Process Modelling Simulation
Subject contains
• Basics of Modeling- Definitions, Modeling and its type,
Procedure for modeling, Benefits, Use in Chemical Engg ,
Disavantages etc
•
Unsteady state modelingSimple models(Derivation)
Numerical Problems
•
Numerical Technique
•
Lumped Parameter Models-Tank , Reactor models etc.
•
Distributed parameter (Steady state)
•
Distributed parameter (Unsteady state)
Process Modelling & Simulation (CHE-4101)
•
•
•
•
•
Text/Reference Books:
Computational Methods in Process SimulationW. F. Ramirez
Modelling and Simulation in Chemical EnggRoger E Franks
Process Modelling, simulation and control for
chemical engg.- W.L.Luyben
Numerical methods for engg. – S.K.Gupta
Lab:
Process Simulation & Control using ASPEN- 2nd Ed.
Amiya.K. Jana
Definition
• Process: It is physical or chemical changes that takes
place in a system.
• Model: It is mathematical representation of a process
OR Imitation of reality
• Simulation : Actual experimentation of mathematical
model OR solving the mathematical model.
• Microscopic Balance: Ex:PFR , partial
𝜕
derivative(
𝜕𝑡
• Macroscopic Balance: Ex: CSTR , total derivative
𝑑
( )
𝑑𝑡
)
Steady state:
• values of all variables associated with the process do
not change with time.
• At any given location in the process, the values of
temperature, pressure, composition, flow rates, etc. are
independent of time.
Unsteady State:
• process variables change with time
Note: 1)Batch and semi-batch
processes must be
transient.
2) Continuous processes may be transient or steady-state.
General Material Balance Equation
input + generation – output – consumption =
accumulation
1) batch process
• material is placed in the vessel at the start and (only)
removed at the end
• no material is exchanged with the surroundings during
the process.
• Ex: baking cookies, fermentations, small-scale
chemicals (pharmaceuticals)
2) continuous process
• material flows into and out of the process during the
entire duration continuously.
• Ex: distillation processes
input + generation – output – consumption =
accumulation
3) semi-batch process
• Material flow into the process but product is removed
after the process is complete.
• Ex: washing machine, fermentation with purge.
Differential balance :
• A balance at one particular instant in time -- deals
with rates (for mass balances: mass per time [kg/s]).
• best suited for continuous processes
Integral balance :
• deals with the entire time of the process at once (so it
uses amounts rather than rates: e.g., mass NOT
mass/time).
• This form of the equation is best suited for batch or
semi-batch operation.
• simply integrating the differential balance over the
length of time the system is operating
(i.e., from tinitial to tfinal.)
System:
• The assemblage of elements which are tied together by common
flow of material and/or information
Parameter:
• property of the process that can be assigned arbitrary numerical
value ALSO called as constants/coefficient of the equation.
Flux:
• Any property per area per time . Ex: momentum flux
Independent variable :
• Quantities describing the system that can be varied by choice
during experiment. EX: Time and Space
Dependent variable:
• Properties of a system which change when
independent variables are altered in value
• There is no direct control over the dependent
variable
• Calculated from the solution of model equations
Note: 1) The relation between Independent and
dependent variable is one of cause and effect.
i.e y= f(x)
2) Independent variable measures cause and
dependent variable measures effect.
Types of Variable
• Input & Output
• Random
• Exogenous – a constant value variable
• Manipulated (In PDC) – Which is independent
variable. Controlled Variable
• State: variables which describes mathematical
state of the dynamic system
• Design : Externally specified variable
• Process variables: mass transfer coefficients,
kinetic rate constants, and so forth.
Modeling of a tank
Fi & Fo = Flow rates of water in & out of the tank(m3/s)
V= Volume (m3)
h = height of the liquid in the tank(m)
 Constants
• A= C/S area of tank(m2)
• 𝜌 = density (Kg/m3 )
• Temp remains constant
 Relationship : V= A *h
 Mass Balance:(Rate)
input + generation – output – consumption = Accumulation
Fi* 𝜌 –Fo* 𝜌
𝑑(𝑉∗𝜌)
=
𝑑𝑡
Fi* 𝜌 –Fo* 𝜌 = A* 𝜌
=
𝑑(𝐴∗ℎ∗𝜌)
𝑑𝑡
𝑑(ℎ)
𝑑𝑡
Fi –Fo = A
𝑑(ℎ)
𝑑𝑡
Information Flow diagram
Model Classification
1)Mechanistic or Phenomenological Model
• Based on mechanism or underlying phenomena
• Derivation is done from system phenomena or
mechanism such as mass, heat and momentum
transfer
• Most mechanistic models also contain empirical
parts (like rate expression or heat transfer
relation)
• Termed as white box models since mechanism are
evident in model description
• White box model is transparent or understandable
• Ex: CSTR
2)Empirical or data based Model
 Based on I/P and O/P data or Experimentation
 Does not rely on knowledge of basic principles
& mechanism OR Internal working
 Termed as Black box model since little is
known about mechanism
 Ex: 1)Human brain
2) Flight recorder or Black box (I/p parameter
is control instruction & O/P parameter is flight
sensor , without the knowledge of internal
working.
