Process simulation of natural gas steam reforming

F U E L P RO CE SS I NG T EC H NOL O G Y 8 9 (2 0 0 8) 6 22 –6 3 2

w w w. e l s e v i e r. c o m / l o c a t e / f u p r o c

Process simulation of natural gas steam reforming: Fuel distribution optimisation in the furnace Agostino Olivieri⁎, Francesco Vegliò Università degli Studi di L'Aquila-Dipartimento di Chimica, Ingegneria Chimica e Materiali, Monteluco di Roio-67040 L'Aquila, Italy

AR TIC LE I N FO

ABS TR ACT

Article history:

This paper describes a two-step method to simulate the natural gas steam reforming for

Received 7 May 2007

hydrogen production. The first step is to calculate reforming tube length and fuel distribution

Received in revised form

with equilibrium approach associated with heat transfer. The second step is to calculate and

5 December 2007

validate reforming performance with kinetic model. A short-cut simulation of hydrogen

Accepted 5 December 2007

plant has also been performed to calculate inputs for the reformer model, such as total flow rate and composition of mixed fuel burning in the furnace chamber. Heat transfer, especially

Keywords:

radiative heat transfer, is the key role in the steam reforming technology, due to the high heat

Natural gas

fluxes involved. For this reason, energy modelling of the furnace chamber has been

Heat transfer

performed. The simulation evaluates the most important design variables, as tubes height,

Design

maximum tube-wall temperature, and tube pressure drop. The heat flux profile can be

Simulation

selected to have suitable metal temperatures to lengthen the reformer tube life. The model

Steam reforming

calculates the design parameters for reforming tube and fuel distribution among burners.

Hydrogen

1.

Introduction

Natural gas is a high quality energy and chemical raw material, mainly used in chemical industry, fuel and power generation [1]. One of the essential techniques to add a high additional value to natural gas is the steam reforming. Steam reforming of hydrocarbons has been in use for several years as the principal process for the generation of hydrogen and synthesis gas needed in the chemical industry. The popularity of this process [2] can be attributed to its higher efficiency and cost effectiveness in comparison to competing processes. Today, natural gas is the most common feedstock for steam reforming, being used in more than 75% of the operating units. In the future, deteriorating quality of crude oils, stringent petroleum product specifications and environmental regulations will lead to increased hydrogen demand for hydroprocessing in refineries. In recent years, there has been much interest in the production of hydrogen for high efficiency generation of electricity in fuel cells [3]. On the other side, hydrogen is a well-known fuel that

© 2008 Elsevier B.V. All rights reserved.

in the future must be leading the energy production sources because of its high calorific value without generating pollutants or residues [4]. Among all the sources of hydrogen available, the natural gas, composed mainly of methane, has been used most widely because this gas is very abundant, clean and can easily be converted to hydrogen. The existence of a widespread infrastructure for the supply of natural gas makes this an excellent fuel [5] for the solid oxide fuel cell (SOFC). However, it must be first converted to a hydrogen-rich gas before using it in the SOFC. Steam reforming on nickel-alumina catalysts is the main process for the production of hydrogen or synthesis gas. It is a large scale operation carried out in rows of tubular reactors inserted into a gas-fired furnace. In these systems, the techniques belong to KTI, Kellogg, Topsoe, ICI, Selas and TEC companies [6]. The technical difference mainly displays in the chamber size, burner structure and distribution, inner and outer diameter of the reformer tubes and their arrangement. In new engineering research and development [1], the method

⁎ Corresponding author. Monteluco di Roio-67040 L'Aquila, Italy. Tel.: +39 0862 434255; fax: +39 0862 434203. E-mail address: [email protected] (A. Olivieri). 0378-3820/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.fuproc.2007.12.001

