Design of Isothermal Reactors

Journal Pre-proofs Water Gas Shift Reactor Modelling and New Dimensionless Number for Thermal Management/Design of Isothermal Reactors Fabian Rosner, Ashok Rao, Scott Samuelsen PII: DOI: Reference:

S1359-4311(19)37712-9 https://doi.org/10.1016/j.applthermaleng.2020.115033 ATE 115033

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

7 November 2019 14 January 2020 1 February 2020

Please cite this article as: F. Rosner, A. Rao, S. Samuelsen, Water Gas Shift Reactor Modelling and New Dimensionless Number for Thermal Management/Design of Isothermal Reactors, Applied Thermal Engineering (2020), doi: https://doi.org/10.1016/j.applthermaleng.2020.115033

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Advanced Power and Energy Program Manuscript

Manuscript for Applied Thermal Engineering http://www.apep.uci.edu

Water Gas Shift Reactor Modelling and New Dimensionless Number for Thermal Management/Design of Isothermal Reactors Fabian Rosner, Ashok Rao+ and Scott Samuelsen Advanced Power and Energy Program, University of California, Irvine, CA 92697-3550, USA

Highlights  

Simplified integration of power law kinetics into reactor model Simulation of isothermal WGS with internal heat transfer and steam generation





New dimensionless number is effective in optimizing reaction rates even under transport limitations Isothermal WGS can reduce catalyst volume by 57.5% versus adiabatic WGS

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Article Info

Abstract

________________________________________________

________________________________________________________________________________________________________________________________________________________________________

A new simplified modelling approach for using power law kinetics has been presented together with a methodology for modelling internal heat transfer inside the catalyst bed to a heat exchanger steam generator. The model has been validated and shown to be in Water Gas Shift good agreement with the performance of industrial scale water gas shift reactors. Power Law Kinetics Furthermore, a case study has shown that isothermal shifting is able to reduce the Carbon Deposition catalyst volume compared to adiabatic shifting, however, a strong dependency upon the cooling density is observed. The here introduced rate optimization number (Ro) which Adiabatic Reactor compares the impact of temperature on the thermal driving force to the chemical driving Isothermal Reactor force can help reactor designs to make effective use of the catalyst. For the water-gasReactor Size Optimization shift reaction, a value of -1 represents the optimum reaction rate. By designing the heat Rate Limitations exchanger in the isothermal shift reactor in accordance with the Ro number a reduction Process Intensification Strategy of the required catalyst volume from initially 112.1 m3 (adiabatic reference case) to Driving Force Optimization 54.9 m3 was possible; a reduction of 57.5%. The optimization with the Ro number has shown that an adiabatic inlet section is favorable and most of the cooling is needed after the adiabatic inlet length. The ideal temperature profile follows an almost linear temperature increase at the adiabatic inlet followed by an exponential decay along the reactor axis. Moreover, the application of the Ro number has shown to be highly accurate even under severe transport limitations. ____________________________________________________________________________________________________________________

Keywords:

1. Introduction Syngas has been a driver of economic growth from the beginning of the industrial revolution until today. In 1812 the London Gas, Light and Coke Company started distributing town gas, which was mainly composed of H2 and CO, for illumination and heating purposes to commercial and private customers. Since then commercial large-scale applications like the Haber-Bosch for NH3 synthesis in 1910, and for Methanol synthesis in 1923 have been developed which continue to play crucial role in today’s society. More recently integrated gasification + Corresponding Author: Tel.: +1 949 824 7302; Fax: +1 949 824 7423

E-mail address: [email protected]

combined cycles (IGCCs) and fuel cell technology aimed at reducing CO2 emissions have increased the interest in syngas generation coupled with the water gas shift (WGS) reaction. Also in the context of renewable hydrogen from biomass and biogas as well as negative emission technologies, WGS plays a key role. In chemical applications, the WGS reaction is used in tuning the syngas’ chemical composition. In IGCCs WGS is used in pre-combustion carbon capture where CO is shifted to CO2, a gas with no net-heating value, prior to syngas decarbonization. Other applications may focus on the hydrogen yield to produce hydrogen for transportation applications or clean power generation. Due to the large variety and enormous scale of

Advanced Power and Energy Program Manuscript WGS applications even modest improvements can have significant impact considering the global scale. Under the aspects of process intensification strategies (PIS), researchers are seeking to improve efficiency, economic performance and resource management of catalysts supporting the WGS reaction. Experimental work is one important part of obtaining insights into the reaction mechanisms and kinetics. However, mechanisms and kinetics are strongly influenced by the catalyst material, support material, dispersion, state, impurities in the gas and many other factors which is why over the past decades numerous reaction mechanisms and rate equations have been proposed [1]. Although various rate expressions have been proposed, power law rate expressions offer a good data fit over a wide range of operating conditions making them convenient to use, and thus, adapted by a majority of authors [1]. Catalyst research has thus been an important area aimed at improving the performance of the WGS reactors. Fail [2] and Plaza et. al [3] conducted kinetic measurements of wood gas with 100 ppm H2S over a sour shift catalyst composed of Co/Mo and a high temperature sweet shift catalyst consisting of Fe/Cr. Other studies on sour WGS include: Lund [4] and Hla et al. [5]. Another study by Hla et al. [6] examines the kinetics of high temperature sweet shift catalysts which has also been studied by Dijk et al. [7]. Low temperature sweet shifting has been the research interest of : Choi and Stenger [8],Koryabkina et al. [9],Mendes et al. [10] and Ovesen et al. [11]. Catalyst research is important for improving performance of the WGS reactors; however, reactor design is equally important in the overall process optimization. Mass transfer, heat transfer, thermodynamics, reaction kinetics and cost have a significant impact on reactor design and thermal management. Simulations provide an efficient and cost-effective tool to assist reactor operation in the catalyst’s operating window as well as to optimize the design of the reactor. Simulations can be used to identify critical heat and mass transfer limitations within the catalyst pellet as well as in the intra-particle space providing important information to the catalyst engineer. One of the earlier WGS reactor models was presented by Moe [12]. The modelling approach considers first order reaction kinetics with respect to CO and H2O but does not account for diffusion limitations which significantly limit its application range with respect to inlet composition and temperature. Moe [12] suggests that the reaction rate is maximized when the temperature is about 56 °C below the equilibrium temperature of the gas mixture. Keiski et al. [13] conducted kinetic measurements of a commercial Fe-based catalyst in an adiabatic reactor and developed a reactor model for their lab scale reactor. Although Keiski et al. [13] determined power law rate equations, first order irreversible kinetics were considered for intraparticle diffusion limitations in the reactor model due to simplicity. Francesconi et al. [14] modeled a small scale low temperature shift reactor for optimization of reactor length and diameter, and the optimal catalyst particle diameter. Giunta et al. [15] simulated WGS of ethanol reformate and

