[Computer Aided Chemical Engineering] Integrated Design and Simulation of Chemical Processes Volume 35 || Synthesis of Reaction Systems

CHAPTER

SYNTHESIS OF REACTIONSYSTEMS 88.1 CHEMICAL REACTION NETWORK8.1.1 STOICHIOMETRYThe chemical transformation between the components involved in a network of chemical reactions can

be described quantitatively by means of stoichiometric relations. In the case of multiple reactions, the

stoichiometric relations form a system of linear algebraic equations:XSi1

ni, jAj 0, i 1, . . . ,R (8.1)

where ni, j is the stoichiometric coefficient in the reaction i of the species j, the network consisting of Scomponents and R reactions. The relation (8.1) may be extended to the atomic balance. If the atomicspecies are Ek (k1, . . ., N) and the atomic coefficients are ejk, then the material balance is constrainedby the atomic balance as follows:

Aj XNk1

ej,kEk, j 1, . . . ,S (8.2)

XSj1

njej,k 0, k 1, . . . ,N (8.3)

It is worth noting that only independent reactions are employed to express the composition of a reaction

mixture. This is usually the case for complex reactions, such as the cracking of hydrocarbons, where

much more stoichiometric equations may be written than strictly necessary. The number of indepen-

dent reactions can be simply determined as the rank of the matrix of stoichiometric coefficients.

EXAMPLE 8.1 STOICHIOMETRIC-INDEPENDENT REACTIONSThe following reactions can be written for the catalytic reforming of methane with water at high temperature:

CH4 +H2O!CO+3H2 (i)

Continued

Computer Aided Chemical Engineering. Volume 35. ISSN 1570-7946. http://dx.doi.org/10.1016/B978-0-444-62700-1.00008-5

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CH4 + 2H2O!CO2 + 4H2 (ii)

CO+H2O!CO2 +H2 (iii)

CH4 !C+ 2H2 (iv)

CO2 +C! 2CO (v)

C+H2O!CO+H2 (vi)

Find the number of stoichiometric-independent reactions.

Solution. The species are CH4, H2O, H2, CO, CO2 and C. By convention, the stoichiometric coefficients are negativefor reactants and positive for products. The matrix of stoichiometric coefficients of the reactions (i)(vi) is

CH4 H2O H2 CO CO2 C

v

1 1 3 1 0 01 2 4 0 1 00 1 1 1 1 00 0 0 2 1 10 1 1 1 0 1

266664377775

The rank of the above matrix may be found by standard methods. For example, by elementary row operations (inter-

changing two rows, multiplying one row by a nonzero constant and adding two rows), the matrix can be brought the fol-

lowing upper-triangular form:

n

1 1 3 1 0 00 1 1 1 1 00 0 0 0 0 0

0 0 0 2 0 00 0 0 0 0 0

266664377775

There are three nonzero diagonal elements, so the rank of the matrix is three. As a result, there are three independent

reactions, (i), (ii) and (iv), corresponding to the nonzero entries on the main diagonal. Note that the set of independent

reactions is not unique, depending on the order in which the elementary row operations are performed.

8.1.2 REACTION EXTENT, CONVERSION, SELECTIVITY AND YIELDWemay express the variation of the number of moles in a reaction system in a generic manner bymeans

of the molar extent of reaction x, as

Nj Nj0 + njx (8.4)

Note that x characterises the reaction itself and not a particular component. In the case of multiple re-actions, a molar extent of reaction xi can be attributed to each independent reaction. The number ofmoles of component j involved in R reactions is

Nj Nj0 +XRi1

ni, jxi (8.5)

302 CHAPTER 8 SYNTHESIS OF REACTION SYSTEMS

The total number of moles becomes

Nt N0 +XSj1

XRi1

ni, jxi N0 +XRi1

Dnixi (8.6)

where Dni is the variation of the number of moles in the reaction i.The molar extent of reaction x previously introduced is an extensive variable, since it depends on

the amount of reactants. It is often convenient to introduce intensive variables by dividing the molar

extent by the initial number of moles N0, initial volume V0 or mass m. The following variables areobtained:

xni xiN0

, xvi xiV0

, xmi xim

(8.7)

For single reactions, it is often more convenient to use conversion as an intensive measure of a chemicaltransformation. The use of a reference reactant is compulsory. If NA0 is the initial molar amount of thereactant A, and NA is the amount after reaction, the conversion XA is by definition

XA NA0NANA0

(8.8)

The number of moles of other species can be expressed as a function of XA as follows:

Nj Nj0 njnANA0XA (8.9)

The total number of moles in the system is

Nt N0NA0DnnA XA (8.10)

From Equations (8.4) and (8.9), it follows that the link between conversion and molar extent of reaction

is simply

XA nANA0

x

The use of conversion is suited for a single reaction, while the molar extent of reaction is more con-

venient for multiple reactions.

Selectivity and yield are important concepts when dealing with multiple reactions. Three types of

components are of interest: reactants, including the reference; main product; and by-products. In this

book, we use the following definitions:

Selectivity sP=A Amount of useful productP formed

Amount of reference reactantA transformed(8.11)

Yield P=A

Amount of useful productP formedInitial amount of reference reactant A

(8.12)

3038.1 CHEMICAL REACTION NETWORK

Yield, selectivity and conversion are linked by the relation:

P=A sP=AXA (8.13)

Let us consider the simple reaction aA+bB!pP+ rR, where A is the reference reactant and P is thedesired product. The following relations define selectivity and yield:

sP=A NPNP0NA0NA (8.14)

P=A NPNP0

NA0(8.15)

Note that the selectivity and yield defined by the previous relationships are measured in kmol P/kmol Aand can take values higher than 100%. Other definitions are possible, for example, using mass instead

of moles (kg P/kg A). For single reactions, one may take into account the stoichiometric coefficientsand define the dimensionless quantities:

s0P=A nAnP

NPNP0NA0NA (8.16)

0P=A nAnP

NPNP0NA0

(8.17)

Taking into account that selectivity and yield can be expressed in many ways, when reporting their

values we strongly advice to specify the definition used and, eventually, the units.

EXAMPLE 8.2 COMPLEX REACTIONSThe following reactions may be considered at the catalytic burning of ammonia:

4NH3 + 5O2 ! 4NO+6H2O (i)

2NO+O2 ! 2NO2 (ii)

2NO!N2 +O2 (iii)

4NH3 + 3O2 ! 2N2 + 6H2O (iv)

4NH3 + 6NO! 5N2 + 6H2O (v)

N2 +O2 ! 4NO+6H2O (vi)

The feed reactionmixture has the following composition: NH3, 20%; NO2, 2%; NO, 3%; N2, 5%; O2, 35%; and H2O, 5%,

the rest being other inert gases. The following molar fractions have been measured at the reactor exit: y100.086 (NH3),y200.1075 (NO2), and y300.064 (N2). Determine the conversion of ammonia. Calculate the amounts of NO and NO2for 2000 Nm3/h initial mixture. Determine the yield and selectivity in nitric oxides, the reference reactant being ammonia.


Solution. Following Example 8.1, three reactions are stoichiometric-independent. We select the reactions (i), (ii) and

(iii) with the extent of reaction x1, x2 and x3. The number of moles of each component is

NH3 :N1 N104x1

NO2 :N2 N20 + 2x2

N2 :N3 N30 + x3

O2 :N4 N405x1x2 + x3

H2 :N5 N50 + 6x1

NO :N6 N60 + 4x12x22x3

Inert: N7N70Total flow: NtNt0+x1x2

y1 N104x1

Nt0 + x1x2, y2

N20 + 2x1Nt0 + x1x2

, y3 N30 + x3

Nt0 + x1x2

Using as variables the extents of reaction with respect to the initial number of moles xni, the above equations become

y1 y104xn11 + xn1xn2

0:086, y2 y20 + 2xn2

1 + xn1xn2 0:1075, y3

y30 + xn11 + xn1xn2

0:064

By solving the system, the following values are obtained: xn10.0288, xn20.0428 and xn30.0131. The other molarfractions are y40.1788, y50.226, y60.0334 and y70.3043. The ammonia conversion is XNH3 1N1/N101(y104xn1)/y100.576.

The molar flow rates are

Input: F02000/22.489.285 kmol/h.Output: FF0 (1+xn1xn2)88.036 kmol/h.The flow rates (kmol/h) of the main components are

Input Output Change

NH3 17.857 7.571 10.386NO 2.678 2.940 0.262

NO2 1.786 9.460 7.678

By definition, the yield is obtained as the amount of product formed divided by the initial reference reactant: in molar

units, the yield and selectivity for NO and NO2 are

sNO=NH3 0:262

10:386 0:0252 kmolNO

kmolNH3; NO=NH3

0:262

17:857 0:0147 kmolNO

kmolNH3

sNO2=NH3 7:678

10:386 0:7393kmolNO2

kmolNH3; NO2=NH3

7:678

17:857 0:43kmolNO2

kmolNH3

The above values verify the relation between conversion, yield and selectivity.

3058.1 CHEMICAL REACTION NETWORK

8.2 CHEMICAL EQUILIBRIUMChemical equilibrium is a key issue in process design. In many cases, chemical equilibrium might set

an upper limit for the achievable conversion if nothing is done to remove one of the products from

the reaction space. Because the equilibrium conversion is independent of kinetics and reactor design,

it is also convenient to use it as reference. Note that important industrial reactions take place close to

equilibrium, such as the synthesis of ammonia and methanol, esterification of acids with alcohols and

dehydrogenation, particularly when the reaction rate is fast. Therefore, the investigation of chemical

equilibrium should be done systematically in a design project.