F U E L P R O CE SS I NG T EC H NOL O G Y 8 9 (2 0 0 8 ) 6 2 2–6 3 2

combining mathematical simulations and prototype reformers is more effective than the methods of laboratory, pilot plant and industrial plant with graduated enlargement, in terms of capital and time-saving effects. Natural gas steam reformation is a strong endothermic reaction where a large amount of heat is supplied by fuel burning (commonly natural gas and purge gas recovered from hydrogen purification unit) in the furnace chamber. The quantity of radiation heat transfer occupies [1] above 95% of the reformer tube heat load. Simulation of tubular reactors requires information on thermodynamics and kinetics. Whereas the first aspect is fairly well accounted for in the design, the second is often neglected or reduced to very simple elements. Extensive studies on the kinetics and reaction mechanism of steam reforming have been reported in the open literature. Several reactions have to be considered for a proper description of the process. Xu and Froment [7] obtained a generalized Langmuir-Hinshelwood kinetic type model considering the water-gas shift (WGS) reaction to occur in parallel with the steam reforming (SR) reactions. They validated their kinetics by successfully using it to simulate an industrial reformer. Their kinetic model has gained wide acceptance [2] and it is considered adequate to model industrial steam reformers. The behaviour of natural gas reformer relates to its structure parameters and operating conditions. The structure parameters mainly include: furnace tube diameter, length, wall thickness, heat conduction property, blackness, tube pitch (or pitch between two rows of tubes if multiple rows); burner pattern and arrangement; chamber structure size; flue gas tunnel arrangement, and so on. The operating conditions include: natural gas components, water carbon ratio, inlet temperature and pressure, operating load; catalyst property, structure, size and bed void factor; fuel property, temperature, pressure, air surplus coefficient, and so on. Heat transfer is the most important aspect in the design of steam reforming furnaces. The purpose of this paper is to strengthen heat transfer in order to lengthen the reformer tube life. In fact, the wall temperature of the catalytic tube is limited by the creep limit of alloy steel tubes, so the fuel distribution among the burners is optimized in order to avoid temperature peaks. At the same time, energy use efficiency and material utilization can be improved, reducing the investment costs. This optimization is achieved through a detailed model of the furnace, taking into account structures parameters and operating conditions.

2.

Mathematical model

The complexity of the reforming process necessitates [8] the use of computer simulation when designing and optimizing the process, because several objectives and constraints are involved. Reformer consists of the tubes and chamber but, in view of the fact that the reaction inside tubes is closely related to the external radiation heat transfer, simulation considers the reformer as a system. The convective section for flue gas heat recovery defines the inlet process gas temperature, but it is relatively independent and it is not discussed in this work. Reforming tube heat flux represents the fundamental parameter for the simulation developing, due to its critical role in furnace design. Reformer model receives heat flux profile as

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input, to have suitable metal temperatures, and calculates reforming tube length and fuel distribution among burners. Choosing a heat flux profile represents a different philosophy in reformer design. In this way it will be possible to simulate new configuration with innovative combustion system under development. Modelling of a side-fired steam reforming furnace in hydrogen plant has been developed according to the operating conditions shown in Table 1, where a water carbon ratio of 3.2 and a reforming pressure of 2300 kPa have been selected, according to typical ranges for industrial reformers reported in other works [9–14,1,2]. Steam reforming apparatus (see Fig. 1) is simulated by splitting the computational domain into two regions: 1) “reaction zone”, which comprises catalytic bed and reforming tube; 2) “heating zone”, which is the tubes external region, bounded by refractory wall; this zone is divided into two sub-zones: 2a) “firing zone”, where burners are installed; 2b) “no-firing zone”, without burners. The simulated system consists of a rectangular-base chamber, 2.1 m lengthwise and 3.0 m wide, with five reforming tubes (centre distance: 0.35 m) packed with supported nickel catalyst. Inner and outer tube diameters are 0.13 m and 0.15 m respectively, according to Yu et al. [1] and KTI experience [15], while 0.01 m equivalent catalytic pellet diameter is assumed. Burners are installed in the lower zone (“firing zone”), while no burners are provided in the upper zone (“no-firing zone”) where the reduced cross section increases the convective heat transfer contribution. The process gas is fed to the reactor top, passes through the catalytic bed and comes out from the reactor bottom. After heating reforming tube in countercurrent, the burned gas leaves the “heating zone” from the top. Total burning fuel has been computed by a short-cut simulation of a hydrogen plant performed in PROII. This process simulator is also used to obtain correlations for specific heat, viscosity and thermal conductivity of the process gas. Burning fuel is a mix of purge gas from hydrogen recovery section (e.g. pressure swing adsorption — PSA) and make-up natural gas. Reforming conditions (see Table 1) and flue gas outlet temperature (1148 K, bridge-wall temperature) are given as input. The overall simulation is necessary to evaluate fuel gas composition and flow rate, which depend on all unit operations (reforming reactor, heat exchangers, WGS reactor, condensate separator and PSA). Table 1 – Reference operating conditions Pressure (Pa) TINLET (K) TOUTLET (K) Tube inlet molar flow rate (kmol/h): CH4 H 2O CO2 H2 N2

2.3 · 106 803 1123

4.75 15.20 0.05 0.30 0.40

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solving two equilibrium equations, Eqs. (4) and (5), relevant to two independent reactions, Eqs. (1) and (2): eq

KSR ¼

aCO a3H2 aCH4 aH2 O

eq

KWGS ¼

aCO2 aH2 aCO aH2 O

ð4Þ ð5Þ

Assuming pure ideal gas at system temperature and atmospheric pressure as reference state, the following expression (Eq. (6)) is numerically correct for components in gaseous phase: eq

K

Fig. 1 – Schematic view of the steam reforming furnace: frontal section and cross section.

