novel reactor temperature and recycle flow rate policies

7/29/2019 Novel Reactor Temperature and Recycle Flow Rate Policies

1/12

Novel Reactor Temperature and Recycle Flow Rate Policies for

Optimal Process Operation in the Plantwide Context

Jeffrey D. Ward, Duncan A. Mellichamp, and Michael F. Doherty*

Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080

Ward et al. (Ward, J. D.; Mellichamp, D. A.; Doherty, M. F. Ind. Eng. Chem. Res. 2004, 43,3957) investigated the effect of process chemistry on the selection of the operating policy forplants with recycle. This paper extends that work to consider the possibility of reactortemperature as a degree of freedom in plantwide process operation. It is possible to predict,based on the process chemistry, when it may be appropriate to implement a variable-temperatureoperating policy, and, alternatively, when a constant-temperature operating policy is appropriatein the face of a production rate change or other disturbances. An interesting and nonobviousresult is also developed: For so-called bounded chemistries, it is usually optimal to operate theprocess with the reactor at its high-temperature constraint, even if the activation energy of theundesired reaction is greater than the activation energy of the desired reaction. This meansthat the plantwide operating policy is the same for almost all bounded chemistries. In contrast,for nonbounded chemistries, the operating policy follows conventional wisdom and changesdepending on the relative magnitude of the activation energies. Implications of the optimization

analysis for control structure design are also discussed.

1. Introduction

The influence of reactor temperature on the selectivityand yield of a reactor network is well-known and isdiscussed by many authors and in many textbooks onreactor design; e.g., Fogler2 and Levenspiel.3 For ex-ample, for the case of one desired reaction and oneundesired reaction, where the rates of reaction aretemperature dependent via the Arrhenius equation

and the desired reaction has an activation energygreater than the undesired reaction, then both selectiv-ity and yield are improved by operating the reactor athigh temperature. If the activation energy condition isreversed, then selectivity is improved by operating atlower temperature, but yield may be reduced becauseboth reactions will proceed more slowly.

What is less well-known, but even more important,is what role the reactor temperature should play as anindependent variable in plantwide optimization. Therehas been considerable discussion in the literature aboutthe choice of a plantwide inventory/flow operating policy(and control structure) for plants with recycle. Asdiscussed by Ward et al.1 the chemistry of the processunder investigation plays a critical role in the proper

selection of a plantwide operating policy. This workconsidered plants which are operated with a constantreactor temperature. A critical question in the selectionof a plantwide operating policy is how to accommodatea production rate change. Luyben4 recommends thatrecycle flow rates be held constant, Skogestad and co-workers5,6 recommend that reactor holdup be heldconstant, and Yu and co-workers7,8 recommend thatboth the reactor level and recycle flow rates be permit-

ted to change. Several authors have noted6,8 thatanother possible way of accommodating a productionrate change is to vary the reactor temperature. Mon-roy-Loperena et al.9 recently considered the use ofreactor temperature as a degree of freedom for a parallelcontrol structure. However, the chemistry under inves-tigation by all of these authors (A f B) does notrepresent the most general case, because there is nodownside to a temperature increase. If a production rateincrease is desired, then the reaction rate constant kcan simply be increased (via the reactor temperature)so that the rate of production of the desired product is

increased while maintaining the same reactor holdupand recycle flow rates.

In many cases, however, there is a downside toincreasing the reactor temperature, namely that anundesired reaction may experience a rate increase thatis greater than that for the desired reaction. In this case,the issue of how reactor temperature should be em-ployed as part of a plantwide operating policy is not soclear. Furthermore, in some cases the reactor temper-ature operating policy may influence the level/flow ratepolicy, because lower temperatures generally requirelonger reactor residence times and therefore greaterreactor holdup.

The purpose of this paper is to extend the analysis of

Ward et al.1

to include the use of reactor temperatureas an independent variable in the selection of anoperating policy. Because this work is an extension ofresults presented in a previous paper, the reader mayfind it useful to refer to that paper for backgroundinformation. It is shown in the present work that theproblem of selecting a plantwide operating policy isdifferent from the problem of designing a reactornetwork, and in some instances the intuition that isdeveloped from the point of view of plantwide operationis radically different from the intuition that is developedfrom the reactor network design perspective. For ex-

* To whom correspondence should be addressed. [email protected].

k ) k0e-EA/RT (1)

6729Ind. Eng. Chem. Res. 2005, 44, 6729-6740

10.1021/ie0491589 CCC: $30.25 2005 American Chemical SocietyPublished on Web 07/13/2005


2/12

ample, it is shown here that for bounded chemistries,it is usually optimal to operate the process with thereactor at its high-temperature constraint, even ifthe activation energy of the undesired reaction isgreater than the activation energy of the desired reac-

tion.The operating policies that are developed specify

which process constraints will be active, which will beinactive, and which may switch during operation as theproduction rate is changed. Maarleveld and Rijnsdorp10

were among the first authors to recognize that it is oftenthe case that the optimal operating point for a processis at a constraint rather than at the hilltop.

Recently, self-optimizing control has been advocatedby several authors11,12 as a basis for designing distrib-uted feedback control structures for chemical processes.The idea behind self-optimizing control is to selectvariables for control which, when kept near theirsetpoints, keep the process near to its economic opti-

mum over the expected range of disturbances. Theanalysis presented in this paper provides insight intowhether a self-optimizing control structure will beadequate to achieve good economic performance of theprocess, and if so how such a control structure shouldbe designed. If the optimal operating point for a plantalways lies at the intersection of the same constraints,then it is straightforward to design a self-optimizingcontrol structure. The process variables selected forcontrol are those that lie on the constraints. If one ormore optimization variables lie away from constraintsand move considerably as properties of the processchange, or if the active constraints are expected to shiftover the range of process operation, then a centralized

process optimizer may be required to supervise thedecentralized regulatory control structure.

2. Methodology

2.1. Review of Previous Results. This sectionbriefly reviews results that were presented in Ward etal.1 The reader may wish to refer to this paper forfurther details.

