Heat and Power Integration of Methane Reforming Based Hydrogen

2168 K, is calculated as its adiabatic flame temperature for 110% combustion air and whose outlet temperature,. Tout. HU ) 313 K, is estimated for emi...
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Ind. Eng. Chem. Res. 2005, 44, 9113-9119

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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 based hydrogen production plant by formulating and solving the minimum hot/cold/electric utility cost problem for the associated heat exchange network. The formulation of the problem allows for the optimal integration of heat exchangers, heat engines, and heat pumps, and its solution shows a 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 (albeit nonoptimized) process. 1. Introduction Hydrogen is receiving ever increasing attention by the government and industry1 as an environmentally attractive and clean fuel, because its oxidation leads only to water formation. There is an abundance of hydrogen in nature, although it is only available for exploitation in a combined state, in either water, hydrocarbons, or coal.2 Its recovery from these natural resources requires the addition of energy.3 The most common industrial process for the production of hydrogen from methane is steam reforming,2-4 which involves the incomplete endothermic transformation of methane and water to hydrogen, carbon dioxide, and carbon monoxide. Optimization of the use of energy in this process can lead to reduction of the cost of the production of hydrogen and, therefore, to faster development of the hydrogen economy.1 Tindall and King5 have summarized important factors to keep in mind when designing steam reformers for hydrogen production that include recovering heat from the hot flue gas by preheating the reformer feed and the generation of steam by extracting heat from the reformer outlet process gas. Scholz2 considers a process block diagram with a unit that he calls the steam/energy system where heat from the flue gas and from the reformed and converted product gas is used for the generation of steam and heating of the feed gas, water, and combustion air. Shahani et al.6 have suggested alternative design features that include the following: operating hydrogen plants as a source of steam (from waste heat recovery) apart from their primary purpose of producing hydrogen on the basis that, “up to a point, a steam reformer has the ability to produce steam more efficiently than a conventional boiler” and also generating electricity for export from the steam produced. Rajesh et al.7,8 have presented an integrated approach to obtain possible sets of steadystate operating conditions for improved performance of an existing plant, using an adaptation of a genetic † Part of this work was first presented in Session 22 at the AIChE 2004 Annual Meeting, paper 22f. * To whom correspondence should be addressed. Tel.: +1310-206-0300. Fax: +1-310-206-4107. E-mail: [email protected].

algorithm that seeks simultaneous maximization of product hydrogen and export steam flow rates. Here, we carry out heat and power integration studies for a conventional methane reforming based hydrogen production plant with the purpose of finding the minimum hot/cold/electric utility cost. 2. Process Description A conventional methane reforming based hydrogen production plant can be represented with the block diagram in Figure 1.4,8-10 Hot methane and steam are fed to the steam methane reformer (SMR) where the reversible reactions r1, r2, and r3 take place:

CH4 + H2O ) CO + 3H2 (r1) CO + H2O ) CO2 + H2 (r2)

∆H°1: 206.1 kJ/mol ∆H°2:-41.15 kJ/mol

CH4 + 2H2O ) CO2 + 4H2 (r3) ∆H°3: 164.9 kJ/mol The kinetics of these reactions on a Ni/MgAl2O4 catalyst have been studied by Xu and Froment.11 The overall reactor operation requires that heat be provided to the reformer, and this is done through the combustion of methane (fuel) and pressure swing adsorption (PSA) waste gas. Hydrogen is produced together with all the other species, and its generation is further increased in the water gas shift (WGS) reactor(s) where only the exothermic reaction r2 is catalyzed at temperatures lower than that of the reformer. Keiski et al.12 studied the kinetics for the high-temperature water gas shift reaction on an Fe3O4-Cr2O3 catalyst for temperatures around 600 K, and Rase13 proposed a kinetic model for the low-temperature water gas shift reaction on a copper-zinc oxide catalyst for temperatures below 560 K. Most of the water is separated by condensation as the gas stream is cooled to almost ambient temperatures before entering the PSA unit where hydrogen can be purified to 99.999+%.14,15 Species other than hydrogen are selectively adsorbed on a solid adsorbent (e.g., activated carbon, 5A zeolite15) at a relatively high pressure by contacting the gas with the solid in a packed column in order to produce a hydrogen enriched gas

