chapter 5

1

CHAPTER

FIVE

REACTION ENGINEERING

5.1. Determination of Kinetic Parameters of the Saponification Reaction in a PFR

5.2. Determination of Kinetic Parameters of the Saponification Reaction in a CSTR

5.3. Experimental and Numerical Determination of Kinetic Parameters of the

Saponification Reaction in a Series of CSTRs

5.4. Determination of Optimal Agitation Conditions in a Stirred Tank

5.5. Determination of Residence Time Distribution in a Packed Bed

5.6. Modeling of Water Level in a Tank under Steady State and Dynamic Conditions

Everything should be made as simple as possible,

but not simpler.

ALBERT EINSTEIN

2

5.1. DETERMINATION OF KINETIC PARAMETERS OF THE SAPONIFICATION

REACTION IN A PFR

Keywords: Tubular reactor, plug flow reactor, saponification, integral method, differential

method.

Before the experiment: See your TA before the experiment. Read the booklet carefully. Be aware

of the safety issues. Make sure to do all solution preparation calculations before you come to lab.

Ethyl Acetate Mol wt.: 88.10, Density: 0.898 g/cm3 (liquid)

Sodium Hydroxide Mol wt.: 40.00 (pellet)

5.1.1. Aim

To study the saponification of ethyl acetate in a plug-flow reactor and to determine the kinetic

parameters using integral and differential methods.

5.1.2. Theory

5.1.2.1. Plug Flow Reactor

In a tubular reactor, the feed enters at one end of a cylindrical tube and the product stream leaves at

the other end. The long tube and the lack of stirring prevent complete mixing of the fluid in the

tube. Hence the properties of the flowing stream will vary from one point to another, namely in both

radial and axial directions.

In the ideal tubular reactor, which is called the “plug flow” reactor, specific assumptions are made

about the extent of mixing:

1. no mixing in the axial direction, i.e., the direction of flow

2. complete mixing in the radial direction

3. uniform velocity profile across the radius.

The absence of longitudinal mixing is what defines this type of reactor [1]. The validity of the

assumptions will depend on the geometry of the reactor and the flow conditions. Deviations, which

are frequent but not always important, are of two kinds:

3

1. mixing in longitudinal direction due to vortices and turbulence

2. incomplete mixing in radial direction in laminar flow conditions

For a time element t and a volume element V at steady state, the mass balance for species ‘i’ is

given by Eq. 5.1.1

vA CA │v t- vA CA│v+Δv t - rAVt = 0 (5.1.1)

where

vA : volumetric flow rate of reactant A to the reactor, L/s

CA : concentration of reactant A, mol/L

rA : rate of disappearance of reactant A, mol/Ls

Dividing Eq. 5.1.1 by V and t results in Eq. 5.1.2

𝑣𝐴𝐶𝐴|𝑉 − 𝑣𝐴𝐶𝐴|𝑉+∆𝑉

∆𝑉=

r𝐴

𝑣𝐴 (5.1.2)

and taking limit as V 0 gives Eq. 5.1.3.

dC𝐴

dV= −

r𝐴

𝑣𝐴 (5.1.3)

Eq. 5.1.4 is the relationship between concentration and size of reactor for the plug flow reactor.

Here rate is a variable, but varies with longitudinal position (volume in the reactor, rather than with

time).

dV

𝑣𝐴= −

dC𝐴

r𝐴 (5.1.4)

The conversion, X, is defined by Eq. 5.1.5

X =(initial concentration – final concentration)

(initial concentration) (5.1.5)

and Eq. 5.1.4 can be rewritten as Eq. 5.1.6.

dV

𝑣𝐴C𝐴0= −

dX

r𝐴 (5.1.6)

Equation 5.1.6 can be used with differential method to obtain the reaction parameters [2].

4

If the equation 5.1.4 is integrated with following boundary conditions,

At the entrance: V = 0

CA = CA0 (inlet concentration of reactant A)

At the exit: V = VR (total reactor volume)

CA = CA (exit conversion)

∫dV

𝑣𝐴

V𝑅

0

= − ∫dC𝐴

r𝐴

C𝐴

C𝐴𝑂

(5.1.7)

With the elementary reaction assumption, reaction rate equation can be simplified as in Eq. 5.1.8.

where C𝐵 is concentration of reactant B and 𝜃𝐵 is the ratio of inlet concentrations of reactant B and

A (C𝐵0 /C𝐴0 )

r𝐴 = 𝑘C𝐴C𝐵

C𝐴 = C𝐴0(1 − 𝑋); C𝐵 = C𝐴0 (𝜃𝐵 − 𝑋) (5.1.8)

Combining equations 5.1.7 and 5.1.8, the following expression (Eq. 5.1.9) is obtained.

∫dV

Q𝐴

V𝑅

0

= − ∫dC𝐴

kC𝐴C𝐵

C𝐴

C𝐴𝑂

(5.1.9)

It can be written in terms of conversion as Eq. 5.1.10

∫dV

Q𝐴

V𝑅

0

= − ∫dC𝐴

kC𝐴02(1 − 𝑋)(𝜃𝐵 − 𝑋)

C𝐴

C𝐴𝑂

(5.1.10)

This expression can be solved using the integral method to determine the reaction parameters [3].

5.1.2.2. Saponification Reaction

Sodium Hydroxide + Ethyl Acetate → Sodium Acetate + Ethanol

The reaction is 2nd

order elementary within the range of 0-0.1 M concentration and 20-40 °C.

5

5.1.2.3. The Conductivity and Concentration Relations

The conductivity of the reaction mixture changes with conversion and therefore the extent of the

reaction can be monitored by recording the conductivity with respect to time. A calibration curve is

needed to relate conductivity data to concentration values.

5.1.3. Experimental Setup

The apparatus used in this experiment is shown in Figures 5.1.1 and 5.1.2. The plug flow reactor is

0.4 L.

Figure 5.1.1. Chemical reactor service unit.

Figure 5.1.2. Tubular reactor.

6

5.1.4. Procedure

1. Prepare 100 ml of 0.05 M NaOH solution in a 1000 ml beaker, record conductivity data.

2. Add 100 ml distilled water to the beaker to dilute the NaOH solution, make sure it is perfectly

mixed, and record conductivity data. Repeat this step six more times to prepare a calibration

curve.

3. Prepare 5 L of 0.05 M ethyl acetate and 0.05 M NaOH solutions. Pour these solutions into the

feed tanks.

