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2003 Course Process Modeling & Simulation

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Total No. of Questions : 12] [Total No. of Pages : 4 [3864] - 334 P 1265 B.E. (Chemical) PROCESS MODELING & SIMULATION (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answers to the two sections should be written in separate books. 2) Neat diagrams must be drawn wherever necessary. 3) Figures to the right indicate full marks. 4) Your answers will be valued as a whole. 5) Use of logarithmic tables slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, if necessary. SECTION - I Q1) a) b) Attempt the following : [8] i) What is process model? ii) Why develop a process model? iii) How to determine the form of a model, give the typical form of models? iv) What is the difference between lumped parameter and distributed parameter systems, give examples of each. Assume that two chemical species A and B are in a solvent feed stream entering a liquid phase chemical reactor that is maintained at a constant pressure. The two species react irreversibly to form a third species, P. Develop a model to find out the reactor concentration of each species as a function of time. [8] State your assumptions clearly. OR P.T.O. Q2) Consider a perfectly mixed stirred tank heater, with a single feed stream and a single product stream as shown below. Assuming that the flow rate and temperature of the inlet stream can vary, that the tank is perfectly insulated, and the rate of heat added per unit time (Q) can vary, develop a model to find out the tank temperature as a function of time. State your assumptions. [16] Q3) A component material balance around a chemical reactor yields the following steady state equation O= F F C in C KC 3 V V where F = 0.1min 1, Cin = 1.0 Kg mol/m3, K = 0.05 m6 / Kg mol2.min. V a) How many steady state solutions are there? b) Write two different direct substitution methods and assess the convergence of each. [16] OR Q4) The batch still shown in figure initially contains 25 moles of n-octane and moles of n heptane. If the still is operated at a constant pressure of 1 atmosphere, f compute using Euler s method, the final mole fraction of n-heptane X H j if the remaining solution in the still, Sf, total 10 moles. [3864] - 334 -2- Data : At 1 atmosphere pressure the relationship between XH and the mole 2.16 X H fraction of n-heptane in the vapour phase, YH is Y H = . [16] 1 + 1.16X H Q5) A reservoir discharging through sluices at a depth h below the water surface has a surface area A for various values of h as given below h in meter 10 11 12 13 14 A in sq. meter 950 1070 1200 1350 1530 If t denotes the time in minutes, the rate of fall of the surface is given by dh 48 = h dt A Estimate the time taken for the water level to fall from 14 meter to 10 meter above sluices. [18] OR Q6) The reaction 3A 2B + C is carried out in an isothermal semibatch reactor. Product B is the derived product. Product C is very volatile by product that must be vented off to prevent a pressure buildup in a reactor. Gaseous C is vented off through a condenser to prevent any A & B to go out with C. Assume that from condenser only pure C is vented off. The reaction is first order. The relative volatilities of A and C to B are AB and CB . Assume perfect gases and constant pressure system. Write the equations describing the system. List all assumptions. [18] SECTION - II Q7) Develop the model equations of a double pipe heat exchanger wherein the resistance to heat transfer from a condensing fluid to inner fluid can be represented by convective heat transfer coefficients on both sides of the heat transfer wall. Assume that resistance of the wall is negligible but the wall has finite heat capacity. [16] OR Q8) Develop the equations describing a batch distillation column during the startup period when no product is withdrawn and the column is coming to equilibrium conditions. Reflux drum and tray holdups are not negligible but can be assumed constant. [16] [3864] - 334 -3- Q9) Derive the governing balance equations (Heat and mass transfer equations) for counter current rotary dryer which operates continuously. Assume that only moisture is removed from wet solids by means of heating medium. Explain briefly the procedure to evaluate total number of transfer units. [16] OR Q10)Benzene is nitrated in an isothermal CSTR in three sequential irreversible reactions. Benzene + HNO3 K1 nitrobenzene + H2O K2 Nitrobenze + HNO3 dinitrobenzene + H2O Dinitrobenzene + HNO3 K 3 trinitrobenzene + H2O Assuming each reaction is linearly dependent on the concentrations of each reactant, derive a dynamic mathematical model of the system. There are two feed streams, one pure benzene and one concentrated nitric acid (98 wt%). Assume constant densities and complete miscibility. [16] Q11)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 kinetics A and B; A + B K1 R. Tank is filled to 40% level initially and pure B is charged into reactor. Maximum cooling water flow is begun to keep temperature constant. Derive model equations. [18] OR Q12)a) b) c) State the law of mass action. Give different uses of mathematical model. What are limitations of mathematical models. Give examples. [18] [3864] - 334 -4-

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