compared an adiabatic reactor to an ideal isothermal reactor which showed higher conversion although the initial kinetics are slower at reactor inlet. Furthermore, they found that the catalyst pellets can be assumed as isothermal for adiabatic low temperature WGS reactors. This finding has been confirmed by Levent [16]. Chen et. at [17] studied adiabatic high temperature and low temperature WGS using CFD, however, ignoring diffusion limitations inside the catalyst pellet. Ding and Chan developed a 2D transient model for adiabatic WGS reactors. Other dynamic models have been developed by Adams and Barton [18] and Mobed et al. [19]. Over the recent years isothermal WGS reactors have gained interest. Several patents have been granted [20], [21] and Linde introduced its Linde Ammonia Concept with isothermal WGS reactor [22]. Also, Air Products offers innovative solutions with isothermal shifting [23] as it offers lower energy consumption, lower investment costs and is applicable to a wider product slate [22], [23]. Beyond its applicability for the synthesis of products such as ammonia, methanol and hydrogen, recent findings in IGCCs with carbon capture suggest that isothermal sweet gas shifting may be an effective way to reduce cost and increase efficiency [24], [25]. The isothermal WGS reaction has also sparked the interest of the micro-channel reactor research community. Bac et al. [26] model a WGS micro channel reactor and saw increased CO conversion with isothermal operation over adiabatic operation. Kim et al. [27] compared an adiabatic micro channel reactor to an isothermal microchannel reactor and found that a catalyst volume reduction of 50% can be achieved with isothermal operation. At the same time, Kim et al. [27] realized that there is an optimal temperature profile to maximize kinetics. Baier and Kolb [28] as well as Rebrov et al. [29] optimized their micro channel reactors by finding this optimum temperature profile which showed to have significant impact on the reactor size. In summary, this illustrates the need to account for pore diffusion and predict the catalyst effectiveness correctly in order to span a wide range of applicability of the model. Prediction of the catalyst effectiveness can however, be cumbersome depending on the form of the rate equation. Here we present a new model that can use any type of reaction kinetics (demonstrated here with power law kinetics) to estimate the catalyst effectiveness. Furthermore, a model for simulating real fixed bed, isothermal WGS reactors is presented which has not been addressed in literature to the best of the authors’ knowledge. Based upon the thermal engineering challenges of isothermal reactors a novel dimensionless number to optimize the reaction kinetics in such a reactor has been proposed.

2. Methodology

Page 2 of 26

Advanced Power and Energy Program Manuscript A short review of the WGS reaction including reaction kinetics and catalyst properties for sweet and sour WGS catalysts is presented in the appendix.

2.1 Water Gas Shift Reactor Model 2.1.1 Solid Carbon Equilibrium Predicting whether a gas mixture will form solid carbon under certain conditions of temperature, pressure and chemical composition is not an exact science and requires experimental validation. However, taking thermodynamic equilibrium into consideration, it is possible to identify safe regions where the formation of solid carbon is impossible. From a thermodynamic equilibrium standpoint, carbon monoxide decomposes to solid carbon if the temperature is too low. Methane on the other hand cracks if the temperature is too high. Based on this information alone, it is impossible to predict whether the gas mixture is stable, unless it is in equilibrium with other components of the gas phase. Major components in syngas are methane, carbon monoxide, carbon dioxide, hydrogen and water. For simplicity, these compounds will be the only compounds considered for determining the equilibrium. Based upon these compounds there are three heterogeneous reactions involving solid carbon which can be in the form of graphite or amorphous carbon. For gas stability investigations the stability limiting compound is chosen as basis for steam addition in order to move the gas composition into the stable gas regime. CH4 ⇌ 2H2 + C

(1)

CO2 + C ⇌ 2CO

(2)

H2O + C ⇌ CO + H2

(3)

