conversion and reactor sizing

CH2: Conversion and Reactor Sizing

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Chemical Reaction Engineering Methodology

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Content• Section 1: Conversion and Molar Balances

– Conversion– Molar Balances in terms of Conversion– CSTR & PFR vs. PBR (Gaseous phase)

• Section 2: Reactor sizing– Sizing of a CSTR– Sizing of a PFR– CSTR vs. PFR sizing

• Section 3: Reactor in series– CSTR in series– PFR in series– CSTR+PFR in series and its sequence

• Section 4: Space-Time and Spatial-Velocity– Space-Time– Spatial-Velocity

Section 1

Conversion and Molar Balances

Introduction to Conversion

• We choose the limiting reactant as a basis of calculation

• Relate to all other species

• Then we quantify “how far” does the reaction goes

aA+bB cC + dD

A+b/a ·B c/a ·C + d/a ·D

Definition of Conversion

• XA= Moles of A reacted / Moles of A fed

• By logic means… 0 <= XA <= 1

• Note that as X increases, the reaction converts more reactant of A to (a) given product(s)

Conversion Example

• 284.4 gmol of A is fed to a reactor. After 4 hours, the outlet stream contains 20.3 gmol of A… What is the conversion

– a) moles of A reacted b) moles of A fed

– Moles of a reacted = (284.4– 20.3)gmol = 264.4 gmol

– Moles fed (is given in the data) = 284.4 gmol

– XA= 264.4/284.4 = 0.9296 as fraction or 92.96%

XA= Moles of A reacted / Moles of A fed

Why Conversion?

• It help us to establish a “standard” – e.g. not speak of flows (there are many flows possible)– conversion is only between 0 and 1

• Its easier to get a 100% of reaction progress• Example:

– 100 gmol of A are fed and 70 gmol of A are transformed to products• 70% conversion is achieved

– 35.4 gmol of A are fed and 12.4 gmol of A are transformed to products• 35% conversion is achieved

– We could say that the first reaction is 2 times efficient as the second one, independent of the flows

Molar Balances of Reactors in terms of Conversion

• We’ve seen before how to change from Flowsto Concentration (by volume or volumetric flow rate)

• This time we use the definition of conversionto transform all the design equations to Equations in terms of Conversion!

• This is very useful

• Specially in one-reaction reactors

Batch Reactor & Conversion

XA= moles of A reacted / moles of A fed

NA= moles of A at the outlet (exit or final)

NA0 = moles of A at the inlet (initial)

Moles of A reacted = NA0-NA

Moles of A fed = NA0

XA= (NA0-NA)/NA0 or express it for NA (moles of A at any moment)

NA = NA0(1-XA)

• Now lets apply these concepts and equations to our existing Design Equations

Differential From

Integral Form

Continuous Flow Reactors & Conversion

XA= moles of A per unit time reacted / moles of A per unit time fed

FA= moles of A at the outlet per unit time (exit or final)

FA0 = moles of A at the inlet per unit time (initial)

Moles of A reacted per unit time = FA0-FA

Moles of A fed per unit time = FA0

XA= (FA0-FA)/FA0 or express it for FA (moles of A per unit time, any moment)

FA = FA0(1-XA)

Continuous Flow Reactors & Conversion

• Now lets apply these concepts and equations to our existing Design Equations

– CSTR

– PFR

– PBR

• The conversion equation is exactly the same!

CST-Reactor & Conversion

Substitute this into original equation

Plug Flow Reactor & Conversion

Differential Form

Integral Form

• Very similar to PFR…

Packed Bed Reactor & Conversion

Differential Form of a PBR

Packed Bed Reactor & Conversion

Integral Form of a PBR

Exercise: Which one is which?

Batch Reactor

Summary of Reactor in terms of Conversion

Batch Reactor

Problems

• Go to next Section: Reactor Sizing

• Here we will apply the equations we just got

Section 2

Reactor Sizing

• It is normal to calculate the size needed for a certain reaction/process to achieve certain conversion XA

• The size is an important factor and it implies $

• The bigger the reactor gets, the higher the price

CSTR Sizing

• Sizing implies calculation of Volumes…

• Normally you calculate a volume– With this volume and the type of reactor you:

• Choose a Diameter

• Choose a Height/Length of the reactor

• In a CSTR, the Volume is represented in a graph by the “Rectangle”– The height is Fa0/-rA

– The base is the conversion XA

CSTR Sizing

• It is common that the student thinks the volume is the “shaded” area under the curve

• This is not the case

• A CSTR is an Algebraic calculation, it will never be an area under the curve

• A CSTR’s Volume is always the area of the rectangle– Height

– Base

CSTR Sizing

• Examples for different rates of reaction “shapes”

• The red-marked area is the “Volume” of that CSTR tank

• 80% Conversion in this case…

CSTR Sizing

• Note that the data of rate of reaction does not depends on the reactor!