4. Adjust a constant flow rate by setting the pump speeds of both reactants.

5. Record the conductivity when steady state is reached.

6. Repeat the same procedure for different flow rates.

Safety Issues: In this experiment, sodium hydroxide (NaOH) and ethyl acetate (EtAc) will be used

as reactants. NaOH is poisonous and corrosive. It may be fatal if swallowed and harmful if inhaled.

It causes burns to any area of contact and reacts with water, acids and other materials. EtAC is a

flammable liquid and vapor. It causes eye irritation. Breathing it may cause drowsiness and

dizziness. It may also cause respiratory tract irritation. Prolonged or repeated contact causes

defatting of the skin with irritation, dryness, and cracking. During the experiment, beware of risks

when handling with reactants. Make sure all the tanks are emptied, and all the electronic devices are

unplugged at the end of the experiment. In case of eye or skin contact, remove any contact lenses or

contaminated clothing or shoes. Immediately flush eyes or skin with plenty of cold water for at least

15 minutes. Cover the irritated skin with an emollient. In case of inhalation, remove to fresh air. If

breathing is difficult get medical attention immediately. In case of ingestion, do not induce

vomiting. Never give anything by mouth to an unconscious person. For further information, check

MSDS of sodium hydroxide and ethyl acetate [4, 5]. The solutions used in this experiment are dilute

in terms of the chemicals, therefore no need to a special treatment.

5.1.5. Report Objectives

1. Evaluate the data using the Integral Method. Calculate conversion.

2. Evaluate the rate constant using the Differential Method.

3. Compare the results of the two methods.

7

References

1. Perry, R.H. and D. Green, Perry’s Chemical Engineers’ Handbook, 8th

edition, Mc Graw-Hill,

New York, 2008.

2. Levenspiel, O., Chemical Reaction Engineering, 3rd

edition, Cambridge University, 1999.

3. Fogler, H. S., Elements of Chemical Reaction Engineering, 4th

edition, Prentice-Hall Inc., 2006.

4. Sodium Hydroxide MSDS, http://www.sciencelab.com/msds.php?msdsId=9924998.

5. Ethyl Acetate MSDS, http://www.sciencelab.com/msds.php?msdsId=9927165.

8

5.2. DETERMINATION OF KINETIC PARAMETERS OF THE SAPONIFICATION

REACTION IN A CSTR

Keywords: Continuous stirred tank reactors, saponification, mathematical modeling, differential

equations.

Before the experiment: See your TA. Read the booklet carefully. Be aware of the safety

precautions. Make sure to do all solution preparation calculations before you come to lab.



5.2.1. Aim

To study the dynamics of a CSTR during different stages of its continuous operation by using the

saponification of ethyl acetate reaction.

5.2.2. Theory

5.2.2.1. Continuous-Stirred Tank Reactors

Continuous-stirred tank reactors (Fig. 5.2.1) are used very commonly in industrial processes. For

this type of reactor, mixing is complete, so that the temperature and the composition of the reaction

mixture are uniform in all parts of the vessel and are the same as those in the exit stream [1].

Figure 5.2.1. Continuous stirred tank reactor.

Three stages of the continuous operation of a CSTR can be modeled.

9

1. From beginning to overflow

2. From overflow to steady state

3. Steady state operation

The first and second stages are transient and they produce differential equations. The third stage is

represented by a steady state model which contains algebraic equations.

Stage One

This stage is semibatch. There is no output because the reactor contents do not yet reach the

overflow level. With assuming that the saponification reaction of ethyl acetate with sodium

hydroxide is second order overall, a material balance on either NaOH or ethyl acetate (both

reactants are at the same concentration and flow rate) gives Eq. 5.2.1 or 5.2.2:

rate of accumulation = rate of input - rate of consumption

𝑑(𝑉𝐶)

𝑑𝑡= 𝑣𝐶0 − 𝑉𝑘𝐶2

(5.2.1)

or

𝑉𝑑𝐶

𝑑𝑡+ 𝐶

𝑑𝑉

𝑑𝑡= 𝑣𝐶0 − 𝑉𝑘𝐶2

(5.2.2)

where

C = concentration (M)

C0 = initial concentration (M)

𝑣 = volumetric flow rate (L/min)

k = reaction rate constant

t = time (min)

V = volume of reactor (L)

But ‘V’ is a function of time, and since the system is of constant density and flow rate, a total mass

balance gives:

𝑑𝑉

𝑑𝑡= 𝑣 or 𝑉 = 𝑣𝑡

since at t 0, V 0. Eq. 5.2.2 gives Eq. 5.2.3

10

𝑑𝐶

𝑑𝑡=

𝐶0

𝑡−

𝐶

𝑡− 𝑘𝐶2

(5.2.3)

Eq. 5.2.3 is subject to C C 0 at t 0.

Stage Two

The second stage is continuous but not yet steady. The concentration is changing with time but the

volume of the reactants is constant. A material balance takes the form of equations 5.2.4 and 5.2.5

rate of accumulation = rate of input - rate of output - rate of consumption

𝑉𝑑𝐶

𝑑𝑡= 𝑣𝐶0 − 𝑣𝐶 − 𝑉𝑘𝐶2

(5.2.4)

and therefore,

𝑑𝐶

𝑑𝑡=

𝐶0

𝑡−

𝐶

𝑡− 𝑘𝐶2

(5.2.5)

where

𝑇 = 𝑡 − 𝜏 (min)

𝑡 = 𝑉/𝑣 (min)

At steady state, C Cs , which is a particular solution to Eq. 5.2.5.

Stage Three

This is the easiest stage to model. A material balance results in equations 5.2.6 and 5.2.7

rate of input = rate of output + rate of consumption

𝑣𝐶0 = 𝑣𝐶𝑠 + 𝑉𝑘𝐶𝑠2 (5.2.6)

𝑘𝜏𝐶𝑠2 + 𝐶𝑠 − 𝐶0 = 0 (5.2.7)

The calculation of the specific rate constant k can be carried out by the Eq. 5.2.8,

𝑘 =(𝑣𝐴+𝑣𝐵)

𝑉(𝐶𝐴0−𝐶𝐴)

𝐶𝐴2 L / mol.s (5.2.8)

11

For a reactant A in a reactor operating at steady state, the volume (V) may be assumed constant and

the steady state concentration of NaOH in the reactor (CA) may be used to calculate the specific rate

constant (k) [2, 3].

In this experiment, the kinetic parameters of the saponification reaction will be calculated based on

the conductivity data collected during the experiment performed in a CSTR, and the results will be

compared with the literature. Using a computational tool, NaOH concentration on stream and the

rate constant will be determined and compared with the experimental data.