The Reaction (1) is known as reverse hydrogasification, Reaction (2) is the Boudouard reaction and Reaction (3) is the water gas reaction. Using the temperature-dependent equilibrium constant for the above-mentioned reactions and the partial-pressure-based definitions according to the above-mentioned reactions an equilibrium relationship between H-atoms, O-atoms and C-atoms can be obtained. The detailed calculation procedure together with the expressions for the equilibrium constants can be found in [30]. The results can be displayed in a ternary diagram as seen in Figure 1. The area above the equilibrium is the unstable gas region where carbon deposition can occur. Below the equilibrium line, the gas mixture is thermodynamically stable and carbon deposition is impossible. For the operation of WGS reactors this area constitutes safe reaction conditions. For the WGS reactors in this work, the solid carbon equilibrium criterion will be used for determining the steam requirement while maintaining a

Figure 1: Ternary equilibrium curves for solid carbon formation at 300 °C and 600 °C.

safety margin by not operating the reactors exactly on the equilibrium curve. 2.1.2 Finite Volume Reactor Model The chemical kinetic shift reactor model developed to determine reactor size and pressure drop of the catalyst bed is described next. With carbon capture approaching 90%, the large majority of CO has to be shifted to CO2. Thermodynamic equilibrium favors CO2 at low temperatures but slows down the reaction kinetics making it important to evaluate the catalyst volume and pressure drop across the catalyst bed which increases with catalyst volume. Assumptions for the shift reactor model are: I. II. III. IV. V. VI.

Peng-Robinson Equation of State Shift Reaction is the only Reaction to Occur Equal Catalyst Distribution Plug Flow through Reactor and Catalyst Bed Isothermal Catalyst Pellets No Axial Dispersion

Real gas behavior is approximated with the PengRobinson equation of state which is well suited for syngas applications. The shift reaction is the only reaction considered in this analysis since this study focuses on sweet shifting over a Fe/Cr catalyst under operating conditions that suppress the formation of Fischer-Tropsch liquids. Since the catalyst pellet dimension is small compared to the rector dimension it can be assumed that the catalyst is uniformly distributed inside the reactor. Industrial scale shift reactors having large diameters and high flow velocity can be approximated by plug flow conditions. The catalyst pellet is assumed to be isothermal since the pellets are small. Under sufficiently high gas velocities, as in commercial reactors, axial diffusion can be

Page 3 of 26

Advanced Power and Energy Program Manuscript neglected. The validity of assumptions IV, V and VI are checked as calculations proceed from one finite volume to the next and are further discussed at the end of this section. The model is a finite volume model which requires inlet molar flows, temperature and pressure as inputs, as well as the reactor dimensions and catalyst properties. The volumetric flow rate 𝑉 for every volume element q is calculated by, 𝑉𝑞 =

𝑖 𝑀𝑞∑0𝑛𝑞

𝜌𝑞

(4)

,

where 𝑀 is the average molecular weight of the gas mixture, 𝑛 is the molar flow rate and 𝜌 the gas density of the mixture. The gas velocity 𝑣 and superficial gas velocity 𝑢 are determined by, 𝑣𝑞 =

𝑉𝑞 2

() 𝐷 2

(5)

⋅ πεbed

outlet pressure drop is approximated with a sudden contraction and is calculated by the following equation [31]. 𝜌 Δ𝑝outlet = 𝜁 𝑢2pipe 2

𝜁 is the friction coefficient and is estimated with 0.5 in this

study [31]. The total pressure drop composes of the inlet pressure drop, pressure drop across the catalyst bed and the outlet pressure drop. The use of a flow distribution system is neglected in this study. In case of kinetic reactor studies, the reaction kinetics have to be known to determine the temperature increase, due to the exothermic character of the WGS reaction. The difference in enthalpy of formation between reactants and products leads to an increase of sensible heat in the stream. Kinetic rate expressions are often given in the form of power laws. The generalized power law for the WGS reaction can be described as follows: ― 𝐸A

𝑉𝑞

,

2

() 𝐷 2

(

n o p 𝑟 = 𝑘0 e 𝑅g 𝑇  𝑝m CO 𝑝H2O 𝑝CO2 𝑝H2 ⋅ 1 ―

and 𝑢𝑞 =

(11)

(6)

⋅π

with 𝐷 the inner reactor diameter, π the circle constant and εbed the catalyst bed void fraction. The calculation of the pressure drop is accomplished by applying the Ergun equation. 150𝜇𝑞(1 ― 𝜀bed)2𝑢𝑞 1.75(1 ― εbed)ρ𝑞𝑢2𝑞 Δ𝑝𝑞 =

Δ𝑥 +

𝜀3bed𝑑2p

ε3bed𝑑p

Δ𝑥

where 𝜇 is the dynamic viscosity, Δ𝑥 the height of the reactor volume element and 𝑑p is the catalyst pellet's diameter. For a cylindrical catalyst pellet, the diameter is approximated with the equivalent diameter 3 𝑑p = 3 𝑅2pellet ⋅ 𝐿 4

(8)

𝑅pellet is the pellet radius and 𝐿 is the length of the cylindrical pellet. The pressure of the following volume element is given by (9)

𝑝𝑞 + 1 = 𝑝𝑞 ― Δ𝑝𝑞

An additional pressure drop is associated with the inlet and outlet of the reactor. The pressure drop at the reactor inlet Δ𝑝inlet is approximated as sudden expansion. Equation (10) approximates the pressure drop of the inlet within an error margin of 5% for turbulent flow and 33% for laminar flow [31]. The design gas velocity in pipes is typically around 546 m/s [32] and thus almost always turbulent.