8.2.1 EQUILIBRIUM CONSTANTThe analysis of chemical equilibrium is based on the concept of chemical potential (Chapter 5). Con-

sider a homogeneous gaseous system. The chemical potential of a component j in a mixture is given by

mj P, T, yj

m0j T +RT ln f j (8.18)

where mj0 is the chemical potential of the pure component, function only of temperature. f j is the

fugacity of the component j in mixture, depending on pressure, temperature and composition. Theover-hat designates a component property in a mixture. In the case of singular reaction involving Scomponents, the following relation describes the chemical equilibrium:

DGXSj1

njmj 0 (8.19)

In the case of R multiple reactions, a similar expression is

DGXRi1

XSj1

ni, jmj 0 (8.20)

From Equation (8.19), we find the following relationship between the equilibrium constant and the free

Gibbs energy:

DG0 T RT lnKf (8.21)

where DG0 is the variation of Gibbs free energy of the system given by

DG0 T X

njm0j (8.22)

The equilibrium constant Kf based on fugacity is given by

Kf YSj1

fnjj (8.23)

By convention, the stoichiometric coefficients nj are positive for products and negative for reactants.Similarly with Equation (8.21) for multiple reactions, we obtain a system of equilibrium relations:


DG0i T RT lnKf , i, i 1,2, . . . ,R (8.24)

Now, the problem is to express fugacity as a function of P, T and composition, and on this basis todetermine the equilibrium composition. Two possibilities exist: assume ideal or real solutions.

8.2.1.1 Ideal solutionsIn the case of ideal solutions, the LewisRandall approximation can be used:

f j f 0j yj P0j yj (8.25)

The equilibrium constant becomes

Kf KyK0PDn (8.26)

where Ky YS

j1ynjj , K

0

YSj1

0j

njand DnP j1S nj

Note that the equilibrium constant of fugacity coefficients of pure components K0 is independent of

composition and can be calculated with a suitable equation of state, as viral or cubic EOS. The pressure

correction PDn depends on the variation of the number of moles. It follows that the equilibrium com-position may be calculated from Ky, by expressing the composition of each species as a function ofconversion or of the molar extent of reaction.

8.2.1.2 Real solutionsIn this case, the component fugacity is f j jPyj, where j is the fugacity coefficient of the componentthat now considers the effect of composition. This can be accounted for by means of mixing rules (seeChapters 5 and 6). Equation (8.26) remains formally valid, but takes now into account the equilibrium

constant of fugacity coefficientsK YS

j1 j nj

. For liquid-phase reactions, the treatment is similar,

by replacing fugacity with activity. Because the relation ajgjxj links the activity with composition, weobtain

Ka KgKx (8.27)

The equilibrium constant of the activity coefficients Kg YS

j1gnjj can be calculated by means of a

liquid activity model (see Chapter 6).The case of heterogeneous equilibrium is more difficult, but less frequent in practice. Supplemen-

tary material may be found in more specialised books on thermodynamics.

8.2.2 EQUILIBRIUM COMPOSITIONIn the case of simple reactions, the equilibrium composition can be calculated by solving

Equation (8.23) with conversion as variable for chemical transformation. On the contrary, the extent

of reaction is more suitable for multiple reactions. The solution may be obtained by solving a system of

algebraic equations of type (8.24).

A second possibility to calculate the equilibrium composition is byGibbs free energy minimisation.The starting point is the system of equations generated by the relation (8.20). Phase equilibriummay be

included in analysis. This method is particularly powerful, because it does not imply necessarily the

3078.2 CHEMICAL EQUILIBRIUM

knowledge of the stoichiometry. However, the user should consider only species representative for

equilibrium. As in any optimisation technique, this approach might find local optimum. Specifying

explicitly the equilibrium reactions is safer.

The effect of temperature on equilibrium is given by the vant Hoff equation:

dlnK

dTDHR

RT2(8.28)

K stands for either Kf or Ka, while DHR is the heat of reaction. If the reaction is exothermic (negativeheat effect), then both equilibrium constant and conversion decrease with increasing temperature. On

the contrary, in endothermic reactions, the equilibrium conversion increases with the temperature

(Figure 8.1).

The above discussion has important practical consequences. In endothermic reactions, the

operating temperature must be kept as high as possible, while in exothermic reactions, the temperature

should follow an optimal profile, which should start at higher temperature and ends up at lower

temperature.

8.3 REACTION RATEThe extensive reaction rate is defined as the rate of reactant consumption or product formation in a

closed system (batch reactor). Let us consider the singular reaction A!products. By reference tothe reactant A, the reaction rate might be seen simply as the number of moles of reactant

A transformed in one time unit. More useful for design is an intensive definition, in which we may

introduce an element characterising the reaction device itself, such as volume, mass or contact surface.

Here, we adopt the convention that the reaction rate is positive for products and negative for reactants.

Selecting the product j as reference, the following definitions of the reaction rate may be written(Levenspiel, 1999):

XAe

Temperature0

1

Exothermic reaction

Endothermic reaction

Irreversible reaction

FIGURE 8.1

Effect of temperature on equilibrium conversion.


rj 1V

dNjdt

moles j formedvolume of fluid time (8.29)

rj 1W

dNjdt

moles j formedmass of solid time (8.30)

rj 1S

dNjdt

moles j formedsurface of contact time (8.31)

Equation (8.29) is suitable for a homogeneous system, Equation (8.30) is useful for fluid/solid catalyst

reactors, while Equation (8.31) is applicable to gasliquid or liquidliquid reactors.

For the stoichiometric-independent reaction i, the equivalent reaction rate is defined as

ri 1V

dxidt

(8.32)

This time xi defines the molar extent of the reaction i. If the component j is implied in several reactions,the net reaction rate is given by

rj XRi1

ni, jri, j 1,2, . . . ,S (8.33)

or in matrix notation

rj ni, j ri (8.34)

The relationship (8.33) can be used also to analyse kinetic experimental data in the case of complex

reactions. Usually the number of species is much larger than the number of independent reactions.

Therefore, it is sufficient to choose a number of R key species among the components that can be mea-sured with good accuracy. Let us denote byj the known measured (components) reaction rates. Thenthe system can be solved to find the equivalent reaction rates ri as

ri j

ni, j 1

(8.35)

The other species may be determined easily from the remaining set of equations (8.33).

As an example, we consider the following consecutive-parallel reactions, often found in organic

chemistry processes, such as nitration, alkylation and chlorination:

A+B!C + S r1C+B!D+R r2D+B!E+F r3

There are six chemical species and three reactions.We select A, B and C as key components. Thematrix

of stoichiometric coefficients is

ni, j 1 1 10 1 1

0 1 0

24 35, ni, j 1 1 1 20 0 10 1 1

24 35 (8.36)

3098.3 REACTION RATE

Equation (8.35) becomes

r1 r2 r3 rA rB rC 1 1 20 0 10 1 1

24 35 (8.37)from which one gets

r1 rA; r2 rA rC; r3 2rA rB + rC (8.38)

The reaction rates of the other species can be obtained from the relation (8.34) as

rD rE rS r1 r2 r3 0 0 1

1 0 1

1 1 1

24 35 (8.39)rD r2 r3, rE r3, rS r1 + r2 + r3 (8.40)

8.3.1 KINETICSThe reaction rate is a function of concentration, temperature and pressure. In a large number of practical

cases, the reaction rate may be expressed as a function of only temperature and concentration, as

follows:

ri f 1 T f 2 cj

(8.41)

The dependency on temperature is given by the Arrhenius law:

f 1 T k0exp E=RT (8.42)

where k0 is the pre-exponential factor and E is the activation energy. The dependency on concentrationcan be formulated as a power-law function:

f 2 cj caAcbB . . . (8.43)

In the relation (8.43), a, b,. . . are partial orders of reaction. Their sum gives the global order of reactionna+b+ . If the reference component is A then the reaction rate is expressed in general by the fol-lowing relation:

rA k0eE=RTcaAcbB . . . (8.44)

Note that the partial orders of reaction a, b,. . . correspond to the stoichiometric coefficients only forelementary reactions. In the case of non-elementary reactions, the apparent orders of reactions are dif-ferent from stoichiometric coefficients, and more than one reaction step must be considered to explain

the reaction mechanism.

It is worthy to note that there is a thermodynamic constraint in formulating kinetic expressions for

reversible reactions: the partial reaction orders must be consistent with the equilibrium. Let us examine

the reversible reaction aA+bB$pP+ rR, for which the following reaction rate expression is proposed:


rA k1caAcbBk2cpPcrR (8.45)

Since at equilibrium cPpcR

r KccAacBb , reaction orders and stoichiometric coefficients should respect thecondition

aa bbpp r

r(8.46)

8.4 REACTORS FOR HOMOGENEOUS SYSTEMSIn this section, we will review basic equations for calculating the reaction volume necessary to achieve

a given conversion for simple reactions.

8.4.1 REACTOR VOLUMEWe may distinguish between two approaches in calculating the volume of a chemical reactor: kinetic

and shortcut design. In kinetic design, at least the kinetics of the main reaction must be known. Perfect

mixing and plug flow are known as ideal models, such as continuous stirred tank reactor (CSTR) and

plug flow reactor (PFR), respectively. Real models, with intermediate degree of mixing, can be de-

scribed as combinations of ideal models.

8.4.1.1 Continuous stirred tank reactorIn a CSTR, the reaction rate is uniform in space, corresponding to the exit concentrations (Figure 8.2).