10.1021/ie049041k CCC: $30.25 © 2005 American Chemical Society Published on Web 10/14/2005

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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.

stream. The adsorbed species are then desorbed from the solid by lowering the pressure and purging with high-purity product hydrogen, and thus, the PSA waste gas is generated. Continuous flow of product is maintained by using multiple, properly synchronized adsorption beds. Combustion of the PSA waste gas and methane (fuel) is used to provide heat for the reformer and also for the preheating of feeds and the generation of the export steam. Recovery of the waste heat from the still-hot gases leaving the reformer is also used to the same end.2,5,6 A computer simulation of a high-pressure hydrogen production flow sheet, that uses conventional reforming, shifting, and PSA technologies, is described in section 3. Application of intuitive heat recovery to the simulated flow sheet results in a heat exchange network like the one shown in Figure 2. 3. Process Simulation The process has been simulated using AspenTech’s process engineering software HYSYS version 3.1.16 Peng Robinson’s equation of state was used as the thermodynamic fluid package for this simulation, based on AspenTech’s recommendation of this package for highhydrogen-content systems and after ensuring that the process conditions are within the package’s temperature and pressure applicability ranges.17 A process flow diagram of the simulation done in HYSYS is presented in Figure 3. The process feed consists of liquid water and methane gas at ambient temperature. Each stream is compressed to 25.7 atm and heated to 811 K, corresponding to values within typical entrance conditions for the reformer,5,6,8-10,18 in addition to 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 plug flow reactor (PFR) with the kinetic models proposed by Xu and Froment11 (see Appendix A), producing a gas with 46% (molar) H2, which is close to the value of 48% (see Figure 1) considered by Hufton et al.10 Heat, in the amount of 233.67 kJ/s, is provided to the reformer, since it is required by the endothermic reactions r1 and r3 and in order to increase the temperature of the reacting gases and maintain a high reaction rate. The PFR is approximated in HYSYS through a series of continuous stirred tank reactors (CSTRs): 20 were considered in this study. A high-temperature water gas shift reactor (HT WGS) is used to raise the concentration of hydrogen to 52.8%, and a low-temperature water gas shift reactor (LT WGS) provides an additional 1% increase in the hydrogen content. Only the exothermic reaction r2 takes place in these last two reactors, which are simulated as adiabatic PFRs using the kinetic models proposed by Keiski et al.12 and Rase,13 respectively (see Appendix A). Coolers are used before these two reactors in order to adjust the temperature of the gases to appropriate values for the proper operation of the catalysts.4,12,13 Hydrogen purification starts with the condensation and flash separation of liquid water by cooling the gases and is finalized in the PSA unit with adsorption of the majority of the remaining contaminant gases. The PSA process is approximately isothermal and does not require any significant heat load. Thus, for the purposes of this heat/power integration study, it can be modeled as a component splitter. Exit compositions for this component splitter were assigned based on typical PSA performance reported in the literature,9,10 resulting in the production of 20.98 kg/h of a gas stream with 99.8% H2

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

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, allowing for 311.02 kJ/s of heat exchange. Conventionally, these gases are cooled to around 422 K;10 most of their thermal energy is used to provide heat to the reformer and the steam boiler,2,5,8-10 but in this study, no constraint is imposed regarding the matching of streams for heat exchange, with the purpose of having total freedom in the calculation of the minimum hot/cold/electric utility cost. The hydrogen produced from the PSA unit is compressed in three stages up to 300 atm, which is within the typical storage pressure for hydrogen powered vehicles and related hydrogen fueling stations. Considering compressors with 85% adiabatic efficiency, the total work required for the compression of hydrogen is 26.7 kJ/s and the energy removed by cooling between stages adds up to 26.01 kJ/s. 4. Formulation of the Optimization Problem The approach proposed by Holiastos and Manousiouthakis19 for the calculation of the minimum hot/cold/electric utility cost for heat exchange networks is employed for the heat/power integration of the above methane reforming based hydrogen production process. The problem statement is the following:19 given a set of process streams with specified flow rates, inlet temperatures, and fixed outlet target temperatures; hot and cold utility streams with known temperatures and unit costs; and an electrical (work) utility with known unit cost, identify, among all possible heat exchange/pump/engine networks, the minimum total (hot/cold/electric) utility cost necessary to accomplish the desired thermal tasks. For the application at hand, the set of process streams is defined by the material streams in the process flow diagram of Figure 3; the specifications of the hot, cold, and electric utilities considered available are defined in Table 1. Methane combustion gas is considered as the hot utility available, whose inlet temperature, THU in ) 2168 K, is calculated as its adiabatic flame temperature for 110% combustion air and whose outlet temperature, THU out ) 313 K, is estimated for emission. Cooling water with inlet temperature TCU in ) 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 of an optimization problem slightly different than the one solved by Holiastos and Manousiouthakis for utilities with constant temperatures,19 and it is presented below (hot and cold utilities not allowed to be used for work): n

