Thermodynamics Analysis of Processes. 1. Implications of Work Integration

Thermodynamics Analysis of Processes. 1. Implications of WorkIntegration

Bilal Patel, Diane Hildebrandt,* David Glasser, and Brendon Hausberger

School of Process and Materials Engineering, University of the Witwatersrand, Private Bag 3, WITS 2050,Johannesburg, South Africa

This paper describes a new technique to analyze processes with a positive change in the Gibbsfree energy, ∆G, based on the second law of thermodynamics. In particular, the application ofa two-stage process, consisting of an endothermic high-temperature first stage and an exothermiclow-temperature second stage, has been investigated. This paper considers chemical reactionprocesses as heat engines and that by the appropriate flow of heat at a specific temperature(and, hence, with a specified exergy level) work can be added or removed from a process. Thetechnique also investigates the integration of such processes in terms of work flows. The techniqueis useful in the early stages of the design process as well as for retrofitting. It helps identifyopportunities and set targets for the process. The method does not require detailed informationregarding the process and is based only on thermodynamic properties of the system.

1. Introduction

Chemical processes are usually characterized in termsof flows of mass and energy. Therefore, in the develop-ment of processes that are cost- and energy-efficient,there is a growing need to integrate processes in termsof mass and energy. In light of this, two branches ofprocess integration have been developed: mass integra-tion and energy integration. Energy integration is asystematic methodology for analyzing the energy flowswithin a process to identify targets and determine theoptimal system for a minimum consumption of energy.For example, pinch analysis is an energy integrationtool for designing heat-exchanger networks.1 Massintegration aims at systematically identifying perfor-mance targets for the mass flows in a process. Thesynthesis of a mass-exchange network has been suc-cessfully applied to waste recovery and separationproblems.2

The use of thermodynamic methods, especially thesecond law analysis, has proved to be a valuable tool inprocess synthesis and integration.3,4 In particular, theapplication of the second law to processes involvingchemical reactions, first introduced by Denbigh5 andthen considered by numerous researchers, reveals thatchemical reactors usually are the main cause of ther-modynamic inefficiency because of the irreversible man-ner in which reactions occur. Although present daytechnology does not allow for reactions to be carried outreversibly, not all of the exergetic losses are inevitable;it is possible to reduce the irreversibility of chemicalprocesses. One possibility is to carry out chemicalprocesses under a “prescribed degree of irreversibility”,5i.e., the consumption of a specific amount of exergy toaccount for technological constraints. Glavic et al.7performed a thermodynamic analysis of reactors inorder to heat integrate the reactors into the process. DeRuyck8 also proposed a way in which to include chemicalreactions in composite curve theory by defining a

“reversible temperature”. Hinderdrink et al.9 investi-gated the exergy losses associated with chemical reac-tions and suggested ways in which the exergy losses canbe minimized. Leites et al.10 also suggested variousmethods of reducing exergetic losses, and in turn energylosses, for chemical reactions and other chemical pro-cesses.

This paper will investigate the specific case of pro-cesses that have positive Gibbs energy changes (whichmeans the process requires work) and explore thepossibilities of saving energy by considering the secondlaw analysis.

2. Positive Gibbs Energy Change of Reaction

2.1. Significance. The production of many industrialchemicals, such as methanol and ammonia, by directroutes (i.e., by a single-step isothermal process) isinfeasible because these reactions possess a positivechange in the Gibbs energy. A positive ∆G has thefollowing significance to a designer: first, it signifies asmall equilibrium conversion and, second, that workmust be supplied to a steady-state isothermal system.Several methods of overcoming the positive ∆G and thusovercoming small equilibrium conversion have beensuggested.4,11 One of these methods suggests staging ofthe overall reaction; i.e., the feed is first converted intointermediates at certain operating conditions, andthereafter these intermediates are reacted to the desiredproduct under different operating conditions. Usually,one of stages runs an endothermic reaction and theother stage an exothermic one.

