CFD modeling and control of a steam methane reforming reactor ...

Chemical Engineering Science 148 (2016) 78–92

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Chemical Engineering Science

http://d0009-25

n Corrgineerin

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journal homepage: www.elsevier.com/locate/ces

CFD modeling and control of a steam methane reforming reactor

Liangfeng Lao a, Andres Aguirre a, Anh Tran a, Zhe Wu a, Helen Durand a,Panagiotis D. Christofides a,b,n

a Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095-1592, USAb Department of Electrical Engineering, University of California, Los Angeles, CA 90095-1592, USA

H I G H L I G H T S

� Computational fluid dynamics modeling of steam methane reforming reactor.
� Model calibration and comparison with industrial plant data.� Integration of computational fluid dynamics modeling and boundary feedback control.� The use of feedback control improves closed-loop dynamics and feed disturbance rejection.
a r t i c l e i n f o

Article history:Received 4 December 2015Received in revised form17 March 2016Accepted 24 March 2016Available online 29 March 2016

Keywords:Steam methane reformingCFD modelingProcess dynamicsProcess identificationProcess controlDistributed parameter systems

x.doi.org/10.1016/j.ces.2016.03.03809/& 2016 Elsevier Ltd. All rights reserved.

esponding author at: Department of Chemg, University of California, Los Angeles, CA 90ail address: [email protected] (P.D. Christofid

a b s t r a c t

This work initially focuses on developing a computational fluid dynamics (CFD) model of an industrial-scale steam methane reforming reactor (reforming tube) used to produce hydrogen. Subsequently, wedesign and evaluate three different feedback control schemes to drive the area-weighted average hy-drogen mole fraction measured at the reforming tube outlet ( x̄H

outlet2

) to a desired set-point value ( x̄Hset

2)

under the influence of a tube-side feed disturbance. Specifically, a CFD model of an industrial-scale re-forming tube is developed in ANSYS Fluent with realistic geometry characteristics to simulate thetransport and chemical reaction phenomena with approximate representation of the catalyst packing.Then, to realize the real-time regulation of the hydrogen production, the manipulated input and con-trolled output are chosen to be the outer reforming tube wall temperature profile and x̄H

outlet2

respectively.On the problem of feedback control, a proportional (P) control scheme, a proportional-integral (PI)control scheme and a control scheme combining dynamic optimization and integral feedback control togenerate the outer reforming tube wall temperature profile based on x̄H

set2are designed and integrated

into real-time CFD simulation of the reforming tube to track x̄Hset

2. The CFD simulation results demon-

strated that feedback control schemes can drive the value of x̄Houtlet

2toward x̄H

set2in the presence of a tube-

side feed disturbance and can significantly improve the process dynamics compared to the dynamicsunder open-loop control.

& 2016 Elsevier Ltd. All rights reserved.

1. Introduction

The steam methane reforming (SMR) process, which producesbulk hydrogen gas from methane through catalytic reactions, isthe most common commercial method for industrial hydrogenproduction. A general industrial-scale SMR process can be de-scribed by the schematic of Fig. 1. The steam methane reformer(for simplicity, it is denoted as “reformer” in the following text) isthe core unit in a SMR process which has a process (tube) side and

ical and Biomolecular En-095-1592, USA.es).

a furnace side that interact through heat exchange through thewalls of reforming reactors (for simplicity, they are denoted as the“reforming tubes”). In the furnace side, combustion of the furnace-side feed, usually a mixture of methane, hydrogen, carbon dioxide,carbon monoxide and air, heats the reforming tubes via radiativeheat exchange; inside the reforming tubes, catalytic reactions takeplace, converting steam and methane into hydrogen and carbonoxides (including CO and CO2). A traditional top-fired, co-currentfurnace usually includes top burners which are fed with the fur-nace-side feed, refractory walls enveloping the combustion pro-ducts, flue gas tunnels transporting the flue gas out of the re-former, and reforming tubes.

For the last 50 years, extensive work has been performed on

Fig. 1. Steam methane reforming process diagram (Othmer).

L. Lao et al. / Chemical Engineering Science 148 (2016) 78–92 79

the development of first-principles reformer models. The mathe-matical modeling methodology of the complete reformer was firstproposed and developed in the 1960s (McGreavy and Newmann,1969). With the improved understanding of both physical andchemical phenomena inside the reformer, more comprehensivemathematical models have been developed considering more de-tailed and precise radiation mechanisms, combustion models, fluegas flow patterns, SMR reaction kinetics and packed bed reactormodels (Latham, 2008). However, solving these complete reformermodels is computationally expensive due to the increasing com-plexity of the fundamental nonlinear partial differential equationsdescribing reformer physico-chemical phenomena. Also, for largereformers with complicated geometry, the geometry character-istics and various boundary conditions (Latham, 2008) makemathematical modeling very difficult.

On the other hand, with the dramatic increase of computingpower, computational fluid dynamics (CFD) modeling has becomean increasingly important platform for reformer modeling anddesign, combining physical and chemical models with detailedrepresentation of the reformer geometry. When compared withfirst-principles modeling, CFD is a modeling technique withpowerful visualization capabilities to deal with various geometrycharacteristics and boundary conditions. Moreover, CFD modelingprovides flexibility to modify design parameters without the ex-pense of hardware changes which brings large economic and timesavings (Uriz et al., 2013). CFD technology has been successful incarrying out the simulation of industrial furnaces (Baburić et al.,2005; Han et al., 2006; Stefanidis et al., 2006; Noor et al., 2013)and SMR tube reactors, i.e., reforming tubes modeled as packed-bed reactors (Calis et al., 2001; Behnam et al., 2012; Dixon, 2014;Guardo et al., 2004). Specifically, recent attempts to use CFDmodeling to characterize the physico-chemical phenomena oftransport and reaction processes inside reforming tubes have beendone exclusively on a microscopic or bench-scale level, e.g., theeffect of catalyst orientation on catalytic performance is in-vestigated with a CFD model of a single catalyst particle (Dixon,2014), and the validation of CFD simulation results to experimental

data is performed with a CFD model of a bench-scale reformingtube (Behnam et al., 2012). In the present work, we focus on anindustrial-scale reforming tube, i.e., the external diameter, internaldiameter and exposed length of the reforming tube are 14.6 cm,12.6 cm and 12.5 m respectively. It is noteworthy that the CFDmodel of the industrial-scale reforming tube in this work is de-veloped based on a unit currently employed in a commercial plant.Therefore, the CFD model has the geometry characteristics of anindustrial-scale reforming tube, i.e., the length and inner and outertube radii, includes an industrially relevant representation of thecatalyst network, and incorporates appropriate boundary condi-tions including the reforming tube outer wall temperature andtube-side feed conditions. A major purpose of the CFD modeling inthis work, in addition to its purpose as a means for evaluatingvarious control strategies, is to propose a method of industrialreforming tube modeling with considerable modeling accuracythat can help evaluate various modeling assumptions usuallyemployed.

The production rate of hydrogen fuel from a typical SMR pro-cess strongly depends on the operating temperature of the fur-nace, where the aforementioned reforming tubes are en-capsulated, and more specifically the outer reforming tube walltemperature. Because of the endothermic nature of SMR reactions,a higher outer reforming tube wall temperature theoretically re-sults in a higher production rate of hydrogen fuel. On the otherhand, operating the reforming tubes at excessively high tem-perature can lead to disastrous consequences and significant ca-pital loss. Particularly, the formation of carbon on the catalystsurface and on the inner reforming tube surface prevents the re-actants from entering the catalyst active sites and reduces the rateof heat transfer to the tube-side gas mixture respectively. As aresult, the reaction progress and hydrogen production might bedisrupted. Additionally, the expected lifetime of reforming tubes isextremely sensitive to changes in operating temperatures, i.e., anincrease in tube wall temperature of 20 K can reduce the tubelifetime by half (Pantoleontos et al., 2012; Latham, 2008). More-over, reforming tubes are one of the most expensive plant

Fig. 2. The top view of an industrial-scale top-fired, co-current reformer with 336reforming tubes, for which each reforming tube is denoted by a smaller circle, and96 burners, for which each burner is denoted by a larger circle.

L. Lao et al. / Chemical Engineering Science 148 (2016) 78–9280

components as they account for approximately 10% of the capitalcost of an entire hydrogen plant (Latham, 2008) and the total re-placement of a typical industrial-scale reformer is expected to cost5–8 million USD (Pantoleontos et al., 2012). Consequently, theouter reforming tube wall temperature is required to be closelymonitored and kept slightly below the design tube wall tem-perature in industrial standard operation in order to eliminate thepotential stress-to-rupture of tube materials (Beyer et al., 2005).Through CFD simulation, these above critical issues can be de-tected and predicted, and corresponding changes can be applied toimprove the reforming tube design and operating parameters.

