P02 CL 302
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Transcript of P02 CL 302
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Stirred Tank Blending Process
Assumptions Perfect MixingDensity of the liquid is constant (that is, it does not change appreciably with composition)Volume is variable -
Degrees of Freedom
8 Entitiesr,x,x1,x2,w,w1,w2One parameter rThat leaves seven unknowns (VARIABLES)
If x, V are the controlled variables (OUTPUT)
There are five degrees of freedom.
x1,x2,w1 can be disturbances and w,w2, the manipulated variable.
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Remember the bar above V and w (discuss..)
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Degrees of Freedom
8 Entitiesr,x,x1,x2,w,w1,w2Two parameters r, VX2 is constant and w=w1+w2
when V and x2 are constantsThat leaves four unknowns (VARIABLES)
If x is the controlled variables (OUTPUT)
There are three degrees of freedom.
x1, w1 can be disturbances and w2, the manipulated variable.
*
Remember the bar above V and w (discuss..)
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Stirred Tank Blending
Governing EquationIf V is assumed constantLet t = V r / w*
Remember the bar above V and w (discuss..)
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Stirred Tank Blending Problem
Given V = 2m3 and r = 900 kg/m3Assume that the tank was fed with w1=500kg/min with x1=0.4 and w2=200kg/min with x2=0.75 for a long time. Get the Steady State Value of xCase b. w1 suddenly changed to 400. Plot x vs. t.Case c. w2 suddenly changed to 100 (w1 being 500). Plot x vs. tCase d. with w2=200, w1 suddenly changed to 400, and x1, to 0.6 plot x vs. t -
Solution : Stirred Tank Blending
For all cases w1+w2 = 600t = V r / w =(2m3 * 900kg/m3)/600kg/min= 3 min -
Stirred Tank Blending : Results
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Stirred tank blending normalized plot
The response of the system to changes in
Flowrate w1
Flowrate w2
Simultaneous change in w2
And x1
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Electrically Heated Stir Tank
AssumptionsConstant Hold up (V). Inlet flow = Outlet flowPerfect MixingDensity r and Heat Capacity C are constantsHeat losses are negligibleMetal heating element has significant capacityMetal heating element has uniform temperature. -
Electrically Heated Stir Tank
Governing Equations -
Electrically Heated Stir Tank
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Response of an electrically heated stirred tank to a step change
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A dynamic model for CSTR
AssumptionsPerfect MixingV is constantr Is constantThe reaction is of first order, that is,Rate r = k CAReaction rate r has units of moles per unit volume.
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A dynamic model for multistage (3-stage absorption) systems
Note that the individual equations are linear differential equations.They are Coupled as well, that is, x2 appears in the expression for dx1/dt and both x1 and x3 appear in the expression for dx2/dt. -
Distributed Parameter Systems
In the models we considered thus far, we examined variables that were a function of time. In the simple double pipe exchanger, that is not the case as temperature varies with position. For rigorous characterization, we will have to employ partial differential equations. Alternately, we can opt for a DISTRIBUTED PARAMETER (as against LUMPED parameter) model, dividing the length in a number of zones, in each of which, T can be assumed to be constant. -
Motivation for Studying
Improve understanding of the processTrain plant operatorsAs a basis for developing control strategyOptimize operating conditions
Process Dynamics -
Disadvantages of using Theoretical Models
The simplest models are based on a long list of assumptions.A model quickly gets complicated when some of the assumptions are replaced by more realistic equations/conditions.Complex models are often non-linear, not amenable to easy analysis.For the analysis of dynamic response and getting insight for Process Control, we need to work with linear dynamic models. -
Arrhenius Equation
Expresses the rate of reaction as a function of temperatureK0 is frequency factor, as it has units of time-1.E is the activation energy and R is the gas constant.Typically, k0 and E are determined by fitting experimental data.Thus, as used, it is a semi-empirical equation. -
Classification of Process Models
Theoretical ModelsProvide physical insightCan be extrapolatedAre difficult, expensive to develop.Empirical ModelsEasy to developShould not be used for extrapolationSemi-empirical ModelsAttractive compromise of simplicity and applicability