Multi-objective optimisation of steam methane

Journal of Cleaner Production 180 (2018) 655e665

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Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro

Multi-objective optimisation of steam methane reforming considering stoichiometric ratio indicator for methanol production Hamid Reza Shahhosseini a, Davood Iranshahi b, *, Samrand Saeidi c, Ehsan Pourazadi d, Ji
rí Jaromír Kleme
s e a

Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Avenue, Tehran 15914, Iran €t Bremen, Badgasteiner Str. 1, 28359 Bremen, Germany Technische Thermodynamik, Universita d Department of Chemical and Process Engineering, University of Canterbury, Christchurch 8140, New Zealand e Sustainable Process Integration Laboratory e SPIL, NETME Centre, Faculty of Mechanical Engineering, Brno University of Technology e VUT Brno,  2896/2, 616 00 Brno, Czech Republic Technicka b c

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 29 December 2017

This work proposes a novel configuration for steam methane reformers (SMR) in order to improve their syngas stoichiometric ratio (SR). This is a decisive element for methanol producers to increase their production tonnage. While the optimum theoretical SR value is around 2, many conventional SMRs operate far beyond this value due to thermodynamic equilibrium limitations. In the new SMR design CO2, which could be an industrial off gas, is injected into the reactor in multiple stages. The corresponding CO2 injection flow rate is determined by a multi-objective optimization method. The optimum flow rate at each stage is chosen to minimise abs (SR-2) while maintaining the CH4 conversion at its highest value (about 68%). Furthermore, the new design helps to improve the thermodynamic equilibrium conversion in SMR resulting in 33% more CO production. As well as this, the pressure drop along the new reactor is proved to be substantially lower than the conventional SMR. © 2018 Elsevier Ltd. All rights reserved.

Keywords: Steam reforming Methanol synthesis Multi-objective optimisation Pareto frontier Methanol economy Stoichiometric ratio SR

1. Introduction Abundant amounts of energy have been consumed to continuously improve humanity's living standards. Natural gas, oil and coal, still constitute our major energy sources and offer the raw

materials for producing a large variety of derivatives (Cu cek et al., 2015). However, those resources are still not sustainable, even with discoveries of new sources. It has been assessed that mankind will probably run out of coal, oil and natural gas within the next

cek et al., 2012). For this reason, all feasible althree centuries (Cu ternatives have to be investigated to find feasible and long-term solutions. Alongside the problem of power generation (Rozali et al., 2015), an important task has been how to store and efficiently use energy (Alwi et al., 2013). Numerous literature reports have discussed the importance of H2 and methanol as alternative fuel options to secure the future of energy market (Van-Dal and Bouallou, 2013; Riaz et al., 2013; Dutta,

* Corresponding author. E-mail address: [email protected] (D. Iranshahi). https://doi.org/10.1016/j.jclepro.2017.12.201 0959-6526/© 2018 Elsevier Ltd. All rights reserved.

2014). However, a hydrogen-based energy economy requires substantial technological advancement in storage and transportation, as well as addressing socioeconomic and infrastructural barriers. There are also some safety concerns in this area (Edwards et al., 2008). Meanwhile, methanol (MeOH) is considered to be a more feasible alternative (compared to H2) since it is a safer liquid and easier to store and distribute (Masih et al., 2010). The role of MeOH in delivering a cleaner energy model has been further explored in the ‘Methanol economy’e a novel conceptual framework which has been proposed by Olah et al. (2011). MeOH can be used as fuel by blending with gasoline for internal combustion engines (ICE). Problems still are to be addressed with regard to the metal corrosion issue (i.e. especially for aluminium, zinc, and magnesium) and cold engine start. Mixtures of methanol and gasoline are already being marketed in China for internal combustion engines. In Shanxi province alone, there are more than 1000 petrol stations which distribute M15, M85 and M100 (100% methanol) gasoline/methanol blends (Mendes et al., 2014; Siriworarat et al., 2017). Methanol is also a solvent and building block for producing intermediates, complex chemical compounds, and synthetic hydrocarbons. Primarily it is used for formaldehyde (which consumes