The most important reactions taking place are SR reactions (Eq. (1), (3)) and WGS reaction (Eq. (2)): CH4 þ H2 O↔CO þ 3H2

ð1Þ

CO þ H2 O↔CO2 þ H2

ð2Þ

CH4 þ 2H2 O↔CO2 þ 4H2

ð3Þ

The simulation is carried out in two steps, the first one to design the system and the second one to validate the results: I. “Design Mode”, with a ΔT profile for equilibrium approach, calculates reforming tube length and fuel distribution among burners, considering furnace heat transfer model when process gas outlet conditions and heat flux profile in “firing zone” are imposed; II. “Rating Mode”, with the kinetic model reported by Xu and Froment [7], calculates reforming tube performances by using tube length, metal skin temperature and heat transfer coefficient profiles calculated by step I.

2.1.

Design mode

2.1.1.

Equilibrium approach

The equilibrium compositions can be calculated for the steam reforming system at every temperature by simultaneously

0 1 mi mi mi fî @ A ¼ j 0 ¼ j fî ¼ Pm j yi /ˆ i fi

ð6Þ

Assuming ideal mixture /ˆ i = /i of ideal gases (/i = 1), equilibrium equations (Eqs. (4) and (5)) can be expressed as partial pressure functions. Equilibrium conditions are ideal. An equilibrium approach profile has been considered to approximate effective gas compositions along the catalytic tube. Consequently, at every temperature in the reactor, the composition is calculated as function of pressure, temperature and equilibrium approach. Operating conditions aid direct methane conversion reaction and, as a consequence, process gas composition at reformer outlet is close to the equilibrium composition. Approach temperature differences of 150 K and 10 K have been assumed for process gas at inlet and outlet respectively, with linear trend along the tube elevation. Approach profile is influenced by all factors preventing equilibrium achievement and it can be given to the model as input. In “Design Mode”, the reaction zone is simulated by dividing the catalytic tube into elements where global heat and material balances are carried out. The system is modelled as CSTR's arranged in series, considering that the number of elements is an important parameter for the reliability of the simulation. Process gas inlet and outlet temperatures are defined in input, so this temperature range is divided into 32 elements with constant ΔT. The resulting vector represents a series of process gas temperatures along the tube elevation. After equilibrium constants calculation for steam reforming and water gas shift reactions, two non-linear equations (Eqs. (7) and (8)) system is solved with Newton method: K1 ¼

P

nTOT

2.1.2.

! ðnH2 þ 3nSR þ nWGS Þ3 ðnCO þ nSR nWGS Þ ðnH2 O nSR nWGS Þ ðnCH4 nSR Þ

ðnH2 þ 3nSR þ nWGS Þ ðnCO2 þ nWGS Þ nTOT ðnH2 O nSR nWGS Þ ðnCO nWGS Þ

K2 ¼

2

P

ð7Þ

ð8Þ

Heat transfer inside the catalytic tube

Heat transfer inside the catalytic tube is the limiting factor for a steam reformer. Currently, ceramic catalysts are used. Catalyst presence reduces the radiation mean beam length and, as a consequence, radiative heat transfer is very low. Conductive heat transfer is negligible due to the low thermal conductivity of ceramic packed bed. Therefore, convective heat transfer is the principal way to supply energy to the reactor. In literature many expressions [16–23] are available for heat transfer coefficient.

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Large differences can be observed among these expressions and, as a consequence, temperature profiles can be different. Therefore, simulations reliability depend on the correct estimation of the heat transfer coefficient. Beek's correlation [16] is very conservative but it is also one of the most used by researchers. A similar expression (Eq. (9)) is adopted in this work, where the parameter B has been increased from 0.4 (Beek's value) to 0.45, in order to achieve values for heat transfer coefficient on average with other Authors [18,23,24]. U¼B

KG 2:58 Re1=3 Pr1=3 þ 0:094 Re0:8 Pr0:4 dP

ð9Þ

Heat transfer coefficient close to the tube wall depends on Prandtl number, Reynolds number, gas conductivity and equivalent catalyst pellet diameter. By varying geometric catalyst properties it is possible to improve the heat transfer coefficient, usually increasing pressure drops. Generally, catalyst vendors supply catalytic pellet properties, e.g. equivalent diameter. In the calculation code, expression for heat transfer coefficient is an easily changing input. Model discretization involves a high number of elements (32) to represent the reactor accurately. Fig. 2 shows a single element of the catalytic tube with the main quantity characterizing the system. For each element, gas properties and compositions are evaluated at mean temperature. Due to the symmetrical geometry, the half of the transferred heat (Q/2) is only considered. By defining the outlet temperature and the associated outlet conversion, Eq. (10) is used to calculate the required heat duty. out T in þ eSR DH0R;SR T out Q ¼ nin TOT cPmix T þeWGS DH0R;WGS T out

ð10Þ

Kirchoff equation (Eq. (11)) is used to estimate the standard enthalpy of reaction at each temperature: Z DH0R ðTÞ

¼

DH0R ð298Þ

þ

T

5 X

298 i¼1

2.1.3.