(

Δ𝑝inlet = 1 ―

𝐶pipe

2

)

𝜌 2 𝑢 𝐶reactor 2 pipe

(10)

𝐶pipe is the cross-sectional area of the pipe which is determined by the volumetric flow and the gas velocity. 𝐶reactor is the cross sectional area of the reactor, 𝜌 the density of the gas mixture and 𝑢pipe the gas velocity in the pipe. The gas velocity, 𝑢pipe, is limited to 46 m/s in industrial applications to avoid noise, vibrations and damaging wear and tears of pipes and fittings [32]. The

1 𝑝CO2 𝑝H2 ⋅ 𝐾 𝑝CO 𝑝H2O

)

(12)

𝑘0 is the reaction constant, 𝐸A the activation energy, 𝑅g the universal gas constant, 𝑇 the temperature, 𝑝𝑗 the partial pressure of component 𝑗. The exponents 𝑚, 𝑛, 𝑜 and 𝑝 are constants and 𝐾 is the equilibrium constant of the WGS reaction. According to Moe [12], the equilibrium constant can be calculated using the following equation, which is fairly accurate in the range from 200-550 °C. (7)

( 𝐾=e

4577.8 ― 4.33 𝑇 + 𝑇m

)

(13)

The temperature in this equation is in Kelvin (note that the constant in the numerator carries the unit Kelvin as well in order to make the exponent dimensionless). The equilibrium is considered to be a function of temperature alone. Influence of pressure on the equilibrium constant due to non-ideality is quite small under typical operating conditions with pressure being less than several hundreds of bars. The relation developed by Moe has been modified by the term 𝑇m which accounts for the temperature approach for middle of run condition which makes 𝐾 a pseudo “equilibrium” constant. Typically, kinetic rate expressions are determined under conditions without external and/or internal transport limitations, also known as intrinsic rate. This is achieved by grinding the catalyst pellet into small particles in order to expose the internal surface area entirely to the gas flow. Intrinsic rate equations have the advantage that they can be applied to many different types of problems. On the other hand, when designing a reactor, diffusion inside the catalyst pellet needs to be considered. Considering one-dimensional mass transfer inside the catalyst, e.g., a slab or inner region of a flat cylinder, the mass balance is governed by species diffusion and chemical reaction as illustrated in Figure 2.

Page 4 of 26

Advanced Power and Energy Program Manuscript diffusion is governed by wall interaction and not by molecule-molecule interaction, a regime of pure Knudsen diffusion is reached. In the transition between bulk diffusion and Knudsen diffusion both mechanisms have to be considered. The effective diffusivity is determined according to [33]. 𝐷eff = min

{ ( 𝜀pellet

1

𝜏pellet 𝐷𝑖,Mix

+

) }

1 𝐷K,𝑖

―1

(22) 𝑖 = CO,CO2,H2O,H2

𝜀pellet is the porosity of the catalyst pellet, 𝜏pellet is the

tortuosity of the catalyst pellet, 𝐷𝑖,Mix is the diffusivity of component 𝑖 in the gas mixture and 𝐷K,𝑖 is the Knudsen diffusivity of component 𝑖. 𝐷eff is evaluated for all in the reaction participating components 𝑖, in every volume Figure 2: Finite volume element inside a catalyst pellet. element of the reactor and the slowest diffusivity is used in the calculation as it constitutes the rate limiting step. In the As shown in the image, 𝑛CO is the flux of carbon case of diffusion limitation of a reactant; the supply of monoxide at the top and the bottom of the volume element reactants limits the reaction rate. In the case of product and 𝑟vCO is the volumetric reaction rate. In order to balance diffusion limitation; the removal of product species limits the species the reaction as under steady state condition the reactant cannot be supplied at a higher rate as the products are Rate of Input CO ― Rate of Output CO ― Rate of Consumption CO = 0 (14) removed. Knudsen diffusion can be calculated by the following equation [34]. g Δ𝑥Δy 𝑛CO|𝑧 ― Δ𝑥Δ𝑦 𝑛CO|𝑧 + Δ𝑧 ― 𝑟CO𝜌pelletΔ𝑥Δ𝑦Δ𝑧 = 0

𝑟gCO is the gravimetric reaction rate which is more commonly found in literate than the volumetric reaction rate and 𝜌pellet is the density of the catalyst pellet. Applying Fick's Law Equation (16) and the Taylor expansion Equation (17), d𝑐CO

𝑛CO = ― 𝐷eff

(16)

d𝑧

𝑛CO|𝑧 + Δ𝑧 = 𝑛CO|𝑧 +

d 𝑛CO Δ𝑧 d𝑧

(17)

d𝑐CO d ― 𝐷eff ― 𝑟gCO 𝜌pellet = 0 d𝑧 d𝑧

(

)

(18)

𝑐CO is the carbon monoxide concentration and 𝐷eff is the effective diffusivity in the catalyst pellet and is the only transport mechanism inside the pellet. Realizing that the effective diffusivity is independent from the z-direction, the equation can be simplified, and the differential equation of the catalyst pellet is given by d2𝑐CO 𝐷eff 2 ― 𝑟gCO 𝜌pellet = 0 d𝑧

(19)

The boundary conditions to solve the differential equation are: 𝑐CO|𝑧 = 𝐿 = 𝑐COsurface d𝑐CO d𝑧

|

=0

(21)

The concentration at distance 𝐿 (characteristic length) is the surface concentration. Due to axis symmetry the change of concentration in the middle of the slab or flat cylinder (𝑧 = 0) is zero. If the pore size of the catalyst pellet is very small, molecules will increasingly interact with the walls. If

3

(23)

π𝑀𝑖

𝑘B𝑇

(24)

