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PROCESS DESIGN AND CONTROL

Heat and Power Integration of Methane Reforming Based Hydrogen

Production

Alberto Posada and Vasilios Manousiouthakis*

Chemical Engineering Department, University of California, Los Angeles, California 90095

Heat and power integration studies are carried out for a conventional methane reforming basedhydrogen production plant by formulating and solving the minimum hot/cold/electric utility costproblem for the associated heat exchange network. The formulation of the problem allows forthe optimal integration of heat exchangers, heat engines, and heat pumps, and its solution showsa utility profit due to electricity production in excess of process needs. Heat integration alone(pinch analysis) results in a 36% reduction in utility costs with respect to a conventional (albeitnonoptimized) process.

1. Introduction

Hydrogen is receiving ever increasing attention by thegovernment and industry1 as an environmentally at-tractive and clean fuel, because its oxidation leads onlyto water formation. There is an abundance of hydrogenin nature, although it is only available for exploitationin a combined state, in either water, hydrocarbons, orcoal.2 Its recovery from these natural resources requiresthe addition of energy.3 The most common industrialprocess for the production of hydrogen from methaneis steam reforming,2-4 which involves the incompleteendothermic transformation of methane and water tohydrogen, carbon dioxide, and carbon monoxide. Opti-mization of the use of energy in this process can lead toreduction of the cost of the production of hydrogen and,therefore, to faster development of the hydrogen

economy.1

Tindall and King5

have summarized impor-tant factors to keep in mind when designing steamreformers for hydrogen production that include recover-ing heat from the hot flue gas by preheating thereformer feed and the generation of steam by extractingheat from the reformer outlet process gas. Scholz2

considers a process block diagram with a unit that hecalls the steam/energy system where heat from the fluegas and from the reformed and converted product gasis used for the generation of steam and heating of thefeed gas, water, and combustion air. Shahani et al.6 havesuggested alternative design features that include thefollowing: operating hydrogen plants as a source ofsteam (from waste heat recovery) apart from theirprimary purpose of producing hydrogen on the basis

that, up to a point, a steam reformer has the ability toproduce steam more efficiently than a conventionalboiler and also generating electricity for export fromthe steam produced. Rajesh et al.7,8 have presented anintegrated approach to obtain possible sets of steady-state operating conditions for improved performance ofan existing plant, using an adaptation of a genetic

algorithm that seeks simultaneous maximization ofproduct hydrogen and export steam flow rates. Here,

we carry out heat and power integration studies for aconventional methane reforming based hydrogen pro-duction plant with the purpose of finding the minimumhot/cold/electric utility cost.

2. Process Description

A conventional methane reforming based hydrogenproduction plant can be represented with the blockdiagram in Figure 1.4,8-10 Hot methane and steam arefed to the steam methane reformer (SMR) where thereversible reactions r1, r2, and r3 take place:

The kinetics of these reactions on a Ni/MgAl2O4catalyst have been studied by Xu and Froment.11 Theoverall reactor operation requires that heat be providedto the reformer, and this is done through the combustionof methane (fuel) and pressure swing adsorption (PSA)waste gas. Hydrogen is produced together with all theother species, and its generation is further increasedin the water gas shift (WGS) reactor(s) where only theexothermic reaction r2 is catalyzed at temperatureslower than that of the reformer. Keiski et al.12 studiedthe kinetics for the high-temperature water gas shift

reaction on an Fe3O4-Cr2O3 catalyst for temperaturesaround 600 K, and Rase13 proposed a kinetic model forthe low-temperature water gas shift reaction on acopper-zinc oxide catalyst for temperatures below 560K. Most of the water is separated by condensation asthe gas stream is cooled to almost ambient temperaturesbefore entering the PSA unit where hydrogen can bepurified to 99.999+%.14,15 Species other than hydrogenare selectively adsorbed on a solid adsorbent (e.g.,activated carbon, 5A zeolite15) at a relatively highpressure by contacting the gas with the solid in a packedcolumn in order to produce a hydrogen enriched gas

Part of this work was first presented in Session 22 at theAIChE 2004 Annual Meeting, paper 22f.