Heating zone

After heat duty profile evaluation (Eq. (10)), the model computes the heating zone. “Firing zone” height is estimated according to the heat flux imposed in input and the fuel flow rates to the burners are calculated to obtain this heat flux. In “no-firing zone” the heat flux cannot be imposed because burners are not present and modelling is different. The radiative heat transfer [25,26] is predominant in the heating zone due to the high temperatures involved and the absence of obstacles for the radiation. Furnace simulation [27] is carried out considering two ideal surfaces: the “hot” one represents the burned gas or “flue gas”, while the “cold” one (Ape = NT·iT·l) represents the catalytic tubes. Adsorption efficiency factor (α) depends on the tubes layout and has been graphically estimated [25] assuming an emissivity of 0.9 for reforming tubes. Furnace volume has been considered in the mean beam length (L = 3.6 V/A). Molar composition has high influence on the radiative heat transfer and [25] reported an expression (Eq. (12)) to evaluate flue gas emissivity. ej ¼ exp a0;j þ a1;j k þ a2;j k2

Total pressure and mean beam length determine λ parameter in Eq. (12). Coefficients a0,j, a1,j, a2,j depend on the absolute temperature and they have different expressions for carbon dioxide or water, considered at atmospheric pressure and at partial pressure close to zero respectively. These values are adjusted to consider operating conditions by means of corrective factors for carbon dioxide and water. Radiation reduction due to CO2 and H2O mixing is kept into account by means of Egber factor. According to the operating conditions found in this work, the following values have been adopted for corrective factors: CC = 1, CW = 1.1 and CSO = 0.04. Eq. (13) has been selected to estimate the flue gas emissivity. eG ¼ ðeCO2 CC þ eH2 O CW Þ ð1 CSO Þ

mi cP;i dT

ð11Þ

where νi is negative for reactants and positive for products, 5 P while DH0R ð298Þ ¼ DH0F;i . i¼1

ð12Þ

ð13Þ

Fire box walls are considered in the radiative exchange factor, F, estimated through Eq. (14). F¼

1 1 1 þ 1 eF eT

ð14Þ

The exchange factor is a function (Eq. (15)) of gas emissivity and ratio γ = α·Ape / (A − α·Ape), where the denominator quantity represents the refractory effective surface. 0 B eF ¼ eG B @1 þ

1 C C 1 eG A 1þ FRC 1 eG g

ð15Þ

The parameter FRC also depends on ratio γ:

▪ FRC = 1 / (1 + γ) when γ ≤ 0.5, ▪ FRC = 1 / γ when γ ≥ 4 and 4:5g0:5 ▪ FRC ¼ 3:5gð1þgÞ when 0.5 b γ b 4. Therefore, radiative heat transfer between flue gas and tubes wall is calculated by Eq. (16). Fig. 2 – Catalytic tube discretization: single element.

QR ¼ r Ape a F TG4 TT4

ð16Þ

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Relevance of the convective heat transfer is less than the radiative one. The model also computes the heat transfer (Eq. (17)) associated to the convection. QC ¼ hC AT ðTG TT Þ

ð17Þ

Convective heat transfer coefficient has been assumed constant and equal to 10 kcal h− 1 m− 2 K− 1 (11.63 W m− 2 K− 1), according to the experience [25,26]. In “firing zone”, the presence of burners [2] is considered to compute the radiative heat transfer associated to the flames zone (Eq. (18)), where adiabatic flame temperature is used for heat transfer calculation. Qf ¼ r

Nb Af ef eT ð1 eG Þ 4 Tf AT

ð18Þ

Heating zone modelling is carried out by discretization. The furnace volume has been divided into elements where heat and material balances are carried out. The furnace is represented by a set of CSTR in series and the model reliability is influenced by the number of elements, although this parameter has minor impact with respect to the reaction zone. For this reason, the number of elements in “firing zone” is coincident with the burner rows, considering a uniform distribution of the burned gas [6]. Each burner row supplies the duty required by 4 elements of the catalytic tube. In the side fired furnaces only a limited number of burner rows can be installed. However, the model can easily work reducing the rows, simply increasing the number of catalytic tube elements heated by a single burner row. In “no-firing zone”, instead, it is necessary to increase the mesh because burned gas properties (e.g. temperature, specific heat) change with monotonic trend along the elevation. “No-firing zone” discretization has been realized with 0.30 m elements to achieve a reliable modelling. A typical element in “firing zone” is shown in Fig. 3. Catalytic tubes duty is mostly supplied by radiative heat transfer (Eq. (16)); convective heat transfer (Eq. (17)) and flames presence (Eq. (18)) are also considered. For each element, the mean gas temperature (TG) is evaluated after adiabatic flame temperature calculation. The heat flux is imposed and the model estimates corresponding fuel flow rates for burners at different elevation. In this way, useful metal skin temperature profile is achieved by considering furnace heat transfer according to burned gas flow

Fig. 3 – “Firing zone” discretization: single element.