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about 30% of the total methanol production in the worldwide), acetic acid, methyl-tert-butyl ether (MTBE) and dimethyl ether synthesis (Chuah et al., 2016; Kliopova et al., 2016; Riaz et al., 2013). It can also be used in on-grid and off-grid power turbines and a hydrogen carrier for fuel cell technology (Nikoo et al., 2015). Predictions show a steady growth in the methanol market especially through China as the biggest consumer of methanol for formaldehyde and as an alternative to transportation fuel (Liran et al., 2015). Using methanol as fuel substantially reBarraga duces the emissions of greenhouse gases, haze initiators such hydrocarbons, NOx, SOx and particulate materials. The forecasted global methanol demand as well as its production capacity are illustrated in Fig. 1 (Alvarado, 2016). 1.1. Methanol-economy players and barriers Methanol as a clean and sustainable energy supply can be produced from variety of feed sources such as natural gas, coal, biomass and landfill gas (Kravanja et al., 2015). However, natural gas is considered to be the most viable and primary feedstock for syngas production in methanol plants mainly because of its abundance, availability of well-established refining and processing technologies/infrastructures as well as its environmental merits compared to coal and oil (Velasco et al., 2010). Evaluation of around 25 available methanol production technologies by Shell Research and Technology Centre, suggests that although various commercialized reactor designs and catalyst vendor technologies are crucial factors of the methanol economy and its cost (i.e. mainly due to the balance between production and market demand), synthesis gas manufacturers are playing a more vital role. In conventional reforming reactors, thermodynamic equilibrium limitations results in inappropriate syngas composition and stoichiometry ratio (SR) which could be a barrier for additional methanol production. Improving SR of syngas in traditional reformers can be considered as the most practical factor to improve the methanol plant production capacity while saving the processing and manufacturing costs (Lange, 2001). Hence our focus in this work is to optimize syngas molar ratio in reformers for subsequent downstream methanol plants. 1.2. Methanol production and the importance of syngas stoichiometric ratio (SR) Major industrial scale methanol production processes include

two main units (Bozzano and Manenti, 2016): (i) Production of syngas (i.e. a mixture of H2, CO and CO2) via steam methane reforming which includes the following reactions (Bulatov and Kleme
s, 2011; Xu and Froment, 1989b)

CH4 þ H2 O4CO þ 3H2

(1)

CO þ H2 O4CO2 þ H2

(2)

CH4 þ 2H2 O4CO2 þ 4H2

(3)

A simplified schematic of steam methane reforming (SMR) process is illustrated in Fig. 2. The refined and desulphurised natural gas is sent to the performer. The performer is an adiabatic reactor which eliminates traces of remaining sulphur and converts heavy hydrocarbons to methane (Rajesh et al., 2000). The outlet stream is mixed with steam and fed to reformer where the synthesis gas is produced. Afterwards, to reduce the amount of CO, the outlet stream is sent to at least two water-gas shift (WGS) adiabatic reactors. These two reactors are high temperature (HT) and low temperature (LT) (Saeidi et al., 2014, 2015) WGS reactors which accommodate an H2-rich gas mixture. (ii) Conversion of the syngas to methanol through two main reactions (Lange, 2001)

CO þ 2H2 4CH3 OH

(4)

CO2 þ H2 4CO þ H2 O

(5)

Here, the ideal composition of syngas for methanol synthesis is usually characterised by the stoichiometric number SR which is the ratio of the difference between moles of H2 and CO2 over the sum of CO and CO2 (eq. (6)).

SR ¼

H2  CO2 CO þ CO2

(6)

Note that the stoichiometric value SR should include the CO2 molar flow rate as well since H2 reacts with CO2 through the reverse wateregas shift reaction (reaction 5). Methanol operators prefer to feed their rectors with SR ¼ 2.0e2.1 (Rostrup-Nielsen, 2000) which results in substantial economic benefits by improving single pass syngas conversion and decreasing purges and unconverted gas

Fig. 1. Global methanol production and market demand forecast by 2020 (Alvarado, 2016).

H.R. Shahhosseini et al. / Journal of Cleaner Production 180 (2018) 655e665

657

Fig. 2. Diagram for the conventional steam methane reforming (SMR).

recycling (Lange, 2001). Theoretically, SR ¼ 2 is expected to be the best ratio for maximum methanol production. Larger values necessitate additional technologies for hydrogen separation and recycling while SR < 2 yields excessive by-products such as alcohols with more than two carbons. The synthesis gas which is produced by one step reforming has a typical SR of 2.8e3 and contains H2 surplus of about 40% (Aasberg-Petersen et al., 2001). This needs expensive external technologies such as membranes or end-of-pipe treatment processes to separate and recycle excess H2 (Alwi et al., 2016). Another option is to adjust excess H2 ratio by injecting CO2. However, based on experimental work conducted by Ryi et al. (2014), the addition of CO2 to the inlet feed stream of SMR considerably decreases the methane conversion (specially at T < 1073 K) due to lower activity of Ni/MgAL2O3 catalyst in the cofeeding approach. Hence in this work we will adopt a new strategy to inject CO2 and optimize the SR value for methanol units while maintaining high degree conversion of methane. Note that the CO2 with the natural gas (i.e. separated in absorbers in gas refineries) as well as power plants, cement industries, steel manufacturers, aluminium smelters and fermenter exhaust streams are feasible carbon dioxide sources and may easily be accessible for CO2 injection in SMRs. Using purges from these industries will also help to alleviate environmental concerns regarding their contribution to greenhouse gas emission (Olah et al., 2011).

