Multiobjective Optimization of a Hydrogen Production System with Low

Article pubs.acs.org/IECR

Multiobjective Optimization of a Hydrogen Production System with Low CO2 Emissions Wei Wu,*,† Yan-Chi Liou,‡ and Ya-Yan Zhou‡ †

Department of Chemical Engineering, National Cheng Kung University, Tainan 70101, Taiwan, Republic of China Department of Chemical and Materials Engineering, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, Taiwan, Republic of China

‡

ABSTRACT: Since the steam methane reforming usually increases the temperature of stream and concentration of CO2, this work introduces a CO2 reformer that can produce syngas by consuming CH4 and CO2. In the proposed configuration, a CO2 reformer is directly added between the steam methane reforming (SMR) process and a high-temperature shift (HTS) converter. To pursue the process optimization with respect to maximizing hydrogen production and minimizing carbon dioxide emission, a nondominated sorting genetic algorithm-II (NSGA-II) is employed to solve a constrained multiobjective optimization (MOO) problem. Finally, the proposed system configuration with heat recovery manner is validated by an Aspen HYSYS simulator.

and heat supplies, and Montazer-Rahmati and Binaee10 used the same genetic algorithm to solve the multiobjective optimization (MOO) problem for an industrial hydrogen plant with a CO2 absorber and a methanator. Recently, Masuduzzaman and Rangaiah11 provided a brief review for MOO applications in chemical engineering. Moreover, NSGA-II is a further improvement of NSGA, using a fast nondominated sorting approach to solve constrained multiobjective problems efficiently.12 The significant performance improvement on the feasible operation of solid oxide fuel cell could be achieved when the MOO was performed using NSGA-II.13 In this article, we introduce a CO2 reformer which is utilized to produce hydrogen by consuming carbon dioxide and methane. A hydrogen production process with a new combination including a SMR, a CO2 reformer, and a high-temperature shift converter is treated as a CO2 reformer-aided steam methane reforming process. To address the feasible operating manner, the multiobjective optimization algorithm for maximizing H2 production and minimizing CO2 emission is presented. With aid of the GA toolbox in Matlab, the NSGA-II method is employed to determine the set of Pareto-optimal solutions. Since the presented system requires external heat supplies, a simple heat integration design is implemented to reduce energy consumption. Using the Aspen HYSYS simulation, the proposed system configuration is successfully verified.

1. INTRODUCTION The steam reforming of methane is an essential process in the production of any hydrogen-rich gas. Xu1 indicated that the methane reforming-based hydrogen production process is composed of three main stages. In the first stage, hot methane and steam are fed into the steam methane reformer (SMR) to produce syngas and carbon dioxide. In the second stage, the water-gas shift reaction in high-temperature and low-temperature shift converters attempts to eliminate carbon monoxide and increase hydrogen yield. In the third stage, pressure swing adsorption (PSA) carries out the procedure of hydrogen purification. The PSA off-gas is fed into the combustor to generate the high-temperature waste gas and produce a large amount of carbon dioxide simultaneously. With a view to reduce the energy consumed in a conventional hydrogen plant, Posada and Manousiouthakis3 performed the pinch analysis to establish a heat-integrated hydrogen production process. Simpson and Lutz4 indicated that the performance of hydrogen production via SMR was evaluated using exergy analysis. The exergy efficiencies of the SMR system are low, because the majority of the exergy destruction occurs and a large amount of exergy is wasted in the exhaust stream. In considering a hydrogen plant subject to CO2 reduction, Tarun et al.5 proposed a modified scheme for capturing CO2 in modern SMR plants with minimum energy penalty. Felice et al.6 used a CO2 absorber to recover CO2 in a fluidizedbed reactor, and Song and Pan7 presented the trireforming of methane to improve CO2 conversion and avoid the separation of CO2 from the flue gas. Recently, Collodi and Wheeler8 reviewed the possibilities of CO2 capture in a steam reformingbased plant and evaluated its impact on the economics of hydrogen production. Maximizing the cost-effectiveness of the operation of hydrogen plants depends on maximizing the hydrogen yield. Rajesh et al.9 presented an adaptation scheme of the nondominated sorting genetic algorithm (NSGA) to perform a multiobjective optimization subject to the costs of processing requirements © 2012 American Chemical Society