Fig. 4 – Calculation block flow diagram for “firing zone”.

rate and conditions. Specific heat correlations for the flue gas are obtained by Perry et al. [28]. A calculation block flow diagram for each element in “firing zone” is shown in Fig. 4. The first step in calculation sequence is the assumption of a fuel fraction to burn in that element. A subroutine performs the combustion reaction and, afterwards, heat and material balances are carried out considering flue gas coming from previous element, burned fuel and process gas duty. Subsequently, radiative properties are estimated at mean flue gas temperature and heat transfer to the catalytic tube is computed. If the difference between the required duty and the heat transferred is greater than the tolerance (err), a new fuel fraction is assumed and the calculation sequence is performed again. Iterations continue until the convergence between duty and heat transferred is achieved. The element computation is now complete and the model starts next element estimation. This calculation sequence is applicable until the fuel is available. At a certain elevation, a “transition” element is reached and the corresponding duty is partially supplied by residual fuel, while remaining duty can not be supplied with the imposed heat flux. “Firing zone” calculation outputs are height of this zone and fuel distribution versus burner elevation, as well as the inputs for “no-firing zone” modelling. A typical element in “no-firing zone” is shown in Fig. 5. The main difference with respect to the other zone is the absence of burners. Consequently, the heat flux is not an input but a calculation result and the flue gas flow rate becomes constant.

627


[10,11,29,30]. The adopted intrinsic kinetic expressions are listed below: k1 R1 ¼ 2:5 p H2

R2 ¼

k2 p H2

k3 R3 ¼ 3:5 p H2

Fig. 5 – “No firing zone” discretization: single element.

In fact, without a burning system, heat flux and temperature profiles are outputs to be estimate. Radiative heat transfer (Eq. (16)) is predominant in this zone, although the temperatures are lower and the convection contribution (Eq. (17)) is more important than in “firing zone”. Flame zones (Eq. (18)) are not considered. For this reason, a section reduction is useful to promote heat transfer. A calculation block flow diagram for each element in “nofiring zone” is shown in Fig. 6. In this case, the element height is fixed in input at 0.30 m and the model computes the number of elements required to supply remaining duty to the catalytic tube. The first step is the assumption of the process gas inlet temperature. The model estimates relevant duty and heat transfer coefficient inside the tube. Afterwards, the flue gas outlet temperature and the wall temperatures (inner and outer) are calculated. Flue gas properties are evaluated at the mean temperature of the element and heat transfer calculation is performed. Comparing required duty and heat transferred, the iterative procedure continues by changing process gas inlet temperature. Element computation is completed when the convergence is achieved. The calculation sequence is applicable until the value assumed for process gas temperature at element inlet is higher than 803 K (reformer inlet temperature). The element where this condition is not satisfied is named “last” element, which is computed by fixing process gas inlet temperature at 803 K. Therefore, the “last” element height is not assumed, but it is calculated to supply the remaining duty.

2.2.

p3H pCO pCH4 pH2 O 2 K1

!

=DEN

ð19Þ

=

ð20Þ

2

pH pCO2 pCO pH2 O 2 DEN2 K2

pCH4 p2H2 O

p4H pCO2 2 K3

!

=DEN

2

ð21Þ

where DEN = 1 + KCO·pCO + KH2·pH2 + KCH4·pCH4 + KH2O·pH2O / pH2. Eqs. (19) and (21) are the corresponding rate equations for the SR reactions, Eqs. (1) and (3) respectively, while the Eq. (20) is related to the WGS reaction (Eq.(2)). Kinetics rate coefficients and adsorption equilibrium constants are given by Xu and Froment [7].

2.2.2.

Heat and material balance

The model consists of mass, momentum and energy balance; the following assumptions have been considered to represent the steam reformer: (a) a single catalytic tube is representative of any other tube in the furnace; (b) steady-state conditions; (c) plug flow reactor;

Rating mode

The catalytic tube has been sized according to Section 2.1 and it is now simulated by means of one-dimensional, pseudohomogeneous model. In fact, tube length, metal skin temperature profile and heat transfer coefficient profile are “Design Mode” outputs to be used in “Rating Mode” as inputs.

2.2.1.

Kinetics

Currently, there is an accurate kinetics to represent the reforming reactions. The Langmuir–Hinshelwood (Houghen– Watson) type expressions reported by Xu and Froment [7] have been successful in simulating industrial reactors

Fig. 6 – Calculation block flow diagram for “no-firing zone”.