Consider the process flow diagram shown schemati-

cally in Figure 1, and the following process chemistry,hereafter called chemistry 1 (Table 1)

The independent variables for the economic optimiza-tion are the recycle flow rates of species A and B, RAand RB. Therefore, it is necessary to express the byprod-uct production rate PD in terms of these degrees offreedom. From a global steady-state material balance,it is seen that

The concentrations of species A and B in the reactorcan be replaced by recycle flow rates by introducing thereactor effluent volumetric flow rate q

where vA is the molar volume of species A, etc. Thus

Dividing the expression for the undesired reaction bythe expression for the desired reaction gives

Flow rates are made dimensionless by dividing them

by the production rate of the desired product, PC.Reaction rate constants are made dimensionless bydividing by the rate constant of the desired reaction.Therefore, in dimensionless form

where k1 ) k1/k0, PD ) PD/PC, RA ) RA/PC, and RB )RB/PC. For this chemistry, PD f0 as RAf0, reflectingthe fact that byproduct production rate becomes smallin the limit of high per-pass conversion of species A, oras RB f , because a large excess of species B sup-presses the undesired reaction.

Figure 1. Generic process flow diagram.

Table 1. Chemistries

1 A+ B fC r0 ) k0[A][B]A+AfD r1 ) k1[A]2

2 A+ B fC r0 ) k0[A][B]A+ C fD r1 ) k1[A][C]

3 A+ B fC r0 ) k0[A][B]C + C fD r1 ) k1[C]2

4 A+ B fC r0 ) k0[A][B]C fD + E r1 ) k1[C]

5 A+ B fC r0 ) k0[A][B]A+AfD r1 ) k1[A]2

C + C fE r2 ) k2[C]2

6 AfC r0 ) k0[A]C fD r1 ) k1[C]

7 AfC r0 ) k0[A]A+AfD r1 ) k1[A]2

8 A+ C f2C r0 ) k0[A][C]A+AfD r1 ) k1[A]2

9 A+AfC r0 ) k0[A]2

A+ C fD r1 ) k1[A][C]10 A+ C f2C r0 ) k0[A][C]

A+AfD r1 ) k1[A]2

C + C fE r2 ) k2[C]2

A+ B fC r0 ) k0[A][B] desired

A+ AfD r1 ) k1[A]2 undesired (2)

PC ) k0[A][B]V (3)

PD ) k1[A]2V (4)

q ) RAvA + RBvB + PCvC + PDvD (5)

PC ) k0RARBV

q2 (6)

PD ) k1RA2 V

q2(7)

PD

PC)

k1RA2

k0RARB)

k1RA

k0RB(8)

PD ) k1RA

RB(9)

6730 Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005
http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-000.png&w=209&h=99


3/12

By contrast, the result for chemistry 3

is

In this case, species A and B are symmetric (inter-changeable). PD f 0 if either RA f or RB f. Theper-pass conversion of both species should be kept lowto dilute the product species C and suppress theundesired reaction. These results have important im-plications for the plantwide optimization problem. Thismethodology can be generalized in a number of ways,including to undesired reactions with a different overallreaction order than the desired reaction, multipleundesired reactions, equilibrium reactions, and plugflow reactors (Ward et al.1).

The simplest model for the economic potential of a

chemical plant that will capture the tradeoff betweenrecycle costs and byproduct production costs is

where C is the cost of operating the plant (smallervalues of C imply larger profit), CC is the negative ofthe revenue from the production of one mole of desiredproduct (CC < 0), CD is the cost of producing one moleof undesired byproduct (including raw materials costsand separations costs) (CD > 0), and CR is the cost ofseparating and recycling one mole of reactant species(CR > 0). Because PC is fixed, the term CC PC is constantand its value will affect the value of the total profit butnot the location of the minimum cost. Therefore, the

following dimensionless cost objective function is defined

where CD is the ratio of the cost of producing one moleof byproduct to the cost of recycling one mole of reactantspecies. Typically, CD is a relatively large number, onthe order of 100. When C is minimized, the plant is atits most profitable operating point.

2.2. Byproduct Production Rates with VariableReactor Temperature. If the reactor temperature isavailable as an operational degree of freedom, then k1will be a function of temperature

It is assumed here that all EA,i are temperature inde-pendent. A dimensionless temperature is defined basedon the activation energy of the desired reaction

Activation energies and Arrhenius preexponential con-stants are rendered dimensionless by dividing by thecorresponding quantity for the desired reaction. There-fore, eq 14 becomes

If EA,1 > EA,0 then EA,1 > 1, the exponent in eq 16 willhave a negative value, and k1 will increase with increas-ing temperature. Therefore, conventional wisdom sug-gests that increasing the reactor temperature favors theproduction of byproduct species.

Note that for many liquid-phase chemistries, theactivation energy is an order of magnitude or more

greater than the average thermal energy of the mol-ecules in solution, i.e., EA/(RT) > 10. The explanationis that only a small fraction of intermolecular collisionshave enough energy to overcome the energetic barrierand react to form products. One consequence is that atypical value of the dimensionless temperature T issmall, usually T < 0.1

2.3. Reactor Volume with Variable Reactor Tem-perature. In our previous paper, the following resultwas developed for chemistry 1

where vC is the molar volume of the desired product C,and q is the dimensionless reactor effluent volumetricflow rate

where vi ) vi/vC. If the reaction rate constant is tem-perature dependent via the Arrhenius equation, then

and, therefore, the dimensionless reactor volume is

Note that with variable reactor temperature, thisprocess has three independent operational degrees offreedom: RA, RB, and T. In eq 20, q is a function ofT(as well as RA and RB) because PD is a function of T.However, it is usually the case for profitable processoperation that PD , 1. If this is the case, then q will beessentially independent of temperature, and dimension-less reactor volume V will depend on the dimensionlesstemperature T only via the exponential term (and notby q). In this case, the reactor holdup required to

achieve a given production rate will decrease as thereactor temperature is increased.Note also that for most liquid-phase chemistries the

Arrhenius factor k0 is typically a large number. There-fore the dimensionless reactor volume defined in thisway is also a large number, typically V > 106.

3. Results

This section presents the optimization landscapes fora variety of process chemistries. It is important to bearin mind the nature of the constraints which may becomeactive during process operation. Generally speaking,every process variable has an upper and lower bound.