Motivated by the above considerations, we initially develop aCFD model of an industrial-scale reforming tube in ANSYS Fluentwith realistic tube geometry characteristics to simulate thetransport and reaction phenomena with an approximate re-presentation of the catalyst packing inside the reforming tube.Next, we utilize publicly available SMR plant data to construct theproper boundary conditions for the reforming tube inlet, the re-forming tube outlet and the outer reforming tube wall, so that thesimulation results and the available industrial plant data areconsistent (Latham, 2008). Due to the high Reynolds number ofthe tube-side gas mixture, significant pressure gradients across thereforming tube and well-acknowledged radial gradients near thereforming tube inlet, the standard − ϵk turbulence model withenhanced wall treatment is implemented. Furthermore, an in-trinsic SMR reaction kinetic model (Xu and Froment, 1989), widelyaccepted in academia and industry, is used to derive the chemicalconversion rate equations, which account for the effect of internaland external diffusion limitations on the observed rates as well asfor the presence of the catalyst particles inside the reforming tube.Subsequently, to adjust the hydrogen production of the reformingtube in real-time, we propose the design and implementation offeedback control schemes into the CFD model. Specifically, themanipulated input and the controlled output are chosen to be theouter reforming tube wall temperature and the area-weightedaverage hydrogen mole fraction measured at the reforming tubeoutlet ( x̄H

outlet2 ) respectively, and the objective is to drive x̄H

outlet2 to

the desired set-point ( x̄Hset

2 ) under the influence of a tube-side feeddisturbance. On the problem of feedback control, firstly, a pro-portional (P) control scheme and a proportional-integral (PI)control scheme generating the outer reforming tube wall tem-perature trajectory based on the desired x̄H

set2

are designed torealize the closed-loop CFD simulation. Finally, motivated by in-dustrial concerns, we also design a feedback control schemecombining dynamic optimization and integral feedback control.The control performance of these three control schemes is eval-uated with respect to tracking the set-point, improving the speedof the closed-loop responses and compensating for the effect ofthe tube-side feed disturbance on x̄H

outlet2 .

Table 1Furnace-side inlet operating conditions.

Pressure (kPa) 132.4Temperature (K) 524Flow rate (kg/s) 1.08xCH4 0.0517

xH o2 0.0306

xCO 0.0211xH2 0.0540

xO2 0.1530

xAr 0.0077xN2 0.5793

2. Single reforming tube model

2.1. Industrial level geometry

The reforming tube investigated in this work belongs to anindustrial-scale top-fired, co-current reformer designed by SelasFluid Processing Corporation (Figs. 2 and 3). The furnace of thisreformer contains seven rows of 48 reforming tubes whose ex-ternal diameter, internal diameter and exposed length are 14.6 cm,12.6 cm and 12.5 m respectively. Each reforming tube is tightlypacked with specially designed nickel oxide over alpha aluminasupport (i.e., Ni/⍺�Al2O3) catalyst particles, which not only facil-itate the formation of hydrogen fuel from steam and methanethrough the highly endothermic SMR reactions, but also play a role

as an intermediate medium to enhance the rate of heat transfer tothe tube-side gas mixture. These rows of tubes are separated byeight rows of twelve burners (Fig. 2) which are fed with the fur-nace-side gas composed of three parts, i.e., natural gas, combus-tion air (Ar, N2 and O2) and tail gas (CO and H2). Based on thecomposition of a typical furnace-side gas that is given in Table 1,the combustion is a fuel lean process so that the fuel can becompletely combusted over a flame length of 4.5–6 m releasingthe thermal energy needed to drive the highly endothermic SMRreactions (Latham, 2008). The thermal energy released by thecombustion of furnace fuel is transferred to the reforming tubespredominantly by radiation inside the high-temperature furnacechamber. At the bottom of the furnace, the rows of tubes are se-parated by the rectangular intrusions known as flue gas tunnels orcoffin boxes (Fig. 3). The flue gas tunnels extend from the front tothe back of the furnace with a height of 2.86 m from the floor andallow the furnace flue gas to exit the furnace. Thirty-five extractionports are distributed in a row along the sides of each flue gastunnel. The furnace flue gas enters the tunnels from the furnacechamber through the extraction ports and then exits the furnacethrough the front openings of the coffin boxes. It is worth notingthat the dynamics of all aforementioned components are tightlycoupled inside the furnace during operation.

Under ideal operating conditions, the environments

Fig. 3. The front view of an industrial-scale top-fired, co-current reformer. It isimportant to note that the refractory wall is modeled to be transparent, so that theinterior components can be seen. Specifically, eight rectangular boxes located onthe floor represent the flue gas tunnels, eight frustums of cones located on theceiling represent the corresponding rows of burners and seven slender rectanglesconnecting the ceiling and floor represent the corresponding rows of reformingtubes.

(a)

(b)

Fig. 4. Two-dimensional axisymmetric reforming tube geometry (a) and meshstructure (b).


surrounding all reforming tubes of the SMR furnace unit are verysimilar, such that it is necessary to model only a single reformingtube to characterize the conditions in all 336 reforming tubes.Thus, the scope of the modeling part in this work only aims todevelop a CFD model with realistic dimensions, geometry andcharacteristics of one industrial-scale steam methane reformingtube, and in this regard, we develop and evaluate all essential si-mulation settings of the reforming tube model to accomplish themodeling objective in the following sections. By focusing on onereforming tube, we are able to accomplish the primary objective ofthis work, which is presented later, and which is to demonstratethat real-time feedback control schemes can be incorporated intothe CFD model of an industrial-scale reforming tube to buildclosed-loop systems that have desired dynamic response behaviorand produce a desired amount of hydrogen.

2.2. Tube geometry and meshing

Mesh quality is the most critical issue for accurate and suc-cessful CFD modeling, i.e., a low quality mesh requires the mostrobust CFD solver and significantly greater computing resources todetermine a converged solution. Due to the axisymmetric geo-metry property of the reforming tube as shown in Fig. 4(a), a two-dimensional (2D) axisymmetric reforming tube geometry and itscorresponding mesh structure were employed. The 2D axisym-metric reforming tube mesh which is shown in Fig. 4(b) wasconstructed in the meshing software ICEM-CFD. The 2D axisym-metric reforming tube mesh only contains 24 690 quadrilateralcells, with a 100% orthogonal quality. Also, the CFD simulation ofthe single reforming tube only performs calculations for half of thetube mesh considering its 2D axisymmetric properties. Conse-quently, this 2D axisymmetric reforming tube mesh brings largecomputational efficiency over a three-dimensional reforming tubeCFD model.

In terms of mesh size of this single reforming tube, open-loopsimulation results of CFD models with different mesh sizes in-dicate that 24 690 cells are enough to represent this specific tube,and that the further increase of the mesh size achieves identicalresults but requires significantly higher computation time.

For this reforming tube CFD model, boundary layer design isvery critical to the modeling of the heat convection from the innerreforming tube wall to the tube-side gas mixture and the heatconduction from the inner reforming tube wall to the catalystparticles. To calculate the first node height from the inner re-forming tube wall for the boundary layer design, NASA's ViscousGrid Spacing Calculator (National Aeronautics and Space Admin-istration) is adopted based on a suitable +Y value (ANSYS Inc.,2013a). For this specific single reforming tube geometry, five nodesare applied in the boundary layer at the inner reforming tube wallas requested by the two-equation − ϵk turbulence model with theenhanced wall treatment function (which will be discussed be-low). The first node height is × −8.26 10 m4 , and the node spacingratio in the boundary layer is 6:5. The detailed mesh structure forthe boundary layer design is demonstrated in Fig. 4(b). We notehere that NASA's Viscous Grid Spacing Calculator (National Aero-nautics and Space Administration) uses fixed viscosity, pressureand temperature values for the fluid properties which may not besuitable for most SMR calculations. Through a decompiling of thecalculator, a revised algorithm based on the original calculator isdeveloped for our specific inlet conditions of the tube-side gasmixture.

2.3. Kinetic model

The conversion rates of reactants, i.e., steam and methane, intoproducts, i.e., hydrogen fuel, and the direction of the reformingreactions and the water–gas shift reaction under different condi-tions (reactant concentration, temperature and pressure) must beaccurately accounted for by using a reaction kinetics model. In areforming tube, the reforming reactions and water–gas shift re-action occur at the catalyst active sites. In particular, reactantsneed to diffuse from the bulk tube-side gas mixture to the surfaceof the catalyst particle and then into the catalyst pores; after theformation of the products, products need to desorb from the cat-alyst cores and reenter the bulk tube-side gas mixture. However, areaction kinetics model that provides a detailed treatment of thesecatalyst-specific phenomena would be unnecessarily complex.Additionally, the catalyst particles and the detailed packing pat-tern inside an industrial-scale packed-bed reactor are not ex-plicitly modeled in this study.

