Process Simulation

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Introduction

• Process Simulation

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Classification of the models

• Black box white box
• Black box know nothing about process in
  apparatus, only dependences between inputs and
  outputs are established. Practical realisation of
  Black box is the neural network
• White box process mechanism is well lt??gt known
  and described by system of equations

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Classification of the models

• Deterministic Stochastic
• Deterministic 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

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Classification of the models

• Microscopic- macroscopic
• Microscopic includes part of process or
  apparatus
• Macroscopic includes whole process or apparatus

5
Elements of the model

• Balance dependences
• Based upon basic nature laws
• of conservation of mass
• of conservation of energy
• of conservation of atoms number
• of 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

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Elements of the model

• Constitutive equations
• Newton eq. for viscous friction
• Fourier eq. for heat conduction
• Fick eq. for mass diffusion

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Elements of the model

1. Phase equilibrium equations important for mass
   transfer
2. Physical properties equations for calculation
   parameters as functions of temperature, pressure
   and concentrations.
3. Geometrical dependences involve influence of
   apparatus geometry on transfer coefficients
   convectional streams.

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Structure of the simulation model

• Structure corresponds to type of model equations
• Structure depends on
• Type of object work
• Continuous, steady running
• Periodic, unsteady running
• Distribution of parameters in space
• Equal in every point of apparatus aggregated
  parameters (butch reactor with ideal mixing)
• Parameters are space dependent displaced
  parameters

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Structure of the model
Steady state Unsteady state
Aggregated parameters Algebraic eq. Ordinary differential eq.
Displaced parameters Differential eq. Ordinary for 1-dimensional case Partial for 23-dimensional case (without time derivative, usually elliptic) Partial differential eq. (with time derivative, usually parabolic)
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Process simulation

• the 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.

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Process simulation (steady state)

• Flowsheeting problem
• Specification (design) problem
• Optimization problem
• Synthesis problem

by Rafiqul Gani
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Flowsheeting problem

• Given
• All of the input information
• All of the operating condition
• All of the equipment parameters
• To calculate
• All of the outputs

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R.Gani
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Specyfication problem

• Given
• Some input some output information
• Some operating condition
• Some equipment parameters
• To calculate
• Undefined inputsoutputs
• Undefined operating condition
• Undefined equipment parameters

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Specyfication problem

• NOTE degree of freedom is the same as in
  flowsheeting problem.

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Given feed composition and flowrates, target
product composition
Assume value to be guessed D, Qr
Find product flowrates, heating duties
Solve the flowsheeting problem
Adjust D, Qr
Is target product composition satisfied ?
STOP
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Process optimisation

• the act of finding the best solution (minimize
  capital costs, energy... maximize yield) to
  manage the process (by changing some parameters,
  not apparatus)

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Given feed composition and flowrates, target
product composition
Assume value to be guessed D, Qr
Find product flowrate, heating duty
Solve the flowsheeting problem
Adjust D, Qr
Is target product composition satisfied AND
?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 parameters
• operations conditions

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Process synthesis/design problem
flowsheet undefined
INPUT
OUTPUT
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Given feed composition and flowrates, target
product composition
Assume value to be guessed D, Qr, N, NF, R/D
etc.
Find product flowrate, heating duty, column
param. etc.
Solve the flowsheeting problem
Adjust D, Qr As well as N, NF, R/D etc.
Is target product composition satisfied AND
?min.
STOP
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Process simulation - why?

• COSTS
• Material easy to measure
• Time could be estimated
• Risc hard to measure and estimate

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Modelling objects in chemical and process
engineering

• Unit operation
• Process build-up on a few unit operations

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Software for process simulation

• Universal software
• Worksheets Excel, Calc (Open Office)
• Mathematical software MathCAD, Matlab
• Specialized software process simulators.
  Equipped with
• Data base of apparatus models
• Data base of components and mixtures properties
• Solver engine
• User friendly interface

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Software process simulators (flawsheeting
programs)

• Started in early 70
• At the beginning dedicated to special processes
• Progress toward universality
• Some actual process simulators
• ASPEN Tech /HYSYS
• ChemCAD
• PRO/II
• ProSim
• Design II for Windows

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Chemical plant system

• The 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 technology
• Project step new plants (technology exists),
• Runtime problem identification/solving existing
  systems (technology and plant exists)

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Chemical plant system

• characteristic parameters can be specified for
  every system separately according to
• Material streams
• Apparatus

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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?
• Its make calculations easier

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Streams parameters

• Flow rate (mass, volume, mol per time unit)
• Composition (mass, volume, molar fraction)
• Temperature
• Pressure
• Vapor fraction
• Enthalpy

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Streams degrees of freedom

• DFsNC2

• e.g. NC2 -gt DFs4
• Assumed F1, F2, T, P
• Calculated
• enthalpy
• vapor fraction

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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

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Types of flowsheeting calculation

• Steady state calculation
• Dynamic calculation

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Calculation subject

• Number of equations of mass and energy balance
  for entire system
• Can be solved in two ways

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Types of balance calculation

• Overall balance (without use of apparatus
  mathematical model)
• Detailed balance on the base of apparatus model

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Overall balance

• Apparatus is considered as a black box
• Needs more stream data
• User could not be informed about if the process
  is physically possible to realize.

