# Numerical Modeling and Performance Prediction of COS Hydrolysis Reactor in an Integrated Gasification Fuel Cell in terms of Thermo-Chemical Transport Phenomena

^{*}

## Abstract

**:**

_{2}S and COS. The most significant design parameters affecting performance of the COS hydrolysis reactor were selected to be gas hourly space velocity (GHSV), reaction temperature, and length ratio, and numerical modeling was performed considering heat and fluid flow transfer as well as chemical reaction kinetics. Effect of the selected design parameters on the variation of conversion rate and reactant gas mixture concentration were comprehensively investigated to predict performance of the COS hydrolysis reactor. Stochastic modeling of reactor performance was finally performed using Monte Carlo simulation and linear regression fitting.

## 1. Introduction

_{2}S, carbonyl sulfide (COS)), particulates, minute quantities of HCl, NH

_{3}, and heavy metal elements. These inherently undesirable constituents should be properly removed for the subsequent operation of fuel cells installed downstream. A series of apparatuses are used to remove acidic gases, and a COS hydrolysis reactor is presently selected for numerical modeling to estimate its performance in terms of operational and geometrical parameters.

_{2}O

_{3}catalyst, and Ni and Zn were found to have the best properties [5]. Bachelier et al. investigated catalytic activity of various oxide catalysts (Z

_{r}O

_{2}, TiO

_{2}, Al

_{2}O

_{3}) [6]. Shishao et al. also performed COS hydrolysis studies, especially related to its advancement on catalytically active areas of alkali metal oxides at 45–100 °C [7]. Wang et al. studied how to improve catalytic activity of Al

_{2}O

_{3}under low humidity conditions as well as how to remove COS by adsorption [8]. Similar adsorption of COS on activated carbon was also investigated by Wang et al. [9,10]. They also efficiently performed COS removal using a metallic catalyst and activated carbon. Wang et al. evaluated adsorption and desorption of low concentrations of carbonyl sulfide by impregnating active carbon [11]. Yi et al. investigated the effects of catalyst composition on catalytic hydrolysis of COS [12]. Ping et al. evaluated the effects of Fe/Cu/Ce loading on the coal-based activated carbons for COS hydrolysis [13]. Sun et al. performed a study on catalytic hydrolysis of carbonyl sulfide and carbon disulfide over an Al

_{2}O

_{3}-K/CAC catalyst at low temperature [14]. COS hydrolysis using noble metal catalysts was also performed by Zhang et al. [15] and Yang et al. [16] who evaluated the catalytic removal efficiency of such noble metal catalysts.

## 2. Numerical Model Development

#### 2.1. COS Hydrolysis Reactor Model

- ➢
- Mass conservation equation$$\frac{\partial \rho}{\partial t}+\nabla \cdot \left(\rho \overrightarrow{u}\right)=0$$
- ➢
- Momentum conservation equation$$\frac{\partial \left(\rho \overrightarrow{u}\right)}{\partial t}+\nabla \cdot \left(\rho \overrightarrow{u}\overrightarrow{u}\right)=-\nabla p+\nabla \cdot \left(\mu \nabla \overrightarrow{u}\right)$$
- ➢
- Transport equation for κ (standard k-ε model)$$\frac{\partial \left(\rho k\right)}{\partial t}+\nabla \cdot \left(\rho k\overrightarrow{u}\right)=\nabla \cdot \left[\left(\mu +\frac{{\mu}_{t}}{{\sigma}_{k}}\right)\nabla k\right]+{G}_{k}+{G}_{b}-\rho \epsilon $$
- ➢
- Transport equation for ε (standard k-ε model)$$\frac{\partial \left(\rho \epsilon \right)}{\partial t}+\nabla \cdot \left(\rho \epsilon \overrightarrow{u}\right)=\nabla \cdot \left[\left(\mu +\frac{{\mu}_{t}}{{\sigma}_{\epsilon}}\right)\nabla \epsilon \right]+{C}_{1\epsilon}\frac{\epsilon}{k}\left({G}_{k}+{G}_{3\epsilon}{G}_{b}\right)+{C}_{2\epsilon}\rho \frac{{\epsilon}^{2}}{k}$$
- ➢
- Energy conservation equation$$\frac{\partial \left(\rho {C}_{p}T\right)}{\partial t}+\nabla \cdot \left(\rho {C}_{p}T\right)=\nabla \cdot \left({k}_{eff}\nabla T\right)+{S}_{e}$$
- ➢
- Species transport equation$$\frac{\partial \left({C}_{k}\right)}{\partial t}+\nabla \cdot \left({C}_{k}\overrightarrow{u}\right)=\nabla \cdot \left({D}_{k}\nabla {C}_{k}\right)+{S}_{k}$$