2.2. Staging Reactions. The procedure of “stagingreactions” can be examined using the synthesis methodapproach suggested by May and Rudd12 for the develop-ment of Solvay Clusters. Consider a reaction with apositive change in the Gibbs energy:

To carry out this reaction under practical conditions,consider a two-stage route* To whom correspondence should be addressed. Tel.:

+27 11 717 7527. Fax: +27 11 717 7557. E-mail:[email protected].

A + B S Z (1)

A + B S X + Y (1a)

3529Ind. Eng. Chem. Res. 2005, 44, 3529-3537

10.1021/ie048787f CCC: $30.25 © 2005 American Chemical SocietyPublished on Web 04/14/2005

The Gibbs energy difference of both stages should beless than a small positive number, ε (ε < 42 kJ/mol), toensure a reasonable equilibrium conversion.12

Therefore, for reaction 1

and for reactions 1a and 1b

These inequalities can be plotted on a temperature-free energy curve to determine the temperatures of eachreaction that satisfy these criteria.

2.3. Synthesis of Methanol. Consider, for example,the production of methanol by the following overallreaction:

Reaction 3 has a large positive standard Gibbs energychange (84.8 kJ/mol), is endothermic (36.8 kJ/mol), andhas a negative entropy change (-161.0 J/mol‚K). There-fore, the Gibbs energy difference is positive at alltemperatures, becoming more positive as the tempera-ture increases.

The reaction can be accomplished by using a two-stage process as outlined below. The first stage is theproduction of synthesis gas by reforming methane (gasphase)

Although reaction 3a has a large positive standardGibbs energy change (113.8 kJ/mol), the enthalpy (164.9kJ/mol) and entropy (171.3 J/mol‚K) changes are bothpositive; therefore, the Gibbs energy difference is posi-tive at low temperatures and negative at high temper-atures. This implies that this reaction would be run athigh temperatures.

The second stage requires the conversion of thesynthesis gas to methanol

The enthalpy (-128.2 kJ/mol) and entropy (-332.5J/mol‚K) changes are both negative; therefore, the Gibbsenergy change is negative at low temperatures butbecomes positive at high temperatures. This impliesthat this reaction would be carried out at low temper-atures.

The approach outlined in section 2.2 can be appliedto the methanol synthesis example in order to determinehow the two-stage process helps to overcome the positivechange in the Gibbs energy. This will be discussed inthe paragraphs that follow.

Figure 1 shows three lines (lines a-c). Line a repre-sents the sum of the Gibbs free energy of the reactant(including the corresponding stoichiometric coefficients)in reaction 3a. Line b represents the sum of the Gibbsfree energy of the products of reaction 3a (which is the

same as that of the reactants of reaction 3b). Line crepresents the Gibbs free energy of the product (reaction3b), in this case methanol.

The objective is to have ∆G e ε at the reactionconditions for both reactions 3a and 3b, as explained insection 2.2. These criteria are shown in Figure 1.

Figure 1 forms a ladder-like plot, with each jumpcorresponding to a reaction. It is clear that the twostages must be run at different conditions, with reaction3a operating at a high temperature (T g T1) andreaction 3b carried out at a low temperature (T e T2).

Figure 1 also gives information regarding the en-thalpy change of reaction at a temperature equal toabsolute zero, assuming that the Gibbs energy changevaries linearly with temperature. This requires assump-tion of a constant enthalpy change of reaction (∆H) aswell as a constant entropy change of reaction (∆S). It isclear from Figure 1 that reaction 2a is endothermic, soenergy must be added to drive the reaction, and thatreaction 2b is exothermic, so energy must be removed.

Therefore, by carrying out the reaction in two stages,one can achieve a reasonable conversion at industriallyattainable temperatures.

This paper will use the second law analysis to furtherexplain this concept and explore the possibilities of suchan arrangement.

3. Second Law Analysis

3.1. Background. The exergy analysis is a combina-tion of the first and second laws of thermodynamics. Theanalysis of a process in terms of exergy proves to beuseful because it provides quantitative informationabout irreversibilities and exergy losses in the process.In this way, the thermodynamic efficiency can bequantified, areas of poor efficiency can be identified, andtargets can be determined in order that processes canbe designed and operated to be more efficient. Exergycan be defined as the maximum amount of work thatcan be obtained from a system during a reversiblechange from a given state to the environmental (refer-ence) state13 and can be represented by B:

where H is the enthalpy, S is the entropy, and To is thetemperature of the environment (reference state) takento be 298.15 K. The kinetic and potential terms areneglected.

