ERT 208

REACTION ENGINEERING

MISMISURAYA MEOR AHMAD School of bioprocess engineering

Unimap

“MOLE BALANCE”

Course Outcome No.1:

• Ability to solve the rate of reaction and their kinetics.

objectives

DESCRIBE and DEFINE the rate of reaction, DERIVE the general balance equation, APPLY the general mole balance to the three most common types of industrial reactors.

Definition Chemical Reaction Engineering (CRE): Combines the study of chemical kinetics with the reactors in which the reaction occur. Chemical kinetics: the study of chemical reaction rates & reaction mechanisms.

“Chemical kinetics & reactor design are important things in chemical industrial”

Distinguishes between other engineers is:

CHEMICAL ENGINEER

a knowledge of Chemical Kinetics & Reactor Design

Select reaction system that operates in the safest and most efficient manner key to economic success or failure of a chemical plant.

Aim

Chemical Reaction Engineering principle can be applied in:

Waste treatment Microelectronics Nanoparticles pharmaceutical living system of chemical manufactures

Points of view

Achieved through overall mole balances on individual species in the reacting system.

Before discuss the conditions that effect chemical reaction rate mechanisms & reactor design

it is necessary to account for the various chemical species entering & leaving a reaction system.

Batch Reactor (BR), Continuous-Stirred Tank Reactor (CSTR), Plug Flow Reactor/ Tubular

(PFR) & Packed Bed Reactor (PBR)

So that, we will develop a general mole balance that can be applied to any species entering, leaving or

remaining within the reaction system volume

After that, used general mole balance equation to develop a preliminary form of the design equations

of the most common industrial reactor:

THE RATE OF Reaction (-rA)

The Rate of Reaction show how fast a number of moles of one chemical species are being consumed to form another chemical species. (The rate at which a species loses its chemical identity per unit volume)

Chemical identity

• A chemical species is said to have reacted when it has lost its chemical identity.

• The identity of a chemical species is

determined by the kind, number, and configuration of that species' atoms.

Three ways a chemical species

can lose its chemical identity

1) Decomposition

2) Combination

3) Isomerization

• The rate of a reaction can be expressed in several ways:

1) The rate of disappearance of a reactant, -rj

–rj is the number of moles j reacting (disappering) per unit time per unit volume (mol/dm3.s) The numerical value –rj is positive number

2) The rate of appearance of species j, rj rj is the rate of formation (generation) of species j.

If species j is reactant The numerical value of rj will be a negative number. (i.e: rA = - 4 mole A/dm3.s)

If species j is product The numerical value of rj will be a positive number. (i.e: rB = 4 mole A/dm3.s)

“The relation between the rate of formation of one species

and the rate of disapperance of another species in chemical

reaction will be discuss in Chapter 3”

Example:

A + 2B C + D

A B

• For a catalytic reaction, we refer to -rA', which is the rate of disappearance of species A on a per mass of catalyst basis.

• 2 types of reaction systems:

1) Homogeneous system (one phase)- rate of reaction measure in volume

2) Haterogeneous system (more than one phase)- rate of reaction measure in reaction surface area or catalyst weight

• Is an algebraic equation that is solely function of the properties of the reacting materials & reaction condition [i.e: species concentration, temperature, pressure and the type of catalyst].

• The rate equation is independent of the type of reactor (batch, plug flow,cstr etc.) in which the reaction is carried out.

THE RATE Equation (rate law) for -rj

• However, because the properties & reaction

conditions of the reacting materials may vary with position in chemical reactor, rj can turn be function of position & can vary from point to point in the systems.

• Rate law is essentially an algebraic equation involving concentartion (is not a differential equation)

THE RATE Equation (rate law) for -rj

• Example, the algebraic form of the rate law for –rA for the reaction:

A products

may be a quadratic function of concentration:

may be a linear function of concentration:

determined from

experimental observation

The rate of disappearance of A is equal to a rate constant K (which is a function of temperature) times the square of the concentration of A.

General mole balance equation (gmbE)

• To perform a mole balance on any system, the system boundary must be specified.

• The volume enclosed by these boundaries is referred as system volume, V.