#### 2.2. Kinetics and Mathematical Model of Catalyst Bed

_{2}O

_{3}and its high catalyzing area enabled improved reaction efficiency.

- ➢
- Ergun Equation (Porous Medium)$$\frac{dP}{dL}=\frac{150\mu {\left(1-\phi \right)}^{2}}{{\theta}^{2}{D}_{cat}^{2}{\phi}^{3}}\overrightarrow{u}+\frac{1.75\rho \left(1-\phi \right)}{\theta {D}_{cat}^{}{\phi}^{3}}{\overrightarrow{u}}^{2}$$

- ➢
- Kinetics of COS hydrolysis reaction (Kaiser 201)$$COS+{H}_{2}O\to C{O}_{2}+{H}_{2}S$$$$-{r}_{\mathrm{cos}}={k}_{1}^{}{K}_{3}\frac{{P}_{\mathrm{cos}}{P}_{{H}_{2}O}}{1+{K}_{3}{P}_{{H}_{2}O}}$$$${k}_{1}^{}=\mathrm{exp}\left(0.835-\frac{3.039\times {10}^{3}}{T}\right)$$$${K}_{3}^{}=\mathrm{exp}\left(-15.89+\frac{1.001\times {10}^{4}}{T}\right)$$

#### 2.3. Properties and Boundary Conditions of the COS Hydrolysis Reactor

- ➢
- Binary-Diffusivity$${D}_{12}=\frac{0.01013{T}^{1.75}{\left(\frac{1}{{M}_{1}}+\frac{1}{{M}_{2}}\right)}^{0.5}}{P{\left[{\left(\sum {\nu}_{1}\right)}^{1/3}+{\left(\sum {\nu}_{2}\right)}^{1/3}\right]}^{2}}$$

^{3}/h was converted to velocity, which was varied to estimate its effect on reactor performance. Inlet gas temperature and chemical composition were specified considering the overall Integrated Gasification Fuel Cell (IGFC) process gas temperature and composition; the gas temperature was also carefully cross-checked with variations of the internal heater temperature.

#### 2.4. Numerical Procedures

^{−5}of relative uncertainty level.

## 3. Results and Discussion

_{2}O) gases, highest concentration at the inlet of the catalytic layer, and gradual reduction in concentration with passage into the porous catalytic layer. The reactant flow is concentrated into the central portion of the catalytic layer by the inlet tube and renders a slow reaction rate caused by low thermal energy from the external heater. Reactant concentration is thus maintained at a high level, and this effect becomes insignificant with passage into the reaction area. On the other hand, H

_{2}S and CO

_{2}product gas concentration increases with passage into the catalytic reaction area. The reaction rate of the reactants renders a low concentration at the central region and this effect is gradually cancelled with passage into the outlet. Figure 5c graphically illustrates reactant concentration, products concentration, and temperature variation at the center of the reactor. The reactants’ concentration rapidly decreases as they pass the reaction zone, while proportionately increasing the products’ concentration.

^{−1}, 0.884–7.062, and 543–603 K, respectively. Variation ranges were taken as a 3σ level considering reasonably efficient reactor performance and normal distribution with relevant average and standard deviation values, as listed in Table 5. Table 6 lists the distribution of individual performance parameters obtained by using normalization of individual performance parameters as specified in Table 5.