A+ B fC r0 ) k0[A][B] desired

C + C fD r1 ) k1[C]2 undesired (10)

PD )

k1

RARB (1 - 2

k1

RARB)

-1

k1

RARB(11)

C) CC PC + CD PD(RA, RB) + CR(RA + RB) (12)

C )C

PCCR- CC ) CDPD + (RA + RB) (13)

k1 ) k1/k0 )k1,0

k0,0e

-(EA,1-EA,0)/RT (14)

T ) RT/EA,0 (15)

k1 ) k1/k0 ) k1,0 e(1-EA,1 )/T (16)

Vk0

vC2

PC)

1RARB

q2 (17)

q )q

PC vC) vARA + vBRB + 1 + vDPD (18)

Vk0,0e-1/T

vC2PC

)1

RARBq2 (19)

V )Vk0,0

vC2PC

)e1/T

RARBq2 (20)

Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005 6731


4/12

For reactor temperature, the upper bound may be givenby safety considerations, coking or catalyst degradation,or the limits of materials of construction; the lowerbound may, for example, be given by the cooling waterapproach temperature, the area available for heattransfer in the reactor, or the limits of a refrigerationsystem. We have assumed that the lower bound on thereactor temperature is constant independent of theproduction rate or the operating point. This assumption

will generally be conservative if the lower bound iscalculated for the maximum possible production rate.Table 2 summarizes the operating policy for each classof process chemistry on the basis of which constraintsare guaranteed to be active, which are guaranteed tobe inactive, and which may switch during processoperation.

3.1. EA,1 < 1. The least interesting case is when EA,1< 1. In this case, the reactor temperature should be heldconstant at the upper limit. This policy will simulta-neously maximize the process selectivity (by minimizingthe ratio of reaction rate constants) and minimize therequired reactor holdup. The reactor temperature policydoes not influence the level/flow policy in this case: ifthe overall process chemistry is bounded, then theprocess should be operated with the reactor completelyfull; if the overall process chemistry is nonbounded, thenthe process should be operated with reactor levelproportional to production rate, as suggested in ourprevious paper.

Figure 2 illustrates the optimization problem forchemistry 6, a nonbounded chemistry. For reference,values of dimensionless groups in Figures 2-10 areshown in Table 3. The optimal operating point is on thehigh temperature constraint, and away from the reactorvolume constraint. A production rate increase (Figure3) does not change either the optimal operating tem-perature or optimal dimensionless recycle flow rate.This situation corresponds to an operating policy where

the recycle flow rate scales linearly with the productionrate. For a process chemistry of this type, a self-optimizing control structure could be designed whichkeeps constant both the reactor temperature (at the

Table 2. Summary of Derived Heuristics for Plantwide Operating Policy Based on Active/Inactive Constraints forProcesses with One Recycle Stream

chemistry: bounded nonbounded

constraint: Vmax RA, max Tmin Tmax Vmax RA, max Tmin Tmax

isothermal active inactive may switch may switchEA,1 > 1 activea inactivea inactivea activea may switch may switch may switch inactiveEA,1 < 1 active inactive inactive active inactive may switch inactive active

a Note: following the analysis of Section 3.3 there are certain cases where this heuristic is not be valid, depending on the relativemagnitude of the activation energies and the ratio of the exponents in the kinetic rate expressions. Because this heuristic has been

derived, it is possible to determine following the analysis of Section 3.3 when it is valid and when it is not.

Figure 2. Chemistry 6 (nonbounded chemistry) with EA,1 < 1before production rate increase. marks the optimal operatingpoint.

Figure 3. Chemistry 6 (nonbounded chemistry) with EA,1 < 1 afterproduction rate increase. marks the optimal operating point.

Figure 4. Chemistry 7 (bounded chemistry) with EA,1 < 1 beforeproduction rate increase. marks the optimal operating point.

Figure 5. Chemistry 7 (bounded chemistry) with EA,1 < 1 afterproduction rate increase. marks the optimal operating point.

http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-004.jpg&w=153&h=148http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-003.jpg&w=153&h=146http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-002.jpg&w=157&h=149http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-001.jpg&w=157&h=149


5/12

high temperature constraint) and the ratio of the recycleflow rate to the production rate. However, such a controlstructure would only work properly in the region ofproduction rates where the maximum recycle flow rateconstraint was inactive. A supervisory control structurewith a mechanism for constraint handling may berequired to operate the process most profitably over theentire range of production rates.

Figure 4 shows the optimization landscape for chem-istry 7, a bounded chemistry. The optimal operatingpoint lies at the intersection of the high temperatureconstraint and the reactor volume constraint. When theproduction rate is increased (Figure 5), the location ofthe optimal operating point shifts to the new intersec-

tion of the reactor volume constraint and the hightemperature constraint. This situation corresponds toan operating policy in which both the reactor temper-ature and the reactor holdup are kept constant at theirmaximum values at all times. For chemistries of thistype, a self-optimizing control structure would be rela-tively easy to design and implement. The controlstructure would keep the reactor temperature constant(at the high-temperature constraint), and the reactorholdup constant (at the maximum value). Such a controlstructure would keep the process at its optimal operat-ing point over the entire possible range of productionrates.

3.2. EA,1 > 1, Nonbounded Chemistry. IfEA,1 > 1,then low reactor temperatures will minimize the reac-tion rate constant ratio k1. Furthermore, for a non-bounded chemistry, it is not desirable to maximize theper-pass conversion of any species. However, as thetemperature is decreased with fixed recycle flow rates,the reactor holdup must increase, as argued earlier (eq20). Therefore, at all times either the low-temperatureconstraint or the maximum reactor holdup constraint

Figure 6. Chemistry 6 (nonbounded chemistry) with EA,1 > 1before production rate increase. marks the optimal operatingpoint.

Figure 7. Chemistry 6 (nonbounded chemistry) chemistry withEA,1 > 1 after production rate increase. marks the optimaloperating point.

Figure 8. Chemistry 7 (bounded chemistry) with EA,1 > 1 beforeproduction rate increase. marks the optimal operating point.

Figure 9. Chemistry 7 (bounded chemistry) with EA,1 > 1 afterproduction rate increase. marks the optimal operating point.

Figure 10. Chemistry 8 (bounded chemistry) with EA,1 > 1 afterproduction rate increase. marks the optimal operating point.

Table 3. Values of Dimensionless Groups in Figures

figure chemistry CD k1, 0 EA,1 Vmax R A,max

2 6 100 0.08 0.9 3 105 93 6 100 0.08 0.9 2 105 4.5

4 7 100 0.1 0.9 3

107

0.85 7 100 0.1 0.9 2 107 0.536 6 100 1 1.2 1.8 108 4.57 6 100 1 1.2 0.9 108 2.258 7 100 1 1.2 3 107 0.89 7 100 1 1.2 2 107 0.53

10 8 100 1 1.2 2 107 0.53

http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-009.jpg&w=156&h=147http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-008.jpg&w=152&h=146http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-007.jpg&w=154&h=148http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-006.jpg&w=157&h=147http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-005.jpg&w=157&h=147


6/12

will be active, but not both. It is possible that the activeconstraint (low temperature or reactor holdup) mayswitch during operation as the production rate ischanged or other disturbances are encountered.