min ηi,θi,δi,FHU,FCU

(Fcp)C,i(TCi ∑ i)1

cHUFHU + cCUFCU + cW( n

C Ti+1 )(1 - θi) -

H (Fcp)H,i(TH ∑ i - Ti+1)(1 - ηi)) i)1

(1)

subject to the following constraints: H δi + [(Fcp)H,iηi + FHUcp,HURi](TH i - Ti+1) - δi+1 C ))0 [(Fcp)C,iθi + FCUcp,CUγi](TCi - Ti+1 ∀i ∈ [1, n] (2)

( )

n

(Fcp)H,i(1 - ηi) ln ∑ i)1

TH i

-

H Ti+1 n

( )

(Fcp)C,i(1 - θi) ln ∑ i)1 δi g 0 ∀i ∈ [2, n]

Ri ) γi )

{ {

TCi

C Ti+1

) 0 (3) (4)

δ1 ) δn+1 ) 0

(5)

0 e ηi e 1 ∀i ∈ [1, n]

(6)

0 e θi e 1 ∀i ∈ [1, n]

(7)

- ∆Tmin,H ∀i ∈ [1, n] - ∆Tmin,H

(8)

C 0 if Ti+1 g TCU out + ∆Tmin,C ∀i ∈ [1, n] C 1 if Ti+1 < TCU out + ∆Tmin,C

(9)

0 if 1 if

TH i TH i

e >

THU out THU out

FHU, FCU g 0

(10)

Nomenclature is provided at the end of the paper. The hot temperature scale (TH) is defined for hot streams, such that TH ) T - ∆Tmin,H, and the cold temperature scale (TC) is similarly defined for cold streams, with TC ) T + ∆Tmin,C; thus, the resulting minimum approach temperature (∆Tmin) for heat exchange between hot and cold streams is ∆Tmin ) ∆Tmin,H + ∆Tmin,C. The objective

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Table 1. Utilities Specification utilitya

Tin (K)

HU: CH4 combustion gas CU: cooling water W: electricity

Tout (K)

2168 298

313 308

cp,avgb (kJ/(kg K)) 1.44 4.31

cost ($/kg) 10-2 c

1.724 × 8 × 10-5 d

cost ($/kJ) 6.45 × 10-6 1.85 × 10-6 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 for CH4. 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

conventional process

heat integration

heat and power integration

CH4 (kg/kg of H2) CO2 (kg/kg of H2) HU (kJ/g of H2) CU (kJ/g of H2) W (kJ/g of H2) MUC ($/kg of H2)

3.05 8.25 10.7 22.3 6.2 0.19

2.84 7.71 0 24.2 6.2 0.12

2.84 7.71 0 15.1 -3.0 -0.01

a CH : methane consumed as raw material and hot utility. CO : 4 2 carbon dioxide generated from combustion of methane and PSA waste. HU: hot utility consumed. CU: cold utility consumed. W: electricity consumed (negative if produced). MUC: minimum utility cost.

