Simulation and Control of Steam Reforming of Natural GasâReactor

Subscriber access provided by University of Newcastle, Australia

Article

Simulation and Control of Steam Reforming of Natural Gas - Reactor Temperature Control Using Residual Gas Bruno Francisco Oechsler, Julio Cesar Sampaio Dutra, Roberto Carlos Bittencourt, and José Carlos Pinto Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b03665 • Publication Date (Web): 22 Feb 2017 Downloaded from http://pubs.acs.org on February 22, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Industrial & Engineering Chemistry Research is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

Simulation and Control of Steam Reforming of Natural Gas - Reactor Temperature Control Using Residual Gas Bruno F. Oechsler1*, Julio C. S. Dutra1†, Roberto C.P. Bittencourt2, José C. Pinto1

1

Programa de Engenharia Química/COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitária CP 68502, Rio de Janeiro, RJ, 21941-972 2

Petróleo Brasileiro, S.A., Petrobrás, Ilha do Fundão, Cidade Universitária, Rio de Janeiro, RJ, 21941-598, Brazil

KEYWORDS: Steam reforming; natural gas; modeling; control; residual gas. Corresponding Author *[email protected] Present Addresses † Programa de Pós-graduação em Engenharia Química, Universidade Federal do Espírito Santo, UFES. Campus de Alegre, Guararema, CP 16. Alegre 29.500-000 ES, Brasil.

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT: The present work discusses the mathematical modeling and the control design of the steam reforming of gas natural. The developed model comprises a set of differential and algebraic equations, based on energy and mass balances for reactions performed in a fixed catalyst bed reactor, where gas natural and water are transformed mainly into a mixture of hydrogen and carbon oxides. Normally, after removal of hydrogen and purification of the output stream, the residual gas can be also directed to the furnace to provide heat to the reactor. This is a common practice in industrial sites in order to minimize losses. As the global reactions are exothermic, the reactor temperature may reach prohibitive high values, leading to coke formation and catalyst deactivation. For this reason, a control scheme is proposed to account for regulation of the reactor outlet temperature, using residual and fuel gas streams as manipulated variables, allowing the analyze of effect of several process variables in reactor performance. The obtained results indicate that the proposed mathematical model can accurately represent the steam reforming process and that the proposed control scheme can allow for efficient operation of the reactor, even when the residual gas stream is not sufficient to reach the desired operation temperature.

1. Introduction The catalytic conversion of hydrocarbons is of great importance in the petrochemical and refining industries, including the catalytic reforming of naphtha and natural gas to obtain synthesis gas (CO and H2). Among many other uses, the synthesis gas can be used as feedstock in the Fischer-Tropsch process for production of liquid fuels.1 Another very significant motivation for production of synthesis gas is the generation of hydrogen, which finds many industrial uses, including the hydrogenation of refining streams to produce high quality fuels. However, the production of hydrogen can be 2 ACS Paragon Plus Environment

Page 2 of 58

Page 3 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


costly, due to operation at high temperatures. Therefore, catalysts are used to allow the process operation in lower temperatures. Moreover, this process presents many relevant technological challenges, such as the formation of coke during the operation and the consequent deactivation of process catalysts.2 Particularly, the production of hydrogen through the steam reforming of natural gas, naphtha, heavy oil and coal has received great importance in last years. This is due to the increasing industrial demand of hydrogen for use in petroleum refining processes (such as hydrotreating and hydrocracking), production of chemicals (such as methanol and ammonia) and Fischer-Tropsch processes.3 The main commercial route for production of hydrogen is the steam reforming of hydrocarbons, especially the steam reforming of natural gas, which involves the reaction between methane and water and the consequent production of mixtures that contain hydrogen, carbon monoxide and carbon dioxide.4 This endothermic process is normally performed in the gas phase at very high temperatures over nickel catalyst pellets in tubular reactors placed inside industrial furnaces, where a fuel (usually natural gas) is burned. The furnace provides the heat required to obtain the desired high reaction temperature and to achieve high methane conversions.5 It is important to observe that modeling of the natural gas steam reforming reactor does not constitute a trivial task. Particularly, the complex kinetic expressions, the complex reaction-diffusion effects that occur inside the catalyst pellets and the complex heat transfer phenomena that take place inside the furnace are peculiar features of this process. Perhaps because of this, most of the work reported in the literature is focused on kinetic studies and modeling of particular kinetic aspects of these systems. Peña et al.3 reviewed the catalytic routes used for production of syngas and hydrogen, discussing catalytic alternatives for conversion of natural gas and including discussions



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

about partial oxidation, auto thermal reforming, combined reforming and carbon dioxide reforming. Particularly, the energetic efficiencies of direct and indirect methane conversions were compared. Finally, the effects of heat transfer profiles on the performances of tubular reactors were evaluated, in order to maximize the methane conversion. Armor et al.6 also reviewed different catalytic approaches used for production of hydrogen, extending the discussion presented by Peña et al.3 Kvamsdal et al.7 discussed the operational performance of heated fixed bed reactors for production of syngas and hydrogen. In particular, the performance of a fixed bed catalytic reformer was simulated with the aid of a dynamic two-dimensional pseudohomogeneous dispersion model. It was shown that the use of different heat transfer correlations to describe heat transfer to the reactor walls exerted little effect on the predicted conversions, although significantly affected the predicted wall temperatures. The authors concluded that the reactor operation range is limited by the reactor wall temperature and it influences on the formation of coke. Rajesh et al.8 performed the optimization of the operation conditions for steam reforming in tubular reactor, using a model based on the detailed description of the reaction mechanism, of heat transfer in the furnace and of diffusion in the catalyst pellet. A multi-objective approach was proposed for the simultaneous minimization of the feed rate of methane and the maximization of the flow rate of carbon monoxide, while keeping fixed the rate of hydrogen. The simulation results indicated the existence of opportunities to increase the productivity, reduce the operating costs and increase the profits in the analyzed range of operation conditions. Afterwards, Rajesh et al.9 performed the optimization of an entire industrial hydrogen plant, including sections for steam reforming and shift conversion. A modified genetic algorithm was used to perform the proposed multi-objective optimization task, considering the simultaneous


Page 4 of 58

Page 5 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


maximization of the produced hydrogen and exported steam to others units, assuming a fixed feed rate of methane. Pantoleontos et al.10 also performed the analysis of the steam methane reforming process with help of a model used to simulate the heterogeneous catalytic packed bed reactor. Particularly, the heat provided to the reactor wall and the wall temperature were described with linear and quadratic functions of the reactor length, as obtained through maximization of hydrogen yields. Pedernera et al.11 proposed a two-dimensional model to describe the steam reforming of methane, assuming the existence of significant axial and radial temperature gradients inside the tubular reactor. As observed through simulation, temperature gradients might cause significant variations of reaction rates along the radial direction, recommending the careful design of tube diameters to avoid waste of catalyst activity at the central region of the reactor, where temperatures were lower. Zamaniyan et al.12 presented a mathematical model for a top fired steam reformer, including its furnace. A one-dimensional heterogeneous model, with mass transfer limitation in the catalyst pellets, was used to describe the reactor. The furnace was described with a three-dimensional model. In particular, the model was validated with literature results and data collected at an industrial site. It was shown that variation of the extinction coefficient of the combustion gas and of the effective emissivity of the reaction tubes might exert significant influence on the reactor wall and process gas temperatures, indicating that these parameters should not be neglected during the analysis of real industrial operations. Latham et al.13 reviewed steam methane reforming models presented in the literature and the possible applications of these models for plant design, process monitoring, plant simulation and optimization. Particularly, a model was developed to allow for



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

monitoring of reactor wall temperatures, assuming that the reactor might be split into distinct operation zones and considering the detailed description of radiative heat transfer inside the furnace.14,15 It is also important to emphasize that the calculation of effectiveness factors is of fundamental importance for simulation of industrial catalytic reactors, since catalyst pellets may be subject to significant internal mass and heat transfer limitations. The effectiveness factor is generally expressed as a function of the Thiele modulus, although analytical solutions are only available for axial or radial diffusion in catalyst pellets with regular geometries (slab, sphere or cylinder) and simple reaction rate expressions. For this reason, efforts have also been made to describe effectiveness factors for more complex reactions, as discussed by Alberton et al.16. For example, analytical expressions for effectiveness factors as functions of modified versions of the Thiele modulus have been derived for reversible reactions17, complex kinetic rate expressions18,19, endo/exothermic reactions20, catalyst particles with multimodal pore distributions21, catalyst particles with complex catalytic pellet geometries22,23, among others. Additionally, model simplifications have been proposed in the literature11 in order to describe catalyst pellets with unusual geometry as particle pellets of regular geometry (slab, sphere, cylinder)9, although such approximations do not perform well when very complex pellet geometries are considered. As discussed by Schwaab et al.5, most published studies neglected the complex kinetic, mass transfer and heat transfer interactions that take place inside the tubular reforming reactors and the furnaces and the complex geometrical characteristics of the catalyst particles. For instance, proposed models usually described the complex geometry of catalyst pellets in terms of very simple and regular geometries (slab, sphere, cylinder), which cannot be supported by real applications. For these reasons,