Changes in exergy, ∆B, from state 1 to state 2 istherefore given by

For a steady-state flow process as shown in Figure 2,the exergy balance can be represented by the followingmathematical description:14

where Ws is the shaft power, m represents the mass ofthe streams entering (i) or leaving (o), Q is the rate ofheat transfer from the energy reservoir r, and Tr is thetemperature of the reservoir. I is the irreversibility rateor the exergy loss associated with the process.

B ) H - ToS (4)

∆B ) (H2 - H1) - To(S2 - S1) (5)

I ) ∑i

(mB)i - ∑o

(mB)o + ∑r

Qr(1 - To/Tr) + ∑Ws

(6)

X + Y S Z (1b)

∆G ) GZ - (GA + GB) > ε at all temperatures (2)

∆G1a ) (GX + GY) - (GA + GB) e ε

at conditions T1 (2a)

∆G1b ) GZ - (GX + GY) e ε at conditions T2 (2b)

34CH4(g) + 1

4CO2(g) + 1

2H2O(g) S CH3OH(l) (3)

34CH4 + 1

4CO2 + 1

2H2O S CO + 2H2 (3a)

CO + 2H2 S CH3OH(l) (3b)

3530 Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005

3.2. Black-Box Exergy Analysis of a ReactiveSystem. 3.2.1. Endothermic Reactions. Consider anendothermic reactor, as shown in Figure 3.

Figure 3 shows an endothermic reaction carried outat a temperature TH. The heat required for the reactionis QH. The product and reactant streams are assumedto enter and leave the process (defined as a “black box”between the input and output streams) at a temperatureTo and pressure Po.

Applying eq 6, but replacing mass (m) with moles (n),to the system shown in Figure 3 gives

Substituting for the availability function, B, and rear-ranging give

Noting that H2 - H1 ) ∆Hendo (the enthalpy change ofthe endothermic reaction), that S2 - S1 ) ∆Sendo (theentropy associated with the endothermic reaction), andthat QH is equal to the enthalpy change of reaction atTo (i.e., QH ) ∆Hendo) as given by the energy balance(first law balance), the equation can be simplifiedfurther to give

To keep the derivation simple, it is assumed that∆Hendo and ∆Sendo are not functions of temperature (i.e.,they remain constant). This assumption can be modified,which leads to the algebra becoming more complex, butthis will not affect the approach or interpretation of thederivation.

Equation 9 is an expression for the irreversibility orlost work of an isothermal endothermic reactor. It isclear that the irreversibility is dependent on the tem-perature of the reactor and that, by varying the tem-perature, one may be able to reduce the irreversibilityof the reaction.

Equation 9 can also be expressed in terms of the Gibbsenergy change of the endothermic reaction (because∆Gendo ) ∆Hendo - TH∆Sendo) as derived by Denbigh:5

Equations 9 and 10 apply to a reactor where heat isbeing supplied from the surroundings at the reaction

Figure 1. Gibbs energy-temperature plot for the synthesis of methanol using a two-stage route.

Figure 2. Exergy balance for an open control volume at steadystate.

Figure 3. Schematic diagram of an isothermal endothermicreactor.

Iendo ) (nB)1 - (nB)2 + QH(1 - To/TH) (7)

Iendo ) (n1H1 - n2H2) - To(n1S1 - n2S2) +QH(1 - To/TH) (8)

Iendo ) To(∆Sendo - ∆Hendo/TH) (9)

Iendo ) -∆Gendo

To

TH(10)

Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005 3531

temperature. Therefore, to reduce the irreversibilityassociated with the reaction, there is a need to reducethe change in the Gibbs energy of the reaction, ∆Gendo-(TH).

An alternative view is that the reactor could beconsidered in terms of a Carnot engine, as shown inFigure 4.

