ENCH3115Chemical

Reaction
Engineering
Chapter 5a-
Design Structure for Isothermal Reactors
5.1 Design Structure for Isothermal Reactors
One of the primary goals of this chapter is to solve chemical reaction engineering
(CRE) problems by using logic rather than memorizing which equation applies
where.

It is the author’s experience that following this structure, shown in Figure 5-1,
will lead to a greater understanding of isothermal reactor design

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Applying our general mole balance equation (level 1) to a Specific reactor to
arrive at the design equation for that reactor (level 2).

If feed conditions are specified (e.g., NA0 or FA0), all that is required to evaluate
design equation is rate of reaction as a function of conversion at same conditions
of T & P of reactor.
When -rA =f (X) is known or given, direct from
level 3 to level 9
to determine either batch time or reactor volume necessary to achieve specified
conversion.

If rate of reaction is not given explicitly as a function of conversion,

proceed to level 4 where rate law must be determined by either finding it in
books or
journals or by determining it experimentally in laboratory.
After rate law has been established, one has only to use stoichiometry (level 5)
together with conditions of the system (e.g., constant volume, temperature) to
express concentration as a function of conversion. 4
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For liquid-phase reactions & for gas-phase reactions with no pressure drop (P
= P0), one can combine the information in levels 4 & 5, to express rate of
reaction as a function of conversion & arrive at level 6.
It is now possible to determine either time or reactor volume necessary to
desired
achieve conversion by substituting relationship linking conversion & rate of
reaction into the appropriate design equation (level 9).
For gas-phase reactions in packed beds where there is a pressure drop,
need to proceed to level 7 to evaluate pressure ratio (P/P0) in concentration
term using Ergun equation (Section 5.5).

In level 8, we combine equations for pressure drop in level 7 with information in

levels 4 & 5, to proceed to level 9 where equations are then evaluated
in appropriate manner (i.e., analytically using a table of integrals, or numerically
using an ODE solver).
Although this structure emphasizes determination of a reaction time or reactor
volume for a specified conversion, it can also readily be used for other types of
reactor calculations, such as determining conversion for a specified volume.
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Different manipulations can be performed in level 9 to answer different types of
questions mentioned here.
Fortunately, by using an algorithm to formulate CRE problems shown in Fig. 5-2.
Step 1 is to begin by choosing appropriate mole balance for one of three types
of reactors shown.
In Step 2 we choose rate law, &

In Step 3 we specify whether reaction is gas or liquid phase .

Finally, in Step 4 we combine Steps 1, 2, & 3 & either obtain an analytical
solution or solve the equations using an ODE solver.

Suppose as shown in Figure 5-2, mole balances for three reactors, three rate
laws,
& equations for concentrations for both liquid & gas phases.
In Figure 5-2, see how algorithm is used to formulate the equation to calculate the
PFR reactor volume for a first-order gas-phase reaction.
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(5-2) 7
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The pathway to arrive at this equation is shown by ovals connected to the dark
lines through the algorithm.
The dashed lines & boxes represent other pathways for solutions to
other situations.
The algorithm for the pathway shown is
1. Mole balance, choose species A reacting in a PFR

2. Rate law, choose the irreversible first-order reaction

3. Stoichiometry, choose the gas-phase concentration

4. Combine Steps 1, 2, & 3 to arrive at Equation A

5. Evaluate. The combine step can be evaluated either

a. Analytically (Appendix A1) b. Graphically (Chapter 2)

c. Numerically(Appendix A4 ), or d. Using software (Polymath).
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In Figure 5-2 we chose to integrate Equation A for constant temperature &
pressure to find volume necessary to achieve a specified conversion (or calculate
the conversion that can be achieved in a specified reactor volume).
For isothermal operation with no pressure drop, we were able to obtain
an analytical solution, given by equation B, which gives reactor volume
necessary to achieve a conversion X for a first-order gas-phase reaction
carried out isothermally in a PFR.
However, in the majority of situations, analytical solutions to the ordinary
differential equations appearing in the combine step are not possible.

Consequently, we include Polymath, or some other ODE solver such as

MATLAB, in our menu in that it makes obtaining solutions to differential
equations much more palatable.

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 5.2 Batch Reactor (BRs)

One of jobs in which chemical engineers are involved is scale-up of laboratory

experiments to pilot-plant operation or to full-scale production.
In past, a pilot plant would be designed based on laboratory data. However, owing
to high cost of a pilot-plant study, this step is beginning to be surpassed in many
instances by designing a full-scale plant from operation of a laboratory-bench-
scale unit called a microplant.
To make this jump successfully requires a thorough understanding of the chemical
kinetics & transport limitations.
In this section, show how to analyze a laboratory-scale batch reactor in which a
liquid-phase reaction of known order is being carried out.
After determining specific reaction rate, k, from a batch experiment, we use it
in design of a full-scale flow reactor.
In modeling a batch reactor, assumed that there is no inflow or outflow of
material
& that reactor is well mixed.
be neglected
For (i.e., V = reactions,
most liquid-phase V0), density change with reaction is usually small &10
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In addition, for gas-phases reactions in which the batch reactor volume remains
constant, we also have V = V0.
5.2.1 Batch Reaction Time
Let’s calculate time necessary to achieve a given conversion X for irreversible
second-order reaction
2A → B + C