function (1) is the sum of the costs of hot, cold, and electrical utilities. Equation 2 represents the energy balance in the heat exchanger (HE) subnetwork for each temperature interval. The HE subnetwork is built with heat exchangers; fractions ηi and θi of the enthalpies from the hot and cold composite curves in interval i, respectively, are used in this subnetwork. The respective complementary fractions (1 - ηi) and (1 - θi) are used in the heat engine and pump (HEP) subnetwork, which is built with reversible heat engines and heat pumps. Equation 3 is the overall entropy balance for the HEP subnetwork. The second law of thermodynamics is expressed in the HE subnetwork by the fact that the available heat at each interval, δi, should be nonnegative (constraint 4). The overall enthalpy balance in the HE subnetwork is ensured by constraint 5. The solution to the formulated problem provides results for the heat and power integration of the process. The heat integration only (no power) or pinch analysis20 can be done by considering only the HE subnetwork, i.e., by setting ηi ) 1 and θi ) 1 in constraints 6 and 7, respectively. 5. Results and Discussion The optimization problem is solved using the linear programming software MINOS 5.5.21 The calculated minimum utility cost (MUC), expressed per kilogram of hydrogen produced, is included in the bottom row of Table 2, where complete results are summarized. The values in the first column of Table 2 correspond to simple heat recovery (no optimization) applied to our simulated process, as shown in Figure 2. This design is here referred to as a conventional process because it does not involve our proposed heat exchange optimization. The second column corresponds to the results after heat (no power) integration of the process, and the third column corresponds to the results after heat and power integration. The utility cost of the conventional process is 19 cents/kg of H2, and a 36% reduction is achieved after heat integration; a small utility profit can even be generated after heat and power integration due to electricity produced in excess of process needs. Of course, it should be emphasized that these savings are in comparison to a conventional process whose heat integration characteristics may have been surpassed by proprietary industrial designs.

Figure 4. Temperature-enthalpy diagram of a HE network featuring the minimum hot/cold utility cost for the methane reforming based hydrogen production process. ∆Tmin ) 10 K.

The temperature-enthalpy diagram of a HE network featuring minimum hot/cold utility cost, obtained after heat integration of the process, is presented in Figure 4. The solid line corresponds to the hot composite curve, and the dotted line represents the cold composite curve. The minimum approach temperature considered here is ∆Tmin ) 10 K, being the smallest temperature difference that two streams leaving or entering a heat exchanger can have. It is attained at the pinch temperature of 500 K. This value corresponds to the saturation temperature of steam at the process operating pressure (25.7 atm). The use of the cold utility of 140.88 kJ/s is represented by almost the complete percentage of the enthalpy change of the section of the cold composite curve between 298 and 308 K. (It looks approximately horizontal in Figure 4 due to the scale of the plot. It also represents a small enthalpy change due to heating of raw materials between these temperatures.) The cold utility requirement can be reduced if a higher combustion gas emission temperature is used, i.e., above 313 K; for instance, a temperature of 422 K results in a total cold utility need of 100.08 kJ/s and, thus, an additional cost reduction of 1 cent/kg of H2. The hot utility is not required if heat integration is accomplished, which means that there is no need to burn additional methane to generate heat for the reformer, as is usually done in the conventional process. This brings not only a 36% reduction in utility cost but also a 6.5% reduction in carbon dioxide emission. The temperature-enthalpy diagram of the HE subnetwork of a network featuring minimum hot/cold/ electric utility cost, obtained after heat and power integration of the process, is presented in Figure 5. This HE subnetwork does not use any cold process streams and contains only hot process streams with temperatures below 398 K, resulting in a reduction of the need for the cold utility with respect to that of the HE network in Figure 4. The hot process streams with temperatures above 398 K are used in the HEP subnetwork, whose temperature-enthalpy diagram is shown in Figure 6. There is a combined use of the hot composite curve in the interval 388-398 K between the two subnetworks (ηi ) 0.1125). In the HEP subnetwork, heat