To supply a quantity (QH) of heat to the reaction attemperature TH, work (W) is required. The work can berelated to the temperature of the reactor (TH), thetemperature of the surroundings (To), and the heatrequired (QH) by the second law:

Equation 11 is useful in relating the temperature of thereactor to the amount of work required to supply thenecessary heat of reaction (because QH ) ∆Hendo).

Consider reaction 3a, which is endothermic. A plot ofthe work input as a function of the reaction tempera-ture, TH, is shown in Figure 5.

The work required increases as the temperature ofthe reactor increases and asymptotes to the heat ofreaction (∆Hendo). At a certain temperature, TH*, thework required is equal to the standard Gibbs energychange of the process, ∆G(To,Po) (which is equivalent

to the change in the exergy of the process, ∆B). Thiscorresponds to the temperature at which the reactionis carried out reversibly and with a minimum workinput. This can be proven by setting Iendo) 0 in eq 7,which gives

Also, considering eqs 9 and 10, the reversible tem-perature of the endothermic reaction, TH*, is obtainedwhen the Gibbs energy change of the endothermicreaction, ∆Gendo(TH) ) 0; thus, the reversible tempera-ture, TH*, is given by

Under the assumption that ∆Hendo and ∆Sendo areconstant, the reversible temperature, TH*, will beconstant. The reversible temperature was also definedby Shinnar4 and De Ruyck.8

If the reaction is carried out at a temperature greaterthan TH*, the work term is larger than the exergychange, ∆G(To,Po), and therefore there is a loss of work(this corresponds to the irreversibility or a potential torecover work from the stream). If the reaction is carriedout below TH*, the work term is less than the exergychange; therefore, external work has to be supplied tomeet the requirements of the process, as shown inFigure 5.

3.2.2. Exothermic Reactions. A similar second lawanalysis can be performed for an exothermic reactioncarried out at temperature TC, while the streams enterand leave the process at temperature To. The irrevers-ibility of an exothermic reactor can be expressed as

Again, the entropy change of the exothermic reaction∆Sexo and the enthalpy change of the exothermic reac-tion ∆Hexo were assumed to be constant.

Just as the endothermic reactor could be thought ofin terms of a heat pump, the exothermic reactor couldbe considered as the “hot reservoir” of a heat engine, asshown in Figure 6.

In order for work Wout to be produced, the heat sourceQC, which is equal to the heat of the exothermic reaction(∆Hexo) is taken from the reactor temperature TC andheat is released to the surroundings at the temperatureof the surroundings, To. The work produced can beexpressed in terms of TC and To as follows:

Equation 15 gives an expression for the maximumwork that could be obtained from the reaction if the heatof reaction was recovered and converted to work.

Equation 15 is plotted in Figure 7 for reaction 3b,which is exothermic.

Again, a reversible temperature for the exothermicreaction, TC*, can be defined where the exergy change

Figure 4. Endothermic reactor as a reservoir of a Carnot heatpump.

Figure 5. Work required for reaction 2a as a function oftemperature.

Win ) QH(1 - To/TH) (11)

∆B ) ∆G(To,Po) ) W ) QH(1 - To/TH*) (12)

TH* ) ∆Hendo/∆Sendo (13)

Iexo ) To(∆Sexo -∆Hexo

TC)

) -∆Gexo

To

TC(14)

Wout ) QC(1 - To/TC) (15)


for the exothermic process [∆G(To,Po)] equals the workproduced by the exothermic reactor, i.e.

In this case, TC* is the ratio of the enthalpy change tothe entropy change for the exothermic reaction, i.e.

At temperatures below the reversible temperature,TC*, the work term is smaller than the change in theexergy for the process, i.e., ∆G(To,Po); thus, heat isrejected to the surroundings, and work is lost (irrevers-ibility or an opportunity to recover work from thestream). When the temperature of the exothermicreaction is higher than the reversible temperature, themagnitude of the work term is larger than the changein exergy for the process, thus implying that work mustbe externally supplied in order to meet the workrequirements for the process.