5.2.2.2. The Conductivity and Concentration Relations


reaction can be monitored by recording the conductivity with respect to time. A calibration curve is

needed to relate conductivity data to concentration values.


The apparatus used in this experiment is shown in Figures 5.2.2 and 5.2.3. The reactor volume in

this experiment is 1.6 L.


CSTR (see Fig. 5.2.3.)

12

Figure 5.2.3. Continuous stirred tank reactor.

5.2.4. Procedure

1. Prepare 100 ml of 0.05 M NaOH solution in a 1000 ml beaker, record conductivity data.

2. Add 100 ml distilled water to the beaker to dilute the NaOH solution, make sure it is perfectly

mixed, and record conductivity data. Repeat this step six more times to prepare a calibration

curve.

3. Make up 5 liter batches of 0.05 M sodium hydroxide and 0.05 M ethyl acetate.

4. Remove the lids of the reagent vessels and carefully fill the reagents. Refit the lids.

5. Set the pump speeds of both reactants to give 50 ml/min flow rate.

6. Set the agitator speed controller to 7.0.

7. Switch on the feed pumps and agitator motor. Start the stopwatch.

8. Collect conductivity data each minute for 45 minutes.

Safety Issues: In this experiment, sodium hydroxide (NaOH) and ethyl acetate (EtAc) will be used

as reactants. NaOH is poisonous and corrosive. It may be fatal if swallowed and harmful if inhaled.

It causes burns to any area of contact and reacts with water, acids and other materials. EtAC is a

flammable liquid and vapor. It causes eye irritation. Breathing it may cause drowsiness and

dizziness. It may also cause respiratory tract irritation. Prolonged or repeated contact causes

defatting of the skin with irritation, dryness, and cracking. During the experiment, beware of risks

when handling with reactants. Make sure all the tanks are emptied, and all the electronic devices are

unplugged at the end of the experiment. In case of eye or skin contact, remove any contact lenses or

contaminated clothing or shoes. Immediately flush eyes or skin with plenty of cold water for at least

15 minutes. Cover the irritated skin with an emollient. In case of inhalation, remove to fresh air. If

breathing is difficult get medical attention immediately. In case of ingestion, do not induce

vomiting. Never give anything by mouth to an unconscious person. For further information, check

13

MSDS of sodium hydroxide and ethyl acetate [4, 5]. The solutions used in this experiment are dilute

in terms of the chemicals, therefore no need to a special treatment.


You may assume that the saponification reaction of ethyl acetate with sodium hydroxide is second

order overall.

1. Prepare a calibration chart for NaOH concentration and conductivity.

2. Prepare a spreadsheet to calculate sodium hydroxide concentration, sodium acetate concentration

and the degree of conversion of sodium hydroxide and sodium acetate for each of the

conductivity data taken over the period of the experiment.

3. Draw sodium hydroxide concentration versus time, sodium acetate concentration versus time,

and the degree of conversion of sodium hydroxide versus time graphs.

4. Calculate experimental specific rate constant (k) from material balance and compare it with the

one obtained from Arrhenius equation using the data found from literature.

5. Draw sodium hydroxide concentration versus time using MATLAB starting from differential

equation obtained from material balance, estimate steady state concentration of sodium

hydroxide and compare it with the experimental one.

6. Derive all of the equations you use in the theory part.

References


edition, Prentice-Hall Inc., 2006.



3. Perry, R.H., and D. Green, Perry’s Chemical Engineers’ Handbook, 7th


New York, 1997.


5. Ethyl Acetate MSDS, http://www.sciencelab.com/msds.php?msdsId=9927165.

14

5.3. EXPERIMENTAL AND NUMERICAL DETERMINATION OF KINETIC

PARAMETERS OF A REACTION IN A SERIES OF CSTRS

Keywords: CSTR, CSTR in series, saponification, conversion.

Before the experiment: Make sure to do all solution preparation calculations before you come to

lab. For further information about the chemicals, look over [1, 2].



5.3.1. Aim

To observe transient changes in concentrations of three CSTRs in series using of experimental

measurements and computational methods and to determine the rate constant of the saponification

reaction under steady state conditions.

5.3.2. Theory

In continuously operated chemical reactors, the reactants are pumped at constant rate into the

reaction vessel and the chemical reaction takes place as the reaction mixture flows. The reaction

products are continuously discharged to the subsequent separation and purification stages. The

extent of the required separation and purification process depends on the efficiency of the reactor,

and so the selection of the correct type of the reactor for a given duty is most important since the

economics of the whole process could hinge on this choice. Normally, the efficiency of a chemical

reactor is measured by its ability to convert the reactants into the desired products with the

exclusion of unwanted by-products; this is measured by yield. However, additional factors such as

safety, ease of control and stability of the process must also be considered. Many of these factors

depend on the size and shape of the reactor. The size of reactor for a purposed feed rate depends on

the reaction kinetics of the materials undergoing chemical change and on the flow conditions in the

reactor. On the other hand, the flow conditions are determined by the cross sectional area of the

path through which the reaction mixture flows; i.e. the shape of the reactor. Thus, it is apparent that

size and shape are interrelated factors, which must be taken together when considering continuous

reactors [3].

15

5.3.2.1. Continuously Stirred Tank Reactors (CSTRs)

CSTRs are usually cylindrical tanks with stirring provided by agitators mounted on a shaft inserted

through the vessel lid. In addition, the tank is fitted with auxiliary equipment necessary to maintain

the desired reaction temperature and pressure conditions [3].

The well-stirred tank reactor is used mostly for liquid phase reactions. In normal operation, a steady

continuous feed of reactants is pumped into the vessel and since there is usually negligible density

change on reaction, an equal volume of the reactor contents is displaced through an overflow pipe

situated near the top of the vessel [3].

Figure 5.3.1. Single continuous stirred tank reactor.

For a single stirred tank reactor (Figure 5.3.1), it is assumed that the design of the agitator provides

complete mixing of the vessel contents to achieve uniform temperature and composition distribution

throughout the vessel. This premise of complete mixing then implies that the reactor outlet stream is

identical in temperature and composition to the bulk reactor contents [4].

For an effective reactor volume ‘V’, molar input and output ‘F’, and moles N the mole balance for

component A is given by Eq. 5.3.1:

𝐹𝐴0 − 𝐹𝐴1 + 𝑟𝐴𝑉𝑅 =𝑑𝑁𝐴

𝑑𝑡 (5.3.1)

For an irreversible reaction, the reaction rate term defined as Eq. 5.3.2 [3]:

𝑟𝐴 = 𝑘𝐶𝐴1𝑛 (5.3.2)

The reaction rate 𝑟𝐴 is constant within the reactor and time when steady state operation has been

established. The right hand side of the Equation 5.3.1 vanishes under steady state operation

therefore the equation becomes algebraic.