* To whom correspondence should be addressed. Tel.: +1-310-206-0300. Fax: +1-310-206-4107. E-mail: [email protected].

CH4 + H2O ) CO + 3H2 (r1) H1: 206.1 kJ/mol

CO + H2O ) CO2 + H2 (r2)

H2: -41.15 kJ/molCH4 + 2H2O ) CO2 + 4H2 (r3) H3: 164.9 kJ/mol

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stream. The adsorbed species are then desorbed fromthe solid by lowering the pressure and purging withhigh-purity product hydrogen, and thus, the PSA wastegas is generated. Continuous flow of product is main-tained by using multiple, properly synchronized adsorp-

tion beds. Combustion of the PSA waste gas andmethane (fuel) is used to provide heat for the reformerand also for the preheating of feeds and the generationof the export steam. Recovery of the waste heat fromthe still-hot gases leaving the reformer is also used tothe same end.2,5,6

A computer simulation of a high-pressure hydrogenproduction flow sheet, that uses conventional reforming,shifting, and PSA technologies, is described in section3. Application of intuitive heat recovery to the simulatedflow sheet results in a heat exchange network like theone shown in Figure 2.

3. Process Simulation

The process has been simulated using AspenTechsprocess engineering software HYSYS version 3.1.16 PengRobinsons equation of state was used as the thermo-dynamic fluid package for this simulation, based onAspenTechs recommendation of this package for high-hydrogen-content systems and after ensuring that theprocess conditions are within the packages temperatureand pressure applicability ranges.17

A process flow diagram of the simulation done inHYSYS is presented in Figure 3. The process feed con-sists of liquid water and methane gas at ambient tem-perature. Each stream is compressed to 25.7 atm andheated to 811 K, corresponding to values within typicalentrance conditions for the reformer,5,6,8-10,18 in additionto a steam/CH4 molar ratio of 3.12; excess steam is used

to reduce byproduct carbon formation.4,5,8 Reactions r1,r2, and r3 take place in the reformer, simulated as a plugflow reactor (PFR) with the kinetic models proposed byXu and Froment11 (see Appendix A), producing a gaswith 46% (molar) H2, which is close to the value of 48%

(see Figure 1) considered by Hufton et al.10

Heat, in theamount of 233.67 kJ/s, is provided to the reformer, sinceit is required by the endothermic reactions r1 and r3 andin order to increase the temperature of the reactinggases and maintain a high reaction rate. The PFR isapproximated in HYSYS through a series of continuousstirred tank reactors (CSTRs): 20 were considered inthis study. A high-temperature water gas shift reactor(HT WGS) is used to raise the concentration of hydrogento 52.8%, and a low-temperature water gas shift reactor(LT WGS) provides an additional 1% increase in thehydrogen content. Only the exothermic reaction r2 takesplace in these last two reactors, which are simulatedas adiabatic PFRs using the kinetic models proposedby Keiski et al.12 and Rase,13 respectively (see Appendix

A). Coolers are used before these two reactors in orderto adjust the temperature of the gases to appropriatevalues for the proper operation of the catalysts.4,12,13

Hydrogen purification starts with the condensationand flash separation of liquid water by cooling the gasesand is finalized in the PSA unit with adsorption of themajority of the remaining contaminant gases. The PSAprocess is approximately isothermal and does not re-quire any significant heat load. Thus, for the purposesof this heat/power integration study, it can be modeledas a component splitter. Exit compositions for this com-ponent splitter were assigned based on typical PSA per-formance reported in the literature,9,10 resulting in theproduction of 20.98 kg/h of a gas stream with 99.8% H2

Figure 1. Conventional process for methane reforming based hydrogen production.

Figure 2. Simple heat recovery applied to the conventional process for methane reforming based hydrogen production. CU: cold utility.W: electric utility or work.