• Large number of unknown parameters
• Dangerous to extrapolate
3) Grey box Model
• called as semi-empirical model
• based on mechanistic & empirical model
• Used widely in process engg.
• Good versatility, can be extrapolated
• Can be run in real-time
4) Stochastic Models
• It contains model elements that are
probabilistic in nature .
• Not easy to work with
• Uncertainty is introduced.
• Ex: catalytic process in packed bed in which
yield of product diminishes with decrease in
activity of the catalyst.
5)Linear model
Models where superposition principle applies
 Super position principle
• If O/P , Y of a system or subsystem is completely
determined by I/P , X . The system can be
represented symbolically by Y= H*X , where H
represents any form of conversion of X into Y.
• Suppose two separate
I/P
are applied
simultaneously to the system /subsystem so that
• Y= H(X1+X2)= H(X1) +H(X2) = Y1 +Y2
• This is called additivity or superposition
• Operator H is by definition a linear operator
1)
2)
3)
4)
5)
6)
LUMPED
Doesn’t vary with space but varies
with time
Various properties & state
(dependent variable ) of the entire
system can be considered to be
homogenous
Assumptions are made so that the
problem can be converted to lumped
parameter system
It can be described by algebraic or
Ordinary differential eqn.
Ex-1:
Equilibrium stage concept of
distillation , extraction column
Ex-2:
Mixing tank(CSTR)
DISTRIBUTED
Varies with both space & time
Detailed variation in behavior from
point to point throughout the system.
All the real system are under this
category
It can be described by either ODE or
PDE
Ex- 1:
Tubular or packed bed reactor.
(here radial temperature gradient
occur . Hence necessary to use 2D or
3D distributed model)
Ex-2:
Mixing tank with baffles
7)
Deterministic or Rigid
Describes deterministic process
Each variable can be assigned a definite
fixed number
There is no uncertainty
Relatively easier than stochastic
Not difficult to analyze & grasp
Different classical techniques of
mathematics are used like differential
eqn.,Integral eqn. etc.
A constant value is obtained
8)
Ex-
1)
2)
3)
4)
5)
6)
CSTR
Stochastic or Probabilistic
Probability distribution is needed
Variables are not precisely known
Uncertainty is introduced
Not easy to work with
Difficult to analyze and grasp
It represents distribution of discreet and
continuous variables & also sample
distribution.
Here it becomes necessary to fall back
on statistical devices e.g., value of x is
a±b with 95% probability.
It means that in the long run the value of
x will be greater than a+b or less than a-b
in 5% of cases.
Ex- contact catalytical process( Packed
bed in which the yield of product
diminishes with decrease in activity of
catalyst as it ages with time.
Classification of model - Based on Variation of
Different Models
• Physical models Ex: Model of ship/building,
Pilot plant
• Drawings & maps
• Theories. Ex: Liquid drop theory
• Mathematical equations
• Analog models
Ex: Electrical/Electronic and mechanical
devices
Note : If an engineer wishes to construct a
model of a real process, then 3 types of model
and combination of these 3 models will be used
extensively
3 models are• Transport phenomena model based
on
physico-chemical principles
• Population balance model. Ex: RTD studies or
age distribution
• Empirical models. Ex: Data fitting (Least
square method), if input and output data is
given a relation can be obtained.
Step by step procedure for modeling
1) Define the goal:
a) To have a specific design decision
b) Provide numerical values i.e values to a parameter
c) Establish functional relationship between variables
d) Give required accuracy
2) Preparation of Information
a) Sketch the process & Identify the system
b) Identify the variable of interest (always the state
variable)
3)Formulate the model
a) Conservation of
i) mass
ii) heat
iii)momentum
b)Constitutive Relation
( Any mathematical description of the response of
material to spatial gradient is called constitutive relation.