Figures 6 and 7 show the optimization landscape forchemistry 6, with EA,1 ) 1.2, before and after a produc-tion rate increase. Before the production rate increase(Figure 6), the optimal operating point lies on theminimum reactor temperature constraint, away fromthe reactor volume constraint. Because the reactorvolume and recycle flow rate constraints are nondimen-sionalized by dividing by the production rate PC, anincrease in the production rate causes these constraintsto shift. In contrast, the reactor temperature is notnondimensionalized by the production rate, and the highand low-temperature constraints do not shift. If thereis a significant change in the production rate, then thereactor volume constraint may become active, while theminimum temperature constraint becomes inactive, asshown in Figure 7. Generally, as the production rate isincreased, the reactor volume constraint will sweepthe optimal operating point to higher temperatures (andrecycle flow rates), until the high temperature con-straint or recycle flow rate constraint becomes active

and finally the process becomes inoperable as thefeasible region shrinks to zero and the desired produc-tion rate can no longer be achieved.

In this case, it would be difficult to design a self-optimizing control structure, because there are twoconstraints which may switch during the course ofprocess operation. There are no obvious process vari-ables that can be kept constant to ensure most profitableprocess operation when the production rate is changed.Therefore, a supervisory control structure may benecessary.

3.3. EA,1 > 1, Bounded Chemistry. As before, sinceEA,1 > 1, low reactor temperatures will minimize thereaction rate constant ratio k1. However, because theprocess chemistry is bounded, it is also optimal from a

selectivity point of view to maximize the per passconversion of one or more species. Reducing the reactortemperature will reduce the conversion of all species.Since the maximum reactor holdup is fixed, these twocompeting effects give rise to a surprising result thatcontradicts the conventional wisdom regarding reactortemperature operating policy.

Consider chemistry 7

and the case where EA1 ) E

A1/E

A0> 1. Because this

chemistry is reactor-volume bounded, it is expected thatthe optimal operating policy will require operation withthe reactor completely full at all times. However, it isnot immediately clear what the optimal policy shouldbe with regard to the reactor temperature, as a resultof competing contributions to the selectivity. BecauseEA,1 > EA,0, decreasing the reactor temperature willimprove the ratio of the reaction rate constants (de-crease k1). However, lowering the temperature willdecrease the rate of both reactions and therefore limitthe per-pass conversion in the reactor, inhibiting theability of the system to suppress the undesired reactionby driving the concentration of the reactor-volumebounded species (A) to zero.

From previous results, we can write

Again, because this chemistry is reactor-volume bounded,

the process should be operated with the reactor volumecompletely full at all times. Under this assumption, wecan write

and

however note that

and therefore

Thus, unless EA,1 > 2, which is unlikely, the byproductproduction rate will decrease with increasing temper-ature when the reactor is operated completely full atall times. This result is exactly the opposite of whatwould be expected on the basis of activation energiesalone. The undesired reaction is suppressed more ef-fectively at higher temperatures because higher tem-

peratures maximize conversion and reduce the concen-tration of the bounded species, which reduces the rateof byproduct formation. For bounded chemistries, it isusually best to maximize the per-pass conversion of thebounded species (minimize the recycle flow rate of thatspecies) even at the expense of operating at hightemperature, which increases the reaction rate constantratio k1. This is in contrast to the case of a nonboundedchemistry, where it is not desirable to make the per-pass conversion as high as possible, and therefore it isnot desirable to operate on the high-temperature con-straint.

Figures 8 and 9 show the optimization landscapebefore and after a production rate change. The optimumlies at the intersection of the high-temperature con-straint and the reactor volume constraint for all produc-tion rates. An increase in the production rate of 50%(Figure 9) shrinks the feasible region, however the sameconstraints remain active. In this case, as for the caseof a bounded chemistry with EA,1 < 1, it is straightfor-ward to design a self-optimizing control structure. Boththe reactor temperature and reactor holdup should bekept constant at their maximum allowable values.

In the remainder of this section, analytical results aredeveloped for several other process chemistries in thiscategory (EA,1 > 1, bounded chemistry).

It was just a coincidence that all of the terms of RAand q canceled out in the expression for PD (eq 26). Foran example where such cancellation is not exact,

AfC r0 ) k0[A] desired (21)


PD ) k1RA

q(23)

V )e1/T

RAq (24)

RA

q)

e1/T

Vmax(25)

PD ) k1e1/T

Vmax(26)

k1 ) k1,0 e(1-EA,1

)/T

(27)

PD )k1,0

Vmaxe(2

-EA,1 )/T (28)



7/12

consider chemistry 8

then

where it is assumed for the last equality that the massdensity of all species is the same. Because this chemistryis reactor-volume bounded, the optimal operating policywill have RA as small as possible. Therefore as asimplifying assumption, we consider the case that RA, 1. A consequence of operating the process near to thislimit is that PD , 1 and q 1. Therefore

and, as before, we can write

and

Figure 10 shows the optimization landscape forchemistry 8, without the simplifying assumption of eq

33, using the same values for dimensionless groups(EA,1 , k0,0 ) as in Figure 8. The shape of the cost contoursand reactor volume constraint are qualitatively quitesimilar to those of Figure 8 over the domain 0 < RA m for a bounded chemistry and EA,1 > EA,0and m and n are not necessarily integers. We follow

previous analysis to obtain

Dividing eq 39 by eq 38 gives

Also from Section 2.3

Solving this expression for RA with the assumption thatthe reactor holdup is at its maximum value gives

And substituting this result into the expression for the

byproduct production rate (eq 40) yields

Therefore, to maximize selectivity, a reactor with thischemistry should be operated on the low-temperaturebound iff

not

Otherwise it should be operated on the high-tempera-ture bound.

4. Case Study: Benzene Chlorination

This section presents results from a case study basedon a process to produce chlorobenzene. More details areprovided in the Supporting Information. The benzenechlorination process was the subject of a previous casestudy by Ward et al.1 Here, the case study is expandedto consider the situation involving nonisothermal reac-tor operation. This section first reviews the previousresults for the isothermal case, and then presents newresults for the nonisothermal case.