2 π 𝑑2k 𝑝 𝑑pore

𝑘B is the Boltzmann constant, 𝑑k the kinetic diameter of the molecule and 𝑑pore is the pore diameter. If the Knudsen number is much greater than unity, laws of kinetic gas theory apply. For Kn values much smaller than unity, continuum theories can be applied. The diffusivity of a particular component 𝑖 in a gas mixture can be estimated by [35]: 1 ― 𝑦𝑖

𝐷𝑖,Mix =

∑

(25)

𝑦𝑗 𝑗,𝑗 ≠ 𝑖𝐷

𝑖,𝑗

where 𝑦 is the mole fraction of component 𝑖 or 𝑗 and 𝐷𝑖,𝑗 the binary diffusivity of components 𝑖 and 𝑗. Binary diffusivity, in cm2/s is estimated using the Fuller equation [36]. 𝐷𝑖,𝑗 =

(20)

𝑧=0

𝑑(15) pore 8𝑅g𝑇

𝑑pore is the pore diameter of the catalyst pellet, 𝑅g the universal gas constant and 𝑀𝑖 is the molecular weight of component 𝑖. The Knudsen number is a good measure to estimate the importance of Knudsen diffusion. Kn =

to Equation (15), results in Equation (18). ―

𝐷K,𝑖 =

0.00143 𝑇1.75 1 𝑝 𝑀2𝑖,𝑗

[

1 (𝛴𝑣)3𝑖

+

1 2 (𝛴𝑣)3𝑗

]

(26)

The temperature 𝑇 is in Kelvin and the pressure 𝑝 is in bar. The average molecular weight is in g/mol and is calculated as follows:

[( ) ( )]

𝑀𝑖,𝑗 = 2

1 1 + 𝑀𝑗 𝑀𝑖

―1

The diffusion volumes (𝛴𝑣)𝑖 are given in Table 1 .

Page 5 of 26

(26)

Advanced Power and Energy Program Manuscript After transformation of the boundary conditions, new boundary conditions are obtained. Table 1: Diffusion Volumes of the Fuller Equation [36] Component Diffusion Volume CO CO2 H2O H2

𝑐 ∗ |𝑧 ∗ = 1 = 1

18.0 26.9 13.1 6.1

d𝑐 ∗ d𝑧 ∗

Inserting Equation (12) into Equation (19) and converting the partial pressure into concentrations using the ideal gas law the following equation is obtained.

|

(34)

=0

(35)

𝑧∗ = 0

The dimensionless quantity in Equation (33) is commonly known as Thiele Modulus and will be referred to as Φ𝑏. Φ2b =

1 𝑘 𝑐𝑏CO―surface  𝜌pellet L2

(36)

𝐷eff

The Thiele Modulus is a measure of the ratio between surface reaction rate and diffusion rate inside the catalyst (27) pellet. If the Thiele Modulus is large, internal diffusion is usually limiting the reaction. If the Thiele Modulus is small, the reaction kinetics are usually the rate limiting factor. By using the generalized Thiele Modulus for irreversible Under isothermal, isobaric conditions, the total reactions (no rate constant for reversible reaction included concentration of carbon containing species involved in the in the kinetic expression) of the form: WGS reaction remains constant, as well as the total 𝑏―1 𝑉2𝑏 + 1𝑘 𝑐COsurface 𝜌pellet concentration of hydrogen containing species. 2 (37) Φg = 2 𝐷eff Furthermore, the concentration difference between carbon 𝑆 2 monoxide and water remains constant due to equimolar the value of 1/Φg for large Thiele Moduli coincides for product consumption. different reaction orders and all reaction orders in such cases can be approximated with the analytical results for 𝑐C = 𝑐CO + 𝑐CO2 (28) first order reaction kinetics [37] (note: the Thiele Modulus keeps the real reaction order). 𝑉 is the volume of the 𝑐H = 𝑐H2O + 𝑐H2 (29) catalyst pellet and 𝑆 is the surface area of the catalyst pellet. The second order differential equation is then: ― 𝐸A

d2𝑐CO + 𝑛 + 𝑜 + 𝑝) (𝑚 + 𝑛 + 𝑜 + 𝑝) 𝐷eff 2 ― 𝑘0 e 𝑅g 𝑇  𝑅(𝑚  𝑇   g d𝑧 1 𝑐CO2 𝑐H2 𝑛 𝑜 𝑝  𝜌 =0 ⋅ 𝑐𝑚 CO 𝑐H2O 𝑐CO2 𝑐H2 1 ― 𝐾 𝑐CO 𝑐H2O pellet

(

)

𝑐D = 𝑐CO ― 𝑐H2O

(30)

Thus, the differential equation can be expressed as function of the carbon monoxide concentration alone. d2𝑐CO

𝐷eff

― 𝐸A + 𝑛 + 𝑜 + 𝑝) (𝑚 + 𝑛 + 𝑜 + 𝑝) ― 𝑘0 e 𝑅g 𝑇  𝑅(𝑚  𝑇   g

d𝑧2 𝑝 𝑛 𝑜 ( 𝑐𝑚   CO 𝑐CO ― 𝑐D)  (𝑐C ― 𝑐CO) (𝑐H ― (𝑐CO ― 𝑐D)) 1 (𝑐C ― 𝑐CO) (𝑐H ― (𝑐CO ― 𝑐D)) 1― ⋅  𝜌pellet = 0 𝐾 𝑐CO (𝑐CO ― 𝑐D)

(

)

(31)

― 𝐸A

Non-dimensionalization of the equation above with 𝑐 ∗ = 𝑐CO/𝑐COsurface and 𝑧 ∗ = 𝑧/𝐿 leads to: (33)