To deal with this issue, in this single reforming tube CFD model,


an intrinsic SMR reaction model (Xu and Froment, 1989) is used todescribe the reactions happening inside the reforming tube. TheSMR reaction kinetics are given in Eq. (1) below which is widelyadopted in both CFD modeling and mathematical modeling ofreforming tubes:

( ) + ( ) ⇄ ( ) + ( )

= −( )

⎛⎝⎜⎜

⎞⎠⎟⎟

g g g g

rk

pp p

p p

KDEN

CH H O CO 3H ,

/1aH

CH H OH CO

4 2 2

112.5

3

1

2

24 2

2

( ) + ( ) ⇄ ( ) + ( )

= −( )

⎛⎝⎜⎜

⎞⎠⎟⎟

g g g g

rk

pp p

p p

KDEN

CO H O CO H ,

/1bH

CO H OH CO

2 2 2

22

2

2

22

2 2

( ) + ( ) ⇄ ( ) + ( )

= −( )

⎛⎝⎜⎜

⎞⎠⎟⎟

g g g g

rk

pp p

p p

KDEN

CH 2H O CO 4H ,

/1cH

CH H OH CO

4 2 2 2

333.5

24

3

2

24 2

2 2

= + + + +( )

DENK p

pK p K p K p1

1d

H O H O

HCO CO H H CH CH

2 2

22 2 4 4

where pH2, pCH4

, pH O2, pCO and pCO2

are the partial pressures of H2,CH4, H2O, CO and CO2 respectively in the bulk tube-side gasmixture inside the reforming tube, KH2, KCH4 and KCO are adsorp-tion constants for H2, CH4 and CO, respectively, KH O2 is a dis-sociative adsorption constant of H O2 , k1, k2 and k3 are rate coef-ficients of the SMR reactions and DEN is a dimensionless para-meter. To realize this reaction kinetic model in CFD simulations byFluent, each reversible reaction in Eq. (1) is split into two irre-versible reactions. The reaction rates in Eq. (1) are implemented inFluent by designing a user defined function (UDF) file. Since theseintrinsic reaction kinetics do not consider the internal and externaldiffusion resistances of the catalyst particles, the reaction rates inEq. (1) are multiplied by an effectiveness factor, 0.1 (Wesenbergand Svendsen, 2007), to account for the overall diffusion effects onthe intrinsic reaction rates.

2.4. Compressible gas flow

The tube-side inlet operating conditions of the reforming tubesare given in Table 2 (Latham, 2008). Based on the inlet conditionsof the tube-side gas mixture, the Mach number is determined tobe greater than 0.3, and therefore, the density variations of thefluid flow due to high static pressure cannot be ignored. From thepoint of view of CFD simulation, when a pressure-based solver isused, like the one we chose for the simulation in this work, anaccurate gas state equation is very critical to simulation accuracy.

Table 2Process-side gas inlet operating conditions.

Pressure (kPa) 3038.5Temperature (K) 887Flow rate (kg/s) 0.1161xCH4 0.2487

xH O2 0.7377

xCO 0.0001xH2 0.0018

xCO2 0.0117

Based on this consideration, the compressible ideal gas stateequation is adopted to describe the compressibility of the tube-side gas mixture.

A pressure-based solver that enables the pressure-based Na-vier–Stokes solution algorithm (ANSYS Inc., 2013b) is chosen overa density-based solver. The pressure-based solver is more suitedfor a wider range of physical models and has features which areunavailable to the density-based solver, e.g., the physical velocityformulation for porous media which is adopted by this work tosimulate the flow through the catalyst network in the reformingtube (this will be discussed later). It also provides more freedomfor the simulations while converging to the same results obtainedby the density-based solver.

2.5. Porous zone design

Pressure drop is significant in industrial-scale reforming tubeswhen the tube-side gas mixture flows through the catalyst net-work made of many tightly packed catalyst particles. To estimatethe pressure drop across the porous zone in the CFD modeling ofturbulent flows, a semi-empirical expression, the Ergun equation(Ergun and Orning, 1949), which is applicable over a wide range ofReynolds numbers and for many packing patterns, is adopted asfollows:

μ γγ

ρ γγ

Δ = ( − ) + ( − )( )

∞ ∞P

L Dv

Dv

150 1 1.75 1

2p p2

2

3 32

where ΔP is the pressure drop through the porous media, L is thedepth of the porous media, μ is the viscosity of the fluid, γ is theporosity of the packed bed, ∞v is the bulk velocity of the fluid, ρ is

the density of the porous media, μ γγ

( − )D

150 1

p2

2

3 is the viscous resistance

coefficient and ρ γγ

( − )D

1.75 1

p 3 is the inertial resistance coefficient. We

assume that the viscous and inertial resistance coefficients aredefined along the direction vectors = [ ]v 1, 01 (i.e., the principalaxis direction) and = [ ]v 0, 12 (i.e., the radius direction) in theCartesian two-dimensional (2D) coordinate system.

The modeling objective of this work is to develop a CFD modelof an industrial-scale reforming tube for a commercial plant. Thus,a common, readily available commercial catalyst, i.e., JohnsonMatthey's Katalco − Q23 4 (Matthey) also known as α −Ni/ Al O2 3,is chosen for this purpose, and its properties are shown in Table 3.It is noted that the intrinsic kinetic model used (Xu and Froment,1989) was developed for a Ni/MgAl O2 4 catalyst, i.e., the catalystsupport material is different than that utilized in this work. Weconsidered the potential effects of the support material on thecatalytic activity of the catalyst prior to selecting the kinetic modeldeveloped in Xu and Froment (1989) based on the work conductedby Jeong et al. (2006). First of all, the reduction peaks of both theNi/MgAl O2 4 and α −Ni/ Al O2 3 catalyst types are in the neighbor-hood of ∼1083 K, which means that they require similar heat inputto become activated. Even though Ni/MgAl O2 4 is more active atlower temperatures than α −Ni/ Al O2 3, we speculate that bothcatalyst types have similar catalytic activity in our operatingtemperature range. Additionally, although the estimated surfacearea of Ni/MgAl O2 4 is higher than that of α −Ni/ Al O2 3 per unit

Table 3Johnson Matthey's Katalco − Q23 4 catalyst properties.

Density, ρc 3960 kg/m3

Heat capacity, Cp c, 880 J/(kg K)

Thermal conductivity, kc 33W/(m K)Particle diameter, Dp 3.5 mm (average)

Table 4Reforming tube material properties.

Density, ρt 7720 kg/m3

Heat capacity, Cp t, ( )502 J/ kg K at 1144 KThermal conductivity, kt ( )29.58 W/ m K at 1144 KEmissivity, ϵt 0.85 at 1144 K


mass of the catalyst, due to the large porosity of the packed bedinside the reforming tube, i.e., the void volume is approximately60.9% of the reactor volume, and small inner reforming tube dia-meter of 0.126 m, the mass of catalyst inside a single reformingtube is not significant. As a result, we decided to adopt the kineticmodel developed in Xu and Froment (1989) in the CFD model todescribe the chemistry inside the reforming tube using the John-son Matthey's Katalco − Q23 4 catalyst. Finally, the consistency ofour simulation results in later sections with the data with which itis validated also demonstrates the effectiveness of the choice ofthe α −Ni/ Al O2 3 catalyst for the kinetic model based on aNi/MgAl O2 4 catalyst. Additionally, from Tables 2 and 3, the mass ofthe catalysts per reforming tube is 242 kg, and the space–time ofthe tube is about 2080 s.

2.6. Reforming tube wall boundary conditions

For an industrial-scale reformer, the outer reforming tube walltemperature is usually in the range of 1100–1178 K (Latham, 2008).In this single reforming tube simulation, to construct the tem-perature boundary condition of the outer reforming tube wall, theavailable plant data (Latham, 2008) are fit with a fourth-orderpolynomial function by using a least squares linear regressionmethod. The result of the fit shown in Fig. 5 is

[ ]( ) =

−

−

( )

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

T x x x x x x

0.02210.800310.734

64.416997.16 3

Wall4 3 2 1 0

where TWall(x) is the outer reforming tube wall temperature at alocation ( )x m away from the reforming tube inlet, =x 0 m. Usingthe boundary condition in Eq. (3), the reforming tube here ismodeled as a heat sink, and thermal energy is transferred from theouter reforming tube wall to the inner reforming tube wall by heatconduction. The corresponding tube material properties are listedin Table 4 (Davis, 2000) which assumes that all the tube propertiesare temperature independent and the values at =T 1144 K areadopted in the CFD simulation. However, a constant outer re-forming tube wall temperature profile is neither sufficient tomaintain the current x̄H

outlet2 when the reforming tube operating

condition is subjected to a change in the tube-side mass flow rate

0 2 4 6 8 10 12Distance down the reforming tube (m)

1000

1050

1100

1150

Out

er re

form

ing

tube

wal

l tem

pera

ture

(K)

Outer reforming tube wall of a typical SMR plantCFD outer reforming tube wall

Fig. 5. Outer reforming tube wall temperature versus distance down the reformingtube for the CFD simulations, which depicts the direct comparison between thefourth-order polynomial temperature profile, i.e., Eq. (3) and that of publiclyavailable SMR plant data (Latham, 2008).

(e.g., tube-side feed disturbance), nor capable of driving the cur-rent x̄H

outlet2 to a new desired x̄H

set2 . To fulfill the overall scope

of this work, which is to design and implement feedback controlschemes to drive x̄H

outlet2 to the desired x̄H

set2 under the influence of a

tube-side feed disturbance, additional temperature profiles areconstructed based on the most essential criterion that the shapes(in the axial direction) of these additional temperature profileshave to match that of the original outer reforming tube walltemperature profile (owing to the overall shape and location ofburner flames which does not change appreciably with time). Theadditional profiles (Fig. 6) are given by the following fourth-orderpolynomial:

[ ]( ) =

−

−

− ( )

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

T x x x x x x

T

0.02210.800310.734

64.416151.83 4

Wall

Wall

4 3 2 1 0

max

where TmaxWall is the maximum outer reforming tube wall tempera-

ture of the temperature profile. Eq. (4) allows one to construct anentire outer reforming tube wall temperature profile along thereforming tube length based on its maximum temperature valueand consequently affect the x̄H

outlet2 .