At constant volume V, the material balance of the reactant A is

VdcAdt

FA,0FA rA V (8.47)

At steady state, the following characteristic equation is obtained:

cA,0

cA,f

Inlet

Outlet

cA,0

cA,f

FA,0V

FIGURE 8.2

Illustration of a continuous stirred tank reactor.

3118.4 REACTORS FOR HOMOGENEOUS SYSTEMS

V

FA0 XAfrA XAf

or t VQv0

cA0XAfrA XAf (8.48)

where the subscript f refers to the outlet conditions. Equation (8.48) can be used to calculate the res-idence time t and the reaction volume V for a given conversion.

For multiple reactions, the solution of the characteristic equation involves a system of algebraic

equations as follows:

t VQv0

cjcj0rj

cjcj0XRi1nijri

(8.49)

We may write cjcj0P

i1R nijxvi, making use of the extent of reaction with respect to the reaction

volume, xvixi/V. Equation (8.49) becomes

tXRi1

ni, jri XRi1

ni, jxvi, j 1,2, . . . ,S (8.50)

Equation (8.50) is equivalent with the following system of algebraic equations:

xvi tri xv1, xv2, . . . , xvi , i 1,2, . . . ,R (8.51)

The system (8.51) is nonlinear but can be solved by means of standard techniques.

8.4.1.2 Plug flow reactorIn a PFR, the component concentrations and the reaction rate vary continuously along the reactor length

(Figure 8.3). A component balance on an infinitesimal volume gives

FA0dXA rAdV (8.52)

The elementary volume is dVSdz, where Spd2/4 and d is the reactor diameter. By introducing thespecific molar flux of the reference reactant A, eFA0 FA0=S, the characteristic equation of a PFR can bewritten in differential form as

dXAdz

rA XA eFA0 (8.53)Equation (8.53) can be integrated analytically or numerically for simple reactions in isothermal con-

ditions to get the reactor volume or the spacetime defined as tV/Qv0.

VFA0XA, f0

dXArA XA or t cA0

XA, f0

dXArA XA (8.54)

For multiple reactions, the set of the stoichiometric-independent reactions must be integrated simul-

taneously. Molar extent of reaction is more convenient as reaction variable, at best by reference to

the total mass flow xmixi/m. The mass balance equations become


dxmidz

ri xm1, xm2, . . . eG , i 1,2, . . . ,R (8.55)where eGG=S ruz is the mass flux, G being the total mass flow rate, also the product between massdensity r and linear velocity uz.

For nonisothermal operation, the heat balance equation must be considered. It is easy to demon-

strate that the equation giving the temperature profile may be written as

dT

dz 1eGCp

XRi1

DHR, i ri4dU TTa

!(8.56)

The heat involved in each independent reaction is the product of reaction rate (ri) by the heat of reaction(DHR,i). The heat transferred is proportional with the overall heat transfer coefficient U and the tem-perature difference (TTa) between the reaction mixture and the thermal agent. Hence, the solution ofEquations (8.55) and (8.56) will provide profiles of concentrations and temperature.

The computation methods described above require the knowledge of reaction kinetics. Unfortu-

nately, this is not the case in a large number of cases, particularly in an evaluation project. In this case,

shortcutmethods are handy, in which the reactor volume may be estimated from information about theresidence time. The following definitions of the reaction time are mostly used:

Space time t as the ratio of reactor volume V by the inlet volumetric flow Qv,0:

t VQv,0

(8.57)

Space velocity as the reciprocal of the space time:

SV 1t

(8.58)

L

z

cA,0

cA

T

FA,0

G

T0

dz

S

FIGURE 8.3

Illustration of a plug flow reactor.


Three measures for space velocity (measured in h1) are commonly used:

LHSV (liquid hourly space velocity) (inlet liquid flow rate at standard temperature and pressure(STP)/reactor volume)

GHSV (gas hourly space velocity) (inlet gas flow rate at STP/reactor volume) WHSV (weight hourly space velocity) (inlet mass flow rate/mass of catalyst)In order to avoid severe errors attention has to be paid to the units used in the above definitions. If the

reaction volume can be reasonably estimated by a shortcut calculation, then some hydrodynamic con-

straints, such as the allowable pressure drop or minimum/maximum fluid velocities, are other elements

used to assess the final sizing.

8.4.2 PERFORMANCE OF IDEAL REACTORS IN SIMPLE REACTIONSLet us consider the reaction A!products with the kinetics rAkcAn . Figure 8.4 shows a graphicalqualitative comparison between the volumes of a CSTR and a PFR needed to reach the same conver-

sion. It may be observed that for an nth order reaction, a PFR always needs a smaller volume than aCSTR, the difference being significant at high conversion of A. The explanation is that in a CSTR, thereaction rate is lower than in a PFR, being limited at the value of the final concentration.

Figure 8.5 presents a quantitative comparison for first-order and second-order reactions. It may be

observed that at low conversions, say below 30%, the difference in volumes is small. The choice be-

tween CSTR and PFR is determined by other considerations, such as the need of mixing for a better

contact, heat transfer rate, safety or mechanical technology. However, the difference in reaction vol-

umes becomes considerable at conversions larger than 90%. For a first-order reaction at XA0.99, theratio VCSTR/VPFR is 10, while for a second-order reaction, this ratio becomes 100.

A question arises: how to reduce this difference? The solution consists of using a series of CSTRs

instead of a single PFR. Since the reaction rate is higher in each intermediate volume, finally a much

higher productivity than in a single equivalent reactor is obtained (Figure 8.6). At limit, an infinite

series of CSTRs behaves as a single PFR of the same volume.

-1/rA

cA,0cA,fcA

Area~VCSTR

Area~VPFR

a

b

d

c

e

FIGURE 8.4

Qualitative comparison of CSTR and PFR.


Let us examine an isolated reactor l in a series. The characteristic equation is

cA, l1cA, l

QV, l1QV, l

1 + rA, l tlcA, l

, l 1, . . . ,N (8.59)

For first-order reaction and constant density mixture, the analytical solution is

cA,0cA,N

YNl1

1 + kltl (8.60)

Design of a series of CSTR aims to find the number of reactors N and/or the residence time tl of eachreactor, needed to achieve the reactant transformation from cA,0 to cA,N. Several cases can be distinguished:

1

10

100

0.01 0.1 1

VC

ST

R/V

PF

R

1-XA

n = 2

n = 1

FIGURE 8.5

Comparison of CSTR and PFR for first- and second-order reactions.

cA,0

cA,f

FA,0V1

cA,1 cA,2 cA,n-1

1 2 n

V2 Vn

FIGURE 8.6

Series of CSTRs.


The residence times tl, l1 . . . N are known. The number of reactors is obtained by applyingEquation (8.59) to successively compute cA,1, cA,2, . . ., until the required final concentration isreached.

The number of reactors N is known. In this case, Equation (8.59) provides N equations, from whichN residence times tl, l1 . . . N and N1 concentrations, cA,l, l1 . . . N1 must be determined.The additional equations can be obtained as follows:

Assume equal residence times: t1 t2 tN. Formulate an optimisation problem, where the intermediate concentrations are the decision

variables. The objective function f can be the total volume or and economic criteria like thetotal cost.

Figure 8.7 illustrates the difference between a series of CSTRs and PFRs for a first-order reaction. Sim-

ilar results may be shown for second-order reactions. Diagrams are presented in standard textbooks

(Levenspiel, 1999). It may be observed that the improvement is considerable, already starting with only

two reactors. Hence, a series of CSTRs can advantageously replace a single large reactor, particularly

when high conversions are desirable. The series of CSTRs may consist of individual units or compart-

ments arranged in the same unit.

8.4.3 PERFORMANCE OF IDEAL REACTORS IN COMPLEX REACTIONSThe relative performances discussed earlier, valid for single reactions, consider only the productivity

as comparison criteria. In the case of multiple reactions, the issue is the selectivity to the desired

product.

1

10

100

0.01 0.1 1

n = 1

n = 2

34

610

VnC

ST

R/V

PF

R

1-XA

FIGURE 8.7

Comparison of performance of a series of n equal-size CSTRs and a PFR.


8.4.3.1 Parallel reactionsConsider the following parallel reactions:

A!P, r1 k1caA

A!R, r2 k2cbA

P is the desired product, while R is a waste. The relative rate of formation of P to R is

rPrR

k1k2cabA (8.61)

The selection of a suitable reactor can be analysed by means of the following heuristics:

If the desired reaction has a higher reaction order than the unwanted reaction (a>b), a high reactantconcentration is favourable; PFRs or batch reactors are suitable.

If the desired reaction has lower reaction order than the unwanted reaction (aE2, the reaction temperature should be maximised. If E1

8.4.3.3 Seriesparallel reactionsAs example, we examine the reactions

A +B!k1 PP +B!k2 R

The designer has a wide choice inmanipulating variables andmixing patterns. However, these reactions

can be analysed in terms of their constituent reactions. The optimum contacting device for favourable

product distribution is the same as for the constituent reactions (Levenspiel, 1999). If P is desired, theabove reaction system can be analysed by analogy with the series reaction A!P!R. In this case, PFRgives always a higher yield in intermediate, the feeding policy of B being irrelevant.

As mentioned, selectivity is the key issue in selecting a chemical reactor for multiple reactions.

Typically, high selectivity might be obtained at low conversion, but this implies a large amount

of reactant to be recycled. Heuristics do not offer simple solutions. Again, the design of the reactor

should be seen not as isolated, but in the context of the separations with recycles. The type and the

size of reactor, as well as the operating parameters, should be optimised against the cost of separations.