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Table 2 – Fuel gas and combustion air conditions 5

1.2 · 10 313 573

Pressure (Pa) TFUEL (K) TAIR (K) Fuel gas molar flow rate (kmol/h) CH4 H 2O CO2 H2 N2 CO Combustion air molar flow rate (kmol/h) O2 N2

1.320 0.081 3.633 3.132 0.400 0.342

5.25 19.75

(d) ideal gas behaviour; (e) pseudo-homogeneous catalyst bed; (f) constant effectiveness factor.

2.2.3.

Mass balance

dnCH4 ¼ g q 1 eV p r2 ðR1 þ R3 Þ dz

ð22Þ

dnH2 O ¼ g q ð1 eV Þ p r2 ðR1 þ R2 þ 2 R3 Þ dz

ð23Þ

dnCO ¼ g q ð1 eV Þ p r2 ðR1 R2 Þ dz

ð24Þ

dnCO2 ¼ g q ð1 eV Þ p r2 ðR2 þ R3 Þ dz

ð25Þ

dnH2 ¼ g q ð1 eV Þ p r2 ð3 R1 þ R2 þ 4 R3 Þ dz

ð26Þ

The following values have been assumed: ρ = 1500 kg m− 3, εV = 0.575 and η = 0.01 [2,11,29].

2.2.4.

Non-linear differential equations (Eqs. (22), (23), (24), (25), (26), (27), (28)) system is solved to calculate molar flow rates, nCH4, nH2O,nCO,nCO2,nH2, and thermodynamic conditions, P and T, along the catalytic tube elevation.

3.

Results and discussion

Modelling results are relevant to a natural gas feed (see Table 1) for a steam reforming furnace in hydrogen plant. Natural gas is also burned as make-up fuel mixed with purge gas from PSA. Total burning fuel flow rate and composition (see Table 2) have been estimated by a hydrogen plant simulation performed with PROII. Thermodynamic equilibrium in steam reforming reactor is compared with equilibrium approach results. Fig. 7 shows SR and WGS reaction progress when the temperature increases. In case of SR reaction, a monotonic trend is shown, while it is well know [32] that the WGS reaction rate (Eq. 2) reverses its direction to a finite axial position. The same trend is also shown in Fig. 10, where carbon dioxide yield along the reforming tube is represented. Thermodynamic equilibrium is a theoretic representation of the catalytic tube, so an equilibrium approach profile is considered to characterize the real situation. Divergences are highlighted at low temperature, where a higher approach temperature difference is present. Significant hydrogen yields are achieved only at high temperatures (1100–1150 K), so natural gas steam reforming requires high heat fluxes between the flue gas and the reactor. Consequently, heat transfer plays a leading role in the behaviour of non-autothermal reactors. A heat flux of 60,000 kcal h− 1 m− 2 (69780 W m− ²) has been assumed, according to Dybkjær [6] and KTI experience [15], to perform the furnace simulation in “design mode” (see section 2.1). With this heat flux as input, “firing zone” height is about 8.35 m, while seven row of burners are calculated, considering also the seventh element, where remaining fuel is burned before switching to “no-firing zone”. For this reason, the “transition” element is the shortest one and, similarly, the relevant burned fuel ratio is the lowest one. Table 3 shows the burner position along the furnace elevation and the fuel distribution among burners. In “no

Energy balance

3 P UðTÞ 2 p r ðTT ðTÞ TÞ þ q eV r2 g Rk DH0R;k dT k¼1 ! ¼ 5 dz P ni cP;i

ð27Þ

i¼1

Functions U(T) and TT(T), like total tube length, are calculated by “design mode” simulation.

2.2.5.

Momentum balance

dP AG ð1 eV Þ2 ¼ f G 2 dz qG dP e3V

ð28Þ

According to Ergun [31] theory, the friction factor (Eq. (29)) for packed bed can be evaluated in turbulent flow by means of the following equation: f ¼ 150 þ 1:75

Re 1 eV

ð29Þ

Fig. 7 – SR and WGS reactions progress versus temperature: equilibrium with and without approach.


