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Chemical Reaction Engineering

Youn-Woo LeeSchool of Chemical and Biological Engineering

Seoul National University155-741, 599 Gwanangro, Gwanak-gu, Seoul, Korea [email protected] http://sfpl.snu.ac.kr

Lecture #2

CHAP. 1MOLE BALANCE

反應工學I

Seoul National University

The first step to knowledgeis to know that we are ignorant

Socrates (470-399 B.C.)

개요


이 장에서는 화학반응공학 알고리즘 블록 쌓기의 첫 번째 블록인 몰수지를

세운다. 이 몰수지는 이 책을 통틀어서 계속적으로 사용될 것이다.

이 장을 공부한 후에 독자들은

(1)반응속도를 기술하며 정의할 수 있고

(2)일반 몰수지식을 유도할 수 있으며

(3)이것을 가장 일반적인 네 가지 형태의 반응기에 적용할 수 있을 것이다.

개요


화학반응속도 및 반응기 설계에 영향을 미치는 조건에 대한 논의를 시작하기 전에 반응계에 들어가고 나가는 여러 가지 화학종에 대한 양적인 고찰이 필요하다. 이러한 양적인 고찰은 반응계 내에서의 개별 화학종에 대한 총괄 몰수지 (General Mole Balance Equation)를 세움으로써 달성할 수 있다. 이 장에서는 반응 대상부피 내에서 유입, 유출 및축적되는 임의의 종(일반적으로 화학제품)에 모두 적용할 수 있는 일반몰수지를 세울 것이다.

개요


반응속도, rA를 정의하고, 화학반응속도를 적절히 정의하는 것이 쉬운일이 아니라는 점을 논의한 후에, 일반 몰수지식을 사용하여 일반적인공업용반응기들, 즉 회분식반응기, 연속교반탱크반응기 (CSTR), 관형반응기 및 충전층반응기 (PBR)에 대한 예비적인 형태의 설계방정식(design equation)을 유도하는 방법을 설명한다. 이 식들을 구하기 위해서 각 형태의 반응기의 모델화에 관련되는 가정을 설명한다.

Modeling of Chemical reactors

Potato

100oC

PhysicalPhenomena

H2O

100oC

Actual Ideal(simplification)

ModelingPhysical

Principles & laws

2

2

xtt

ODE, PDE

Mathematicalformulation

Solution

Supercritical Fluid Process Lab

dtdN

dVrFF jV

jjj 0

Solutionjj r

dVdF

ODE, PDE

Actual Ideal(simplification)

Mathematicalformulation

Modeling

Batch Reactor

Characteristics No charge or discharge during reaction

Phases Gas, Liquid, Liquid/Solid

Application Small scale productionIntermediate or one shot productionPharmaceuticalFermentationagricultural chemistry

Advantages High conversion per unit volume for one passFlexibility of operation(same reactor can produce one product one timeand a different product the next)Easy to clean

Disadvantages High operation costProduct quality can be changed batch to batch


Characteristics Either one reactant is charged and the other is led continuously(at small concentrations) or else one of the product can beremoved continuously to avoid side reaction.

Phases Gas/Liquid, Liquid/Solid

Application Small scale productionCompeting reactions

Advantages High conversion per unit volume for one runGood selectivityFlexibility of operation(can be used with a reflux condenser for solvent recoveryor in bubble type runs)

Disadvantages High operation costProduct quality more variable than with continuous operation

Semi-batch Reactor


Characteristics Run at steady state with continuous flow of reactantsand products: the feed assumes a uniform compositionthrough the reactor, exit stream has the samecomposition as in the tank

Phases Liquid, Gas/Liquid, Liquid/Solid

Application When agitation is required, Series configurations fordifferent concentration streams

Advantages Continuous operationGood temperature controlEasily adapts to two phase runsLow operating (labor) costEasy to clean

Disadvantages Lowest conversion per unit volumeBy-passing and channeling possible with poor agitation

