2 Classification of the models Black box – white boxBlack box – know nothing about process in apparatus, only dependences between inputs and outputs are established. Practical realisation of Black box is the neural networkWhite box – process mechanism is well <??> known and described by system of equations
3 Classification of the models Deterministic – StochasticDeterministic – for one given set of inputs only one set of outputs is calculated with probability equal 1.Stochastic – random phenomenon affects on process course (e.g. weather), output set is given as distribution of random variables
4 Classification of the models Microscopic- macroscopicMicroscopic – includes part of process or apparatusMacroscopic – includes whole process or apparatus
5 Elements of the model Balance dependences Based upon basic nature laws of conservation of massof conservation of energyof conservation of atoms numberof conservation of electric charge, etc.Balance equation (for mass): (overall and for specific component without reaction) Input – Output = Accumulation or (for specific component if chemical reactions presents) Input – Output +Source = Accumulation
6 Elements of the model Constitutive equations Newton eq. – for viscous frictionFourier eq. – for heat conductionFick eq. – for mass diffusion
7 Elements of the modelPhase equilibrium equations – important for mass transferPhysical properties equations – for calculation parameters as functions of temperature, pressure and concentrations.Geometrical dependences – involve influence of apparatus geometry on transfer coefficients – convectional streams.
8 Structure of the simulation model Structure corresponds to type of model equationsStructure depends on:Type of object work:Continuous, steady runningPeriodic, unsteady runningDistribution of parameters in spaceEqual in every point of apparatus – aggregated parameters (butch reactor with ideal mixing)Parameters are space dependent– displaced parameters
9 Structure of the model Steady state Unsteady state Aggregated parametersAlgebraic eq.Ordinary differential eq.Displaced parametersDifferential eq.Ordinary for 1- dimensional casePartial for 2&3- dimensional case (without time derivative, usually elliptic)Partial differential eq.(with time derivative, usually parabolic)
10 Process simulationthe act of representing some aspects of the industry process (in the real world) by numbers or symbols (in the virtual world) which may be manipulated to facilitate their study.Facilitate - ułatwiać
12 Flowsheeting problem Given: To calculate: All of the input information All of the operating conditionAll of the equipment parametersTo calculate:All of the outputsFLOWSHEETSCHEMEINPUTOPERATINGCONDITIONSEQUIPMENTPARAMETERSPRODUCTS
17 Assume value to be guessed: D, Qr Given: feed composition and flowrates,target product compositionAssume value to be guessed:D, QrFind: product flowrates, heating dutiesSolve the flowsheetingproblemAdjust D, QrIs target productcomposition satisfied?STOP
18 Process optimisationthe act of finding the best solution (minimize capital costs, energy... maximize yield) to manage the process (by changing some parameters, not apparatus)
20 Assume value to be guessed: D, Qr Given: feed composition and flowrates,target product compositionAssume value to be guessed:D, QrFind: product flowrate, heating dutySolve the flowsheetingproblemAdjust D, QrIs target productcomposition satisfiedAND =min.STOP
21 Process synthesis/design problem the act of creation of a new process.Given:inputs (some feeding streams can be added/changed latter)Outputs (some byproducts may be unknown)To find:Flowsheet (topology)equipment parametersoperations conditions
22 Process synthesis/design problem flowsheetundefinedINPUTOUTPUT
24 Assume value to be guessed: D, Qr, N, NF, R/D etc. Given: feed composition and flowrates,target product compositionAssume value to be guessed:D, Qr, N, NF, R/D etc.Find: product flowrate, heating duty,column param. etc.Solve the flowsheetingproblemAdjust D, QrAs well asN, NF, R/D etc.Is target productcomposition satisfiedAND =min.STOP
25 Process simulation - why? COSTSMaterial – easy to measureTime – could be estimatedRisc – hard to measure and estimate
26 Modelling objects in chemical and process engineering Unit operationProcess build-up on a few unit operations
27 Software for process simulation Universal software:Worksheets – Excel, Calc (Open Office)Mathematical software – MathCAD, MatlabSpecialized software – process simulators. Equipped with:Data base of apparatus modelsData base of components and mixtures propertiesSolver engineUser friendly interface