2. SYSTEM DESCRIPTION Figure 1 shows, in detail, the design of a modified hydrogen production system. Two gas-phase streams of steam and methane with a fixed prescribed ratio of steam-to-carbon (S/C)in) flow into the steam reforming reactor (SMR) at the prescribed inlet temperature, TSMR,in. The reversible reactions in Received: March 28, 2011 Accepted: January 8, 2012 Published: January 9, 2012 2644

dx.doi.org/10.1021/ie202789j | Ind. Eng.Chem. Res. 2012, 51, 2644−2651

Industrial & Engineering Chemistry Research

Article

Figure 1. CO2 reformer-aided steam methane reforming process.

the SMR are as follows:

and the energy balance of the SMR is πDSMR 2ρb 4U (Tv − T ) dT + = cpρbDSMR FSMR,in dl 4cp FSMR,in

CH4 + H2O ↔ CO + 3H2(r1) ΔH10

= 206.2 kJ/mol

(1)

3

∑ ( − ΔHi)rj j=1

T = TSMR,in

CO + H2O ↔ CO2 + H2(r2) ΔH20 = −41.2 kJ/mol

(2)

R CH4 = r1 + r3

(3)

R CO2 = r2 + r3

and the corresponding kinetic models3 are 15

4.225 × 10 r1 = Den2

⎛ PH2 0.5PCO ⎞ ⎛ 240.1 ⎞⎜ PCH4PH2O ⎟ ⎟ exp⎜ − ⎟ ⎝ RT ⎠⎜ P 2.5 K1 ⎝ H2 ⎠

r2 =

PCO2 ⎞ ⎛ 67.13 ⎞⎛ PCOPH2O 1.955 × 106 ⎟⎟ ⎜ ⎟⎜ exp − ⎜ ⎝ RT ⎠⎝ PH K Den2 2 ⎠ 2

r3 =

2 ⎛ PH2 0.5PCO2 ⎞ ⎛ 243.9 ⎞⎜ PCH4PH2O 1.02 × 1015 ⎟ ⎜ ⎟ exp − ⎝ RT ⎠⎜ P 3.5 K1K2 ⎟⎠ Den2 H2 ⎝

R H2O = r1 + r2 + 2r3

yCH

4,SMR

(5)

1 − xCH4

=

1 + (S/C)in

1 + (S/C)in

2

(6)

xCO2 yCO ,SMR = 2 1 + (S/C)in

yCO,SMR =

yH ,SMR = 2

(11)

(S/C)in − xCH4 − xCO2

yH O,SMR =

(12)

(13)

xCH4 − xCO2 1 + (S/C)in

(14)

3xCH4 + xCO2 1 + (S/C)in

(15)

Remark 1: It is assumed that the total pressure should satisfy the Peng−Robinson equation of state,14

P=

(7)

RT aα − Vm − b Vm + 2bVm − b2

(16)

0.46R2TC2 PC

(17)

0.08RTC PC

(18)

where

In the steady state, the species mass balances of the SMR are

a=

ρbR i d xi πDSMR 2 = × dl 4 FSMR,in xi = 0 at l = 0, i = CH4 , CO2 , H2O

(10)

The mole fractions of the components at any axial location of the SMR are simplified as

(4)

where K1 = exp(−26830/T + 30.114), K2 = exp(4400/T − 4.036), and

⎛ − 70.65 ⎞ ⎟P Den = 1 + 8.23 × 10−5 exp⎜ ⎝ RT ⎠ CO ⎛ − 82.90 ⎞ ⎟P + 6.12 × 10−9 exp⎜ ⎝ RT ⎠ H2 ⎛ − 38.28 ⎞ ⎟P + 6.65 × 10−4 exp⎜ ⎝ RT ⎠ CH4 ⎛ 88.68 ⎞⎛ PH2O ⎞ ⎟ ⎟⎜ + 1.77 × 105exp⎜ ⎝ RT ⎠⎜⎝ PH ⎟⎠ 2