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at 21 atm. The simulated PSA waste gas contains 16%CH4 and 26% H2, and its adiabatic combustion with 110%air (10% excess over the stoichiometric requirement)generates combustion gases at 1868 K. In this study,

these gases are cooled to 313 K before emission, allowingfor 311.02 kJ/s of heat exchange. Conventionally, thesegases are cooled to around 422 K;10 most of their thermalenergy is used to provide heat to the reformer and thesteam boiler,2,5,8-10 but in this study, no constraint is im-posed regarding the matching of streams for heat ex-change, with the purpose of having total freedom in thecalculation of the minimum hot/cold/electric utility cost.

The hydrogen produced from the PSA unit is com-pressed in three stages up to 300 atm, which is withinthe typical storage pressure for hydrogen poweredvehicles and related hydrogen fueling stations. Consid-ering compressors with 85% adiabatic efficiency, thetotal work required for the compression of hydrogen is26.7 kJ/s and the energy removed by cooling betweenstages adds up to 26.01 kJ/s.

4. Formulation of the Optimization Problem

The approach proposed by Holiastos and Manousiou-thakis19 for the calculation of the minimum hot/cold/elec-tric utility cost for heat exchange networks is employedfor the heat/power integration of the above methane re-forming based hydrogen production process. The prob-lem statement is the following:19 given a set of processstreams with specified flow rates, inlet temperatures,and fixed outlet target temperatures; hot and cold utilitystreams with known temperatures and unit costs; andan electrical (work) utility with known unit cost, iden-tify, among all possible heat exchange/pump/engine

networks, the minimum total (hot/cold/electric) utilitycost necessary to accomplish the desired thermal tasks.

For the application at hand, the set of process streamsis defined by the material streams in the process flowdiagram of Figure 3; the specifications of the hot, cold,and electric utilities considered available are defined inTable 1. Methane combustion gas is considered as thehot utility available, whose inlet temperature, Tin

HU)

2168 K, is calculated as its adiabatic flame temperaturefor 110% combustion air and whose outlet temperature,Tout

HU) 313 K, is estimated for emission. Cooling water

with inlet temperature TinCU

) 298 K is the cold utility,which is allowed a 10-deg increase prior to emission,following heat exchange. This consideration of utilities

with varying temperatures requires the formulation ofan optimization problem slightly different than the onesolved by Holiastos and Manousiouthakis for utilitieswith constant temperatures,19 and it is presented below

(hot and cold utilities not allowed to be used for work):

subject to the following constraints:

Nomenclature is provided at the end of the paper. Thehot temperature scale (TH) is defined for hot streams,such that TH ) T - Tmin,H, and the cold temperaturescale (TC) is similarly defined for cold streams, with TC

) T + Tmin,C; thus, the resulting minimum approachtemperature (Tmin) for heat exchange between hot andcold streams is Tmin ) Tmin,H + Tmin,C. The objective

Figure 3. Process flow diagram of HYSYS simulation for methane steam reforming based production of high-pressure hydrogen. Themagnitudes of energy flows are shown as positive (+) for heating or work done on the fluid and as negative ( -) for cooling.

mini,i,i,FHU,FCU

cHUFHU + cCUFCU + cW(i)1

n

(Fcp)C,i(TiC

-

Ti+1C )(1 - i) -

i)1

n

(Fcp)H,i(TiH

- Ti+1H )(1 - i)) (1)

i + [(Fcp)H,ii + FHUcp,HURi](TiH

- Ti+1H ) - i+1 -

[(Fcp)C,ii + FCUcp,CUi](TiC

- Ti+1C ) ) 0

i [1, n] (2)

i)1

n

(Fcp)H,i(1 - i) ln(TiH

Ti+1H ) -i)1

n

(Fcp)C,i(1 - i) ln(Ti

C

Ti+1C ) ) 0 (3)

i g 0 i [2, n] (4)

1 ) n+1 ) 0 (5)

0 e i e 1 i [1, n] (6)

0 e i e 1 i [1, n] (7)

Ri )

{0 ifTi

He T

out

HU- T

min,H

i [1, n]

