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Hydrogen Production via Low Temperature Water Gas Shift Reaction: Kinetic Study, Mathematical Modeling, Simulation and Optimization of Catalytic Fixed Bed Reactor using gPROMS

Davood Mohammady Maklavany, Ahmad Shariati, Mohammad Reza Khosravi-Nikou and Behrooz Roozbehani

Abstract

The kinetics study, modeling, simulation and optimization of water gas shift reaction were performed in a catalytic fixed bed reactor. The renowned empirical power law rate model was used as rate equation and fitted to experimental data to estimate the kinetics parameters using gPROMS. A good fit between predicted and experimental CO conversion data was obtained. The validity of the kinetic model was then checked by simulation of plug flow reactor which shows a good agreement between experimental and predicted values of the reaction rate. Subsequently, considering axial dispersion, a homogeneous model was developed for simulation of the water-gas shift reactor. The simulation results were also validated by checking the pressure drop of the reactor as well as the mass concentration at equilibrium. Finally, a multi-objective optimization was conducted for water-gas shift reaction in order to maximize hydrogen formation and carbon monoxide conversion, whereas the reactor volume to be minimized. Implementation of optimal controls leads to increase in hydrogen formation at reactor outlet up to 25.55 %.

Appendices

A.1 Heat of reaction

The heat of reaction, also named enthalpy change of reaction, is defined as follows [3]:

(35)ΔHr,T=ΔHr,298K+T=298TΔCpTdT

For the water-gas shift reaction

(36)ΔHr,TJmol=41100+T=298KTCp,CO2+Cp,H2Cp,CO+Cp,H2OdT
(37)ΔHr,TJmol=4.193164204×108+15464.04×T2.24478×T2+9.677496×108T

Heat capacity (Cp,i) data are shown in Table 5 [4]:

Table 5:

Gas phase heat capacity constants.

SpeciesABCD
CO6.601.20×10300
CO210.342.74×10301.955×105
H26.620.81×10300
H2O8.220.15×1031.34×1060
N26.501.00×10300

It should be noted that corresponding equation to calculate Cp,i is as follows:

(38)Cp,i=A+BT+CT2+DT2

there, T is in Kelvin and Cp,i is in cal/mol-Kelvin.

A.2 Correlations for transport parameters

A.2.1 Effective Diffusion Coefficient

The effective mass diffusion coefficient is expressed [43]:

(39)Deff,i=εbτDi,mix

Where Deff,i and Di,mix are effective and molecular diffusion coefficients of species i , εb is bed porosity, and τ is the tortuosity factor.

A.2.2 Axial diffusion coefficient

The effective axial diffusivity coefficient can be estimated by [44]:

(40)Dax,i=0.73Di,mix+0.5usDp1+9.49Di,mixusDp

where us is superficial velocity, and Dp is catalyst particle diameter.

A.2.1 Effective thermal conductivity

The effective thermal conductivity is calculated by [45]:

(41)λeffλg=εb+1εb0.139εb0.0339+6.667λg+0.75εbPrRep

where Pr is the Prandtl number Pr=Cpμ/λg.

A.3 Physical properties and mixing rules

A.3.1 Gas diffusivity

Binary gas phase diffusivities for a wide range of temperatures and pressures applicable are estimated through published correlations detailed in Table 6 [46].

Table 6:

Binary gas diffusivity for component pairs.

PairABCDEFEq.
H2–CO15.39×1031.5480.316×1081–2.80106743
H2–CO23.14×1051.75011.7043
H2–H2O1.02044
H2-N26.007×103–1.02045
CO–CO23.15×1051.570113.6043
CO–H2O0.187×1052.07200043
CO–N200.32245
CO2–H2O9.24×1051.50307.9043
CO2–N23.15×1051.570113.6043
H2O–N20.187×1052.07200043

It should be noted that:

(42)Dij=Dji

Equations a, b, and c are as follow:

(43)Dij=ATBPlnCT2DexpETFT2
(44)Dij=BP
(45)Dij=AT+BP

Here, T is in Kelvin, P is in atm, and Dij is in cm2/sec.

Gas diffusion in the mixture can be approximated by [4]:

(46)Di,mix=1yijij=1NyiDeff,ij

where Di,mix is diffusivity of species i in the mixture, and yi is the mole fraction of species i .

A.3.2 Gas phase viscosity

Useful correlation data for gas phase viscosity are shown in Table 7 [46].

Table 7:

Gas phase viscosity constants.

SpeciesABCD
CO1.1127×1060.533894.70
CO22.148×1060.462900
H21.797×1070.685–0.59140
H2O1.7096×1081.11460
N26.5592×1070.608154.7140

It should be noted that corresponding equation to calculate μi is as follows:

(47)μi=ATB1+CT1+DT2

Where, T is in Kelvin and μiis in N-sec/m2.

The viscosity of the gas phase mixtures is estimated by [13]:

(48)μ=i=1Nyiμij=1NyjMjMi

where μ is the mixture viscosity, μi is the viscosity of species i , and Mj is the molecular weight of species j .

A.3.3. Gas phase thermal conductivity

The thermal conductivity of components as well as are calculated using the Euckan’s formula as [4]:

(49)λi=μi4.189×104Cpi2.394×104+2.48Mi

The thermal conductivity of the mixture is calculated using [4]:

(50)λg=iλiyiMi3iyiMi3

A.3.4. Gas phase thermal conductivity

The heat capacity of the mixture (Cp) is taken as the molar average of the gas component heat capacity.

(51)Cp=iyiCp,i

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Received: 2016-8-31
Revised: 2017-1-6
Accepted: 2017-1-23
Published Online: 2017-3-23

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