2.7. Governing equations

In the microscopic view of the reforming tube, the physico-chemical phenomena of transport and reaction processes thatgenerate hydrogen fuel from steam and methane are closely cou-pled and utterly complex. Initially, a convective mass transferprocess driven primarily by the reactant concentration gradientsbetween a flowing bulk gas mixture and an infinitesimally thinstationary layer around the catalytic surface takes place. Next, amolecular diffusion process mainly driven by the reactant con-centration and temperature gradients (Eq. (6g)) between an in-finitesimally thin stationary layer around the catalyst surface and acatalyst medium allows the reactants to diffuse into the catalystpores and then finally arrive at the catalyst active sites, where theendothermic SMR reactions take place. Upon the formation of theproducts, they immediately desorb from the catalyst active sites,diffuse back to the catalyst surface and eventually reenter theflowing bulk gas mixture. It is worth noting that the series ofconsecutive molecular-level elementary steps of the endothermicSMR reactions is still largely unknown. As a result, a kinetic modelthat provides a detailed treatment of these catalyst-specific phe-nomena would be unnecessarily complex from the point of view ofCFD modeling; therefore, the kinetic model used in this paper isderived based on a widely-accepted intrinsic SMR reaction kineticmodel (Xu and Froment, 1989) to lessen the computationalburden without sacrificing the accuracy of the simulation results(Section 2.3).

In the macroscopic view of the reforming tube, the significantaxial pressure gradient across the reforming tube length and radialgradients near the reforming tube entrance are well-acknowl-edged. This, in turn, motivates us to develop two-dimensional (2D)


governing equations that are capable of accounting for the pre-sence of the catalyst network formed by the solidly packed catalystparticles. It is important to thoroughly understand the contribu-tion of the catalyst network to the SMR reactions in order to de-velop an appropriate process model. Specifically, the catalystnetwork not only facilitates the formation of hydrogen fuel fromthe naturally stable and slowly-reacting materials, i.e., steam andmethane, but also enhances the rate of convective thermal energytransfer from the heated outer reforming tube wall to the flowingbulk gas mixture by expanding its contact area.

Additionally, due to the intrinsic resistance properties of thecatalyst network, i.e., the inertial resistance and viscous resistancepreviously mentioned in Section 2.5, the catalyst network acts as aphysical obstacle that interferes with the flow of the tube-side gasmixture to generate turbulence. This obstacle enhances mixingefficiency to radially homogenize the moving fluid. Furthermore,under the influence of flow resistances induced by the catalystnetwork, the residence time of all species in the reforming tube isalso increased, which allows the SMR reactions (Xu and Froment,1989) to reach equilibrium prior to the process gas exiting thereforming tube. Based on the aforementioned considerations, the2D governing equations, i.e., the continuity equation (Eq. (5)) andthe momentum (Eq. (6a)), energy (Eq. (6b)) and species material(Eq. (6c)) balances, of the SMR process taking place inside thereforming tube are formulated as follows, so that the presence ofthe catalyst network is explicitly accounted for:

γρ γρ∂∂

( ) + ∇·( →) = ( )tv 0 5fluid fluid

| |

γρ γρ

γ γ τ γ γ μα

γ ρ

∂∂

→ + ∇· →→

= − ∇ + ∇· → +→

− → + → →( )

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

tv v v

P B vC

v v2 6a

fluid fluid

f

2 32

( )

∑ ∑

γρ γ ρ ρ

ϕ

∂∂

+ ∂∂

( − ) + ∇· → +

= ∇· ∇ − +→

+ Δ( )

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎛⎝⎜⎜

⎞⎠⎟⎟

⎞⎠⎟⎟

⎡⎣⎢⎢

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤⎦⎥⎥

tE

tE v E P

k T h J H

1

6b

fluid fluid solid solid fluid fluid

effi

i ii

rxn i,

γρ γρ γ∂∂

+ ∇· → = − ∇·→

+( )

⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎛⎝

⎞⎠t

Y v Y J R6cfluid i fluid i i i

with

γ→ = →( )v v 6dsuperficial

τ μ→ = ∇→ + ∇→ − ∇·→( )

⎜ ⎟⎡⎣⎢

⎛⎝

⎞⎠

⎤⎦⎥v v v I

23 6e

T

( )γ γ= + − ( )k k k1 6feff fluid solid

ρμ→

= + ∇ − ∇( )

⎛⎝⎜

⎞⎠⎟J D

ScY D

TT 6gi fluid m i

t

ti T i, ,

ϕ μ μ→

= ∂∂

+∂∂

− (∇·→) +∂∂

+ ∂∂ ( )

⎜ ⎟⎡⎣⎢⎢

⎛⎝

⎞⎠

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥

⎡⎣⎢

⎤⎦⎥

vx

vy

vvx

vy

213 6h

x y y x2 2

22

where μ, μt,→v , →vsuperficial, ρfluid and

→Bf are the molecular viscosity,

turbulent viscosity, physical velocity vector, superficial velocityvector, average density, and body force of the bulk tube-side gasmixture respectively, γ, ρsolid and α are the porosity, density and

absolute permeability of the catalyst network respectively,α1 and

C2 represent the viscous resistance coefficient and inertial re-sistance coefficient (previously introduced in Section 2.5), Efluidand Esolid are the total energy of the tube-side gas mixture and ofthe catalyst network, P is the static pressure, ∑ ΔHi rxn i, is the totalthermal energy generated by the SMR reactions, kfluid, ksolid and keffare the thermal conductivities of the tube-side gas mixture, of the

catalyst network and of the overall medium, Yi, Dm i, , DT i, ,→Ji and Ri

are the mass fraction, mass diffusion coefficient, thermal diffusioncoefficient, turbulent mass diffusion flux and overall rate of che-mical reaction of species i, Sct is the turbulent Schmidt numberand is set to 0.7 by default, and τ→ and I are the stress tensor andunit tensor, respectively. It is important to note that the chemicalrate equations are formulated to account for the effects of internaland external diffusion limitations on the observed rates as well asfor the presence of the catalyst particles inside the reforming tube,and therefore, it would be unnecessary and incorrect to multiply Riin Eq. (6c) and ∑ ΔHi rxn i, in Eq. (6b) by γ in an attempt to accountfor the effects of the catalyst network. Additionally, detailed mi-croscopic transport and chemical reaction processes are describedby the 2D governing equations, i.e., [∇·(∑ )]h Ji i i in Eq. (6b) re-presents the transport of enthalpy due to molecular diffusion, and

[(∇→ + ∇→ ) − ∇·→ ]v v v IT 2

3in Eq. (6e) represents the effect of volume

dilation.Due to the high Reynolds number of the tube-side gas mix-

ture, which is estimated to be ∼5500 based on the inlet condi-tions of the tube-side feed as shown in Table 2, the semi-em-pirical standard two-equation turbulent kinetic energy andturbulent dissipation rate ( − ϵk ) model (Jones and Launder,1972; Launder and Sharma, 1974) developed from the Reynolds-averaged Navier–Stokes (RANS) equations is employed to de-scribe the complex turbulence phenomena inside the reformingtube. The − ϵk turbulence model presented in Eq. (7) below isapplicable for a wide range of flows and is relatively computa-tionally inexpensive, though it still yields reasonably accurateestimates, and it is relatively simple to implement and easy toconverge from the point of view of CFD simulation. This modelhas the form:

γρ γρ

γ μμσ

γ γ γρ γ

∂∂

+ ∇· →

= ∇· + ∇ + + − ϵ −( )

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

tk v k

k G G Y7a

fluid fluid

t

kk b fluid M

γρ γρ

γ μμσ

γ γ ρ

∂∂

ϵ + ∇· ϵ→

= ∇· + ∇ϵ + ϵ + − ϵ( )ϵ

ϵ ϵ ϵ

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

⎛⎝⎜

⎞⎠⎟

tv

Ck

G C G Ck 7b

fluid fluid

tk b1 3 2

2

Contours of Static Temperature (k) Nov 17,2015ANSYS Fluent 15.0 (axi,dp,pbns,spe,ske)

Fig. 7. Temperature profile from the reforming tube CFD simulation, where theouter reforming tube wall temperature profile (Fig. 5) is that fitted based on theavailable SMR plant data (Latham, 2008).