1.3. Multi-objective optimisation Chemical process industries are seeking to maximise their production capacities and products quality. This also applies to methanol industries and their corresponding SMR which determines the final methanol throughput (Mohanty, 2006). However, there is usually a trade-off between production capacity and quality. A promising decision can be made using multi-objective

cek, 2013; Li optimisation (MOO) technique (Kravanja and Cu et al., 2009; Tian et al., 2011; Sayyaadi et al., 2011). Using MOO, the problem can be mathematically formulated as follows:

! ! ! ! minimise fð x Þ ¼ ½f 1 ð x Þ; f 2 ð x Þ; …; f k ð x ÞT Subject to : !! gðxÞ  0 !! hðxÞ ¼ 0 !! !! !! ! x 2Rn ; f ð x Þ2Rk ; g ð x Þ2Rm and h ð x Þ2Rp

(7)

where k; n; m and q are the number of objective functions, independent variables xi , inequality and equality constraints. In this !! ! regard, x 2Rn is a vector of decision variables and f ð x Þ2RK is a vector of objective functions. The feasible decision space X and feasible criterion space (feasible search region) W are defined as follow:


! !  ! X ¼ x gi ð x Þ  0; i ¼ 1; 2; …; m and hj ð x Þ ¼ 0; j ¼ 1; 2; …; p ! ! W ¼ fFð x Þj x 2Xg (8) Since a MOO problem requires simultaneous satisfaction of different and often conflicting objectives, there is no single global solution. Therefore, among various objectives, it is necessary to determine a set of points from which the optimal trade-off parameters are selected. Pareto frontier helps to find such a set of optimal points which result in the maximized conditions. Pareto frontier is defined as follows:

! ! f i ð x Þ  f *i ð x Þ for all i2f1; 2; …; kg ! * ! f i ð x Þ < f i ð x Þ for alteast once i2f1; 2; …; kg

(9)

Vector f * is a Pareto optimal solution if there is no other f in the feasible search region (Madetoja et al., 2008). Fig. 3 displays Pareto frontier and the feasible search region for four possible combinations of two types of objectives. The solutions in the Pareto set are mathematically equivalent and there is no preference among them, but a user should select a single final solution. There are two techniques to find the only solution to MOO problems: (i) techniques with previous preferences

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H.R. Shahhosseini et al. / Journal of Cleaner Production 180 (2018) 655e665

Feasible search region

Feasible search region

1

1

Minimise 2

CH4 conversion using multi-objective optimization (MOO) method. To best of our knowledge this is the first time that such strategy has been employed for SMRs. The basics of multi-objective optimization technique and its application in industries including reformers is explained subsequently.

2

2

Minimise

Minimise 2

Feasible search region

Maximise

Maximise

Minimise

2.1. Mathematical modelling of conventional SMR and the novel configuration description

Feasible search region

Our steady state mathematical modelling of conventional SMR reactor was validated against Pantoleontos et al. (2012) experimental data. Our major assumptions for this modelling are: 1

1

Maximise

Maximise

Fig. 3. Pareto set for four combinations of two types of objectives.

and (ii) techniques with subsequent preferences (Marler and Arora, 2004). In previous preferences techniques, the relative significance of various objective functions can be estimated by employing the higher level information. According to the estimation, the MOO problem could then be transferred into a single-objective optimization (SOO) problem to be solved in an evolutionary or a classical way. Transformation could happen using the Weighted Product Method (WPM). In this method, the compound function is introduced by multiplication of objectives with a user-defined power as below:

Y ! ! minimise Feq ð x Þ ¼ ½f i ð x Þwi

2. Results and discussion

k

(10)

i¼1

where w is a vector of powers which is selected by user (Deb, 2005). The attribution of weight factors to various objectives depends on the decision makers' viewpoint, therefore various solutions may be attained for identical problems. In the subsequent preferences techniques, the decision makers play a critical role and directly perform their priority on Pareto frontier to select one of the equivalent choices as the only solution point. In this technique, the decisive solution exactly refers to decision makers priorities (Marler and Arora, 2004; Taghdisian et al., 2015).