## 4. Conclusions

- With other parameters fixed, the COS conversion rate decreased with increased GHSV. This is attributed to the increased reactant amount afforded by the higher GHSV, thus decreasing the conversion rate of COS.
- The COS conversion rate increased by 9.2% with a longer length ratio under the same GHSV and reactor tube wall temperature. This is caused by the more facile heat transfer and gas diffusion along and inside of a reactor tube with a larger length ratio.
- The COS conversion rate increased by a maximum of 19.3% with increased reactor wall temperature with the GHSV and length ratio unchanged. However, this results in a higher energy cost, and a more efficient setting of temperature is needed.
- A Monte Carlo simulation was performed under a 3σ level for more stable and reliable operation control, and operational process efficiency was modeled within an individual parameter variation range. This confirmed the maximum possible COS conversion rate of 95% with a reliability level of 98.9%.
- Within the limit of sensitivity evaluation of individual parameters, temperature was rated as the most sensitive (57.3%) with GHSV as the next most sensitive (−38.6%) parameter.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${C}_{p}$ | specific heat, J/kg-K |

${C}_{k}$ | mass fraction of each species |

${C}_{1\epsilon}$ | constant |

${C}_{2\epsilon}$ | constant |

${C}_{3\epsilon}$ | constant |

${D}_{bed}$ | diameter of reactor, m |

${D}_{cat}$ | diameter of catalyst, m |

${D}_{k}$ | diffusivity of each species, m^{2}/s |

$E$ | activation energy, kJ/mol |

${G}_{b}$ | production of turbulence kinetic energy due to buoyancy, kg/s^{3}-m |

${G}_{k}$ | production of turbulence kinetic energy due to the mean velocity gradient, kg/s^{3}-m |

${H}_{bed}$ | length of reactor, m |

$k$ | turbulence kinetic energy, m^{2}/s^{2} |

${k}_{eff}$ | effective conductivity, W/m-K |

${k}_{1}$ | constant |

${K}_{3}$ | constant |

$M$ | molar weight, g/mol |

$P$ | pressure, Pa |

${P}_{COS}$ | partial pressure of COS, Pa |

${P}_{{H}_{2}O}$ | partial pressure of H_{2}O, Pa |

${r}_{COS}$ | reaction rate of COS, mol/h-g |

${S}_{e}$ | heat source, W/m^{3} |

${S}_{k}$ | source term of each species, kg/m^{3}-s |

$t$ | time, s |

$T$ | temperature, K |

$\overrightarrow{u}$ | velocity, m/s |

${V}_{inlet}$ | velocity of inlet, m/s |

$\epsilon $ | dissipation rate of turbulent kinetic energy, m^{2}/s^{3} |

$\theta $ | sphericity |

$\mu $ | viscosity, Pa-s |

${\mu}_{t}$ | turbulent viscosity, Pa-s |

$v$ | group contribution value |

$\rho $ | density, kg/m^{3} |

${\sigma}_{k}$ | turbulent Prandtl number for k |

${\sigma}_{\epsilon}$ | turbulent Prandtl number for ε |

$\phi $ | porosity |

## References

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**Figure 4.**Predicted results of the COS hydrolysis reactor; (

**a**) pressure, (

**b**) velocity, (

**c**) temperature (Gas Hourly Space Velocity (GHSV) = 1.0, length ratio = 1.0, Temperature = 573 K).

**Figure 5.**Predicted results of the COS hydrolysis reactor; (

**a**) reactant, (

**b**) product, (

**c**) concentration profiles (GHSV = 1.0, length ratio = 1.0, Temperature = 573 K).

**Figure 6.**Predicted results of the COS hydrolysis reactor according to GHSV; (

**a**) COS conversion rate, (

**b**) COS concentration and temperature profiles.

**Figure 7.**Predicted results of the COS hydrolysis reactor according to length ratio; (

**a**) COS conversion rate, (

**b**) COS concentration and temperature profiles.

**Figure 8.**Predicted results of the COS hydrolysis reactor according to temperature; (

**a**) COS conversion rate, (

**b**) COS concentration and temperature profiles.

**Figure 9.**Comparison of the COS conversion rate between the proposed regression equation and the numerical data.

**Figure 10.**Probability distribution of the COS conversion rate and sensitivity of performance parameters in the COS hydrolysis reactor.

