# Modeling and simulation of an industrial secondary reformer reactor in the fertilizer plants

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## Abstract

In this paper, the industrial secondary reformer reactor has been modeled and simulated at steady-state operation conditions. It aims to modify a complete mathematical model of the secondary reformer design. The secondary reformer is a part of a subprocess in a higher scale unit of ammonia synthesis. It is located after the primary reformer in the ammonia plant where it is used in the synthesis of ammonia. The reactions in the secondary reformer reactor are assumed to be carried inside two reactors in series. The first reactor, upper section, is the combustion zone, while the second reactor, bottom section, is the catalyst zone with nickel catalyst based on the alumina. In order to create a reactor design model for the secondary reformer in the industrial ammonia plant, combustion and catalyst zones have been studied. The temperature and compositions of gas in the combustion zone are predicted using the atomic molar balance and adiabatic flame temperature model. In the catalyst zone, the temperature and composition profiles along the axial distance are predicted using a one-dimensional heterogeneous catalytic reaction model with the assumption that the reactions are first order in methane partial pressure.

Most of the methane is converted in the part of one fourth to one half of the catalyst zone length from inlet to outlet. The temperature gradient between the gas and catalyst surface decreases along the axial distance, and both temperatures approach the same value at the bottom of the catalyst bed. Finally, the results of this simulation have been compared with the industrial data taken from the existing ammonia unit in the State Company of Fertilizers South Region in the Basra/Iraq, which show a relatively good compatibility.

### Keywords

Ammonia Autothermal reformer Steam reforming Reforming reactions Hydrogen production### Abbreviations

- CDR
carbon dioxide reforming reaction

- SCFSR
State Company of Fertilizers South Region

- SMR
methane steam reforming reaction

- WGS
water-gas shift reaction.

## Background

_{2}will be produced through this section. The partially oxidized gas passes through the catalyst zone to produce the hydrogen, and it is provided with a Ni/MgAl

_{2}O

_{4}catalyst inside the reactor shell. Finally, the reformat gases leave the secondary reformer through the outlet nozzle at the bottom of the secondary reformer reactor.

The results of previous studies by various researchers mainly by Ebrahimi et al. [1], Khorsand and Deghan [2], Yu [3], Raghunandaqnan and Reddy [4], and Ravi et al. [5] have included the design and evaluation of the performance of a secondary reformer with different parameters.

Mathematical models which combine the predictions of the overall consumption of the reactants with a prediction of the product distribution are very scarce for the secondary reformer in literature. Only few research groups studied the combustion zone in the secondary reformer reactor explicitly. One reason might be the unavailability of the mechanism of methane and hydrogen combustion in the literature due to the wide distribution of detailed mechanisms for the combustion of natural gas only, which consists mainly of methane. Therefore, numerous researchers focused attention on the autothermal reformer which represented a stand-alone process wherein the entire natural gas conversion is carried out by an internal combustion with oxygen as presented by Amirshaghaghi et al. [6], Li et al. [7], Pina and Borio [8], Skukri et al. [9], and Hoang and Chan [10].

Conversional technology employs a single reactor and single nickel catalyst, but in this study, the reactor is divided into two reactors in series. The first reactor, upper section, is the combustion zone that is filled with inert gases from the primary reformer without catalyst; the combustion is carried out by adding an air stream, not oxygen as in the previous studies in autothermal reformer; in the second reactor, bottom section, which is the catalyst zone filled with nickel catalyst, the classic reforming reactions occur. The originality of the work lies in this proposal.

The results of the mathematical model such as mole fraction, temperature profile, and pressure drop of the combustion and catalyst zones will be compared relative to the industrial values taken from the secondary reformer reactor in the State Company of Fertilizers South Region (SCFSR) in the Basra/Iraq to show the degree of accuracy.