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Overall balance Example
Countercurrent, tube-shell heat exchanger Given
three streams data 1, 2, 3 hence parameters of
stream 4 can be easily calculated from the
balance equation.
DF5
There is possibility that calculated temp. of
stream 4 can be higher then inlet temp. of
heating medium (stream 1).
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Overall balance Example

• Given
• mA10kg/s
• mB20kg/s
• t1 70C
• t240C
• t320C
• cpAcpBidem

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Apparatus model involved

• Process is being described with use of modeling
  equations (differential, dimensionless etc.)
• Only physically acceptable processes taking place
• Less 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

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Loops and cut streams

• Loops occur when
• some products are returned and mixed with input
  streams
• when output stream heating (cooling) inputs
• some input (also internal) data are undefined
• To solve
• one stream inside the loop has to be cut (tear
  stream)
• initial parameters of cut stream have to be
  defined
• Calculations have to be repeated until cut
  streams parameters are converted.

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Loops and cut streams
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Simulation of system with heat exchanger using
MathCAD
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I.Problem definition
Simulate 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.
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II. Flawsheet
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Numerical data
Stream s1 Ps1 200kPa, ts1 85C, f1s1
10000kg/h Stream s6 Ps6 200kPa, ts6 20C,
f2s6 10000kg/h
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Equipment parameters

1. L17m d10,025m
2. L25m d20,16m, s0,0016m, n31...
3. L36m, d30,05m
4. z450
5. L57m d50,05m
6. L610m, d60,05m
7. z740

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III. Stream summary table

• UknownTs2, Ts3, Ts4, Ts5, Ts7, Ts8, Ts9, Ts10,
  Ps2, Ps3, Ps4, Ps5, Ps7, Ps8, Ps9, Ps10, f1s2,
  f1s3, f1s4, f1s5, f2s7, f2s8, f2s9, f2s10
• number of unknown variables 26
• WE NEED 26 INDEPENDENT EQUATIONS.

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Equations from equipment information

• f1s2 f1s1 f1s7 f1s6
• f1s3 f1s2 f1s8 f1s7
• f1s4 f1s3 f1s9 f1s8
• f1s5 f1s4 f1s10 f1s9

14 equations. Still do define 26-1412 equations
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Heat balance equations
New variable Q Still to define 121-211
equations
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Heat exchange equations
New variables k, DTm number of equations to
find 112-211
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Heat exchange equations
Two new variables aT and aS number of equations
to find 112-112
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Heat exchange equations
Three new variables NuT, NuS, deq, number of
equations to find 123-312
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Heat exchange equations
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Heat exchange equations
Two new variables ReT and ReS, number of
equations to find 122-410
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Pressure drop
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Pressure drop

Two new variables Re1 and l1, number of
equations to find 102-39
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Pressure drop

One new variables and l2T, number of equations
to find 91-37
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Pressure drop

Two new variables Re3 and l3, number of
equations to find 72-36
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Pressure drop

Number of equations to find 6-15
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Pressure drop

Two new variables Re5 and l5, number of
equations to find 62-34
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Pressure drop

One new variables and l2S, number of equations
to find 41-32
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Pressure drop

Two new variables Re6 and l6, number of
equations to find 22-31
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Pressure drop

Number of equations to find 1-10 !!!!!!!!!!!!!!
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Agents parameters
Temperatures are not constant Liquid properties
are functions of temperature

• Density ?

• Viscosity ?

• Thermal conductivity ?

• Specyfic heat cp

• Prandtl number Pr

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Agents parameters
Data are usually published in the tables
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Agents parameters
Data in tables are difficult to use
Solution
Approximate discrete data by the continuous
functions.
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Approximation

• Approximating function
• Polynomial
• Approximation target find optimal parameters of
  approximating function
• Approximation type
• Mean-square sum of square of differences
  between discrete (from tables) and calculated
  values is minimum.

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Polynomial approximation
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The end as of yet.