(9)

where xi represents the conversion of component i at any axial location in the SMR; T represents the SMR reactor temperature at any axial location; Tv is the heating temperature; DSMR is the inside diameter of the SMR; ρb is bulk density, and

CH4 + 2H2O ↔ CO2 + 4H2(r3) ΔH30 = 165.0 kJ/mol

at l = 0

b= (8) 2645



⎧⎧ ⎪⎪ 2 ⎪ ⎨1 + (0.37 + 1.54ω − 0.27ω ) ⎪ ⎪⎩ 2 ⎪ ⎡ ⎛ T ⎞0.5⎤⎫ ⎪ ⎪ ⎢ ⎥ ⎪ ⎢1 − ⎜ ⎟ ⎥⎬ T ⎝ ⎠ C ⎦⎪ ⎪ ⎣ ⎭ ⎪ ⎪ if ω ≤ 0.49 α=⎨ ⎪⎧ ⎪⎪ 2 ⎨ ⎪ ⎪1 + [0.38 + (1.49ω − 1.16ω ⎪⎩ 2 0.5⎤⎫ ⎪ ⎡ ⎞ ⎛ ⎪ T ⎪ + 1.02ω3)]⎢1 − ⎜ ⎟ ⎥⎬ ⎪ ⎢ ⎝ TC ⎠ ⎥⎦⎪ ⎣ ⎭ ⎪ ⎪ ⎩ if ω > 0.49

Article

dl

=

πDCO2R 2 4

×

yCO ,CO R = yCO ,SMR (1 − xCO2) 2 2 2

(26)

yCH ,CO R = yCH ,SMR (1 − xCO2) 4 2 4

(27)

(28)

(29)

and the corresponding kinetic model of the HTS is

⎛ − 95 ⎞ 1.1 ⎟P r5 = 7.79 × 1014 exp⎜ P 0.53 ⎝ RT ⎠ CO H2O ⎛ PCO2PH2 ⎞ ⎟ × ⎜⎜1 − K2PCOPH2O ⎟⎠ ⎝

(20)

(30)

Similarly, the steady-state equations of the adiabatic HTS process are as follows.

(21)

ρbr5 dxCO πD HTS2 = × dl 4 FHTS,in xCO = 0

at l = 0

(31)

πD HTS2ρb dT = ( − ΔH5)r5 dl 4cbFHTS,in

FCO2R,in

at l = 0

xCO2

ΔH50 = − 41.2 kJ/mol

T = THTS,in at l = 0

(32)

where xCO represents the conversion of CO at any axial location in the HTS, DHTS is the inside diameter of the HTS, and THTS,out = T|l=LHTS is the outlet temperature of the HTS where LHTS is the length of this tubular reactor. Since the operating temperature of the HTS is lower than that of the CO2 reformer, the second cooler (cooler-2) is added to adjust the inlet temperature of the HTS, THTS,in. The heat duty of cooler-2 is written as

(22)

πDCO2R 2ρb dT = ( − ΔH4)r4 dl 4cpFCO2R,in T = TCO2R,in

2 ,SMR

2

CO + H2O ↔ CO2 + H2

ρbri

xCO2 = 0 at l = 0

= yH ,SMR + 2yCO

Notably, the average specific heat, cp̅ , is 2.89 kJ/(kg K). To reduce the large amount of CO in the outlet stream of the CO2 reformer, a high-temperature shift (HTS) converter is utilized. The water-gas-shift reaction that proceeds in the converter is given by

where K3 = exp(−30782/T + 42.97). Notably, the CO2 reformer may increase the amounts of both carbon monoxide and hydrogen produced by consuming CO2 and unreacted CH4. If the process in the CO2 reformer is considered to be adiabatic, then the steady-state models of the CO2 reformer are

dxCO2

(25)

2R

Q E1 = FSMR,out cp̅ (TSMR,out − TCO2R,in)

(19)

15

2 2 ⎛ ⎞ PCO PH ⎛ 23.7 ⎞ 2 ⎜1 − ⎟ ⎟P r4 = 8.71 × 10−2 exp⎜ P × CH CO ⎜ 4 2 ⎝ RT ⎠ K3PCH4PCO2 ⎟⎠ ⎝

yH ,CO

Since the operating temperature of the CO2 reformer is lower than that of the SMR, the first cooler (cooler-1) is added to adjust the inlet temperature of the CO2 reformer, TCO2R,in. The heat duty of cooler-1 is written as

