Reactors Design, Adiabatic and non- Adiabatic processes

Ideal ReactorsTypes of Ideal Reactors

(Semi-)Batch reactor

Plug-Flow Reactor (PFR)

Continuous stirred tank (CSTR)

Recycle reactor

Stirred tank cascade

Reactor Design

Volumetric flow rate

Rate of reaction

Outlet concentrationInlet concentration

Reaction volume

Model

Outlet = f(inlet, kinetics, contacting pattern)

Ideal Reactors

Batch Reactor – 1

Material Balance

Energy Balance(1) constant pressure

(2) constant volume

Ideal Reactors

Batch Reactor – 2Conversion and Temperature Profiles in Batch Reactor

Ideal Reactors

ADIABATIC POLYTROPIC

Numerical solution necessary!

t t

CST Reactor

Material Balance

mean residence time

steady state conversion

Ideal Reactors

Transient behavior in CSTRIdeal Reactors

Transient behavior in CSTRIdeal Reactors

Phenol Production in CSTRIdeal Reactors

Energy BalanceCSTR Reactors

Where:

of feed stream


0

-feed



from material balance

General Energy Balance Equation for CSTR

Summary of Energy Balance-1CSTR

Summary of Energy Balance-1CSTR

(1) Please derive the constant volume-ideal gas for a CSTR reactor

Energy Balance

Special Case: Incompressible fluid

CSTR

Energy BalanceSimplifying Assumptions

CSTR Reactors

(1) Steady-State Condition

0

(2) Liquid Phase(3) Excess Solvent or Diluent

heat capacity is constant independent of pressure

Temperature Control in CSTR – 1 CSTR

Aqueous solution of specie A undergoes a reversible isomerization reaction in a 2000 L CSTR.

1. Find the reactor temperature for 80 % conversion.2. What are the heat duties of the two heat exchangers ? Approximate the

heat capacity of the reaction mixture with that of water.


(1) Steady-State Condition

whereAns.


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1. (a) Plot conversion versus T (K) for CAf = 0.25, 4, 16.(b) Plot conversion versus T(K) for CAf = 4, if VR is 0.5 or 2 x the given value. (c) Plot conversion versus T(K) for CAf = 4, if activation energy of k1 is 0.5 or 2 x the

given values.(d) Plot conversion versus T(K) for CAf = 4, if activation energy of K1 is 0.5 or 2 x the

given values.Please summarize your observations.


(2) Heat duties of the two heat exchangers

CSTRMultiple Steady-State

(1) The coupling between material and energy balances in CSTR can lead to complex behavior,

(2) The presence of multiple steady-state is possible even for the simplest kinetic mechanism.

Adiabatic CSTR – 1 Multiple Steady-State


(1) Material Balance

(2) Steady-State, Liquid Phase, Constant Density


(3) Heat Capacity is Constant

heat transfer

where:


(4) Material and Energy Balance for Adiabatic CSTR

(5) Solve the Nonlinear Equations(a) For isothermal case:


(5) (b) For nonisothermal case:

1. Find and for

2. You can then plot for different values of ∆HR

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(6) Multiple Steady-State(a) Reactions more exothermic than –10 x 104 kJ/kmole, there are multiple steady states,(b) Points at which steady-state curve turns correspond to the ignition and extinction

points.

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(7) Hysteresis

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ignition

decreasing flowrate decreasing flowrate

ignition

extinctionextinction


(8) Stability of Steady-Statevan Heerden Diagram

Dynamic Model

Solving

Procedure(1) Qr = Qg then steady state condition occurs,(2) Qg(θ) vs. T is nonlinear, but Qr(θ) vs. T is linear,(3) The resulting plots is known as van Herdeen diagram

heat generation heat removal


(8a) van Heerden Diagram


(8b) van Heerden Diagram


(9) Mechanical Analogy

Single Steady-State A Ignition Point A

Standardized Stirred Tank Reactor Sizes Heat Exchanger in CSTR

Volume VR (m3) Diameter db (m) heat exchanger area A (m2)