Contours of mole fraction of h2 Nov 17,2015ANSYS Fluent 15.0 (axi,dp,pbns, spe,ske)

Fig. 8. Hydrogen mole fraction profiles from the reforming tube CFD simulation,where the outer reforming tube wall temperature profile (Fig. 5) is that fitted based


μ ρ

βμ

ρ

βρ

ρ

=ϵ

=

= ∂∂

= − ′ ′∂∂

= − ∂∂

μ

ϵ

⎜

⎧

⎨

⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪ ⎛⎝

Ck

Cvu

G gPr

Tx

G u uux

T

tanh

1

t fluid

b it

t i

k i jj

i

P

2

3

where k and ϵ are the turbulent kinetic energy and turbulentdissipation rate respectively, Gk and Gb are the generation ofturbulent kinetic energy due to the mean velocity gradients andbuoyancy respectively, YM is the contribution of the fluctuatingdilation in compressible turbulence to the overall dissipationrate, σ =ϵ 1.0 and σ = 1.3k are the turbulent Prandtl numbers for ϵand k respectively, =ϵC 1.441 , =ϵC 1.922 and =μC 0.09 are defaultconstants of the standard − ϵk model, Prt¼0.85 is the turbulentPrandtl number for energy, gi is the component of the gravita-tional vector in the ith direction, β is the thermal expansioncoefficient, and v and u are the components of the flow velocityparallel and perpendicular, respectively, to the gravitationalvector. It is worth noting that all default values of the afore-mentioned constants are determined empirically by experi-ments for fundamental turbulent flows, i.e., boundary layers andmixing layers, and have been verified to be suitable for a widerange of wall-bounded and free shear flow applications (ANSYSInc., 2013a). Furthermore, turbulent flows are significantly af-fected by the walls. The accuracy of the near-wall modelingdecides the fidelity of numerical solutions. Specifically, it is inthe near-wall region that the solution variables have large gra-dients, i.e., the momentum, material and energy fluxes havelarge magnitudes. Therefore, an accurate representation of theflow in the near-wall region is required for successful predic-tions of wall-bounded turbulent flows. For this single reformingtube CFD model, the enhanced wall treatment function in Fluentis applied as the near wall treatment method. The enhancedwall treatment ϵ-equation is suitable for certain fluid dynamicsespecially for those with lightly turbulent flow, and it only re-quires a few nodes in the boundary layer when using the − ϵkmodel (ANSYS Inc., 2013a).


950

1000

1050

1100

1150

1200

Out

er re

form

ing

tube

wal

l tem

pera

ture

(K)

Tmax = 1190 KTmax = 1170 KTmax = 1146.6 K Tmax = 1130 KTmax = 1110 K

Fig. 6. Outer reforming tube wall temperature versus distance down the reformingtube for the CFD simulations, which represents the calculated outer reforming tubewall temperature profiles generated by Eq. (4) and the fitted outer reforming tubewall temperature profile (solid line) based on the publicly available SMR plant data(Latham, 2008).

on the available SMR plant data (Latham, 2008).

2.8. Simulation results

2.8.1. CFD model of single reforming tube: results comparisonUsing a parallel computational environment with message

passing interface technology, the simulation of the single re-forming tube CFD model converges in about 5 min with the steadysolver in a 4-core CPU desktop computer. The steady-state resultsof the simulations are displayed in Figs. 7 and 8. We note here thatdue to the large length to diameter ratio of the reforming tube, inall plots of the simulation results, the radius is scaled up by 20times which is convenient and is done for display purposes only. Itis worth noting that the pressure profile in this simulation is ra-dially uniform, which is the result of the direction definitions ofthe resistance coefficients in Section 2.5. In addition, based on thewall temperature profile in Fig. 5, the corresponding inner re-forming tube wall temperature profile at the steady-state from theconverged model is displayed in Fig. 9, and the correspondingsteady-state heat flux profile through the tube wall is shown inFig. 10.


900

950

1000

1050

1100

1150

Ref

orm

ing

tube

wal

l tem

pera

ture

(K)

Outer reforming tube wallInner reforming tube wall

Fig. 9. Inner (dashed line) and outer (solid line) wall temperature profiles of thereforming tube.


0

50

100

150

200

250

300

Hea

t flu

x ac

ross

refo

rmin

g tu

be w

all (

kW/m

2 )

CFD heat flux profileCFD average heat fluxDybkjaer’s average heat fluxFroment and Bischoff’s average heat fluxLatham’s estimated average heat flux

Fig. 10. Heat flux profile across the reforming tube wall.

Table 5Single reforming tube results.

CFD Result Pro/II % Difference withrespect to CFD result

Δ ( )P kPa 212.83 N/A N/A¯ ( )P kPaoutlet 3044.0 3044.0 0.00

x̄Houtlet

20.4645 0.4650 0.11

x̄H Ooutlet

20.3467 0.3452 0.43

x̄CHoutlet

40.0426 0.0422 0.94

x̄COoutlet 0.0873 0.0869 0.46

x̄COoutlet

20.0588 0.0607 3.23

( )−Average heat flux kW/m 2 68.972 N/A N/A

( )Total absorbed heat kW 341.045 341.055 ∼0.00


Reforming tube outlet data (not reported here for proprietaryreasons) from a typical hydrogen plant with the same tube-side inletconditions, the same tube geometric structure and similar catalystand tube material properties as described in Sections 2.1, 2.4 and 2.5,and also the same wall temperature profile as that reported in Fig. 5,is used to validate the CFD single tube model. The validation is per-formed by comparing the data of the process gas at the reformingtube outlet (Table 5) from the CFD simulation to that of the availableproprietary industrial plant. All mole fraction values in Table 5 are

area-weighted average values at the tube outlet. We found that oursimulation results reported in Table 5 are very close to the plant datafor temperature and species compositions.

Additionally, the average heat flux across the reforming tubewall produced by the CFD model is within the range of

−45 90 kW/m2 (Rostrup-Nielsen, 1984), a typical range reportedin industry, and closely resembles that reported throughout lit-erature. Namely, Dybkjaer (1995) reports the average value of78.5 kW/m2 and Froment and Bischoff (1990) report the averagevalue of 75.6 kW/m2. Moreover, the work of Pantoleontos et al.(2012) on modeling and optimization of a reforming reactor alsorestricts the average heat flux to be less than 80.0 kW/m2. Fur-thermore, the estimated average heat flux of 65.6 kW/m2 based onthe outer and inner reforming tube wall temperature profiles,thermal conductivity of 106 500 J/m h K and thickness of the re-forming tube wall reported by Latham (2008) validates the accu-racy of the CFD model.

Remark 1. The outlet tube-side mixture compositions are at theirequilibrium state at the exit of the reactor which is determined bythe outlet tube-side mixture temperature. Further, the averagehydrogen mole fraction in the tube-side mixture measured at thetube outlet, x̄H

outlet2 , can be mathematically expressed as a function

of the maximum reforming tube wall temperature, TmaxWall. It is im-

portant to note that TmaxWall is not necessarily the temperature of the

tube-side mixture at the outlet, which depends not only on TmaxWall,

but also depends on the thermal conductivity of the reformingtube wall, the effective heat transfer coefficient between the tube-side mixture and the catalyst network, and especially, the rate ofenergy consumption by the endothermic SMR reactions. A majorbenefit of creating a CFD model of the industrial-scale reformingtube is that it allows relationships between important quantitieswithin the reformer to be determined for control or other analysispurposes. For example, it allows the generation of the collection ofdata at constant tube-side feed conditions needed to construct therelationship between x̄H

outlet2 and Tmax

Wall used for control purposeslater in this work. Additionally, the industrial-scale reforming tubeCFD model creates more opportunities for future investigations.Specifically, the CFD model allows us to access additional in-formation about the tube-side mixture at the reforming tubeoutlet, e.g., the area-weighted average temperature of the tube-side mixture denoted by T̄Mixture

outlet , which can be used to constructthe relationship between T̄Mixture

outlet and TmaxWall to construct, for ex-

ample, a Gibbs reactor model.

Additional effort to validate the simulation result generated bythe single reforming tube CFD model in order to declare with highcertainty that the CFD model can replace expensive traditional on-site parametric study, and to also demonstrate that the tube-sidegas mixture at the reforming tube outlet is at equilibrium condi-tions is conducted. Specifically, a Gibbs reactor model of a steady-state chemical and petroleum process simulation software knownas Pro II/ is adopted to simulate the reforming tube to determinethe species composition at chemical equilibrium by solving theenergy and material conservation equations based on minimizingthe Gibbs free energy of all chemical species involved in thisprocess. Furthermore, the greatest advantage of the Gibbs reactormodel is that it does not require the knowledge of the chemicalprocess in the reforming tube including detailed reaction me-chanism or kinetic model, which in turn validates the global re-action mechanism and kinetic models of the SMR process weimplemented in the single reforming tube CFD model. In this ef-fort, the Gibbs reactor model, which requires only two inputparameters, i.e., a Gibbs reactor feed stream, which is identical tothat of the tube-side feed (shown in Table 2), and a Gibbs reactorduty, which is set to the total thermal energy absorbed by the

0.46

0.48

0.50


reforming tube of 341.045 kW, is simulated, and the correspondingsimulation results are shown in Table 5. The simulation resultsgenerated by the Gibbs reactor model are in close agreement withthose generated by the single reforming tube CFD model, which inturn supports the accuracy of the CFD model, validates our choiceof the global reaction mechanism and kinetic model of the SMRprocess, and also demonstrates that the tube-side gas mixture atthe reforming tube outlet is at equilibrium conditions.

1100 1120 1140 1160 1180 12000.42

0.44

Fig. 12. The expected steady-state value of x̄Houtlet

2at different constant outer re-

forming tube temperature profiles which are presented by their correspondingTmaxWall. The relationship between x̄H

outlet2

and TmaxWall is captured by the second-order

polynomial, = ( ¯ ) − ¯ +T x x5648.6 3814.7 1699.5Wall Houtlet

Houtletmax

22

2, which is used to gen-

erate an appropriate manipulated input for the open-loop CFD simulations basedon the desired x̄H

set2(Fig. 11).