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Table 3 – “Firing zone” results Burner row (#) 1 2 3 4 5 6 7

Burner elevation (m)

Fuel fraction (%)

0.720 2.230 3.789 5.250 6.541 7.645 8.244

10.55 21.23 20.71 18.30 15.16 12.01 2.04

firing zone” the burners are absent and the heat flux decreases with the elevation up to 31,550 kcal h− 1 m− 2 (36,693 W m− 2) at flue gas outlet. “No firing zone” height is about 3.90 m, while the total catalytic tube height is 12.25 m. This reactor length is within the industrial reformer range of 12–13 m, in accordance with KTI experience [15] and other Authors [1,2,11,32,33]. Temperature profiles in steam reforming furnace calculated in “design mode” are shown in Fig. 8. Process gas outlet temperature has been fixed at 1123 K and heat flux in input has been selected to have a maximum value for metal skin temperature close to 1200 K [2]. This value for the outer wall temperature of the tube is based on the creep limit of alloy steel tubes at operating conditions and it is required to avoid the tube rupture. Results shown in Fig. 8 are close to the value reported in other papers [2,6]. In the future, operating range of material adopted in catalytic tubes could increase and higher metal temperatures could be accepted. In any case, heat flux defined in input is easily modifiable and the model can compute the fuel distribution to achieve optimal temperature profiles for the selected materials. Performing “design mode” simulation, catalytic tube height and inside wall temperature profile, with convective heat transfer coefficient profile, are evaluated. Therefore, kinetic

Fig. 8 – Temperature profiles in steam reforming furnace simulated in “design mode”.

Fig. 9 – Process gas temperature profile and methane conversion along a reforming tube.

expressions are adopted to simulate the behaviour of a steam reforming catalytic reactor where boundary conditions have been estimated by “design mode” simulation. “Rating mode” simulation is performed by using these results as input. Process gas temperature profile associated to Xu and Froment [7] kinetics equations is shown in Fig. 9. The graph highlights a non-monotonic trend at low temperatures, as reported by Grevskott et al. [8] and Rajesh et al. [2]. A temperature decreasing is present close to the tube inlet, due to the high endothermic nature of SR reactions. Reactor modelling with equilibrium approach is not able to observe this trend because process gas temperature profile is an input and the model estimates the elevation to achieve this profile. In any case, when the distance from tube inlet rises, process gas temperature increases with a monotonic trend. This is achieved when transferred energy is sufficient to supply total reaction enthalpy and sensible heat for temperature increasing.

Fig. 10 – Hydrogen yield and carbon dioxide yield along a reforming tube.

630


Fig. 11 – Process gas pressure profile.

Reactor performances are evaluated through methane conin out in in in − nCH ) / nCH , hydrogen yield, (nout version, (nCH H2 − nH2 ) / nCH4, and 4 4 4 out in in carbon dioxide yield, (nCO2 − nCO2 ) / nCH4. Methane conversion profile is shown in Fig. 9. Differently from temperature profile, a continuous increasing trend is highlighted close to the tube inlet, although with different slope. Methane conversion at reformer outlet is more than 80%, according to other Authors [2,9–12]. Fig. 10 shows hydrogen yield and carbon dioxide yield at different elevation along the catalytic tube. Higher values for the hydrogen yield are achieved close to the tube outlet, where this parameter reaches about 2.84 kmol H2 per kmol CH4, close to the values of 2.812 kmol H2 per kmol CH4 reported by Elnashaie and Elshishini [11]. For carbon dioxide yield (see Fig. 10), higher values (0.34 kmol CO2 per kmol CH4) are reached at an elevation close to 10.0 m, while outlet CO2 yield is less than 0.32 kmol CO2 per kmol CH4. A similar trend, with a reverse direction, is also shown in Fig. 7 and it is in accordance with other works [2,32]. The pressure profile inside the catalytic tube is shown in Fig. 11, where a pressure drop slightly higher than 200 kPa is highlighted, close to the values reported by Rajesh et al. [2]. The reforming reactors are catalytic packed bed where high pressure drops are necessary to achieve a similar distribution of the process gas among the reforming tubes.

4.

Conclusions

A side-fired steam reformer in hydrogen plant has been simulated by using a non-isothermal, one dimensional, pseudo-homogeneous model with proven reaction kinetics, incorporating aspects of heat transfer in the furnace. For these designs, high heat fluxes are transferred to the catalytic tubes and, therefore, the tube skin temperature appears as a key variable to be optimised. This is important because even a slight increasing in the maximum tube wall temperature may result in a serious decline of the expected tube lifetime [1]. The model works in two steps. The first step, “design mode”, performs a simulation considering an equilibrium approach profile to estimate tube length, heat transfer

coefficient and wall temperature profiles. The second step, “rating mode”, uses these results as input to simulate the reformer with kinetic expression. Physical data are updated at every section along the axial position to account for changes of temperature and composition with the reaction progress. The principal target of this work is a steam reforming furnace design, with reference to the furnace characteristics described in Section 2 and to the operating conditions shown in Table 1. According to these inputs, the furnace design has been optimized with respect to the catalytic tube life. The optimum fuel distribution among burners at different elevation has been evaluated to achieve the required conversions with suitable metal skin temperatures. In particular, as shown in Table 3, the fuel is not uniformly distributed among the burners. This model can be used with different operating conditions and structure parameters. In the event that alloy steel tubes with higher creep limits are available in the future, the model will be able to estimate the relevant fuel distribution. A further development could be the extension of the model to simulate the reaction zone with a two-dimensional heterogeneous reactor model.

