CHEE 321: Chemical Reaction Engineering

Module 5: Multiple Reactions (Chapter 6, Fogler) Course (Content) Organization

Isothermal, Ideal Reactor (Single Reaction) Design Output Mole Balance Rate Law Design Algorithm (Module-1) (Module-2) (Module-3) • Reactor Volume In – Out + Con = Acc n 1. GMBE, 2. Rate Law • Reaction Time (rA) = kCA FA,in-FA,out+(rA)V = dCA/dt 3. Stoich 4.Combine • Rate Constant Analysis of Rate law (Module-4) Kinetics: How to obtain k and rxn order • Conversion Multiple Reactions • Product Composition (Module-5) Selectivity, Yield

Non-Isothermal Reactor Design Output (Module-6) • Energy Balance • Temperature Profile dT/dz = ? • Heat Transfer Rate • Heat Removal • Equilibrium Reactions • Heating Requirement T -T =? • Multiple Steady State in out Topics to be covered in this Module

• Types of multiple reactions

• Introduction to selectivity and yield

• Qualitative Analyses (Parallel and Series Reactions) – Maximizing the reactor operation for single reactant systems – Maximizing the reactor operation for two reactant systems

• Algorithm for Reactor Design of Multiple Reactions – Mole Balance – Net Rates of Reactions – Stoichiometry Multiple Reactions Types of Multiple Reactions

1. Series Reactions 1 ⎯→⎯⎯→⎯ kk 2 CBA Use molar flow rates and concentrations; 2. Parallel Reactions DO NOT use conversion!

⎯→⎯k1 BA ⎯→⎯k2 CA 3. Complex Reactions: Series and Parallel k1 +⎯→⎯ CBA ⎯→⎯+ k2 DCA Cannot use stoichiometric tables to relate

4. Independent change in CB to change in CA ⎯→⎯k1 CA B ⎯→⎯k2 D Selectivity and Yield Desired Reaction: Instantaneous Global kD A ⎯→⎯ D rD ~ FD Selectivity SDU = SDU = r F Undesired Reaction: U U k U rD A⎯⎯→U FNDD Yield YD =  YD == kU2 −rA DU⎯⎯→ FFNNA00−−AAA • What should be the criterion for designing the reactor ? • Is it necessary that reactor operates such that minimum amount of undesired products are formed ?

D

S Total Cost E P Reactor D A A R Cost System U A T O R

U Reactant Conversion Instantaneous vs. Global Yield

 • For a CSTR: SSDUDU=  YYDD= For proof, see Fogler Ex. 6-1 (pg 308)

• For a PFR, concentrations and rxn rates are changing along reactor length:

rdFDD instantaneous yield: YD == −−rdFA A

 D formed FD global yield YD == A reacted (FFA0 − A )

−1 CA YY = dC′ for v=v : DD∫C A 0 A0 ()CCAA0 − Series Reactions

Batch reactor, isothermal, incompressible

, t=0 CA=CA0

From Fogler website http://www.engin.umich.edu/~cre/06chap/frames_learn.htm Series Reactions

See Appendix A3 Series Reactions

What about byproduct C? This can be calculated by integration, or by stoichiometry

dC C = k C , t = 0 C = 0 dt 2 B C

You would have the same set of equations for an isothermal PFR, replacing t with τ ; see Fogler Ex. 6-4 Parallel Reactions: Selectivity for Single Reactant Systems

Example (parallel reaction)

k Desired Reaction: A ⎯→⎯D D αD = Ckr ADD α Undesired Reaction: kU U A ⎯→⎯ U = Ckr AUU

What is the net rate of reaction of A ??

r Ck α D k S D == AD = D C ( −ααUD ) DU α U A rU Ck AU k U

Let us examine some reactor operating scenarios to maximize selectivity.

Fogler, 6.2 Parallel Reactions: Selectivity for Single Reactant Systems

Case 1: αD-αU >0

rD kD −ααUD )( SDU == CA High CA favors D rU kU

How can we accomplish this?

• For gas phase reactions, maintain high pressures • For liquid-phase reactions, keep the diluent to a minimum

• Batch or Plug Flow Reactors should be used • CSTR should NOT be chosen Parallel Reactions: Selectivity for Single Reactant Systems

Case 2: αD-αU < 0

rD kD S == Low CA favors D DU −ααDU )( rU Ck AU

How can we accomplish this? C • For gas phase reactions, operate at low pressures A0 • For liquid-phase reactions, dilute the feed CA • CSTR is preferred CA

Reactant concentration maintained at low level Parallel Reactions: Selectivity for Single Reactant Systems

Case 3: αD-αU = 0

Concentration cannot be used operating parameter for selectivity maximization What now?

r k A D D AD − D RTE ]/[exp D SDU == = −−= UD RTEE ]/)([exp r k A U U AU − U RTE ]/[exp U

(a) If ED > EU • Operate reactor at highest possible temperature None of these discussions / strategies examine yield. Both must be considered (b) If E > E U D in reactor design! • Operate reactor at lowest possible temperature Parallel Reactions: Selectivity for Two Reactant Systems

Example

kD βα11 Desired Reaction: ⎯+ ⎯→ DBA = CCkr BADD βα Undesired Reaction: kU 22 ⎯+ ⎯→ UBA = CCkr BAUU

rD kD − −ββαα2121 )()( SDU == CC BA rU kU Parallel Reactions: Selectivity for Two Reactant Systems