This is possible by taking advantage of the optimisation capabilities offered by the flowsheeting

programs.

8.4.4 NONIDEAL REACTOR MODELSPerfect mixing and plug flow are ideal mixing patterns. Real reactors may deviate considerably from

these models. The following aspects could affect the behaviour of a real reactor:

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

XA

c P/(

c A0

c A

)

k2/k1 = 0.1

k2/k1 = 1

k2/k1 = 10

PFR

CSTR

FIGURE 8.8

Comparison of selectivity in CSTR and PFR for reactions in series.


Residence time distribution (RTD)

The state of aggregation (micro- and macrofluids)

The earliness and lateness of mixing

The two latest factors are difficult to handle, so that we may assume as workable hypotheses the micro-

fluid state and perfect mixing of reactants at the reactor inlet. The problem of the RTD remains. This

can be solved by adopting one of the following methods:

Compartment model. A real reactor may be approximated by the combination of zones with idealmixing patterns, such as perfect mixing or plug flow, connected by streams (Figure 8.9). The

volume of different zones and the corresponding flows can be optimised to fulfil some criteria of

productivity or selectivity. The idea has been developed in the recent years in a much more

sophisticated manner. Ideal models may be assembled in a superstructure, from which the final

configuration is determined by means of optimisation techniques. This topic will be discussed later.

Tank-in-series model. A series of CSTRs can be used to describe moderate deviations from the plugflow. The approach is much simpler than dispersion models and can be easy implemented in a

process simulator.

8.5 REACTORS FOR HETEROGENEOUS SYSTEMSIn the case of a heterogeneous reaction, the overall process rate must consider the kinetics of both

chemical and physical steps. If a very slow step can be identified, this controls the global reaction rate.

More often, the analysis should consider several limiting steps, both of physical and chemical nature.

Therefore, the computation of the reaction rate in heterogeneous systems requires information that is

hardly available at the conceptual stage.

m

m

Mixing zone

Mixing zone

Plug flow

FIGURE 8.9

Modelling of a real reactor by compartments with ideal mixing pattern.

3198.5 REACTORS FOR HETEROGENEOUS SYSTEMS

Flow modelling of each phase is another difficult problem. Simplified assumptions are often not

realistic. The hold-up of the reacting phase is particularly important, depending on the design and hy-

drodynamic characteristics of the reaction device.

Therefore, the analysis of heterogeneous reactions is a complex topic and out of the scope of this

book. We limit the discussion only at basic aspects regarding the selection of the reactor, as well as the

simulation of the reactor system at conceptual design stage.

8.5.1 SOLID-CATALYSED REACTIONS8.5.1.1 KineticsIntrinsic reaction rate. A solid-catalysed reaction is the result of several steps involving adsorption onactive sites, reaction between sites and desorption from sites. Following the LangmuirHinshelwood

HougenWatson (LHHW) approach, the reaction rate has the form

r kinetic term driving force adsorption term

(8.64)

EXAMPLE 8.3 DERIVATION OF A LHHW KINETIC EXPRESSIONConsider the solid-catalysed chemical reaction A+B>R. The reaction mechanism involves the following steps:

Adsorption of the reactants to the active sites X of the catalyst:

A+X>AX, r1 k1pAcXk01cAX, KA cAXpAcX

B+X>BX, r2 k2pBcXk02cBX, KB

cBXpBcX

Chemical reaction on the active sites

AX +BX>RX +X, r3 k3cAXcBX k03cRXcX , K3 cRXcXcAXcBX

Desorption of the product from the active sites

RX>R+X, r4 k4cRXk04cXpR, KP cRXpRcX

A usual assumption is that one of the steps is much slower compared with the other ones, which are at equilibrium.

Therefore, the overall reaction rate is given by the rate-limiting step. Let us consider that the chemical reaction on the

active sites is the rate-limiting step, while reactants adsorption and product desorption are at equilibrium.

The total concentration of active sites is given by

cX0 cX + cAX + cBX + cRX cX 1 +KApA +KBpB +KRpR

Therefore,

r3 k3KAKBc

2X0pApB 1

1

KAKBK3KR

pRpApB

1 +KApA +KBpB +KRpR 2


After grouping the constants,

r r3 kpApB 1

1

Kp

pRpApB

1 +KApA +KBpB +KRpR 2

which has the same form as Equation (8.64).

The equilibrium constant Kp can be found from the Gibbs free energy of reaction, as described inEquation (8.21). The adsorption constants KA, KB, KR can be independently determined from adsorp-tion experiments (without chemical reaction). They have to satisfy certain thermodynamic constraints,

for example, dKA/dT

exothermal reactions such as methanol or ammonia synthesis, direct or indirect cooling is performed

after each stage in order to move the reactions mixture away from the equilibrium composition. Sim-

ilarly, for endothermal reversible reactions, such as ethylbenzene dehydrogenation to styrene, higher

conversion can be achieved if the reaction mixture is heated between the catalytic beds. Multitubular

reactors have a large specific heat transfer area, enabling better temperature control, and are recom-

mended in the case of highly exothermal reactions.

The gassolid catalytic reactors can be designed based on pseudohomogeneous models with gas-

phase in-plug flow. In the case of very exothermic reactions, accounting for radial dispersion of heat

and mass might be useful to prevent excessive particle overheating. The reaction time must find a com-

promise with the hydrodynamic design, namely, the maximum gas velocity and pressure drop.

Fluidised bed reactors. Intense mixing in a fluidised bed gives high mass and heat transfer rates, lead-ing to good temperature control. Figure 8.11 presents two types: (a) stable catalyst and (b) catalyst that

needs regeneration. The last type is used in fluid catalytic cracking of hydrocarbon. The description of

different models can be found in Levenspiel (1999).

8.5.1.2.2 Gasliquid reactors on solid catalystThe following discussion refers to the reaction:

A gas + bB liquid !catalystProducts (8.67)

Figure 8.12 presents the main types as follows: The packed-bed reactor (a) is similar with an absorption

column, where the packing can possess catalytic properties (coated catalyst) or host catalyst in special

arrangements, for example, tea bags. In the trickle-bed reactor (b), the gas dissolved or dispersed in

liquid flows downwards through the bed of catalyst in co-current with the liquid phase. This reactor

is suited for high-pressure operation and large gasliquid ratios. In the last two devices, the catalyst

A B C

Reactant Reactant

Reactant

Thermalagent

FIGURE 8.10

Types of fixed-bed catalytic reactor.


dispersed in liquid as very fine particles is brought in contact with the gas either in a slurry bubble

column (c) or in an agitated slurry reactor (d).

8.5.2 HETEROGENEOUS FLUID/FLUID REACTORSHere, we will pay attention to the gasliquid reactors. The reaction takes place usually in the liquid

phase. Three main types of contact may be distinguished following the phase ratio: (1) gas bubbles

dispersed in liquid, (2) liquid drops dispersed in gas and (3) gas and liquid in film contact. In the first

category, we may cite gasliquid bubble columns, plate or packed absorption columns, agitated tanks,

agitated columns, static mixer columns and pump-type reactors. As examples in the second class,

we may name spray columns or liquid injection systems. The third category can be used with very

exothermic reactions or viscous liquids.

Gas

Coolingagent

Gas

Reactor

Regenerator

Air

A B CO2

FIGURE 8.11

Fluidised bed reactors.

A B

Lout

Lin

Lin

LinLin

Lout

C D

Gout

Gout

Gout

Gout

Gin

Gin Gin

Gin

Lout

FIGURE 8.12

Reactor types for gas-liquid reactions catalyzed by solids.

3238.5 REACTORS FOR HETEROGENEOUS SYSTEMS

The heterogeneous process can be seen as a combination of physical absorption with chemical re-

action. The reaction zone penetrates in the liquid phase, if the reaction is relatively slow, or is located at

the interface, if the reaction rate is infinite. The chemical reaction can accelerate considerably the pure

physical process. The ratio of actual process rate by the physical process rate is known as enhancementfactor E. In the case of a bimolecular reaction, the enhancement factor can be expressed as a function ofHatta number Ha ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikcBLDALp =kAL, where k is the chemical kinetic constant, cBL is the liquid-phaseconcentration of the reactant B, DAL is the diffusivity of gas through the liquid film and kAL is the filmmass transfer coefficient in the liquid phase.

8.6 REACTORS FOR BIOCHEMICAL PROCESSESIn a biochemical process, the transformation of reactants into products is catalysed by enzymes.

In the simplest case, the enzyme is simply added to the reaction mixture, where it plays the role of a

catalyst. When the enzyme is not isolated, the living cell becomes part of the process.

8.6.1 ENZYMATIC PROCESSESConsider the enzymatic process S!P, catalysed by the enzyme E. The reaction mechanism involvesformation of a substrate (S)enzyme (E) complex, which further leads to the product (P):

S+E>k1

k1SE!k2 E +P

Assuming that the substrate is in equilibrium with the complex and the last step is rate-determinant, the

following kinetic expression, known as the MichaelisMenten law, can be derived:

rS rmax SS+Km

(8.68)

where rmaxk2E0 and Kmk1/k1.Enzymatic reactions can be performed using the enzyme in either free (soluble) or immobilised

(insoluble) forms. The reactors are similar to the usual catalytic chemical reactors, where chemical

reaction and diffusion to the active sites play an important role. The reactors are stirred tanks,

bubble columns, packed, fluidised or trickle beds. The can be operated in batch, fed-batch or

continuous mode.