CH4 + CO2 ↔ 2CO + 2H2(r4)

with the corresponding kinetics model

(24)

2

Notably, the molar volume (Vm), critical pressure (PC), and critical temperature (TC) for each component is found from the Aspen Plus Physical Property Database. The outlet temperature of the SMR is TSMR,out = T|l=LSMR , where LSMR is the length of this tubular reactor. Since the outlet temperature of the SMR is up to 1100 K and its outlet stream contains carbon dioxide and unreacted methane, a CO2 reformer with a reaction temperature of 900− 1100 K is appropriately used to produce hydrogen by consuming carbon dioxide and methane. We assume the reversible endothermic reaction in CO2 reformer is mainly described by

ΔH40 = 247.0 kJ/mol

yCO,CO R = yCO,SMR + 2yCO ,SMR xCO2 2 2

(23)

where xCO2 represents the conversion of CO2 at any axial location in the CO2 reformer, DCO2R is an inside diameter of CO2 reformer, and TCO2R,out = T|l=LCO2R is the outlet temperature of the CO2 reformer where LCO2R is the length of this tubular reactor. Moreover, the mole fractions of the components in the CO2 reformer are

Q E2 = FCO2R,out cp̅ (TCO2R,out − THTS,in)

(33)

In the pressure swing adsorption (PSA) unit, carbon oxides are almost adsorbed on a solid adsorbent (e.g., activated carbon), such that hydrogen can be purified to 99.95+%. The PSA 2646



Article

12.3% CO2. Apparently, the simulation by Aspen HYSYS shows that the hydrogen yield increases sequentially but the amount of CO2 is also generated through the HTS process. In our system configuration, there are four manipulating variables to affect the hydrogen yield and CO2 emissions. Therefore, it is expected to address the system with low CO2 emissions by virtue of changing manipulating variables.

process is assumed as an isothermal process, so it does not require any heat supply. Moreover, the outlet composition of the PSA is expressed

yH ,PSA,out = SPSA

(34)

2

yi ,PSA,out = (1 − SPSA )

yi ,PSA,in

3. MULTIOBJECTIVE OPTIMIZATION To pursue the hydrogen production process with low CO2 emissions, the multiobjective optimization (MOO) with regard to maximizing the H2 productivity and minimizing the CO2 emission rate arises. Moreover, the MOO algorithm is stated as follows:

∑ yi ,PSA,in

i = CH4 , CO, CO2 , H2O

(35)

and the outlet composition of PSA off-gas is shown by yi ,PSA,in yi ̃,PSA,out = ∑ yi ,PSA,in + (1 − SPSA ) × yH ,PSA,in

max J1 = FH2

u ∈Ω

2

i = H2 , CH4 , CO, CO2 , H2O

max J2 = FCO2

(36)

where SPSA(= 99.95%) represents the purity of H2 from the PSA unit (SPSA(= 99.95%). Moreover, the mass flow rates of H2 and CO2 at two exits of the PSA unit are

FH2 = yH ,PSA,out FPSA,in

(37)

FCO2 = yCO ̃

(38)

2

2 ,PSA,out

FPSA,in

subject to

Q Ei ≤ 1.2Q Ei,max

i = 1, 2, 3

F ≤ 1.2Fmax

(41)

where the system decision variables are u = [(S/C)in,TSMR,in,TCO2R,in,THTS,in]T and Ω represents the bounded set. The inequality by eq 41 shows the physical constraints for the heat duties of each cooler (QEi, i = 1, 2, 3) and the feed flow rate F. QEi,max represents the maximum heat duty of each cooler, and Fmax is the upper limit of the feed flow rate. In general, the design margin with respect to the operation flexibility is required. Therein, the upper limits multiplied by 1.2 are specified. In determining the Pareto optimal sets with respect to each decision variable, the modified objective functions associated with the penalty functions are