Page 6 of 58

Page 7 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


proposed modeling studies may present some severe limitations for analysis of real industrial sites, where perturbations of the furnace operation and of the reactor feed are frequent, and for design of catalysts, as the real complex features of the catalyst geometry are not taken into consideration. It must be considered that the rigorous description of catalyst beds formed by pellets of complex geometries and of complex kinetic mechanisms (and the respective rate expressions) cannot be performed without involving numerical analysis. One possible alternative is the use of computational fluid dynamics (CFD) for detailed modeling of the reactor, which may provide useful information about the flow, concentration and temperature profiles inside reactor, as presented by Dixon et al.24,25 However, this approach usually leads to severe limitations for routine and real-time applications, such as monitoring, optimization and control, due to the excessive computational effort required to perform the required numerical analysis. In order to take into account the complex geometrical features of the catalytic pellets during the simulation of industrial steam reforming reactors, Schwaab and coworkers5,16 proposed a hybrid methodology. The proposed approach was based first on the implementation of a CFD model in a standard computational platform to describe the reaction rate profiles inside catalytic pellets of complex geometry. Then, simulations were performed at different reaction conditions and for distinct pellet geometries, providing a set of pseudo-experimental data for catalyst performances and reaction rates. In particular, Alberton et al.16 showed that the complex geometry of the catalyst pellets may lead to remarkable modifications of the effectiveness factors of the steam methane reforming reactions, when compared to the usual approaches that consider pellets with regular geometry. Finally, the rigorous CFD results were used to build



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

empirical models (metamodels) for the effectiveness factor, as a function of catalyst properties and operation conditions, for posterior use in the tubular reactor model. The metamodels could be easily inserted into the balance equations used to describe the operation of the tubular reactor, allowing for analysis of the effects caused by the complex-shaped catalyst pellets on the industrial operation without oversimplification of the reaction phenomena and mass and heat transfer limitations inside the catalyst pellets. This also allowed for much faster numerical solution of the full industrial reactor, when compared to the usual CFD approach. Consequently, the metamodels made possible the routine evaluation of the industrial reactor operation and the catalyst design, where fast solution of the mathematical model is an obligatory requisite, as discussed by Schwaab et al.5 Notably, the authors showed that these models could be successfully applied for simulation and design of industrial reformers, allowing for analysis of the effects introduced by different catalyst geometries on the performance of industrial operations. In the present manuscript, the model proposed originally by Schwaab et al.5 is extended to allow for analysis of the effect of residual gas reuse (obtained as the exhaust gas of a Pressure Swing Adsorption unit and used for combustion in the reformer furnace, as described in the following sections) on the reactor performance. It is important to emphasize that the effect of this stream on the performance of steam reforming reactors has never been evaluated in the literature, although residual gas reuse constitutes a common practice in real industrial sites. Therefore, this may be regarded as a significant gap of the steam reforming literature. For instance, Rajesh et al.8,9 performed the simulation and optimization of steam reforming reactors operating with residual gas, but the authors only considered the optimal operation conditions of the


Page 8 of 58

Page 9 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


process plant, avoiding the complex numerical interactions that result from the detailed modeling of the gas recycling operation. In order to accomplish the proposed task, simplified models are included to describe the Shift and PSA (Pressure Swing Adsorption) units and allow for updating of the residual gas composition. The residual gas is directed to the furnace to provide heat to the reactor. As the reactions are globally exothermic, the outlet temperature may reach prohibitive high values. As coke can be formed at high temperatures, this can lead to deactivation of the catalytic bed. For this reason, a control scheme is proposed to account for the regulation of the outlet reactor temperature using residual and fuel gas streams as manipulated variables, as also performed in real industrial sites. Particularly, the axial temperature profiles, fuel consumption in the furnace and coke formation are analyzed for different catalyst activities, using (and not using) residual gas in the furnace. It is shown that the proposed split-range control structure allows for the reduction of the natural gas consumption in the furnace; however, the control strategy based on residual gas manipulation can lead to oscillatory behavior due to the changing gas composition, which has been completely overlooked in previous studies. Despite that, it is shown in all tested events that the control scheme offers a robust performance for the reactor and the furnace operation.

2. Process Description A simplified flowsheet of the steam reforming process considered in the present study can be seen in Figure 1. As discussed by Rajesh et al.8, in the steam reforming, natural gas is mixed with appropriate quantities of steam and recycled hydrogen before entering the reformer. The recycle of some of the produced hydrogen in the feed is necessary because H2 is essential to keep the catalyst at the initial part of the reformer tubes in the



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

reduced (active) state.8 The important following reactions take place in the process, as shown in Scheme 1:

+ ⇆ + 3

(Reforming)

+ ⇆ +

(Shift) (Reforming)

+ 2 ⇆ + 4

Scheme 1. Chemical reactions involved in steam reforming natural gas

The two reforming reactions occur (in parallel) in the steam reformer (first reactor), while thermodynamics favors the shift reaction in the near-adiabatic shift converter (second reactor). Shift reactions can also occur in the steam reformer, although higher conversions are only attained in the shift reactors (in the high and low temperature shift reactors that usually follow the steam reformers in commercial processes) due to thermodynamic constraints. The hot syngas produced in the reformer is used to generate very high pressure (VHP) steam, used for mixing with the feed and in other areas outside the unit. The cooled syngas flows to the shift converter, operating at lower temperatures, where additional H2 is produced. In this work, the shift converter is described as a Gibbs reactor at thermodynamic equilibrium at 400 °C. This is supported by independent analysis of actual industrial data, as discussed by Lima et al.26 The H2-rich exhaust stream from the shift converter is cooled and the H2 is recovered from the off-gas with help of a PSA unit, performed with packed bed columns in two steps: (i) adsorption, when hydrogen is preferentially adsorbed onto a solid adsorbent from the feed stream; (2) regeneration or desorption, when hydrogen is removed from the adsorbent by pressure reduction. PSA operates under approximately isothermal conditions so that the capacity of hydrogen recovery is defined essentially by the difference between the feed (high) and regeneration (low) pressures of the isotherm.27 10 ACS Paragon Plus Environment

Page 10 of 58

Page 11 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The off-gas (also called residual gas), with additional fuel, is used for combustion in the reformer furnace. In the present work, it was assumed that the recovery of hydrogen in the PSA unit was equal to 90%, that the purity of the obtained hydrogen was close to 100% and that the PSA unit operated at quasi steady state conditions.28 Besides, it was assumed that the water present in the exhaust gas from the shift converter could be fully removed by condensation before the PSA unit. Finally, it was assumed that the off-gas temperature before and after the PSA unit was constant and equal to 35 °C. All these conditions are supported by real industrial operation.

Figure 1. Simplified diagram of hydrogen production process.