8.6.2 BIOLOGICAL PROCESSESThe processes are more complex when living cells are involved. The purpose of a biochemical reactor

(also known as fermentor) can be biomass production (as in Bakers yeast and single-cell protein

production), consumption of a substrate (as in wastewater purification) or obtaining a useful product

of the cell metabolism (alcohol, citric acid, etc.). Denoting by X, Sk and Pk the biomass, substrates andproducts, respectively, the following stoichiometric relationship can be written:

X +YS1S1 + +YSnSn ! 2X +YP1P1 + +YPmPm


YSk and YPk are substrate utilisation and product yields. Because of the complex composition of theliving cells, the stoichiometric equation is usually written in terms of mass. Therefore, the yields

are expressed in kg/kg biomass.

The substrates are sources of carbon (such as molasses, starch andmalt extract), nitrogen (ammonia,

salts of ammonia, amino acids, proteins and urea), energy (carbohydrates, lipids and proteins), minerals

(magnesium, phosphorous, potassium, etc.) and oxygen (provided as sparging air).

The reaction rates are given by

rX mX, rSk YSkrX, rPk YPkrX (8.69)

The specific growth rate includes the substrate, the inhibition effect of the products and the cell death:

m mmaxY Sk

KSk + Sk

Y 1KPk +Pk

md (8.70)

The simplest case is represented by the Monod kinetics, which assumes one substrate, no inhibition

effects and no cell death:

m mmaxS

KS + S(8.71)

The biological reactors (fermenters) can be batch, fed-batch or continuously operated reactors. Because

biochemical processes are slow, large volumes are necessary. Batch reactors are suited for expensive

products, small-scale operation and processes where flexibility is needed or that are difficult to be op-

erated in a continuous mode. Fed-batch reactors give better control over the reaction rate and product

distribution, as one of the substrates is supplied in limited quantity. A typical example is an aerobic

process, where the air (oxygen source) is continuously bubbled through the reaction mixture. Common

continuous reactors are fluidised bed, immobilised cell and air-lift types.

In wastewater treatment, the cells are usually separated from the reactor effluent and recycled back

to the reactor inlet. Thus, the following reactorseparationrecycle structure is obtained (Figure 8.13).

Reactor

Feed Cells Substrate

Settler

Recycle Cells

Purge Cells

Treatedwastewater

FIGURE 8.13

Reactorseparationrecycle process for wastewater treatment.

3258.6 REACTORS FOR BIOCHEMICAL PROCESSES

8.7 THERMAL DESIGN ISSUES8.7.1 TEMPERATURE PROFILE8.7.1.1 Optimum temperature profileThe temperature profile should maximise the reaction rate to ensure maximum productivity, but re-

specting safety and other technological constraints. For simple reactions, the best path is the isothermalprofile, both for irreversible reactions and for endothermic reversible reactions (Figure 8.14a). As men-

tioned, in the case of the reversible exothermic reactions, the equilibrium conversion decreases with the

temperature. Consequently, for a given conversion, the reaction is slow both at low and high temper-

atures. Therefore, an optimum temperature profile exists leading to the highest reaction rate. In prac-

tice, the reaction should start at the maximum allowable temperature and decrease continuously or

stage-wise along a path that gives a reaction rate close to optimum (Figure 8.14b). For this reason,

the design of reactor for exothermic reversible reactions is a challenging optimisation problem.

The treatment of multiple reactions is more complex, because it involves not only the objective ofoptimal productivity but also the desired selectivity. The optimal temperature path in a reactor can be

found by computer simulation.As a qualitative guideline, it should be kept inmind that high temperature

favours reactions with higher activation energy, while low temperature is recommended for reactions

with low activation energy. Let us consider the following consecutive-series first-order reactions:

A!k1,E1 P!k2,E2 SA!k31,E3R

P is the desired product. If E1>E2 and E1>E3, high temperature is recommended. If E1 is thelowest, then low reaction temperature should be applied. If E1>E2 but E1

A!products. The feed with the mass throughput G enters the reactor at T1. The mixture leaves thereactor at T2. The inlet molar flow rate of the reactant A is FA0 (G/r)cA0, where r is the densityand cA0 is the initial concentration. The following energy balance may be written:

Gcp1 T1T0 Gcp2 T2T0 +FA0XA DHR (8.72)

T0 is a reference temperature, not very far from T1 and T2. Further we assume that the mass heatcapacity is almost constant, so we may write cp1cp2cp. It follows immediately the relation

DTDTadXA (8.73)

where DTad is the adiabatic temperature rise defined by

DTad DHR rcp cA0 (8.74)

Hence, a good approximation in an adiabatic operation is that the temperature change is given by the

adiabatic temperature rise multiplied by conversion.

The adiabatic temperature rise DTad is an important characteristic in designing chemical reactors.As the relation (8.74) indicates, DTad depends on the heat of reaction, the heat capacity of the mixtureand on the reactant concentration in feed. Figure 8.15 presents typical temperature profiles. For both

endothermic and exothermic reactions, the use of a large amount of inert brings the operation close to

an isothermal regime, but the reactor productivity decreases by dilution. Therefore, the use of inert

may be uneconomical. Another solution could be imagined, such as the use of intermediate heating

(endothermic reactions) or intermediate cooling (exothermic reactions).

The heat of reaction developed by an exothermal reaction in an adiabatic reactor can save energy

by means of a feedeffluent heat exchanger device, as in the case of the toluene hydro-dealkylation

(HDA) process. Even if PFR is stable as stand-alone unit, it may become unstable in such energy

recovery loop.

1

0

XA

Isothermal

Exothermic reactions

Endothermic reactions

Less inertLess inert

More inert

T0 T

FIGURE 8.15

Temperature profiles for adiabatic operation.

3278.7 THERMAL DESIGN ISSUES

8.7.1.3 Nonadiabatic operationThe polytropic mode makes use of a thermal agent. The temperature profile inside the reactor can de-

viate more or less from the (ideal) constant temperature, depending on the rate of the heat transfer to the

cooling agent. If the heat transfer is too low, a hot spot may occur, which in general is dangerous foroperation.

A useful representation of the thermal regime is the XAT diagram. By dividing the relation (8.53)by (8.56) and by taking into account (8.74), the following equation is obtained for the conversion

temperature profile:

dXAdT

1DTad 4UcA0rcpd rA XA, T TTa

(8.75)

Figure 8.16 displays several trajectories for an exothermic reversible reaction. The optimal reaction

rate is located close to the equilibrium curve. The points A, E, G and H correspond to several feed

temperatures. Let us consider a high feed temperature (point A). Initially, the reaction rate is high,

and the second term in the denominator of Equation (8.75) is nearly zero, so that the slope dXA/dTis close to 1/DTad. As a result, the temperature increases with an initial adiabatic trend. As the reactionadvances, the difference between the two terms becomes smaller, while the slope dXA/dT becomeslarger. When the two terms are equal, the slope goes to infinity the temperature reaching a maximum.

The profile exhibits a hot spot given by the relation

TTa rcpd4UcA0

rA DTad (8.76)

After reaching the maximum, the second term becomes larger than the first one, and the slope dXA/dTbecomes negative. The temperature decreases steadily, although the conversion still increases, up to the

final point D. It may be observed that a trajectory of type ABCD is close to the optimum reaction rate. If

the inlet temperature is somewhat lower (point E), the temperature profile still shows a maximum, but

the reactor is operating globally at a lower reaction rate. If the feed temperature is low, as indicated by

XA

Equilibrium

A

C

G

D

B

E

F

H

Maximumrate

Tf

FIGURE 8.16

Conversiontemperature trajectories for exothermic reversible reaction in nonadiabatic operation.


the points G or H, the temperature profile decreases monotonically. The profile is almost isothermal,

but globally the reaction rate is low, and in consequence a large reactor volume is needed.

Hence, trajectories exhibiting maximum temperature, such as ABCD or EFD, are more economical

than isothermal profiles. This should be obtained not by less intensive heat transfer but by selecting

suitable temperatures for the feed and the thermal agent. Naturally, the maximum reactor temperature

should be acceptable. But more important is to check that the proposed design does not exhibit an ex-

cessive parametric sensitivity, which can lead to a complete destabilisation of the operation. This as-pect, together with other safety topics, will be discussed in Section 8.7.2.

8.7.2 STABILITY OF THE THERMAL REGIMEIn this section, we will discuss basic aspects regarding the stability of the thermal regime of chemical

reactors. More material can be found in specialised books, for example, Levenspiel (1999).

8.7.2.1 Parametric sensitivityThe concept of parametric sensitivity designates the behaviour of a chemical reactor for which a tiny

change in one operating parameter (such as initial concentration of the reactant(s), feed temperature T0or coolant temperature Ta) leads to a huge change of reactor performance (conversiontemperatureprofile). Very often, parametric sensitivity is shown by chemical reactors operated near adiabatic con-

ditions, carrying on very exothermal reactions with high activation energy. Parametric sensitivity leads

to undesired phenomena such as reaction ignition or reaction extinction.

Figure 8.17 shows qualitatively the behaviour of a PFR. The temperature profiles correspond to a

feed temperature of 340 K, and the coolant temperature between 300 and 342.5 K. Up to 335 K, the

temperature profiles show a gradual variation. If Ta has low values, say below 330 K, the reactantsare cooled, the temperature decreases, and the reaction does not start. Contrary, higher Ta can startthe reaction and give a satisfactory conversion over the whole reactor length. However, above a certain

value of Ta, the temperature profile becomes very sensitive with the coolant temperature. Thus, when

z (m)

T (K)

340

440

Ta (K) = 320

342.5

330

335

337.5

340

FIGURE 8.17

Parametric sensitivity of a PFR.