(38)

― Φ2g 𝑐 ∗ = 0

The solution for this differential equation with the boundary conditions Equation (34) and Equation (35) is [33]:

[ ( ])

𝑐CO = 𝑐COsurface

d2𝑐CO d2𝑐CO 𝐷eff 2 ― 𝑘0 e 𝑅g 𝑇 𝑎𝑐𝑏CO 𝜌pellet = 𝐷eff 2 ― 𝑘 𝑐𝑏CO 𝜌pellet = 0 d𝑧 d𝑧

1 𝑘 𝑐𝑏CO―surface  𝜌pellet 𝐿2 ―  𝑐 ∗ 𝑏 = 0 𝐷eff d𝑧 ∗ 2

d𝑧 ∗ 2

cosh Φg 1 ―

In order to simplify the integration of the differential equation, a part of the expression of the reaction rate can be regressed over the range of the bulk concentration of each of the individual cells in the reactor domain and expressed in the form of an exponential relation. This relation can be represented by a factor 𝑎 and an exponent 𝑏. The regression is necessary for every single volume element of the reactor model since the reaction rate is not only dependent on the carbon monoxide concentration but also on parameters like temperature and pressure. Thus, a matrix of differential equations of the following form is obtained.

d2𝑐 ∗

d2𝑐 ∗

𝑧 𝐿

(39)

cosh[Φg]

In order to get the real reaction rate of the catalyst pellet with internal diffusion limitation, the reaction rate needs to be integrated over the catalyst volume. Since the carbon monoxide concentration changes from the surface of the pellet to the center of the pellet, the reaction rate is a function of the location. By defining the effectiveness factor of the catalyst this factor can be used in every volume element to determine the true reaction rate. 𝑉 𝑟apperent 1 ∫0 𝑟(𝑐CO)d𝑉 𝜂=

𝑟intrinsic

=

𝑉 𝑟(𝑐COsurface)

(40)

After integration, the following relation for a slab geometry (32) is obtained [33]. tanh(Φg) 𝜂=

Φg

(41)

With the appropriate Thiele Modulus, the expression in Equation (41) can be used to approximate any catalyst pellet shape [33]. The catalyst effectiveness is calculated for every volume element.

Page 6 of 26

Advanced Power and Energy Program Manuscript A measure for the limitation of the reaction rate through internal mass transfer is the Weisz-Prater criterion which relates the apparent reaction rate to the diffusion rate [38]. Ψ = 𝜂 Φ2g =

― 𝑟gintrinsic 𝜌pellet 𝑉2𝑏 + 1 𝐷eff 𝑐surface 𝑆2

2

< 0.15

(42)

If Ψ is smaller than 0.15 intra-particle diffusion limitations can be neglected. In order to determine the reaction rate, the surface concentrations of the species have to be determined under consideration of external mass transport phenomena. For steady state operation the molar flux from the bulk flow to the surface of the catalyst pellet has to equal the reaction rate. Since the molar flux is area specific, the reaction rate of the catalyst is normalized to the external surface area of the catalyst pellet. 𝑟aapparent = 𝑟gapparent𝑎c

(43)

with 𝑎c the specific external surface area of the catalyst pellet. 𝑎c =

𝑆pellet

The Carberry number relates the reaction rate to the external mass transfer rate and if Ca is smaller than 0.05 external mass transport limitations can be neglected [40]. After determining the actual reaction rate under consideration of external and internal mass transport the change in carbon monoxide concentration per volume element can be calculated by: 𝐹actual Δ𝑐rCO,𝑞 = 𝑟gactual,𝑞 𝜌reactor 𝜏𝑞  𝐹reference

with Δ𝑐rCO,𝑞 the concentration change in volume element 𝑞 per reactor volume, 𝜌reactor the catalyst density per reactor volume and 𝜏𝑞 being the residence time in the reactor volume element 𝑞. 𝐹 is a pressure correction factor that accounts for differences between the pressure at which the power law kinetics were experimentally established and the actual operating pressure of the reactor. Power law kinetic rate expressions tend to over-predict the reaction rates at high pressure operation if measured at atmospheric pressure. A correction factor that can be applied up to a pressure of 55 atm is given in Equation (50) [18]:

(44)

𝜌pellet𝑉pellet

0.5 ―

𝐹=𝑝

Thus, under steady state conditions and after applying Fick's Law the following equation has to hold true. 𝑟aCO,apparent = 𝑛CO = 𝛽(𝑐CO,bulk ― 𝑐CO,surface)

(45)

where 𝛽 is the mass transfer coefficient. The mass transfer coefficient can be determined via a correlation, e.g. using the Colburn J-factor. The relationship between the Colburn factor and various dimensionless numbers is:

(49)

𝑝 500

(50)

𝑝 is the pressure in atmospheres. For the reference case, this would be the pressure at which the reaction kinetics were measured and for the actual case this is the operating pressure of the reactor. Due to the equimolarity of the WGS reaction, the subsequent volume element on a per reactor volume basis has the following new concentrations:

( )

𝑐rCO,𝑞 + 1 = 𝑐rCO,𝑞 ― Δ𝑐rCO,𝑞

(51)

𝑐rH2O,𝑞 + 1 = 𝑐rH2O,𝑞 ― Δ𝑐rCO,𝑞

(52)

𝑐rCO2,𝑞 + 1 = 𝑐rCO2,𝑞 + Δ𝑐rCO,𝑞

(53)

