Simulation and Optimization of Various Hydrogen and Synthesis Gas

182

Energy Sci. & Tech. Vol. 11: Hydrogen & Other Technologies

9 Simulation and Optimization of Various Hydrogen and Synthesis Gas Producing Methods H. ALE EBRAHIM1*, M.J. AZARHOOSH1, A. AFSHAR1, M. TALEBI1, S.H. POURTARRAH1 AND A.R. RAHIMI1

ABSTRACT

Hydrogen can be the future clean fuel and nowadays is widely used in the hydrocracking and hydrotreating refinery units. Also synthesis gas is the most important intermediate for natural gas conversion into petrochemical products. The conventional methods for synthesis gas production are catalytic steam reforming, auto-thermal reforming and dry reforming. Moreover, all above methods can be used for hydrogen production after watergas shift reaction, CO 2 absorption and methanation. In this chapter simulation of the above mentioned methods were accomplished by applying suitable mathematical models. Then the effects of operating variables on the reactors performance were studied by simulation program. Finally, optimization of some of above methods was performed by genetic algorithm for maximizing the hydrogen production rate. Key words: Hydrogen, Synthesis gas, Production methods, Simulation, Optimization. INTRODUCTION

In this work the most important synthesis gas (CO + H2 mixtures) and hydrogen production methods from natural gas are considered. These basic methods are catalytic steam reforming, auto-thermal reforming (high and 1

Chemical Engineering Department, Petrochemical Center of Excellence, Amirkabir University (Tehran Polytechnic), Tehran 15875-4413, Iran *Corresponding author: E-mail: [email protected]

Simulation and Optimization of Hydrogen and Syngas Producing Methods

183

low pressures) and recent dry reforming. The appropriate mathematical models for the above mentioned production methods were selected and differential equations were solved for simulation of the various reactors. Then the simulation framework was used for predicting the performance of these reactors at different operating conditions. Finally, optimization of the above various synthesis gas and hydrogen production methods was accomplished by genetic algorithm. The best operating parameters were determined for the maximum hydrogen production rate as the main optimization goal. NATURAL GAS PREFERENCES

Natural gas is one of the most important energy sources, due to the great available reservoirs and also its environmental preferences. The world natural gas reserves are estimated at 3000 billion barrel oil equivalent (each barrel of oil is equivalent to about 170 m3 of natural gas), compared with the 2000 billion barrel of known crude oil reservoirs (Dry, 2001). Environmental preferences of natural gas over crude oil or coal are evident. Natural gas sweetening by amine solutions is a simple absorption unit leading to complete H2S removal, whereas the crude oil fractions hydrotreating is a tedious process. The latter needs special catalysts for the resistant hydrodesulphurization compounds such as 4,6 dimethyldibenzothiophene to reach the level of 10 ppm remaining sulfur in diesel fuel, for the new standards (Costa et al., 2002). Finally, the coal desulphurization is almost impossible and therefore, the costly flue gas desulphurization from power plants by lime-throwaway method is needed (Shimizu et al., 2002). For example, the SO2 emission from natural gas based power plants can be completely eliminated compared to the coal based power plants with about 15 kg of SO2/MWh (Kirk Othmer, 1991). The second environmental advantage of natural gas over heavy fuels is its lower greenhouse gas (CO2) production. For example, the greenhouse gas emissions from combined-cycle natural gas based power plants (with 53% efficiency) is about 400 kg of CO2/MWh and is less than the 900 kg of CO2/MWh of steam turbine coal based power plants (38% efficiency) (Dawe, 2000). One of the most important environmental problems in the recent decades is global warming due to greenhouse gas effect (Chakraborty et al., 2000). There are extensive papers for CO2 concentration from the flue gas and its further conversion in the literature (Bonenfant et al., 2003; Gupta and Fan, 2002; Na et al., 2002; Wang et al., 1996). Since the above mentioned methods are very expensive, another interesting approach is to propose new production methods with inherently reduced greenhouse gas emission. For example in the direct reduction of iron ore by synthesis gas from natural gas reforming, the CO2 emission can be decreased considerably

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with respect to the usual coke-based blast furnace method (Morrison et al., 2004). The main problem against extensive consumption of natural gas is its transportation difficulties (Thomas and Dawe, 2003). The transport of natural gas by pipelines is only economic for short distances and high flow rates. On the other hand, liquefied natural gas (LNG) may be transported to far distances. However, the cryogenic cost and price of special LNG ships are very high. Therefore, an interesting alternative is chemical conversion of natural gas to the transportable liquid hydrocarbons such as middistillates via gas to liquids (GTL) process and petrochemical products such as methanol. In this field, the main intermediate material for natural gas conversion into final products is synthesis gas. Finally, natural gas is the basic raw material for hydrogen production through the synthesis gas intermediate. IMPORTANCE OF SYNTHESIS GAS

Methane, the main component of natural gas, is a stable molecule. Therefore, direct methane conversion into final products shows low yields. Consequently, natural gas conversion to the petrochemical products is done by indirect processes via synthesis gas as an intermediate. The main synthesis gas applications in the petrochemical industry are production of methanol, ammonia, hydrogen, acetaldehyde, acetic acid, isopropyl alcohol, dimethyl ether and vinyl acetate (Chauvel and Lefebvre, 1989). Methanol is a material for the production of formaldehyde, acetic acid, methyl acetate and methyl tertiary butyl ether. On the other hand, ammonia is used for the production of nitric acid, ammonium nitrate, ammonium phosphate and urea. In addition, liquid hydrocarbons can be produced from synthesis gas by GTL process. The GTL process may be based on either methanol or synthesis gas as intermediates. The methanol-based GTL process consists of larger number of steps and often produces gasoline via methanol to olefins and olefin oligomerization (Krishna et al., 1996). On the other hand, the low temperature Fischer-Tropsch reaction on the cobalt catalyst is done in the synthesis gas-based GTL path to reach a high quality diesel fuel as the main product (Dry, 2001). The quality of diesel fuel from this FischerTropsch reaction is excellent. Such diesel is essentially linear with a high cetane number and its sulfur content is zero (Dry, 2001). Finally, synthesis gas is known as the reducing gas in the metallurgical industries. This means that it is possible to reduce iron oxides by synthesis gas instead of coke. The direct reduction process is used for production of sponge iron by reducing gases from steam and dry reforming of natural gas in a moving packed bed reactor (Parisi and Laborde, 2004).


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HYDROGEN IMPORTANCE

Environmental considerations will probably change the automobile fuels from gasoline and gas-oil to hydrogen fuel cells in future. The problems of fossil fuels are producing gaseous pollutants such as NOx, CO and even SO2 (from incomplete-hydrotreated fuels) which need catalytic converters and greenhouse gas (CO2) emission from exhaust with its drastic effect on global warming. Hydrogen usage in fuel cells generates only harmless water vapor and the produced CO2 from hydrocarbon feed can be separated in the hydrogen production plant simply. This concentrated CO 2 can be converted to synthesis gas and finally petrochemicals by dry methane reforming (Wang et al., 1996). While, CO 2 separation from numerous outspread gasoline fueled vehicles is impossible. Another future promising application for the hydrogen fuel cells may be in the small power plants without any pollutant or greenhouse gas emission. Nowadays, power plants in the industrial countries are coal-based with high SO 2 , NOx , CO 2, mercury and fly-ash emissions. Flue gas desulphurization of such power plants with CaO (dry method) or Ca(OH)2 (wet method) is a costly process (Kirk Othmer, 1991). In addition, SO2 reaction with lime shows the pore mouth closure and incomplete conversion problems due to the high molar volume ratio of CaSO4 to CaO. Special methods such as producing of large pores in the lime by a weak acid are necessary for solving of this problem (Wu et al., 2002; Ale Ebrahim, 2010). This SO2 can be completely eliminated from power plants by using sweet natural gas instead of coal as the fuel. Also, the amount of greenhouse gas emission from natural gas combustion is nearly one-half that of coal-based power plants. Possible using of hydrogen as future power plant fuel will eliminate this greenhouse gas but with remaining some NOx. Finally, hydrogen usage as a fuel cell in an ideal power plant will omit this NOx too. Nowadays in a modern refinery, hydrogen is used for hydrotreating and hydrocracking units. In the hydrotreating unit medium pressure (50 bar) hydrogen is used to break C-S bond of sulfur compounds in gasoline and diesel, while a high pressure (190 bar) hydrogen is necessary for C-C bond breakage of heavy feeds in the hydrocracking unit. HYDROGEN AND SYNTHESIS GAS PRODUCTION METHODS