Continuous-Stirred Tank Reactor (CSTR)


Characteristics One long reactor or many short reactors in a tube bankNo radial variation in reaction rate (concentration)Changes with length down the reactor

Phases Gas

Application Large scale production/Continuous ProductionFast reactionHigh Temperature

Advantages High conversion per unit volumeLow operating (labor) costContinuous operationGood heat transfer

Disadvantages Undesired thermal gradientsPoor temperature control (hot spot)Shutdown and cleaning may be expensive

Plug Flow Reactor (PFR)


Characteristics Tubular reactor that is packed with solid catalyst

Phases Gas/Solid catalyst, Gas/Solid

Application Heterogeneous gas phase reaction with a catalyst

Advantages High conversion per unit mass of catalystLow operating (labor) costContinuous operation

Disadvantages Undesired thermal gradientsPoor temperature control (hot spot)ChannelingShutdown and cleaning may be expensive

Packed-Bed Reactor (PBR)


Characteristics Heterogeneous reactionLike a CSTR in that the reactants are well mixed

Phases Gas/Solid catalyst, Gas/Solid

Application Heterogeneous gas phase reaction with a catalyst

Advantages Good mixingGood uniformity of temperatureCatalyst can be continuously regeneratedwith the use of an auxiliary loop

Disadvantages Bed-fluid mechanics are not well knownSevere agitation can result in catalyst destructionand dust formationUncertain scale-up

Fluidized-Bed Reactor (PBR)


회분식반응기 (Batch Reactor)

특성 반응이 진행되는 동안에 채우거나 비우지 않음

상 기상, 액상, 액-고상

응용분야 작은 규모의 생산중간생성물 또는 일회 생산 (One shot production)의약품발효농약

장점 단위 부피당 높은 전환율청소가 쉬움운전 유연성 (같은 반응기로 한번은 제품1을 생산하다가

다음 번은 제품2를 생산할 수 있음)

단점 운전비가 높음제품의 품질이 매회 달라질 수 있음

특징 반응물/생성물이 연속으로 흐르면서 정상상태로 운전반응기내의 조성이 일정하게 유지출구 농도는 반응기내의 농도와 동일

상 액상, 기-액, 고-액

응용분야 교반이 필요한 반응반응기 연속배열

장점 연속운전온도조절이 용이2상의 운전이 용이운전비용이 낮음청소가 쉬움

단점 단위부피당 낮은 전환율교반이 불량할 경우 By-passing과 channeling 가능

연속교반조반응기 (CSTR)

특징 연속반응하나의 긴 튜브반응기또는 여러 개의 짧은 튜브반응기 뭉치반경방향으로의 반응속도 (농도) 구배가 없음반응기 길이를 따라서 반응속도 구배가 존재

상 기상

응용분야 대량생산/연속생산고속반응고온

장점 단위부피당 높은 전환율낮은 운전비용연속운전

단점 바람직하지 않은 온도구배 발생가능온도조절이 어려움 (hot spot)운전정지와 청소가 비쌈

플러그 흐름반응기 (Plug Flow Reactor: PFR)

특징 고체촉매가 충전된 튜브반응기

상 기-고, 기-고체촉매

응용분야 고체촉매 기상반응

장점 고체촉매무게당 높은 전환율낮은 운전비용연속운전

단점 바람직하지 않은 온도구배 발생가능온도조절이 어려움 (hot spot)편류(Channeling)운전정지와 청소가 비쌈

충전층 반응기 (Packed-Bed Reactor: PBR)

특징 기-고반응CSTR과 같이 반응물이 잘 교반

상 기체/고체 촉매, 기체/고체

응용분야 기상 고체촉매반응

장점 우수한 혼합온도 균일성 유지부속 장치사용으로 촉매가 연속으로 재생될 수 있음

단점 유체역학 정보가 부족격한 교반으로 인한 촉매마모scale-up이 불확실

유동층 반응기 (Fluidized-Bed Reactor, FBR)

General Mole Balance on control volume


Follo

w th

e is

othe

rmal

re

actio

n de

sign

alg

orith

m

Follow the Reaction Design Algorithm

Follow the Yellow Brick Road

Reaction rate

The reaction rate is the rate at which a species looses its chemicalidentity per unit volume. The rate of a reaction can be expressedas the rate of disappearance of a reactant or as the rate ofappearance of a product.