4.1. Description of the Process. Chlorination isoften employed to introduce reactive sites on organicmolecules. For example, one route in the production ofphenol (C6H5OH) from benzene is via the intermediatechlorobenzene (C6H5Cl). In this case care must be takento minimize the production of higher chlorinated ben-zenes. The reactions are

These reactions can be carried out in the liquid phaseat temperatures between 25 and 70 C. Dichlorobenzenehas no value and must be disposed of safely.

Silberstein et al.13 report kinetic data for thesereactions. The kinetic rate expressions they suggest arethird-order overall, being first-order each in the con-centration of catalyst (stannic chloride, SnCl4), chlorine,and benzene (or chlorobenzene). Because the catalyst

A+ C f2C r0 ) k0[A][C] desired (29)


PD ) k1RA (31)

V )e1/T

RAq2 )

e1/T

RA(RA + 1 + 2PD)

2 (32)

V e

1/T

RA(33)

RA e

1/T

Vmax(34)

PD k1,0

Vmaxe(2

-EA,1 )/T (35)

AfC r0 ) k0[A]m desired (36)

AfD r1 ) k1[A]n undesired (37)

PC ) k0,0 exp(-EA,0

RT)(RA)m(q)-mV (38)

PD ) k1, 0exp(-EA,1

RT)(RA)n(q)-nV (39)

PD ) k1,0 exp(1 - EA,1

T )(RA)n-m(q)m-n (40)

Vmax ) exp( 1T)(RA)-m(q)m (41)

RA ) (Vmax)-1/m exp( 1mT)q (42)

PD ) k1,0 exp(1 - EA,1

T )(Vmax )-(n-m)/m

exp(n - mmT )(q)n-m(q)m-n (43)

PD ) k1,0 exp(n

m- EA,1

T)(Vmax )(m-n)/m (44)

EA,1

EA,0>

n

m(45)

EA,1

EA,0> 1 (46)

benzene + Cl2 f chlorobenzene + HCl (47)

chlorobenzene + Cl2 fdichlorobenzene + HCl (48)



8/12

concentration and chlorine concentration influence bothreaction rates in the same manner, their values do notinfluence the selectivity-conversion profile. Therefore,it is assumed that these parameters are fixed and notavailable as degrees of freedom: [SnCl4] ) 0.030 mol/Land [Cl2] ) 0.25 mol/L. With these assumptions, thereaction rates are given by

where k0,0 ) 2.39 105 min.- 1, k1,0 ) 2.30 105 min.-1,

EA,0 ) 34.8 kJ/mol, and EA,1 ) 42.7 kJ/mol.The process was designed according to the methods

of Douglas.14 The process flow diagram at level 4 inDouglas hierarchy is shown in Figure 11. The distilla-tion columns were designed and costed using themethods of Doherty and Malone.15

4.2. Results: Isothermal Operation. Figure 12shows the optimization landscape for the process afterit has been built. The solid line shows the operatingeconomic potential of the flexible process as a functionof the single operational degree of freedom, the recycleflow rate of benzene. The operating economic potentialof the plant after it has been built includes the fixedcapital cost associated with the process equipment aswell as the variable operating costs. The vertical dashedlines show the reactor volume constraint (on the left)and the recycle capacity constraint (on the right). Againas expected, there is a maximum in the economicpotential function. However, the location of the maxi-mum has shifted now that capital costs are fixed, andlies outside the feasible region. As is sometimes the casefor nonbounded chemistries, the optimal operating pointlies on the recycle capacity constraint, at 290 kmol/h.This operating point corresponds to a reactor holdup of72% of the maximum value. The economic potential ofthe process at this point is $3.1 million/year. Note thatthis is somewhat less than the maximum achievableeconomic potential at the design stage, because thisvalue reflects the additional cost for oversizing the

process equipment. An alternative, inferior operatingpolicy would be to operate with the reactor completelyfull. The economic potential of the process with thisinferior operating policy is $2.2 million/year, a loss ofnearly 30% compared to the maximum achievableeconomic potential.

Now consider a decrease in the production rate of50%. The optimization landscape is shown in Figure 13.Because much less product is being produced, theeconomic potential of the process is significantly re-duced. Another consequence is that the optimal recycle

flow rate has been reduced by 50%, and now lies withinthe process constraints, at 202 kmol/hr, where theeconomic potential of the process is $494 000/year andthe reactor holdup is at 34% of the maximum value. Theprocess is within the region of operation where theoptimal operating policy is to scale the reactor holdupand recycle flow rate linearly with production rate. Incontrast, the process incurs a loss of $1.6 million/yearif it is operated with the reactor completely full. Theeconomic potential of the process when it is operatedon the recycle capacity constraint is $458 000/year,corresponding to a loss of 7.3% relative to the maximumachievable economic potential.

4.3. Results: Nonisothermal Operation. Up to thispoint, the design and operation of the benzene chlorina-

tion process has assumed that the reactor will beoperated at a constant temperature T) 333 K, in whichcase the process has a single degree of freedom, therecycle flow rate of benzene RB. Now we consider thecase where the reactor temperature also can be ad-justed. In this case, the process has two operationaldegrees of freedom, and the optimization landscape canbe represented using a contour plot diagram. There isa lower bound on the reactor temperature that isdetermined by the minimum temperature differencerequired for heat exchange with the cooling water: Tg 308 K (Tg 35C).

Figure 14 shows the optimization landscape for thecase where the process is operated at 50% of the basecase production rate. Because the activation energy ofthe undesired reaction is greater than the activationenergy of the desired reaction and the process chemistryis nonbounded, it is expected (based on the analysis ofWard et al.1) that the reactor should be operated at thelowest possible temperature, where either the reactorlow-temperature constraint or the reactor volume con-straint is active. This is a different result from the casewhere a process with the same chemistry and the samevalues of the activation energies is operated isother-mally. In this case, we expect the reactor volumeconstraint not to be active. The difference is that withthis relative magnitude of reaction rate constants, inthe nonisothermal case it is beneficial to operate at thelowest possible temperature, which requires the greatest

Figure 11. Process flow diagram for benzene chlorination.