Industrial hydrogen production units are usually in continuance of the synthesis gas (CO+H2) production plants. These units consist of water-gas shift reaction for converting CO to CO2, CO2 absorption and methanation of trace remaining carbon oxides. However, pressure swing adsorption has been suggested instead of CO2 absorption and methanation in the new hydrogen plants. Therefore, the start point of a hydrogen production plant

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is synthesis gas preparation. The conventional methods for synthesis gas production from natural gas are divided into following basic groups:

1. Steam Reforming The catalytic steam reforming method produces synthesis gas with high H2/CO ratio that is suitable for the ammonia production (Kirk Othmer, 1995). The steam reforming is an endothermic reaction as: CH4 + H2OCO + 3H2

...(1)

This reaction is performed in the catalytic packed-bed tubes between 750–850°C and 20–30 atm, which are heated indirectly in a furnace (Kirk Othmer, 1995). The high pressure steam reforming is favorable to decrease the load of ammonia synthesis gas compressors and also to produce higher mass flow rate of synthesis gas in a constant reactor volume. The furnace flares and tubes are designed as top-fired or side-fired configurations (Dybkjaer, 1995). In addition, simultaneous water-gas shift reaction takes place as: CO + H2O  CO2 + H2

...(2)

Therefore, the H2/CO ratio of the final synthesis gas in this method is above five. Moreover, a part of carbon monoxide is converted to carbon dioxide. The basic problem of the steam reforming method is deactivation of the Ni-based catalysts due to carbon deposition (Snoeck et al., 2009). Therefore, an excess steam/methane ratio is applied. The kinetics of the steam reforming method has been studied extensively (Xu and Froment, 1989). The mathematical modeling for the steam reforming tubes must be two-dimensional, due to external heating in furnace and axial and especially radial temperature gradients in tubes. The heterogeneous and two-dimensional steam reformer model equations have been presented in the literature (Pedernera et al., 2003).

2. Auto-thermal Reforming Auto-thermal reforming is the steam reforming with oxygen input (Dybkjaer, 1995). Therefore, the required heat for endothermic steam reforming reaction is supplied by the exothermic partial oxidation. The partial oxidation of methane is as follows (Deutschmann and Schmidt, 1998): CH4 + ½O2CO + 2H2

...(3)

The ratio of H2/CO = 2 in the produced synthesis gas is desirable for Fischer-Tropsch units or methanol production plants. However, oxygen


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separation cost from the air by distillation is relatively high. In the partial oxidation method, the Ni-group catalysts are widely used. But the deactivation problem for these catalysts is serious due to coke deposition. The noble metal catalysts for partial oxidation are more reactive and selective, but are very expensive. The highly exothermic reaction in the partial oxidation method causes hot points problem in the fixed bed reactors (Gosiewski, 2001). Therefore, simulation of these reactors is highly recommended because of the safety considerations and prevention from run-away. In the auto-thermal method, reactions (1) and (3) take place simultaneously. The required heat for endothermic steam reforming reaction is supplied directly by the exothermic partial oxidation reaction. Consequently the overall temperature is lowered with respect to partial oxidation, which is acceptable. Adiabatic fixed bed reactors for the catalytic auto-thermal reforming of methane are designed for the production of hydrogen for fuel cells and also synthesis gas production for the methanol plants. In the case of a 10 kW fuel-cell unit, atmospheric operating is applied and air is used as the oxygen source. The auto-thermal system for the production of 1000 metric tons per day methanol needs high pressures (40 bar) and the oxygen feed is used instead of air (Smet et al., 2001). The one-dimensional heterogeneous model has been applied for autothermal reforming (Smet et al., 2001). In this system there is a high difference between the catalyst surface and bulk gas temperatures in the initial reactor lengths, due to fast exothermic partial oxidation reaction. Then, the catalyst surface and bulk gas temperatures remain approximately constant, because of thermal balance of the endothermic steam reforming reaction and exothermic partial oxidation reaction by remaining oxygen.

3. Dry Reforming The CO2 or dry reforming has been suggested as the following reaction in the recent years as a method for converting of the greenhouse gas (Wang et al., 1996): CH4 + CO22CO + 2H2

...(4)

The above equation is a highly endothermic reaction with nickel based catalysts. In this method, there is a preference of greenhouse gas consumption for production of the liquid hydrocarbons or petrochemical products. The complete kinetic study of the carbon dioxide reforming of natural gas has been presented in the literature (Froment, 2000). The catalysts of this reaction are also deactivated by the coke deposition even faster than steam reforming method. A two-dimensional pseudohomogeneous model has been used for the packed bed reactors for the dry reforming (Akpan et al., 2007). However, there is reverse water gas shift

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reaction simultaneous with equation (4). Consequently, outlet CO mole fraction is slightly greater than H2 mole fraction.

4. Other Methods In the tri-reforming method, there are three oxidants (oxygen, steam and carbon dioxide) for converting methane to the synthesis gas. Therefore, reactions (1), (3) and (4) take place simultaneously. In other words, trireforming process consists of a combination of dry reforming, steam reforming and partial oxidation. In such a tri-reforming system, it is possible to adjust the final H2/CO ratio in synthesis gas by variation of inlet H2O/ CH4 and CO2/CH4 ratios to the reactor (Song and Pan, 2004). Moreover, a balance between the heat supply and heat consumption can be controlled by adjusting the input oxygen flow rate with respect to input methane flow rate (Halmann and Steinfeld, 2006). It is also possible to use dry reforming, accompanying with the steam reforming to decrease the high H2/CO ratio of steam reforming to a desired value. However, both the above reactions are highly endothermic. Thus, heat must be supplied to such reactor from a furnace indirectly. This combined synthesis gas production method is usually used for reducing gas preparation in direct iron oxide reduction process (Aydinoglu, 2010). Finally, it must be noted that in addition to the four above mentioned main synthesis gas producing methods, several ancillary methods for synthesis gas production have been introduced in literature. For example in the chemical looping reforming process, a circulating oxygen carrier material (such as NiO) transfers oxygen of air from oxidizing reactor into reduction reactor for the reaction with methane and synthesis gas production (Ryden et al., 2006; Rashidi et al., 2013). Moreover, it is possible to get synthesis gas as a valuable by-product in the ZnO reduction by methane (instead of coke) as an alternative process for metallic zinc production (Ale Ebrahim and Jamshidi, 2004; Ale Ebrahim, 2012). The mathematical modeling and experimental data for this new synthesis gas production method in a packed bed reactor and also in a fast fluid bed reactor has been presented elsewhere (Afshar et al., 2010; 2012).

Mathematical Models In this section, the suitable mathematical models for the reactors of the main synthesis gas and hydrogen production methods from natural gas are selected. Then the model assumptions are described and the differential conservation equations are presented. The related rate equations for each method with the conventional catalysts are also expressed. These differential and algebraic equations are solved in the next section for simulating of the reactors performance.