1 if TiH

> ToutHU

- Tmin,H(8)

i ) {0 if Ti+1Cg Tout

CU+ Tmin,C i [1, n]

1 if Ti+1C

< ToutCU

+ Tmin,C(9)

FHU, FCU g 0 (10)

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function (1) is the sum of the costs of hot, cold, andelectrical utilities. Equation 2 represents the energybalance in the heat exchanger (HE) subnetwork for eachtemperature interval. The HE subnetwork is built withheat exchangers; fractions i and i of the enthalpiesfrom the hot and cold composite curves in interval i,respectively, are used in this subnetwork. The respectivecomplementary fractions (1 - i) and (1 - i) are usedin the heat engine and pump (HEP) subnetwork, whichis built with reversible heat engines and heat pumps.Equation 3 is the overall entropy balance for the HEPsubnetwork. The second law of thermodynamics isexpressed in the HE subnetwork by the fact that theavailable heat at each interval, i, should be nonnega-tive (constraint 4). The overall enthalpy balance in theHE subnetwork is ensured by constraint 5. The solution

to the formulated problem provides results for the heatand power integration of the process. The heat integra-tion only (no power) or pinch analysis20 can be done byconsidering only the HE subnetwork, i.e., by settingi) 1 and i ) 1 in constraints 6 and 7, respectively.

5. Results and Discussion

The optimization problem is solved using the linearprogramming software MINOS 5.5.21 The calculatedminimum utility cost (MUC), expressed per kilogramof hydrogen produced, is included in the bottom row ofTable 2, where complete results are summarized. Thevalues in the first column of Table 2 correspond tosimple heat recovery (no optimization) applied to oursimulated process, as shown in Figure 2. This design ishere referred to as a conventional process because itdoes not involve our proposed heat exchange optimiza-tion. The second column corresponds to the results afterheat (no power) integration of the process, and the thirdcolumn corresponds to the results after heat and powerintegration. The utility cost of the conventional processis 19 cents/kg of H2, and a 36% reduction is achievedafter heat integration; a small utility profit can evenbe generated after heat and power integration due toelectricity produced in excess of process needs. Ofcourse, it should be emphasized that these savings arein comparison to a conventional process whose heatintegration characteristics may have been surpassed byproprietary industrial designs.

The temperature-enthalpy diagram of a HE networkfeaturing minimum hot/cold utility cost, obtained afterheat integration of the process, is presented in Figure 4.The solid line corresponds to the hot composite curve, andthe dotted line represents the cold composite curve. Theminimum approach temperature considered here is Tmin) 10 K, being the smallest temperature difference thattwo streams leaving or entering a heat exchanger canhave. It is attained at the pinch temperature of 500 K.This value corresponds to the saturation temperatureof steam at the process operating pressure (25.7 atm).The use of the cold utility of 140.88 kJ/s is representedby almost the complete percentage of the enthalpy change

of the section of the cold composite curve between 298and 308 K. (It looks approximately horizontal in Figure4 due to the scale of the plot. It also represents a smallenthalpy change due to heating of raw materials be-tween these temperatures.) The cold utility requirementcan be reduced if a higher combustion gas emission tem-perature is used, i.e., above 313 K; for instance, a tem-perature of 422 K results in a total cold utility need of100.08 kJ/s and, thus, an additional cost reduction of 1cent/kg of H2. The hot utility is not required if heat inte-gration is accomplished, which means that there is noneed to burn additional methane to generate heat forthe reformer, as is usually done in the conventional pro-cess. This brings not only a 36% reduction in utility costbut also a 6.5% reduction in carbon dioxide emission.