1.4. Current study objective Although there have been studies and reviews regarding new reactor configurations, gas recovery technologies and emission policies for methanol industries to enhance production (Saeidi et al., 2014; Luu et al., 2016; Kleme
s, 2010), there are few modelling studies on SMR reactors for this purpose. The aim of the present study is to introduce a new configuration for SMR to achieve SR ¼ 2 and eliminate the implementation of downstream H2 separation and recycling practises. Here, we propose a multi-step CO2 shot along the SMR reactor tubes which is also expected to enhance the reaction rates based on the Le Chatelier's principle. The length of the conventional SMR reactor is discretised into several segments for CO2 injections. Iranshahi et al. (2011) and Arabpour et al. (2012) integrated this strategy combined with differential evolution (DE) optimization in the naphtha reformer and Fischer-Tropsch reactors for conversion enhancement. In this work, the optimal CO2 injection is determined by minimising abs (SR-2), and maximising

(i) Ideal gas phase behaviour (The compressibility factor z of the feed stream is calculated to be 0.990 and 0.991 based on the Peng-Robinson and Soave-Redlich-Kwong equations of state. For the product stream the values are 1.002 and 1.001, respectively). (ii) Plug flow and negligible axial dispersion of heat and mass. (iii) No radial concentration and temperature gradients. (iv) Uniform particle size and constant bed porosity (v) Only reactions (1) to (3) from Xu and Froment (1989b) are considered to reduce the complexity of modelling and optimization The corresponding SMR reaction rates are provided in Table 1. Equilibrium constants, Arrhenius kinetic parameters and Van't Hoff parameters for species adsorption are presented in Table 2 (Xu and Froment, 1989a). The consumption or formation rate for species “i”, ri (kmol/ kgcat.h), are evaluated by summing the reaction rates of species i, in reaction j, Rj (kmol/kgcat.h), in all three reactions. Effectiveness factors hj are also applied which account for the intra-particle transport restriction. Regarding the reactions (1) to (3), one can obtain the reaction rate of SMR species as follows:

rCH4 ¼ h1 R1  h3 R3 rH2 O ¼ h1 R1  h2 R2  2h3 R3 rH2 ¼ 3h1 R1 þ h2 R2 þ 4h3 R3 rCO ¼ h1 R1  h2 R2 rCO2 ¼ h2 R2 þ h3 R3

(15)

where h1 ¼ 0.07, h2 ¼ 0.7, h3 ¼ 0.06 (De Groote and Froment, 1996). Table 1 SMR kinetic reaction model. Reaction rate equation

R1 ¼

k1 p2:5 H2

R2 ¼

k2 pH2

R3 ¼

k3 p3:5 H2

pCH4 pH2 O 

p3H2 pCO

!

Ke1



1

(11)

U2

  p p 1 pCO pH2 O  H2 CO2  2 Ke2 U

pCH4 p2H2 O 

p4H2 pCO2 Ke3

! 

(12)

1

(13)

U2

U ¼ 1 þ kCO pCO þ kH2 pH2 þ kCH4 pCH4 þ kH2 O

p H2 O p H2

(14)

H.R. Shahhosseini et al. / Journal of Cleaner Production 180 (2018) 655e665

659

Table 2 Reaction equilibrium constants, Arrhenius kinetic parameters and Van't Hoff parameters for adsorption of species. Reaction; j ðsee Table 1Þ

koj ðkmol=kgcat hÞ

Ej ðkJ=kmolÞ

4:2251015 ðbar0:5 Þ

240100

1:955106

67130

1:0201015 ðbar0:5 Þ

243900

  DH H O kH2 O ¼ ko;H2 O exp  RT2

  DH H kH2 ¼ ko;H2 exp  RT 2

  HCO kCO ¼ kCO exp  DRT

ko;H2 O ¼ 1:77105

ko;H2 ¼ 6:12109 ðbar1 Þ   kj DHH2 ¼ 82:9103 kmol

ko;CO ¼ 8:23105 ðbar1 Þ   kj DHCO ¼ 70:65103 kmol

Equilibrium constant; kej 

1

ke1

2

ke2

3

ke3 

E



kj ¼ koj exp  RTj   DHCH kCH4 ¼ ko;CH4 exp  RT 4 ko;CH4 ¼ 6:65104 ðbar1 Þ   kj DHCH4 ¼ 38:2103 kmol

 3 ¼ 4:7071012 exp  206:110 ðbar2 Þ 8:314T   3 ¼ 1:142102 exp 41:1510 8:314T   3 ¼ 5:3751010 exp  164:910 ðbar2 Þ 8:314T

DHH2 O ¼ 88:68103





kj kmol

temperature, reactor dimensions and catalyst characteristics are also shown in Table 4. Table 5 compares our modelling outcomes with the data from Pantoleontos et al. (2012). As shown, our model predictions are very consistent with the actual industrial SMR data. Treating the effectiveness factor as a constant value through the entire catalytic bed as well as ignoring axial dispersion of heat and mass could be the main sources of relative and absolute errors. As discussed before, based on the previous studies, the single shot addition of CO2 to the SMR feed stream may result in decreasing CH4 conversion. Hence, in this study multiple locations along the SMR reactor length are considered for CO2 dosing (see Fig. 4). It is obvious that increasing number of CO2 injection points will enhance reactor performance (i.e. shifting equilibrium reactions) by providing an optimal CO2 profile along the reactor length (Note: our study illustrates that the effect of injected CO2 is