Notation fire box surface area, m2. flame surface area, m2. cold equivalent surface area, m2. tube wall surface area, m2. activity of component i. a2,j coefficients for emissivity estimation of component j. B parameter for heat transfer coefficient (Eq. (9)). corrective factor for carbon dioxide. CC Egber factor. CSO corrective factor for water. CW specific heat of component i, kJ kmol− 1 K− 1. cP,i process gas specific heat, kJ kmol− 1 K− 1. cPmix equivalent diameter of catalyst pellets, m. dP F radiative exchange factor. f friction factor. fugacity of component i. fî fi0 standard fugacity of component i. G mass velocity of process gas, kg s− 1 m− 2. 0 standard enthalpy of formation of component i, kJ ΔHF,i kmol− 1. ΔH0R(T) standard enthalpy of reaction, kJ kmol− 1. convective heat transfer coefficient for flue gas, kJ hC h− 1 m− 2 K− 1. centre to centre distance, m. iT equilibrium constant for Eq. (19), Pa2. K1 equilibrium constant for Eq. (20). K2 equilibrium constant for Eq. (21), Pa2. K3 rate coefficient for Eq. (19), kmol Pa0.5 kg− 1 h− 1. k1 rate coefficient for Eq. (20), kmol Pa− 1 kg− 1 h− 1. k2 k3 rate coefficient for Eq. (21), kmol Pa0.5 kg− 1 h− 1. eq reaction equilibrium constant. K process gas thermal conductivity, kJ h− 1 m− 1 K− 1. KG adsorption equilibrium constants, Pa− 1 (dimensionKi less for i = H2O). L mean beam length, m. l tube height, m. A Af Ape AT ai a0,j, a1,j,


Mf

burned molar flow rate at generic element in furnace chamber, kmol h− 1. in inlet molar flow rate at generic element in furnace MG chamber, kmol h− 1. out outlet molar flow rate at generic element in furnace MG chamber, kmol h− 1. number of burners. Nb number of tubes. NT molar flow rate of component i, kmol h− 1. ni 0 inlet molar flow rate of component i, kmol h− 1. ni total molar flow rate of process gas, kmol h− 1. nTOT in inlet molar flow rate at generic element in catalytic nTOT tube, kmol h− 1. P total pressure of process gas, Pa. partial pressure of component i, Pa. pi cP AG Prandtl number for process gas. Pr ¼ KG Q heat duty of a single element in catalytic tube, kJ h− 1. convective heat transfer rate, kJ h− 1. QC heat transfer rate due to flame zones, kJ h− 1. Qf radiative heat transfer rate, kJ h− 1. QR kinetic rate of reaction for Eq. 1, kmol m− 3 h− 1. R1 kinetic rate of reaction for Eq. 2, kmol m− 3 h− 1. R2 R3 kinetic rate of reaction for Eq. 3, kmol m− 3 h− 1. r inner tube radius, m. d G Reynolds number for process gas. Re ¼ P AG T process gas temperature, K. adiabatic flame temperature, K. Tf flue gas temperature, K. TG process gas inlet temperature at generic element in T in catalytic tube, K. process gas outlet temperature at generic element in T out catalytic tube, K. in process gas inlet temperature at generic element in TG furnace chamber, K. out process gas outlet temperature at generic element in TG furnace chamber, K. tube wall temperature, K. TT U heat transfer coefficient inside the catalytic tube, kJ h− 1 m− 2 K− 1. V fire box volume, m3. molar fraction of component i. yi z axial coordinate for catalytic tube, m.

Greek letters a εT η εj ni n0 n¼ m i i εf εG /ˆ I ρ ρG µG σ εV k

adsorption efficiency factor. catalytic tube emissivity. effectiveness factor. emissivity of component j. extent of reaction, kmol h− 1 flame emissivity. flue gas emissivity. fugacity coefficient of component i. process gas apparent mean density, kmol m− 3. process gas density, kg m− 3. process gas viscosity, kg m− 1 h− 1. Stefan–Boltzmann constant, kJ h− 1 m− 2 K− 4. void fraction. parameter for emissivity estimation of component j.

ν

sum of νi.

νi

stoichiometric coefficient of component i.

631

Subscripts i

CH4, H2O, H2, CO, CO2 in process gas.

j SR WGS

CO2, H2O in flue gas. steam reforming reaction. water gas shift reaction.

Acknowledgements The authors wish to acknowledgement Dr. Davide Carassai and Dr. Chiara Olevano, process engineers in Technip-KTI, and Dr. Andrea Pichelli, researcher at Macquarie University of Sydney, who contributed to this work.

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