𝑐rH2,𝑞 + 1 = 𝑐rH2,𝑞 + Δ𝑐rCO,𝑞

(54)

𝛽 𝑑p

JM =

Sh 1 3

𝐷𝑖,Mix

=

1 3

(46) 𝑢 𝜌 𝑑p

( )( ) 𝜈

Sc Re

𝐷𝑖,Mix

𝜇

𝑢 is the superficial velocity, 𝜌 is the bulk density of the mixture and 𝜇 is the dynamic viscosity of the gas mixture. The Dwidevi-Upadhyay correlation relates the Colburn factor to the Reynolds number and is valid for fixed beds with Reynolds numbers greater 10. The error introduced by using the Dwidevi-Upadhyay correlation in estimating the Colburn factor is less than 20% [39]. 𝜀bedJM =

0.765 0.82

Re

+

0.365 0.386

Re

(47)

Thus, the concentration gradient from the bulk to the catalyst pellet can be calculated. Reactant species will experience a concentration decrease from the bulk medium to the catalyst surface and product species will increase from the bulk medium to the catalyst surface. A measure for the significance of external mass transport limitation is the Carberry number, Ca. Ca =

𝑟gapparent |𝑏| 𝑎c 𝛽 𝑐bulk

< 0.05

(48)

The released energy per volume element 𝑄𝑞 is calculated based on the amount of shifted carbon monoxide and is described in Equation (55). 𝐹actual 𝑄𝑞 = Δℎ𝑞 ⋅ 𝑟gactual,𝑞 𝜌reactor 𝑉𝑞  𝐹reference

(55)

with 𝑉 the volume of element 𝑞 and Δℎ𝑞 the reaction enthalpy at cell condition 𝑞 and is a function of temperature. In case of an adiabatic reactor the energy release from the chemical reaction per cell is used to increase the temperature from one element to the next element. The temperature increase per cell, which is determined by Equation (56), is related to the molar flow and the heat capacity of the gas mixture. Δ𝑇𝑞 =

𝑄𝑞 𝑐p,𝑞 ⋅ 𝑁𝑞

(56)

with 𝑐p the specific heat capacity of the gas mixture and 𝑁 the total molar flow. In case of an ideal isothermal reactor Δ 𝑇𝑞 = 0 and 𝑄𝑞 has to be met by a cooling load. For an isoflux

Page 7 of 26

Advanced Power and Energy Program Manuscript (constant heat flux) reactor 𝑄𝑞 is lowered by the cooling flux before the temperature change is determined. For the modeling of a real isothermal reactor the energy release per volume element is given by 𝐹actual 𝑄𝑞 = Δℎ𝑞 ⋅ 𝑟gactual,𝑞 𝜌reactor 𝑉𝑞  𝐹reference + 𝛼exchanger 𝐴exchanger(𝑇𝑞 ― 𝑇coolant)

(57)

𝐴exchanger is the surface area of the heat exchanger and tubes. In this model only the outside heat transfer coefficient of the heat exchanger is considered since it constitutes largest resistance. The resistance of the tube is small due to its relatively thin wall thickness and high thermal conductivity (manufactured from metal) and the heat transfer coefficient on the inside of the tube is very large as a result of boiling/steam generation. The heat transfer coefficient 𝛼exchanger is approximated with a tubular fixed bed reactor wall correlation developed by Li and Finlayson [41]. Heat transfer correlations for horizontal tubes submerged in packed beds were not available. However, depending on the reactor design, reactor wall heat transfer coefficients are a good approximation for isothermal reactors that use U-shaped tubes which are installed parallel to the flow direction. 𝑢 𝜌 𝑑p

( )

0.79

𝜇

𝜆 𝑑p

(58)

After determining 𝑄𝑞 and Δ𝑇𝑞 for the reactor type of interest, the temperature of the subsequent volume element is given by 𝑇𝑞 + 1 = 𝑇𝑞 + Δ𝑇𝑞

(59)

Important for the validity of the model are the correctness of initial assumptions. Especially errors caused by the assumptions of plug flow or isothermal catalyst pellets can have a significant impact on the simulation results. Pure plug flow requires two criteria that have to be met: uniform velocity profile and no axial dispersion. In general catalyst bed operating conditions in industrial applications approximate plug flow. Non-uniform velocity distribution is a result of wall effects inside the reactor. Chu and Ng [42] showed that wall effects can be neglected if 𝐷 > 25 𝑑p

(60)

and a uniform velocity distribution inside the reactor is obtained. In order to assess the extent of axial dispersion, the following criterion is considered during the reactor design [43]: 𝐿bed 𝑑p

>

20 𝑏 1 ln Pedisp 1 ― 𝑋

𝑢 𝐿bed

(62)

𝐷ax

The axial dispersion 𝐷ax is determined by the Gunn correlation which has shown to be accurate for low and high Reynolds numbers and various particle sizes [44], [45]. max {𝐷𝑖,Mix}𝑖 = CO,CO2,H2O,H2 1 𝑢 𝑑p 𝐷ax =

𝛼exchanger is the heat transfer coefficient on the outside of the

𝛼exchanger = 0.17 

Pedisp =

(61)

where Pedisp is the dispersion Peclet number or Bodenstein number, Bo, which is more commonly found in European literature and 𝑋 is the conversion. The dispersion Peclet number is defined as

+   2 𝜀bed

𝜏bed

(63)

The axial diffusivity consists of a momentum and diffusion term whereby the maximum diffusion rate among the species 𝑖 is selected. The tortuosity of the catalyst bed, 𝜏bed can be approximated by [46]. 4