Description | Value | Unit |
---|---|---|

Shape | Sphere | - |

Diameter | 4.5–5.0 | mm |

Surface Area | 296 | m^{2}/g |

Al_{2}O_{3} | 93.60 | % (by wt.) |

SiO_{2} | 0.20 | % |

Fe_{2}O_{3} | 0.02 | % |

TiO_{2} | 0.02 | % |

Na_{2}O | 0.30 | % |

Description | Density [kg/m^{3}] | Viscosity [Pa-s] | Specific Heat [J/kg-K] | Thermal Conductivity [W/m-K] |
---|---|---|---|---|

H_{2} | 0.91 | 1.22 × 10^{−5} | 14,522 | 0.269 |

CO | 13.79 | 2.49 × 10^{−5} | 1071 | 0.038 |

H_{2}S | 17.48 | 2.06 × 10^{−5} | 1137 | 0.031 |

COS | 31.40 | 2.30 × 10^{−5} | 850 | 0.032 |

N_{2} | 13.78 | 2.53 × 10^{−5} | 1063 | 0.037 |

H_{2}O | 9.80 | 1.61 × 10^{−5} | 3169 | 0.042 |

Condition | Value | Unit | ||
---|---|---|---|---|

Inlet | Velocity | 4.9–19.6 | m/s | |

Temperature | 473 | K | ||

Mass Fraction | H_{2} | 0.019 | - | |

CO | 0.675 | - | ||

H_{2}S | 0.573 × 10^{−3} | - | ||

COS | 0.880 × 10^{−4} | - | ||

N_{2} | 0.156 | - | ||

H_{2}O | 0.031 | - | ||

CO_{2} | 0.117 | - | ||

Outlet | Pressure Outlet | - | - | |

Wall | Constant Temperature | 543–603 | K |

Case | Gas Hourly Space Velocity (GHSV) [h^{-1}] | Length Ratio [-] | Temperature [K] |
---|---|---|---|

1 | 29,214 | 0.35 | 543 |

2 | 573 | ||

3 | 603 | ||

4 | 1.00 | 543 | |

5 | 573 | ||

6 | 603 | ||

7 | 2.83 | 543 | |

8 | 573 | ||

9 | 603 | ||

10 | 58,429 | 0.35 | 543 |

11 | 573 | ||

12 | 603 | ||

13 | 1.00 | 543 | |

14 | 573 | ||

15 | 603 | ||

16 | 2.83 | 543 | |

17 | 573 | ||

18 | 603 | ||

19 | 116,858 | 0.35 | 543 |

20 | 573 | ||

21 | 603 | ||

22 | 1.00 | 543 | |

23 | 573 | ||

24 | 603 | ||

25 | 2.83 | 543 | |

26 | 573 | ||

27 | 603 |

Parameter | Mean Value | Standard Deviation | Distribution |
---|---|---|---|

GHSV [h^{−1}] | 12,500 | 833 | |

Length Ratio [-] | 3.97 | 1.03 | |

Temperature [K] | 573 | 10 |

Normalized Parameter | Mean Value | Standard Deviation | Distribution |
---|---|---|---|

A | 2.23 | 0.10 | |

B | 0.39 | 0.35 | |

C | 0.02 | 0.33 |

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**MDPI and ACS Style**

Noh, J.-H.; Ko, D.-S.; Lee, S.-J.; Hur, D.-J.
Numerical Modeling and Performance Prediction of COS Hydrolysis Reactor in an Integrated Gasification Fuel Cell in terms of Thermo-Chemical Transport Phenomena. *Appl. Sci.* **2018**, *8*, 1196.
https://doi.org/10.3390/app8071196

**AMA Style**

Noh J-H, Ko D-S, Lee S-J, Hur D-J.
Numerical Modeling and Performance Prediction of COS Hydrolysis Reactor in an Integrated Gasification Fuel Cell in terms of Thermo-Chemical Transport Phenomena. *Applied Sciences*. 2018; 8(7):1196.
https://doi.org/10.3390/app8071196

**Chicago/Turabian Style**

Noh, Jung-Hun, Dong-Shin Ko, Seung-Jong Lee, and Deog-Jae Hur.
2018. "Numerical Modeling and Performance Prediction of COS Hydrolysis Reactor in an Integrated Gasification Fuel Cell in terms of Thermo-Chemical Transport Phenomena" *Applied Sciences* 8, no. 7: 1196.
https://doi.org/10.3390/app8071196