The temperature-enthalpy diagram of the HE sub-network of a network featuring minimum hot/cold/electric utility cost, obtained after heat and powerintegration of the process, is presented in Figure 5. ThisHE subnetwork does not use any cold process streamsand contains only hot process streams with tempera-tures below 398 K, resulting in a reduction of the needfor the cold utility with respect to that of the HEnetwork in Figure 4. The hot process streams withtemperatures above 398 K are used in the HEP sub-network, whose temperature-enthalpy diagram is shownin Figure 6. There is a combined use of the hot compositecurve in the interval 388-398 K between the twosubnetworks (i ) 0.1125). In the HEP subnetwork, heat

Table 1. Utilities Specification

utilitya Tin (K) Tout (K) cp,avgb (kJ/(kg K)) cost ($/kg) cost ($/kJ)

HU: CH4 combustion gas 2168 313 1.44 1.724 10-2 c 6.45 10-6

CU: cooling water 298 308 4.31 8 10-5 d 1.85 10-6

W: electricity 1.25 10-5 e

a HU: hot utility. CU: cold utility. W: electric utility or work. b Average mass heat capacity. c Calculated from a cost of 0.3422 $/kg forCH4. The cost of CH4 is estimated to be energetically equivalent to the cost of natural gas (0.3299 $/kg24). d Reference 25. e Reference 24.

Table 2. Heat and Power Integration Results

resource usea conventionalprocess heatintegration heat and powerintegration

CH4 (kg/kg of H2) 3.05 2.84 2.84CO2 (kg/kg of H2) 8.25 7.71 7.71HU (kJ/g of H2) 10.7 0 0CU (kJ/g of H2) 22.3 24.2 15.1W(kJ/g of H2) 6.2 6.2 -3.0MUC ($/kg of H2) 0.19 0.12 -0.01

a CH4: methane consumed as raw material and hot utility. CO2:carbon dioxide generated from combustion of methane and PSAwaste. HU: hot utility consumed. CU: cold utility consumed. W:electricity consumed (negative if produced). MUC: minimumutility cost.

Figure 4. Temperature-enthalpy diagram of a HE networkfeaturing the minimum hot/cold utility cost for the methanereforming based hydrogen production process. Tmin ) 10 K.


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from the hot process streams is transferred only to the

working fluid in heat engines/pumps, with a minimumapproach temperatureTmin ,H ) 5 K, and heat from theworking fluid is transferred to cold process streams witha minimum approach temperature Tmin,C ) 5 K.

The difference in the enthalpy change of the hotcomposite curve with respect to that of the cold com-posite curve in Figure 6 is the net work produced bythe HEP subnetwork (-Ws ) 53.72 kJ/s). If it isassumed that 100% of this work is converted intoelectricity, the amount of electricity generated is inexcess of the process needs (36.24 kJ/s), and if thisexcess is sold, a small utility profit of 1 cent/kg of H2 isgenerated after covering the cost of the cold utility. Thehot utility is again not needed after heat and powerintegration, suggesting that the production of a largequantity of export steam (10-12 tons of steam/ton ofH222), from conventional hydrogen plants, could be seenas the result of unnecessary combustion of additionalmethane (fuel) and as the lack of a need for pressuriza-tion of the hydrogen product to 300 atm.

The HEP subnetwork is composed of both heatengines and heat pumps, whose corresponding sectionscan be visualized in the temperature-entropy diagramof Figure 7. Those sections where the hot curve is abovethe cold require a heat engine, while those where thecold is above the hot require a heat pump. The largeheat engine section on the right side of Figure 7 (at thehighest temperatures) is a clear example of the existingopportunity for power generation when heat is to be

exchanged between streams with a large temperaturedifference, as happens here between the PSA waste gasand the reacting gases in the reformer (see Figure 4).The optimal operation of the HEP subnetwork, as

described in Figure 7, presumes the existence of aworking fluid that can circulate (in a heat engine/pump)between the hot scale temperature of the hot processstream and the cold scale temperature of the coldprocess stream and with the same heat capacity rate(Fcp) of the process stream with which the working fluidexchanges heat; it also considers that the adiabaticprocesses undergone by the working fluid are reversible,which finally leads to the overall entropy balance SC) -SH, as illustrated in Figure 7. SC and SH arecalculated using the cold and hot temperature scales (eq3), respectively, and are, thus, equivalent to the overallentropy changes of the working fluids as they exchangeheat with the cold and hot streams, respectively.