• It can be used for all types of reactors!

• Even though you use one specific reactor

– It applies to any reactor!

CSTR Sizing

• Example 2-2 Sizing CSTR

CH2: Elements of Chemical Reaction EngineeringH. Scott Fogler (4th Edition)

CSTR Sizing

• B) Shade the Volume in the graph

PFR Sizing

• Sizing a PFR is a little bit more complex than CSTR due to the “Integral” concept

• This is NOT an algebraic calculation

• It is common that the student thinks the area under the curve is the volume

– He is RIGHT!

• The area under the curve of the rate of reaction will give you the volume

PFR Sizing

• Many rates of reaction get “under”

• The area is generally lower as a CSTR

• Take care, this is NOT always the case

– When not?

– We will see this case later on…

PFR Sizing

• A)

PFR Sizing

PFR SizingFlow = 4 mol/s

PFR Sizing

Flow = 4 mol/s

PFR Sizing

• A)

PFR Sizing

• A)

PFR Sizing

• Volume vs. Different Conversions

PFR Sizing

• Volume vs. Rate of Reactions

Comparing CSTR vs. PFR• If you’ve done the problems, you will see that when

we use CSTR or PFR the volumes change for the SAME reaction!

• This is due to the “Volume” calculation in our Design Equations

– CSTR Algebraic Concept (b·h)

– PFR Integral Concept (area under curve)

Comparing CSTR vs. PFR

• But when do we use CSTR and PFR?

• Main concept

– Assume that minimizing the Volume is priority!

– Ignore all costs associated to engineering the project!

• You WILL need to have the rates of reactions for every conversion (at least intervals)

CSTR vs. PFR Sizing

• CSTR Volumes (min, NA, max)

• PFR Volumes (min, NA, max)

CSTR vs. PFR Sizing

• Lets analyze these two cases

CSTR vs. PFR Sizing

• Lets analyze these two cases

Green PFR VolumePink CSTR Volume

CSTR vs. PFR Sizing Exercise

PFR volume for 0%

PFR volume for 20%

PFR volume for 40%

PFR volume for 60%

PFR volume for 80%

CSTR volume for 0%

CSTR volume for 20%

CSTR volume for 40%

CSTR volume for 60%

CSTR volume for 80%

Section 3

Reactor in Series

• Now lets suppose we have different existing reactors in the plant

• We could arrange them to maximize our production/conversion

• What order are the best orders?– PFR + PFR

– CSTR + CSTR

– CSTR + PFR

– PFR+ CSTR

• The fun starts here!

Single Pass Conversion vs. Global Conversion

• Single Pass conversion: Conversion of ONE unit (one reactor)– XAi= Moles reacted in that reactor / Moles fed to that reactor

• Global Conversion: Conversion so far– XA= Moles reacted so far / Moles fed to first reactor

CSTR in Series

NOTE X2: Global Conversion to this point

CSTR in Series

• We get these two equations…

Similar:

Rate of Reactions valued @ Outlet conversions: 40% and 80%

CSTR in Series

TIP:a) Calculate Volume for CSTR #1 (easy)b) Calculate Volume for CSTR #2 (not so easy)

CSTR in Series

Volume of CSTR #1

Volume of CSTR #2

Total Volume

CSTR in Series

• Note that

– For 1 CSTR to get 80% Conversion 6.4 m3

– For this new arrangement (2 CSTR @ 40% and 80%) We needed 4.02 m3 which is 30% less

• Is it worth it?

• Reactor Sizing is not the only $$ to decide!

CSTR in Series

• Try 3 and more CST-Reactors in series

• If you want to see examples like this, go to the web page!

• Check out the Reactor Engineering Course!

Approximation of a PFR with CSTR

• What would happen if we add a lot of CSTR in our process?

• The volume will approximate that of a PFR

• Similar to trapezoidal rule (rectangles in this case)

CH2: Elements of Chemical Reaction Engineering

H. Scott Fogler (4th Edition)

• Therefore

• If N is the number of CSTR reactors placed in Series

• And N infinity

• Then the Volume required for those CSTR in total is the same as ONE PFR

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