3.2.3. Discussion. Sections 3.2.1 and 3.2.2 discussedhow the work required/ released by a reaction is relatedto the heat of the reaction. Of particular importance isthe relationship between the minimum (or maximum)

work and the heat of the reaction as given by eqs 12(endothermic reaction) and 16 (exothermic reaction).One is able to get an indication of the temperature atwhich the reaction should be carried out in order toreduce irreversibilities. It should be noticed that theheat and work requirements can be matched only incases when ∆G(To,Po) is less than ∆H because

For example, reaction 3 has ∆G(To,Po) > ∆H, and thusthere is no value that satisfies the above relation.Therefore, it is not possible to match the heat and workrequirements in terms of a heat pump for this reactionby carrying out this reaction in a single stage.

One way of matching the work and heat requirementsis by staging the reaction, i.e., carrying out the processin two stages. The first stage is endothermic andnonspontaneous (reaction 3a) with ∆Gendo(To,Po) <∆Hendo, whereas the second stage is exothermic andspontaneous (reaction 3b) with ∆Gexo(To,Po) < ∆Hexo.Therefore, it is possible to match the heat and workrequirements in the two-stage process. An extension ofthe analysis performed in sections 3.2.1 and 3.2.2 shouldbe able to reveal information about the operatingtemperatures when the overall two-stage process isreversible, thereby matching the work and heat require-ments.

3.2.4. Two-Stage Process. In sections 3.2.1 and3.2.2, reactions 3a and 3b were considered in isolation.Now consider the two reactions of the system shown inFigure 8 as a black-box system.

Applying the exergy balance (eq 6) to Figure 8 gives

Substituting for the availability (exergy) function usingeq 4 gives

It can be noted that ∆H31 ) ∆H32 + ∆H21, that QH )∆H21, and that QC ) ∆H32. Substituting these relation-ships into eq 18 gives

It is clear from eq 19 that the irreversibility of theoverall process depends on the temperature of both theendothermic and exothermic reactors. Therefore, to

Figure 6. Exothermic reactor in terms of a heat engine.

Figure 7. Work obtained from reaction 2b as a function oftemperature.

∆B ) ∆G(To,Po) ) W ) QC(1 -To

TC*) )

∆Hexo(1 -To

TC*) (16)

TC* ) ∆Hexo/∆Sexo (17)

Figure 8. Schematic diagram of the two-stage process.

∆G(To,Po)∆Hrxn

) [1 -To

TH] e 1

Ioverall ) (nB)1 - (nB)3 + QH(1 -To

TH) + QC(1 -

To

TC)

Ioverall ) -(∆H31 - To∆S31) + QH(1 -To

TH) +

QC(1 -To

TC) (18)

Ioverall ) To[∆S31 - (∆H21

TH+

∆H32

TC)] (19)


reduce the irreversibility of the entire process, one needsto carefully decide on the temperature of the tworeactors simultaneously.

It must be noted that, if no additional work is addedto the process, Ioverall must be either equal to or greaterthan zero because of the second law. A “negativeirreversibility” would imply that external work has tobe supplied to such a process in order to meet the workrequirements.

For the overall process to be reversible, assuming noexternal work is added to the process, the irreversibilityterm (Ioverall) must be equal to zero. Putting Ioverall ) 0in eq 19 gives

Equation 20 is an interesting result that reveals thatfor a reversible overall process there is a specificrelationship between the temperatures of the two reac-tors. The implications of this result will be discussedextensively later.

The above equation could also be attained by consid-ering the process as a combination of Carnot engines:the endothermic reaction as a heat pump and theexothermic reaction as a heat engine. This is depictedin Figure 9.

One is able to integrate the work flows between theendothermic and exothermic reactors. Because theoverall process has a positive ∆G, the overall balancestill requires work to be input into the process, shownin Figure 9 as Wnet.

The net work, Wnet, is given as the sum of Win andWout, where Win and Wout are given by eqs 8 and 13,respectively. Therefore, Wnet equals

For a reversible process, the net work, Wnet, must beequal to the change in the exergy change of the overallprocess, i.e., ∆B31 [or ∆G31(To,Po)]. Rearranging leadsto eq 20. If the net work, Wnet, is equal to the exergychange [∆G31(To,Po)], the process is defined as being workintegrated.

Consider a plot of the endothermic reactor tempera-ture against the exothermic reactor temperature, asshown in Figure 10. One can plot the reversible tem-perature of the endothermic and exothermic reactors inorder to classify the work flows for the endothermic andexothermic reactors.