0,1 0,508 0,80,16 0,6 1,160,25 0,7 1,480,4 0,8 2,32

0,63 1 2,871 1,2 3,87

1,6 1,4 5,62,5 1,6 7,94 1,8 9,1

6,3 2 13,18 2,210 2,4 18,7

12,5 2,416 2,8 2520 2,625 3 34,632 3,440 3,6 46

Types of Heat Exchangers – 1

(1) Jacketed Heating and Cooling

Heat Exchangers in CSTR

)(T- TcQUA

cQUA

)(T- TcQ

)UA(T- TQ

WFpww

pww

WFpww

Ww

+=

=

=

)(T- TcQUA

cQUA

)(T- TcQ

)UA(T- TQ

WFpww

pww

WFpww

Ww

+=

=

=

(2) Integrated Heat Exchanger

T

)T(T)cQUA/(exp1cQQ

A

TcQ) TU(T

A

Q

WFpwwpwww

wpwwW

−−−=

∂∂

=−=∂

∂

⎥⎦

⎤⎢⎣

⎡)T(T)cQUA/(exp1cQQ

A

TcQ) TU(T

A

Q

WFpwwpwww

wpwwW

−−−=

∂∂

=−=∂

∂

⎥⎦

⎤⎢⎣

⎡

Types of Heat Exchangers – 2

(3) External Heat Exchanger with Recycle


Heat exchanger

Ratio between residence time and reaction time

Stable and Unstable Limit Cycle

Damköhler Number

0j

i0ji c

r)(Da

θν−=

0j

i0ji c

r)(Da

θν−=

0kj0jk

0j2jjj0j0k2jk2

0j2j2

j20j2

2j2

1jj0j1

0j

0j0

a0

c/c

ck)(-)X-1)(-X1(cck)cck(r2

ck)(-)-X1(ck)ck(r2

k)(--X1ck1

c

k)(-1k0

D(X) rorderreaction

νν=λ

τ⋅⋅⋅νλ⋅⋅=

τ⋅⋅⋅ν⋅=

τ⋅⋅ν⋅

θ⋅νΦ

0kj0jk

0j2jjj0j0k2jk2

0j2j2

j20j2

2j2

1jj0j1

0j

0j0

a0

c/c

ck)(-)X-1)(-X1(cck)cck(r2

ck)(-)-X1(ck)ck(r2

k)(--X1ck1

c

k)(-1k0

D(X) rorderreaction

νν=λ

τ⋅⋅⋅νλ⋅⋅=

τ⋅⋅⋅ν⋅=

⋅⋅ν⋅

⋅⋅νΦ

θ

θ

θ

)X()T(rr);X()T(rr j0i0ii Φ⋅=Φ⋅=( for any reaction) )X()T(rr);X()T(rr j0i0ii Φ⋅=Φ⋅=( for any reaction)

)X1(c)T(kc)T(kr j0j1j1 −⋅=⋅=e.g. for 1st order kinetics)X1(c)T(kc)T(kr j0j1j1 −⋅=⋅=e.g. for 1st order kinetics

where

Da < 0,1 low conversion ; Da < 100 nearly quantitative conversion⇒ ⇒

Analysis – 1

(1) CSTR Energy Balance


Relative Cooling Intensity

Stanton Number, St =

Adiabatic Temperature Increase

∆Tad =cA0

vi

cA0

-viDa(T)Φ(X)1

θ

St ∆Tad (X)

Analysis – 2

(2a) Jacketed Heating and Cooling


St (T – TW) = κ (T – TWF)

=QWcPW

+ QWcPW

(T – TWF)

(2b) Integral Heat Exchanger

T

St (T – TW) = κ (T – TWF)

=QWcPW [1 – exp (- / QWcPW](T – TWF)

TW

TWF

T0

St ∆Tad (X)

Analysis – 3

(3) Calculation of Reactor Temperature


κ ∆Tad (X)(T – TWF)

(T – T*W) = ∆Tad (X)(1 + κ)

T*W = (Tf – κTWF)

(1 + κ)where outlet temperature in

absence of temperature

(T – T*W) = ∆Tad (1 + κ) Daœ exp (-E/RT)