VR

C1 C1

F1

F0

C0

16

The conversion of the reactant can be defined as Eq. 5.3.3:

𝑥 =𝐹𝐴0 − 𝐹𝐴1

𝐹𝐴0 (5.3.3)

Combining equations 5.3.1 and 5.3.3 under steady-state conditions, the design equation of a single

CSTR is obtained as Eq. 5.3.4 [4].

𝑉𝑅 = 𝐹𝐴0 𝑥

−𝑟𝐴 (5.3.4)

Single Tanks with Simple Reactions

For a first order reaction under steady state conditions, dividing Eq. 5.3.1 by volumetric flow rate

yields 𝑄 (𝑣𝑜𝑙𝑢𝑚𝑒 𝑡𝑖𝑚𝑒⁄ ) as in Eq. 5.3.5 [3]:

𝐶𝐴0 = 𝐶𝐴1 (1 +𝑘𝑉𝑅

𝑄) (5.3.5)

𝑉𝑅 𝑄⁄ is the space time and will be given the symbol ‘’. Hence, Eq. 5.3.6 forms as

𝐶𝐴1

𝐶𝐴0=

1

(1 + 𝑘𝜏) (5.3.6)

Since the input and the outlet volumetric flow rates are equal, the conversion ‘𝑥’ can also be written

as Eq. 5.3.7:

𝑥 =𝐶𝐴0 − 𝐶𝐴1

𝐶𝐴0= 1 −

1

(1 + 𝑘𝜏) (5.3.7)

and as is usual with first order reactions the result is independent of the feed concentration.

For a second order reaction starting from the overall mole balance around each tank individually at

steady state conditions, Equation 10.3.1 under equimolar feed becomes as Eq. 5.3.8:

𝐶𝐴0 = 𝐶𝐴1 + 𝑘𝜏𝐶𝐴12 (5.3.8)

and the positive root of this quadratic equation gives Eq. 5.3.9:

𝐶𝐴1 =(−1 + √1 + 4𝑘𝜏𝐶𝐴0)

2𝑘𝜏 (5.3.9)

17

hence the conversion equation becomes as Eq. 5.3.10,

𝑥 = 1 +−1 + √1 + 4𝑘𝜏𝐶𝐴0

2𝑘𝜏𝐶𝐴0 (5.3.10)

Transient Behavior

Under unsteady state conditions the mass balance turns out to be an ordinary differential equation

that can be solved numerically in order to simulate the theoretical behavior of concentration and

conversion with respect to time. For a second order reaction this equation is derived from the Eq.

5.3.1 by substituting the expressions of concentration, space time, and conversion as Eq. 5.3.11 [4].

𝑑𝑥

𝑑𝑡= 𝑘𝐶𝐴0(1 − 𝑥)2 −

𝑥

𝜏 (5.3.11)

where

𝑥 = conversion of reactant A

𝐶𝐴0= Initial concentration of A

𝑘 = Reaction rate constant

𝜏 = Space time (V/Q)

Multiple Tank Cascade with Simple Reactions (CSTRs in Series)

A major shortcoming of a single stirred tank is that all of the reaction takes place at the low final

reactant concentration and hence requires an unduly large reactor hold-up. If a number of smaller

well-stirred reactors are arranged in series, only the last one will have a reaction rate governed by

the final reactant concentration and all of the others will have higher rates. Hence, for a given duty

the total reactor hold-up will be less than for a single tank. This saving in reactor volume increases

as the required fractional conversion increases and also as the number of installed tanks increases.

In fact, all of the desirable features of the CSTR may be retained while the low hold-up

characteristics of a plug flow tubular reactor are approached, e.g. five to ten tanks in a cascade are

likely to give high conversion values at low hold-up times similar to a pug-flow reactor. It is a

matter of economics to balance the cost of the number of tanks against their reduced size [3].

There are other operational advantages in carrying out reactions in series of stirred tanks. For

example if one vessel in the cascade has to be put out of commission for any reason, it may be by-

18

passed and production continued at a slightly reduced rate whereas failure of a single CSTR would

entail complete loss in production [3].

5.3.2.2. Saponification Reaction

NaOH + CH3COOC2H5 CH3COONa + C2H3OH

Sodium Hydroxide

(A)

+

Ethyl Acetate

(B)

Sodium Acetate

(C)

+

Ethyl Alcohol

(D)

The reaction can be considered first order with respect to sodium hydroxide and ethyl acetate i.e.

second order overall, within the limits of concentration (0-0.1M) and temperature (20-40°C) studied

[5].

To calculate the specific rate constant k, the overall mass balance may be written as [4]:

Rate of change within the reactor = Input – Output + Accumulation

i.e. for NaOH in a reactor operating at steady state the volume may be assumed constant. The steady

state concentration of NaOH in reactor (CA) may be used to calculate the specific rate constant (k)

as in Eq. 5.3.12 and Eq. 5.3.13:

𝑘 =𝑄

𝑉

(𝐶𝐴0 − 𝐶𝐴)

𝐶𝐴2 (5.3.12)

𝑘 =(𝑄𝐴 + 𝑄𝐵)

𝑉

(𝐶𝐴0 − 𝐶𝐴)

𝐶𝐴2

(5.3.13)

5.3.2.3. Conductivity and Concentration Relations


reaction can be monitored by recording the conductivity with respect to time. Conductivity data

obtained throughout the experiment has to be converted into concentration data of the system. A

calibration chart showing the relation between the conductivity of the fluid and the concentration of

the ionized material can be obtained by measuring known concentrations of the material's

conductivity.

19

The reaction carried out in a Continuous Stirred Tank Reactor or series CSTRs eventually reaches

steady state when a certain amount of conversion of the starting reagents has taken place. The

steady state conditions will depend on concentration of reagents, flow rate, volume of reactor and

temperature of reaction.

In this experiment, the reaction rate constant for the saponification reaction will be calculated based

on the conductivity data collected during the experiment carried on three CSTR in series and

compared with the literature value. In addition, the final conversion will calculated numerically

using suitable computational tools.


The experimental setup used in this experiment is shown in Figure 5.3.2.


5.3.4. Procedure

1. Prepare a calibration curve for the conductivity vs. concentration of NaOH (for the solutions

with the concentrations 0.005M, 0.01M, 0.02M, 0.03M, 0.04M, 0.05M).