Consider species A:

A → BrA: the rate of formation of species A per unit volume-rA: the rate of disappearance of species A per unit volumerB: the rate of formation of species B per unit volume

What is –r A (–r´A )?

rA에 대한 속도식은 계 내의 어떤 점에서 반응물의 성질과 반응조건 (예, 성분들의 농도, 온도, 압력, 또는 촉매의 형태 등)만의 함수인 대수식(algebraic equation)이다. 이 속도식은 반응이 일어나는 반응기의 형태(예,회분식 또는 연속흐름식) 에는 무관하다. 그러나 반응물의 성질과 반응조건은 화학반응기 내의 위치에 따라 다를 수 있으므로, rA는 위치의 함수가 될수 있으며, 계 내의 위치에 따라 달라질 수 있다.

균일반응속도, rA는 단위시간당 단위부피당반응하는 A의 몰수 (mol/dm3s)이다.

불균일반응속도, 즉 r´A의 차원은 단위시간당 단위촉매질량당반응하는 A의 몰수(mol/s g catalyst)이다.

2AA kCr AA kCr

A

AA Ck

Ckr2

1

1

Balance on control volume

A mole balance on species j, at any time, t, yields

NjGj = rj · V

Fj0 Fj

control volume

Rate of flow of j into the

system (mole/time)

Rate of generationof j by chem. rxn within the system

(mole/time)

Rate of accumulation of j within the system

(mole/time)

Rate of flow of j out ofthe system (mole/time)

- + =

in - out + generation = accumulation

dtdN

GFF jjjj 0

volumevolumetime

molestime

molesG j

molesN j


(1-3)

Rate of formation of species j by chem. rxn

rj1rj2

V1 V2

V

Suppose that the rate of formation of species j for the reaction varies withthe position in the control volume. The rate of generation, Gj1, in terms ofrj1 and sub-volume V1 is

M

iiji

M

ijij VrGG

11

If the total control volume is divided into M sub-volume, the total rate of generation is

111 V jj rG

By taking the limits (i.e., let M → and V → 0) and making use of thedefinition of integral, we can rewrite the foregoing equation in the form

V

jj dVrG

r j can have different values at difference locations in the reactor since theproperties of the reacting materials (e.g., conc., temp.) Seoul National University

1.2 The General Mole Balance Equation

(GMBE)

dtdN

dVrFF jV

jjj 0

With this GMBE, we can develop the design equations for thevarious types of industrial reactors: batch, semi-batch, andcontinuous-flow. Upon evaluation of these equations we candetermine the time (batch) or reactor volume (continuous-flow)necessary to convert a specified amount of reactants to products.

(1-4)


The most common industrial reactors

batch reactor CSTR(backmix reactor)

Reactants

Products

Reactants Products Reactants Products

PFR(tubular reactor)

PBR(packed-bed reactor)


Ideal Reactor Type

Batch Reactor uniform composition everywhere in the reactor the composition changes with time

Continuous-Stirred Tank Reactor (CSTR) uniform composition everywhere in the reactor (well mixed)

same composition at the reactor exit

Tubular Reactor (PFR)

fluid passes through the reactor with no mixing of earlier

and later entering fluid, and with no overtaking.

