One-dimensional Modelling and Optimisation of an Industrial Steam Methane Reformer

M. Sinaei Nobandegani,a,* T. Darbandi,b M. Kheirinik,c M. R. Sardashti Birjandi,d F. Shahraki,d and L. Yua aChemical Technology, Luleå University of Technology, SE-971 87 Luleå, Sweden bLuleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science, Luleå, Sweden cPersian Gulf Star Oil Company, Bandar Abbas, Hormozgan Province, Iran dDepartment of Chemical Engineering, University of Sistan and Baluchestan, P.O. Box 98164-161, Zahedan, Iran


Introduction
Hydrogen energy has been proposed as a promising energy carrier over the past decades. 1,2 Environmental legislation and market forces have increased the demand for hydrogen in oil refineries. Hydrocarbon reforming has been identified as the main process to produce hydrogen and other synthesis gases. 3,4 The first atmospheric pressure reforming unit was established in the 1930s. 5 After three decades, a steam reformer with operating capacity at 15 bar pressure came on stream in the United Kingdom. 6 Due to the high ratio of hydrogen to carbon in methane, natural gas (mainly consisting of methane) is considered as a preferable feedstock in reforming to produce hydrogen. 7 This ratio also minimises the amount of carbon dioxide produced as by-product. 7 As already proven, 8,9 steam methane reforming (SMR) is a common industrial process in hydrogen production.
Since SMR is the most commonly used technique in hydrogen production, there exist extensive industrial experience and research background in this area. One of the earliest studies on SMR was conducted by Fischer and Tropsch in 1928. 10 They studied various catalysts in steam methane reforming at temperature range of 870-983 °C, and reported that nickel and cobalt were the best catalysts for this process. So far, many catalysts have been investigated, 11,12 and SMR processes have been studied extensively to improve the performance. [13][14][15] However, SMR processes, like many industrial chemical/petrochemical processes, are complex in nature because of complicated reaction chemistry, nonlinear relations, and numerous variables involved (such as inlet steam-to-carbon ratio, wall temperature, tube geometry, flowrates and catalysts). 16 Therefore, there is a great interest in modelling and optimisation of SMR reactor with a simple and reliable model. This study aimed to describe and optimise an industrial SMR using a one-dimensional model, since the ratio of diameter to the length of reformer was considerably small. 17 Singh and Saraf 18 simulated a side-fired hydrocarbon reformer using one-dimensional model in axial direction. Their results were in good agreement with experimental data. De Deken et al., 3 by studying the SMR on a commercial catalyst at tem-perature range of 550-675 °C and pressure range of 5-15 bar, suggested a kinetic mechanism for this process. They simulated the reformer based on continuity, energy, and momentum equations by one and two-dimensional models. The SMR was simulated by Alatiqi et al. 19 using a rigorous kinetic model. They showed that the rigorous model could be confidently utilised for design purposes. In one of the major studies related to SMR kinetics, Xu and Froment 20 successfully derived an intrinsic rate equation for the SMR on Ni/MgAl 2 O 3 catalyst. Alhabdan et al. 21 developed a heterogeneous model for industrial steam reformers and compared the results with a number of side-fired and top-fired industrial reformers. Using a numerical method, Nummedal et al. 22 minimised the total entropy production rate. This optimal path reduced the entropy production by more than 60 % in comparison with the typical path. Riaz et al. 23 investigated the inert gas on SMR using a heterogeneous model. They reported that using xenon as the inert gas can reduce the outlet temperature 20 % compared to traditional mode. Pantoleontos et al. 24 examined the dynamic behaviour of industrial heterogeneous steam reforming of methane. Using a set of partial differential equations, their model was capable of describing physicochemical processes, which occur in solid and gas phase considering the diffusional limitations in catalyst particles. They validated the computed results through the literature-reported data. They also optimised the provided heat for the reactor wall in terms of the optimal hydrogen production. The synthesis gas production by SMR was simulated by a pseudo-heterogeneous model by Sadooghi and Rauch. 25 The results proved that the radial concentration gradient was insignificant in the reformer. Shinde and Modras 26 reported a sonochemical-assisted synthesis of a highly active and coke resistant Ni/TiO 2 catalyst for SMR. The results showed that the synthesised catalyst was remarkably active and stable even after a long period, and no appreciable coke deposition was observed. Industrial reformer performance has been modelled by our group in another study, 15 where the response surface methodology was used to optimise the reformer performance, and the optimum values were reported.
In the present work, the same industrial SMR unit and the process were modelled using the genetic algorithm, within different operating constraints, and optimum values to maximise the hydrogen production and minimise the unreacted methane, simultaneously. The aim of this study was associated with describing SMR using a one-dimensional mathematical model in an axial direction in steadystate conditions to investigate the effect of operating parameters on methane conversion. To the best of our knowledge, this is the first attempt to model and optimise the industrial side-fired steam methane reformer located in Bandar Abbas refinery, using a simple and reliable model and genetic algorithm. Genetic algorithm was chosen since it is one of the popular metaheuristics optimisation techniques with a strong capability in global optimisation. 27 The results would be helpful in optimisation of SMR performance in this refinery, as well as in designing other SMR reactors.