3. Process model 3.1. Reactor Modeling In the present work, the steam reforming reactor was described as proposed by Schwaab et al.5 The kinetic model of Xu and Froment29 was used to represent the reaction rate constants, as this model has already been used successfully to simulate industrial sites. The reforming reactor comprises a set of tubular reactors placed inside a furnace that provides the energy required for endothermic reactions, so as to keep the



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

reaction temperature at sufficient high values. A one-dimensional pseudo-homogeneous model with axial mass and heat dispersion is considered to describe the mass and energy balances inside the packed reactor, as described in Table 1. Initial and boundary conditions are presented in Table 2. The boundary condition used for the wall temperature at the entrance was the null gradient condition, since there is no energy flow at the entrance of the wall tube (considered isolated). The boundary condition at the furnace inlet consists of mixing of three streams: natural gas, air and residual gas. Thus, temperature at the furnace entrance is calculated as an adiabatic mixture of these three streams. In addition, the initial wall temperature was assumed to be the same of the catalytic bed. This modeling approach is based on the results of Ziolkowski and Szustek30, who showed that it was possible to obtain similar numerical results with both one and twodimensional models for real reactor geometries. Regarding the effectiveness factor of catalyst pellets, as well known in the open literature, this parameter depends on the particular geometry, temperature and physical properties of the catalyst particle. In the present work, the effectiveness factor was calculated with the help of empirical metamodels obtained through CFD analysis, as shown by Alberton et al.16 The proposed reactor model also comprises the energy balance in the thin tubular reactor wall, where both the heat transfer by convection with the catalytic bed and the furnace and the heat transfer by radiation with the furnace were considered. It is assumed implicitly that the heat exchange by radiation is negligible inside the tubular reactor, given the very low lower absorptivities of the flowing gas medium and the existence of the solid residence times, the relatively catalyst bed.5 Additionally, the pressure drop along the reactor length was calculated with the popular Ergun equation.31


Page 12 of 58

Page 13 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1 – Equations of the Steam Reforming Reactor Model Mass Balance in the Catalytic Bed

∂Ck ∂F ∂ 2 Ck 1− ε = − k + Dk +η  2 ∂t ∂z ∂z  ε

  Rk ; 

Fk = υ z Ck

Energy Balance in the Catalytic Bed

(1 − ε ) NR r −∆H ∂T ∂T k ∂ 2T 2U int η = −υ zφ + T − − + T T [ ] ∑ ( s) W ρ Cp s =1 s ∂t ∂z ρ C p ∂z 2 ρ C p R Energy Balance in the Reactor Wall ∂TW kW ∂ 2TW U int U U = − [TW − T ] − ext [TW − TF ] − rad TW4 − TF4  2 ∂t ρW C pW ∂z ρW C pW δ ρW C pW δ ρW C pW δ

Energy Balance in the Furnace Q( z) ∂TF ∂T k F ∂ 2TF U ext N tubπ Dext U N πD = −υ zF F + − [TW − TF ] − rad tub ext TW4 − TF4  + 2 ∂t ∂z ρ F C pF ∂z ρ F C pF AF ρ F C pF AF ρ F C pF AB  z  Q ( z ) = Q0   L L

B −1

  z B  exp  − A      L  

Ergun Equation ∂P υ  1− ε =− z  3 ∂z Dp  ε

  150 µ gas (1 − ε ) + 1.75 ρ gasυ z   Dp   

Finally, the furnace was modeled in accordance with a one-dimensional flow reactor, where the heat generated by the furnace can be described as a function of the axial distance.12 It is important to point out that the flame length was assumed to be constant in this work, although this does not constitute a serious drawback, as this assumption can be easily relaxed, as described by Schwaab et al.5 In addition, the combustion was assumed to occur instantaneously, due to the very high reaction rates and to the relatively low impact of the gas properties on the attained temperature profiles. Besides, the burned gas combustion was computed by assuming that combustion reactions were



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 58

complete, as observed at plant site. Deviations should only be expected when the excess of supplied oxygen is very low, which is unusual at a plant site.5

Table 2 – Boundary and Initial Conditions Model Equations Mass Balance in the Catalytic Bed

Boundary Conditions Ck ( z , t ) z =0 = Ckf ,

∂Ck ( z , t ) ∂z

T ( z, t ) z =0 = T f ,

Energy Balance in the Reactor Wall

∂TW ( z, t ) ∂T ( z , t ) = W ∂z ∂z z =0

Energy Balance in the Furnace

TF ( z , t ) z = 0 = Tad ,

Ergun Equation

P ( z , t ) z =0 = Pf ,

∂z

=0

Ck ( z , t ) t = 0 = C f

z=L

∂T ( z, t )

Energy Balance in the Catalytic Bed

Initial Condition

=0

T ( z , t ) t =0 = T f

=0

TW ( z , t ) t =0 = T f

z=L

z=L

∂TF ( z , t ) =0 ∂z z=L ∂P ( z, t ) =0 ∂z z = L

TF ( z , t ) t =0 = Tad

-------------------

Regarding to the energy balance of the furnace (presented in Table 1), Q0 is the total heat amount generated by the combustion fuel. This value is calculated taking into account the mixture of natural gas and residual gas fed into the furnace. Natural gas and off-gas flowrates are determined by the controller. It must be emphasized that the model equations were solved with the well-known method of lines, after discretization along the axial direction with the orthogonal collocation method. The resulting differentialalgebraic equations were solved numerically as functions of time with the DASSL code32, implemented in Fortran®. The computational times needed to provide numerical solutions for this system of equations were always smaller than 1 min, using an Intel®


Page 15 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Core™ i7. For additional details about the model equations and parameters values, the interested reader must refer to the work of Schwaab et al.5

3.2. Carbon Formation

The need to operate the reforming processes at temperatures in the range of 450 to 950 °C makes the industrial catalysts susceptible to sintering.33 Especially, the major problem in these processes is the formation of coke, due to the following chemical reactions34, as shown in Scheme 2:

2 ⇆ + ;

∆ = −172 /

(Boudouard)

+ ⇆ + ;

∆ = −131 /

(Water Gas)

∆ = 75 /

(Methanation)

⇆ + 2 ;

Scheme 2. Carbon formation reactions in the steam reforming of natural gas.

The minimization of coking is the most significant challenge during the development of catalysts for the reforming process. The process thermodynamics establishes that the coke formation is spontaneous and cannot be avoided, but operating conditions can be changed in order to minimize coke formation. The most obvious way to prevent coke formation is to increase the steam/carbon ratio (however, this can be expensive due to the heat required for vaporization of water and reduction of carbon products) or to increase the ratio of carbon dioxide/hydrocarbon to favor the reverse reaction.33 Coke can be defined as the carbonaceous deposits that are formed during the steam reforming process. As discussed in the works of Rostrup-Nielsen and co-workers33,34, coke may occur in steam reforming catalysts as pyrolytic carbon, encapsulated coke and coke whiskers.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 58

In this work, the “Principle of Equilibrated Gas” was used to analyze carbon formation34. According with this principle, for a fixed reforming gas composition, there is a temperature (named Tb), below which there is a thermodynamic potential (affinity) for the exothermic Boudouard reaction, and a temperature (designed Tm), above which there is an affinity for carbon formation by the endothermic decomposition of methane. The principle is justified by the fact that the gas will be at equilibrium in most of the catalyst particle because of the low effectiveness factor35. Therefore, carbon will be formed if the equilibrated gas shows affinity for carbon. Following Sandler36, the Gibbs free energy can be defined by:

NC NC  fˆ  G t ( n&i , P, T ) = ∑ν i G 0fi + RT ∑ν i ln  i0  f  i =1 i =1  

(1)

Furthermore, the equilibrium and stability analysis establishes that a system at constant temperature and pressure evolves towards a state of minimum Gibbs energy. Therefore, if, at any instant, the mole fractions of the reacting species in an ideal mixture are such that36:

  fˆ ν i  ν iG + RT ln ∏  i0   < 0 ∑  i f   i =1   NC

0 fi

(2)

From equation (2), reactants (species with negative stoichiometric coefficients,ν i ) are consumed to form the reaction products (species with positive stoichiometric coefficients) until the equilibrium composition is reached. In the case of an ideal gas


Page 17 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


mixture and considering that the fugacity in the standard state ( f 0 ) is equal to atmospheric pressure, the equation (2) can be rewritten as:

ν

 P ∏i yνi i  P0  < K j

(3)

Where the equilibrium constant for reaction j is defined by:

 NC 0   −∑ν iG fi   K j (T ) = exp  i =1  RT   

(4)

Therefore, in the present work, coke formation along of the catalytic bed was described with the thermodynamic approach for equilibrium constants ( K j ) presented by Colton37 (for the graphite and amorphous carbon) and Mendiondo et al.38 (for coke). Considering the Principle of equilibrated gas for the Boudouard reaction, equilibrated gas shows affinity for carbon if the following equation is satisfied:

Kg =

2 yCO P > K j (T ) yCO2

(5)

3.3. Shift Reactor and PSA Unit Approaches

In this section, the considered approaches for simulation of the Shift Reactor and the PSA unit are described. The Shift Reactor was modeled as a Gibbs Reactor. For the sake of simplicity, the adiabatic temperature was assumed to be equal to 400 °C, as typically observed at plant site. Besides, the pressure drop between the reforming