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1. Steam Reforming For a steam reforming packed tube with nickel catalyst which indirectly heated in a furnace, the suitable mathematical model must be heterogeneous and two dimensional. The assumptions for steam reforming modeling are steady state, negligible axial dispersion and conduction, rapid external mass transfer, the same catalyst and bulk gas temperatures and the catalyst pellet is equivalent to a hallow cylinder. The steam reforming chemical reactions with their rate equations are as follows (Pedernera et al., 2003):  p3 p  r1 = k1  pCH pH O – H2 CO  4 2  K eq,1  p2.5 H2  2 /(DEN) for CH4 + H2O  3H2 + CO

r2 =

k2 p H2

...(5)

pH2 pCO2    pCO pH2O –  K eq,2   /(DEN)2 for CO + H2O  H2 + CO2

...(6)

 p4H2 pCO2  2 r3 = k3  pCH pH  – 4 2O  K eq,3  p3.5 H2  /(DEN)2 for CH4 + 2H2O  4H2 + CO2

...(7)

DEN = 1 + KCOpCO + KH pH + KCH pCH + KH OpH O/pH 2

2

4

4

2

2

2

...(8)

Therefore, rate of components production are as: rCH = (r1 + r3)

...(9)

rCO = r1 – r2

...(10)

rCO = r2 + r3

...(11)

4

2

rH = 3r1 + r2 + 4r3

...(12)

= (r1 + r2 + 2r3)

...(13)

2

rH

2O

The Arrhenius equations for rate constants and also Vant-Hoff equations for equilibrium constants and adsorption constants were presented elsewhere (Pedernera et al., 2003). Now two dimensional and heterogeneous mass balance equations for methane and carbon dioxide in the tube are expressed as follows:

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xCH4 z

2 Der g  1 xCH4  xCH4  BMav  + + (r11 + r33 ) = G  r r r 2  Gy 0CH

...(14)

2 Der g  1 xCO2  xCO2  BMav  + + (r22 + r33 ) G  r r r 2  Gy 0CH

...(15)

4

xCO2

=

z

4

Where extents of reactions are based on input methane molar flow and are defined as: xCH4 =

xCO =

xCO2 =

xH 2 =

xH2O =

0 FCH – FCH4 4

...(16)

0 FCH 4

0 FCO – FCO

...(17)

0 FCH 4

0 FCO2 – FCO 2

...(18)

0 FCH 4

0 FH2 – FH 2

...(19)

0 FCH 4

0 FH – FH2O 2O

...(20)

0 FCH 4

The remaining equations are mass balances for carbon, hydrogen, and oxygen: FCO = F0CH + F0CO + F 0CO – FCO – FCH 4

2

FH = 1/2[4F0CH + 2F0H 2

FH

2O

4

= F0H

2O

2

2O

...(21)

4

+ 2F 0H – 4FCH – 2FH O] 2

4

+ F0CO + 2F 0CO – FCO – 2FCO 2

2

2

...(22) ...(23)

Two dimensional and heterogeneous heat balance equation is as follows:   1 T  2T   3  T M av =  2    B   (Hri )rii       z G s ykCPk   r r r   i1 

Finally, the momentum balance is as:

...(24)


f  gus2 dPt = dz 2 grp

191

...(25)

The boundary conditions for the above equations are expressed as: At

z = 0xCH = xCO = 0;

At

r = 0

At

r = rw

At

z = 0T = T0;

At

r = 0

At

r = rw 

At

z = 0Pt = Pt0

4

...(26)

2

xCH4 r



xCH4 r

xCO2



r

= 0;

xCO2

...(27)

= 0;

r

...(28) ...(29)

T = 0; r

...(30)

T  U (Tw  Tr  ti ) r

...(31) ...(32)

The wall temperature profiles for side-fired and also top-fired steam reforming furnace configurations were extracted from reference (Dybkjaer, 1995). The diffusion-reaction equations of methane and carbon dioxide for the inside of a hollow-cylinder catalyst pellet with their boundary conditions are as follows: e DCH 4

1 d  dpCH4    = RT (r1 (pj) + r3 (pj))B d   d 

...(33)

e DCO 2

1 d  dpCO2    = RT (r2 (pj) + r3 (pj))B d   d 

...(34)

At

 = in  pCH = pbCH ;

At

 = eq 

4

4

dpCH4 d



pCO = pbCO

dpCO2 d

4

...(35)

2

=0

...(36)

For other components, the partial pressures in the catalyst pores can be computed as: pH – pbH = (DeCO /DeH )(pCO – pbCO ) – (3DeCH /DeH )(pCH – pbCH ) 2

2

2

2

2

2

2

2

4

4

...(37)

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pH

2O

– pbH

pCO –

2O

pbCO

=

= (DeCO /DeH O)(pCO – pbCO ) + (DeCH /DeH O)(pCH – pbCH ) (38) 2

2

2

(DeCO /DeCO)(pCO 2 2

–

2

pbCO ) 2

–

4

2

(DeCH /DeCO)(pCH 4 4

4

–

pbCH ) 4

4

...(39)

After determination of partial pressures for all components inside the catalyst volume, it is possible to compute the effectiveness factors: V

 ri ( p j ) 0

i =

dV V

ri ( psj )

i  1, 2, 3

...(40)

By solving the above differential equations, the molar flow rate of each gas is determined. The mole fractions of gaseous ingredients with consideration of volume change in gas phase due to the reaction can be computed as: yi =

Fi F  i Fi Ft

i  1, 2, 3, 4, 5

...(41)

Finally, the produced hydrogen mass flow rate is calculated from radial average total molar flow rate and radial average H2 mole fraction as follows:

 H = 2 Ft yH m 2 2

...(42)

2. Auto-thermal Reforming For auto-thermal reforming reactor with internal heating by partial oxidation reaction, one dimensional heterogeneous model is appropriate. The external concentration and temperature gradients as well as intraparticle concentration gradients are taken into account. Also the increase of the total number of moles due to reforming is considered. Other assumptions for modeling of auto-thermal reforming reactor are steady state, isothermal condition for inside the catalyst pellet, the plug flow reactor, adiabatic system and using effective binary diffusivities in the catalyst pellet with semi-spherical shape. The gas phase conservation equations for this system are as follows (Smet et al., 2001): G

d  Ci dz   g

Gc p

 s   kg av (Ci  Ci,s )  0 

dTg dz

 hf av (Tg  Ts )  0

...(43)

...(44)


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The solid phase mass and heat balance equations are expressed as (Semet et al., 2001): g

1 Die d  2 d  Ci, s        ri B  0 rp2 2 d  d   g  

hf av(Tg – Ts) + (1 – B) i (–Hri)B ri j = 0

...(45) ...(46)

The boundary conditions for above equations are: z=0

Ci = C 0i, Tg = T 0g

...(47)

= 0

d  Ci,s   0 d   g 

...(48)

= 1

g

Die d  Ci, s    rp d   g 

 kg (Ci  Cis,s )

...(49)

1

The auto-thermal reforming is assumed to consist of total methane oxidation and subsequent steam reforming and water-gas shift reactions. The following reaction kinetic equations on nickel catalyst with their parameters were extracted from literature (Trimm and Lam, 1980; Numaguchi and Kikuchi, 1988): r1 =

k1a PCH4 PO2

ax P (1 + kCH + K Oax2 PO2 )2 4 CH4

+

k1b PCH4 PO 2

ax P (1 + kCH + kOax2 PO2 ) 4 CH4

for CH4 + 2O2CO2 + 2H2O

r2 =

k2Num (PCH4 – PH32 PCO /K eq,2 /PH2O ) 

2 PH2O PCH 4 2

for CH4 + H2OCO + 3H2 r3 =

...(50)

...(51)

k3Num (PCO – PH2 PCO2 /K eq,3 /PH2O ) 3 3 PCH PCO 4

2

for CO + H2OCO2 + H2

...(52)

The combination of rate of reaction and effectiveness factors in equation (46) is as: ri j = [–1 r1 – 2 r2, 2 r2 – 3 r3, 1 r1 + 3 r3 – 21 r1, 32 r2 + 3 r3 + 21 r1 – 2 r2 – 3 r3]

...(53)

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3. Dry Reforming For the relatively slow dry reforming reaction and with fine catalyst pellets, it is possible to use a homogeneous model. However the mathematical model must be two dimensional, due to a high endothermic reaction and external heating. The assumptions for dry reforming reactor modeling are steady state condition, no temperature difference between fluid and catalyst pellets, constant values for physical properties and negligible pressure drop. The mass balance equation for CH4 is as follows (Akpan et al., 2007): us

FA  2 FA  2 FA 1 FA  Der     B B (rw2 )us rA  0 ...(54) D D er ea 2 2 z r r r z

Two dimensional heat balance equation is expressed as:  g c pus

  2T 1 T  T  2T  2  2     B B rA (Hri )  0 r r  z z  r

...(55)

Boundary conditions for the above equations are as follows: z = 0  us(FA – FA) = –Dea 0

dFA dz

...(56)

z=L

dFA =0 dz

...(57)

r=0

dFA =0 dr

...(58)

z = rw 

dFA =0 dr

z = 0  g us cp (T 0 – T) = – 

...(59) T z

...(60)

z=L

T =0 z

...(61)

r = 0

T =0 r

...(62)

r = rw  – 

T = U(T – Tw) r

...(63)