## Methods

### Mathematical model of combustion zone

_{2}will be converted to H

_{2}O in the combustion zone. The overall reaction mechanism of methane and hydrogen with oxygen in the combustion zone can be considered as follows:

An input–output model of the combustion zone based on global mass and energy balances using a simple mathematical model consists of atomic molar balance and adiabatic flame temperature with the assumption that the feed and inlet air to the reactor are fully mixed along the flame, that complete oxygen consumption is considered, and that the conditions inside and outside of the combustion zone are equal.

where *F*_{IN,1} is the molar flow rate of inlet process gases in the stream number.1 (kmol/h), *F*_{IN,2} is the molar flow rate of inlet air in the stream number 2 (kmol/h), *F*_{OUT} is the molar flow rate of each gas from the combustion zone (kmol/h), *F*_{tot} is the total molar flow rate of outlet gases from the combustion zone (kmol/h).

where, Δ*H* is the enthalpy change (kJ/kmol), *F* is the molar flow rate (kmol/h), *H*_{i} is the specific enthalpy of the *i*-component (kJ/kmol).

### Mathematical model of catalyst zone

_{2}O

_{4}catalyst are based on a Langmuir-Hinshelwood reaction mechanism in which rate expressions can be described by the following equations [11]:

where *R*_{k} is the rate of reaction for reaction *k* (kmol/kg_{cat}·h), *k*_{k} is the constant of reaction rate for reaction *k* (accordant to the Arrhenius constant), *K*_{e,k} is the equilibrium constant for reaction *k* (bar^{2}), *K*_{ad,i} is the adsorption coefficient of the *i*-component (accordant to the unit of pre-exponential factor for adsorption of *i*-component *A*_{ad,i}), DEN is the denominator in the expressions for the reaction rates (dimensionless unit), and *P*_{i} is the partial pressure of *i*-components (bar).

where *η*_{k} is the reaction effectiveness factor for reaction *k* (dimensionless unit) and the *Φ* Thiele modules (dimensionless unit).

*D*

_{s}/6, as noted by previous researchers including Rostrup-Nielsen and Froment and Bischoff [12]:

*D*

_{S}is the equivalent pellet diameter (m). This is defined as the diameter of a sphere with the same external surface area per unit volume of the catalyst pellet, ${D}_{s}=6.(1-{\u03f5}_{B})/{S}_{B}$; where, the

*S*

_{B}is the specific surface area of bed (m

^{3}/m

^{2}) and, the

*S*is the specific surface area of pellet (m

^{3}/m

^{2}), the A

_{p}is surface area of pellet while, v

_{p}is the volume of pellet ϵ

_{B}is the porosity of packed bed (m

^{3}

_{void}/m

^{3}

_{r}).

*k*

_{υ,k}is the volumetric kinetic constant for reaction

*k*(to convert the unit of constant of reaction rate) (m

^{3}/Kg

_{cat}·h).

*ρ*

_{b}is the bulk density (kg/m

^{3}).The effective diffusivity of the

*i*-component for reaction

*k*is defined as follows [3]:

where *D*_{e,k} is the effective diffusivity of reaction *k* (m^{2}/h). *D*_{i,mix} is the molecular diffusivity of the *i*-component (m^{2}/h). *D*_{Kn,I} is the Knudsen diffusivity (m^{2}/h).

*i*-component and heat balance in axial direction based on an adiabatic one-dimensional heterogeneous catalytic reaction model can be described by the following equation [3]:

*ℓ*corresponds to axial coordinates (m) and

*υ*

_{i}is the stoichiometric coefficient of the

*i*- component in the chemical reaction equations (dimensionless unit).