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 58

reactor and the shift reactor was assumed to be low, not affecting significantly the chemical equilibrium. An equilibrium model was used to describe the shift reactor, because the conditions typically observed at plant site approach the equilibrium conditions. Moreover, the dynamics induced by the shift reactor and the PSA units in the residual gas stream directed to the reforming reactor was neglected. Additionally, catalytic bed resistances and intra-particle diffusional limitations also have not been considered, due to the reasons discussed before. As a consequence, the simulation of the Shift Section consisted in calculating the chemical equilibrium composition at the established temperature and pressure conditions. However, although the total pressure appears in Equation (6), it is important to emphasize that in the case of an ideal gas mixture, the equilibrium of the shift reaction is not dependent on the total pressure, since Equation (6) can be expressed in terms of the mixture gas composition and temperature. Under kinetic limitations, the reaction rate of the water-gas shift reaction can be enhanced for elevated pressures.39,40 One way to evaluate the chemical equilibrium is to calculate the equilibrium constants of the involved reactions. However, in the case of multiple reactions, the approach of equilibrium constants does not allow for appropriate standardization of the computer program written to find the solution. A more attractive approach is based on the fact that the total Gibbs energy attains a minimum value at the equilibrium. Following Smith et al.41, the total Gibbs free energy of a single phase system can be given by the following equation:

NC NC NC  NC  G t ( n&i , P, T ) = ∑ n&i ∆G °fi + RT ∑ n&i ln ( n&i P ) − RT ∑ n&i ln  ∑ n&i  i =1 i =1 i =1  i =1 


(6)

Page 19 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Therefore, the proposed problem is finding the set of molar flows that minimizes the function described above with specified T and P, subject to the mass balance constraints. It is convenient to formulate the mass balance constraints in terms of elementary balances. If Ak represent the total number of atomic weights of the k-th element in the system, determined by the composition in the inlet stream, and ai , k define the total number of atoms of the k-th element present in each molecule i, the mass balance for each element k can be written as: NC

∑ n& a

i i ,k

− Ak = 0 , k = 1,K , Ne

(7)

i =1

The problem of minimization of the total Gibbs free energy, with the mass balance constraints is solved using a SQP (sequential quadratic programming) method, based on the algorithm presented by Spelluci42. Table 3 summarizes the expressions used to calculate the dependence of the Gibbs free energy and enthalpy with temperature.

Table 3. Equations for the calculation of Gibbs free energy and Enthalpy. Cpio (T ) = Ai + BiT + CiT 2 + DiT 3 + EiT 4 ∆ G of = ∆ H of − T ∆S of NC

T

i =1

Tref

∆H of (T ) = ∑ ( n&i − n&i 0 ) H ofi (Tref ) + ∫

∆Cpo (T ) dT

NC

∆Cpo = ∑ ( n&i − n&i 0 ) Cpio i =1

T

∆Cpo (T )

Tref

T

∆S of (T ) = ∆S of (Tref ) + ∫

dT

NC  H ofi (Tref ) − G ofi (Tref )   ∆S of (Tref ) = ∑ ( n&i − n&i 0 )  Tref   i =1



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 58

The PSA unit was simulated as a “black box” at quasi-steady state condition, with hydrogen recovery of 90% and hydrogen purity of 100% at the exhaust line. As discussed by Rajesh et al.9, this is justified mainly because the critical performance criteria are largely insensitive to nominal changes of the PSA feed composition and pressure. Moreover, water is completely removed through in the steam separator. Therefore, the model equations used to simulate the PSA unit are:

FH 2 , PSAin = yH 2 , PSAin × FPSA

(8)

FH 2 = YH 2 × FH 2 , PSAin

(9)

(

)

FH 2 ,offgas = 1 − YH 2 × FH 2 , PSAin

(10)

Fi ,offgas = yi , PSAin × FPSA , i = CH 4 , CO, CO2 , N 2

(11)

4. Temperature control design In this section, the design for the outlet temperature control of the reforming reactor is described. Since there are three degrees of freedom (air, natural gas and off-gas flow rates) to perform this task, a split-range control scheme was proposed and implemented43, using a standard feed-back PI controller to manipulate the control variables. In the proposed scheme, the streams fed to the furnace were used as manipulated variables: the off-gas (or residual gas), as primary manipulated variable, and the natural gas, as secondary manipulated variable. To analyze the effect of the residual gas stream (from the PSA unit) on the performance of the steam reforming reactor, a controller was used to maintain the outlet temperature reactor at the desired level, since reuse of the off-gas constitutes an additional disturbance in the process. More specifically, the outlet temperature controller has been implemented since open-loop operation with residual gas reuse does


Page 21 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


not guarantee that the reactor operates within the temperature range of the industrial process. In particular, operation of the reforming reactor under high temperature conditions may lead to catalytic deactivation due to the formation of coke. Furthermore, the remaining degree of freedom (that is, air flow rate) was manipulated according to the desired and specified amount of excess air (or molar air/fuel ratio). This temperature control scheme is important because it determines the amount of residual gas to be fed into the furnace. Therefore, the natural gas stream is used only for fine adjustment of the process operation, in order to complement the thermal load of the furnace. Moreover, it is assumed that the upper limit for the control action is the total amount of residual gas reported by the operator or the available residual gas resulting from the PSA unit. Feed flowrate of the reformer and gas composition in the entrance of the catalytic bed are input variables and remained constant in all performed simulations. Disturbances in feed flowrate and gas composition were performed only in simulations carried out to analyze the steam-carbon ratio effect on the reforming reactor performance. The configuration of the feed-back split-range control scheme can be seen in Figure 2. Whenever the primary temperature controller (called TC1) demands residual gas beyond c a the available value (i.e., when Foffgas > Foffgas is checked by a selector), a secondary

controller (called TC2) is triggered to make use of the natural gas stream. Note that priority is given to the use of the residual gas stream and that only when the heat load provided by the residual gas is not sufficient, the natural gas is used. According to this proposal, depending on the operation conditions, residual gas is wasted only when the energy available in the exhaust gas is sufficient to maintain the desired output reactor temperature. Therefore, at this particular condition, it is not necessary to feed all available off-gas into the furnace. Natural gas is fed into the furnace only when the



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

available off-gas stream is not sufficient to maintain the desired output reactor temperature. After setting the control action, the air flow rate is updated by a feedforward ratio controller (called FC) according to the total fuel fed into the combined stream (FCC = Foffgas + FGN) in order to reach the requirement of excess air (i.e., the air flow rate, represented by Fair, is adjusted from FCC given the desired air/fuel ratio).

Figure 2. Configuration of temperature control in split-range scheme.

The feed-back PI controllers were implemented according to the discrete speed algorithm41 given by Equation (12) and tuned parameters are shown in Table 4. These parameters were determined through observation of the behavior of the state variables, when subject to changes of the input variables. Thus, the signals and the magnitude of the controller gains were found and refined over the simulations. During the tuning tests, the offset of 1 ºC was considered satisfactory, as also required at the plant. It is important to emphasize that the controller parameters (presented in Table 4) were determined by simulation under the considered operation conditions in order to avoid undesirable temperature overshoots. Additionally, the constraints for the maximum wall and furnace temperatures were assumed to be equal to the adiabatic temperatures of the flowing gases. 22 ACS Paragon Plus Environment

Page 22 of 58

Page 23 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


 e  uk = uk −1 + KC  ek − ek −1 + Ts k  τI  

(12)

Table 4. PI controllers parameters. Split-range control loops Parameters

T ↔ Foffgas T ↔ FGN

K c [ºC·s/mol] 0.4

7.5×10-4

τ I [s]

10

7.5

PS1: Sampling time (Ts) = 2.5 min. PS2: The syntax y ↔ u means that y is controlled by the manipulation of u .

5. Results and Discussion Initially, several simulation tests were performed with the objective to verify the performance of the control scheme. Regarding the accuracy of the numerical solution, simulation tests with the increase of the number of discretization points on the orthogonal collocation method were performed by Schwaab et al.5. In that work, the number of collocation points required to guarantee that numerical inaccuracies were negligible in all analyzed conditions was equal to 15. For this reason, in this work, unless stated otherwise, the number of collocation points was also equal to 15 in all simulations. Among the major results, the performance of reforming reactor, including natural gas and residual gas burning in the furnace, methane conversion and temperature axial profiles were analyzed for different conditions of activity and geometry of catalyst, excess air in the furnace and steam/carbon ratio in the feed. The effect of the outlet temperature control and of the residual gas recycle on the reforming reactor performance was also analyzed.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

5.1. Outlet Temperature Control

In addition to the typical range of outlet temperatures of the reforming reactor (800950 °C), simulations were also performed considering the temperature of 775ºC. Thus, the following temperature values were considered: 775, 800, 850 and 900 °C. In these simulation tests, the steam carbon ratio was made equal to 3.0. Amounts of H2, CO, and CO2 were calculated according the Shift and PSA units, as the off-gas stream is mixed with fresh natural gas to compose the furnace feed. The pressure at the entrance of the tubular reactor was assumed to be equal to 27.7 bar. All the operation conditions resemble real plant operation data. In turn, the dimensions of the catalyst pellets, with shape of Raschig rings, used in these simulations were: 17 mm of diameter and height and 7 mm for the diameter of the central hole. The responses of the temperatures and methane conversion profiles along the reactor length can be seen in Figure 3.