Figure 12. Optimization of the flexible benzene chlorinationprocess at the nominal production rate of 50 kmol/h. marks theoptimal operating point.

r0 ) k0 [benzene] k0 ) k0,0e-Ea,0/RT

r1 ) k1[chlorobenzene] k1 ) k1, 0e-Ea,1/RT (49)

Figure 13. Optimization of the flexible benzene chlorination

process after production rate decrease of 50%. marks the optimaloperating point.

http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-012.png&w=135&h=88http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-011.png&w=137&h=88http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-010.png&w=192&h=113


9/12

possible reactor holdup. Therefore, the process shouldbe operated at the reactor volume constraint (or the low-

temperature constraint) for the purpose of achieving lowtemperature even though it is not beneficial to operatewith the greatest possible per-pass conversion of reac-tant species.

Because the production rate is small (50%) comparedto the nominal production rate, it is possible to reducethe reactor temperature to the minimum value withoutviolating the reactor holdup constraint. This situationis reflected in Figure 14 by the location of the optimaloperating point X on the low-temperature constraintand away from the reactor volume constraint.

Now consider how the operation of the process shouldchange as the production rate is increased from thispoint. Figure 15 shows the optimization landscape whenthe production rate is at 65% of the nominal value. Atthis production rate, it is not possible to cool the reactorall the way to the low-temperature constraint withoutviolating the reactor volume constraint. This circum-stance is reflected in the figure by the optimal operatingpoint now situated on the reactor volume constraint.Thus, the active constraint has shifted from reactortemperature to reactor holdup. The optimal recycle flowrate is still away from the constraint; its value must bedetermined by solving a nonlinear optimization problem.

Finally, Figure 16 shows the optimization landscapewhen the production rate is at 80% of the nominal value.At this production rate, the optimal recycle flow ratehas shifted to sufficiently high values that the recycleflow rate constraint is active. Therefore the optimal

operating point lies at the intersection of the reactorvolume constraint and the recycle flow rate constraint.This constraint switch is the last one that can take placefor a chemistry of this type as the production rate isincreased. As the production rate is further increased,it remains optimal to operate the process at the inter-section of these constraints until the feasible regionshrinks to zero and the process is no longer operable.

4.4. Case Study Conclusions. Table 4 summarizesthe process conditions and active constraints illustratedin the optimization landscapes presented in this casestudy. If the process is operated isothermally, because

the benzene chlorination chemistry is nonbounded, thenthe recycle flow rate constraint can shift from active toinactive, but the reactor holdup constraint is inactiveas is usually the case for nonbounded chemistries.Because the activation energy of the undesired reactionis greater than that for the undesired reaction, whenthe process is operated with variable reactor tempera-ture both the reactor low temperature constraint, thereactor volume constraint, and/or the recycle flow rateconstraint may be active, but the high temperatureconstraint is always inactive. These results are exactlyconsistent with the derived heuristics for optimal plant-wide operation given in Table 2.

5. Case Study: Novel High Molecular Weight

Ethers for Gasoline Blending

This section presents results from a case study basedon a process to produce 2-methoxy-2-methylheptane.Full details are available in a web-published supplementto this document.

5.1. Description of the Process. Alkyl ethers areused as fuel additives in gasoline to improve combus-tibility and octane number and to meet legislativerequirements for oxygenate content. In the early 1990s,methyl tert-butyl ether (MTBE) was thought to be avaluable additive for this purpose. However, one criticaldrawback of MTBE is that it is moderately soluble inwater: 4.3 wt %. Since its introduction, MTBE has beendetected in the groundwater in many communities.

Figure 14. Optimization landscape for benzene chlorinationprocess at 50% of the nominal production rate. marks theoptimal operating point.



Table 4. Summary of Figures 12-16

figure conditions active constraints

12 PC ) Ph Ca T) Th a RB ) RB,max13 PC ) 0.5Ph C T) Th none14 PC ) 0.5Ph C T) variable T) Tmin15 PC ) 0.65Ph C T) variable V) Vmax16 PC ) 0.8Ph C T) variable V) Vmax, RB ) RB,maxa Note: Ph C ) 50 kmol/hr, Th ) 60 C.

http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-015.jpg&w=160&h=152http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-014.jpg&w=157&h=152http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-013.jpg&w=161&h=152


10/12

Consequently, MTBE is being phased out as a gasolineadditive in California, and other states may follow.

The solubility of ethers in water decreases withincreasing molecular weight, so one possible way ofovercoming this drawback is to use ethers with a highermolecular weight. Recently, Krause and co-workers16-19

have investigated the kinetics of the production of highmolecular weight ethers from C6 to C8 alkenes and C1to C4 alcohols. In this case study, we consider theproduction of 2-methoxy-2-methyl heptane (MMH, Fig-ure 17) from 2-methyl-1-heptene (MH) and methanol.

It is assumed that the hydrocarbon feed to the process

is a mixture of alkenes and alkanes. This situation isrepresented in the case study as a stream which is 80mol % 2-methylheptane and 20 mol % 2-methyl-1-heptene. Because of the difficulty of separating thealkane from the alkene, unconverted alkene is notseparated and recycled back to the reactor, but ratheris fed along with the alkane to a downstream blendingprocess. A requirement for the blending process is thatthe hydrocarbon stream contain no more than 2 mol %alkene. Therefore, it is necessary to achieve an alkeneconversion of approximately 90%, but there is no incen-tive to go beyond this value. Unfortunately, highermolecular weight olefins are considerably less reactivethan isobutene in etherification reactions. To achievethis high conversion with a reasonable reactor residence

time, it is necessary to operate the process at a highertemperature than the MTBE process, and with a molarexcess of methanol. Both of these considerations willtend to promote the undesired reaction and makeselectivity losses a greater concern.

Kinetic data are taken from papers by Krause andco-workers cited earlier. They generally develop sophis-ticated kinetic models for these types of reactions basedon the activity of the species in solution and assumingeither a Langmuir-Hinshelwood or Eley-Rideal typereaction mechanism. As is the case for the MTBEprocess, the reactions are typically equilibrium limitedand high conversion can be achieved by employingmultiple reactors with distillation columns between to

remove the desired product.

20,21

However, such a reactornetwork is too complicated for the pedagogical purposeof this case study. Therefore, the reactions are assumedhere to be kinetically limited over the range of conver-sion of interest. Data reported by Krause and co-workersand/or data generated from the models suggested byKrause and co-workers were fitted to pseudo-homoge-neous models of the form

where x is the mole fraction of species. The values ofthe parameters are given in Table 5. Because the per-pass conversion of the alkene is fixed, the processchemistry is effectively of the type AfC, A+ AfD,where A is methanol, C is the desired ether, and Drepresents undesired byproducts. Therefore, the etheri-fication chemistry is a bounded chemistry.