It is as if the fluid moved in single file through the reactor

There is no radial variation in concentration (plug-flow reactor)Seoul National University

Vrdt

dNA

A

VrdNdt

A

A

0

11

A

A

N

NA

A

VrdNt (1-6)

Integrating with limits that at t = 0, NA = NA0at t = t1, NA = NA1

dtdN

dVrFF jV

jjj 0

0 0 If the reaction mixture isperfectly mixed so that thereis no variation in the rate ofreaction throughout thereactor volume, we can take rjout of the integral and writethe GMBE in the form

V

jj VrdVrGMBE

Design Equation for Batch reactor

What time is necessary toreduce the initial number ofmoles from NA0 to a finaldesired number NA1?

1.3 Batch Reactors

(1-5)


1.3 Batch Reactors

Vrdt

dNA

A

t

NA

NA0

A B

t

NB

NB1

t1t1

NA1

0

11

A

A

N

N A

A

VrdNt

Moles of A change with time Moles of B increase with timeSeoul National University

Fig. 1-6

1.4.1 Continuous-Stirred Tank Reactor (CSTR)

The CSTR is normally run at steady state andis assumed to be perfect mixed.- No temporal, spatial variations in conc., temp.,

or rxn rate throughout the vessel- Conc. and temp at exit are the same as they are

elsewhere in the tank- Non-ideal mixing, residence-time distribution

model is needed

dtdN

dVrFF jV

jjj 0

0

j

jj

rFF

V

0

j

jj

rFF

V

0

Fj0

Fj

(1-7)

V

jj VrdVrGMBE

Design Equation for CSTR

(1-9)

The reactor volume, V,necessary to reduce theentering flow rate from Fj0to the exit flow rate Fj atreaction rate of rj.

A

AA

rvCCv

V

00

A

AA

rvCCv

V

00

vCF jj time

volumevolumemoles

timemoles

vCF jj

(1-8)


1.4.2 Tubular Reactor (PFR)

- The reactants are continually consumed as they flow down the length of the reactor - The concentration varies continuously in the axial direction through the reactor.- Consequently, the reaction rate will also vary axially.- To develop the PFR design equation, we shall divide (conceptually) the reactor intoa number of sub-volumes so that within each sub-volume V, the reaction rate may beconsidered spatially uniform.

0jF exitFj ,

)(yFj )( yyFj V

y

y yy

Let Fj(y) represent the molar flow rate of species j into volume V at yFj(y+ y) represent the molar flow rate of species j out of volume V at (y+ y)

In a spatially uniform sub-volume V,

VrdVrV

jj


dtdN

dVrFF jΔV

jΔVVjVj

0

jVjVVj

Vr

V

FF

0lim j

VjVVj

Vr

V

FF

0lim

(1-10)GMBEin V

Design Equation for PFR

(1-13)

The reactor volume, V1,necessary to reduce theentering molar flow rate FA0to some specified value FA1at reaction rate of rA.

(1-11)

VrdVrV

jj


jj r

dVdF

Integrating with limits that

at V = 0, FA = FA0at V = V1, FA = FA1

1

01

A

A

F

FA

A

rdFV


V

FA

FA0

A B

V

FB

FB1

V1V1

FA1

0

11

A

A

F

F A

A

rdFV

AA r

dVdF


Figure 1-12 profiles of molar flow rates in a PFRSeoul National University

1.4.3 Packed-Bed Reactor (PBR)

For a fluid-solid heterogeneous system, the rate of reaction of a substance A is defined as

catalystgreactedAgmolrA

sec

'

The mass of solid is used because the amount of the catalyst is what is important to the –r’A

0AF AF

)(WFA )( WWF A

WrA'

W

W WW

0)()( ' WrWWFWF AAAIn - out + generation = accumulation

A

A

F

FA

A

rdFW

0' No pressure drop

No catalyst decay

Design Equation for PBR


(1-14)

The first-order reaction (liquid phase rxn)

A Bis carried out in a tubular reactor in which the volumetric flow rate, v0, isconstant.