Kinetics of dry reforming reaction is expressed as follows (Akpan et al., 2007):


195

 F2 F2   FCH – CO H2  4 K eq FCO2   kgCH   – E   4 rA = k0 exp    kg  h  1/2 5  RT  [1 + 34.3FH ] cat   2

for CO2 + CH42CO + 2H2

...(64)

In addition, it is assumed that reverse water-gas shift reaction at equilibrium determines the gaseous mole fractions of CO2, H2, H2O and CO at each point. The Gibbs free energy for this reaction is as: G0 = 8545 – 7.8T

CO2 + H2  H2O + CO

for

...(65)

Now, elemental balance for C is as follows: 0 0 FCH + FCH = FCH + FCO + FCO 4

2

4

...(66)

2

Elemental balance for O: 0 2FCO = 2F CO + FCO + FH 2

...(67)

2O

2

Elemental balance for H: 0 4FCO = 4F CH + 2FH 4

2O

4

+ 2FH

...(68)

2

Equilibrium equation: PCO2 PH2

WGS = K eq

PCO PH2O

= =

(yCO2 Pt )(yH2 Pt )

...(69)

(yCO Pt )(yH2O Pt ) (FCO2 /Ft )(FH2 /Ft ) (FCO /Ft )(FH2O /Ft )

=

FCO2 FH2 FCO FH2O

Which: 1 WGS K eq

=

PCOPH2O

WGS ln(K eq ) = –3.798 +

PCO2 PH2

4160 T

...(70)

These set of equations can be written as follows: WGS K eq FCO FH

2O

– FCO FH = 0 2

...(71)

2

FCH + FCO + FCO – (F0CH + F0CO ) = 0 4

2

4

4FCH + 2FH 4

2O

+ 2FH – 4F0CH = 0 2

2FCO + FCO + FH 2

2

2O

4

– 2F0CO = 0 2

...(72) ...(73) ...(74)

196


Therefore, solution of differential equations (54-55) with dry reforming rate equation (64) determines methane molar flow rate. Then algebraic equations (71-74) are used for calculating the molar flow rates of other components based on reverse water gas shift reaction. Thus in these equations, the increase on total molar flow rate due to the reforming reaction is also considered.

Simulation In this section, the solutions of mathematical models for simulation of reactors at the base case are presented. Some of the simulation results are validated by comparison with existing literature experimental data. Moreover, the effect of changing the operating variables on the performance of reactors is studied. Thus from such sensitivity analysis, the important operating variables are selected for optimization at the next section.

1. Steam Reforming The governing two dimensional coupled partial differential equations (with three independent variables) for steam reforming reactor were solved from inlet tube direction. By using inlet conditions as the guess for the first axial grid, diffusion-reaction equations inside the catalyst pellet were solved. Then effectiveness factors were computed and it is possible to solve the gas phase equations in various reactor radial coordinate grids. Now the average temperature and concentrations in this axial grid were compared with the previous guess. After correcting and reaching to convergence, the procedure was repeated for the next axial grid. The diffusion-reaction equations inside the catalyst pellet with nonlinear source terms were discretized by central approximation finite difference. Then Newton-Raphson method was used and the sparse matrix was solved by Jacobian algorithm. For solving the gas phase partial differential equations, line method with 4th order RungeKutta algorithm was applied. The total gaseous molar flow rate was determined by addition of each gas computed average radial molar flow rates. Therefore, the increase in total gaseous molar flow rate in the reactor due to the reactions was accounted. Finally by dividing each gas average radial molar flow rate to the total gaseous molar flow rate, the average radial gaseous mole fraction profiles can be plotted along the reactor. The base case for steam reforming reactor was selected as operating condition of SRI synthesis gas production unit. There are 508 vertical reforming tubes packed with nickel/alumina catalyst in a furnace with sidefired configuration (SRI Report, 1976). The tube length is 40 ft. and its inner and outer diameters are 4 inch and 5.5 inch, respectively. The inlet natural gas and steam mass flow rates for each tube are 52.7 and 237 kg/h, respectively (SRI Report, 1976). The catalyst pellet diameter is 1.2 mm, the inlet feed temperature is 538°C and inlet pressure in the tube is 25.3


197

bar. The radial and axial gas phase temperature profiles are presented in Fig. 1. It is clear from Fig. 1 that there is maximum radial temperature gradient at inlet tube and this radial gradient is decreased along the reactor coordinate. In addition, it is possible to plot the radial-averaged bulk gas temperature versus reactor length. The competition between endothermic reforming reactions inside the tube and indirect heating from tube wall causes an increase of bulk gas temperature from 538 at inlet to about 898°C at outlet. There is a reasonable agreement between this predicted outlet temperature and reported SRI value (885°C) for outlet temperature (SRI Report, 1976). Moreover, outlet predicted pressure (22.3 bar) is very close to the reported SRI value (23.4 bar).

Fig. 1: Radial and axial temperature profiles in the steam reformer tube

The two-dimensional methane mole fraction profiles are indicated in Fig. 2. As this figure shows there is lower methane mole fraction near the tube wall, due to higher temperatures and consequently higher reaction rates at these points. It is also possible to plot three-dimensional methane mole fraction profile based on radial tube, axial tube and radial catalyst pellet coordinates. For example at z/L = 0.002 and r/rw = 0.8, the methane reaction rate decreased from 7 kmol/kgcat.s at catalyst surface to zero at about middle catalyst depth. Therefore, intrapellet diffusion controls the system and the effectiveness factor is extremely low for the steam reforming reaction. The radial-averaged gas phase mole fractions for all ingredients are plotted versus tube length in Fig. 3. This figure shows decreasing trend of gaseous reactants (CH4 and H2O) and increasing trend of gaseous products (CO, H2 and CO2) along the steam reforming tube. The outlet mole fractions for CH4, CO and H2 are predicted as 0.0104, 0.0809 and 0.4359, respectively.

198


Fig. 2: Two-dimensional methane mole fraction profiles in the steam reformer tube

Fig. 3: Radial-averaged gaseous mole fraction profiles along the steam reformer tube at the base case

These values are in good agreement with SRI reported outlet mole fractions as 0.0104, 0.0811 and 0.4228 (SRI Report, 1976). The H2/CO ratio of produced synthesis gas from simulation program is 5.39, while SRI reported ratio is 5.58. Finally the mass flow rate of produced synthesis gas in each tube is predicted as 66.4 kg/h from simulation, while the SRI reported value is 70 kg/h (SRI Report, 1976). Therefore, the accuracy of simulation framework is verified. Now the effect of variation in operating parameters on the steam reformer reactor performance with respect to the above base case is studied.


199

The comparisons are presented based on radial-averaged methane mole fraction profiles. The first operating parameter is inlet gas temperature. For example, by increasing of inlet gas temperature from 538 to 650°C, the unreacted methane mole fraction is decreased from 0.0104 to 0.0088. In this condition the H2/CO ratio is remained approximately constant, while the synthesis gas mass flow rate can be increased up to 1.25%. However, very high temperatures may cause rapid coke deposition and catalyst deactivation. The next parameter is operating pressure. The radial-averaged methane mole fraction profiles at various operating pressures are presented in Fig. 4. As this figure shows, by increasing the total pressure the methane conversion is decreased due to thermodynamics effect. For example, the unreacted methane mole fraction is increased from 0.0104 (at 25.3 bar) to 0.0250 (at 35 bar). However, the synthesis gas mass flow rate can be increased considerably (up to 22.6%) with respect to the base case, due to higher inlet density of methane at higher operating pressures. The H2/CO ratio is slightly increased from 5.39 (at 25.3 bar) to 5.46 (at 35 bar). But operation at higher pressures needs thicker alloys for constructing reformer tubes and increased capital costs.

Fig. 4: Radial-averaged methane mole fraction profiles along the steam reformer tube for various operating pressures

The variation on inlet steam/carbon ratio is now considered. This ratio at the base case is 4.45, which is more than stoichiometric ratio, because for prevention of coke deposition. If the steam/carbon ratio is reduced to 3, the final methane mole fraction will be reduced from 0.0104 to about 0.07. This effect is due to higher methane bulk gas concentrations at lower steam/ carbon ratios. However, operation under such condition causes severe coke deposition and catalyst deactivation and thus has not been recommended.