Because of the large temperature difference between HTS and PSA, a third cooler (cooler-3) is added to adjust the inlet temperature of the PSA unit, TPSA,in. The heat duty of cooler-3 is written as

Q E3 = FHTS,out cp̅ (THTS,out − TPSA,in)

(40)

u ∈Ω

(39)

Simulation and Discussion. Referring the process simulation, we assumed that (i) all reactions in each unit occur in the gas phase; (ii) the SMR, CO2 reformer, and HTS reactor are considered to be plug-flow reactors; and (iii) the thermodynamic properties of some species are evaluated using the Peng−Robinson equation of state. Referring to the conventional hydrogen production process,4 we assume two feed streams with a fixed (S/C)in = 3.5, one is a mass flow rate 209.52 kg/h H2O and another is a mass flow rate 59.68 kg/h CH4, are mixed well and fed into the SMR. In Figure 2, if inlet temperatures of every reactor are set by TSMR,in = 538 °C, TCO2R,in = 575 °C and THTS,in = 318 °C, respectively, then the outlet stream of HTS contains a mass flow rate 27.94 kg/h, 61% H2 and a mass flow rate 123.21 kg/h,

4

1 max J1 = + 104 ∑ fi FH2 u ∈Ω i=1 4 4

max J2 = FCO2 + 10

u ∈Ω

∑ fi

(42)

i=1

where fi = (Q Ei − 1.2Q Ei ,max ) + |(Q Ei − 1.2Q Ei ,max )| i = 1, 2, 3

(43)

Figure 2. Aspen HYSYS simulation of a CO2 reformer-added steam methane reforming process. 2647



Article

and

f4 = (F − 1.2Fmax ) + |F − 1.2Fmax|

(S/C)in, TSMR,in, TCO2R,in and THTS,in, are depicted in Figures 3a−d, respectively. To study the effect of individual decision variable, Table 2 indicates that the increase of TSMR,in and

(44)

An adaptation version of genetic algorithm, called NSGA-II, is employed to perform a multiobjective optimization with specific weights. When upper limits are given, such as, Fmax = 269.2 kg/h, QE1,max = 60 kW, QE2,max = 85 kW and QE3,max = 10 kW, a set of Pareto-optimal solutions can be found using the GA toolbox in Matlab. In this optimization algorithm, each point in the Pareto set, represented a chromosome, is associated with a set of decision variables under the prescribed set Ω by

Table 2. Effects of Decision Variables objective

(S/C)in ↑

TSMR,in ↑

TCO2R,in ↑

THTS,in ↑

FH2

↑

↑

↑

↑

FCO2

↑

↓

↑

↓

Based on known values of GA parameters in Table 1, the set of Pareto-optimal solutions, with respect to decision variables,

THTS,in, could reduce CO2 emissions, and the higher ratio of steam-to-carbon as well as higher inlet temperatures of each reactor could effectively increase the hydrogen production. Because of design margins by eq 41 and input constraints by eq 45, we found the optimal operating points from the set of Pareto-optimal solutions are close to the upper limit of each variable while the maximum hydrogen production should be satisfied. Therein, new operating conditions shown in Table 3 are determined.

Table 1. NSGA-II Parameters

Table 3. Selected Pareto-Optimal Operating Conditions

2.5 ≤ (S/C)in ≤ 4.5 520 °C ≤ TSMR,in ≤ 570 °C 560 °C ≤ TCO2R,in ≤ 610 °C 300 °C ≤ THTS,in ≤ 340 °C

(45)

parameter

value

(S/C)in

TSMR,in

TCO2R,in

THTS,in

population size number of generations crossover probability mutation probability Pareto front population fraction

60 1000 0.8 0.01 0.7

4.00

565 (°C)

600 (°C)

325 (°C)

Simulation and Discussion. Referring to a conventional hydrogen production process,4 its system shown in Figure 4a is simplified by a combination of a SMR, a high-temperature shift

Figure 3. Pareto-optimal solution (chromosome) with regard to four decision variables: (a) inlet steam-to-carbon ratio vs H2 flow; (b) inlet temperature of SMR vs H2 flow; (c) inlet temperature of CO2 reformer vs H2 flow; and (d) inlet temperature of HTS vs H2 flow. 2648



Article

Figure 4. Aspen HYSYS simulation of (a) a conventional steam methane reforming process4 (b) a CO2 reformer-aided steam methane reforming process with optimal operating conditions.

