5. Algorithm for Isothermal Reactor Design^*

Topics

1. Algorithm for Isothermal Reactor Design
2. Applications/Examples of CRE Algorithm
3. Reversible Reactions
4. ODE (Polymath) Solutions to CRE Problems
5. General Guidelines for California Problems
6. PBR with Pressure Drop
7. Engineering Analysis

Mole Balances in Terms of Conversion

French Menu Analogy                                          

The reaction (2A+B-->C) carried out in a CSTR, PFR and a Batch Reactor.

The reaction from the movie. (or with more explanation.)

Here is a short movie about the use of the CSTR in the Senior Chemical Engineering Lab at the University of Michigan. You will need Quicktime to view these movies.

This Powerpoint Presentation details the reaction being carried out in the movie.

Semilog plot to find reaction rate constant

to a closed ended PFR/CSTR example.

CHEMKIN Reactor Models

Example: The elementary liquid phase reaction

is carried out isothermally in a CSTR. Pure A enters at a volumetric flow rate of 25 dm³/s and at a concentration of 0.2 mol/dm³.

What CSTR volume is necessary to achieve a 90% conversion when k = 10 dm³/(mol*s)?

Mole Balance
Rate Law
Stoichiometry	liquid phase (v = vo)
Combine
Evaluate	at X = 0.9,
	V = 1125 dm3
	Space Time

Here are some links to example problems. You could also use these problems as self tests.

CSTR Type 1 Home Problem

CSTR Type 2 Home Problem

CSTR Type 3 Home Problem

Critical Thinking Questions for CSTR

The following humorous videos were made by Professor Lane's 2008 Chemical Reaction Engineering class at the University of Alabama, Tuscaloosa.

You may access the videos by connecting to the internet and clicking on the images below

Gas Phase Elementary Reaction	Additional Information
	only A fed	P0 = 8.2 atm
	T0 = 500 K	CA0 = 0.2 mol/dm3
	k = 0.5 dm3/mol-s	vo = 2.5 dm3/s

Solve for X = 0.9

Applying the algorithm to the above reaction occurring in a Batch, CSTR, and PFR.

	Batch	CSTR	PFR
Mole Balance:
Rate Law:
Stoichiometry:	Gas: V = V0 (e.g., constant volume steel container)	Gas: T =T0, P =P0	Gas: T = T0, P = P0
		Per Mole of A:	Per Mole of A:
Combine:
Integrate
Evaluate
For X = 0.9:		V = 680.6 dm3	V = 90.7 dm3

Visual Encyclopedia of Reaction Engineering Equipment

Gas Phase Reaction Example

CSTR and PFR Example

Calculate V for a Zero-Order Reaction

To determine the conversion or reactor volume for reversible reactions, one must first calculate the maximum conversion that can be achieved at the isothermal reaction temperature, which is the equilibrium conversion. (See Example 3-8 in the text for additional coverage of equilibrium conversion in isothermal reactor design.)

Calculate Equilibrium Conversion (X_e) for a Constant Volume System

Example: Determine X_e for a PFR with no pressure drop, P = P₀

Given that the system is gas phase and isothermal, determine the reactor volume when X = 0.8 X_e.

Reaction	Additional Information
	CA0 = 0.2 mol/dm3 KC = 100 dm3/mol	k = 2 dm3/mol-min FA0 = 5 mol/min

First calculate X_e:

X_e = 0.89

X = 0.8X_e = 0.711

One could then use Polymath to determine the volume of the PFR. The corresponding Polymath program is shown below.

Equations

Plot of X vs. V

Results in Tabular Form

A volume of 94 dm³ (rounding up from slightly more than 93 dm³) appears to be our answer.

Batch Reactor With a Reversible Reaction

Every state has an examination engineers must pass to become a registered professional engineer.  In the past there have typically been six problems in a three hour segment of the California Professional Engineers Exam. Consequently one should be able to work each problem in 30 minutes or less. Many of these problems involve an intermediate calculation to determine the final answer.