Figure 3. Profiles of conversion, reactor temperature and wall temperature for different set point values.


Page 24 of 58

Page 25 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


It must be noted that the responses present stable behavior and that the performance of the controller is satisfactory, since the offset magnitude meets the desired tolerance of 1°C in all simulations. As expected, the increase of the set-point of the outlet temperature increases the reaction rates of the reforming reactions, justifying the increase of the outlet methane conversion. About the wall temperature profile, the increase of the set-point of the outlet reactor temperature is responsible by the increase of the thermal load (residual gas and natural gas flow rates), which, in turn, increases the maximum wall temperature and the temperature difference between the wall and the reactor bed. Dynamic trajectories for reactor wall temperature, outlet stream temperature and methane molar fraction in the residual gas are shown in Figure 4.

Figure 4. Dynamic profiles of outlet reactor temperature, wall temperature and methane molar fraction in residual gas for different set point values.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

In all simulations, the outlet reactor temperature reached the set point 2 hours after the introduction of the perturbation, as shown in Figure 4. In order to simulate the real reactor operation, dynamic simulations were performed first with residual gas recycling, in open loop mode, until attainment of stationary conditions (after approximately 3 hours of operation). Afterwards, the temperature controller was turned on, using the residual gas as manipulated variable.

(A)

(B)

(C)

(D)

Figure 5. Dynamic profiles of manipulated variables for different set point values: (A) 775°C, (B) 800°C, (C) 850°C and (D) 900°C.

As one can see, oscillations of small amplitude were observed immediately after initiation of the controller. These oscillations can be attributed to the fast changes of the 26 ACS Paragon Plus Environment

Page 26 of 58

Page 27 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


methane molar fraction in the residual gas. As one can see in Figure 4, and considering the controlled temperature condition, the methane molar fraction in the off-gas decreases when the set-point value for the outlet reactor temperature increases. One must note that methane conversion in the reformer reactor increases with temperature (as shown in Figure 3). Furthermore, as the energy available for combustion in the offgas decreases (due to the decrease in the molar fraction of methane), all available offgas must be used to achieve the desired reactor temperature. Additionally, it can be necessary to use fresh natural gas together with the off-gas to reach the desired temperature (as shown in Figure 5). In Figures 5 and 6, dynamic profiles for the natural gas, residual gas and air flow rate are presented for different outlet reactor temperatures.

Figure 6. Dynamic profiles of air flow rate for different set point values.

As expected, when the set-point of the outlet temperature increases, the thermal load of the furnace increases, justifying the increase of the natural gas, residual gas and air



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

flow rate into the furnace. These results illustrate the performance of the split-range control scheme. It can be seen that, in order to increase the outlet reactor temperature, it is necessary to increase also the thermal load of the furnace, through the simultaneous use of the residual gas and natural gas. For this particular case, the outlet temperature of the reforming reactor was approximately equal to 820°C at steady-state conditions during the open loop operation, as shown in Figure 4. Hence, if all residual gas is sent to furnace, this observed temperature can be seen as the maximum reachable temperature in the catalytic bed. In case of further heating, natural gas should be added to the residual gas stream (combined streams), so as to achieve the necessary thermal load. However, for desired temperatures below 820°C, temperature control can be performed only with adjustment of the residual gas molar flowrate. Fast and small oscillations were also observed in the manipulated variables profiles at the beginning of the closed loop period. Again, these oscillations can be attributed to the fast changes of the methane molar fraction in the residual gas, as previously discussed. Additionally, axial profiles for gas composition in the reforming reactor are presented in Figure 7. As one can observe, the H2/CO ratio is high, since the main purpose of the steam reform process considered here is the generation of hydrogen. In addition, the carbon dioxide content in the gas at the exit of the reforming reactor shows a slight decrease with the increasing temperature, since the equilibrium of the shift reaction is displaced towards the formation of carbon monoxide. One must also note that the carbon monoxide content presented a slight increase with increasing temperature.


Page 28 of 58

Page 29 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(A)

(B)

(C)

(D)

Figure 7. Axial profiles of gas composition in reforming reactor for different set point values: (A) 775°C, (B) 800°C, (C) 850°C and (C) 900°C.

Figure 8 presents the axial profiles for the potential of carbon formation in the catalytic bed. The equilibrium constants for coke, graphite and amorphous carbon and the equilibrium constant for the equilibrated gas ( K g , as defined in equation (5)) were calculated in the catalytic bed using the axial temperature and compositions profiles. For all evaluated conditions, the calculated values of equilibrium constants were higher than values of equilibrium constants of equilibrated gas. This indicates that the carbon formation process is not favorable at these conditions, due to the high steam/carbon 29 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ratio in the feed and the high temperatures in the catalytic bed. In these simulations, the feed steam/carbon ratio was kept constant and equal to 3.0. Usually, coking occurs for steam/carbon ratios smaller than 1.5.

(A)

(B)

(C)

(D)

Figure 8. Axial profiles of equilibrium constants of carbon formation: (A) 775°C, (B) 800°C, (C) 850°C and (C) 900°C.

5.2. Effect of the Activity of Catalyst on Controller Performance

In this section, the performance of the tubular reactor is analyzed for different catalyst activities, with and without outlet temperature control. Figure 9 presents the axial temperature profiles for different catalyst activities for open loop operation. In order to


Page 30 of 58

Page 31 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


simulate the effect of the catalyst activity, the specific rates of the kinetic reaction model of Xu and Froment29 were multiplied by an empirical multiplying factor (k).

(A)

(B)

(C) Figure 9. Profiles of conversion, reactor temperature and wall temperature for different catalyst activities: (A) = 0.01; (B) = 0.05; (C) = 0.5.

As expected, when the specific rates are increased, the methane conversion also increases and the axial reactor temperature decreases. In these simulations, as the thermal load of the furnace was kept constant (as an open loop control); the wall temperature is decreased, due to the increased amount of heat required by the reactor. Then, the performance of the controller was evaluated for different catalyst activities. In



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

this case, the outlet temperature set-point was always kept at 800 °C. Figure 10 presents the axial profiles for conversion, reactor and wall temperatures for these simulations.

(A)

(B)

(C) Figure 10. Profiles of conversion, reactor temperature and wall temperature for different catalyst activities with outlet temperature control: (A) = 0.01; (B) = 0.05; (C) = 0.5.

As discussed previously, with the increase of catalyst activity, the rates of the endothermic reforming reactions also increase. As a consequence, the increase of the methane conversion along the catalytic bed can be observed. Moreover, the heat load required by the reactor also increases with the higher rates of reaction, leading to the increase of the required thermal load of the furnace to attain the outlet set-point 32 ACS Paragon Plus Environment

Page 32 of 58

Page 33 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


temperature. For this reason, the axial reactor and wall temperature profiles decrease with the increase of the reaction rates. Dynamic trajectories for the outlet reactor temperature, reactor wall temperature and methane molar fraction in the residual gas are shown in Figure 11.

(A)

(B)

(C)

(D)

Figure 11. Dynamic profiles of outlet temperatures and methane molar fraction in residual gas for different catalyst activities: (A) = 0.01; (B) = 0.05; (C) = 0.5; (D) = 0.5 and = 0.0075.

In Figures 12 and 13, the dynamic profiles for the natural gas, residual gas and air flow rates are presented for different catalyst activities, with outlet temperature set-point of 800 °C. As expected, the increase of the reforming reaction rates increased the heat 33 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

amount required by the reactor, since the process is globally endothermic. Therefore, the thermal load in the furnace is increased to meet the outlet temperature set-point. For this reason, the residual gas and air flowrate in the furnace is also increased. Again, it is possible to notice the performance of the split-range scheme control, where the preferential increase of the residual gas flow rate and reduction of the natural gas flow rate with the increase of the catalyst activity can be seen.

(A)

(B)

(C)

(D)

Figure 12. Dynamic profiles of manipulated variables for different catalyst activities: (A) = 0.01; (B) = 0.05; (C) = 0.5; (D) = 0.5 and = 0.0075.