The developed mathematical model is a one-dimensional heterogeneous one and includes mass and energy balance for gas and solid phases. Conservation balances including the boundary conditions as well as auxiliary equations are summarised in Table 3. The pressure drop along the axial direction of the SMR is calculated by the Ergun equation. Here KD and KV are parameters corresponding to the viscous and kinetic loss terms (Alpay et al., 1995). The overall wall-bed heat transfer coefficient is selected from Dixon (1996). The model consists of a set of ordinary differential mass and energy balance equations (ODEs), kinetic model and empirical correlations. The ODEs are solved by finite difference approximation. In this method, the length of the reactor is divided into 10,000 separate segments and the GaussNewton algorithm is used to solve the set of nonlinear algebraic equations for each segment (Iranshahi et al., 2011). The initial feed composition and

Table 3 Mass and Energy models with corresponding boundary conditions and empirical correlations.

Mass and energy balances in thegas phase

us

  dCi þ kg;i av Ci  Ci;s ¼ 0 dz

us rf Cpg

Mass and energy balances in the solid phase

i ¼ CH4 ; H2 O; H2 ; CO; CO2

dT 4U ¼ hf av ðTs  TÞ  ðT  Tw Þ dz dtube;i

  kg;i av Ci  Ci;s ¼ ð1  εb Þrcat ri hf av ðTs  TÞ ¼ ð1  εb Þrcat

dP ¼ KD us  KV u2s dz

Pressure drop

KD ¼ overall wall  bed heat transfercoefficient

150mg ð1εb Þ 2

dp ε3b ðPa s=m2 Þ

dtube;o 1 1 ¼ þ U aw 6ler

KV ¼

(17)

i ¼ CH4 ; H2 O; H2 ; CO; CO2

X  DHrxn;j hj Rj

(16)

j ¼ 1; 2; 3

(18)

(19)

(20) 1:75ð1εb Þrf dp ε3b ðPa s2 =m2 Þ

  Bi þ 3 Bi þ 4

(21)

1=3

aw dtube;o NRe Npr 0:95ð1  εb Þ    l0 ¼ εb ðlg þ 0:95aru dp;i Þ þ    ler ¼ l0er þ 0:111lg 2=3ls þ 1=10lg þ ars dp;i 2ler 1 þ 46ðdp;i =dtube;o Þ er 0 !1:5 1 dtube;i 0:8171ðT=100Þ3 em A lg N0:59 N1=3 ðT=100Þ3     aw ¼ @1  1:5     ars ¼ 0:8171 ¼ pr 2  em 1 þ εb =2ð1  εb Þð1  emÞem dp;i dp;i Re

Bi ¼ am

Boundary conditions

At the reformer inlet z ¼ 0:0 Ci ¼ Ci;o T ¼ To

i ¼ CH4 ; H2 O; H2 ; CO; CO2 P ¼ Po

(22)

660

H.R. Shahhosseini et al. / Journal of Cleaner Production 180 (2018) 655e665 Table 4 Additional data for the SMR process. Parameter

Value

TðKÞ LðmÞ

rcat ðkg=m3 Þ

700.15 12 2355.2

dp ðmÞ dtube;i ðmÞ

0.0084 0.1016

dtube;o ðmÞ

0.1322

FCH4 ;o ðkmol=hÞ FH2 O;o ðkmol=hÞ FH2 ;o ðkmol=hÞ FCO;o ðkmol=hÞ FCO2 ;o ðkmol=hÞ Po ðbarÞ ls ðW=m KÞ em

5.17 17.35 0.63 0.0 0.29 25.7 0.3489 0.8

gradually decreased along the reactor length). However, using a large number of injection points is not feasible mainly due to operation limitations and costs. Considering that the reactor length is 12 m, here we considered eleven CO2 injection nodes (i.e. with equal distances from each other) to obtain optimized injection flow rate at each node. Note: optimization is expected to decrease the impact of number of injection points. The optimum CO2 dose at each section is determined by MOO as described below.

2.2. MOO and SOO joined procedure for the new SMR reactor The joined procedure contains three main steps for creating a MOO problem: (i) defining a multi-objective model, (ii) producing optimal Pareto set and (iii) converting the MOO model to a SOO model for finding the single solution point. Fig. 5 illustrates the applied joined procedure in this study. Simply, the multi-objective model is formulated by using the SMR mathematical model. Subsequently, the Pareto frontier is produced and the convex nature of the Pareto set is evaluated. Finally, the WPM is used to transform the problem into SOO. By means of the Prior Articulation of Preferences Approach (PAPA), the authors will select a single solution in MOO. Subsequently, WPM (i.e. a common technique in PAPA) is applied to transfer the MOO problem into a single objective optimisation via multiplication of objectives and applying the power factors to different objectives. The single final optimal point is determined by the genetic algorithm (GA) which is a well-placed method in computational optimisation. GA does not need gradient information and therefore is an appropriate method regardless of the nature of the objective function (Harris et al., 2000). A population size of 80, generations of 100 with two basic operations, i.e., crossover probability of 0.9 and mutation probability of 0.08 are chosen.