2. Prepare 3.0 liter batches of 0.05M sodium hydroxide and 0.05M ethyl acetate.

3. Remove the lids of the reagent tanks and carefully, fill with the reagents. Refit the lids.

4. Set the pump speed control to give 50 ml/min flow rate.

5. Start agitators.

6. Switch on both feed pumps and agitator motor, and start recording conductivity.

7. Collect conductivity data for 30 minutes in 30 seconds intervals.

Safety Issues: In this experiment, sodium hydroxide (NaOH) will be used as reactant. NaOH is

poisonous and corrosive. It may be fatal if swallowed and harmful if inhaled. It causes burns to any

20

area of contact and reacts with water, acids and other materials Prolonged or repeated contact

causes defatting of the skin with irritation, dryness, and cracking. During the experiment, beware of

risks when handling with reactant. Make sure all the tanks are emptied, and all the electronic

devices are unplugged at the end of the experiment. In case of eye or skin contact, remove any

contact lenses or contaminated clothing or shoes. Immediately flush eyes or skin with plenty of cold

water for at least 15 minutes. Cover the irritated skin with an emollient. In case of inhalation,

remove to fresh air. If breathing is difficult get medical attention immediately. In case of ingestion,

do not induce vomiting. Never give anything by mouth to an unconscious person. For further

information, check MSDS of sodium hydroxide and ethyl acetate [6]. The solutions used in this

experiment are dilute in terms of the chemicals, therefore no need to a special treatment. After the

experiment make sure all the tanks are emptied, and all the electronic devices are unplugged.


1. Find the reaction rate constants for each CSTR starting from the design equation of a CSTR.

2. Find the rate constant of the reaction from the literature and calculate the error.

3. Find the NaOH conversion corresponding to each measurement.

4. Draw conversion vs time graphs for each reactor during the whole experiment (Draw on the

same graph).

5. Solve the differential equations numerically to find the conversions using MATLAB or

POLYMATH software (Use literature value for the reaction rate constant).

6. Compare the conversion values obtained from numerical solution with experimental

observations, showing experimental and numerical conversions on a single graph.

References

1. http://akkimyaas.com/urunler/aspx.

2. http://www.merckmillipore.com/pharmaceutical-ingredients/

3. Cooper, A. R. and G. V. Jeffreys, Chemical Kinetics and Reactor Design, Oliver & Boyd,

Norwich, 1971.

4. Fogler, H. G., The Elements of Chemical Reaction Engineering, 2nd

edition, Prentice Hall, New

York, 1992.

5. Perry, R. H. and D. Green, Perry’s Chemical Engineers’ Handbook, 6th


New York, 1988.


21

5.4. DETERMINATION OF OPTIMAL AGITATION CONDITIONS IN A STIRRED TANK

Keywords : Mixing, baffle, propeller, impeller, mixing efficiency, impeller Reynolds number.

Before the experiment: Read the booklet carefully. Be aware of the safety issues. See your TAs.

5.4.1. Aim

To observe various flow patterns with respect to different sizes of impellers and baffles and to

investigate the effect of size and types of agitators on mixing efficiency and power consumption.

5.4.2. Theory

Agitation means forcing a fluid mechanically such that it flows with any type of flow pattern inside

a vessel. The operation of agitation, which includes mixing as a special case, is now well

established as an important component in a wide variety of chemical processes. Mixing can be

defined as putting two or more separate phases together and allowing them to be randomly

distributed with respect to one another. Specifically, agitators are applied to three general classes of

problems:

(i) To produce static or dynamic uniformity in multicomponent multiphase systems,

(ii) To faciliate mass or energy transfer between the parts of a system not in equilibrium,

(iii) To promote phase change in a multicomponent systems with or without a change in

composition.

Mixing in tanks is an important area when one considers the number of processes, which are

accomplished in tanks. Essentially, any physical or transport process can occur during mixing in

tanks. Qualitative and quantitative observations, experimental data, and flow regime identifications

are needed and should be emphasized in experimental pilot studies in mixing [1].

Fluid mechanics and geometry are key points to understand mixing. The fluid mechanics transports

the material about the tank, whereas the geometry determines the fluid mechanics. In fact, the

geometry is so important that the processes can be considered geometry specific. Liquid-liquid

dispersion depends on the geometry of the impeller, blending, the relative size of the tank to the

impeller, and power draw.

22

Mixing efficiency in a stirred tank is affected by various number of parameters such as presence of

baffles, impeller speed, impeller type, clearance, tank geometry, solubility of substance, eccentricity

of the impeller.

A vortex is produced owing to centrifugal force acting on the rotating liquid. If vortex reaches the

impeller severe air entrainment occurs. The depth and the shape of the vortex depend on impeller

and vessel dimensions as well as on rotational speed [2].

Baffles are flat vertical strips set radially along the tank wall. Baffles prevent vortex formation. In

baffled tanks, a better concentration distribution throughout the tank and therefore improvement in

the mixing efficiency is achieved. The larger the width of the baffles, the better is the mixing. In the

unbaffled vessel with the impeller rotating in the center, centrifugal force acting on the fluid raises

the fluid level at the wall and lowers the level at the shaft [2, 3].

Flow patterns can be changed according to the type of impellers, and fall into three categories:

axial, radial and tangential [2]:

Radial Flow: Radial Flow discharge is parallel to the impeller radius toward to the vessel wall. If a

radial impeller is not positioned close to the surface or the tank bottom, the flow will split into two

streams upon impinging on the tank wall. Each flow loop will continue along the wall and then

return to impeller.

Axial Flow: Axial flow discharge coincides with the axis of impeller shaft, so when the impeller

operates in a down pumping mode, the flow impinges on the bottom of the tank and spreads out in

all directions toward the wall. The flow rises along the walls up the liquid surface and is pulled back

to the impeller. Since axial flow impeller produce only one loop, fluids mix faster and blend time is

reduced compared to radial flow impellers. The fluid does not take sharp turns near impellers and

because of this, power consumption is less than that of radial flow impellers at the same speed and

same diameter.

23

Figure 5.4.1. Axial and radial flow impellers showing time-averaged flow patterns

in a stirred tank [2].

Tangential Flow: A tangential flow pattern is naturally induced by swirling or vortexing flow that

fluids assume in an unbaffled tank. Tangential flow patterns offer very little mixing because the

velocity gradients are very small.