It is assumed that the acid resin catalyst employedin these reactions costs $10/kg and will deactivate attemperatures above 120 C. These values are represen-tative of typical properties of commercial acid resincatalysts such as Amberlyst.

Figure 18 shows the process flow diagram at Douglaslevel 4.

5.2. Results. Figure 19 shows the economic optimiza-tion landscape. All of the process constraints are shownas dashed lines. The reactor volume constraint prohibitslow temperatures and low recycle flow rates. Thecapacity of the separations system prohibits high recycleflow rates. The properties of the catalyst impose a high-temperature constraint: the catalyst cannot be usedover 120 C. The feasible operating region then is theregion of space that is bounded by these curves. Thelocation of the base-case design is marked with an X.However it is clear from the contour plot, as expectedbased on the analysis in this paper (Table 2) for mostbounded chemistries with EA,1 > EA,0, that it is best tooperate the reactor at the high-temperature constraint,the opposite of what would be expected on the basis ofthe activation energies of the reactions alone. Thereason for this result is that increasing the reactortemperature allows for a greater per-pass conversion ofthe bounded species A, which suppresses the undesiredreaction even though the ratio of the rate constants (k1/k0) increases. The optimal operating point is markedwith an O. The operating economic potential of the

process at the optimal operating point is $2.41 million/year, while the operating economic potential at the basecase design point is $2.14 million/year, which wouldcorrespond to a loss of 11% relative to the greatestpossible economic potential.

Figure 20 shows the byproduct production rate versusreactor temperature when the reactor is operatedcompletely full. Although the activation energy of theundesired reaction is greater than the activation energyof the desired reaction, selectivity nevertheless improveswhen the process is operated at higher temperatures.The reason for this is that it is possible to achieve ahigher conversion at higher temperatures, which sup-presses the undesired reaction by decreasing the con-centration of the methanol, the bounded species.

If the production rate were increased, the feasibleregion would shrink, but the optimal operating pointwould remain at the intersection of the reactor volumeconstraint and the upper reactor temperature con-straint.

5.3. Case Study Conclusions. This case study alsoillustrates results which are summarized in Table 2. Fora bounded chemistry with the activation energy of theundesired reaction greater than that of the desiredreaction, it is usually best to operate the process at thehighest possible temperature, which is the opposite ofwhat would be expected on the basis of the activationenergies alone. The optimal operating point is alwaysat the intersection of the reactor volume constraint and

Figure 17. 2-methoxy-2-methylheptane.

Table 5. Values of Kinetic Parameters

k0,0)

7.5

1011

mol/(kg cat s) EA,0)

90 kJ/molk1,0 ) 2.1 1011 mol/(kg cat s) EA,1 ) 102.6 kJ/mol

MH + MeOH fMMH

r0 ) k0xMHxMeOH k0 ) k0,0e-EA,0/RT

2MeOH fDME + H2O

r1 ) k1xMeOH2 k1 ) k1,0e

-EA,1/RT

MH + H2O fMHOH r2 ) fast (50)

http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-016.png&w=125&h=61


11/12

the high temperature constraint. Such a process is agood candidate for self-optimizing control, because theprocess can be kept at its economic optimum simply bycontrolling the reactor holdup and reactor temperatureso that they always lie on their constraints.

6. Conclusions

This paper presents an analysis of the problem ofdetermining the optimal plantwide operating policy forplants with recycle, when reactor temperature is alsoavailable as a degree of freedom. It is shown that theoptimal reactor temperature operating policy in theplantwide context is sometimes radically different fromwhat conventional wisdom based on reactor designwould suggest. Process chemistries are classified asbounded or nonbounded and as having dimensionlessactivation energy EA,1 greater than or less than one. Onthe basis of this classification, processes are assignedan operating policy that is defined in terms of the

constraints that are active, inactive, or may switchduring the course of operating the process. The analysisalso provides insight as to whether it may be possibleto design a self-optimizing control structure for theprocess. If the optimal point of operation of the processis always at the intersection of the same constraints,then it is straightforward to design a self-optimizingcontrol structure: the process should be controlled so

that those constraints are always active. By contrast,if constraints shift during operation it may be difficultto design a self-optimizing control structure.

All of the analysis presented in this paper and theone which preceded it has focused on liquid-phasereactions with pseudo-homogeneous kinetics, and al-most all of the analysis has been limited to the casewhere the reactor network consists exclusively of asingle ideal CSTR. The reason for this is that it ispossible to obtain analytical results in this case whereasit is not possible to obtain analytical results in manyother cases. It is worthwhile to consider how the insightwhich is developed from this simple case could beapplied to other cases, such as nonhomogeneous kinet-ics, gas-phase reactions, more complex reactor networks,

and even the case where the only information availableabout the process chemistry is the stoichiometry andsome selectivity-conversion data from a pilot plant orlaboratory experiment.

What are here termed bounded chemistries consti-tute a subset of all chemistries for which selectivityincreases with conversion for at least one reactantspecies, and what are here termed nonbounded chem-istries constitute a subset of all chemistries for whichselectivity is decreasing with conversion for all reactantspecies. As a heuristic, one could argue that if pilot plantdata suggest that selectivity is increasing with conver-sion, then the chemistry is bounded, whereas if it isdecreasing then the chemistry is nonbounded. This

heuristic, coupled with good engineering judgment,could be used to extend the results developed in thesepapers to many other, more complicated cases and inparticular to reaction systems where a formal kineticrate expression is not available.

Appendix A. Multiple Recycled Species andMultiple Undesired Reactions

All of the results presented in this paper are for thecase of a single undesired reaction. The case of multipleundesired reactions could be the subject of a separatepaper. However we present here just a few commentsand observations about that situation. All of the frame-work and methodology presented in this paper and

Figure 18. Etherification process at Douglas14 level 4.

Figure 19. Optimization landscape for the etherification processwith reactor volume constraint. marks the design operatingpoint, O marks the optimal operating point.

Figure 20. Byproduct production rate vs reactor temperaturealong the reactor volume constraint.

http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-019.png&w=158&h=102http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-018.jpg&w=155&h=156http://dontstartme.literatumonline.com/action/showImage?doi=10.1021/ie0491589&iName=master.img-017.png&w=382&h=144


12/12

Ward et al.1 can be generalized to the case of multipleundesired reactions.