For these cases, the outlet temperature of the reforming reactor reached values above the desired set-point temperature in steady-state conditions during the open loop 34 ACS Paragon Plus Environment

Page 34 of 58

Page 35 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


operation, as shown in Figure 11. Therefore, temperature control can be again performed only with adjustment of the residual gas molar flowrate. Particularly, Figure 12(C) shows that residual natural gas flowrate is required (unlike other cases, where the natural gas flowrate was reduced to null values). It is also important to observe that the controller signal presents a slower response in this case, due to the low mismatch observed in the controlled variable. Increasing the value of the proportional gain, it becomes possible to operate the reforming reactor without use of natural gas, as shown in Figure 12(D). Dynamic trajectories for the outlet reactor temperature, reactor wall temperature and methane molar fraction in the residual gas are shown in Figure 11(D).

Figure 13. Dynamic profiles of air flow rate for different catalyst activities.

5.3. Effect of the Steam Carbon Ratio on Controller Performance

The system sensitivity to the variations of the steam/carbon ratio in the reactor feed was also investigated. In this case, the following values for this parameter were



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

considered: 1.3, 2.0, 4.0 and 5.0. The process was operated with outlet temperature setpoint of 850 °C. The obtained responses can be seen in Figure 14.

(A)

(B)

(C)

(D)

Figure 14. Profiles of conversion, reactor and wall temperatures for different steamcarbon ratios with outlet temperature control: (A) / = 1.3; (B) / = 2.0; (C) / = 3.0; (D) / = 5.0.

It must be noted that the increase of the steam/carbon ratio leads to the increase of the methane conversion, due to the increase of rates of endothermic reforming reactions in the closed loop mode. Additionally, axial profiles for gas composition in the reforming reactor are presented in Figure 15.


Page 36 of 58

Page 37 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(A)

(B)

(C)

(D)

Figure 15. Axial profiles of gas composition in reforming reactor for different steamcarbon ratios with outlet temperature control: (A) / = 1.3; (B) / = 2.0; (C) / = 3.0; (D) / = 5.0.

Regarding the axial temperature profiles, the increase of the steam-carbon ratio leads to the decrease of the axial reactor and wall temperature profiles, due to the increase of the amount of heat required by the reactor. Dynamic trajectories for the outlet reactor temperature, reactor wall temperature and methane molar fraction in the residual gas are shown in Figure 16.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(A)

(B)

(C)

(D)

Figure 16. Dynamic profiles of outlet temperatures and methane molar fraction in residual gas for different steam-carbon ratios: (A) / = 1.3; (B) / = 2.0; (C) / = 3.0; (D) / = 5.0.

Regarding Figure 16, it is possible to notice the influence of the steam/carbon ratio on the performance of the reforming reactor operating with recycle. Particularly, higher temperatures can be observed when the steam/carbon ratio decreases, when the tubular reactor operates in open loop. In case of the open loop operation, although increasing steam carbon ratio enables the increase of the reaction rates, reactor and wall temperatures decrease due to the higher thermal load required by reactor, while the available heat load of the furnace remains fixed. Consequently, the effect of reducing the reactor temperature provides the reduction in rate specific constants. Therefore, for 38 ACS Paragon Plus Environment

Page 38 of 58

Page 39 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the open loop process, the variation of the steam/carbon ratio exerts little effect on methane conversion due to the existence of two opposing effects, unlike the closed-loop process. Particularly, the methane molar fraction in the residual gas presented a substantial increase in the closed loop operation, as shown in Figure 16(A), due to the decrease of the methane conversion in the reforming reactor. One must observe that high methane molar fractions in the residual gas are not desirable, because this can lead to reduction of the hydrogen production. Figure 17 presents the dynamic profiles of natural and residual gas flowrates into the furnace.

(A)

(B)

(C)

(D)

Figure 17. Dynamic profiles of manipulated variables for different steam/carbon ratios: (A) / = 1.3; (B) / = 2.0; (C) / = 3.0; (D) / = 5.0.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The increase of the steam/carbon ratio provides the increase of the manipulated variables, as shown in Figure 17. For conditions with steam/carbon ratio of 1.3 and 2.0 and in open loop mode, stationary outlet reactor temperature remains above the desired value, as shown in Figure 17(A) and Figure 17(B). Therefore, the temperature control can be performed with the residual gas stream only, with increase of the residual gas flowrate with the increase of the steam/carbon ratio, due to the higher heat load required by the reactor. However, in cases with steam/carbon ratio of 3.0 and 5.0, natural gas had to be used for temperature adjustment, while the residual gas was kept constant at the operation constraint, as shown in Figure 17(C) and Figure 17(D). Figure 18 presents the influence of the steam/carbon ratio on the axial profiles for potential carbon formation in the catalytic bed. The kinetic constants for the coke, graphite and amorphous carbon and the equilibrium constant for the Boudoaurd reaction were calculated in the catalytic bed using the available axial temperature and composition profiles. Once more, the calculated values of kinetic constants were higher than values of equilibrium constants for the Boudouard reaction, indicating that the carbon formation process is not favorable at these conditions, due to the high temperatures of the catalytic bed. The exothermic Boudouard and carbon gasification reactions, which possibly contribute to deposition of coke at low temperatures, are disadvantageous for carbon deposition at elevated temperatures.


Page 40 of 58

Page 41 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(A)

(B)

(C)

(D)

Figure 18. Axial profiles of equilibrium constants of carbon formation at 850 °C: (A) / = 1.3; (B) / = 2.0; (C) / = 3.0; (D) / = 5.0.

5.4. Effect of the Catalyst Geometry on Controller Performance

In order to verify the effect of the shape of the catalyst pellet on the performance of the control of the industrial reactor, several catalyst geometries were analyzed. The effect of different geometries on methane conversion and reactor temperature profiles was analyzed for some specific catalyst geometries, including cylindrical pellets, Raschig rings (with different central pore diameters) and perforated cylinders with six lateral holes and a central hole, as described in Table 5. Figure 19 illustrates the influence of the pellet geometry on the methane conversion and temperature profiles for three selected geometries of Table 5. 41 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(A)

Page 42 of 58

(B)

(C) Figure 19. Profiles of conversion, reactor and wall temperatures for different catalyst pellet dimensions with outlet temperature control: (A) Case 1; (B) Case 2; (C) Case 3.

Table 5. Analyzed Catalyst Pellet Dimensions Catalyst geometries

Case

Central hole Number of Lateral hole diameter (mm) lateral holes diameter (mm)

Full cylinder

Case 1

0

0

0

Raschig rings

Case 2

6

0

0

Six lateral holes

Case 3

3

6

3


Page 43 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


As shown in Figure 19, the effect of the catalyst geometry on the methane conversion inside the reactor tube was slightly higher when the catalyst pellets have the shape of full cylinders. The low effect of the catalyst geometry shows that the temperature of the reactor is more important on the methane conversion than intraparticle diffusive effects. On the other hand, the use of perforated pellets caused the increase of the temperature of the reactor walls. As discussed by Schwaab et al.5, both effects are related to the bed porosity and to the different pressure drop values and flow velocities observed in these cases. Moreover, several factors are expected to be influenced by the change of the bed porosity, such as the catalyst activity, the average residence time of the gaseous species inside the reactor, the heat capacity of the flowing gas (because of the different heat capacities of reactants and products), and the heat exchange by conduction and convection, among others. Particularly, the convective heat transfer coefficient increases with the Reynolds number, and therefore, it is greater for nonporous geometries (e.g., full cylinder). Consequently, the heat exchange between the wall and the catalyst bed is increased for nonporous geometries and the maximum temperature of the wall becomes smaller in these cases. Figure 20 presents dynamic profiles for outlet variables, including an additional simulation with a high proportional constant to guarantee the temperature control, using only residual gas stream, as discussed in section 5.2.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(A)

(B)

(C)

(D)

Figure 20. Dynamic profiles of outlet reactor temperature, wall temperature and methane molar fraction in residual gas for different catalyst pellet dimensions: (A) Case 1; (B) Case 2; (C) Case 3; (D) Case 3 e = 0.0075.