Figure 10 shows the point where both reactors arerun reversibly in isolation and operate at the reversibletemperature, TH* (for the endothermic reaction 3a)defined in section 3.2.1 and TC* (for the exothermicreaction 3b) defined in section 3.2.2. The reversibletemperatures of the two reactions (TH* and TC*) dividethe plot into four regions labeled A-D in Figure 10:

(i) In region A, additional work is required for reaction3a (endothermic reaction) because the temperatures areless than TH*, meaning that the work supplied is lessthan the exergy change for the process, ∆Gendo(To,Po).Additional work is also required in region A for reaction3b (exothermic reaction) because the temperatures aregreater than the exothermic reversible temperature,TC*. Thus, the work obtained from the reaction isgreater than the exergy change for the process, ∆Gexo-(To,Po).

(ii) In region B, work can be potentially produced/lostfrom reaction 3a (endothermic reaction) because thetemperature is greater than TH* because the work putin at these temperatures is less than the exergy changefor the process, ∆Gendo(To,Po). Reaction 3b (exothermicreaction) requires extra work in region B because thetemperatures are above TC*.

(iii) Region C is the region where reaction 3a requiresadditional work because the temperature is less thanTH* and reaction 3b loses work because the temperatureis less than TC*.

(iv) In region D, work is lost by reaction 3a becausethe temperature is greater than TH* and reaction 3balso loses work because the temperature is less thanTC*.

Regions B and C are the two regions in which thereis a possibility of work integrating the process becausethese are the regions where one reactor/process loseswork while the other reactor/process requires work. Inregion A, both reactors/processes require work input,and in region D, both reactors/processes lose work; thus,there is no opportunity for work integration.

Assuming that the enthalpy and entropy changes ofreactions do not vary considerably with temperature,

Figure 9. Two-stage process in terms of Carnot engines.

∆S31 )∆H21

TH+

∆H32

TC(20)

Wnet ) Win + Wout ) ∆H21(1 -To

TH) + ∆H32(1 -

To

TC)

(21)

Figure 10. Endothermic and exothermic reversible temperatures.


the relationship between the temperatures of the tworeactors (i.e., reactions 3a and 3b) as given by eq 20 canbe plotted and is shown in Figure 11.

Figure 11 shows how the endothermic reactor tem-perature, TH, is related to the exothermic reactortemperature, TC, for the overall process to be reversibleand thus for a minimum work input. It is clear thatconsidering the two reactors together as a system allowsan entire curve of temperatures of the endothermic andexothermic reactors to be defined instead of just a singlepoint where the overall process would be reversible.Above the curve, the irreversibility is “negative”. Thismeans that the net work to the process is less than theexergy change for the process (i.e., the minimum workrequired for the process), and therefore external workhas to be supplied to the process. In the region belowthe curve, the irreversibility is positive, signifying thatthe net work to the process is greater than the exergychange for the process. Therefore, there is a loss ofexergy to the surroundings, or work can be produced inthis region.

Overlapping Figures 10 and 11, as shown in Figure12, gives more insight into the two stages of the process.It is clear that the work-integrated curve falls in regionsB and C. Regions B and C can be divided even further

into regions B1, B2, C1, and C2, as shown in Figure 12.Region B1 corresponds to the region where additionalwork must be added to reaction 3b (exothermic reaction)because region B1 lies above the reversible curve.Region B2 is the region where reaction 3a (endothermicreaction) will produce/lose work because the region liesbelow the reversible curve. In region C1, additional workmust be added to reaction 3a (endothermic reactions),while in region C2, work can be produced/lost fromreaction 3b (exothermic reaction).

Figure 12 informs one of the work requirements toeach stage of the process and is thus useful for analyzingprocesses. One can determine which stage requires workand which stage loses work and whether the overallprocess still requires extra work or not. One can alsoquantify the amount of work to be supplied to each stageas well as the work produced/lost in each stage.

An alternative view is to plot the irreversibility of thetwo reactors as a function of temperature, as shown inFigure 13.