Ta increases from 335 to 337.5 K, an excessive temperature rise (hot spot) appears, with a maximumtemperature of 420 K. In this case, a modification of Ta with 2.5 K gives an increase in the reactortemperature of 80 K. For 5 K variation in Ta, the hot spot rise is of 100 K!

The situation described above is not acceptable for operation. Therefore, hot-spot occurrence is

very likely with highly exothermic reactions having large activation energy and must be avoided by

a proper design and selection of operating parameters. Computer simulation is a powerful method that

can be used to detect such behaviour.

8.7.2.2 Multiple steady statesThe stationary operation points of a chemical reactor are the solutions of the steady-state mass and en-ergy balance equations. In most cases, there is a single operating point or a single steady state. However,

there are a number of cases displaying multiple steady states. In other words, for the same values of the

control parameters (such as feed rate, feed concentration and coolant temperature), there are possible

more than one set of system state variables (such as temperature and conversion). Which steady state

is actually reached depends on theway the reactor is started and how the control parameters achieve their

value (the history). Some states could be stable, but some states could be unstable. The reactor design

should be adapted to ensure that the desired stable state will be always reached, even for large variations

in the control parameters.Working in an unstable point is in principle possible, but the designer must be

aware of this and provide a stabilising control system. Note that in designing chemical reactors, safety is

more important than any other economic or performance consideration. State multiplicity is not limited

to stand-alone reactors, but also occurs in reactorseparationrecycle systems.

The occurrence of multiple steady states can best be illustrated by a CSTR in which a highly

exothermic reaction takes place. A simple method is to examine separately the behaviour of the

two terms of the energy balance: heat generated by reaction and heat transferred from the reactor.

The heat generated is proportional with the reaction rate and the thermal effect:

QG V DHR,A rA XA, T DHR,A FA0XA (8.77)

For a first-order reaction, we have rAkcA0(1XA)k0 exp(E/RT)cA0(1XA). From the charac-teristic equation of a CSTR, we obtain

XA k0texp E=RT 1 + k0texp E=RT (8.78)

where tVcA0/FA0 is the residence time. It follows that the heat generated can be expressed as functionof temperature by the relation

QG FA0 DHR,A k0texp E=RT

1 + k0texp E=RT (8.79)

Similarly, in the case of a first-order reversible reaction A$k1k2P, we find

QG FA0 DHr,A k0texp E=RT

1 + k1,0texp E1=RT + k2,0texp E2=RT (8.80)

Numerical exploration of Equations (8.79) and (8.80) shows that the curves QGT have an S shape forirreversible reactions and amaximum for reversible reactions. The shape is more complex in the case of


multiple reactions because of the simultaneous exothermic or endothermic reactions in the individual

steps.

The heat transferred displays a much simpler trend, being in general a linear function of temper-

ature. We may distinguish two contributions:

Sensible heat of the reaction mixture QT1Gcp(TT0). Heat transferred to the thermal agent QT2UAt(TTa), with Ta constant.Hence, the heat transferred is given by

QT Gcp TT0 +UAt TTa (8.81)

Plotting QT against T shows a family of lines that can be shifted up and down by means of T0 or Ta.Modifying the heat transfer coefficient and the heat transfer area changes the slope. With these el-

ements, we may examine how multiple steady states might occur. The intersection of QG and QT givesthe temperature of the stationary states, which can be further used to compute conversion and concen-

trations. Figure 8.18 presents three typical situations:

Low-conversion state, when either the temperature Ta is too low or the product UAt is too high. High-conversion state, which may occur at higher Ta or lower UAt. Three or more steady states. In the case of a first-order reaction, there are three steady states, while

in the case of a first-order consecutive reaction, there are up to five stationary points.

It is important to note that the behaviour of these steady states is not identical with respect to inherent

disturbances in operating conditions (control parameters), for example, feed temperature, composition

or flow rate, and temperature and flow rate of the cooling agent. Some are insensitive to such variations,

in the sense that after the disturbance vanishes the system naturally returns to the original state. These

are stable steady states. In the case of the point B from Figure 8.18, the situation is essentially different.This is an unstable steady state because in the absence of a control action, small disturbances will movethe system either to the high-conversion state (reaction ignition) or to the low-conversion state (reaction

extinction). This type of behaviour is dangerous for operation and must be avoided.

A physical explanation of the instability can be found by examining the slope of the curves QG andQT against T at the stationary points, as presented in Figure 8.18. Consider the middle point B(Figure 8.18c) and a small, temporary disturbance that leads to a decrease of the reactor temperature,

Q

A

QG

QT

QG

QG

QTQT

C

A

B

C

A B C

T T T

FIGURE 8.18

Stationary steady states for a CSTR for an irreversible exothermic reaction.


such as T

The transfer of the heat of reaction may be achieved by means of an external jacket, or/and by the

use of an internal heating/cooling coil. In a more efficient set-up, the thermal agent circulates in a semi-

closed loop, in which the temperature of the thermal agent is regulated by make-up from a constant

temperature source. In some very exothermic reactions, such as polymerisation, the operation at the

bubble point of the mixture is possible. The cooling takes place by the vaporisation of a solvent or

of a reactant. The vapour phase is condensed in an external heat exchanger and refluxed back.

A very efficient heat transfer may be achieved by pumping the reaction mixture via an external heat

exchanger. This solution is also applicable to a PFR. If the recycle rate is high, the global behaviour will

be close to a mixed reactor.

8.7.3.2 Plug flow reactorPFRs are applied mainly for gas-phase reactions. Heat transfer coefficient inside the reactor tube usu-

ally controls the overall heat transfer. Highly turbulent flow regime is recommended. However, the

fluid velocity is constrained by the allowable pressure drop, the feasible reactor length, catalyst attrition

and so on. Figure 8.20 illustrates two types, pipe-tube and heat exchanger reactor. Pipe reactor is suit-

able when the gas velocity should be high, as in the case of cracking of hydrocarbons, typically between

30 and 50 m/s. Fixed bed and heat exchanger types are recommended when the gas velocity should be

kept low, as when using solid catalysts. In this case, the superficial gas flow rate is typically between

0.5 and 2 m/s.

8.8 SELECTION OF CHEMICAL REACTORSA central issue in process design is the selection of the best reactor that could meet the process require-

ments before starting the flowsheet development. An ideal reactor configuration should conciliate

process operability with productivity requirements. In this respect, we may mention

Safe operation within the feasible range of temperature, pressure, concentration and residence time.

Environmental acceptability.

Good controllability properties: stable operation and easy rejection of disturbances.

Acceptable flexibility to feedstock quality. Capacity to handle large variations in throughput.

FIGURE 8.20

Types of thermal design for PFR.

3338.8 SELECTION OF CHEMICAL REACTORS

Maximum selectivity to desired products and minimum waste production.

Constant product quality.

Low capital and operating costs.

Some preliminary information should be collected before starting the evaluation. The following check-

list may be of help:

Write down the network of chemical reactions.

Determine the number of independent reactions.

List by-products and impurities.

List quality requirements, maximum tolerable impurities.

Compile physicochemical data: physical state of the reactant, reaction enthalpy and Gibbs free

energy in standard conditions.

Specify the operating conditions, such as temperature and pressure.

List safety problems, such as flammability and explosion limits.

Study chemical equilibrium issues, such as conversion, effect of temperature and pressure and

reactants ratio.

Study selectivity issues linked with conversion.

8.8.1 REACTORS FOR HOMOGENEOUS SYSTEMSTaking into account the elements discussed in the preceding text, we may formulate some guidelines

for reactor selection. The strategy may be applied also for heterogeneous reactions described by pseu-

dohomogeneous models, such as some gassolid catalyst reactors or gasliquid reactions with reaction

in the liquid phase.

8.8.1.1 Continuous versus batch reactorsContinuous processes are preferred for large-scale production of commodities or intermediates, such as

in basic organic, inorganic, petrochemical and polymer industries. The boundary might be placed be-

tween 5000 and 10,000 tonnes/year. Batch reactors are more difficult to control. Therefore, continuous

processes might be suitable even for small rates of dangerous products, which could be at best produced

and consumed on site and not stored and transported. Semibatch processes may also be suitable for

temperature-sensitive reactions.

8.8.1.2 CSTR versus PFRCSTR can offer intense heat and mass transfer. Beside, this reactor is compatible with the manner in

which most of the reactions are carried out in laboratory. PFR brings the advantage of productivity, but

here the mixing is detrimental. Thus, PFR is not the best when high heat and mass transfer is required.

Hence, the designer is confronted with the dilemma to mix or not to mix! To answer this question,

two aspects should be examined: (1) the contact mode of reactants and (2) the magnitude of the heat of

reaction. The first aspect may be solved by pre-mixing, either in separate devices or when feeding the

reactor. The second problem is solved in principle better in a mixed reactor, but it can be treated also

conveniently in a PFR if sufficient specific heat transfer area is available (small tube diameter).

With respect to an isothermal operation, we may formulate the following rules (adapted from

Levenspiel, 1999):


Rule 1. For single reactions, minimise the reaction volume by keeping the concentration as high aspossible for reactant whose order is n>0, otherwise keep the concentration low. Some applicationtips may be distinguished:

(a) For normal reactions, where n>0, CSTR requires a larger volume than PFR. The differenceincreases with the conversion, particularly in the region of high conversions, and is also larger

for higher reaction orders.