1 + Daœ exp (-E/RT)

Heat Removal Heat Generation

Oscillatory BehaviorNonadiabatic CSTR – 1

Nonadiabatic CSTR – 2

(1) Solving the New Problem

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(2) Temperature and Conversion Oscillation – 1

Phase Plot

limit cycle

Oscillatory Behavior

Nonadiabatic CSTR – 4 Multiple Steady-State

(3) Initial Conditions

CA0 = CAf, T0 = Tf

CA0 = 0, T0 = Tf

global attractor


(4) Temperature and Conversion Oscillation – 2



(5) Stable and Unstable Limit Cycle



(6) Complex Phase Plots


X

Separatrix

Tmperature

Con

vers

ion

In General:Cooling Capacity > Heat Generationlead to a stable steady-state.

Heat Generation > Cooling Capacityusually lead to unstable steady-state such as (1) ignition, (2) extinction and(3) oscillatory behavior.


(7) General Analysis(a) Effects of feed temperature (Tf)

Heat Removal in CSTR

(T – T*W) = ∆Tad (X)(1 + κ) T*W = (T0 – κTWF)

(1 + κ)where

•

Q Heat removal

Heat generation

•

Q Heat removalHeat removal

Heat generationHeat generation

Thermal Hysteresis


(b) Effects of residence time (θ)

Heat Removal in CSTR

(T – T*W) = ∆Tad (1 + κ) Daœ exp (-E/RT)

1 + Daœ exp (-E/RT)

Q

TWF

Flow Hysteresis

CSTR – 1 Mixing and Residence Time Distribution

(1) Fluid Flow Pattern in Reactor(a) Computational Fluid Dynamics (CFD)

- fluid mixing is calculated by solving the equations of motion for fluid,- type of fluid flow (e.g., laminar and turbulent), and various transport

mechanisms (e.g., molecular and eddy diffusions) must be accounted.


(b) Residence Time Distribution (RTD)- classical approach based on experimental probe,- do not use any structure of equation of motion, approximate idea of

mixing.- at short length scale: condition that maximizes diffusion also enhances

mixing and uniformity,at reactor length scale: condition that maximizes convection enhances mixing and uniformity.


(2) Gedanken Experiment

a

b

c

tracer

(a) Probability function


(b) RTD MeasurementExperimental Method

Cf

C0

C0

Cf


(3) CSTR Experiment

Step response experiment

t ≤ 0, No tracert > 0, Add small amount of tracer


(3) CSTR Experiment

(a) Material Balance

= 1

τ

τ is the mean residence time


(4) RTD in CSTR: Step-Change in Concentration


(5) Mean RTD

2. Describe a Semibatch Reactor(a) Write the governing material balance equation,(b) Write the governing energy balance equation for a incompressible liquid, constant

pressure reactor.

CSTR ReactorGroup No. 1, 3, 5, 7, 9, 11

Mini-Project 2

A → B

CSTR ReactorGroup No. 1, 3, 5, 7, 9, 11

Mini-Project 2

(1) Plot Conversion and T versus q (see below) as function of:(a) Cf 2, 4, 8, 16, 32 kmol/m3

(b) ∆HR -30, -20, -10, -5, 0, 5 x 104 kJ/kmolGroup 1 U° = 50 kJ/(m3minK)-1 Group 7 U° = 400

3 U° = 100 9 U° = 800 5 U° = 200 11 U° = 1600

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CSTR ReactorGroup No. 2, 4, 6, 8, 10

Mini-Project 2

A ↔ B K1 = k1/k-1

Note ∆HR is for the forward reaction, reverse reaction should give - ∆HR

CSTR ReactorGroup No. 2, 4, 6, 8, 10

Mini-Project 2

Plot Conversion and T versus q (see below) as function of ∆HR is -30, -20, -10, -5, 0, 5 x 104 kJ/kmol.

Group 2 K1 = 1 Group 8 U° = 20 4 K1 = 5 10 U° = 100 6 K1 = 10

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Reactors Design, Adiabatic and non- Adiabatic processes

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