*ρ*

_{c}is the density of catalyst (kgc/m

_{r}

^{3}),

*A*is the cross section area (m

^{2}). The change in the temperature throughout the reactor length has been given as follows [12]:

where *F*_{g} is the molar flow rate of gases in the catalyst zone (kmol/h), *C*_{P} is the specific heat capacity (kJ/kmol·K), *T* is the temperature of gases (K), Δ*H*^{o}_{r,k} is the standard heat of reaction *k* (kJ/mol), and *ρ*_{g} is the density of gases (kg/m^{3}).

where *T*_{s} is the temperature surface of the catalyst (K) and *h* is the heat transfer coefficient (kJ/m^{2}·K·h) which is represented as *h* = (Nu·K/*D*_{S}).

where *K* is the thermal conductivity of gases (W/m·K), *C*_{P} is the specific heat capacity (kJ/kg·K), *M*_{wt} is the molecular weight of gases (kg/kmol), and *μ*_{g} is the viscosity of gases (Pa·s).

where *Nu* is the Nusselt number (dimensionless unit), *Pr* is Prandtl’s number (dimensionless unit), and *Re*_{p} is the Reynolds number of a particle (dimensionless unit).

where *P* is the pressure of gases (bar), *u* is the velocity of gases (m/h) $u=Q/A$,and *Q* is the volumetric flow rate (m^{3}/h).

#### Solution procedure

The solution starts with an assumption of the initial total molar flow rate of outlet gases (*F*_{tot}) of the combustion zone. Chemical compositions and temperature are calculated using the atomic molar balance and the adiabatic flame temperature equations. Consequently, the final calculation results will be used as input data to the catalytic zone. The reaction rate equations are used with mass and heat balance to determine the temperature and composition profile for each component as a function of reactor length in the catalyst zone. The set of differential equations will be solved using the numerical analysis, Euler method. The iteration calculation will apply and repeat until the molar fraction calculation and reaction temperature will agree with the industrial value. Otherwise, a new guessing value of the total molar flow rates of outlet gases from the combustion zone will be assumed.

## Results and discussion

### Combustion zone

**Actual operations conditions of industrial secondary reformer in SCFSR in Basra/Iraq**[15]

Parameters | Input feed process gas Stream 1 | Input air Stream 2 |
---|---|---|

Temperature (°C) | 795 | 550 |

Pressure (bar) | 32 | 32 |

Molar flow rates of the components (kmol/h) | ||

CH | 426.040 | - |

H | 3,684.010 | 11.190 |

H | 2,932.100 | - |

CO | 403.460 | - |

CO | 537.440 | 0.520 |

N | 15.990 | 1,357.360 |

Ar | 5.830 | 16.350 |

O | - | 365.080 |

**Output data of the industrial secondary reformer and simulation**[15]

Parameters | Output of combustion zone (simulation data) | Output of secondary reformer(simulation data) | Output of secondary reformer (plant data) |
---|---|---|---|

Temperature (°C) | 1,096.644 | 1,009.630 | 969 |

Pressure (bar) | 32 | 31.918 | 31.570 |

Mole flow rates (kmol/h) of the components | |||

CH | 183.698 | 19.001 | 18.640 |

H | 4,182.983 | 3,985.640 | 3,992.350 |

H | 2,929.004 | 3,455.730 | 3,449.710 |

CO | 645.806 | 777.861 | 785.200 |

CO | 537.947 | 570.589 | 563.600 |

N | 1,373.380 | 1,373.380 | 1,373.360 |

Ar | 22.180 | 22.180 | 22.180 |

O | - | - | - |

Total molar flow rate (kmol/h) | 9,875 | 10,204.400 | 10,205.504 |

H | 2.132 | 2.516 | 2.511 |

(CO + H | 2.602 | 3.082 | 3.083 |

### Catalyst zone

In this section, the influence of temperature has been discussed for describing the effect of these parameters on the design of the secondary reformer relative to Basra Fertilizer Plant.

The effectiveness factor is an important parameter to predict the temperature and composition profiles for realizing the actual reaction rate with pore diffusion.

The theoretical results’ prediction from the mathematical model has been compared with the industrial data collected from the manual and daily log sheet of the Basra Fertilizer Plant as summarized in Table 2. The results depicted high accuracy between simulation results and plant data.

The sharp increase in the H_{2} content is mainly explained by SMR and CDR as shown in Figure 3 along the catalyst bed. Thus, the hydrogen production is dominated by chemical reactions in Equations 10 and 12.