0 100 200 300 400 5000.42

0.43

0.44

0.45

0.46

0.47

Time (s)

Fig. 13. The propagation of x̄Houtlet

2with time under open-loop control with

¯ =x 0.465Hset

2, when the tube-side mass flow rate is kept at its nominal value (solid

line), and when it is increased by 20% (dashed line). Fig. 13 demonstrates that open-loop control is not robust and cannot be used to maintain x̄H

set2

at 0.465 when achange in the operating condition is imposed.

3. Feedback control design and closed-loop simulation results

3.1. Open-loop dynamics

We are primarily interested in the regulation of x̄Houtlet

2 when thereforming tube is subjected to tube-side feed disturbances, wherethe control objective is to maintain the current x̄H

set2 , or when

changes in industrial plant objectives occur, where the controlobjective is to attain a new x̄H

set2 .

Among all simulation settings described in Section 2, the outerreforming tube wall temperature profile is chosen as the singlemanipulated input due to the endothermic nature of the SMR re-actions. As a result, x̄H

outlet2 can be manipulated by adjusting the

outer reforming tube wall temperature profile, which depends onthe fuel flow rates to the burners around the reforming tube. Itshould be noted that the maximum value of an outer reformingtube wall temperature profile (Tmax

Wall) can be used in Eq. (4) toconstruct an entire profile along the reforming tube, and therefore,a specific Tmax

Wall can represent a unique outer reforming tube walltemperature profile. The temperature dependence of x̄H

outlet2 is de-

monstrated in Fig. 12 for a wide range of outer reforming tube walltemperature profiles for which Tmax

Wall varies from 1100 K to 1200 K.Due to the endothermic nature of the SMR reactions, higher valuesof x̄H

outlet2 are observed for temperature profiles with higher Tmax

Wall.In this work, all CFD reforming tube simulations under feed-

back control and under open-loop control are carried out in aparallel computational environment with message passing inter-face technology with a built-in, explicit-time-stepping, transientsolver. Transient simulation may reveal dynamics of a system thatcannot be obtained under steady-state simulation (Pantoleontoset al., 2012). In particular, Adams and Barton reported that thecatalyst core temperatures of the water–gas shift reactors in anIGCC-TIGAS polygeneration plant can exceed the maximum stea-dy-state value by 100 K during start-up, which would not be de-tected under steady-state simulation (Adams and Barton, 2009).Additionally, the transient solver can be used to determine thesteady-state solution when a steady-state model is highly un-stable, e.g., natural convection problems with Rayleigh number inthe transition regime (ANSYS Inc., 2013a). CFD simulations underopen-loop control using a constant pre-determined outer walltemperature trajectory (e.g., Fig. 11) as the process manipulated

0510 0100200300400500

1000

1100

1200

Time (s)Distance down thereforming tube (m)

Out

er re

form

ing

tube

wal

l tem

pera

ture

(K)

Fig. 11. The pre-determined outer reforming tube wall temperature trajectory withtime for open-loop control with ¯ =x 0.465H

set2

.

input and built with fixed simulation settings can successfullydrive x̄H


set2 under a strictly disturbance-free

environment as shown in Fig. 13. However, due to the absence ofthe feedback mechanism, open-loop control is unable to recognizeor handle the tube-side feed disturbances, which results in asubstantial deviation of the steady-state x̄H

outlet2 from the desired

set-point, x̄Hset

2 . The aforementioned robustness issue motivates usto design feedback control schemes including proportional (P),proportional-integral (PI) and optimization-based controlschemes, which are utilized to produce a feedback-based ma-nipulated input in order to drive x̄H


set2in the

presence of tube-side feed disturbances.

3.2. Feedback controller design

In this work, the primary objectives of the feedback controlschemes are to drive x̄H


set2 in the presence of

the tube-side feed disturbance, and to speed up the dynamics ofthe process to allow the system to quickly advance to the opti-mized steady-state operating condition. All simulation settings ofthe closed-loop simulations are the same as those used in thepreviously studied open-loop system. It is important to emphasizethat the disturbance and set-point changes are added to the pro-cess after it has already achieved a steady-state under a constantwall temperature profile.


These feedback control schemes make the control objectivesfeasible and provide robustness against the tube-side feed dis-turbance, and thus resolve the critical drawback of open-loopcontrol. It is desired that under each feedback control scheme, theclosed-loop system is initially operated in a high temperature re-gime favoring the formation of hydrogen fuel resulting in a fastincrease of x̄H

outlet2 toward the desired x̄H

set2 due to the endothermic

nature of the SMR reactions described in Eq. (1). After the initialburst of hydrogen fuel, it is desired that the closed-loop system isthen kept in a moderately high temperature regime, which effec-tively slows down the rapid formation of hydrogen fuel to preventunnecessary aggressive control action. To design feedback controlschemes to accomplish the operating strategy, a data-drivenmodeling technique is used to obtain a process transfer functiondescribing the evolution of x̄H

outlet2 based on the CFD simulation

result for a step-change of the maximum outer reforming tubewall temperature from ( ) =T 0 1100 KWall

max to ( ) =T t 1110 KWallmax

(which is discussed in greater detail below). Then, this approx-imate model capturing the dominant dynamics of the reformingtube is combined with classical feedback control to form a closed-loop system.

It is worth noting that the process transfer function derivedbased on the response of x̄H

outlet2 to a step-change of Tmax

Wall from=T 1100 KWall

max to =T 1110 KWallmax was compared with other transfer

functions derived based on different step-changes of TmaxWall. Speci-

fically, different step changes in the input, i.e., step changes in TmaxWall

from 1110 K to 1130 K, from 1130 K to 1160 K and from 1160 K to1200 K, were considered. The variations between the transferfunctions (normalized) derived from the different sets of simula-tion results are negligible.

The closed-loop system is utilized in a parametric study todetermine the appropriate control parameters, i.e., Kc of P controlor Kc and τI of PI control. Specifically, the initial values of the P/PIparameters are obtained by the Cohen–Coon tuning method basedon the response of the process output, x̄H

outlet2 , to a step-change of

the process input chosen as the maximum outer reforming tubewall temperature. Then the process model derived from the data-driven modeling technique based on the aforementioned simula-tion result is used to build closed-loop models with feedbackcontrol schemes to improve the controller parameter estimates.Finally, the P/PI parameters are incorporated into the closed-loopCFD models, and adjusted until the desired closed-loop responsesare observed.

Furthermore, the maximum allowable temperature value of1200 K is taken into account in the control schemes to avoid therupture of the reforming tube which can occur at exceedingly highoperating temperatures. Additionally, this upper limit on the outerreforming tube wall temperature prevents the deposition of car-bon on the reforming tube wall and on the surfaces of catalystparticles, which would significantly decrease the heat transfer rateto the flowing gas mixture and prevent the reactants from enter-ing the catalyst active sites resulting in a lower x̄H

outlet2 . Next, the

minimum allowable temperature value of 987 K at the tube inlet isconsidered in the formulation of the control schemes to ensurethat sufficient heat is transferred to the flowing tube-side gasmixture to facilitate the highly endothermic SMR reactions.Moreover, since the scope of our current work focuses on CFDmodeling and controller design of the reforming tube instead ofthe SMR furnace, we will disregard the dynamics of the outer re-forming tube wall temperature. Hence, we suppose that the outerreforming tube wall temperature can reach the predicted profileinstantaneously. Lastly, we assume that measurements of x̄H

outlet2

are available at all sampling instances. Classical P and PI controlschemes that are based on the deviation of x̄H

outlet2 from the desired

set-point and account for input constraints are presented as

follows:

( ) = ¯ − ¯ ( )

( ) = ′ ( )( + Δ ) = ( = ) + ( ) ( )

⎧⎨⎪

⎩⎪e t x x t

u t K e t

T t t T t u t

P control scheme

0 8a

k Hset

Houtlet

k

P k c k

Wall k Wall P kmax max

2 2

∫( ) ( )τ

τ τ

( ) = ¯ − ¯ ( )

( ) = +

( + Δ ) = ( = ) + ( ) ( )

⎧

⎨⎪⎪

⎩⎪⎪

⎛⎝⎜

⎞⎠⎟

e t x x t

u t K e t e d

T t t T t u t

PI control scheme

1

0 8b

k Hset

Houtlet

k

PI k c kI t

t

Wall k Wall PI kmax max

k

2 2

0

( + Δ ) ≤ ( )T x t t T, 8cWall k max

( = + Δ ) ≥ ( )T x t t T0, 8dWall k min

[ ]( + Δ ) =

−

−

( + Δ ) − ( )

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

T x t t x x x x x

T t t

,

0.02210.800310.734

64.416151.83 8e

Wall k

Wall k

4 3 2 1 0

max

where tk, t0 and Δ =t 0.04 s are the current time, the initial time,and the sampling time interval of the CFD simulation respectively,

( )e tk represents the current deviation of x̄Houtlet

2 from the desiredset-point x̄H

set2 , Tmin and Tmax are the minimum and maximum al-

lowable reforming tube wall temperatures respectively,′ =K 1856.3c and ( )u tP k are the controller gain and current con-

troller output of the P control scheme, =K 1856.3c , τ = 46.4I and( )u tPI k are the controller gain, controller time constant and current

controller output of the PI control scheme, ( + Δ )T t tWall kmax and

( = )T t 0Wallmax are the predicted (i.e., prior to being saturated with the

temperature constraints) and initial maximum outer reformingtube wall temperatures, respectively, and ( + Δ )T x t t,Wall k is thepredicted outer reforming tube wall temperature profile. At theend of each sampling time interval, the measurement of x̄H

outlet2 is

acquired from the CFD simulation, and the current deviation fromthe desired ¯ ( ( ))x e tH

setk2 is computed. Then, the control output

( ( )u tPI k or ( )u tP k ) is evaluated depending on the implementedcontrol scheme, which allows ( + Δ )T t tWall k

max to be estimated. Thevalue of ( + Δ )T t tWall k

max is subjected to Eq. (8c); if the constraint isnot satisfied, ( + Δ )T t tWall k

max is set to the value of Tmax. Then,( + Δ )T t tWall k

max is used to compute the predicted wall temperatureprofile ( ( + Δ )T x t t,Wall k ), which is applied until the next samplingtime, when the new value of x̄H

outlet2 is obtained from the CFD

simulation.

