modelling of Staged operations 8
3.1 Extraction, Distillation column 4
3.2 Modelling of Distributed systems- tubular reactor, heat exchangers, membrane separation process
4 4 Basics of simulation 7 4.1 Introduction to flow sheet simulation; Sequential modular
approach; Equation oriented approach; Partitioning and tearing;
recycle convergence methods,
3 4.2 Simulation examples of fluid flow processes; Monte Carlo
simulation. Inventory and queuing problem 4
5 Simulation of food process system 7 5.1 simple hydraulic tank, continuous flow tank, mixing vessel with 4
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and without reaction
5.2 Distillation column, heat exchangers