Consider a tank where a newtonian fluid of density , and viscosity is agitated by an impeller of

diameter D and rotating at rotational speed N. Let the tank diameter be T, the impeller width W and

the liquid depth H. The power requirement of the impeller P represents the rate of energy

dissipation within the liquid and depends on the following variables of Eq. 5.4.1:

P = P (,, N, g, D, T, W, H,) (5.4.1)

It is not possible to obtain the functional relationship in Eq. 5.4.1 because of the complex geometry

of the vessel, impeller and other inserts such as heating coils. Using dimensional analysis, the

number of variables describing the problem can be minimized and Eq. 5.4.1 reduces to Eq. 5.4.2

[3]:

𝑃

𝜌𝑁3𝐷5 = 𝑓 (𝜌𝑁𝐷2

𝜇,

𝑁2𝐷

𝑔,

𝑇

𝐷,

𝑊

𝐷,

𝐻

𝐷, 𝑒𝑡𝑐) (5.4.2)

where

P

N D 3 5 is the Power number, Po;

ND2

is the Reynolds number, Re; N D 2

g is the Froud

number, Fr.

24

Power consumption is related to fluid density, fluid viscosity, rotational speed and impeller

diameter. Power is found by Eq. 5.4.3

P =

Here “P” is the power, “𝝎” is angular speed (rad/s) and “𝝉” is torque. Torque generated during the

mixing process can be calculated by Eq. 5.4.4

= F.r (5.4.4)

where “F” is force and “r” is distance of the torque arm [3].

In this experiment, the different types of impellers are used to investigate the effects of size and

types of agitators on mixing efficiency and power consumption. Also, the effect of baffle on mixing

efficiency is studied.


Figure 5.4.2. A stirred tank apparatus.

25

5.4.4. Procedure

Part A

1. Fill the mixing apparatus with distilled water up to a depth of 0.3 m.

2. Attach flat paddle impeller to the end of the shaft and release the torque arm clamp so that the

dynamometer arm moves freely.

3. Set the dynamometer to neutral position and adjust the tension spring.

4. Adjust the length of the cord so that the indicator aligns with the mark on the datum line in the

neutral position.

5. Increase the speed of the impeller in small increments.

6. Observe the behavior of water to note whether there is vortex formation or not.

7. Record the speed, vortex height and force on the balance at each speed.

8. Repeat the experiment for each flat impeller (large-wide, large-narrow, small-narrow), propeller

and turbine with and without baffles.

9. Change the depth of agitator (large-narrow with and without baffles) within the tank and record

the speed, vortex height and force on the balance at each speed.

Part B

1. Attach the small narrow impeller and put the baffles into the tank.

2. Inset the conductometer, insert into the tank. Set the speed of the impeller to 200 rpm.

3. When the conductivity has a fixed value, add 25 grams of NaCl into the tank.

4. Record the time required for the conductivity to reach the steady state using a stopwatch.

5. Repeat the experiment with propeller by adding an additional 25 grams of NaCl.

Safety Issues: Pay attention to injury which is through misuse of motor, from electric shock, from

handling large or heavy components or from rotating components and to damage to clothing. Be

sure of that all valves are closed, the tank is emptied and all the electronic devices are unplugged at

the end of the experiment.

26


1. Discuss the flow patterns observed with different agitators (impeller, propeller and turbine) of

different sizes with and without baffles. In which cases vortex and/or air entrainment occur?

2. Calculate the power consumption for each speed.

3. How do the size and types of agitators affect mixing efficiency and power consumption?

References

1. Geankoplis, C. J., Transport Processes and Separation Process Principles, 4nd

edition, Allyn and

Bacon Inc., 2003.

2. Perry, R. H. and D. Green, Perry’s Chemical Engineers’ Handbook, 8th

edition, McGraw-Hill,

2007.

3. Harnby, N., M. F. Edwards and A. W. Nienow, Mixing in the Process Industries, 2nd

edition,

Butterworth-Heinemann, Oxford, 1992.

27

5.5. DETERMINATION OF RESIDENCE TIME DISTRIBUTION IN A PACKED BED

Keywords: Packed bed, residence time, step input, pulse input.

Before the experiment: Read the booklet carefully. Be aware of the safety precautions.

5.5.1. Aim

To determine the residence time distribution function and the mean residence time for two columns

with different types of packings using step and pulse input experiments.

5.5.2. Theory

The duration the smallest part of the fluid, e.g. a molecule, has spent in the reactor is called its

residence time. The residence time consists of the time elapsed since the molecule entered the

reactor (its age), and the remaining time it will spend in the reactor (its residual life time). It is

important to note that micromixing can occur only between molecules that have the same residual

lifetime. In a packed-bed reactor as shown in Figure 5.5.1, the fluid may flow through the reactor

non-uniformly because some pathways provide little resistance while others create more resistance

to flow [1].

Figure 5.5.1. Packed-bed reactor [1].

The residence time distribution indicates the deviations the from ideal reactor behavior. There are

three kinds of deviations from ideal tubular-flow reactor. Those are (1) channeling of the fluid

through the packing and the presence of stagnant fluid pockets, (2) diffusion in the longitudinal

direction and (3) the presence of the velocity and the temperature gradient in the radial direction.

The residence-time distribution (RTD) mainly is used to characterize and model nonideal reactors

in chemical engineering. The RTD is determined experimentally by using an inert chemical,

molecule, or atom, which is called a tracer, into the reactor at some time t=0 and then measuring the

tracer concentration in the effluent stream as a function of time (C(t)). The RTD function (E(t))

28

describes in a quantitative manner the amount of time different fluid elements spend in the reactor

[1, 2].

The cumulative RTD function (F(t)) can be defined as the fraction of effluent that has been in

reactor for less than time t, and it is expressed as:

∫ 𝐸(𝑡)𝑑𝑡 = 𝐹(𝑡)

𝑡

0

A plot of F(t) vs. time has the characteristics shown in Figure 5.5.2.

Figure 5.5.2. Cumulative RTD curve [2].

Variations in density, such as those due to temperature and pressure gradients, can affect the

residence time and are superimposed on effects due to velocity variations and micromixing. It has to

be supposed that the density of each element of fluid remains constant as it passes through the

reactor. Under these conditions the mean residence time, averaged for all elements of fluid, is

theoretically given by Eq. 5.5.1:

𝑡𝑚 =𝑉

𝑄 (5.5.1)

where Q is the volumetric flow rate and the reactor volume, V, is equal to the volume occupied by

the maize molecules, which are molecules in the reactor completely at time t=0. For constant

density of fluids, Q is the same for the feed as for the effluent stream.