Fig. 4. Proposed SMR catalytic packed bed reactor.

2.2.1. Defining objective functions for the new SMR configuration and determining Pareto line To obtain the optimum injected CO2 flow rate at each node, the multi-objective model is formulated as follow:

! Max f 1 ð x Þ : maximise CH4 conversion  ! Min f 2 ð x Þ : minimise absðSR  2Þ

(23)

It is clear, these are the same classical objectives in SMR design which aim to maximise the CH4 conversion (i.e. higher syngas generation) while minimising abs (SR-2) for enhancing methanol production. For the case of using two objectives, it is possible to visualise Pareto frontier in a two-dimensional space. Visualisation of the Pareto optimal front is forthright for the

Table 5 Modelling results versus industrial data. Variable

Modelling results

Experimental data

Relative error %

Absolute error 

TðKÞ PðbarÞ FCH4 F H2 O FCO F H2 FCO2 Ftotal

1; 101:45 23:45 1:6501 kmol=h 12:5965 kmol=h 2:2334 kmol=h 12:3554 kmol=h 1:5743 kmol=h 30:4097 kmol=h 2:8314

1; 106:01 23:34 1:6766 kmol=h 12:6801 kmol=h 2:2271 kmol=h 12:3237 kmol=h 1:5659 kmol=h 30:4734 kmol=h 2:8362

0:41 0:47 1:58 0:66 0:28 0:26 0:54 0:21 0:17

4:56 0:11 0:0265 0:0836 0:0063 0:0317 0:0084 0:0637 0:0048

68:08%

67:57%

0:75

0:51

SR ¼

FH2 FCO2 FCO þFCO2

CH4 conversion

H.R. Shahhosseini et al. / Journal of Cleaner Production 180 (2018) 655e665

Optimum Operational Decision Variables

Optimisation by GA

SMR Model

Pareto Frontire

MOM

661

Transfering MOO Problem into SOO Problem

Single-Objective Model

Operational decision Variables Producing Pareto Set

Generating MultiObjective Model

Single Solution Point (Optimal Decision Variables)

Fig. 5. Illustrative procedure of the joined methodology.

C

2.8

Stoichiometric ratio (S R)

2.6

feasible search region

2.4

B

2.2

Coordinates relevant to the conventional SMR performance

2 1.8 1.6

Pareto optimal-front (without constraint)

1.4 1.2

A

1 0.655

0.66

0.665

0.67

0.675

CH4 conversion

0.68

Fig. 6. Feasible search region and Pareto optimal-front of Multi-objective model based on eq. (23).

decision makers to compare different solutions according to their location on the Pareto frontier (Madetoja et al., 2008). Fig. 6 indicates feasible search region and Pareto curve for the multiobjective model based on eq. (23). The feasible search region contains 531,441 data over a wide range of decision variables in which SR versus CH4 conversion is illustrated (Note for a better visualisation, SR has been shown in this figure instead of abs (SR-2)). It can be observed that the Pareto frontier is a convex line

between points A and B. Point C represents the coordinates relevant to the conventional SMR performance (SR ¼ 2.831 and CH4 conversion ¼ 68.08%). In addition to SR, CO/CO2 ratio of syngas is another important factor for subsequent methanol factories. CO/CO2 ratio of greater than one may increase methanol production while jeopardizing the catalyst lifetime due to high water formation (Aasberg-Petersen et al., 2007). Hence based on the new constraint, a new feasible

C

2.8

Stoichiometric ratio (S R)

2.6 2.4 2.2 2 1.8

New feasible search region

E

selected by GA decision making method

O

1.6 1.4

D

1.2

pareto optimal-front (with constraint)

A

1 0.655

0.66

0.665

0.67

CH4 conversion

B

Coordinates relevant to the conventional SMR performance

Pareto optimal-front (without constraint)

0.675

0.68

Fig. 7. New feasible search region and convex Pareto line of multi-objective model based on eq. (23) and CO=CO2 ratio restriction, GA decision-making method to specify the final optimal design point.