(b) The use of a series of CSTRs, either as individual units or assembled in a compact construction,can diminish the required total reaction volume. For a sufficiently large number of units, the

total volume of the series approaches the volume of a PFR.

(c) One of two CSTRs followed by a PFR might also be seen as an interesting alternative thatminimises the reaction volume.

(d) At low conversions, up to 30%, the difference between CSTR and PFR is not relevant asperformance. The selection can be done not only on the base of cost but also on controllability

and safety reasons. Hence, in a PFR, the reaction can be stopped easier, by simply cutting the

feed and flushing the reactor with inert. A CSTR would require much more time.

Rule 2. For reactions in series, to maximise any intermediate, do not mix fluids that have differentconcentrations of the reactant and intermediates. PFR gives the most of all intermediates.

Rule 3. For parallel reactions to get the best product distribution, keep in mind that low reactantconcentration cA favours the reaction of lowest order, while high cA favours the reaction ofhighest order. If the desired reaction is of intermediate order then cA should be intermediate. If thereaction orders are the same, the product distribution is not affected by concentration, and the

only solution is to search for a suitable catalyst.

Rule 4. Complex reactions can be analysed by means of simple series and parallel reactions. Inthe case of seriesparallel reactions of first order, the behaviour as series reactions dominates.

A PFR is more advantageous for the production of the intermediate component.

Rule 5. High temperature favours the reaction with larger activation energy. Reactions with smallactivation energy are slightly affected, so that low temperature is preferred.

8.8.1.3 Thermal designThe technical solution depends on the sign of the thermal effect, endothermic or exothermic, as well as

of its magnitude. The following systematisation may be applied:

Endothermic reactions. The reaction temperature should be maximised to ensure high reaction rate.The following reactor types may be considered:

Adiabatic reactors. Premix the reactant with an inert heat carrier, fluid or solid, which can be

recovered and recycled.

Nonadiabatic reactors. Use heating from an external source, for example:

Preheat and reaction coil placed in a furnace, as for hydrocarbon cracking

Shell-and-tube heat exchanger, usually the reaction taking place in tubes

Exothermal reactions. In the case of CSTR, the designer should ensure that the operation does not occurin an unstable steady state (except special cases) or there is no danger of runaway in the case of PFR.

The following solutions may be considered:

CSTR with cooling by external jacket and/or cooling coil.

CSTR operating at the mixture boiling point and external condenser.


CSTR or PFR with external cooling loop.

Adiabatic PFR with inert dilution. Provide quench after reactor to prevent overheating and thermal

decomposition.

PFR with external cooling, either as long length/diameter tube (coil) or as shell-and-tube heat

exchanger.

8.8.2 REACTORS FOR HETEROGENEOUS SYSTEMSThe selection of a reaction system for multiphase reactors is a complicated matter. Krishna and Sie

(1994) addressed this topic by means of a three-level strategy:

Catalyst design.

Injection and dispersion.

Choice of hydrodynamic flow regime.

The first phase, catalyst design, deals with the kinetic problem, namely, determining the rate-limiting

step andmeasures to enhance it. For example, for solid catalyst, the design variables are the particle size,

its shape, porous structure and distribution of activematerial. For gasliquid systems, the decisions con-

cern the choice between gas-dispersed and liquid-dispersed systems and provisions of an appropriate

ratio between liquid-phase bulk flow and liquid-phase diffusion layer.

The second level deals with the contact of reactants. It consists of several strategies:

Reactant and energy injection strategy, such as one-shut (batch), continuous pulsed injection,

reversed flow, and staged injection and use of a membrane

Choice of the optimum state of mixing

Choice between in situ separation of products and postreaction treatment Injection of energy against in situ production Contacting flow pattern as co-, counter- and crosscurrent contacting of phases

The third level deals with issues regarding the details of heat and mass transfer phenomena. Here, the

choice is between different hydrodynamic regimes in multiphase flows, such as dispersed bubbly flow,

slug flow and churn-turbulent flow for gasliquid systems, or dense-phase transport versus dilute-phase

transport for gassolid systems.

The application of this strategy is worthwhile particularly for exploring innovative reaction systems

that goes beyond the combination of classical mixed and plug flow models. More attention should be

paid to the problem of combining the reaction and separations in a compact device (process intensi-

fication), such as reaction with distillation, extraction and membrane diffusion.

EXAMPLE 8.4 SELECTION OF A CHEMICAL REACTOREthylbenzene (EB) is currently produced by alkylation of benzene with ethylene, primarily via two routes: liquid phase

with AlCl3 catalyst or vapour phase in catalytic fixed-bed reactor (Ullmann, 2001). Examine the differences as well as

advantages and disadvantages of these routes. List pros and cons in selecting suitable reactors.

Solution

1. Chemical reaction network

The alkylation of benzene with ethylene is described by a network of complex reactions. The main reaction is

C6H6 +C2H4>C6H5C2H5


The reaction needs Lewis-acid type catalysts. Higher polyalkylbenzenes are formed by successive series reactions,

for example, the formation of diethylbenzene:

C6H5C2H5 +C2H4>C6H4 C2H5 2

Note that diethylbenzene has three isomers with the alkyl groups in ortho, meta and para positions. Up to six sub-

stitutions at the benzene ring might be theoretically possible. Propylene present in ethylene as impurity may also pro-

duce cumene and higher alkylates as by-products. Using an excess of benzene can improve the yield by converting the

polyalkylbenzene into ethylbenzene, for example,

C6H4 C2H5 2 +C6H6>2C6H5C2H5

Hence, the alkylation of benzene with ethylene consists of a complex network of reversible reactions. Globally, the

reaction may be seen as parallel with respect to ethylene consumption and series with respect to transformation of ben-

zene into ethylbenzene and polyalkylbenzenes.

2. Chemical equilibrium

Modern simulators can calculate the equilibrium of complex reactions by the minimisation of Gibbs free energy of

the reaction mixture. Here, we present results obtained from the module RGibbs of Aspen Plus. An appropriate ther-

modynamic model is a cubic equation of state, such as PengRobinson.

Let us start with the equilibrium of the main reaction for a reactants molar ratio 1:1. Figure 8.21a presents the

equilibrium conversion on the interval 500700 K and pressures of 1, 10, 20 and 40 atm. It may be observed that almost

complete conversion of benzene is possible, but the temperature should be kept lower than 500 K. The equilibrium

conversion decreases with the temperature, because the reaction is exothermic. Higher pressure can increase signifi-

cantly the equilibrium conversion, allowing higher reaction temperature and higher reaction rate.

Nowwe consider a mixture of four components: benzene, ethylene, ethylbenzene and diethylbenzene. Figure 8.21b

presents the equilibrium composition at a ratio of reactants 1:1 and 20 atm. The above picture changes considerably.

The equilibrium conversion of benzene drops under 80%. The amount of ethylbenzene at equilibrium drops also sig-

nificantly, because of diethylbenzene. On the contrary, the temperature seems not to play a role. Hence, we must in-

clude in our analysis secondary reactions. The problem is that we would need kinetic data to assess the selectivity.

Fortunately, the thermodynamics can help again. What happens if we would consider an excess of benzene?

Figure 8.21c presents results for a benzene/ethylene ratio of 5:1 at 20 atm. It may be seen that the selectivity in eth-

ylbenzene increases considerably, over 98%. The benzene conversion per pass is low, of 20%, signifying high recycle,

but this is the price for high selectivity.

The yield can be improved by treating the recycled polyalkylbenzenes with an excess of benzene. Figure 8.21d

illustrates that a ratio benzene/diethylbenzene of 1:1 is insufficient, but at 2:1, an equilibrium conversion of diethyl-

benzene higher than 95% may be obtained. Note that at 20 bar and below 200 C, the reaction takes place in a singleliquid phase, after which a second-vapour phase appears.

Summing up, the thermodynamics teaches us that the following elements should be taken into account when select-

ing and designing a reactor system for EB synthesis:

To get high conversion, use higher pressures, larger than 20 bar, and lower temperatures, under 500 K. Use an excess of benzene (4:15:1) to improve the selectivity. Consider complete consumption of ethylene. If polyalkylbenzenes are formed, further improvement in the yield of ethylbenzene can be obtained by reversible

conversion with benzene.

3. Catalyst

First, Lewis-acid catalyst such as AlCl3, FeCl3 or ZrCl4 can be considered. Aluminium chloride catalyst is a com-

plex of AlCl3 in benzene with ethyl chloride as promoter and gives fast reaction rates. The problem is that the removal

of AlCl3 from the final product and its recycle implies costly steps and waste formation. Another catalyst in this cat-

egory is BF3/alumina commercialised by UOP Alkar process. Solid-phase silica-alumina catalysts, such as zeolite

Continued


ZSM-5 developed by Mobil, can be successfully applied. Note that the reaction mechanism is different from the AlCl3catalysis. Ethylene molecules are adsorbed onto Bronsted acid sites, and the activated complex reacts further with ben-

zene. This reaction mechanism gives less polyethylbenzenes, so that a transalkylation reaction is not necessary. Vapour

phase, as well as liquid-phase zeolite, may be applied, depending on the catalyst properties.

4. Kinetics

The first alkylation step is much faster than the subsequent steps, because the alkyl groups decrease the activity of

the aromatic ring. As an order of magnitude, the reaction rates for the first, second and further substitutions are of

1:0.5:0.25:0.1:0.1:0.1.

