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M hnh ha, m phng v tiu hacc qu trnh ha hc
Modeling, simulation and optimization for chemical process
Instructor: Hoang Ngoc Ha
Email: [email protected]
B mn QT&TBCurriculum/syllabi
Seminar group
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Outline General introduction
Structure and operation of chemical
engineering systems
What is a chemical process?
Motivation examples
Part I: Process modeling
Part II: Computer simulation
Part III: Optimization of chemical
processes
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General introduction Structure of chemical engineering system
(Copyright by Prof. Paul Sides at CMU, USA)
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General introduction Conservation laws:
Give some balance equations such as mass balance (or the molar
number by species), energy balance and momentum equation of thesystem under consideration
Equilibrium thermodynamics The extensive variables/intensive variables
The laws of thermodynamics
Reaction engineering Reaction mechanism
The rate of a chemical reaction
Transport processes How materials and energy move from one position to another (heat
conductivity, diffusion and convection) Biological processes
Transform material from one form to another (enzyme process) orremove pollutants (environmental engineering)
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General introduction References (complements) :
1. Sandler S. I. (1999). Chemical and EngineeringThermodynamics. Wiley and Sons, 3rd edition.
2. H.B. Callen. Thermodynamics and an introduction to
thermostatics. JohnWiley & Sons Inc, 2nd ed. New York,1985.
3. De Groot S. R. and P. Mazur (1962) Non-equilibriumthermodynamics. Dover Pub. Inc., Amsterdam.
4. V B Minh. (tp 4) K thut phn ng. NXBHQG Tp. HCh Minh, 2004
5. Nguyn Bin, (tp 5) Cc qu trnh ha hc. NXB Khoa hcv K thut, 2008
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General introduction Conservation laws:
Give some balance equations such as mass balance (or the molar
number by species), energy balance and momentum equation of thesystem under consideration
Equilibrium thermodynamics The extensive variables/intensive variables
The laws of thermodynamics
Reaction engineering Reaction mechanism
The rate of a chemical reaction
Transport processes How materials and energy move from one position to another (heat
conductivity, diffusion and convection) Biological processes
Transform material from one form to another (enzyme process) orremove pollutants (environmental engineering)
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General introduction
Operation of a chemical engineering plant
Copyright by T. Marlin
()
Dynamical behavior
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General introduction
Oil and gas production plant
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General introduction
The system may be
Isolated: There is no transfer of
mass or energy with the
environment
Closed: There may be transfer ofmechanical energy and heat
Open: There is mass transfer withthe environment
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General introduction
Gas
BA,JQ
.
BA BA
Question: determinate physical volume of
the following systems?
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General introduction
What is a chemical process?
Process: A set of actions performed intentionally in order to reach
some result (Longmans Dictionary of Contemporary English)
Processes that involve energy conversion, reaction, separationand transport are called chemical processes (Prof. Erik Ydstie atCMU, USA)
Definition: Chemical processes are a special subclass ofprocesses since their behavior is constrained by a range oflaws and principles which may not apply in othercircumstances (mechanical/electrical systems)
Properties:
Highly nonlinear Complex network May be distributed
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General introduction
Chemical processes
Thermal conductivity process
Transport (reaction) process
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General introduction
Why we need informations about dynamical
behavior?
Research and development
Process design
Process control
Plant operation
Process modeling,
computer
simulation and optimization
()Ordinary Differential Equations
(ODEs) or Partial Differential
Equations (PDEs) or
Differential and Algebraic
Equations (DAEs)
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Motivation examples
Example 1: Gravity-flow tank
The higher the flow rate F, the higherh will beh
F0
F F
F0 =F0(t), h=h(t) and F =F(t)
F0, h and F: steadystate values
Overshoot
How to understand dynamical behavior to design thesystem avoiding Overshoot ?
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Motivation examples
Example 2: Heat exchanger
Thermocouple
Temperature transmitter
Temperature controller
Final control element
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Motivation examples
Example 3: Typical chemical plant and control system
Two liquids feeds are pumped intoa reactor
They react to form products
Reactor effluent is pumped through
a preheater into a distillation
To specify the various piecesof equipment:
Fluid mechanics
Heat transfer
Chemical kinetics
Thermodynamics and mass
transfer
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Motivation examples
Example 4: Optimization of a silicon process
The silicon reactor
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Motivation examples
Example 4: Optimization of a silicon process
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Outline
General introduction
Structure and operation of chemical engineeringsystems
What is a chemical process?