Process description
Although both endothermic and exothermic reactions occur over catalyst, SMR is considered generally as a highly endothermic process. Therefore, to provide the required heat, it can be performed in a set of catalytic tubes located inside a furnace with some burners (224 burners in Bandar Abbas reformer). [28][29][30] The SMR occurs in a tubular reactor at 800-1000 °C and 5-35 bar. Although some metal-based catalysts such as rhodium, ruthenium, platinum, and palladium can be used in SMR process, nickel is the most common one, since it is not as expensive as other candidates. 30,11 The steam reforming of methane is a complex process, in which several reactions may occur at the same time, as described by Xu and Froment. 20 However, it can be described by three main chemical reactions that are endothermic in overall: 20 Because of the endothermicity and mole increased reaction processes, high temperatures and low pressures are desired operating conditions for reactions (1) and (3). Water-gas shift (WGS) reaction (2), which is temperately exothermic, is needed when hydrogen is the desired product. Due to being an exothermal reaction, the WGS benefits from low temperatures. Therefore, for the SMR process, a high-temperature shift convertor (HTSC) followed by a low-temperature shift convertor (LTSC) is profitable. 31,32 Method Mathematical modelling Fig. 1 indicates a simple schematic of a reformer tube. Similar to other modelling studies, our assumptions were as follows: a) The tube is modelled in axial direction, because the ratio of diameter to the length of reformer is considerably small 19 (inner diameter of 0.098 m and heated length of 13.6 m, which corresponds to D/L ≈ 0.007), and the reactions are endothermic in overall. 24 b) The process gas passes through the catalyst tube, following a plug flow pattern. c) For better thermal performance, the SMR works as a set of catalytic tubes located inside a furnace with 224 burners. These tubes have the feed in the same conditions, with an equal input flowrate, pressure, and temperature. Moreover, the boundary conditions for all tubes at z = 0 are the same, and the conversion is equal to zero at this point. Using the assumption that the heat flux passing through each tube wall is identical, all the tubes (regardless of their positions) have the same patterns. Consequently, it is assumed that each tube is representative of any other in furnace, and the model is derived for one tube instead of 328 tubes. d) All the heavier hydrocarbons hydrocrack and convert to methane before entering the tube. e) The ratio of diameter to the length of reformer is too small and the Peclet number is too   (6)×OD (17) Catalyst density (kg m -3 ) 2355.5 Mass of catalyst (kg) 29520 Catalyst bed density (kg m -3 ) 1051 Catalyst bed void fraction 0.605 ( ) Since the catalyst in Bandar Abbas steam reformer is Ni/MgO Al 2 O 3 , the reaction rates given by Xu and Froment were used in the kinetic model based on the Langmuir-Hinshelwood reaction mechanism: 20 high, as a result, the axial dispersion is neglected. f) Catalysts particle temperature and shape are uniform. g) Van der Waals equation of state is applied in gas density calculation. Characteristics of the reformer are presented in Table 1.
Considering the mentioned assumptions, the final model can be expressed as the following governing equations: 20 The kinetic rate coefficients and adsorption equilibrium constants are given as: 33 14.5 1 28879 2.64 10 exp k T 3 1 2 eq eq eq The effectiveness factor has been reported by AL-Dhfeery and Jassem: 34 The effectiveness factor is there to correct the reaction rate, since the molecular diffusion into the catalyst pores can affect the actual reaction rate. In equation 22, φ k is the Thiele modulus that shows the relation between the catalytic activity and particle size. In cylindrical particles, Thiele modulus can be defined as: 35 in which, j shows the reaction number, and i stands for the component. In this equation, D i,k shows the Knudsen diffusivity and is calculated as: 36 In equation 24, D i,mix shows the diffusion of i into the mixture and is calculated as: 36 where x shows the mole fractions, p is pressure, T is temperature, and M is the molecular weight. σ and in which v c and T c are the critical volume and temperature of i component.
The gas density was computed based on the assumption that the Van der Waals equation of state can be used. In equation (6), the overall heat coefficient and enthalpy variations are calculated by equations (34)(35), respectively: 38,39 In equations (8)(9)(10), DEN is defined as follows: C p is the specific heat and can be calculated using the following equation: 40 A, B, C, and D in equations (35-36) are constants and have been reported in Table 2.
Viscosity was calculated as reported by Chung et al. 41 To solve the model, there are different numerical techniques. The second order Rosenbrock method was utilised to solve the introduced model, which is a useful method in solving stiff differential equation. The catalysts pellet equivalent diameter was equal to 0.0109 m (more information about the catalyst properties can be found in Table 1). Moreover, the carbon dioxide to methane, steam to methane, and hydrogen to methane molar ratios in the feed were 0.004, 7.630, and 0.005, respectively. The other input data of model are reported in Table 3.