They are postulated and cant be derived from
fundamental principles)
(i)Phase equilibrium(VLE, Raoults law, Henry’s law etc)
(ii)Transfer equation
• Newtons law/ Fouriers law/ Ficks law
iii) Rate expression
• −𝑟𝐴
=
1 𝑑𝑁𝐴
𝑉 𝑑𝑡
iv) Equation of state
• PV=nRT
,
𝑍=
𝑃𝑉
𝑅𝑇
c) Rationalization of model
d) Check the DOF
• DOF = NV -NE
• Case(i) NV=NE --------- System is exactly specified
• Case(ii) NV-NE< 0, Hence no. of equation> no.of
variable -------- System is over specified & no
solution to the model exists
• Case(iii) NV-NE> 0 ; When NV>NE, the system is
underspecified .There can be infinite solution.
Note: Situation where DOF>0 or DOF<0 should be converted
to DOF=0 before we proceed for modeling.
 Explanation of DOF
A+B=C
(1)
K= B/A
(2)
A= 1000 (3)
C=2000
(4)
K= 4
(5)
Case(i) NV= 4 NE= 5 : DOF < 0
• Math problem is not solvable
• System is over-specified hence no solution.
• Situation results in incorrect formulation of design
problem
Case(ii) Relaxing eq(4), then there is single
unique because DOF=0
Case(iii) DOF>0
 Relaxing eq(4) &(5), then there are infinite
values for B,C,K
 Assign value to one variable to make DOF=0
 System is underspecified
f) Preferably convert the model into dimensionless form
4)Determine the solution
a) Analytical
b) Numerical
5)Analyze the results
a) Check the results for correctness
(i)Limiting and approximate answer
(ii)Accuracy of the numerical method
b)Interpretation of the results
(i) Plot the solution
(ii) Relate the results with the available data and the
assumptions
c)Evaluate the sensitivity
d)Answer What-if questions
6)Validate the model
a) Select the key values for validation
b) Compare the experimental results.
c) Compare with more complex models.
Benefits of Process Modelling and Simulation
1) Economical Experimentation
• Instead of using pilot plant, simulation is done using
computer due to which the cost factor comes down
drastically
2)Extrapolation
• Possible to test extreme ranges with suitable model
which is not possible with real plants
3) Study of commutability & evaluation of alternate
policies
a) New factor or elements can be introduced and old
ones removed
b) Simulation makes it possible to compare various
proposed design and processes not in use.
4)Replication of experiments
a) Simulation makes it possible to study the effect of
changes of variables and parameter with reproducible
results.
b) Error can be introduced and removed at will.
5)Computer control
• Study of closed loop and open loop controls
will be easier
6)Test of sensitivity
• It is done for cost parameter and base system
parameter. Ex : a 10% increase in the input
rate could have minimum effect or serious
effect on plant performance.
7)Study of system stability
• Stability of system and sub system to
disturbances can be examined.
Characteristics of model
1)Can be hierarchical.
2)Most models are imperfect
3)Cost & effort are required
4)Specific in nature
5)Can be used from one discipline to another if it is
applicable
5)Simplify the model if required
6)Gives a lot of insight into the process & also leads to
more experimentation and in-depth investigation
Uses of Modelling
1)Engineering
2)Sciences
3)Economics
4)Warfare
5)Psychology
6)Cosmology Ex: related to Stars
7)Leisure. Ex: Hotel
8)Political Science. Ex: Exit polls
Model application areas in chemical engg.
1)Process Design
a)Feasibility analysis of novel design
b) Analyzing the process interaction
c) Waste minimization in design
2) Process control
a) Analyzing the design for set point changes or
disturbance
b) Optimal start up and shut down policies
c) Optimal control for multiproduct operation
3)Troubleshooting
• Identify the likely cause or quality problem
and process deviation
4)Process safety
a)Detection of hazardous operating regimes
b)Estimation of accidental release events
c)Estimation of effects from release scenarios
5)Operator training
a)Start up and shut down policies
b) Emergency response training
c) Routine operator training
6) Environmental impact
a) Quantifying emission rates for specific design
b) Dispersion prediction for air and water releases
c) Estimating acute accidental effects( fire or explosion)
Limitations /Pitfall/Disadvantages of modeling
1) Availability of data
2) Accuracy of data
3) Cannot Extrapolate
4) Mathematical model/ Tools for solving the model
should not be complicated
5) Any process selected should be physically realizable