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Table 6 The optimum CO2 injection values for the new SMR configuration. CO2 injection  flow rateðkmol=hÞ

Coordinate of inlet nodes along the reactor length ðmÞ

0.4000 0.0925 0.0810 0.1010 0.0890 0.0680 0.0960 0.0749 0.0890 0.0844 0.0986 0.0787

0 1 2 3 4 5 6 7 8 9 10 11

search region, and Pareto curve is determined as shown in Fig. 7. As demonstrated in Fig. 7, the new Pareto frontier is a convex line between points D and E with the highest CH4 conversion (67.13%) at design point E. The SR indicator has its minimum value of 1.45 at point D and increases gradually as the CH4 conversion rises to around 67%. Further increase in CH4 conversion results in a drastic rise in the stoichiometric ratio. In order to determine a single optimal point, the MOO problem is transformed to a SOO problem using WPM (eq. (24)). A single optimum point is then obtained by using GA as shown below:

! ! minimise  f eq ð x Þ¼absðSR 2Þ=CH4 conversion ¼f ðx1 ;x2 ;…;x12 Þ s:t: 0xi ðCO2 =H2 O ¼0:078Þ i¼1;2;3;…;12 12 X xi ¼ðCO2 =H2 O ¼0:078Þ

Fig. 9. H2 molar flow rate along the reactor.

2.3. Comparison between performance of conventional and optimised SMR The performance of SMR is evaluated versus new optimized configuration in Figs. 8e11. Variations in molar flow rates of reforming species, temperature and pressure profiles along reactors are compared here.

i¼1

(24) Point O in Fig. 7 represents the coordination relevant to the new optimised SMR performance (SR ¼ 2.015 and CH4 conversion ¼ 67.11%) which was selected based on the GA results. The corresponding optimum CO2 injection values for eleven nodes are therefore listed in Table 6.

2.3.1. CH4 conversion and H2O molar flow rate CH4 and H2O profiles along conventional and optimized configuration are demonstrated in Fig. 8. Injecting a defined amount of CO2 at various lengths of the reactor shifts the equilibrium of reactions (1) to (3) according to Le ChateliereBrown principle. Fig. 8 (a) demonstrates the similar performance of SMR and

Fig. 8. The profiles along the reactor (a) CH4 conversion percentage and (b) H2O molar flow rate.

H.R. Shahhosseini et al. / Journal of Cleaner Production 180 (2018) 655e665

663

Fig. 10. (a) CO and (b) CO2 molar flow rates along the reactor length.

its optimized configuration regarding the methane reforming. Although the CH4 conversions in both reactors are approximately the same, the water formation tends to be a bit more in the case of new optimized reactor (Fig. 8 (b)). This could be attributed to the shift of reverse reforming reactions as a result of the multi-step CO2 injection. 2.3.2. H2, CO and CO2 products Fig. 9 represents variation in the H2 molar flow rate in both reactors. Hydrogen production rate decreases insignificantly from 12.35 kmol/h to 12.02 kmol/h in the optimized configuration mainly through the reverse of reactions 2 and 3. However, the proposed configuration can successfully adjust the stoichiometric ratio SR ¼ 2:0  2:1 which is considered to be advantageous for methanol producers to improve their production rate. Fig. 10 indicates efficacy of using industrial CO2 purge streams to add additional values to methanol infrastructures. The effect of booster CO2 on CO flow rate is obvious. CO production rate has increased about 0.73 kmol/h following the injection of 1.35 kmol/h of CO2 in total. Higher CO output in the optimized configuration could mainly be due to the synergistic effect of high temperature and additional CO2 concentration which drive the water gas shift

reaction (reaction 2). 2.3.3. Temperature and pressure profiles Fig. 11 (a) shows a slightly lower temperature profile for the second half of the reactor which also improves the pressure drop along the reactor. About 1% temperature drop in new optimized SMR, considerably affects the gas properties such as viscosity, density and velocity which subsequently lowers the pressure drop (Fig. 11 (b)). This will provide further opportunity for process engineers to use smaller catalysts with higher effectiveness factors which improve reaction yields. The lower pressure drop in optimized SMR is also beneficial due to the enhancement of reaction rates because of higher gas phase concentrations on the catalyst surface. 3. Conclusions The current study investigated the possibility of utilizing CO2rich effluents of industrial sites in SMRs for production augmentation of methanol units. Here a new reactor configuration was proposed, capable of adjusting the stoichiometric ratio SR in SMRs while eliminating the expensive and high-energy duty end-of-pipe

Fig. 11. (a) Temperature and (b) Pressure profiles along the reactor length.