Figure 5. Composition profiles versus the length of the reactor.

converter, and a low-temperature shift converter for hydrogen production. According to the prescribed feed flow rate and inlet temperature of each unit, the simulation shows that the outlet stream of LTS contains a mass flow rate 21.59 kg/h, 51.25% H2, a mass flow rate 105.67 kg/h, 11.49% CO2, and a mass flow rate 15.23 kg/h, 4.54% unreacted CH4, etc. By our design with selected operating conditions in Table 3, Figure 4b shows that the outlet stream of HTS contains a mass flow rate of 28.36 kg/h, 57.68% H2, a mass flow rate 129.36 kg/h, 12.65% CO2, etc. Notably, our design can increase 31.36% H2 yield, but the CO2 emissions increases 22.41% CO2. The CO2 reduction is very limit, because the concentration of unreacted CH4 in outlet stream of SMR is very low. Besides, it is verified that the CO2

reformer in place of the conventional LTS design can effectively increase the hydrogen yield. (See Figure 5.) Remark 2: Besides the SMR and HTS require external heat supplies, three coolers in the proposed design shown in Figure 2 are used to regulate the inlet temperature of each reactor. To address a simple heat recovery manner, three heat exchangers, shown in Figure 6, take the place of all coolers by the recirculating water flow which is heated from room temperature, and a combustor is added to produce a few heat flow such that the inlet stream of SMR can be heated to the prescribed operating temperature. In addition, Figure 6 also indicates that the optimal operating conditions of the system with heat recovery manner are executed to produce the equivalent hydrogen amount. 2649



Article

Figure 6. Aspen HYSYS simulation of a CO2 reformer-aided steam methane reforming process with heat recovery.

4. CONCLUSIONS This work introduces a CO2 reformer that is directly added between the SMR and HTS reactors to produce syngas by consuming CH4 and CO2. We used the NSGA-II method to find Pareto-optimal solutions. Based on optimal operating conditions, the proposed system configuration ensures the high hydrogen yield but the ability of CO2 reformer for reducing CO2 is restricted due to a very low amount of unreacted CH4 in the outlet stream of SMR. A simple heat recovery manner in place of the external heating/cooling source added can contribute to effectively reduce energy consumption. In fact, the kinetic mechanisms of the carbon dioxide reforming of methane are usually incomplete due to the challenge catalytic technology.16 If a feasible carbon dioxide reforming system can be accurately developed, the hydrogen production system with respect to CO2 reduction should be significantly improved in the future task.

■

SPSA = purity of H2 from the PSA unit T = temperature of each unit, K TC = critical temperature, K Tv = heating temperature, K TSMR,in = inlet temperature of SMR, K TSMR,out = outlet temperature of SMR, K TCO2R,in = inlet temperature of CO2 reformer, K TCO2R,out = outlet temperature of CO2 reformer, K THTS = outlet temperature of HTS, K TPSA,in = inlet temperature of PSA, K U = heat transfer coefficient, kJ/(h m2 K) Vm = molar volume, m3/mol xi = conversion of species i in the bulk flow yi = mole fraction of species i in the bulk flow Greek Symbols

AUTHOR INFORMATION

Corresponding Author

■

*Tel.:+886 6 2757575. Fax: +886 6 2344496. E-mail address: [email protected].