200


The last operating parameter is inlet natural gas mass flow rate. As this flow increased, the final unreacted methane mole fraction is increased and outlet hydrogen mole fraction is diminished due to lower methane residence time in the reformer tube. This behavior is clearly indicated in Fig. 5. However the produced hydrogen mass flow rate can be increased, because the multiplication of outlet hydrogen mole fraction with inlet natural gas mass flow rate determines the final hydrogen mass flow rate. For example, by increasing of inlet natural gas mass flow rate from 26761

Fig. 5: Radial-averaged methane and hydrogen mole fraction profiles along the steam reformer tube for various inlet natural gas mass flow rates


201

kg/h (52.7 kg/h for each tube, base case) to 35000 kg/h (68.9 kg/h for each tube), the produced hydrogen mass flow rate is increased up to 26.8%. But, the final unreacted methane mole fraction is also increased from 0.0104 (at base case) to 0.0200. Therefore, the produced hydrogen mass flow rate may have a maximum with inlet natural gas mass flow rate. However, a constraint on the allowable final unreacted methane mole fraction in the produced hydrogen must be considered for its quality.

2. Auto-thermal Reforming The model equations (43–46) form a set of differential and algebraic equations. Integration along the reactor co-ordinate was carried out using Runge-Kutta method. The solid-phase continuity equation was solved at each increment of the axial direction by means of the central finite deference method. The axial co-ordinate of reactor length is divided to several points, thus in each increment of reactor length one or several catalysts lie. By guess of components mole fraction in the inlet reactor, catalytic equations for each component solved and partial pressure of each component in the catalyst pellet is calculated. This procedure is continued until convergence obtains. By calculated partial pressures, effectiveness factor of each reaction is specified. Then ordinary equations for gas phase are solved and components mole fraction and temperature in the bulk gas are specified. The information obtained in this increment is used for the next step guess in the reactor length. Therefore, by using this method in all increments of the reactor, the dependent variables are calculated in all nodal points. Two base cases are considered for auto-thermal reforming. The first case is auto-thermal reforming for producing hydrogen and further fuelcell applications. The fixed-bed catalytic reactor is operated at atmospheric pressure in this case. In addition to methane and water vapor, air is injected as the oxygen source to the reactor. The second case is simulation of packed bed reactor with oxygen input to produce a synthesis gas or hydrogen without any nitrogen content. This synthesis gas can be further used for the methanol synthesis. Thus operation of auto-thermal synthesis gas producing reactor at high pressures will reduce the downstream compression costs. Moreover, at high pressure operation the product mass flow rate will be increased considerably. The nickel catalyst on an alumina support is considered for auto-thermal reforming. The reactor length, its diameter and catalyst radius for first case are 0.5 m, 0.1 m and 2.5 mm, respectively (Smet et al., 2001). These values for the second case are selected as 3 m, 1.6 m and 7.5 mm. The input gas temperature, operating pressure and feed mass flux for the first case are 773 K, 1 bar and 0.15 kg/m2.s, respectively. The above parameters for the second case are 773 K, 40 bar and 10 kg/m2.s. Finally, the inlet H2O/CH4 and CH4/O2 ratios in the first case are 1.5 and 2. These values for the second case are 1 and 1.8, respectively.

202


The simulation results of auto-thermal reforming are now explained. The temperature profiles for catalyst and bulk gas versus reactor length are presented in Fig. 6 for the atmospheric pressure and air injected operation. As this figure shows, there is a rapid temperature rise in the initial reactor lengths due to exothermic oxidation reaction. Then endothermic reforming reaction consumes some of this released heat and thus temperature variation diminishes. The catalyst temperature is slightly higher than bulk gas temperature due to the released heat from catalyst surface into bulk gas. However, the simulation results for oxygen injected auto-thermal reforming at high pressures showed a very high initial difference between catalyst surface and bulk gas temperatures. For example, at 773 K inlet gas temperature and 40 bar operating pressure, the initial catalyst surface temperature is calculated as 1373 K. Therefore, this 600°C overheating may cause some sintering or coke deposition on the catalyst.

Fig. 6: Catalyst and bulk gas temperature profiles for the atmospheric pressure auto-thermal reforming

The mole fraction profiles of ingredients along the auto-thermal reactor are indicated in Fig. 7 for atmospheric pressure and air injected condition (first case). There are six gaseous profiles in Fig. 7 with the remaining of nitrogen (from injected air). The same profiles are presented in Fig. 8 for high pressure and oxygen injected system (second case) without any nitrogen. As these figures show, the reactants (CH4, H2O and O2) mole fractions decrease and the products (H2, CO and CO 2) mole fractions increase along the reactor. These simulation profiles are in good agreement with the reported literature results (Smet et al., 2001). Finally, it is possible to express the three dimensional profile (versus reactor length and catalyst radius coordinates) for each component mole fraction. For example, H2 (a product) mole fraction shows an increasing trend along the reactor and a decreasing profile from center of pellet to the catalyst surface.


203

Fig. 7: Mole fraction profiles for atmospheric pressure and air injected auto-thermal reforming

Fig. 8: Mole fraction profiles for high pressure and oxygen injected auto-thermal reforming

Now effects of variation on the operating conditions versus base case on the system performance (especially the produced hydrogen mass flux) are studied. These effects are presented in Table 1 for atmospheric pressure and air injected auto-thermal reforming. The same results are indicated in Table 2 for high pressure and oxygen injected condition. As these tables show by increasing the feed mass flux, the produced hydrogen mass flux can be increased. However, the hydrogen quality is decreased due to increasing of unreacted methane mole fraction. Thus it is required to separate this impurity by pressure swing adsorption process. It is clear that the multiplication of feed mass flux and output hydrogen mass fraction

204


Table 1: Simulation results obtained from surveying parameters effect on the system performance for air injected and atmospheric pressure auto-thermal reforming Base case Inlet gas mass flux (kg m–2s–1) Inlet temp. (K) O2 mole fraction in the feed Outlet temp. (K) H2 mole fraction in the product CO mole fraction in the product CO2 mole fraction in the product CH4 mole fraction in the product Produced hydrogen mass flux (kg m–2s–1)

Inlet flow variation

Inlet temp. variation

Inlet O2 variation

0.15

0.165

0.135

0.15

0.15

0.15

0.15

773 0.1

773 0.1

773 0.1

723 0.1

823 0.1

773 0.12

773 0.8

962 0.3847

951 0.3452

986 0.4012

923 0.3312

1021 0.4197

1015 0.3714

932 0.3859

0.0883

0.0812

0.0907

0.0798

0.0912

0.1189

0.0713

0.0568

0.0496

0.0623

0.0470

0.0637

0.0613

0.0531

0.0025

0.0103

0.0021

0.0121

0.0020

0.0010

0.0212

0.0065

0.0062

0.0061

0.0054

0.0072

0.0060

0.0066

Table 2: Simulation results obtained from surveying parameters effect on the system performance for oxygen injected and high pressure auto-thermal reforming Base case Inlet gas mass flux (kg m–2s–1) Inlet temp. (K) O2 mole fraction in the feed Outlet temp. (K) H2 mole fraction in the product CO mole fraction in the product CO2 mole fraction in the product CH4 mole fraction in the product Produced hydrogen mass flux (kg m–2s–1)

Inlet flow variation

Inlet temp. variation

Inlet O2 variation

10

8

12

10

10

10

10

773 0.217

773 0.217

773 0.217

723 0.217

823 0.217

773 0.18

773 0.25

1364 0.4775

1412 0.4833

1348 0.4731

1326 0.4536

1391 0.4932

1329 0.4811

1434 0.4632

0.2256

0.2311

0.2180

0.2152

0.2313

0.2112

0.2318

0.0183

0.0187

0.0179

0.0174

0.0213

0.0161

0.0227

0.0010

0.0010

0.0010

0.0065

0.0008

0.0231

0.0006

0.7287

0.5926

0.8681

0.6848

0.7602

0.6662

0.7529

determines the produced hydrogen mass flux. The former is increased, while the output hydrogen mole fraction is decreased due to diminishing residence time. The inlet temperature increase or using higher input oxygen mole fractions is not recommended, because for obtaining the high catalyst temperatures. However, decreasing of these parameters shows some effects


205

on hydrogen mass flux and the H2/CO ratio of synthesis gas in Tables 1 and 2. Therefore, it is reasonable to use the feed mass flux with inlet gas temperature (or input oxygen mole fraction) as optimization variables. Moreover, the optimization constraint can be a limiting amount of unreacted methane mole fraction in the produced hydrogen.