Some Hints:

California Professional Engineers Registration Problem

Batch Reactor Optimization

Note: Pressure drop does NOT affect liquid phase reactions

Sample Question:

Analyze the following second order gas phase reaction that occurs isothermally in a PBR: 

                                                               
Mole Balance

Must use the differential form of the mole balance to separate variables

Rate Law

Second order in A and irreversible:

Stoichiometry
  

Isothermal, T = T₀


Combine
                   

Need to find (P/P₀) as a function of W (or V if you have a PFR).

Pressure Drop in Packed Bed Reactors

Ergun Equation
Variable Gas Density
let
Catalyst Weight
where
let
then

English-

 Espanol-

 Svenska-

	We will use this form for multiple reactions:
	We will use this form for single reactions:
Isothermal Operation
recall that
notice that
	The two expressions are coupled ordinary differential equations. We can solve them simultaneously using an ODE solver such as Polymath. For the special case of isothermal operation and epsilon = 0, we can obtain an analytical solution. Polymath will combine the mole balance, rate law and stoichiometry.

Analytical Solution, [e], PFR with

		CAUTION: Never use this form if

Combine
Solve

Could now solve for X given W, or for W given X.

For gas phase reactions, as the pressure drop increases, the concentration decreases, resulting in a decreased rate of reaction, hence a lower conversion when compared to a reactor without a pressure drop. 

Pressure Drop in a Packed Bed Reactor

Pressure and Reaction Orders

Formation of Ethyl Acetate

Here are some links to example problems dealing with packed bed reactors. You could also use these problems as self tests.

PBR Type 1 Home Problem

PBR Type 2 Home Problem

PBR Type 3 Home Problem

POLYMATH

Consider the following gas phase reaction carried out isothermally in a packed bed reactor. Pure A is fed at a rate of 2.5 moles/s and with, and α = 0.0002 kg^-1.

2AB

Mole Balance

Rate Law

        Elementary

Stoichiometry

       Gas with T = T₀

      AB/2

POLYMATH will combine everything - You do not need the combine step. Thank you POLYMATH

Profiles

"What Four Things are Wrong with this Solution?"

Optimum Paritcle Diameter

Laminar Flow, Fix P₀, ρ₀,

ρ₀ = P₀(MW)/RT₀

ρ₀P₀∼P₀²

Increasing the particle diameter descreases the pressure drop and increases the rate and conversion.

However, there is a competing effect. The specific reaction rate decreases as the particle size increases, therefore so deos the conversion.

k ∼ 1/D_p

The larger the particle, the more time it takes the reactant to get in and out of the catalyst particle. For a given catalyst weight, there is a greater external surgace area for smaller particles than larger particles. Therefore, there are more entry ways into the catalyst particle.

In DVD chapter 12, we will learn that effectiveness factor decreases as the particle size increases  

We want to learn how the various parameters (particle diameter, porosity, etc.) affect the pressure drop and hence conversion. We need to know how to respond to "What if" questions, such as:

"If we double the particle size, decrease the porosity by a factor of 3, and double the pipe size, what will happen to D P and X?"

(See Critical Thinking in Preface Table P1 and P2 on pages xvi and xvii.  e.g., Questions the probe consenquences)

To answer these questions we need to see how a varies with these parameters. 

Turbulent Flow                                    

        

Compare Case 1 and Case 2:

For example, Case 1 might be our current situation and Case 2 might be the parameters we want to change to.

For constant mass flow through the system= constant

Laminar Flow

Effect of Reducing Particle Size on Conversion in a PBR

Polymath Book Problem

Chapter 5 Polymath ODE Solver Algorithm

Here are more links to example problems dealing with packed bed reactors. Again, you could also use these problems as self tests.

PBR Type 5 Home Problem

PBR Type 7 Home Problem

PBR Type 8 Home Problem

Objective Assessment of Chapter 5

^* All chapter references are for the 1st Edition of the text Essentials of Chemical Reaction Engineering .

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