3.3. Closed-loop simulation results

In this section, we investigate the closed-loop performance ofthe P and PI controllers, which adjust the manipulated inputvariable chosen to be the outer reforming tube wall temperature,to drive x̄H


set2 in the absence or presence of a

tube-side feed disturbance. At the end of each sampling time in-terval, the measurement of x̄H

outlet2 is acquired from the CFD simu-

lation, and the control action, which is formulated following thescheme described in Eq. (8), is evaluated. Next, the control actionis applied to the closed-loop system until the end of the next

0510 0100200300400500

1000

1100

1200


Out

er re

form

ing

tube

wal

l tem

pera

ture

(K)

(a)

0510 0100200300400500

1000

1100

1200


Out

er re

form

ing

tube

wal

l tem

pera

ture

(K)

(b)

Fig. 14. The outer reforming tube wall temperature profile trajectory in the absenceof a tube-side feed disturbance under P control shown in Fig. 14(a) and under PIcontrol shown in Fig. 14(b) with ¯ =x 0.465H

set2

.

0 100 200 300 400 5000.42

0.43

0.44

0.45

0.46

0.47

Time (s)


2with time in the absence of a tube-side feed

disturbance under P control (solid line) and under PI control (dashed line). Theopen-loop system response (dashed-dotted line) is also included for a wall tem-perature profile for which ¯ =x 0.465H

set2

.

0510 0100200300400500

1000

1100

1200


Out

er re

form

ing

tube

wal

l tem

pera

ture

(K)

Fig. 16. The outer reforming tube wall temperature profile trajectory in the pre-sence of a disturbance in the tube-side feed (20% increase in tube-side mass flowrate) under PI control with ¯ =x 0.465H

set2

.


sampling time, when the new x̄Houtlet

2 is received from the CFD si-mulation. In our work, the performance of the feedback controlschemes is evaluated based on two criteria: the improvement inthe process dynamics and the final deviation of x̄H

outlet2 from the

desired x̄Hset

2. It is important to note that the process dynamics in

this work is defined as the time duration that is needed for thex̄H

outlet2 of the closed-loop system to first attain 99.99% of the desired

x̄Hset

2 . Unfortunately, due to the well-known drawback of P control,

an offset of the final value of x̄Houtlet

2 is expected in the system underP control, and hence, the process dynamics cannot be evaluatedbased on the arrival of x̄H

outlet2 at the desired x̄H

set2. In the case of the P

control scheme, the process dynamics is the time that is requiredfor the closed-loop system to settle at its new steady-state.

In the case of set-point tracking control under a disturbance-free environment, the outer reforming tube wall temperaturetrajectory propagates differently under P control and PI controlthan under open-loop control (Figs. 11 and 14(a) and (b)). Theopen-loop control strategy adopts the outer reforming tube walltemperature profile based on the relationship between x̄H

outlet2 and

TmaxWall as shown in Fig. 12 with ¯ = ¯ =x x 0.465H

outletHset

2 2 . Because of theaforementioned closed-loop operating policy described in Section3.2, the process dynamics is greatly enhanced in the closed-loopsystem shown in Fig. 15. In particular, it takes ∼244 s for x̄H

outlet2 to

attain its final value under open-loop control, while it takes ∼90 scorresponding to an improvement of 63.1% under P control or∼154 s corresponding to an improvement of 36.9% under PI con-trol, respectively. Nevertheless, the closed-loop system im-plemented with P control is unable to drive x̄H

outlet2 completely to

the desired x̄Hset

2 , and the offset is estimated to be 3.18%.Next, we turn our attention to the case of set-point tracking

control under a tube-side feed disturbance to emphasize the im-portance of feedback control. In this case, a 20% increase in thetube-side inlet mass flow rate is introduced into the simulation

settings to simulate the feed disturbance. In the presence of atube-side feed disturbance, PI control and open-loop control yieldsignificantly different temperature trajectories of the outer re-forming tube wall (Figs. 11 and 16). Unlike feedback controlschemes, open-loop control does not possess a self-correctingmechanism, and therefore, open-loop control fails to recognize thepresence of the induced tube-side feed disturbance. As a result,open-loop control fails to drive x̄H


set2 (Fig. 17)

since it blindly applies the pre-determined outer reforming tubewall temperature trajectory, which is independent from x̄H

outlet2 . On

the contrary, under PI control, x̄Houtlet

2 is driven to the desired x̄Hset

2 inthe presence of a tube-side feed disturbance within ∼308 s. Thisresult demonstrates that the performance of PI control is superiorto that of open-loop control (as well as P control) in the presenceof a tube-side feed disturbance. Most importantly, the aboveanalysis confirms that it is possible to utilize CFD software tomodel, design and implement feedback control schemes into aCFD model to form a closed-loop system to study disturbancecompensation.

Remark 2. Although the open-loop, P, and PI set-point trackingand disturbance rejection properties are widely known, the pur-pose of this work is to evaluate the closed-loop properties of theSMR system and, more importantly, to demonstrate that real-timeclassical and advanced feedback control schemes can be in-corporated into CFD models, and specifically within the model ofthe industrial-scale SMR system. P/PI controllers are examples ofreal-time classical feedback control schemes, while dynamic op-timization with integral feedback control (to be presented in detailin the next section) is an example of a real-time advanced feed-back control scheme. The simulation results demonstrate the ex-pected dynamic responses, which in turn provides necessary

0 100 200 300 400 5000.42

0.43

0.44

0.45

0.46

0.47

Time (s)


2with time in the presence of a disturbance in the

tube-side feed (20% increase in tube-side mass flow rate) under PI control (solidline) and under open-loop control (dashed line) for a wall temperature profile forwhich ¯ =x 0.465H

set2

.


evidence to support the accuracy and effectiveness of the pro-posed methodology for real-time closed-loop feedback controldesign based on CFD modeling technology.

3.4. Integrating dynamic optimization and feedback

In previous sections, we demonstrate that we can designclosed-loop CFD models under feedback control schemes in ANSYSFluent CFD software, and analyze and evaluate the performance ofP control and PI control in the presence and absence of a tube-sidefeed disturbance. In both scenarios, PI control possesses the mostenhanced process dynamics and zero-offset in the final x̄H

outlet2 , and

therefore, it is ranked to have the best performance. Nevertheless,we strive to improve the process dynamics further, and in thisregard, we would like to formulate more advanced controlschemes, i.e., optimization-based control schemes, to design aclosed-loop system in CFD software that drives x̄H

outlet2 to the de-

sired x̄Hset

2 .Optimization-based control schemes (e.g., model predictive

control – MPC) have been widely used in the HyCO/SMR plants ofthe gas industry. Successful implementation of optimization-basedcontrol of SMR plants can allow more effective set-point trackingand disturbance rejection properties. Therefore, motivated by in-dustrial practical considerations, we devote the remaining sectionto the development of a dynamic optimization and integral

Fig. 18. Dynamic optimization and integral feedback control scheme, where themanipulated input at + Δt tk is computed based on the reference manipulatedinput profile at + Δt tk and the integral control action at tk, which is described inEq. (10).

feedback control scheme (Fig. 18) which generates the outer re-forming tube wall temperature profile.

