Reactor Design

S,S&L Chapter 7

Terry A. Ring

ChE

Reactor Types

• Ideal– PFR– CSTR

• Real– Unique design geometries and therefore RTD– Multiphase– Various regimes of momentum, mass and

heat transfer

Reactor Cost

• Reactor is– PRF

• Pressure vessel

– CSTR• Storage tank with mixer• Pressure vessel

– Hydrostatic head gives the pressure to design for

Reactor Cost

• PFR– Reactor Volume (various L and D) from reactor

kinetics– hoop-stress formula for wall thickness:

– • t= vessel wall thickness, in.• P= design pressure difference between inside and outside of

vessel, psig• R= inside radius of steel vessel, in.• S= maximum allowable stress for the steel. • E= joint efficiency (≈0.9)• tc=corrosion allowance = 0.125 in.

ctPSE

PRt

6.0

Reactor Cost

• Pressure Vessel – Material of Construction gives ρmetal

– Mass of vessel = ρmetal (VC+2VHead)

• Vc = πDL

• VHead – from tables that are based upon D

– Cp= FMCv(W)

Reactors in Process Simulators

• Stoichiometric Model– Specify reactant conversion and extents of

reaction for one or more reactions

• Two Models for multiple phases in chemical equilibrium

• Kinetic model for a CSTR• Kinetic model for a PFR• Custom-made models (UDF)

Used in early stages of design

Kinetic Reactors - CSTR & PFR

• Used to Size the Reactor

• Used to determine the reactor dynamics

• Reaction Kinetics

/)exp()(

)(1

RT

EkTk

CTkdt

dCr

Ao

C

ii

jj

i

PFR – no backmixing

• Used to Size the Reactor

• Space Time = Vol./Q

• Outlet Conversion is used for flow sheet mass and heat balances

kX

kko r

dXFV

0

CSTR – complete backmixing

• Used to Size the Reactor

• Outlet Conversion is used for flow sheet mass and heat balances

k

kko

r

XFV

Review : Catalytic Reactors – Brief Introduction

Major Steps

A B

Bulk Fluid

External Surfaceof Catalyst Pellet

Catalyst Surface

Internal Surfaceof Catalyst Pellet

CAb

CAs

2. Defined by an Effectiveness Factor

1. External DiffusionRate = kC(CAb – CAS)

3. Surface AdsorptionA + S <-> A.S

4. Surface Reaction5. Surface DesorptionB. S <-> B + S

6 . Diffusion of products from interior to pore mouth

B

7 . Diffusion of products from pore mouth to bulk

Catalytic Reactors

• Various Mechanisms depending on rate limiting step• Surface Reaction Limiting• Surface Adsorption Limiting• Surface Desorption Limiting• Combinations

– Langmuir-Hinschelwood Mechanism (SR Limiting)

• H2 + C7H8 (T) CH4 + C6H6(B)

TB

HTT pp

ppkr

04.139.112

Catalytic Reactors – Implications on design

1. What effects do the particle diameter and the fluid velocity above the catalyst surface play?

2. What is the effect of particle diameter on pore diffusion ?3. How the surface adsorption and surface desorption influence the rate law?4. Whether the surface reaction occurs by a single-site/dual –site / reaction

between adsorbed molecule and molecular gas?5. How does the reaction heat generated get dissipated by reactor design?

Enzyme Catalysis

• Enzyme Kinetics

• S= substrate (reactant)

• E= Enzyme (catalyst)

OHS

SEOHs CkkCk

CCCkkr

2

2

321

31

Problems

• Managing Heat effects

• Optimization– Make the most product from the least reactant

Optimization of Desired Product

• Reaction Networks– Maximize yield,

• moles of product formed per mole of reactant consumed

– Maximize Selectivity• Number of moles of desired product formed per mole of

undesirable product formed

– Maximum Attainable Region – see discussion in Chap’t. 7.

• Reactors (pfrs &cstrs in series) and bypass • Reactor sequences

– Which come first

Managing Heat Effects

• Reaction Run Away– Exothermic

• Reaction Dies– Endothermic

• Preventing Explosions

• Preventing Stalling

Temperature Effects

• On Equilibrium

• On Kinetics

Equilibrium Reactor-Temperature Effects

• Single Equilibrium• aA +bB rR + sS

– ai activity of component I

• Gas Phase, ai = φiyiP, – φi== fugacity coefficient of i

• Liquid Phase, ai= γi xi exp[Vi (P-Pis) /RT]

– γi = activity coefficient of i – Vi =Partial Molar Volume of i

2

ln,exp

RT

H

dT

Kd

RT

G

aa

aaK

orxneq

orxn

aB

aA

sS

rR

eq

Van’t Hoff eq.