Figure 13 shows the irreversibility of the two reactorsin isolation as a function of the temperature of thereactor. The temperature at which the irreversibilityequals zero was defined as the reversible temperature,T*. Running the two reactors at these temperaturescorresponds to the point shown on the two-stage revers-ible curve in Figure 11. It can also be seen from Figure13 that, for the exothermic reactor, the irreversibilityis initially positive but becomes “negative” at highertemperatures. The endothermic reactor works in re-verse; i.e., at low temperatures the irreversibility of theendothermic reactor is “negative” but becomes positiveat higher temperatures. Therefore, by choosing thetemperatures of the two reactors in such a way that theirreversibility of the one reactor is positive and the othernegative (or vice versa), one can find many sets oftemperatures that allow the overall process to bereversible. This allows for the loss of availability in oneof the reactors, yet the overall process remains revers-ible. Figure 13 also allows one to recognize the fourregions classified in Figure 10 in terms of the irrevers-ibility.

Commercial processes are limited by the temperatureat which the reformers are run (requires high temper-atures for a reasonable conversion to be achieved) aswell as the catalyst properties of the methanol synthesisstep (catalysts usually operate between a temperaturerange of 500 and 550 K). It can thus be seen from Figure12 that commercial methanol synthesis processes fall

Figure 11. Reversible work-integrated curve as a function of theexothermic and endothermic temperatures.

Figure 12. Relationship between the temperatures of the reactorsin the two-stage reversible process.

Figure 13. Irreversibility of the endothermic and exothermicreactors.


in the region of “negative irreversibility”, thus implyingthat work needs to be added. Commercial processesoperate in region B, i.e., the region in which reaction3a (similar to steam reforming) loses work whereasreaction 3b (methanol synthesis reaction) requires extrawork.

Equation 21 can be used to calculate the workrequirement, which can be plotted as contours of iso-work (whether work is input or produced/lost) curvesalso shown in Figure 14. Figure 14 also shows thereversible curve where the required minimum workinput, which is equal to ∆G(To,Po) for the overall process,is met by the heat flows. Below the curve, the quantityof work is greater than that of ∆G(To,Po), meaning thatwork is produced or lost, whereas above the curve, thequantity of work is less than the value of ∆G(To,Po);therefore, external work is required.

If one regards the extra work input as an increase inthe operating costs, one can see that by changing thetemperatures of either the endothermic or exothermicreactor one can reduce the operating cost in currentplants.

It can also be noticed from Figure 14 that reducingthe temperature of the methanol synthesis would resultin the reduction of external work required to be suppliedand therefore a reduction in the operating costs. Anincrease in the temperature of the reformer would alsoreduce the amount of external work required.

It can also be noticed that small changes in theendothermic reactor temperature have a much largereffect on the work required than changes in the tem-perature of the exothermic reactor, especially at highertemperatures. Therefore, the temperature of the endo-thermic reactor should be kept as low as possiblebecause the operating costs in terms of work require-ments are very sensitive to this.

4. Practical Applications

The technique described allows one to classify existingprocesses into one of three categories based on theiroperating temperatures:

(i) Processes That Lie on the Reversible Work-Integrated Curve. Processes lying on the reversiblecurve are work-integrated, do not require further work,and do not reject work. When stages 1 and 2 operate atTH* and TC*, respectively, each individual stage is

reversible. At other temperatures (i.e., TH* > TH > TH*and TC* > TC > TC*), each stage would require pumpingheat from one stage to the other stage, depending onwhere the operating temperature lies in relation to TH*and TC*.

(ii) Processes That Lie above the ReversibleWork-Integrated Curve, i.e., Processes That RequireExternal Work. The external work can be supplied byconsidering other unit operations such as separationand compression. This will be considered in a followingpaper.

(iii) Processes That Lie below the ReversibleWork-Integrated Curve, i.e., Processes That AreAssociated with Lost Work.

The authors believe that when designing a process,the designer should aim to operate processes as closeto the reversible curve as possible.