By defining of F(t), dF(t) is the volume fraction of the effluent stream that has a residence time

between t and t+F(t). Hence the mean residence time is also given by Eq. 5.5.2 [1]:

𝑡𝑚 =∫ 𝑡𝑑𝐹(𝑡)

1

0

∫ 𝑑𝐹(𝑡)1

0

= ∫ 𝑡𝑑𝐹(𝑡)1

0 (5.5.2)

1

0

F(t)

Time, t

29

The residence time distribution can be obtained by response-type experiments, where a known

amount of tracer is introduced to the system and its effect on the concentration of the effluent is

measured. The three common types of response-type experiments include pulse, step, and

sinusoidal inputs (Figure 5.5.3). Step and pulse input experiments are figured out in this experiment.

For step input experiment, F(t) is defined as the ratio of concentration of tracer and maximum

concentration. For pulse input, it is the ratio of the area under the curve from t=0 to each selected

time and the whole area under the curve [2].

Figure 5.5.3. Step and Pulse inputs.

Besides the residence time distribution and the mean residence time, the concentrations can also be

used to obtain the effective diffusivity. In tubes, especially in packed beds, formation of eddies

disturbs the flow pattern. The eddy effect is represented by a dispersion coefficient in Fick’s

diffusion law. A plug flow reactor has a dispersion coefficient of 0 and a CSTR of ∞. For a packed

bed, the dispersion model is as follows [3],

𝐷𝐿 =𝑢𝐿

4𝜋(𝑠𝑙𝑜𝑝𝑒)2

where

u: velocity of fluid (m/s)

L: tube length (m)

slope: slope at t/tmean =1 in C vs t/tmean graph

In this experiment, water and methyl orange, used as a tracer, will be flowed into two columns

which are packed with small and large particles. For two packed beds, the residence time

distribution function and the mean residence time will be obtained by using step and pulse input

experiments.

Step input Pulse input

30


The experimental setup used in this experiment is shown in Figure 5.5.4.

Figure 5.5.4. Schematic diagram of a packed column.

1.) Large Packed Column 8.) Water Inlet Valve

2.) Small Packed Column 9.) Three-way Stopcock

3.) Burette 10.) Three-way Stopcock

4.) Rotameter for Water 11.) Three-way Stopcock

5.) Rotameter for Tracer 12.) Tracer Inlet Valve

6.) Constant-Head Device for Water 13.) Water Reservoir Valve

7.) Constant-Head Device for Tracer 14.) Tracer Reservoir Valve

5.5.4. Procedure

5.5.4.1. Column Specifications

Packed-bed Diameter (cm) Length (cm) Void (cm3)

With large particle 1.545 133.5 185

With small particle 1.555 135.5 166

31

5.5.4.2. Pulse Input Experiment

1. Adjust the water flow rate to 120 ml/min using the flow meter (No. 4) and valve (No. 8).

2. Adjust the three-way stopcock (No. 9) of (No. 11) so the water goes into only one column.

3. While the water is flowing through the column at a constant flow rate, inject a known amount of

tracer solution into the column by means of a hypodermic syringe at t = 0.

4. At t = 10 sec. start to collect samples from the outlet of the column at definite time intervals (10

seconds) until the tracer disappears in the effluent.

5. Measure the % transmittance of the samples by spectrophotometer and convert them to

concentration units using the calibration curve that will be given by TA.

6. Perform the same procedure for other column, which contains packing material of different size.

5.5.4.3. Step Input Experiment

1. Adjust the three-way stopcock (No. 9 or No. 11) so that the direction of the tracer is open.

2. Adjust the tracer flow rate with flow meter (No. 5) and the valve (No. 12). Do not allow the

tracer to go in the column, allow that it flows into third column by using valve (No. 10).

3. Then turn the stopcock in the direction that closes the tracer flow and permits water flow (do not

turn off valve (No. 12)).

4. Adjust the water flow rate to the same value as the tracer flow rate.

5. After steady state is reached, turn the stopcock (No. 9 or 11) to let the flow of the tracer into the

column. This moment is taken to be zero time (t = 0).

6. After 10 seconds, start to collect samples until the color of the effluent stream does not change.

7. Perform the same procedure for other column.

Safety Issues: In this experiment, methyl orange will be used. It is toxic if swallowed. It

may cause eye and skin irritation. It may be harmful and cause respiratory tract irritation if inhaled.

During the experiment, beware of risks when handling with methyl orange. Be sure of that all

valves are closed and all the electronic devices are unplugged at the end of the experiment. In case

of eye or skin contact, immediately flush eyes or skin with plenty of water for at least 15 minutes

while removing contaminated parts. Get medical aid immediately. In case of ingestion, wash mouth

out with water and get medical aid immediately. In case of inhalation, remove from exposure and

move to fresh air immediately. If not breathing, give artificial respiration and give oxygen. For

further information about the methyl orange, look over [4]. The solutions used in this experiment

are dilute in terms of methyl orange, therefore no need to a special treatment.

32


1. Calculate the void fraction of each column.

2. Calculate concentrations by using the calibration curve.

3. Plot concentration vs. time graphs in each case.

4. Transform concentration curve to cumulative RTD function curve (F(t)) in each case.

5. Calculate the mean residence time (tm) in each case theoretically and graphically.

6. Calculate percent error.

7. For the step-input experiment cases, estimate the effective diffusivity, (DL) by using the

Dispersion Model.

8. Discuss the effect of the different flow rates on residence time.

References


edition, Prentice Hall Inc., USA,

2006.



3. Perry, R.H. and D. Green, Perry’s Chemical Engineers’ Handbook, 7th


New York, 1997.

4. Methyl orange MSDS, http://www.sciencelab.com/msds.php?msdsId=9927361.

33

5.6. MODELING OF WATER LEVEL IN A TANK UNDER STEADY STATE AND

DYNAMIC CONDITIONS

Keywords: Mathematical model, differential equation, linear vs. nonlinear, system, water tank.

Before the experiment: Read the booklet carefully. Be aware of the safety precautions.

5.6.1. Aim

To propose linear and nonlinear models to describe the dynamic behavior of water level in a tank

and then simulate these two models to compare with the experimental data and in with each other.

5.6.2. Theory

5.6.2.1. Modeling

Modeling is the art of creating mathematical descriptions of, e.g. physical, chemical or

electrotechnical phenomena which appear in reality. These descriptions have to be relatively simple,

yet accurate enough to serve the purpose of the modeler [1].