In the case of the catalytic bed with controlled temperature, the dynamic behavior of the furnace is changed to meet the energy demand of the endothermic reactions occurring in the catalytic bed. Particularly, when porous geometries are used, the effectiveness factors increase with the increase of the specific area (as one can see in the Figure 21). Therefore, the concentration and temperature gradients between the catalyst particle and the bulk fluid are higher, justifying the increase of heat and mass transfer rates. In this case, the heat transfer resistance is increased, justifying the increase of the residual gas consumption in the furnace (as shown in Figure 22) and the higher


Page 44 of 58

Page 45 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


temperatures for reactor wall. In Figure 21, Reaction (1) and (3) are reforming reactions, while Reaction (2) is Shift reaction, as presented in Scheme 1.

(A)

(B)

(C) Figure 21. Profiles of effectiveness factors and wall temperatures for different catalyst pellet dimensions with outlet temperature control: (A) Case 1; (B) Case 2; (C) Case 3.

Therefore, the higher heat transfer coefficient of nonporous catalyst geometries provides the increase of outlet reactor temperature and the decrease of the outlet wall temperature, as shown in Figure 20 for the reactor open loop operation. These results are confirmed also in Figure 22, where it is possible to notice that residual gas flowrates used to meet the outlet temperature were higher when the catalytic bed was composed by porous geometries. 45 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(A)

(B)

(C)

(D)

Figure 22. Dynamic profiles of manipulated variables for different catalyst pellet dimensions: (A) Case 1; (B) Case 2; (C) Case 3; (D) Case 3 and = 0.0075.

5.5. Effect of the Excess Oxygen on Controller Performance

Figure 23 presents the effect of the excess oxygen on the axial profiles for the methane conversion, reactor and wall temperatures. The simulations were performed with set-point value of 800 °C for the outlet temperature reactor. The values for the excess oxygen used in these simulations were 5, 15 and 30%. The results show reduction of the wall temperature when the excess oxygen fed into the furnace is increased, as consequence of decrease in available heat produced by combustion, due to heating of the supplied excess of air.


Page 46 of 58

Page 47 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(A)

(B)

(C) Figure 23. Profiles of conversion, reactor and wall temperatures for different percentages of excess oxygen with outlet temperature control: (A) 5%; (B) 15%; (C) 30%.

Dynamic profiles for outlet variables are presented in Figure 24. Considering the open loop operation, the increase of excess oxygen provides the decrease of outlet reactor and wall temperatures, as discussed previously. Therefore, it is possible to notice that increase of the residual gas flowrate is necessary to reach the desired outlet temperature, when the excess oxygen is increased. Moreover, depending on the set point temperature, high percentages of excess oxygen can lead to use of natural gas for temperature adjustment, due the operation constraint for residual gas use, as shown in Figure 25.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(A)

(B)

(C) Figure 24. Dynamic profiles of outlet reactor temperature, wall temperature and methane molar fraction in residual gas for different percentages of excess oxygen with outlet temperature control: (A) 5%; (B) 15%; (C) 30%.


Page 48 of 58

Page 49 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(A)

(B)

(C) Figure 25. Dynamic profiles of manipulated variables for different conditions of excess oxygen: (A) 5%; (B) 15%; (C) 30%.

6. Conclusion In this work, a hybrid model was used to describe the steam reforming of natural gas in industrial tubular reactors. The model comprises a set of rigorous one-dimensional mass balance and energy balance equations for the reactor tubes and furnace, and is coupled to empirical metamodels, built to represent the effectiveness factor of catalyst pellets of complex geometry, based on detailed CFD simulations to account for mass and heat diffusive effects inside the catalyst pellets. Simplified approaches to describe the Shift and PSA units were developed to allow for the analysis of effects of residual gas recycling on the furnace and the performance of the reforming tubular reactors. In 49 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

addition, a control structure was designed for the reactor outlet temperature through a split-range scheme, performed with the simultaneous manipulation of the natural and residual gas flow rates fed to the furnace. In general, the performance of reforming reactor, including natural gas and residual gas consumption in the furnace, methane conversion and temperature axial profiles, was analyzed for different catalyst activities and geometries, excess of air in the furnace and steam/carbon ratios in the feed of packed tubes. The effect of outlet temperature control and recycling of residual gas on the performance of the reforming reactor were also analyzed. According to the obtained results, the energetic integration through use of residual gas in the furnace for control of the outlet reactor temperature can lead to reduction of the natural gas consumption in the furnace, keeping methane conversions higher and reactor wall temperatures lower, due of the larger heat transfer coefficients. Moreover, in all simulations performed, coke formation was not favorable. However, reforming reactor operation with residual gas recycle and temperature control represents a challenging task, because it constitutes a multivariable process. Depending on the analyzed process conditions, the choice of desired temperature should be careful to ensure the energetic integration and high hydrogen production.


Page 50 of 58

Page 51 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Notation

Ak

Total number of atomic weights of the k-th element

AF

Transversal area of the furnace (m2)

ai , k

Total atoms number of the k-th element present in each molecule of the chemical species i,

Ck

Molar concentration of component k (J/mol)

Cpio

Heat capacity of the chemical specie i (J/mol/K)

Dk

Dispersion coefficient of component k (m2/s)

Dext

External diameter of tubes (m)

Dp

Characteristic particle diameter (m)

eff H 2

Hydrogen separation efficiency

e

Controller error

Fk

Molar flowrate of component k (mol/h)

FCC

Molar flowrate of fuel fed into the combined stream (natural gas and off-gas) (mol/h)

FGN

Molar flowrate of natural gas fed in furnace (mol/h)

FH 2 , PSAin

Molar flowrate of hydrogen on inlet of PSA (mol/h)

FPSA

Total molar flowrate on intlet of PSA (mol/h)

FH 2

Molar flowrate of hydrogen on outlet of PSA (mol/h)

c Foffgas

Total flowrate of residual gas selected by the temperature control (mol/h)

a Foffgas

Total flowrate of residual gas available in the process (mol/h)

Fi , offgas

Molar flowrate of chemical specie i on residual gas (mol/h)

fˆi

Fugacity of the specie i in the mixture

Gt

Total Gibbs free energy rate of a single phase (J/h)

G ofi

Formation Gibbs free energy of the chemical specie i (J/mol)

H ofi

Formation enthalpy of the chemical specie i (J/mol)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

K (T ) k Ntub

Equilibrium constant of Boudouard reaction for carbon formation (atm) Thermal conductivity (W/m/K) Number of tubular reactors inside the furnace

n&i

Molar flowrate of chemical species i on outlet (mol/h)

n&i 0

Molar flowrate of chemical species i on inlet (mol/h)

NC

Component number

Ne

Chemical element number

P

Pressure reactor (bar)

Q

Heat generated by burning of the gas fuel

Rk

Reaction rate for component k (mol/m3/h)

R

Universal gas constant (J/mol/K)

t

Time (h)

T

Temperature reactor (K)

TW

Wall Temperature (K)

TF

Furnace Temperature (K)

Tref

Reference Temperature (K)

U int

Heat transfer constant between the bed and the reactor wall (W/m2/K)

U ext

Convection heat transfer coefficient in the furnace side (W/m2/K)

U rad

Radiation heat transfer coefficient in the furnace side (W/m2/K)

u y H 2 , PSAin YH 2

Manipulated variable Molar composition of hydrogen on inlet of PSA Hydrogen fraction of the feed stream recovered as pure product

Greek characters

∆G °f

Total formation Gibbs free energy of the reaction medium (J/mol)


Page 52 of 58

Page 53 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


∆H of

Total formation enthalpy of the reaction medium (J/mol)

∆H s

Heat of reaction for reactions step s (J/mol)

∆S of

Total formation entropy of the reaction medium (J/mol)

δ

Wall thickness (m)

ε

Bed porosity

φ

Ratio between the heat capacity of the flowing mixture and the heat capacity of the bed (dimensionless)

η

Effectiveness factor (dimensionless)

µ gas

Gas viscosity (kg/m/s)

ρ

Specific Mass (kg/m3)

υz

Gas flow velocity (m/h)

Acknowledgment The authors thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) and FAPERJ (Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro) for providing scholarships and for supporting part of this research. The authors thank Petrobras for providing technical support.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

References (1) Rostrup-Nielsen, J. R. Production of synthesis gas. Catal. Today 1993, 18, 305-324.

(2) Ren, X. H.; Bertmer, M.; Stapf, S.; Demco, D. E.; Blümich, B.; Kern, C.; Jess, A. Deactivation and regeneration of a naphtha reforming catalyst. Appl. Catal., A 2002, 228, 39-52.

(3) Peña, M. A.; Gómez, J. P.; Fierro, J. L. G. New catalytic routes for syngas and hydrogen production. Appl. Catal., A 1996, 144, 7-57.

