Modeling, Simulation and Optimization

for Chemical Engineering

for

CH3133- CC01 and CC02

Ho Chi Minh City University of Technology
 TABLE OF CONTENTS
Example-CSTR

Modeling Semi batch reactor

Modeling Stirred tank heater

Distillation, Types, and Application

Assumptions

Modeling of binary distillation

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Example-CSTR

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Example-CSTR

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Example-CSTR

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Semi batch reactor

A semi-batch reactor allows partial reactants added and/or partial

product removed from the system to allow better control of
reactions Semi-batch reactors are used when:

• Performing highly exothermic reaction

• Minimize formation of undesired product (i.e. high concentration of one of reactant
would allow formation of undesired product)
• Minimize reversible reaction

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Semi batch reactor

Here we discuss a dynamical model for a semi-batch reactor shown in Figure. The
following highly exothermic thiosulphate reaction is considered in the present study:

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Semi batch reactor

The reaction rate is assumed to be proportional to the first order of the concentration
of reactants A and B, and the solution density to be constant:

where k is a function of the temperature according to the Arrhenius expression

The dynamic behaviour of the sample semi-batch reactor could be described by a set of
differential equations resulting from mass and energy balances of the reaction mixture,
the energy balance of the jacket wall and the circulating fluid (cooling water) inside the
jacket

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Semi batch reactor

Total Mass Balance Equation

As density is constant

V represents the volume of reaction mass and F0 is the addition flow rate of reagent A(H2O2)

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Semi batch reactor

Component Mass Balance Equations

Here, CA is the concentration of reactant A, CA0 the initial concentration of reactant A, CB the
concentration of reactant B, and a (= 2) and b (= 1) are the stoichiometric factors of reactant A and B,
respectively.

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Semi batch reactor

Energy Balance Equations

For semi-batch reactor

Here, T is the reactor temperature, Tad the temperature of H2O2 added, (–ΔH) the heat of reaction, Cp the
heat capacity and the inside heat transfer rate:

For jacket wall

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Semi batch reactor

Energy Balance Equations

Here, VM is the wall volume, ρM the density of wall, CM the heat capacity of wall and the outside heat transfer
rate:

For jacket fluid

where FW is the flow rate of jacket fluid stream, TJ0 the inside jacket fluid temperature, VJ the jacket volume, ρJ the
density of jacket fluid and CJ the heat capacity of jacket fluid. It should be noted that the behaviour of the jacket fluid has
been considered as a perfect mixing

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Stirred tank heater

Assumptions

• Perfect mixing
•
• Perfectly installed (no heat loss)

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Stirred tank heater
Total mass balance

Energy balance

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Stirred tank heater
At 𝑇 =0 Degree of freedom

Total variables involved=6

Total equations involved=2

𝑓 =6−2=4
Load variables

𝑓 =4−2=2
Control equations

Control variables, h, T
Manipulated variables, F, Q

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Degree of freedom

To simulate a process, model equation should be solvable set of

relation, In order for a model have a unique solution, number of
solution should be zero

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Stirred tank heater
Self-Assessment:
Consider a stirred heating tank as shown in Figure. Liquid at temperature Ti flowing into
the tank at a volumetric flow rate F, is heated by steam flowing through the steam coil
arrangement at a rate a Q (mass/time). The heated fluid, now at temperature T. is
withdrawn at the same volumetric rate F. The tank volume is V and the latent heat of
vaporization of steam is . You may consider constant density (ρ) and heat capacity (Cp) of
the reacting material.

Derive the overall mass and energy balance equations making appropriate assumptions

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Distillation

Distillation is a process used in chemistry to separate

substances within a liquid mixture by using variations in
their boiling points.

• Simple Distillation
• Fractional Distillation
• Steam Distillation
• Vacuum Distillation
• Azeotropic Distillation

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Distillation
Applications of Distillation

Distillation has a wide range of applications.

• Production of alcoholic beverages,
• Used to separate different components of crude oil. used to purify
chemicals.
• Used to remove contaminants from water.
• The versatility of distillation makes it a crucial process in many
industries.