(1) Derive an equation relating the reactor volume (V) to the enteringconcentration of A (CA0), the rate constant k, and the volumetric flowrate v0.

(2) Determine the reactor volume necessary to reduce the exitingconcentration (CA) to 10% of the entering concentration (CA0) when thevolumetric flow rate (v0) is 10 ℓ/min and the specific reaction rate, k, is0.23 min-1.

Example 1-2 How large is it? (PFR)

CA0 v0 CAV

rA = -kCA


Example 1-2 How large is it? (PFR)

dVCdC

kv

A

A

0

l

lC

ClV

CC

kvV

dVCdC

kv

A

A

A

A

VC

CA

AA

A

100

10ln23.0

101.0

lnmin23.0min/10

ln

0

01

00

00

0

GMBE for PFR

(1st-order reaction)

Tubular, 1st order rxn

AA r

dVdF

AA kCr

dVdCv

dVvCd

dVdF AAA

00 )(

AA kC

dVdCv 0

AA r

dVdF

Combine both side

A reactor volume of 100L is necessary toconvert 90% of species A entering intoproduct B for the parameter given.


The first-order reaction (liquid phase rxn)

A Bis carried out in a CSTR in which the volumetric flow rate, v0, is constant.

(1) Derive an equation relating the reactor volume (V) to the entering concentration of A (CA0), the rate constant k, and the volumetric flow rate v0.

(2) Determine the reactor volume necessary to reduce the exiting concentration (CA) to 10% of the entering concentration (CA0) when the volumetric flow rate (v0) is 10 ℓ/min and the specific reaction rate, k, is 0.23 min-1.

P1-2A How large is it? (CSTR)

V

rA=-kCA

Fj0

Fj


For CSTR, the mole balance on species A was shown to be

P1-2A How large is it? (CSTR)

V

rA=-kCA

Fj0

Fj

3.391)min23.0/(min)/10)(9(

1.09.0

1.0

min23.0min,/10,1.0

1

0

0

000

100

0000

kv

kCvCvCV

kandvCC

kCvCvC

rFFV

A

AA

AA

A

AA

A

AA

3.391)min23.0/(min)/10)(9(

1.09.0

1.0

min23.0min,/10,1.0

1

0

0

000

100

0000

kv

kCvCvCV

kandvCC

kCvCvC

rFFV

A

AA

AA

A

AA

A

AA

The CSTR is almost 4 times larger than the PFR for getting 90% conversion


Reactor Differential Algebraic Integral

Mole Balance on Different Reactor

Vrdt

dNA

A

A

A

F

FA

A

rdFV

0A

A rdVdF

AA r

dWdF

A

A

F

FA

A

rdFW

0

A

A

N

NA

A

VrdNt

0

A

AA

rFFV

0

Batch

CSTR

PFR

PBR


종결


이 교과서의 목표는 화학반응공학의 기본원리를 사용하기 쉽고 다양한 문제에 적용할 수 있

는 알고리듬 속으로 짜 맞추는 데 있다. 이제 겨우 이러한 알고리듬의 블록 쌓기의 첫 번째 블

록인 몰수지를 마쳤다.

몰수지

이 알고리듬과 이 알고리듬의 블록 쌓기의 해당하는 블록들은 다음과 같은 장들에서 전개되

고 논의될 것이다:

몰수지 (제1장)

속도법칙 (제3장)

화학양론 (제4장)

결합 (제5장)

계산 (제5장)

에너지수지 (제11장~제13장)

이러한 알고리듬을 사용하여, 우리는 암기보다는 논리에 의해서 화학반응공학 문제들을 접근

하고 해결할 수 있다.

Isot

herm

al R

eact

ion

Des

ign

Alg

orith

m

Homework #2

1. P1- 4B (foam reactor)

2. P1-10A (설계방정식의 유도에서 어떤 가정들을 사용하였는가?)

3. P1-11A (fluidized CSTR)

Due date: one week

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