It is important to realize that many different models exist, all describing some different parts of the

same reality. It depends on the point of view and intention of the modeler which part of that reality

is described. In studying a chemical process, the modeler may be interested in the chemical

reactions, in the physical working conditions, in the mechanical construction of the reactor, in the

possible environmental impact of the reactor, in the financial return on investments and in the

dynamic behavior of the process [2]. All these different views will yield different models.

The essence of the art of modeling is to select only those characteristics that are necessary and

sufficient to describe the process accurately enough to suit the objects of the modeler. The

simplified models allow the modeler to grasp the essentials from a turbulent and sometimes chaotic

world [1]. So, modeling is grasping the central issue from reality and translating it into an abstract

language such as a mathematical model. An important decision in deriving models is the selection

of the system boundary. The isolated part of the process will be called the system and all the parts of

reality not belonging to the system are attributed to the environment of the system [1].

34

5.6.2.2. Differential Equations

It is often the case that the mathematical models used for describing the systems involve an

equation in which a function and its derivatives play important roles. Such equations are called

differential equations displayed in Eq. 5.6.1, Eq. 5.6.2 and Eq. 5.6.3 [3].

21 kxkdt

dx (5.6.1)

yxxFdx

dy )( (5.6.2)

2Axdt

dx (5.6.3)

When an equation involves one or more derivatives with respect to a particular variable, that

variable is called an independent variable. A variable is called dependent if a derivative of that

variable occurs in the equation [3]. In Equation 5.6.1, x is the dependent and t is the independent

variable. When t is the independent variable, the following notation in Eq. 5.6.4 may be used:

2Axx (5.6.4)

where dt

dxx .

The order of a differential equation is the order of the highest ordered derivative appearing in the

equation, whereas the degree of a differential equation is the power to which the highest derivative

is raised when the equation has been rationalized. For instance (Eq. 5.6.5),

02 3 yycy (5.6.5)

is an equation of order two (or a second order equation) and first degree. Differential equation can

be classified as linear and nonlinear. A linear differential equation is one for which the following

two properties hold [3]:

1. If x(t) is a solution, then cx(t) is also a solution, where c is a constant.

2. If x1(t) and x2(t) is solutions, then x1 + x2 is a solution.

Equations 5.6.1 and 5.6.3 are linear, whereas Equations 5.6.2 and 5.6.5 are nonlinear differential

equations.

35

5.6.2.3. Mass Balance around a Tank

There are several ways of obtaining a model and deduction based on the fundamental physical laws

is one of them. Using the law of conservation of mass, mass of a liquid in a tank where a single

stream of the liquid is entering and another single stream is leaving can be modeled as Eq. 5.6.6 and

Eq. 5.6.7 [4]:

Input – Output = Accumulation

For a short time period of t,

Input = F int

Output = F outt

Accumulation = (inVtt

) - (outVt

)

where F is the inlet flow rate and F is the outlet flow rate,

V is the volume that the liquid occupies in the tank at a certain time.

is the density of the fluid (subscripts in and out denote the inlet and outlet flows),

F int – F outt = (Vtt

) - (Vt

) (5.6.6)

Dividing all terms by t and letting t 0:

F in - F out =dt

Vd )( (5.6.7)

If the fluid is assumed to be incompressible, is constant, therefore all density terms cancel out.

Furthermore, V = A h (assuming the tank is a rectangular prism) and A (base area) is constant,

leading to Eq. 5.6.8:

F – F =dt

dhA (5.6.8)

where h is the liquid level in the tank.

The outlet flow rate, F may be maintained by the help of a pump to keep it constant. However, if

no pump is used, outlet flow rate depends on parameters such as the water height, gravity, the

friction factor of the outlet pipe. To account for the non-time dependent factors (like gravity and

36

friction) an empirical constant R may be used, so the outlet flow rate may be modeled as following

[5]:

a. A linear model (Eq. 5.6.9) where F’ h

F – R

h =

dt

dhA (5.6.9)

b. A nonlinear model (Eq. 5.6.10) where F’ h0.5

F – R

h 5.0

=dt

dhA (5.6.10)


Figure 5.6.1. Process control system with water tank.

1. Centrifugal pump

2. Manual control valve

3. Variable area flow meter

4. Diffuser

5. Sealing stopper

6. Water tank

7. Overflow

8. Motorized flow control valve

9. Drain valve

5.6.4. Procedure

1. Adjust the drain valve to open position.

2. Check the motorized valve by rotating the knob on the positioner clockwise.

3. Adjust the flow rate from 1 L/min to maximum flow rate with 0.1 L/min increase and record the

steady state heights reached at these flow rates (verify that initial water level height does not

affect the steady state value).

37

4. Starting from different initial water level heights (away from the corresponding steady state

values) and at different constant flow rates between 1 L/min to max flow rate, record the

dynamic behavior of the water level until it reaches the maximum water level.

5. Do not forget to measure the length and width of the water tank.

* Be careful to water level in drain tank. Add water when it is necessary.

Safety Issues: Pay attention to injury through misuse of pump and motor. Be sure of that the flow

meter and the system are closed at the end of the experiment.


1. Plot flow rate vs. height data for steady-state and unsteady-state conditions.

2. From the steady state height values, find R (resistance) values for linear and nonlinear models

using linear regression. Discuss whether a difference in R values for different flow rates is

plausible. Which model seems to be a better choice?

3. Using these R values, simulate these two models for the flow rates you performed in the

experiment using numerical integration (simple Euler, Runge-Kutta 4th

order, or by any other

numerical integration method) on FORTRAN, C or by MATLAB/SIMULINK.

4. Show the simulation results and experimental data for the same flow rates on the same graph.

Discuss which model explains to the experimental behavior better. Which parts of the dynamic

response are better modeled? Why do you think it is so? How can you improve the models? Give

recommendations.

References

1. P. P. J. van den Bosch and A. C. van der Klauw., Modeling, Identification and Simulation of

Dynamical System, CRC Press, Boca Raton, FL, 1994.

2. Luyben, W. L., Process Modeling, Simulation and Control for Chemical Engineers, 2nd

edition,

McGraw-Hill, 1990.

3. Rugh, W. J., Linear System Theory, 1st edition, Prentice-Hall, 1993.

4. R.G. Rice and D. D. Do, Applied Mathematics and Modeling for Chemical Engineers, John

Wiley & Sons, 1994.

5. Seborg, D. E., T. F. Edgar and D. A. Mellichamp, Process Dynamics and Control, 1st edition,

John Wiley and Sons, USA, 1989.

chapter 5

Documents

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plug flow reactor

size of reactor

direction of flow

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saponification reaction

reaction parameters

ideal tubular reactor