• We shall perform a mole balance on a particluar chemical species, j in a system volume, V.

• So that, mole balance on species j at any instance in time,t produces the following equation:

How to derive?

• Step 1:

Understand the meaning of all the terms!

(Fj0,Fj, Gj and Nj)

• Fj0= rate of flow of j into the system

• Fj = rate of flow of j out of the system

• Nj =the no of moles of species j in the

system at time,t

• Gj = reaction volume x rate of formation of

species j,

If all the system variable [temp., catalytic activity, conc. of the chemical species] are uniform throughout the system volume, the Rate of Generation of species j, Gj is just the product of the reaction volume, V & the rate of formation of species j, rj.

The rate of formation of species j for the reaction varies with the position in the system volume. So that, it has rj1 at location 1, which is surrounded by a small volume, ΔV1, within which the rate is uniform.

Suppose, rj1 is surrounded by ΔV1 and so on, therefore:

• The total rate of generation within the system volume is the sum of all the rates of generation in each of the subvolumes.

• If the total system volume is divided into M subvolumes, the total rate of generation is:

• Appropriate limit ( let , the equation becomes:

• Now, replace Gj with this equation.

• Therefore, the GMBE for any chemical species j which is entering, leaving, reacting, and/or accumulating within any system volume V.

From this GMBE, we can develop the design equations for the various types of industrial reactors.

Evaluation of GMBE can determine the time (batch) or reactor volume (continuous flow) necessary to convert a specified amount of the reactants into products.

Mole balance equation on different reactor types

The GMBE applied to the major reactor types and the general reaction:

A B

1) Batch Reactor (BR)

BR used for small scale operation:

For testing new processes.

For manufacture expensive products.

For processes that are difficult to convert to continuous operations.

BR advantage:

High conversions (can be obtained by leaving the reactant in the reactor for long period of time).

BR disadvantage:

High labor cost per batch

The variability of products from batch to batch

The difficulty of large-scale production

1) Batch Reactor

Batch derivation

General Mole Balance on System Volume, V

No inflow or outflow while reaction is carried out:

From GMBE:

Mole Balance Equation for Batch reactor become:

Perfect mixing,therefore no variation in reaction rate throughout the reactor volume (Same rate of reaction). So, rj is removed, integrate, rewrite the MBE:

Assumption (BR):

Now, let’s think about isomerization of species A in a BR.

A B As the reaction proceeds:

no of moles of A, NA decreases &

no of moles of B, NB increases.

• Question: what time, t1 is necessary to reduce the initial no of moles from NA0 to final desired number, NA1.

• Step1: Apply the equation:

• Step 2: Rearranging, so that we get t:

• Step 3: Integrate with limits,

at t=0, then NA=NA0

at t= t1, then NA=NA1

Obtain:

This is integral form of mole balance on a BR.

It gives the time, t1 necessary to reduce the

number of moles from NAO to NA1 and also to form NB1

moles of B

2) Continous flow reactors

• Operate at steady state (conditions do not change with times).

• Consider 3 types:

i) Continous Stirred Tank Reactors(CSTR)

ii) Plug Flow Reactors(PFR)/Tubular Reactor

iii) Packed Bed Reactors(PBR)

i) Continous Stirred Tank reactor (CSTR)

• Used commonly in industrial processing the stirred tank operated continuously.

• Also referred as vat or backmix reactor.

• Used primarily for liquid phase reactions.

• Operate at steady-state.

• Is assumed to be perfect mixed/ ideal mixing [no time & no position depends with the temp., conc. or reaction rate inside the CSTR- means every variable is the same at every point inside the reactor ].

• View of CSTR

• GMBE on System Volume V.

• Applying on CSTR(Steady State i.e condition don’t

change with time):

• Also, Perfect Mixing (no variation in rate of reaction):

• So, it becomes a design equation of a CSTR:

• The design equation gives the reactor volume, V necessary to reduce the entering flow rate of species j, Fjo to the exit flow rate, Fj when species j is disappering at a rate –rj.