5. Heat effect and thermal regime

The reaction is moderate exothermic with DHR114 kJ/mol. A measure of exothermicity is the adiabatic tem-perature rise. Table 8.1 gives some values calculated for an inlet temperature of 400 K and 1 atm. The adiabatic tem-

perature rise for the stoichiometric mixture is considerable (441.6 K), but the dilution with benzene in the ratio 5:1

makes it drop to 144.6 K. If diluted ethylene feedstock is considered, the adiabatic rise diminishes further, but less

compared with benzene dilution, because much lower molecular weight. Hence, the reaction needs a heat transfer de-

vice, except for very diluted ethylene feedstock and high benzene recycle.

6. Secondary reactions and product specifications

Ethylbenzene is used mainly for styrene manufacturing. Among impurities, diethylbenzene is very important, be-

cause dehydrogenation to divinylbenzene, which is harmful in polymerisation. It is worth to keep in mind that the for-

mation of troublesome impurities should be prevented by the design of the reaction system. In this respect, the catalyst

plays a determinant role. Zeolite-type catalysts should give less polyalkylbenzene. The use of an excess of reactant can

FIGURE 8.21

Chemical equilibrium by the alkylation of benzene with ethylene.


help to shift the product distribution to higher yield in ethylbenzene. Another possibility is to use a separate reactor for

transalkylation. The trade-off between a larger recycle of benzene and the use of a secondary reactor is a matter of

optimisation.

7. Reactor selection

With the above elements, the following reaction systems may be considered:

A. Liquid-phase alkylation using AlCl3 catalyst (heterogeneous or homogeneous system).

B. Vapour-phase alkylation with BF3/alumina catalyst.

C. Vapour-phase reaction, zeolite catalyst.

D. Liquid-phase reaction, zeolite catalyst.

Table 8.2 presents comparatively the four reactor types proposed above. Liquid-phase alkylation on AlCl3 was

practised in the past but is nowadays completely obsolete, mainly because of pollution problems. Vapour-phase alkyl-

ation (UOP Alkar process) was popular up to 1970, when Mobil/Badger process based on ZMS-5 synthetic zeolite

catalyst was launched. This process dominates themarket nowadays, but is in competition with the liquid-phase process

based equally on zeolite catalyst proposed by UOP/Lummus. The two processes have similar performances. The se-

lection depends greatly on the catalyst behaviour, price and regeneration cost. We would prefer the last, for the fol-

lowing reasons:

Lower temperature is more favourable from equilibrium viewpoint, implying less benzene recycle; Liquid-phase reaction gives also higher productivity compared with a gas-phase reactor; A simpler flowsheet and a better heat integration, because the absence of vaporisation/condensation steps before

and after the reactor.

We are tempted to proceed a little bit further, and examine the development of the whole flowsheet in relation with

the reaction system. Let us suppose that the feedstock is of high purity ethylene and benzene. Because recycling a gas is

much more costly than a liquid, we consider as design decision the total conversion of ethylene. The benzene will be in

excess in order not only to ensure higher conversion rate but also to shift the equilibrium. The equilibrium calculation

can predict with reasonable accuracy the composition of the product mixture for given reaction conditions. Then poly-

alkylates, mainly diethylbenzene can be reconverted to ethylbenzene in a second reactor.

Hence, the reaction section will have two reactors: alkylation and transalkylation. The alkylation reactor should be

operated at higher pressure where the solubility is high enough to ensure a homogeneous reaction. The reaction tem-

perature may be selected such to allow cooling by steam generation. In this case, a temperature in the range of

130150 C can produce low-pressure steam of 36 bar. Higher temperature would be more interesting, because highervalue of the medium pressure steam, and its possible utilisation as heating agent for the distillation section. Thus, the

process might be designed to be energetically self-sufficient.

For the development of the separation section, we will examine the composition and the thermodynamic behaviour

of the outgoing reactionmixture. This contains benzene, ethylbenzene and polyethylbenzenes. The separation sequenc-

ing is simple because the mixture is zeotropic, and the difference in the normal boiling points of components is large.

A first distillation column takes off benzene for recycle, a second one separates the main product, and a third column

recovers polyethylbenzenes for transalkylation. Figure 8.22 presents the final flowsheet.

Continued

Table 8.1 Adiabatic Temperature Rise by the Benzene Alkylation

Case Benzene/Ethylene Ratio F (kmol/h) G (kg/h) cp (kJ/kg/K) ToutTin (K)

1 R1 2 106.5 2.24 441.62 R5 6 418.6 1.74 144.63 R5, 25% ethane 7 448.7 1.77 132.54 R5, 75% ethane 9 508.8 1.82 113.6


Table 8.2 Reactor Selection by the Benzene Alkylation

A B C D

1 Reactor type Stirred tank/bubble

column

Tubular Fixed bed Trickle bed

2 Operating

conditions

15 bar,

100130 C2535 bar,

130150 C400450 C,2030 bar

90% Diluted Diluted Concentrated

4 Benzene/feed

ratio

33.5 57 >4 >4

5 Transalkylation

reactor

Yes Yes No Yes

6 Catalyst handling Removal and

recovery

Recycle Regeneration Regeneration

7 Selectivity Good Good Very good Good

8 Sensitivity to

impurities

High Moderate Low Low

9 Environment Corrosion/water

waste

Corrosion No corrosion/no

waste

No corrosion/no

waste

10 Productivity Good Good Good Very good

11 Thermal regime Isothermal/external

cooling

Adiabatic Adiabatic/

cooling

Adiabatic/

cooling

12 Materials Special CS CS CS

13 Reactor cost High Moderate Moderate Moderate

14 Catalyst cost High Low High High

15 Selection Obsolete Fair Good Very good

FIGURE 8.22

Ethylbenzene manufacture by liquid-phase alkylation of benzene.


In conclusion, this example emphasises important issues in selecting a reactor:

1. Before any other consideration, the analysis of stoichiometry is necessary. This must include secondary reactions,

as well as reactions generated by the existing impurities in the original feed. The analysis of chemistry should take

into account constraints regarding the purity specifications in the final product.

2. Chemical equilibrium calculations may reveal essential features in design, particularly the feasible pressure/

temperature range, as well as achievable composition space.

3. The selection of the operating conditions and the reactor design is subordinated to high selectivity not only by max-

imising the amount of desired product but also byminimising or preventing the formation of components difficult to

remove later.

8.9 SYNTHESIS OF CHEMICAL REACTOR NETWORKSThe methods described so far for developing a reactor system start with the proposal of a device, either

as single reaction space or as combination of zones. The solution is further evaluated by design and

performance calculations. This approach is suitable in the case of simple reactions, where the differ-

ence between the two limiting models, mixed flow and plug flow, is easy to express quantitatively. In

more complex cases, such as multiple reactions in homogeneous systems or multiphase reactions, the

selection and the design of an optimal reaction system are not easy. High productivity, requesting high

per-pass conversion, is usually in conflict with low selectivity, which increases the cost of separations.

The trade-off depends on a large number of variables and is guided by heuristics rather than by rigorous

evaluation. Without a systematic approach, the evaluation of a large number of alternatives is

necessary.

The synthesis problem of a chemical reactor network may be defined as follows. Given the reactionstoichiometry and kinetic expressions, initial feeds, reactor targets (productivity, selectivity and flex-

ibility), and technological constraints, find the optimal reactor network structure, as well as suboptimalalternatives. The following elements should be determined:

Feasible design space in term of temperature, pressure and concentrations

Flow pattern, systems elements (zones) and their connection

Size of zones and optimal distribution of flows

Energy requirements and optimal temperature profile.

Therefore, in the first place, the process synthesis should solve a structural problem, the configuration

of the optimal reactor system. Then detailed design and refinement can follow. If there are several can-

didates close to optimum, these could be assembled in a superstructure and submitted to structural

optimisation.

As it can be observed from the above discussion, the objective of such approach would be not

to replace the principles of designing chemical reactors but to facilitate the invention of more

complex reaction systems. Some researches started in the recent years, but a real breakthrough

in the design practice has not been achieved yet. This area is at the edge of the advanced

research. Here, we present only a brief description of two advanced topics: attainable region con-

cept and optimisation methods. For more details, the reader is referred to the book of Biegler

et al. (1997).

3418.9 SYNTHESIS OF CHEMICAL REACTOR NETWORKS

8.9.1 ATTAINABLE REGION CONCEPTAttainable region (AR) is a systematic geometric method for the synthesis of a complex chemical re-actor network. The concept has been developed starting with the pioneering works of Glasser et al.

(1987) and Glasser and Hildebrandt (1997). One of the last applications is in the field of batch reactors

(Ming et al., 2013). The visit of the Web site www.wits.ac.za (University of Witwatersrand, South

Africa) may serve as tutorial in this topic.

The synthesis problem is the following: given a feed state and a number of fundamental processes,

such as mixing, chemical reactions, heating and cooling, find the best combination of these processes

that will build up the optimal chemical reactor and the optimal operating conditions. Note that the ob-

jective function is usually of economic nature, but it may include safety or environmental elements.

The traditional way is to consider a (large) number of combinations of units, usually CSTRs or

PFRs, and compute their performances for various designs. This method is tedious and never ensures

that the best reactor has been found. Contrary, AR tries to give an answer from a different perspective.First, it looks at the fundamental processes that may occur in the reacting system. The analysis enables

to find a region where all the possibilities for conducting the reaction could be found. This is used to

obtain the optimum layout and the optimum operating cond

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[Computer Aided Chemical Engineering] Integrated Design and Simulation of Chemical Processes Volume 35 || Synthesis of Reaction Systems