664

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separation-recycling steps. Multiple shots of CO2 were considered for conventional SMR along its catalytic bed to adjust the SR and improve the reformer's products. Optimum CO2 injection flow rates were determined by the multi-objective optimization technique and identifying the Pareto frontier regions. CH4 conversion and abs (SR-2) were the objectives to be optimized. Consequently, the stoichiometric ratio of syngas as a critical parameter in methanol production was decreased from SR ¼ 2.831 to SR ¼ 2.015 for the new configuration which is closer to the optimum theoretical value of SR ¼ 2. This is while the CH4 conversion remained at the same level as the conventional SMR at about 68%. The new configuration was capable of producing high amounts of H2; matching the 40% in the conventional SMR. Based on our modelling outcomes, CO2 injection significantly increased the CO generation mainly due to “reverse shift reaction”. The above findings may be beneficial to the SMR operators to redesign and redefine their operations for production enhancement in methanol industries. Acknowledgment The authors would like to express their sincere appreciation to zma ny Pe ter Faculty of Information Technology and Bionics, Pa Catholic University in Budapest, Hungary for their support. We would also like to thank Ms E. Cowey for her kind help in editing the manuscript language. List of symbols

Variables av aru

External catalyst surface area per unit volume of catalyst bed ðm2 =m3 Þ The parameter used in to calculate static radial thermal

ars

conductivity ðkJ m2 h1 K1 Þ The parameter used to calculate static radial thermal conductivity ðkJ m2 h1 K1 Þ

aw Bi Ci;s

Wall thermal transfer coefficient ðkJ m2 h1 K1 Þ The Biot number The concentration of species i in the solid phase

Ci

ðmol=m3 Þ The concentration of species i in the gas phase ðmol=m3 Þ

Cp

The heat capacity ðJ kg1 K1 Þ

Cpg dp dtube;i em Ej Fi;o

The heat capacity of the gas mixture ðJ kg1 K1 Þ Catalyst particle diameter (m) The inner diameter of the reactor tube ðmÞ The emissivity of the solid surface The activation energy of reaction j ðJ=molÞ The molar flow rate of component i in the feed ðkmol=hÞ ði ¼ CH4 ; HO2 ; CO; H2 ; CO2 ; N2 Þ The total flow rate of the mixture in the bed, (kmol/h) The total flow rate of the mixture in the feed, (kmol/h) Thermodynamic equilibrium constant of the reaction Adsorption constant of species i Temperature dependent kinetic rate constant of reaction j The mass transfer coefficient of species i ðm=sÞ Reference adsorption constant of species i The reference temperature dependent kinetic rate constant of reaction j The parameter corresponding to the kinetic loss term

Ftotal Ftotal ; o kej ki kj kg;i koi koj Kv

ðPa s2 =m3 Þ

KD L Npr NRe P pi Po ri Rj T To Ts Tw U us Z !! gðxÞ

The parameter corresponding to the viscous loss term ðPa s=m2 Þ The length of the reactor ðmÞ Prandtl number Reynolds number Total gas pressure ðbarÞ The partial pressure of gas species i ðbarÞ Initial pressure (bar) The rate of consumption or formation of species i ðmol=ðkgcat sÞÞ Rate of reaction j ðkmol=ðkgcat hÞÞ Gas-phase temperature ðKÞ Initial temperature ðKÞ Solid catalyst temperature ðKÞ Wall temperature ðKÞ Overall heat transfer coefficient ðJ m2 s1 K1 Þ Superficial gas mixture velocity ðm=sÞ Axial dimension ðmÞ The vector of inequality constraints

GAGenetic algorithm !! hðxÞ The vector of equality constraints F*

! f eq ð x Þ ! x wi W w X Q k

! f ið x Þ ! Fð x Þ M N

The vector of Pareto optimal points Composite function The vector of decision variables The power factor for objective function f i   (dimensionless) Feasible criterion space (dimensionless) The vector of powers (dimensionless) Feasible decision space Number of equality constraints Number of objectives ith objective function The vector of objective functions Number of inequality constraints Number of independent variables

Greek symbols DHi The heat of adsorption of species i ðJ=molÞ DHrxn;j Heat of reaction j ðJ=molÞ

DHo298 εb

hj lg ls lfz l0er mg rcat rf U

The heat of reaction of at STP ðkJ=kmolÞ Packing bed porosity (dimensionless) Effectiveness factor of reaction j Average gas thermal conductivity ðW=m KÞ Solid thermal conductivity ðW=m KÞ Effective thermal conductivity ðW=m KÞ Static radial thermal conductivity ðkJ m2 h1 K1 ) Average gas viscosity ðkg=ðm sÞÞ The density of the catalyst pellet ðkg=m3 Þ The density of the fluid ðkg=m3 Þ Dominator term in the reaction kinetics

Abbreviations Stoichiometric ratio SR SMR Steam methane reforming SOO Single objective modelling WPM Weighted product method ODEs Ordinary differential equations MOO Multi-objective optimisation MOM Multi-objective modelling GA Genetic algorithm

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WGS APA GTL

Water gas shift Prior Articulation of Preferences Approach Gas to liquid

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