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2-
(5-2)

2
3-
(4-12)
4- Combine

(5-3)

5-

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 (5-4)
R

This time is the reaction time t (i.e., tR) needed to achieve a conversion X for a
second-order reaction in a batch reactor.
Table 5-1 shows algorithm to find batch reaction times, tR, for both 1st -& a 2nd-
order reactions carried out isothermally.
We can obtain these estimates of tR by considering 1st & 2nd order
irreversible (5-1)
reactions of the form 2A → B +C

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 1 1

2 2

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If 99% conversion had been required for this value of kCA0, reaction time, tR,
would jump to 27.5 h.
Table 5-2 gives order of magnitude of time to achieve 90% conversion for first-
& second-order irreversible batch reactions. 5-2

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The total cycle time in any batch operation is considerably longer than reaction
time, tR, as one must account for time necessary to fill (tf) & heat (te) the reactor
together with time necessary to clean reactor between batches, tc:

In some cases, reaction time calculated from Eqs. (5-4) & (5-5) may be only a
small fraction of total cycle time, tt.

Typical cycle times for a batch polymerization process are shown in Table 5-
3. Batch polymerization reaction times may vary between 5 & 60 hours.
Clearly, decreasing reaction time with a 60-hour reaction is a critical problem.

As reaction time is reduced (e.g., 2.5 h for a second-order reaction with kCA0 =
103 s-1), it becomes important to use large lines & pumps to achieve rapid transfers
& to utilize efficient sequencing to minimize cycle time.

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 5-3

Usually one has to optimize reaction time with processing times listed in Table 5-3
to produce maximum number of batches (i.e., pounds of product) in a day.

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In next four examples, we will describe various reactors needed to produce 200
million pounds per year of ethylene glycol from a feedstock of ethane.

We begin by finding rate constant, k, for hydrolysis of ethylene oxide to form

ethylene glycol.
Example 5-1 Determining k from Batch Data

It is desired to design a CSTR to produce 200 million pounds of ethylene glycol

per year by hydrolyzing ethylene oxide.
However, before design can be carried out, it is necessary to perform & analyze a
batch reactor experiment to determine specific reaction rate constant, k.
Because reaction will be carried out isothermally, specific reaction rate will need
to be determined only at reaction temperature of CSTR.
At high temperatures there is a significant by - product formation, while at
temperatures below 40°C the reaction does not proceed at a significant rate;
consequently, a temperature of 55°C has been chosen.
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Because water is usually present in excess, its concentration may be considered
constant during course of the reaction. The reaction is first-order in ethylene
oxide.
In the laboratory experiment, 500 mL of a 2 M solution (2 kmol/ m3) of ethylene
oxide in water was mixed with 500 mL of water containing 0.9 wt % sulfuric
acid, which is a catalyst.

Temperature was maintained at 55°C. Concentration of ethylene glycol was

recorded as a function of time (Table E5-1.1).
a) Derive the equation for the concentration of ethylene glycol as a function
of
time
b)Rearrange the equation derived in (a) to obtain a linear plot of a
fucntion concentration versus time
c)Using data in Table E5-1.1, determine specific reaction rate at 55°C. 19
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5

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 &4

5 5 23
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 5

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 5

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 5

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 5

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5

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5.3 Continuous Stirred Tank Reactors (CSTRs)
Continuous stirred tank reactors (CSTRs), such as the one shown here
schematically, are typically used for liquid-phase reactions.

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 5

(
)exit

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5.3.1 A Single CSTR

5.3.1.1 First-Order Reaction

(4-12)
(4-12)

5
(4-12)

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 Check P 153
We could also combine Equations (4-12) & (5-8) to find the exit
reactor concentration of A, CA.

5.3.1.2 A Second -Order Reaction in a 5

CSTR

Check P 153

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5.3.1.3 The Damkoler
Number

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5

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 5.3.2 CSTRs in Series

A first-order reaction with no change in volumetric flow rate (ν = ν0)

is to be carried out in two CSTRs placed in series (Figure 5-5).

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5

(5-13)

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 (5-14)

(5-15)

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5-6

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 5-6

(5-16)

Example 5-2 Producing 200 Million Pounds per Year in a

CSTR
Close to 12.2 billion metric tons of ethylene glycol (EG) were produced in
2000, economics which ranked it twenty-sixth most produced chemical in the
nation that year on a total pound basis.
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About one-half of ethylene glycol is used for antifreeze while other half is used in
manufacture of polyesters. In polyester category, 88% was used for fibers & 12% for
manufacture of bottles & films. The 2004 selling price for ethylene glycol was $0.28
per pound.

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5
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Check p 159 different unit

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5

5
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 Check p 160 Problem
P5-2(b)

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