Optimisation
The genetic algorithm and Matlab software were employed to optimise the process. During the optimisation, the hydrogen production maximisation and the methane loss (methane slip) minimisation were studied as the objective functions. The optimisation formulation is reported in equation (37). In this optimisation, the decision variables bounds are described as follows:

≤ p in ≤ 27 bar (42)
The lower and upper limits in equation (39) are selected to keep catalysts active at the entrance of the tube and to avoid excess recycling of hydrogen, respectively. In equation (40), the minimum steam to methane ratio was set at 2, which enables neglecting the coke (carbon) formation and deposition Ta b l e 2 -Molar heat constants 41 Material A (J mol -1 K -1 )  6,25,43 The maximum value was selected to prohibit the adverse effects on process economics. The lower boundary of input feed temperature was set at 650 K based on thermodynamic limitation (in order to avoid gum formation on catalyst particles), and the upper was set at 815 K based on maximum practical value in the refinery. For the input feed pressure, the minimum and maximum values were selected based on the hydrogen production pressure in the refinery and the feed supply pressure.

Results and discussion
The output data predicted by the model were compared and validated with the industrial data, which were reported by Bandar Abbas industrial oil refining complex, Iran, to evaluate the accuracy of the model. The results are reported in Table 4, and the model predictions of methane conversion, temperature distribution profiles, and pressure drop are illustrated in Fig. 2. To determine the error in Table  4, equation 43 was used: The average error for the model predictions equalled approximately 3.77 %.
After validating model accuracy, the effects of feed temperature and flowrate, as well as tube wall temperature on the reformer performance were investigated. As may be seen in Fig. 3, the higher wall temperature resulted in higher methane conversion. Indeed, higher wall temperature increased the temperature difference, which is the driving force for the heat transfer to the reaction. Considering reactions 1 and 3, it was observed that the reactions moved forward at higher temperature, and more methane was consumed at higher temperature. Fig. 4a illustrates that the feed temperature had the same effect as the wall temperature. Because of the endothermic nature of the SMR process, increased temperature caused reactions (1) and (3) to shift more to the right and more methane to be converted. Therefore, higher feed temperature led to an increase in methane conversion and, therefore, re-  duced methane loss. The results are consistent with the reported results of thermodynamic analysis. 44 The effect of the feed flowrate on the process is shown in Fig. 4b. Methane conversion decreased with the increase in feed flowrate. The higher feed Moreover, based on Le Chatelier's principle and considering equations (1) and (3), more steam in feed stream would shift these reactions to the right, which in turn, leads to higher methane conversion as well as higher hydrogen production. 48 Fig . 6 shows the temperature and methane conversion profiles at different reformer lengths and diameters. As may be observed, using longer reformer tube leads to higher methane conversion as well as higher temperature of output gas. The same effect may be seen for reformer tube diameter. However, it should be noted that the effect of increasing reformer length and diameter on methane conversion and temperature is moderated at higher values. Indeed, it may be seen that a reformer with a length of 9 to 10 m would be sufficient to achieve the final value of methane conversion. The optimised results are reported in Table 5. For the feed flow of 2761.9 kmol h -1 , the maximum flow of hydrogen production, and the minimum value for the unreacted methane will be 885.2 kmol h -1 and 4.1 kmol h -1 , respectively.

Conclusion
In this work, the steam methane reformer was studied. This process was numerically investigated using a one-dimensional model in length direction in steady state condition. The obtained results were comparatively validated against the experimental data, and the average error was about 3.7 %. Subsequently, the process was simulated, and the effects of feed flowrate and temperature, and the effect of tube wall temperature on the process were investigated numerically. It was observed that the increase in feed temperature, additional steam in the feed, and increase in tube wall temperature had the same effects and led to methane conversion increase. On the other hand, increasing the feed flowrate caused the methane conversion to decrease. The decision variables were optimised using genetic algorithm for the maximum hydrogen production and the minimum methane that could be valuable for the industrial processes. Further studies are needed on elaborating the process optimisation by focusing more on the cost evaluation, as well as on optimisation of steam methane reformer for other purposes like electricity production.

ACKNowLEDGMENT
Hereby, we would like to extend our gratitude to Bandar Abbas Refinery Complex Co. in Iran for their financial support. Mr. Mohammad Jafar Mou savi is also appreciatively acknowledged for techni cal support and collaboration on data gathering.
N o m e n c l a t u r e Symbols C p -specific heat, J mol -1 K -1 d i -internal tube diameter, m D p -equivalent catalyst pellet diameter, m F -reformer feed rate, kmol h -1 G -gas mass velocity, kg s -1 m -2 (H/C) in -recycle hydrogen/methane molar ratio in feed,k 1 , k 3 -rate constants of reactions (1) and (3), kmol Pa 0.5 kg cat.