6. Conclusions

Heat and power integration studies have been carriedout for a conventional methane reforming based hydro-gen production plant with a capacity of 20.98 kg of H2/h. Heat and power integration results in utility profitdue to electricity production in excess of process needs.Heat integration alone results in a 36% reduction inutility cost. Operation at the minimum hot/cold or hot/cold/electric utility cost does not require a hot utility(methane (fuel)), with a consequent reduction of carbondioxide emissions of 6.5%.

Although this work does not consider capital cost,arguments that apply to pinch analysis23 also apply

here:19 a well-designed process that results from ap-plication of the technique will certainly feature lowerenergy demands, that may, however, necessitate largercapital expenditures, in the form of additional heattransfer and/or power compression/expansion equip-ment. Designs can be pursued based on vertical match-ing of streams in the T-S and T-H diagrams,analogous to the pinch analysis method for the designof heat exchange networks. The trade-off among utilityand capital costs can then be quantified by analyzingthe dependence of these costs on the minimum approachtemperature (Tmin). Quantifying this capital/utility costtrade-off for the considered plant will be the subject ofour future research.

Figure 5. Temperature-enthalpy diagram of the HE subnetworkof a network featuring the minimum hot/cold/electric utility costfor the methane reforming based hydrogen production process.Tmin ) 10 K.

Figure 6. Temperature-enthalpy diagram of the HEP subnet-work of a network featuring the minimum hot/cold/electric utilitycost for the methane reforming based hydrogen production process.Tmin,C ) Tmin,H ) 5 K. The work produced (-Ws) is 53.72 kJ/s.

Figure 7. Temperature-entropy diagram of the HEP subnetworkof a network featuring the minimum hot/cold/electric utility costfor the methane reforming based hydrogen production process.Tmin,C ) Tmin,H ) 5 K. The entropy changes are balanced: SC) -SH.


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Appendix A. Kinetic Models

A.1. Rate of Reactions r1, r2, a n d r3 in theReformer. The model proposed by Xu and Froment11

for reaction on a Ni/MgAl2O4 catalyst is as follows:

where

The rate coefficients and adsorption constants aregiven in Table A.1, and the reaction equilibrium con-stants, in Table A.2.

A.2. Rate of Reaction r2 in the HT WGS Reactor.

The model proposed by Keiski et al.12 for reaction onan Fe3O4-Cr2O3 catalyst is as follows:

where

A.3. Rate of Reaction r2 in the LT WGS Reactor.The model proposed by Rase13 for reaction on a copper-

zinc oxide catalyst is as follows:

where

Acknowledgment

The authors gratefully acknowledge the financialsupport of the National Science Foundation under GrantCTS 0301931.

Nomenclature

cCU ) cost coefficient of cold utility, $/kg

cHU ) cost coefficient of hot utility, $/kgcp ) mass heat capacity, kJ/(kg K)cW ) cost coefficient of electric utility, $/kJCk ) concentration of species k ) H2O, CO; mol/LCSTR ) continuous stirred tank reactorCU ) cold utilityDen ) denominator in reaction rate expressions

F ) mass flow, kg/sHE ) heat exchanger subnetworkHEP ) heat engine and pump subnetworkHU ) hot utilityHT WGS ) high-temperature water gas shift reactor

Keq ) equilibrium constant of reaction r2 for eq A.7Kj ) equilibrium constant of reaction rj, j ) 1, 2, 3. The

units are specified in Table A.2kj ) rate coefficient of reaction rj, j ) 1, 2, 3. The units are

specified in Table A.1kk ) adsorption constant of species k ) CH4, H2O, H2, CO.