Overview of CRE – Aspects related to Process Design

1. Levenspiel , O. (1999), “Chemical Reaction Engineering”, John Wiley and Sons , 3rd ed.

Le Chatelier’s Principle

Unfavorable Equilibrium

• Increasing Temperature Increases the Rate

• Equilibrium Limits Conversion

Overview of CRE – Aspects related to Process Design

1. Levenspiel , O. (1999), “Chemical Reaction Engineering”, John Wiley and Sons , 3rd ed.

Feed Temperature, ΔHrxn

Heat Balance over Reactor

CoolingAdiabatic

Adiabatic

Q = UA ΔTlm

Reactor with Heating or Cooling

Q = UA ΔT

Kinetic Reactors - CSTR & PFR – Temperature Effects

• Used to Size the Reactor

• Used to determine the reactor dynamics

• Reaction Kinetics

RT

EkTk

CTkdt

dCr

Ao

C

ii

jj

i

exp)(

)(1

PFR – no backmixing

• Used to Size the Reactor

• Space Time = Vol./Q

• Outlet Conversion is used for flow sheet mass and heat balances

kX

kko r

dXFV

0

CSTR – complete backmixing

• Used to Size the Reactor

• Outlet Conversion is used for flow sheet mass and heat balances

k

kko

r

XFV

Unfavorable Equilibrium

• Increasing Temperature Increases the Rate

• Equilibrium Limits Conversion

Various Reactors, Various Reactions

kX

kko r

dXFV

0

k

kko

r

XFV

Reactor with Heating or Cooling

Q = UA ΔT

Temperature Profiles in a Reactor

Exothermic Reaction

Recycle

Best Temperature Path

Optimum Inlet TemperatureExothermic Rxn

Managing Heat Effects

• Reaction Run Away– Exothermic

• Reaction Dies– Endothermic

• Preventing Explosions

• Preventing Stalling

Inter-stage Cooler

Exothermic Equilibria

Lowers Temp.

Inter-stage Cold Feed

Exothermic Equilibria

Lowers TempLowers Conversion

Optimization of Desired Product

• Reaction Networks– Maximize yield,

• moles of product formed per mole of reactant consumed

– Maximize Selectivity• Number of moles of desired product formed per mole of

undesirable product formed

– Maximum Attainable Region – see discussion in Chap’t. 6.

• Reactors and bypass • Reactor sequences

Reactor Design for Selective Product Distribution

S,S&L Chapt. 7

Overview

• Parallel Reactions– A+BR (desired)– AS

• Series Reactions– ABC(desired)D

• Independent Reactions– AB (desired)– CD+E

• Series Parallel Reactions– A+BC+D– A+CE(desired)

• Mixing, Temperature and Pressure Effects

Examples

• Ethylene Oxide Synthesis

• CH2=CH2 + 3O22CO2 + 2H2O

• CH2=CH2 + O2CH2-CH2(desired)

O

Examples

• Diethanolamine Synthesis

NCHHOCHNHCHHOCHCHCH

O

desiredNHCHHOCHNHCHHOCHCHCH

O

NHCHHOCHNHCHCH

O

32222222

\/

22222222

\/

222322

\/

)()(

)()(

Examples

• Butadiene Synthesis, C4H6, from Ethanol

OHHCCHOCHHC

HCHOCHOHHC

OHHCOHHC

264342

2352

24252

Rate Selectivity

• Parallel Reactions– A+BR (desired)– A+BS

• Rate Selectivity

• (αD- αU) >1 make CA as large as possible• (βD –βU)>1 make CB as large as possible

• (kD/kU)= (koD/koU)exp[-(EA-D-EA-U)/(RT)]– EA-D > EA-U T– EA-D < EA-U T

)()(A

U

Drr

D/UD

U

D Ck

kS UDU

BC

Reactor Design to Maximize Desired Product for Parallel Rxns.

Maximize Desired Product

• Series Reactions– AB(desired)CD

• Plug Flow Reactor• Optimum Time in Reactor

Fractional Yield

OHCOOCHOCH

OHCHOCHOgOHCHCH

2223

23223

222

52

1)(

(k2/k1)=f(T)

Real Reaction Systems

• More complicated than either – Series Reactions– Parallel Reactions

• Effects of equilibrium must be considered

• Confounding heat effects

• All have Reactor Design Implications

Engineering Tricks

• Reactor types– Multiple Reactors

• Mixtures of Reactors

– Bypass– Recycle after Separation

• Split Feed Points/ Multiple Feed Points• Diluents• Temperature Management with interstage

Cooling/Heating

A few words about simulators

• Aspen• Kinetics

– Must put in with “Aspen Units”

• Equilibrium constants– Must put in in the form

lnK=A+B/T+CT+DT2

• ProMax• Reactor type and

Kinetics must match!!• Kinetics

– Selectable units

• Equilibrium constants