3. Dry Reforming For the dry reforming process, partial differential equations (54-55) with rate equation (64) were solved simultaneously using the finite difference technique subject to the boundary conditions. The axial and radial grid lengths used during the solving of the differential equations were changed and tested to find the adequate values. The best results are 1730 grids for axial direction and 30 grids for radial coordinate. The computation of the CO2 reforming reaction together with reverse water gas shift reaction was accomplished by linking the discretized form of differential equations (54– 55) with algebraic equilibrium equations (71–74) for all grids with NewtonRaphson algorithm for finding the roots of resulting simultaneous and nonlinear equations. The dry reforming conservation equations predict an increasing trend for total gas velocity in the reactor, due to net molar increase during the reaction. Therefore, this variable velocity profile was used in the mass balance equation (54) and this procedure was repeated until convergence. However in the energy balance equation (55), the multiplication of gas density and its velocity is mass flux and remains constant in the steady state operation. The final velocity profile predicts about 43% increase in outlet total gas velocity at the base case. The selected base case is a reactor with 30 mm length, 6.3 mm diameter and packed with 0.3 mm Ni/CeO2ZrO2 catalyst pellets (Akpan et al., 2007). The inlet gas temperature (and wall temperature) is 973 K and the reactor pressure is about 1 bar. The inlet superficial gas velocity is 1300 m/h and the feed is consisted of 51.2% CH4 and 48.8% CO2. The radial-averaged mole fraction profiles of CH4, CO2, CO and H2 along the reactor are presented in Fig. 9 as continuous curves. In this figure, the outlet CO mole fraction is slightly higher than H2 mole fraction. In addition, the CO2 mole fraction profile is under CH4 profile. This behavior is due to reverse water gas shift reaction effect on the dry reforming. As this figure shows, there is a very good agreement between the simulation predictions and literature experimental data (Akpan et al., 2007). Therefore, the validity of dry reforming simulation with effect of reverse water gas shift reaction is verified. The simulation results without consideration of reverse water gas shift reaction effect are also presented in Fig. 9 as dot-line curves and show a considerable deviation with respect to output literature experimental data. This means that dot-line curves overestimate CO2 and underestimate

206


CO and predict the same mole fractions for CO and H2, while these predictions are in contrast with experimental data. Therefore, reverse water gas shift reaction must be considered together with dry reforming reaction for accurate simulation of the system. The H2/CO < 1 and also lower output CO2 mole fraction with respect to CH4 have been reported in other recent experimental work for dry reforming (Kambolis et al., 2010).

Fig. 9: Comparison of the radial-averaged mole fraction profiles of CH4, CO2, CO, and H2 from simulation for dry reforming with experimental data of Akpan et al., 2007

The radial-averaged gas temperature profile versus reactor length shows a decreasing trend from 973 K at beginning to about 890 K at outlet in the base case. This drop is due to an extremely endothermic CO2 reforming reaction. The radial gas temperature profile at z = L/2 shows about 1.5°C difference between near wall and centerline temperatures at the base case. However, this low radial temperature gradient causes a considerable radial mole fraction difference. For example, at z = L/2, the CH4 mole fractions at centerline and near wall are about 0.131 and 0.128, respectively. These results confirm the necessity for consideration of radial terms in mass and energy balance equations. Now effects of operating parameters variation are considered by increasing and decreasing of these parameters with respect to the base case. First of all, the effect of the feed inlet temperature variations on the radial-averaged hydrogen and methane mole fraction profiles is presented in Fig. 10. This figure shows a high effect of inlet feed temperature variation on the methane and produced hydrogen mole fractions. However, overheating of dry reforming catalysts in the absence of steam may accelerate coke deposition and deactivation.


207

Fig. 10: The predicted radial-averaged mole fraction profiles of CH4 and H2 for dry reforming at various inlet gas temperatures

The next parameter is inlet total molar flow rate. Total molar flow rate is representative of gas residence time, as its increasing causes decrease in residence time and decrease in methane conversion correspondingly. Results of 10% increase and decrease in the inlet total molar flow rate and

208


comparison with the base case are presented in Fig. 11 for methane and hydrogen mole fractions. As this figure shows by increasing of inlet total molar flow rate, the final hydrogen mole fraction diminishes. However by this variation, the multiplication of inlet mass flow rate and final hydrogen mole fraction can reach to a maximum. This multiplication is equal to the mass flow rate of produced hydrogen from the dry reforming process.

Fig. 11: The predicted radial-averaged mole fraction profiles of CH4 and H2 for dry reforming at various inlet flows


209

OPTIMIZATION

Multi Objective Optimization Optimization is the task of finding one or more solutions which correspond to minimizing or maximizing one or more specified objectives and satisfy all constraints. A multi-objective optimization task considers several conflicting objectives simultaneously. In such a case, there is usually no single optimal solution, but a set of alternatives exists with different tradeoffs, called pareto optimal solutions, or non-dominated solutions. Despite the existence of multiple pareto optimal solutions in practice, only one of these solutions is usually chosen. Thus, compared to single-objective optimization problems, in multi-objective optimization, there are at least two equally important tasks. There are an optimization task for finding pareto optimal solutions involving a computer-based procedure and a decision-making task for choosing a single, most preferred solution (Brank et al., 2008).

Genetic Algorithm (GA) Genetic Algorithm is an optimization tool based on Darwinian evolution (Gosselin et al., 2009). Genetic Algorithms start with randomly chosen parent chromosomes from the search space to create a population. They work with chromosome genotype. The population evolves towards better chromosomes by applying genetic operators which model genetic processes occurring in the nature selection, recombination and mutation. Selection compares chromosomes in the population and chooses them to take part in the reproduction process. Selection also occurs with a given probability on the basis of fitness functions. Fitness functions play the role of an environment to distinguish between good and bad solutions. The recombination is carried out after finishing the selection process. It combines, with predefined probability, features of two selected parent chromosomes and forms similar children. After the recombination, the offspring undergoes mutation. Generally, mutation refers to creation of a new chromosome from one and only one individual with predefined probability. After three operators are carried out, the offspring is inserted in the population, replacing the parent chromosomes, from which they were derived and produces a new generation. This cycle is performed until the optimization criterion is met (Shopova and Bancheva, 2006).

Non Dominated Sorting Genetic Algorithm-II (NSGA-II) The principles on which the NSGA-II relies are the same as those of the single-objective optimization. The strongest individuals or chromosomes are combined to create the offspring by crossover and mutations and this

210


scheme is repeated over many generations. However, the multi-objective optimization algorithm must consider the fact that there are many “best solutions”, which modify the selection process. The NSGA-II sorts individuals based on the non-domination rank and on the crowding distance to ensure a high level of performance as well as good dispersion of the results. NSGA-II main loop Step 1: An initial population N is chosen randomly within the range of the decision variables. This population is showed by Pt. The objective functions are calculated for each of the member of the population. The dominating member is that, which satisfy the conditions that it is not worse in all the objectives than the dominated member and at least better than the dominated member in one objective. Thus the members of the population are ranked according to their domination. The first set of non-dominated members is ranked one. After excluding these members from the population, the procedure is repeated to find the second set which has rank two and so until all the members in the population are ranked. The non-dominated set which has the lowest rank is the best solution. Step 2: Crowding distance for each individual is calculated. Individuals are sorted in each objective domain. The first individual and the last individual in the rank are assigned the infinity. For other individuals, the crowding distance is calculated by difference of the objectives values of two closest neighbors (Deb et al., 2006): m dnm = f n+1 – f mn–1

dn =

N obj

 dnm

...(75) ...(76)

m1

where dn, fn and Nobj are crowding distance of nth individual for objective m, crowding distance of nth individual and number of objectives, respectively. Step 3: Parents are selected by binary tournament selection. Between two solutions with different non-domination ranks the solution with the better rank is preferred. Otherwise if both solutions belong to the same front (rank), the solution which is located in lesser crowded region (has more crowding distance value) is preferred. Step 4: Two parents perform crossover and generate two offspring. Crossover is a genetic operator that combines two chromosomes (parents) to produce a new chromosome (offspring). The idea behind crossover is that the new chromosome may be better than both of the parents if it takes the best characteristics from each of the parents. Crossover occurs during