■

ΔHj0 = heat of reaction, kJ/kmol cp = specific heat of flow in each unit cp̅ = average specific heat of flow in each unit; cp̅ = 2.89 kJ/ (kg K) ρb = bulk density; ρb = 5.843 kg/m3

REFERENCES

(1) Xu, J.; Froment, G. F. Methane steam reforming, methanation and water-gas shift: I. intrinsic kinetics. AIChE J. 1989, 35, 88. (2) Hufton, J. R.; Mayorga, S.; Sircar, S. Sorption-enhanced reaction process for hydrogen production. AIChE J. 1999, 45, 248. (3) Posada, A.; Manousiouthakis, V. Heat and power integration of methane reforming based hydrogen production. Ind. Eng. Chem. Res. 2005, 44, 9113. (4) Simpsona, P.; Lutz, A. E. Exergy analysis of hydrogen production via steam methane reforming. Int. J. Hydrogen Energy 2007, 32, 4811. (5) Tarun, B.; Croiset, E.; Douglas, P. L.; Gupta, M.; Chowdhury, M. H. M. Techno-economic study of CO2 capture from natural gas based hydrogen plants. J. Greenhouse Gas Control 2007, 1, 55. (6) Felice, L. D.; Courson, C.; Jand, N.; Gallucci, K.; Foscolo, P. U.; Kiennemann, A. Catalytic biomass gasification: Simultaneous hydrocarbons steam reforming and CO2 capture in a fluidised bed reactor. Chem. Eng. J. 2009, 154, 375. (7) Song, C.; Pan, W. Tri-reforming of methane: a novel concept for synthesis of industrially useful synthesis gas with desired H2/CO ratios using CO2 in flue gas of power plants without CO2 separation. Chem. Soc., Div. Fuel Chem. 2004, 49, 128. (8) Collodi, G.; Wheeler, F. Hydrogen production via steam reforming with CO2 capture. Chem. Eng. Trans. 2010, 19, 37. (9) Rajesh, J. K.; Gupta, S. K.; Rangaiah, G. P.; Ray, A. K. Multiobjective optimization of industrial hydrogen plants. Chem. Eng. Sci. 2001, 56, 999. (10) Montazer-Rahmati, M. M.; Binaee, R. Multi-objective optimization of an industrial hydrogen plant consisting of a CO2 absorber using DGA and a methanator. Comput. Chem. Eng. 2010, 34, 1813.

ACKNOWLEDGMENTS The authors would like to thank the National Science Council of the Republic of China for financially supporting this research (under Contract No. NSC 99-2211-E-006-256).

■

NOMENCLATURE DSMR = inside diameter of SMR, 1.5 m DCO2R = inside diameter of CO2 reformer, 1.5 m DHTS = inside diameter of HTS, 0.15 m FSMR,in = inlet mass flow rate of SMR, kg/h FCO2R,in = inlet mass flow rate of CO2 reformer, kg/h FHTS,in = inlet mass flow rate of HTS, kg/h FH2 = mass flow rate of species H2i, HTS, kg/h FHTS,in = inlet mass flow rate of HTS, kg/h l = axial location in each reactor, m LSMR = length of SMR; LSMR = 11.95 m LCO2R = total length of CO2 reformer; LCO2R = 11.95 m LHTS = total length of HTS; LHTS = 5.5 m R = universal gas constant; R = 8.314 kJ/(kmol K) P = pressure of each unit, kPa PC = critical pressure, kPa Pi = partial pressure of species i, kPa QE = heat duties of a cooler, kW QE,max = maximum heat duty of a cooler, kW rj = rate of reaction i, kmol/ (kgcat hr) 2650



Article

(11) Masuduzzaman.; Rangaiah; G. P. Multi-objective optimization applications in chemical engineering. In Multi-objective Optimization: Techniques and Applications in Chemical Engineering; Rangaiah, G. P., Ed.; World Scientific: Singapore, 2009; p 27. (12) Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 2002, 2, 182. (13) Quddus, M. R.; Zhang, Y.; Ray, A. K. Multi-objective optimization in solid oxide fuel cell for oxidative coupling of methane. Chem. Eng. J. 2010, 165, 639. (14) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59. (15) Jin, W.; Gu, X.; Li, S.; Huang, P.; Xu, N.; Shi, J. Experimental and simulation study on a catalyst packed tubular dense membrane reactor for partial oxidation of methane to syngas. Chem. Eng. Sci. 2000, 55, 2617. (16) Fan, M.-S.; Abdullah, A. Z.; Bhatia, S. Catalytic technology for carbon dioxide reforming of methane to synthesis gas. ChemCatChem 2009, 1, 192.

2651


Multiobjective Optimization of a Hydrogen Production System with Low

Recommend Documents