Case 1: α >α ; β > β 1 2 1 2 Let, a = α1-α2; b = β1 - β2

rD kD a b SDU == ACC B rU kU

For high SDU, maintain both A & B as high as possible

How can we accomplish this? • Use Batch reactor • Use Plug Flow reactor Parallel Reactions: Selectivity for Two Reactant Systems

Case 2: α1>α2; β1 < β2 Let, a = α1-α2; b = β2 - β1

k a ⎯+ ⎯→D DBA βα11 rD kD CA = CCkr BADD SDU == b k βα rU kU CB ⎯+ ⎯→U UBA 22 = CCkr BAUU

For high SDU, maintain concentration of A high and of B low

How can we accomplish this? See Fogler Figure 6.3 • Use semi-batch reactor where B is fed slowly • Use Tubular reactor with side streams of B being fed continuously • Use series of small CSTR with A fed only to first and B to each reactor Parallel Reactions: Selectivity for Two Reactant Systems

Case 3: α1<α2; β1 < β2 Let, a = α2-α1; b = β2 - β1

rkDD1 SDU == ab rkCCUUAB

For high SDU, maintain both concentration of A and B low

How can we accomplish this?

• For gas phase reactions, operate at low pressures • For liquid-phase reactions, dilute the feed

• CSTR is preferred Parallel Reactions: Selectivity for Two Reactant Systems

Case 4: α1<α2; β1 > β2 Let, a = α2-α1; b = β1 - β2

b rD kD CB SDU == a rU kU CA

For high SDU, maintain concentration of B high and of A low

How can we accomplish this? • Use semi-batch reactor where A is fed slowly • Use Tubular reactor with side streams of A being fed continuously • Use series of small CSTR with B fed only to first and A to each reactor

Same as Case 2, with A and B switched… Why Semi-Batch Reactors?

B

heat C A A, B

• B is slowly fed to A contained • Product C is continuously in the reactor. removed • Unwanted products can be • Higher conversion for minimized reversible reactions can be • exothermic reaction can be obtained carried out at controlled rate Semi-Batch Reactors - GMBE

1. GMBE on a molar basis

Input - Output + Gen = Accu. For Species A FB0 B dN Constant )(00 Vr =+− A v0 A dt Density Systems VV= + vt For Species B 00

dNB FrVBB0 −+0() = Constant dt Flowrate Semi-Batch Reactors - GMBE 2. GMBE on a concentration Basis F B0 B v0

For Species A (no inflow) dN )(00 Vr =+− A A = CVN A ][ A dt CVd )( dC dV )( Vr = A V A += C A dt dt A dt dC dC v ()rV=+ VA vC ⇒ A =−()rC0 A dt 0 A dtA V A Constant flow Similarly for Species B and density []FvC= dNB BB000 FrVBB0 −+0() = dV dt = v B = CVN B ][ 0 dC v dt B =−()rCC0 ( − ) dtBBB V 0 Modification to the CRE Algorithm for Multiple Reactions

Fogler, 6.4 • Mole balance on every species (not in terms of conversion) • Rate Law: Net Rate of reaction for each species,

e.g., rA = Σ riΑ • Stoichiometry

a) Liquid Phase, incompressible: CA=NA/V=FA/v0 b) Gas Phase use Variable volumetric flowrate; ideal gas

• Combine – More difficult: set of algebraic or differential equations for A, B, … Design Equation for Reactors – Multiple Reactions

Gas-Phase Liquid Phase NOTE the design equations are EXACTLY Batch as for a single reaction

but… Semi-Batch (B fed) Balances must be written for all components

CSTR

PFR

PBR What are the assumptions for each reactor type? Net Rate of Reaction

For N reactions, the net rate of formation of species A is:

For a given reaction iai A + bi B → ci C + di D

NOTE: You can use stoichiometric coefficients to relate relative rates of reaction of species for a specific reaction only Example: Net Rate of Reaction

• The following reactions follow elementary rate law:

Write net rates of formation of A, B and C

Fogler, 6.4.2; see Ex. 6-5 Example: Multiple Gas Phase Reactions in an Isothermal PFR

The complex gas phase reactions take place in a PFR. The feed is equal molar in A and B with FA0 = 10 mol/min and the volumetric flow rate is 100 dm3/min. The reactor volume is 1,000 dm3, there is no pressure drop, the 3 total entering concentration is CT0 = 0.2 mol/dm and the rate constants are:

S Plot FA, FB, FC, FD and CD / as a function of V

Taken from http://www.engin.umich.edu/~cre/06chap/frames_learn.htm Gas Phase Multiple Reactions - Algorithm

1. Mole Balance

A Remember, unlike single-reactions, B for multiple reactions mole balance for each species must be written C

D

rA, rB, rC, rD are all NET rates of reactions Example (cont’d) 2. Rate Laws

Species A

⇒ ⇒

Species B

Species C

Species D Example (cont’d) 3. Stoichiometry

4. Combine ⇒ Solution

Also, see example 6-10 What you should know…

• Qualitative Analyses (Parallel and Series Reactions) – Maximizing the reactor operation for single reactant systems – Maximizing the reactor operation for two reactant systems – Consideration of selectivity and yield

• Algorithm for Reactor Design of Multiple Reactions – Mole Balance – Net Rates of Reactions – Stoichiometry – Be able to write the set of equations for the system – usually cannot be solved without computer programs – be able to sketch the expected qualitative behaviour