211

evolution according to a user-definable crossover probability. In this chapter arithmetic crossover is used: off spring 1 =  × Parent 1 + (1 – ) × Parent 2

...(77)

off spring 2 = (1 – ) × Parent 1 +  × Parent 2

...(78)

where  is a random weighting factor (chosen before each crossover operation). Offspring population is showed by Qt. Step 5: Sometimes, one or more gene (operating variable) values in a chromosome from its initial state alerted with mutation. It is analogous to biological mutation. In mutation, the solution may change entirely from the previous solution. Hence genetic algorithm can come to better solution by using mutation. Mutation occurs during evolution according to a userdefinable mutation probability. This probability should be set low. Gaussian mutation is used in this chapter. Mutant population is showed by Rt. Step 6: Non-dominated sorting (step 1) is applied to Pt + Q t + Rt population. All non-dominated fronts of this population are copied to parent population (Pt + 1) rank by rank. Parent population will generate offspring to the next generation. Step 7: Adding the individuals in the parent population is stopped when the size of it is larger than the population size (N). Individuals in the last accepted that make the parents population more than N, sorted by crowded distance sorting (step 2). This cycle is performed until the optimization criterion is met.

Optimization Results Non-dominated Sorting Genetic Algorithm-II (NSGA-II) was used to optimize and obtain pareto-optimal solutions. Population size of 20 was chosen with crossover of 0.7 and mutation probability of 0.05. Input parameters of NSGA-II are given in Table 3. Now the results of optimization for various hydrogen and synthesis gas production methods from natural gas are presented. Table 3: Input parameters of NSGA-II optimization Parameter name

Method and value

Number of decision variables Number of objectives Population size Crossover method Crossover probability Mutation probability 0.05

Different 2 20 Arithmetic crossover 0.7 Gauss method

212


1. Steam Reforming In this section the results of steam reformer optimization are presented. The objectives are: Objective 1: Minimizing 1 – XCH (Maximizing methane conversion) ...(79) 4

Objective 2: Minimizing

1 H ) (Maximizing m 2 H m 2

...(80)

Subject to: 400ºC  feed temperature  650º 20000

...(81)

kg kg  feed mass flux  35000 h h

...(82)

15 bar  feed pressure  35 bar

...(83)

H O 6 3  2   CH4 inlet

...(84)

Other parameters were the same as the base case. Different operations were performed for 20 generations to obtain non-dominated pareto-optimal solutions. By comparing these solutions (chromosomes), the best solution was determined. At this optimized condition, feed temperature, pressure, mass flow rate and H2O/CH4 in feed are 577°C, 15.5 bar, 30120 kg/h and 4.37 respectively. The methane conversion and hydrogen produced mass flow rate are 97.7% and 10975 kg/h. It is obvious that there is a huge increase in methane conversion and produced hydrogen mass flow with respect to the base case. On the other word methane conversion increased from 89.2% to 97.7% and hydrogen mass flow rate increased from 10000 kg/h to 10975 kg/h. Therefore, it shows the importance of optimization of steam reformer for hydrogen production.

2. Auto-thermal Reforming The high pressure packed bed reactor with oxygen input to produce hydrogen without any nitrogen content was optimized. The objectives are the same as steam reforming. The optimization parameters are: 400 C  feed temperature  600 C

8

kg m 2 .s

 superficial feed mass flux  20

...(85)

kg m2 .s

...(86)


213

 O  0.5   2   0.6  CH4 inlet

...(87)

H O  1.5 0.8   2   CH4  inlet

...(88)

Table 4 shows the pareto-optimal solution sets after 20 generations. It can be seen that the chromosome 2 is the best solution for autothermal reformer optimization. Table 4: No n-dominate d pare to-o ptimal solutions fo r autothermal reformer optimization

Sl. TFeed(ºC) no.

1 2 3 4 5 6 7 9

438.18 578.57 538.11 442.68 529.17 539.93 461.03 459.17

 kg  G 2   m .s 

 O2   CH   4  inlet

 H 2O   CH   4 inlet

kg   H  m  2  m 2 .s 

XCH

10.050 18.387 18.242 14.433 18.445 12.360 12.049 11.117

0.55063 0.51639 0.54436 0.55482 0.55801 0.55080 0.55383 0.55111

0.95217 0.97643 0.95252 0.97013 1.09950 1.02590 0.97959 0.97026

0.721865 1.466426 1.392409 1.042970 1.318983 0.881290 0.858959 0792644

0.997544 0.984731 0.996084 0.997342 0.997241 0.997484 0.997514 0.997526

4

CONCLUSIONS

In this chapter various hydrogen and synthesis gas producing methods from natural gas were considered. These methods consist of steam reforming, autothermal reforming and dry reforming. The suitable mathematical models for these production methods were proposed. Then simulation was performed by solution of the related differential equations and the performances of various hydrogen and synthesis gas producing methods were studied. The model validation was carried out by comparison with some experimental literature data. Also the effects of operating conditions on the behavior of reactors were investigated by simulation framework. Finally, optimization of steam reformer and autothermal reformer for maximum hydrogen production rate was performed by genetic algorithm method. NOTATION av Ai cp

External pellet surface area per unit reactor volume, m–1 Pre-exponential factor, reaction dependent Specific heat at constant pressure, J kg–1 K–1

214


Ci Ci,s i Ci,s dr Die Der Dea f Fi g G hf Ir kg ki Keq,i Ki

Molar concentration of species i at bulk gas, mol m–3 Intra-particle molar concentration of species i, mol m–3 Molar concentration of species i, at the external pellet surface, mol m–3 Reactor diameter, m Effective diffusion coefficient of species i in catalyst, m2 s–1 Radial diffusion coefficient in the reactor, m2 s–1 Axial diffusion coefficient in the reactor, m2 s–1 Friction factor Molar flow rate of component i, mol s–1 Acceleration of gravity, ms–2 Superficial mass flux of feed, kgm–2 s–1 Gas-to-solid heat transfer coefficient, W m–2 K–1 Reactor length, m Gas-to-solid mass transfer coefficient, ms–1 Reaction rate constant of reaction i, reaction dependent Equilibrium constant of reaction i, reaction dependent Adsorption constant for component i in reforming and water–gas reactions, bar–1 Adsorption constant for component i in combustion reaction, bar–1 Mass flow rate of produced hydrogen, kg s–1 Mean molecular weight, kg mol–1 Partial pressure of component i, bar Total pressure, bar Radial reactor co-ordinate, m –1 Rate of reaction i, mol kg–1 cat s Pellet radius, m Reactor radius, m Gas-phase temperature, K Solid temperature, K Wall temperature, K Superficial velocity, ms–1 Overall heat transfer coefficient, Wm–2 K–1 Extent of reaction of component i Methane conversion Mole fraction of species i Axial reactor co-ordinate, m Heat of reaction, J mol–1 Void fraction of catalyst in the reactor Effectiveness factor of reaction i Thermal conductivity, W m–1 K–1 Catalyst density, kg m–3 Gas density, kg m–3 Dimensionless pellet co-ordinate

Kiox

H m

Mav2 pi Pt r ri rp rw Tg Ts Tw us U xi XCH 4 yi z Hri B i  B g 

REFERENCES Afshar, A., Ale Ebrahim, H., Jamshidi, E. and Faramarzi, A.H. 2010. Synthesis gas and zinc pro duction in a noncatalytic pack ed be d re actor . Che m. Eng. Te chnol., 33: 1989–98. Afshar, A., Ale Ebrahim, H. and Faramarzi, A.H. 2012. Noncatalytic synthesis gas production by reduction of ZnO with methane in a dilute phase pneumatic conveying reactor. Ind. Eng. Chem. Res., 51: 3271–8. Akpan, E., Sun, Y., Kumar, P., Ibrahim, H., Aboudheir, A. and Idem, R. 2007. Kinetics experimental and reactor modeling studies of the carbon dioxide reforming of methane