• CSTR is modeled based on conditions in the exit stream [conc., temp.] are identical to those in the tank. So that, the molar flow rate, Fj is just the product of the conc. of species j & volumetric flow rate, V

• Fj = concentration of species j x the volumetric flow rate:

• Replace Fj and combine, we can write a balance on species A in CSTR as:

ii) Tubular Reactors

• Consists of a cylindrical pipe.

• Operate at steady-state.

• Used for gas-phase reaction.

Tubular Reactor Schematic

• In the tubular reactor, the reactants are continually consumed as they flow down the lenght of the reactor.

• In modeling the tubular reactor, we assume the concentration varies continously in axial direction through the reactor.

• Therefore, the reaction rate (function of conc.) will also varies axially.

• We consider systems in which the flow field modeled by Plug Flow Profile (uniform velocity as in turbulent flow, no radial variation in reaction rate & the reactor referred to as a Plug Flow Reactor (PFR))

PLUG-FLOW REACTOR (PFR)

There are two ways to developed the design equation of PFR at steady state:

1) Directly from GMBE by differentiating with respect to volume, V

2) From mole balance on species j in a differential segment of the reactor volume ΔV.

Or

• Let’s choose the 2nd ways to arrive at the differential form of the PFR mole balance

The differential volume, ΔV will be chosen sufficiently small (there are no spatial variation in reaction rate within this volume). Thus the generation ΔGj is

• We obtain the differential form of steady state mole balance on a PFR:

To derive MB on PFR:

• At steady state: Accumulation = 0

• Dividing by ΔV and rearranging

The term in brackets resembles the definition of the derivative:

• Taking the limit as ΔV approaches zero, we get the differential form of steady state mole balance on a PFR.

• Pablo Picasso design the reactor for an irregular shape reactor [Pablo Picasso’s reactor]

MBE of tubular reactors of variable & constant cross-sectional area

The conclusion from the application of the design

equation Picasso’s Reactor:

“The degree of completion of a reaction achieved in ideal PFR does not depends on its shape, only on its total volume”

• Consider isomerization of A B in PFR.

• As reactants proceed down the reactor, A is consumed by chemical reaction and B is produced.

• Consequently, the molar flow rate of A decreases and molar flow rate of B increases.

Profile of Molar Flow Rate in a PFR

• Question: What is the reactor volume, V1 necessary to reducethe entering molar flow rate of A from FA0 to FA1.

Rearrange equation to become:

Integrate with limits:

at V=0,FA=FA0

at V=V1, FA=FA1

V1 is the volume necessary to reduce the entering molar flow rate FA0 to FA1 & also the volume necessary to produce a molar flow rate of B, FB1

iii) Packed-bed reactor (PBR) • The principle difference between

rector design calculation which is the reaction occur in the surface of the catalyst (heterogeneous system).

• So that, the reaction is based on mass of solid catalyst, W rather than reactor volume, V.

• The differential form of mole balance for PBR:

• The mass solid catalyst, W used because the amount of the catalyst is important to the rate of product formation.

• The reactor volume that contain catalyst is of secondary significance.

• Shows a schematic of an industrial catalytic reactor with vertical tubes packed with catalyst.

For heterogeneous system, the rate of

reaction of a substance A is define as:

• The derivation of the design equation for PBR will be carried out in a manner analogous to the development of the tubular design equation.

• To do this, we replace the volume, V coordinate in MB of PFR (Tubular) with the catalyst weight, W.

Derivation of mole balance on PBR

• The MB on species A over catalyst weight W produces this equation:

• The differential form of MB for a PBR:

• The dimensions of generation terms in the equation are:

When pressure drop through the reactor & catalyst decay are neglected, the integral form of PBR design equation can be used to calculate the catalyst weight:

Example 1.1: How Large is it?

Question?

Solution

In the BR, PFR & CSTR, the design equation (mole balances) were developed based on reactor volume, V. While design equation of PBR based on mass solid catalyst, W.

SUMMARY

Industrial Reactors

Fixed Bed Reactor 3 Stage Converter used to convert H2S to SO2

British Petroleum Reactor Photos

Fluidized Bed Reactor

Hydrogen Plant

Tutorial 1 Submit on 22 September 2011 before 1200 at Bioprocess main office

Tutorial 1

Q &A

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