Processes of particular interest are those that liebelow the reversible curve. These processes equivalentlyreject work to the surroundings. Because the point ofmost chemical processes is not to produce work, this isnot an effective region to operate in. There is thus aneed to determine ways to shift such processes closerto the reversible curve. Possible ways of achieving thisare (1) changing the temperature at which the processoperates, which is difficult because the temperaturerange is usually limited by physical constraints, (2)using work pumps, and (3) changing the chemistry (i.e.,the reaction involved) of the process such that the ∆G,∆H, and temperature can be matched. These are beinginvestigated by the authors for industrial processes ofinterest.

5. Conclusions

This paper attempts to understand the implicationsof a reaction having a positive change in the Gibbsenergy of reaction. One of the ways of overcoming thispositive change in the Gibbs energy of reaction, stagingthe reaction, was investigated using the “Solvay tech-nique” as well as a second law analysis. A two-stagereaction process for the production of methanol wasconsidered.

Initially, a exergy law analysis of each reactor wasperformed separately, allowing one to find the reversibletemperature, i.e., the temperature at which thermody-namic efficiency is the greatest. The analysis was thenextended to include both reactors. This allows one todefine a reversible curve, i.e., a set of temperatures ofboth reactors that maximizes the efficiency. Regions ofpositive and “negative” irreversibility were also deter-mined. The reversible curve is useful in deciding on thetemperatures of the two reactors. However, because ofnonthermodynamic constraints, such as catalyst limita-tions, the curve is limited in its use. However, byconsidering other ways of putting in work, one is ableto “move” into the regions of negative irreversibility. Thetwo-stage process was also modeled in terms of heatengines, resulting in the same conclusions as the secondlaw analysis.

The tools described in this paper are quite usefulduring the early stage of the design process. The methodallows one to analyze the work flows in the process,thereby giving insight into the work requirements forthe process. It also helps identify opportunities and settargets for the process. The method does not requiredetailed information regarding the process and is basedonly on thermodynamic properties of the system, there-

Figure 14. Net work input or output required by the process asa function of the endothermic and exothermic reactor tempera-tures.


fore allowing process integration to be considered at the“black-box” level.

The technique can be applied to various processes, aswill be discussed in a following paper.

Acknowledgment

The authors are grateful for the support received fromthe National Research Foundation (NRF), the AndrewW. Mellon Foundation, and Sasol.

Literature Cited

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(3) Linhoff, B.; Turner, J. A. Simple Concepts in Processsynthesis give Energy savings and elegant Designs. Chem. Eng.1980, Oct, 621-624.

(4) Shinnar, R. Thermodynamic Analysis in Chemical Processesand Reactor Design. Chem. Eng. Sci. 1988, 43 (8), 2303-2318.

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(6) Riekert, L. The Efficiency of Energy-Utilization in ChemicalProcesses. Chem. Eng. Sci. 1974, 29, 1613-1620.

(7) Glavic, P.; Kravanja, Z.; Hiomsak, M. Modeling of Reactorsfor Process Heat Intgeration. Comput. Chem. Eng. 1988, 12 (2/3),189-194.

(8) De Ruyck, J. Composite Curve Theory with Inclusion ofChemical Reactions. Energy Convers. Manage. 1998, 39 (16-18),1729-1734.

(9) Hinderdrink, A. P.; et al. Exergy Analysis with a Flow-sheeting SimulatorsII. Application; Syntheis Gas Production fromNatural Gas. Chem. Eng. Sci. 1996, 51 (20), 4701-4715.

(10) Leites, I. L.; Sama, D. A.; Lior, N. The theory and practiceof energy saving in the chemical industry: some methods forreducing thermodynamic irreversibility in chemical technologyprocesses. Energy 2003, 28, 55-97.

(11) Resnick, W. Process Analysis and Design for ChemicalEngineers; McGraw-Hill: New York, 1981.

(12) May, D.; Rudd, D. Development of Solvay Clusters ofChemical Reactions. Chem. Eng. Sci. 1976, 31, 59-69.

(13) Kotas, T. J. The Exergy Method of Thermal Plant Analysis;Butterworth: London, 1985.

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Received for review December 15, 2004Revised manuscript received February 24, 2005

Accepted February 28, 2005

IE048787F


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Thermodynamics Analysis of Processes. 1. Implications of Work Integration