215

(CDRM) over a new Ni/CeO2-ZrO2 catalyst in a packed bed tubular reactor. Chem. Eng. Sci., 62: 4012–24. Ale Ebrahim, H. and Jamshidi, E. 2004. Synthesis gas production by zinc oxide reaction with methane: Elimination of greenhouse gas emission from a metallurgical plant. Energy Convers. Manag., 45: 345–63. Ale Ebrahim, H. 2010. Application of random pore model to SO2 capture by lime. Ind. Eng. Chem. Res., 49: 117–22. Ale Ebrahim, H. 2012. New syngas production method based on non-catalytic methane reaction w ith metal oxides, Chapter 2 in Syngas production applic ations and environmental impact, New York: Nova Science Publishers. Aydinoglu, S.O. 2010. Thermodynamic equilibrium analysis of combined carbon dioxide reforming with steam reforming of methane to synthesis gas. Int. J. Hydrogen Energy, 35: 12821–8. Bonenfant, D., Mimeault, M. and Hausler, R. 2003. Determination of the structural features of distinct amines important for the absorption of CO2 and regeneration in aqueous solution. Ind. Eng. Chem. Res., 42: 3179–84. Brank, J., Deb, K., Meittinen, K. and Slowinski, R. 2008. Multiobjective optimization: Interactive and evolutionary approaches. Berlin: Springer-Verlag. Chakraborty, S., Tiedemann, A.V. and Teng, P.S. 2000. Climate change: Potential impact on plant diseases. Environ. Pollut., 108: 317–26. Chauvel, A. and Lefebvre, G. 1989. Petrochemical Processes. Paris: Editions Techn. Costa, P.D., Potvin, C., Manoli, J.M., Lemberton, J.L., Perot, G. and Mariadassou, G.D. 2002. New catalysts for deep hydrotreatment of diesel fuel: Kinetics of 4, 6 dimethyl dibenzothiophene hydrodesulfurization over alumina supported molybdenum carbide. J. Mol. Catal. A: Chem., 184: 323–33. Dawe, R.A. 2000. Modern Petroleum Technology. New York: John Wiley and Sons, 1: 337–82. Deb, K., Sundar, J., Rao, U.B. and Chaudhuri, S. 2006. Reference point based multi-objective optimization using evolutionary algorithms. Int. J. Comput. Intellig. Res., 2: 273–86. Deutschmann, O. and Schmidt, L.D. 1998. Modeling the partial oxidation of methane in a short-contact-time reactor. AIChE J., 44: 2465–77. Dry, M.E. 2001. High quality diesel via the Fischer-Tropsch process: A review. J. Chem. Technol. Biotechnol., 77: 43–50. Dybkjaer, J. 1995. Tubular reforming and auto-thermal reforming of natural gas: An overview of available processes. Fuel Process Technol., 42: 85–107. Froment, G.F. 2000. Production of synthesis gas by steam and CO2 reforming of natural gas. J. Molecular Catalysis A: Chem., 163: 147–56. Gosiewski, K. 2001. Simulation of non-stationary reactors for the catalytic conversion of methane to synthesis gas. Chem. Eng. Sci., 56: 1501–10. Gosselin, L., Tye-Gingras, M. and Mathieu-Potvin, F. 2009. Review of utilization of genetic algorithms in heat transfer problems. Int. J. Heat Mass Trans., 52: 2169–88. Gupta, H. and Fan, L.S. 2002. Carbonation calcinations cycle using high reactivity calcium oxide for carbon dioxide separation from flue gas. Ind. Eng. Chem. Res., 41: 4035–42. Halmann, M. and Steinfeld, A. 2006. Thermoneutral tri-reforming of flue gases from coal and gas fired power stations. Catalysis Today, 115: 170–8. Kambolis, A., Matralis, H., Trovarelli, A. and Papadopoulou, C. 2010. Ni/CeO2-ZrO2 catalysts for the dry reforming of methane. Appl. Catal. A, 377: 16–26. Othmer Kirk 1991. Encyclopedia of Chemical Technology. New York: John-Wiley and Sons, 12: 318–40. Othmer Kirk 1995. Encyclopedia of Chemical Technology. New York: John Wiley & Sons. 2: 638–91. Krishna, R., Ellenberger, J. and Sie, S.T. 1996. Reactor development for conversion of natural gas to liquid fuels: A scale-up strategy relying on hydrodynamic analogies. Chem. Eng. Sci., 51: 2041–50. Morrison, A., Hietkamp, S. and Van Vuuren, D.S. 2004. Direct reduction process using fines and with reduced CO2 emissions. Ironmaking Steelmaking, 31: 285–90.

216


Na, B.K., Lee, H., Koo, K.K. and Song, H.K. 2002. Effect of rinse and recycle methods on the pressure swing adsorption process to recover CO 2 from power plant flue gas using activated carbon. Ind. Eng. Chem. Res., 41: 5498–503. Numaguchi, T. and Kikuchi, K. 1988. Intrinsic kinetics and design simulation in a complex reaction network: Steam methane reforming. Chem. Eng. Sci., 43: 2295–301. Parisi, D.R. and Laborde, M.A. 2004. Modeling of counter current moving bed gas-solid reactor used in direct reduction of iron ore. Chem. Eng. J., 104: 35–43. Pedernera, M.N., Pina, J., Borio, D.O. and Bucala, V. 2003. Use of a heterogeneous twodimensional model to improve the primary steam reforming performance. Chem. Eng. J., 94: 29–40. Rashidi, H., Ale Ebrahim, H. and Dabir, B. 2013. Application of random pore model for synthesis gas production by nickel oxide reduction with methane. Energy Convers. Manag., 74: 249–60. Ryden, M., Lyngfelt, A. and Mattisson, T. 2006. Synthesis gas generation by chemical looping reforming in a continuously operating laboratory reactor. Fuel, 85: 1631–41. Shimizu, T., Peglow, M., Yamagiwa, K., Tamaka, M., Sakuno, S., Misawa, N., Suzuki, N., Udea, H., Sasatsu, H. and Gotou, H. 2002. A simplified model of SO2 capture by limestone in 71 MW pressurized fluidized bed combustor. Chem. Eng. Sci., 57:4117–28. Shopova, E.G. and Bancheva, N.G.V. 2006. BASIC-A genetic algorithm for engineering problems solution. Comp. Chem. Eng., 30: 1293–309. Smet, C.R.H., Croon, M.H.J.M., Berger, R.J., Marin, G.B. and Schouten, J.C. 2001. Design of adiabatic fixed-bed reactors for the partial oxidation of methane to synthesis gas. Application to production of methanol and hydrogen for fuel cells. Chem. Eng. Sci., 56: 4849–61. Snoeck, J.W., Froment, G.F. and Fowles, M. 2002. Steam/CO2 reforming of methane. Carbon formation and gasification on catalysts with various potassium contents. Ind. Eng. Chem. Res., 41: 3548–56. Song, C. and Pan, W. 2004. Tri-reforming of methane: A novel concept for catalytic production of industrially useful synthesis gas with desired H2/CO ratios. Catalysis Today, 98: 463– 84. SRI Report. 1976. Synthesis gas by catalytic steam reforming of natural gas. Thomas, S. and Dawe, R.A. 2003. Review of ways to transport natural gas energy from countries which do not need the gas for domestic use. Energy, 28: 1461–77. Trimm, D.L. and Lam, C.W. 1980. The combustion of methane on platinum alumina fiber catalysts I. Kinetics and mechanism. Chem. Eng. Sci., 35: 1405–13. Wang, S., Lu, G.O. and Millar, G.J. 1996. Carbon dioxide reforming of methane to produce synthesis gas over metal-supported catalysts: State of the art. Energy Fuels, 10: 896–904. Wu, S., Sumie, N., Su, C. and Sasaoka, E. 2002. Preparation of macroporous lime from natural lime by swelling method with water and acetic acid mixture for removal of sulfur dioxide at high temperature. Ind. Eng. Chem. Res., 41: 1352–56. Xu, J. and Froment, G.F. 1989. Methane steam reforming, methanation and water-gas shift: I. Intrinsic kinetics. AIChE J., 35: 88–96.