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

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

from the hot process streams is transferred only to the working fluid in heat engines/pumps, with a minimum approach temperature ∆Tmin ,H ) 5 K, and heat from the working fluid is transferred to cold process streams with a minimum approach temperature ∆Tmin,C ) 5 K. The difference in the enthalpy change of the hot composite curve with respect to that of the cold composite curve in Figure 6 is the net work produced by the HEP subnetwork (-Ws ) 53.72 kJ/s). If it is assumed that 100% of this work is converted into electricity, the amount of electricity generated is in excess of the process needs (36.24 kJ/s), and if this excess is sold, a small utility profit of 1 cent/kg of H2 is generated after covering the cost of the cold utility. The hot utility is again not needed after heat and power integration, suggesting that the production of a large quantity of export steam (10-12 tons of steam/ton of H222), from conventional hydrogen plants, could be seen as the result of unnecessary combustion of additional methane (fuel) and as the lack of a need for pressurization of the hydrogen product to 300 atm. The HEP subnetwork is composed of both heat engines and heat pumps, whose corresponding sections can be visualized in the temperature-entropy diagram of Figure 7. Those sections where the hot curve is above the cold require a heat engine, while those where the cold is above the hot require a heat pump. The large heat engine section on the right side of Figure 7 (at the highest temperatures) is a clear example of the existing opportunity for power generation when heat is to be

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

exchanged between streams with a large temperature difference, as happens here between the PSA waste gas and 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 a working fluid that can circulate (in a heat engine/pump) between the hot scale temperature of the hot process stream and the cold scale temperature of the cold process stream and with the same heat capacity rate (Fcp) of the process stream with which the working fluid exchanges heat; it also considers that the adiabatic processes 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 are calculated using the cold and hot temperature scales (eq 3), respectively, and are, thus, equivalent to the overall entropy changes of the working fluids as they exchange heat with the cold and hot streams, respectively. 6. Conclusions Heat and power integration studies have been carried out for a conventional methane reforming based hydrogen production plant with a capacity of 20.98 kg of H2/ h. Heat and power integration results in utility profit due to electricity production in excess of process needs. Heat integration alone results in a 36% reduction in utility 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 carbon dioxide 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 application of the technique will certainly feature lower energy demands, that may, however, necessitate larger capital expenditures, in the form of additional heat transfer and/or power compression/expansion equipment. Designs can be pursued based on vertical matching of streams in the T-∆S and T-∆H diagrams, analogous to the pinch analysis method for the design of heat exchange networks. The trade-off among utility and capital costs can then be quantified by analyzing the dependence of these costs on the minimum approach temperature (∆Tmin). Quantifying this capital/utility cost trade-off for the considered plant will be the subject of our future research.

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Appendix A. Kinetic Models A.1. Rate of Reactions r1, r2, and r3 in the Reformer. The model proposed by Xu and Froment11 for reaction on a Ni/MgAl2O4 catalyst is as follows:

rr1 )

k1

Den2

rr2 )

rr3 )

(

PCH4PH2O

k2 Den

k3 Den2

(

(

2.5 PH 2

-

PCOPH2O PH2

2

2 PCH4PH 2O 3.5 PH 2

-

-

)

)

(A.1)

(A.2)

1 + kCOPCO + kH2PH2 + kCH4PCH4 + kH2O

)

( ) PH2O P H2

(A.4)

rate coefficient or adsorption constant

preexponential factor

units of pre-exponential factor

k1 k2 k3 kCO* kCH4* kH2O* kH2*

4.225 × 1015 1.955 × 106 1.020 × 1015 8.23 × 10-5 6.65 × 10-4 1.77 × 105 6.12 × 10-9

kmol bar0.5/(kgcat h) kmol/(kgcat h bar) kmol bar0.5/(kgcat h) bar-1 bar-1 dimensionless bar-1

240.1 67.13 243.9 -70.65* -38.28* 88.68* -82.90*

a The asterisk symbol is placed with values corresponding to adsorption.