The majority of approximate models formulated to capture thedominant dynamics of the reforming tube for the purpose of de-signing optimization-based control schemes such as MPC in in-dustry are data-based models. Hence, we first derive a mathe-matical model capturing the relationship between x̄H

outlet2 and the

outer reforming tube wall temperature by utilizing a data-drivenmodeling technique (previously mentioned in Section 3.3) andCFD simulation results. It is worth emphasizing that all CFD si-mulation settings from the previous sections are again used in thissection. From the CFD simulation result of the step-change of themaximum outer reforming tube wall temperature from

( ) =T 0 1100 KWallmax to ( ) =T t 1110 KWall

max , the dynamic response of

x̄Houtlet

2 exhibits a behavior that can be described by a first-ordertransfer function indicated by the initial non-zero slope. Hence,the discrete first-order single-input–single-output (SISO) modelpresented in Eq. (9a) below is formulated to represent the transferfunction of the process. Then, based on this first-order SISO model,the maximum likelihood estimation (MLE) method (Rogers andSteiglitz, 1967; Kumar and Varaiya, 1986) presented in Eq. (9b) isused to identify the appropriate model parameters with a set ofouter reforming tube wall temperature and x̄H

outlet2 data from the

above CFD simulation. The discrete first-order SISO model andMLE formulation are presented as follows:

( ) = ( )( )

( ) +( )

( )( )

y kB sA s

u kA s

e k1

9a

τ θ

( ) = +( ) =

( ( ) ( )) = { ( )| ( ) }( )θ Θ∈

⎧⎨⎩A s a a s

B s b

y k u k y k u k, arg max ,9b

0 1

0

where y(k) and u(k) are the process output and process input re-spectively, s is an independent variable on the Laplace domain ofthe transfer function, k is a discrete time variable, τ ( ( ) ( ))y k u k, isthe maximum likelihood estimator, θ = [ ]a a b0 1 0 is the parametervector of the estimated model, and e(k) is assumed to be a value ofa white noise function with zero mean and a standard deviation of1. Utilizing the aforementioned strategy, a0, a1 and b0 are esti-mated to be × −2.188 10 3, 1.000 and × −1.764 10 5 respectively, andtherefore, the approximate model that describes the dominantdynamics of the reforming tube is created.

Subsequently, this dynamic model is applied in the Matlab MPCDesign Toolbox (see Table 6 for the parameters used) for the cal-culation of an optimal maximum outer reforming tube wall tem-perature trajectory, ( + Δ )T t tWall

pk

max, , based on the desired x̄Hset

2 andaforementioned constraints on the outer reforming tube walltemperature (Eqs. (8c) – (8d)). Then, based on this reference ma-nipulated input trajectory, the proposed dynamic optimization andintegral feedback control scheme is formulated as follows:

Table 6Matlab MPC design toolbox parameters.

Parameter Value

Input weight 0.00Output weight 1.00Overall estimator gain 0.5Control step 0.1 sPrediction horizon 2000 stepsControl horizon 20 steps

0 100 200 300 400 5000.42

0.43

0.44

0.45

0.46

0.47

Time (s)


2with time in the presence of a tube-side feed

disturbance (20% increase in tube-side mass flow rate) under the dynamic opti-mization with integral feedback control scheme (solid line) and under PI control(dashed line). The open-loop system response (dashed-dotted line) is also includedfor a wall temperature profile for which ¯ =x 0.465H

set2

.


∫ττ τ

( ) = ¯ − ¯ ( )

( ) = ( )

( + Δ ) = ( + Δ ) + ( ) ( )

⎧

⎨⎪⎪

⎩⎪⎪

e t x x t

u t e d

T t t T t t u t

1

10a

k Hset

Houtlet

k

I kI t

t

Wall k Wallp

k I kmax max,

k

2 2

0

≤ ( + Δ ) ≤ ( )T T x t t T, 10bWall kmin max

]( + Δ ) = [

−

−

( + Δ ) − ( )

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

T x t t x x x x x

T t t

,

0.02210.800310.734

64.416151.83 10c

Wall k

Wall k

4 3 2 1 0

max

where ( + Δ )T t tWallp

kmax, is the reference manipulated input trajectory

determined at + Δt tk from the dynamic optimization using theMPC algorithm in Matlab. At the end of each sampling time in-terval, a measurement of x̄H

outlet2 acquired from CFD simulation is

used to evaluate the current deviation of x̄Houtlet

2 from the desiredx̄H

set2 , and the corresponding integral control action, ( )u tI k , is de-

termined. Then, ( + Δ )T t tWallp

kmax, , obtained from the strategy de-

scribed in the preceding paragraph, is adjusted by ( )u tI k to yieldthe predicted ( + Δ )T t tWall k

max as the manipulated input to the closed-loop CFD model.

We compare the performance of the dynamic optimization andintegral feedback control scheme with those of PI feedback controland open-loop control based on the two aforementioned criteriafor control performance in Section 3.2. It is worth mentioning thatthe primary role of integral control in the dynamic optimizationand integral feedback control scheme is to guarantee that x̄H

outlet2

can always attain the desired x̄Hset

2 even in the presence of a tube-side feed disturbance. In the case of set-point tracking controlunder a tube-side feed disturbance, both the dynamic optimiza-tion and integral feedback control scheme and the PI controlscheme can drive the system to the desired set-point; however,the dynamic optimization and integral feedback control schemepredicts a slightly different outer reforming tube temperaturetrajectory than that predicted by PI control as shown in Fig. 20.Specifically, the maximum outer reforming tube wall temperatureof the closed-loop system under the dynamic optimization withintegral feedback control scheme is initially maintained at 1200 Kfor nearly 40 s as shown in Fig. 19, which speeds up the processdynamic response. Based on the metric that we previously definedin this study, it only takes ∼33 s for x̄H

outlet2 to first achieve the de-

sired x̄Hset

2 under the dynamic optimization with integral feedbackcontrol scheme as shown in Fig. 20, corresponding to an

0510 0100200300400500

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1200


Out

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ing

tube

wal

l tem

pera

ture

(K)

Fig. 19. The outer reforming tube wall temperature profile trajectory in the pre-sence of a tube-side feed disturbance (20% increase in tube-side mass flow rate)under the dynamic optimization with integral feedback control scheme with¯ =x 0.465H

set2

.

improvement of 89.3% when compared with the system under PIcontrol for which it takes ∼308 s. Nevertheless, the aggressivemanipulated input generated by the dynamic optimization withintegral feedback control scheme also causes the oscillation ofx̄H

outlet2 around the desired x̄H

set2 . Therefore, it is important to notice

that although the dynamic optimization with integral feedbackcontrol scheme allows x̄H

outlet2 to advance to the desired x̄H

set2 much

faster than PI control, it ultimately requires a longer duration toreach the optimized steady-state conditions and results in oscil-lation; therefore, its performance is comparable with that of PIfeedback control.

Remark 3. As discussed above, the PI controller is easier to im-plement than the dynamic optimization with integral feedbackcontrol scheme but it does not use an explicit plant model, and asa result, the closed-loop response is slower because the tuning waschosen to avoid high sensitivity to disturbances. Further, theoverall PI closed-loop response was not improved for other tun-ings investigated that reasonably avoided this sensitivity (anotherresult is discussed below that confirms the sufficiency of the PIcontroller with the chosen tuning by demonstrating its robustnessto various disturbances). However, the dynamic optimization withintegral feedback control scheme achieves a faster closed-loopresponse than the PI controller with the knowledge of the processdynamics; plant-model mismatch, integral action, and the effect ofthe disturbance may contribute to the oscillations in the outputtrajectory. The comparison results demonstrated that both controlschemes force the output to track the set-point and deal well withdisturbances. As noted, the sufficiency of the chosen PI controllertuning is further validated by testing the closed-loop response ofx̄H

outlet2 to a different disturbance than that utilized in the results

presented above. An additional disturbance in the tube-side feed,

0510 0100200300400500

1000

1100

1200


Out

er re

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ing

tube

wal

l tem

pera

ture

(K)

Fig. 21. The outer reforming tube wall temperature profile trajectory in the pre-sence of a disturbance in the tube-side feed temperature under PI control with¯ =x 0.465H

set2

.

0 100 200 300 4000.42

0.43

0.44

0.45

0.46

0.47

Time (s)


2with time in the presence of a disturbance in the

tube-side feed temperature (solid line) and in the presence of a disturbance in thetube-side feed mass flow rate (dashed line) under PI control for a wall temperatureprofile for which ¯ =x 0.465H

set2

.


i.e., the temperature of the tube-side feed is increased by 10% fromits nominal value, is induced to validate the robustness of the PIcontroller against different potential disturbances. The simulationresults including the control action (Fig. 21) and correspondingprocess response (Fig. 22) generated by the PI controller tocounteract the tube-side feed temperature disturbance are similarto those of the previous case in Section 3.3 when the induceddisturbance is the tube-side feed mass flow rate. Specifically, x̄H

outlet2

is successfully driven to the desired x̄Hset

2 in the presence of a tube-side feed temperature disturbance within ∼200 s.

4. Conclusions

This work initially focused on demonstrating that CFD softwarecan be employed to create a detailed CFD model of an industrial-scale steam methane reforming tube, and subsequently focused onthe design and implementation of feedback control schemes intothe CFD model. The simulation results of the reforming tube CFDmodel simulating the transport and chemical reaction phenomenawith an approximate representation of the catalyst packing mat-ched well with the available industrial plant data. The closed-loopCFD simulation results demonstrated that the proposed PI controlscheme and a control scheme combining dynamic optimizationand integral feedback control could drive the value of x̄H

outlet2 to a

desired x̄Hset

2 , and significantly improve the process dynamicscompared to that under open-loop control. In the case of set-pointtracking control under a tube-side feed disturbance, the dynamicoptimization with integral feedback control scheme calculates amore aggressive outer reforming tube wall temperature trajectorycompared to that calculated by PI control but both control systemsdrive the average outlet hydrogen mole fraction to the set-point.

Acknowledgments

Financial support from the Department of Energy is gratefullyacknowledged.

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