Motivation examples
Part I: Process modeling
Part II: Computer simulation Part III: Optimization of chemical processes
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Process modeling
Introduction
Fundamental laws
Continuity equations
Energy equation
Equations of motion
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Introduction
Uses of mathematical models Can be useful in all phases of chemical engineering, from
research and development to plant operations, and even inbusiness and economic studies Research and development:
Determinating chemical kinetic mechanisms and parameters fromlab. or pilot-plant reaction data
Exploring the effects of different operating conditions
Adding in scale-up calculations
Design Exploring the sizing and arrangement of processing equipment
Studying the interactions of various parts Plant operation
Cheaper, safer and faster
Troubleshooting and processing problems
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Introduction
Scope of course
A deterministic system is a system in which norandomness is involved in the evolution of states
of the system
Random effects such as noise
A stochastic system is non-deterministic system
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Introduction
Principles of formulation
Basis Fundamental physical and chemical laws such as laws
of conservation of mass, energy and momentum
Assumptions Impose limitations reasonable on the model
Mathematical consistency of model
Number of variables equals the number of equations(degrees of freedom)
Units of all terms in all equations are consistent
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Introduction
Solution of the model equations
Initial and/or boundary conditions Available numerical solution techniques and tools
Solutions are physically acceptable?
Verification
The mathematical model is proving that the model
describes the real-world situation
Real challenge
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Fundamental laws
Continuity equations
Total continuity equations (total mass balance)
EXERCISE ?
Component continuity equations (component balance)
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Fundamental laws
Energy balance
EXERCISE ?
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Fundamental laws
Equations of motion
Pushing in the i direction (i=x,y,z)
F =
dMv
dt
Where v = velocity,
F= total force and M= mass
Fi =d
Mvi
dt
EXERCISE ?
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Fundamental laws
Consider a system with n components
Number of equations obtained from thefundamental laws
n balance equations by species
1 total mass balance equation 1 energy balance equation
3 equations of motion (if the system is under
movement)
Not independent
n + 1 +(3)equations
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Constitutive equations
Reaction kinetics of
(bio)chemical reaction
Transport equations
k=k(T, C)
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Other equations
As we saw, we need equations that tell us how the
physical properties, primarily density and enthalpy,change with temperature, pressure, and
composition to rewrite alternative mathematicalmodels
Equations of state
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Other equations (cont.)
In some cases, simplification can be made without
sacrificing much overall accuracy
Or more complex, Cp is considered as a function of
temperature
H=CpT (liquid)
H=CpT+v (vapor)
H=RTTref
Cp(T)dT
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Other equations (cont.)
A polynomial in T is used for Cp
We obtain
Cp(T) =A1+ A2T
H =h
A1T+ A2T2
2
iTTref
=A1(T T0) +A22 (T
2 T20 )
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Other equations (cont.)
If the mixture is composed of components
(which we know the pure-componententhalpies) then the total enthalpy can be
averaged
H=P
N
j=1 xjhjMjPNj=1
xjMj
xj
Mj
hj
- mole fraction of jth component
- molecular weight of jth component
- pure-component enthalpy of jth component (energy per unit mass)
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Other equations (cont.)
Liquid densities can be assumed constant in
many systems Vapor densities usually cannot be considered
invariant in many systems and the PVT
relationship is almost always required. The simplest and most often used case is the
perfect gas law
P V =nRT v = nMV
= PMRT
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Examples of mathematical modeling of
chemical process
(Distributed) Transport reaction systems
De Groot S. R. and P. Mazur (1962) Non-equilibrium thermodynamics. Dover Pub. Inc.,Amsterdam.