28 Software process simulators (flawsheeting programs) Started in early 70’At the beginning dedicated to special processesProgress toward universalitySome actual process simulators:ASPEN Tech /HYSYSChemCADPRO/IIProSimDesign II for Windows
29 Chemical plant systemThe apparatus set connected with material and energy streams.Most contemporary systems are complex, i.e. consists of many apparatus and streams.Simulations can be use during:Investigation works – new technologyProject step – new plants (technology exists),Runtime problem identification/solving – existing systems (technology and plant exists)test
30 Chemical plant systemcharacteristic parameters can be specified for every system separately according to:Material streamsApparatus
31 Apparatus-streams separation Assumption:All processes (chemical reaction, heat exchange etc.) taking places in the apparatus and streams are in the chemical and thermodynamical equilibrium state.Why separate?It’s make calculations easier
32 Streams parameters Flow rate (mass, volume, mol per time unit) Composition (mass, volume, molar fraction)TemperaturePressureVapor fractionEnthalpy
34 Apparatus parameters & DF Characteristics for each apparatus type. E.g. heat exchanger :Heat exchange area, A [m2]Overall heat-transfer coefficient, U (k) [Wm-2K-1]Log Mean Temperature Difference, LMTD [K]degrees of freedom are unique to equipment type
35 Types of flowsheeting calculation Steady state calculationDynamic calculation
36 Calculation subjectNumber of equations of mass and energy balance for entire systemCan be solved in two ways:
38 Types of balance calculation Overall balance (without use of apparatus mathematical model)Detailed balance on the base of apparatus model
39 Overall balance Apparatus is considered as a black box Needs more stream dataUser could not be informed about if the process is physically possible to realize.
40 Overall balance – Example 1243Countercurrent, tube-shell heat exchangerGiven three streams data: 1, 2, 3 hence parameters of stream 4 can be easily calculated from the balance equation.DF=5There is possibility that calculated temp. of stream 4 can behigher then inlet temp. of heating medium (stream 1).
41 Overall balance – Example 1, mB243, mAGiven:mA=10kg/smB=20kg/st1= 70°Ct2=40°Ct3=20°CcpA=cpB=idemAt first sight – na pierwszy rzut oka
42 Apparatus model involved Process is being described with use of modeling equations (differential, dimensionless etc.)Only physically acceptable processes taking placeLess stream data required (smaller DF number)Heat exchange example: given data for two streams, the others can be calculated from a balance and heat exchange model equations
43 Loops and cut streams Loops occur when: To solve: some products are returned and mixed with input streamswhen output stream heating (cooling) inputssome input (also internal) data are undefinedTo solve:one stream inside the loop has to be cut (tear stream)initial parameters of cut stream have to be definedCalculations have to be repeated until cut streams parameters are converted.
45 Simulation of system with heat exchanger using MathCAD
46 I.Problem definitionSimulate system consists of: Shell-tube heat exchanger, four pipes and two valves on output pipes. Parameters of input streams are given as well as pipes, heat exchanger geometry and valves resistance coefficients. Component 1 and 2 are water. Pipe flow is adiabatic.Find such a valves resistance to satisfy condition: both streams output pressures equal 1bar.
59 Pressure drop Two new variables Re1 and l1, number of equations to find: =9
60 Pressure drop One new variables and l2T, number of equations to find: 9+1-3=7
61 Pressure drop Two new variables Re3 and l3, number of equations to find: 7+2-3=6
62 Pressure dropNumber of equations to find: 6-1=5
63 Pressure drop Two new variables Re5 and l5, number of equations to find: 6+2-3=4
64 Pressure drop One new variables and l2S, number of equations to find: 4+1-3=2
65 Pressure drop Two new variables Re6 and l6, number of equations to find: 2+2-3=1
66 Pressure dropNumber of equations to find: 1-1=0 !!!!!!!!!!!!!!
67 Agents parameters Temperatures are not constant Liquid properties are functions of temperatureDensity Viscosity Thermal conductivity Specyfic heat cpPrandtl number Pr
68 Agents parametersData are usually published in the tables
69 Agents parameters Data in tables are difficult to use Solution: Approximate discrete data by the continuous functions.
70 Approximation Approximating function PolynomialApproximation target: find optimal parameters of approximating functionApproximation typeMean-square – sum of square of differences between discrete (from tables) and calculated values is minimum.