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Binary Distillation
For any separation process, key performance that
stringently need to be monitored are the purity of
the desired product and their losses. Hence,
monitoring the components composition is
crucial. Moreover, distillation is dependent on the
volatility of the mixture and
controlling/monitoring the reboiler and
condenser is crucial.

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Binary Distillation
Assumptions
The following assumptions have been adopted to develop the mathematical process model.

• Negligible vapour holdup is assumed.

• The molar heats of vaporization of both components are about the same.
• The liquid holdup varies on each tray (excluding reflux drum and column base), and the liquid
hydraulics are calculated from the Francis weir formula. In practice, the liquid holdups in reflux drum
and column base are generally tightly controlled implementing level controllers with the manipulation
of distillate and bottom product flow rates respectively.
• The liquid is perfectly mixed on each stage. For the nth stage, it reveals that
• liquid composition anywhere on the stage = xn
• The total amount of liquid accumulated in the reboiler as well as in the base of the column is
considered as the column base holdup.
• The heat losses from the column to the surroundings are assumed to be negligible.
• The relative volatility is invariant with time and with column length.
• Each tray is assumed to be ideal (i.e., 100% efficient).
• Coolant and steam dynamics are negligible in the condenser and reboiler respectively.
Course: Modeling, Simulation and Optimization for Chemical Engineering
 Binary Distillation

In this balance equation, all the three terms are in gm-moles per minute (gmol/min).
For the sample distillation column, the flow rate of a liquid leaving the rectifying
section (LR) is equal to the reflux flow rate (R), which means,

Similarly, the flow rate of a liquid leaving the feed tray (Lf ) is equal to that of a liquid
leaving the stripping section (LS) and so

The vapour flow rate through all trays of the column is the same.

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Binary Distillation
Condenser–Reflux Drum System
The input and output flows and their respective compositions are shown for the condenser–reflux drum
system in Figure. The balance equations in terms of total mass and a lighter component (ethanol) mass
have been formulated as below
Total continuity equation

Since constant liquid holdup is assumed, the above equation becomes

Component continuity equation

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Binary Distillation
Rectifying Section
Total and component mass balance equations can be derived for the rectifying section
considering the incoming and outgoing flows as shown in Figure

Total continuity equation

Since VR = Vf = V and mR is constant,

Component continuity equation

Substituting LR = R, and VR = Vf = V and rearranging

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Binary Distillation
Feed Tray
The schematic representation of the feed tray is shown in Figure 6.4. Let qF represent the quality of
the feed stream, where qF = LF/F and therefore, 1 – qF = VF/F. Here, LF and VF are the flow rates of
liquid and vapour feeds respectively, and obviously F = LF + VF. The flow rate of a vapour stream
leaving the feed stage (Vf ) can be expressed as:

flow rate of a liquid stream leaving the feed tray can be expressed as

for the case of a partially vaporized feed

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Binary Distillation
Feed Tray
The quality of the feed stream can be expressed by qF = (Lf – LR)/F. Notice that qF has the following
numerical limits for the various conditions:
Superheated vapour feed, qF < 0
Saturated vapour feed, qF = 0
Partially vaporized feed, 0 < qF < 1
Saturated liquid feed, qF = 1
Subcooled liquid feed, qF > 1.

Total continuity equation

Component continuity equation

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Binary Distillation
Stripping Section
The compartment representing the stripping section is shown in Figure. Making balance around the
stripping section, the following continuity equations can be obtained.

Total continuity equation

Component continuity equation

Course: Modeling, Simulation and Optimization for Chemical Engineering

 Binary Distillation
Reboiler–Column Base System
Figure depicts a typical equilibrium stage (vapour stream V is in equilibrium with liquid stream B)
comprising of a partial reboiler and the base of the distillation column. This combined system can
mathematically be represented by the following material balance equations.

Total continuity equation

Since mB is constant, so B = LS – V
Component continuity equation

Course: Modeling, Simulation and Optimization for Chemical Engineering