The sharp increase in CO along the reactor length occurred due to the methane steam reforming and water-gas shift reactions as shown in Figure 3 relative to the chemical reactions in Equations 10 and 11.

The CO_{2} generation is described by the reactions of water-gas shift and carbon dioxide reforming as mentioned in Equations 11 and 12. The increase in CO_{2} production occurred due to carbon dioxide reforming as shown in Figure 3. Then, the decline occurred due to CO_{2} which was consumed by the water-gas shift reaction because of the inversion of the water-gas shift reaction inside the catalyst particles. (It’s negative along the axial distance from the top of the bed). Nitrogen and argon are constant along the reactor length because neither nitrogen nor argon reacted with any other components.

In the gas phase of the packed bed catalytic reaction system, pressure drop is one of the important parameters. From a practical point of view, the value of the pressure drop gives a good indication about catalyst performance inside the reaction shell. There are many reasons for the increase of pressure drop, for example, with a long time of operation; the catalyst may be thermal cracking due to the high operation temperature, so the value of pressure drop will increase.

## Experimental

In this section, the analysis of inlet and outlet synthesis process gases for the industrial secondary reformer reactor in Basra Fertilizer Plant has been carried out. The experimental part will investigate, specify, and tabulate the actual operation conditions of the industrial secondary reformer as summarized in Table 1.

Currently, describing the industrial secondary reformer reactor at Basra Fertilizer Plant, the industrial catalyst and the operation conditions must be understood with more details.

^{3}to protect the catalyst. The nickel catalysts, RKS-2, with one hole are packed with a volume of 26 m

^{3}; the height of the catalyst bed is 2.8 m as depicted in Table 3. The catalyst is supported by a ceramic ball and cone made of high alumina bricks which are comprised of bricks with slot holes that provide a highly stable support for the catalyst which bears the catalyst weight. The catalyst support is covered with alumina balls of 40 mm with heights of 300 mm, 75 mm, and 120 mm and with volumes of 2.800, 4.100, and 4.100 m

^{3}, respectively.

**Physical characteristic of the catalyst**[15]

Catalyst pellet | |
---|---|

Model name | RKS-2 |

Shape | Rings |

Nominal Size: OD × ID × H | 19 × 9 × 19 mm |

Chemical composition | |

NiO wt.% | 9% |

MgAl | Balance |

Filling density | 1.070 Kg/L |

## Conclusion

The secondary reformer for hydrogen and nitrogen production is mathematically investigated by a series of simulation of operation conditions which have been collected from the documents of Basra Fertilizer Plant.

A mathematical model of the industrial secondary reformer in Basra Fertilizer Plant with all assumptions made had been completed. The theoretical results obtained have been compared with the industrial secondary reformer reactor details. The results show a good compatibility as shown in Table 2. The model predicts the temperature and composition profiles of the gas that leaves the combustion chamber and investigates the temperature and concentration gradient inside the catalyst particle. The value of pressure drop depicts low values along the axial distance of the catalyst bed; therefore, pressure drop can be assumed negligible. The overall reaction rate is mainly controlled by the diffusion rate. In the catalyst zone entrance, methane steam reforming and carbon dioxide reforming reaction rates at the catalyst zone inlet were considerably higher than the water-gas shift reaction. The diffusion into the pellet is relatively slow so that these conditions’ mean reaction occurs before the reactant has diffused far into the pellet. The effectiveness factor < <1 means that only the surface near from the outer surrounding of the pellet is effective; therefore, the diffusion and effectiveness factor gave a good indication about the shape of the catalyst that is used in the catalyst zone as a ring without a central portion because the chemical reaction takes place at the outer surface. Finally, this simulation model depicts a high reliability for the designing and testing of an industrial secondary reformer, not for Basra Fertilizer Plant, but it is extended to any secondary reformer reactor in fertilizer plants.

## Acknowledgement

We acknowledge the full cooperation of the State Company Fertilizer Plant South Region in Basra/Iraq to introduce the industrial data for this investigation.

## Supplementary material

## Copyright information

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.