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Examples of mathematical modeling of
chemical process
Distributed reaction systems (reactor tubular
for example)
n chemical species
Inlet material and/orenergetic flux
Outlet materialand/or energetic flux
V,
PkkSk = 0() dV
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Examples of mathematical modeling of
chemical process
Mass conservation by species
dmkdt
= ddt
RV kdV =
RV
kt
dV
RV kMkrvdV
kt
= div(Jk) +kMkrv
= RVdiv(Jk)dV Gauss theoremJk = vkk
R Jk d
Totalma
terialflux
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Examples of mathematical modeling of
chemical process
=P
kk v=P
kJk
Jdk =k(vk v)
Jck =kv
Jk = Jdk+ J
ck
(P
kk)
t = div(Pk Jk)
t = div(v) v=
1
vt
+ v v=vdiv(v)
DvDt
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Examples of mathematical modeling of
chemical process
J0
q
= (u +pv)
| {z }=hv + JqJu =uv+pv + Jq
ut
= divJu= R Ju d
PkhkJ
ck
PkhkJ
dk
dU
dt = RVu
t dV
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Examples of mathematical modeling of
chemical process
Seminar:
Nonisothermal CSTR
Batch reactor
pH systems
Distillation column
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Examples of mathematical modeling of
chemical process
Seminar:
Nonisothermal CSTR
Batch reactor
pH systems
Distillation column
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Phng trnh dng
S vn chuyn trong thit b phn ng cahn hp phn ng, bao gm:
Dng vt liu (khi lng/nng ) Dng nhit nng (nng lng)
Dng ng lng (xung)
C dngi lu, dng dn, dng cp vdng pht sinh Dng i lu hoc dng dn c th tn ti c lp hocng thi nhng ch trong mt pha
S vn chuyn xy ra qua lp bin ca hai pha l dng
cp
(lng/th tch) c c trng bi mt dng
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Phng trnh dng
Cc qu trnh vn chuyn trong thit b
Dng i lu S thay i v tr trong khng gian ca mt dngc gi l i lu (dng vn chuyn vm)
Mt dng i lu c biu th
Dng dn (khuch tn) Chuyn ng phn t trong lng pha kh hoc pha lng
l chuyn ng vi m to thnh dng dn
j c = v (lng/thi gian/din tch)
(lng/thi gian/din tch)j d = D
gradC
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Phng trnh dng
Cc qu trnh vn chuyn trong thit b (tt)
Dng cp S vn chuyn ca i lng c trng t pha ny
sang pha khc gi l s cp
Cc qu trnh xy ra gia cc pha thng c m tbng cc i lng qung tnh
(lng/thi gian/din tch)
- h s cp, - b mt ring (xt trn mt n v th tch)f
j =f
- ng lc
h h d
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Phng trnh dng
Dng pht sinh
Dng pht sinh vt cht do phnng ha hc
G=gradP
Gj =Pm
i=1jiri
Gi = (Hi)ri
Dng pht sinh cu nhit nng do phnng ha hc
Dng pht sinh ca ng lng do chnh lch p sut
c hnh thnh do s thay i ca p sut trong h, tcl c tc dng ca xung lc
Cc qu trnh vn chuyn trong thit b (tt)
Ph h d
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Phng trnh dng
Xt trng hp h tng qut (ng th hay
d th) c phn ng ha hc
n chemical species
Inlet material and/orenergetic flux
Outlet materialand/or energetic flux
dV
PjijSj = 0
Ph h d
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Phng trnh dng
Phng trnh cn bng tng qut c dng caphng trnh vi phn ring phn cDamkhlerthit lp (1936)
j c
j d
Dng cpDng
pht sinh
t
= div(v ) + div(grad) f+ G
= Cj CpT v
Ph h d
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Phng trnh dng
Vit li cc phng trnh cn bng
t = div(v ) + div(
grad) f+ G
t = div(v) + div(D?
grad) ?f+ G
vt
= div(v v) + div(gradv)
f(
v) + G
CpT
t = div(vCpT) + div(T
gradCpT)
?fCpT+ G
Cjt
= div(v Cj) + div(DgradCj)
jfCj+ Gj
Ph h d
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Phng trnh dng
Example: xem chng 5, tp 5 (sch Cc
qu trnh, thit b TRONG CNG NGHHA CHT V T HC PHM, Nguyn Bin)
M hnh ton cho h khuy l tng Chui thit b khuy l tng
Thit b khuy gin on
Thit by l tng Cc bi ton thc t
t = div(v ) + div(
grad) f+ G
O tli
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Outline
General introduction
Structure and operation of chemical engineeringsystems
What is a chemical process?
Motivation examples Part I: Process modeling
Part II: Computer simulation
Part III: Optimization of chemical processes
Ref.: Burden R. L. and Faires J. D. Numerical analysis.