Table A2. Reaction Equilibrium Constants

function of T (K)

units of equilibrium constant

exp(-26830/T + 30.114) exp(4400/T - 4.036) K1 K2

bar2 dimensionless bar2

A.2. Rate of Reaction r2 in the HT WGS Reactor. The model proposed by Keiski et al.12 for reaction on an Fe3O4-Cr2O3 catalyst is as follows:

kJ/mol (-95RT )C

where

β)

1.1 0.53 COCH2O(1

(

)

1 CCO2CH2 K2 CCOCH2O

0.86 + 0.14P for P e 24.8 4.33 for P > 24.8 8640 1.8T

)

(A.8) (A.9)

The authors gratefully acknowledge the financial support of the National Science Foundation under Grant CTS 0301931.

activation energy or adsorption enthalpy (kJ/mol)

rr2 ) 3600 exp(26.1) exp

{

Acknowledgment

Table A1. Parameters of the Rate Coefficients and Adsorption Constants for Related Arrhenius or Van’t Hoff Equationsa

K1 K2 K3

ψ)

(A.3)

The rate coefficients and adsorption constants are given in Table A.1, and the reaction equilibrium constants, in Table A.2.

equilibrium constant

)

(

where

Den )

)(

Keq ) exp -4.72 +

0.5 PCO2 PH 2

K3

(

yCO2yH2 1 3340 yCOyH2O (A.7) 1.8T Keq 379Fb

where

PCO2 K2

rr2 )

ψ exp 12.88 -

0.5 PH PCO 2

K1

zinc oxide catalyst is as follows:

- β) (A.5)

(A.6)

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

Nomenclature cCU ) cost coefficient of cold utility, $/kg cHU ) cost coefficient of hot utility, $/kg cp ) mass heat capacity, kJ/(kg K) cW ) cost coefficient of electric utility, $/kJ Ck ) concentration of species k ) H2O, CO; mol/L CSTR ) continuous stirred tank reactor CU ) cold utility Den ) denominator in reaction rate expressions F ) mass flow, kg/s HE ) heat exchanger subnetwork HEP ) heat engine and pump subnetwork HU ) hot utility HT WGS ) high-temperature water gas shift reactor Keq ) equilibrium constant of reaction r2 for eq A.7 Kj ) equilibrium constant of reaction rj, j ) 1, 2, 3. The units are specified in Table A.2 kj ) rate coefficient of reaction rj, j ) 1, 2, 3. The units are specified in Table A.1 kk ) adsorption constant of species k ) CH4, H2O, H2, CO. The units are specified in Table A.1 LT WGS ) low-temperature water gas shift reactor MUC ) minimum utility cost PFR ) plug flow reactor PSA ) pressure swing adsorption P ) pressure, atm Pk ) partial pressure of species k ) CH4, H2O, H2, CO2, CO; bar SMR ) steam methane reformer R ) universal gas constant, R ) 8.31451 × 10-3 kJ/(mol K) rj ) reaction j ) 1, 2, 3. rrj ) rate of reaction rj, j ) 1, 2, 3; kmol/(kgcat h) T ) temperature, K TH i ) high temperature of interval i in the hot temperature scale, K H Ti+1 ) low temperature of interval i in the hot temperature scale, K W ) 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 utility in interval i

Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005 9119 γi ) variable indicative of the presence of the cold utility in interval i β ) reversibility factor of reaction r2 in the HT WGS reactor δi ) available heat at interval i, kJ/s ∆Tmin ) minimum approach temperature, K ∆Tmin,H ) difference between the real temperature and the temperature in the hot temperature scale of the hot streams, K ∆Tmin,C ) difference between the temperature in the cold temperature scale and the real temperature of the cold streams, K ∆Hj° ) heat of reaction rj, j ) 1, 2, 3; kJ/mol ∆H ) enthalpy change, kJ/s ∆S ) entropy change, kJ/(K s) ηi ) fraction of the hot composite stream from interval i used in the HE (heat exchanger) subnetwork θi ) fraction of the cold composite stream from interval i used in the HE (heat exchanger) subnetwork Fb ) bulk density of copper-zinc oxide catalyst, lb/ft3; e.g., 90 lb/ft3 ψ ) activity factor of copper-zinc oxide catalyst Subscripts C ) cold composite stream CU ) cold utility H ) hot composite stream HU ) hot utility i ) interval i for optimization problem in ) inlet temperature n ) number of intervals for optimization problem out ) outlet temperature W ) electric utility Superscripts C ) cold temperature scale CU ) cold utility H ) hot temperature scale HU ) hot utility

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Received for review October 1, 2004 Revised manuscript received August 29, 2005 Accepted August 31, 2005 IE049041K