The units are specified in Table A.1LT WGS ) low-temperature water gas shift reactorMUC ) minimum utility costPFR ) plug flow reactorPSA ) pressure swing adsorption

P ) pressure, atmPk ) partial pressure of species k ) CH4, H2O, H2, CO2,

CO; barSMR ) steam methane reformer

R ) universal gas constant, R ) 8.31451 10-3 kJ/(molK)

rj ) reaction j ) 1, 2, 3.rrj ) rate of reaction rj, j ) 1, 2, 3; kmol/(kgcat h)

T ) temperature, KTi

H) high temperature of interval i in the hot tempera-

ture scale, KTi+1

H) low temperature of interval i in the hot tempera-

ture scale, KW ) electricity (negative if produced) or work (negative if

work is done by the fluid)Ws ) work provided to the HEP subnetwork (negative if

work is produced)WGS ) water gas shift reactor(s)

yk ) mole fraction of species k ) H2O, H2, CO2, CO

Greek Letters

Ri ) variable indicative of the presence of the hot utilityin interval i

rr1 )k1

Den2(PCH4PH2O

PH22.5

-PH2

0.5PCO

K1 ) (A.1)

rr2 )k2

Den2(PCOPH2O

PH2- P

CO2

K2 ) (A.2)

rr3 )k3

Den2(PCH4

PH2O2

PH23.5

-PH2

0.5PCO2

K3 ) (A.3)

Den )

1 + kCOPCO + kH2PH2 + kCH4PCH4 + kH2O(PH2O

PH2) (A.4)

Table A1. Parameters of the Rate Coefficients andAdsorption Constants for Related Arrhenius or VantHoff Equationsa

rate coefficientor adsorption

constant

pre-exponential

factor

units ofpre-exponential

factor

activationenergy or

adsorptionenthalpy(kJ/mol)

k1 4.225 1015 kmol bar0.5/(kgcat h) 240.1k2 1.955 106 kmol/(kgcat h bar) 67.13k3 1.020 1015 kmol bar0.5/(kgcat h) 243.9

kCO* 8.23

10-5

bar-1

-70.65*kCH4* 6.65 10-4 bar-1 -38.28*

kH2O* 1.77 105 dimensionless 88.68*

kH2* 6.12 10-9 bar-1 -82.90*

a The asterisk symbol is placed with values corresponding toadsorption.

Table A2. Reaction Equilibrium Constants

equilibrium constant function ofT(K)

units ofequilibrium

constant

K1 exp(-26830/T + 30.114) bar2

K2 exp(4400/T - 4.036) dimensionlessK3 K1K2 bar2

rr2 ) 3600 exp(26.1) exp(-95 kJ/mol

RT )CCO1.1CH2O

0.53(1 - )

(A.5)

)1

K2(CCO2

CH2

CCOCH2O) (A.6)

rr2 )

exp(12.88 - 33401.8T)(yCOyH2O -yCO2

yH2

Keq) 1379Fb (A.7)

) {0.86 + 0.14P for Pe 24.8

4.33 for P > 24.8(A.8)

Keq ) exp(-4.72 + 86401.8T) (A.9)


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i ) variable indicative of the presence of the cold utilityin interval i

) reversibility factor of reaction r2 in the HT WGS reactori ) available heat at interval i, kJ/sTmin ) minimum approach temperature, KTmin,H ) difference between the real temperature and the

temperature in the hot temperature scale of the hotstreams, K

Tmin,C ) difference between the temperature in the coldtemperature scale and the real temperature of the cold

streams, KHj ) heat of reaction rj, j ) 1, 2, 3; kJ/molH ) enthalpy change, kJ/sS ) entropy change, kJ/(K s)i ) fraction of the hot composite stream from interval i

used in the HE (heat exchanger) subnetworki ) fraction of the cold composite stream from interval i

used in the HE (heat exchanger) subnetworkFb ) bulk density of copper-zinc oxide catalyst, lb/ft3; e.g.,

90 lb/ft3

) activity factor of copper-zinc oxide catalyst

Subscripts

C ) cold composite streamCU ) cold utilityH ) hot composite streamHU ) hot utilityi ) interval i for optimization problemin ) inlet temperaturen ) number of intervals for optimization problemout ) outlet temperatureW ) electric utility

Superscripts

C ) cold temperature scaleCU ) cold utilityH ) hot temperature scaleHU ) hot utility

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Received for review October 1, 2004Revised manuscript received August 29, 2005

Accepted August 31, 2005

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