(4) Ebrahimi, H.; Behroozsarand, A.; Zamaniyan, A. Arrangement of primary and secondary reformers for synthesis gas production. Chem. Eng. Res. Des. 2010, 88, 1342–1350. (5) Schwaab, M.; Alberton, A. L.; Fontes, C. E.; Bittencourt, R. C.; Pinto, J.C.C.S. Hybrid Modeling of Methane Reformers. 2. Modeling of the Industrial Reactors. Ind. Eng. Chem. Res. 2009, 48, 9376–9382.

(6) Armor, J. N. The multiple roles for catalysis in the production of H2. Appl. Catal., A 1999, 176, 159-176.

(7) Kvamsdal, H. M.; Svendsen, H. F.; Hertzberg, T.; Olsvik, O. Dynamic simulation and optimization of a catalytic steam reformer. Chem. Eng. Sci. 1999, 54, 26972706.

(8) Rajesh, J. K.; Gupta, S. K.; Rangaiah, G. P.; Ray, A. K. Multiobjective Optimization of Steam Reformer Performance Using Genetic Algorithm. Ind. Eng. Chem. Res. 2000, 39, 706-717.

(9) Rajesh, J. K.; Gupta, S. K.; Rangaiah, G. P.; Ray, A. K. Multi-objective optimization of industrial hydrogen plants. Chem. Eng. Sci. 2001, 56, 999-1010.

(10) Pantoleontos, G.; Kikkinides, E. S.; Georgiadis, M. C. A heterogeneous dynamic model for the simulation and optimisation of the steam methane reforming reactor. Int. J. Hydrogen Energy 2012, 37, 16346-16358.


Page 54 of 58

Page 55 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(11) Pedernera, M. N.; Piña, J.; Borio, D. O.; Bucalá, V. Use of a heterogeneous twodimensional model to improve the primary steam reformer performance. Chem. Eng. J. 2003, 94, 29–40.

(12) Zamaniyan, A.; Ebrahimi, H.; Mohammadzadeh, J. S. S. A unified model for top fired methane steam reformers using three-dimensional zonal analysis. Chem. Eng. Process. 2008, 47, 946–956.

(13) Latham, D. A.; McAuley, K. B.; Peppley, B. A.; Raybold, T. M. Mathematical modeling of an industrial steam-methane reformer for on-line deployment. Fuel Process. Technol. 2011, 92, 1574–1586.

(14) Hottel, H. C.; Cohen, E. C. Radiant Heat Exchange in a Gas-filled Enclosure: Allowance for Nonuniformity of Gas Temperature. AIChE J. 1958, 4, 3-14.

(15) Hottel, H. C.; Sarofim, A. F. Radiative Transfer; McGraw-Hill: New York, 1967.

(16) Alberton, A. L.; Schwaab, M.; Fontes, C. E.; Bittencourt, R. C.; Pinto, J. C. Hybrid Modeling of Methane Reformers. 1. A Metamodel for the Effectiveness Factor of a Catalyst Pellet with Complex Geometry. Ind. Eng. Chem. Res. 2009, 48, 9369–9375.

(17) Smith, N. L.; Amundson, N. R. Intraparticle Diffusion in Catalytic Heterogeneous Systems. Ind. Eng. Chem. 1951, 43, 2156-2167. (18) Aris, R. A Normalization for the Thiele Modulus. Ind. Eng. Chem. Fundam. 1965, 4, 227-229. (19) Bischoff, K. B. Effectiveness Factors for General Reaction Rate Forms. AIChE J. 1965, 11, 351-355.

(20) Petersen, E. E. Non-isothermal chemical reaction in porous catalysts. Chem. Eng. Sci. 1962, 17, 987-995.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(21) Dogu, T. Diffusion and reaction in catalyst pellets with bidisperse pore size distribution. Ind. Eng. Chem. Res. 1998, 37, 2158-2171.

(22) Aris, R. On shape factors for irregular particles - I: The steady state problem. Diffusion and reaction. Chem. Eng. Sci. 1957, 6, 262-268.

(23) Burghardt, A.; Kubaczka, A. Generalization of the effectiveness factor for any shape of a catalyst pellet. Chem. Eng. Process 1996, 35, 65-74.

(24) Dixon, A. G.; Taskin, M. E.; Stitt, E. H.; Nijemeisland, M. 3D CFD simulations of steam reforming with resolved intraparticle reaction and gradients. Chem. Eng. Sci. 2007, 62, 4963–4966. (25) Dixon, A. G.; Taskin, M. E.; Nijemeisland, M.; Stitt, E. H. Wall-to-particle heat transfer in steam reformer tubes: CFD comparison of catalyst particles. Chem. Eng. Sci. 2008, 63, 2219-2224.

(26) Lima, D. F. B.; Zanella, F. A.; Lenzi, M. K.; Ndiaye, P. M. Modeling and simulation of water gas shift reactors: an industrial case. In: Petrochemicals [Online]; Patel, V., Ed.; InTech: Rijeka, 1991; Chapter 2, pp. 53-74. http://www.intechopen.com/books/petrochemicals/modeling-and-simulation-ofwater-gas-shift-reactors-an-industrial-case (accessed May 22, 2015).

(27) Ruthven, D. M.; Farooq, S.; Knaebel, K. S. Pressure Swing Adsorption; 1st ed., VCH Publishers: USA, 1994.

(28) Barg, C.; Ferreira, J. M. P.; Trierweiller, J. O.; Secchi, A. R. Simulation and optimization of an industrial PSA unit. Braz. J. Chem. Eng. 2000, 17, 695-704.

(29) Xu, J.; Froment, G. F. Methane Steam Reforming, Methanation and Water-Gas Shift: 1. Intrinsic Kinetics. AIChE J. 1989, 35, 88-96.

(30) Ziólkowski, D.; Szustek, S. Mathematical simulation of the performance of a single tube of a commercial reactor for methane steam catalytic conversion: Comparison of one- and two-dimensional pseudo-homogeneous models. Chem. Eng. Process. 1991, 30, 3-10.


Page 56 of 58

Page 57 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(31) Bird, R. B.; Stewart, W. R.; Lightfoot, E. N. Transport Phenomena; 2nd ed., John Wiley & Sons: New York, 2002.

(32) Petzold, L. R. DASSL code; Computing and Mathematics Research Division: Livermore, CA, 1990.

(33) Rostrup-Nielsen, J. R.; Sehested, J.; Norskov, J. K. Hydrogen and synthesis gas by steam- and CO2 reforming. Adv. Catal. 2002, 47, 65-139.

(34) Rostrup-Nielsen, J. R. Catalytic Steam Reforming. In: Catalysis: Science and Technology; Anderson, J.R.; Boudart, M., Eds., Springer-Verlag: Berlin, 1984, pp. 3-110.

(35) Rostrup-Nielsen, J. R. Sulfur-Passivated Nickel Catalysts for Carbon-Free Steam Reforming of Methane. J. Catal. 1984, 85, 31-43.

(36) Sandler, S. I. Chemical, Biochemical, and Engineering Thermodynamics, 4th ed., John Wiley & Sons: USA, 2006. (37) Colton, J. W. Pinpoint carbon deposition. Hydrocarbon Process. 1981, 60, 177184.

(38) Mendiondo, C. H.; Russo, R. H.; E Cianci, D. D. Estudio del catalizador de steamreforming impacto en la unidad comercial; Boletin de Informaciones Pretroleras, v. 10, pp-50-63, 1994.

(39) Francesconi, J. A.; Mussati, M. G.; Aguirre, P. A. Analysis of design variables for water-gas-shift reactors by model-based optimization. J. Power Sourc. 2007, 173, 467-477.

(40) Adams II, T. A.; Barton, P. I. A dynamic two-dimensional heterogeneous model for water gas shift reactors. Int. J. Hydrog. Energy 2009, 34, 8877-8891.

(41) Smith, J. M.; Van Ness, H. C.; Abbott, M. M. Introduction to chemical engineering thermodynamics, 7th ed., McGraw-Hill: Boston, 2005.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(42) Spellucci, P. An SQP method for general nonlinear programs using only equality constrained subproblems. Math. Prog. 1998, 82, 413-448.

(43) Seborg, D. E.; Edgar, T. F.; Mellichamp, D. A. Process Dynamics and Control, 3rd ed., John Wiley and Sons: New York, 2011.

Table of Contents Graphic


Page 58 of 58

Simulation and Control of Steam Reforming of Natural GasâReactor

Recommend Documents

Simulation and Control of Steam Reforming of Natural GasâReactor