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2003 Course Process Modeling & Simulation

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Total No. of Questions : 12] P1491 [Total No. of Pages : 7 [3764]-334 B.E. (Chemical) PROCESS MODELING & SIMULATION (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to candidates : 1) Answer any 03 questions from each section. 2) Answers to the two sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Figures to the right indicate full marks. 5) Your answers will be valued as a whole. 6) Use of logarithmic tables slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 7) Assume suitable data if necessary. SECTION - I Q1) a) Draw the flow chart of a systematic approach to process modeling showing the interrelations between the flow chart stages. Alongside each major step, list in point form the key issues for each major modeling task. [8] b) Provide a classification of the major categories of equations in process model. What are the subclasses in each major category. [8] OR Q2) a) What is process model? What points should be considered to form the model? [8] b) Give the classification of model. What is the difference between linear and nonlinear model? Explain with suitable examples. [8] Q3) a) Consider the following dynamic model of a constant volume, isothermal continuous stirred tank reactor, dVC A = q (CAO CA) V (K1 CA K3 C 2 ) = f1 (CA, q, CAO) A dt dVC B = q CB + V (K1 CA K2 CB) = f2 (CA, CB, q). dt P.T.O. Where CA, CB are the concentrations of component A & B respectively, V is reactor volume, q and C AO a re the volumetric flow rate and concentration of the inlet stream, respectively. K1, K2 and K3 are reaction constants. Assume both q and CAO vary with respect to time. Find linear deviation model. [8] b) Consider the following dynamic model. dx1 = x1 + (1 + x1 ) u( t t0 ) = f ( x1 , u(t t0 )) dt dx 2 2 = x1 x2 = f 2 ( x1 , x 2 ) dt Find the deviation model at the point x1 = x2 = u = 0. [8] OR Q4) The following diagram shows the scenario of an evaporating pool of a volatile liquid. This is typical of an accident spill from storage facility. In this case the liquid is unsymmetric dimethyl hydrazine, a component of rocket fuel. Develop the problem description if we are interested in the dynamics of pool evaporation under the influence of different environmental conditions. You should consider the key issues of: [16] a) The modeling definition. b) The principle mechanism. c) The key assumptions. d) The principle balance volume of the system. e) The convective flows in the system. f) The key data that might be needed. [3764]-334 2 Q5) Write the component continuity equations describing the CSTR with a) Simultaneous reactions (first order, isothermal) k k2 1 C b) c) k1 Reversible (first order, isothermal) k2 Write the component continuity equations for a perfectly mixed batch reactor (no inflow or outflow) with first order isothermal reactions. i) Consecutive. ii) Simultaneous. [18] OR Q6) Benzene is nitrated in an isothermal CSTR in three sequential irreversible reactions. k Benzene + HNO3 1 nitrobenzene + H2O. k2 Nitrobenzene + HNO3 dinitrobenzene + H2O. k3 Dinitrobenzene + HNO3 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% by wt. Assume constant densities and complete miscibility. [18] [3764]-334 3 SECTION - II Q7) Consider a perfectly mixed stirred-tank heater, with a single feed stream and a single product stream as shown in figure given below. Assuming that the flowrate and the temperature of the inlet stream can vary, that the tank is perfectly insulated and that the rate of heat added per unit time (Q) can vary. Develop a model to find the tank temperature as a function of time. State your assumptions. [16] OR Q8) Develop the equations for a double pipe heat exchanger where in the resistance to heat transfer from the condensing fluid to inner fluid can be represented by convective heat transfer coefficients on both sides of the heat transfer wall. Assume that the resistance of the wall is negligible but the wall has finite heat capacity. [16] Q9) Consider the continuous stirred tank reactor system shown in figure. Stream 1 is a mixture of A & B with composition CA , CB (moles / volume) and has 1 1 a volumetric flow rate F1 and a temperature T1. Stream 2 is pure R. The reaction taking place are k A + R 1 P1 k2 B + R P2 [3764]-334 1 2 4 Both reactions are endothermic and have second order (reaction 1) and third order (reaction 2) kinetics. Heat is supplied to the reaction mixture by steam which flows through the coil immersed in the reactors content with a heat transfer area at. a) What are the state variables describing the natural state of the system. b) What are the balances which you should consider. c) Develop the state model for CSTR system. d) Define the assumptions that should be consider in order to have an isothermal reactor. [16] Q OR k Q10)An isothermal irreversible reaction takes in a liquid phase in a constant volume reactor. The mixing is perfect. Observation of flow pattern indicates that a two tank system with back mixing as shown in fig. below, should approximate the imperfect mixing. Assuming F and FR are constant give the mathematical model describing the system. [16] [3764]-334 5 Q11)An ice cube is dropped into a glass of water at room temperature and then stirred. Develop a mathematical model describing the time varying behaviour of the system. This model should predict. The behaviour for both short term and long term dynamics. Typical values for the problem are 28 C ambient temperature, glass liquid volume of 250 ml at an initial temperature of 24 C and an ice cube of 25 cm3. Typical aspect ratio of the ice cube is 1:1.25 : 2.5 your tasks are to: [18] a) Prepare a model definition for this scenario in the form of modeling goal statement. b) Set out key controlling factors. c) Provide a labelled drawing of the balance volume and relevant flows. d) State all modeling assumptions. e) What data might be necessary? Where it can be obtained? f) Develop a mathematical model. g) Analyse the degrees of freedom. OR Q12)A biochemical reaction is carried out in a CSTR to convert a substrate being fed to the reactor into useful product. The substrate consumption follows variation of Micheles - Menten type Kinetics. [18] S1.5 . KS + S Where S is the substrate concentration in mol/L. Rate of substrate depletion (moles / L-min) = [3764]-334 6 max The following operational and Kinetic parameters are given. F/V = 5 min 1, SO = 3 mol L 1. KS = 1 mol L 1, max = 2 mol0.5 L 0.5 . min 1. Calculate the rate of substrate consumption (in md/s) under the given operating conditions. Y [3764]-334 7

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