With multiple undesired reactions, there are multipleEA,i , one for each undesired reaction. If all EA,i < 1 orall EA,i > 1, then the process chemistry falls into thesame classification as EA,1 < 1 or EA,1 > 1, respectively.If some EA,i < 1 and some EA,i > 1, i.e., then theactivation energy of the desired reaction is between theactivation energies of the undesired reactions, it is well-known from reactor design that there is an intermediatetemperature which balances the losses from the reac-tions and represents the point of maximum selectivity.If this point lies above the maximum temperatureconstraint, then the process behaves as if EA,1 < 1; if itlies below the minimum temperature constraint, thenthe process behaves as if EA,1 > 1. If the point ofmaximum selectivity lies between the minimum andmaximum temperature constraints, and if the processchemistry is nonbounded, then it is generally desirableto operate at a temperature between the constraints.However, if the process chemistry is bounded, it maybe optimal nevertheless to operate at the highestpossible temperature in order to suppress one or moreof the undesired reactions by maximizing the per-pass

conversion of the bounded species.When multiple recycled species are involved andreactor temperature is variable, then the optimizationlandscape cannot be represented on a contour plot. Inthis situation, the benefit of classification of chemistriesas bounded or nonbounded is clear. In general, if evenone reactor volume bounded species is present (whichmeans that the overall process chemistry is classifiedas bounded) then it is usually optimal to maximize theper-pass conversion by maximizing the reactor holdupand reactor temperature. Otherwise, these constraintsmay shift depending on the production rate.

Supporting Information Available: More detailsregarding a process to produce chlorobenzene. Thismaterial is available free of charge via the Internet athttp://pubs.acs.org.

Nomenclature

C) cost ($/h)CP ) cost associated with stream P ($/mol)kn ) reaction rate constant for reaction nk0,n ) Arrhenius pre-factor for reaction n

EA,n ) activation energy for reaction nP ) production rate of species (mol/h)q ) reactor effluent volumetric flow rate (L/h)r ) specific reaction rate [mol/(L h)]

R ) recycle flow rate (mol/h)vA ) molar volume of species A (L/mol)

V ) reactor volume (L)

Literature Cited

(1) Ward, J. D.; Mellichamp, D. A.; Doherty, M. F. Importanceof Process Chemistry in Selecting the Operating Policy for Plantswith Recycle. Ind. Eng. Chem. Res. 2004, 43, 3957.

(2) Fogler, H. S. Elements of Chemical Reaction Engineering,3rd ed.; Prentice-Hall: Upper Saddle River, NJ 1999.

(3) Levenspiel, O., Chemical Reaction Engineering, 3rd ed.;John Wiley and Sons: New York 1999.

(4) Luyben, W. L. Snowball Effects in Reactor/Separator Pro-cesses with Recycle. Ind. Eng. Chem. Res. 1994, 33, 299.

(5) Larsson, T.; Govatsmark, M. S.; Skogestad, S.; Yu, C. C.Control Structure Selection for Reactor, Separator and RecycleProcesses. Ind. Eng. Chem. Res. 2003, 42, 1225.

(6) Larsson, T.; Skogestad, S. Plantwide Control- -A Review

and a New Design Procedure. Model Ident. Control 2000, 21,209.

(7) Wu, K. L.; Yu, C. C. Reactor/Separator Processes withRecycle- -1. Candidate Control Structures for Operability. Comput.Chem. Eng. 1996, 20, 1291.

(8) Wu, K. L.; Yu, C. C.; Luyben, W. L.; Skogestad, S. Reactor/Separator Processes with Recycles- -2. Design for CompositionControl. Comput. Chem. Eng. 2002, 27, 401.

(9) Monroy-Loperena, R.; Solar, R.; Alvarez-Ramirez, J. Bal-anced Control Scheme for Reactor/Separator Processes with Mate-rial Recycle. Ind. Eng. Chem. Res. 2004, 43, 1853.

(10) Maarleveld, A.; Rijnsdorp, J. E. Constraint Control onDistillation Columns. Automatica 1970, 6, 51.

(11) Skogestad, S. Plantwide control: the search for theself-optimizing control structure. J. Process Contr. 2000, 10,487.

(12) Zheng, A.; Mahajanam, R. V.; Douglas, J. M. HierarchicalProcedure for Plantwide Control System Synthesis. AIChE J.1999, 45, 1255.

(13) Silberstein, B.; Bliss, H.; Butt, J. B. Kinetics of Homoge-neously Catalyzed Gas-Liquid Reactions: Chlorination of Ben-zene with Stannic Chloride Catalyst. Ind. Eng. Chem. Fundam.1969, 8, 366.

(14) Douglas, J. M.; Conceptual Design of Chemical Processes;McGraw-Hill: NewYork, 1988.

(15) Doherty, M. F.; Malone, M. F. Conceptual Design ofDistillation Systems; McGraw-Hill: New York, 2001.

(16) Karinen, R. S.; Linnekoski, J. A.; Krause, A. O. I. Etheri-fication of C5 and C8 alkenes with C1 to C4 alcohols. Catal. Lett.2001, 76, 81-87.

(17) Karinen, R. S.; Krause, A. O. I. Reactivity of some

C8-alkenes in Etherification with Methanol. Appl. Catal. A-gen.1999, 188, 247-256.

(18) Kiviranta-Paakkonen, P. K.; Struckmann, L. K.; Linne-koski, J. A.; Krause, A. O. I. Dehydration of the Alcohol in theEtherification of Isoamylenes with Methanol and Ethanol. Ind.Eng. Chem. Res. 1998, 37, 18-24.

(19) Karinen, R. Etherification of Some C8 Alkenes to FuelEthers Sc. D. Diss. Helsinki University of Technology, Espoo,Finland 2002.

(20) Bitar, L. S.; Hazbun, E. A.; Piel, W. J. MTBE productionand economics. Hydrocarb. Process. 1984, 63, 10, 63-66.

(21) Scholz, B.; Butzert, H.; Neumeister, J.; Nierlich, F. MethylTert-Butyl Ether. Ullmanns Encyclopedia of Industrial Chem-istry; Verlagsgesellschaft: Weinheim, Germany, 1990. p 543-550.

Received for review September 3, 2004Revised manuscript received May 4, 2005

Accepted May 16, 2005

IE0491589


novel reactor temperature and recycle flow rate policies

Documents