(1 ― 𝜀bed)3

𝜏bed = 1.23

(

𝜀bed

1 2 2 3

[36π 𝑉 ] 𝑆

(64)

)

The temperature difference between the bulk medium and the catalyst pellet's surface can be described by Δ𝑇interphase =

𝐹actual Δℎ𝑞 ⋅ 𝑟gactual,𝑞 𝜌reactor 𝑉𝑞  𝐹reference

(65)

𝜌bed 𝑉𝑞 𝑎c 𝛼pellet

where 𝛼pellet is the heat transfer coefficient between the catalyst pellet and the bulk fluid. Extra-particular heat transfer can be analyzed by Equation (67). Although catalyst internal heat transfer is not explicitly modeled, criteria for the importance of intraparticular heat transfer can be analyzed by a similar dimensionless quantity as for mass transfer to evaluate the assumption of the isothermal catalyst pellets. For this purpose, Mears developed two moduli: Γ for intra-particle heat transfer limitation and Ω for extra-particle heat transfer limitation [38], [40], [47]. Γ=

Ω=

| |

|

―Δℎ 𝐸A 𝑟gapparent 𝜌pellet 𝑉2 𝑅g 𝑇2 𝜆pellet 𝑆2 ―Δℎ 𝐸A 𝑟gapparent 𝑅g 𝑇2 𝛼pellet 𝑎c

|

< 0.05

< 0.10

(66) (67)

where 𝜆pellet is the thermal conductivity of the catalyst pellet while Γ and Ω assume Arrhenius type temperature dependence of the reaction rate identical to the kinetic rate expression. If Γ is smaller than 0.10 the particle can be assumed as isothermal. If Ω is smaller than 0.05 the temperature difference between the bulk medium and the catalyst surface is negligible. The interphase heat transfer becomes limiting before the intraparticle heat transfer providing Biot numbers of smaller than 10. This condition is typically met in reactors and only heat transfer limitations have to be considered for fast, highly exothermic reactions [47]. Bi =

𝛼pellet 𝑉 𝜆pellet𝑆

< 10

(68)

The Biot number itself is not a good measure for the applicability of an isothermal catalyst pellet. The Biot number does relate the external heat transfer rate to the internal heat transfer rate and provides a measure of the

Page 8 of 26

Advanced Power and Energy Program Manuscript uniformity of the temperature in a body, however, the dependence of the reaction kinetics on the temperature plays an important role as well. This dependence is not captured in the Biot number but by the Mears moduli Γ and Ω. To determine the value of the heat transfer coefficient 𝛼pellet from the Colburn factor JH, the following correlation is used [48]. J𝐻 =

{0.61 Re 0.91 Re

―0.41 ―0.51

 𝜒  𝜒

Re > 50 Re < 50

(69)

where 𝜒 is a shape factor and is 0.91 for cylindrically shaped pellets. Equation (69) is needed for JH, and it cannot be inferred from Equation (47) since the fully dimensionless analogy between heat and mass transfer is only valid in the fully turbulent regime with Re > 10,000 [49]. According to the Re definition for fixed beds as shown in Equation (70), the Re number is typically significantly lower than 10,000. Thus, JM ≠ JH for most cases since the characteristic length of the flow through the catalyst bed (space between the catalyst pellets) is very small. The relation between the Colburn factor and the heat transfer coefficient is: Nu

JH =

1 3

(

𝛼pellet 𝑉

𝜆 𝑆 (1 ― 𝜀)

= 𝑐p𝜇

1 3

) (70)

( )(

Pr Re

𝜆

)

𝑣 𝜌 𝑉 𝜇 𝑆 (1 ― 𝜀)

2.2 Rate Optimization (Ro) Number The rate equation, as presented in Equation (12) has two temperature dependent driving factors. A thermal ― 𝐸A 𝑅g 𝑇

potential factor 𝐹 = e which depends upon temperature in a Arrhenius fashion and a chemical potential factor 𝐺 =

(1 ―

1 𝐾

𝑝CO2 𝑝H2

)

⋅ 𝑝CO 𝑝H O which also relates to temperature in an 2

exponential manner. In order to optimize the reaction temperature with respect to its two driving forces a new dimensionless quantity Ro for rate optimization can be defined. 𝐸A  𝑝CO 𝑝H2O 𝑅g 𝑇2 𝑝CO2 𝑝H2

―

𝐸A  𝑅g 𝑇

1 2

exp

Ro = ―

( 347,657.8 exp

(

4577.8 ― 4.33 𝑇 + 𝑇m

) (71)

)

―4577.8 𝑇 + 𝑇m

 

(𝑇 + 𝑇m)2 (note that the two numerical constants carry the unit Kelvin, based on Equation (13)). The interpretation of Ro is:

Ro > 1 F and G drive the reaction in the same direction, impact of T on F is stronger than on G and an increase in T accelerates the reaction rate.

Ro = 1 F and G drive the reaction in the same direction, impact of T on F is equal to G and an increase in T accelerates the reaction rate. 1 > Ro > 0 F and G drive the reaction in the same direction, impact of T on F is weaker than on G and an increase in T accelerates the reaction rate. 0 > Ro > -1 F and G drive the reaction in the opposite direction, impact of T on F is weaker than on G and an increase in T decelerates the reaction rate. Ro = -1 F and G drive the reaction in the opposite direction, impact of T on F is equal to G, the reaction rate is at its optimum. Ro < -1 F and G drive the reaction in the opposite direction, impact of T on F is stronger than on G and an increase in T accelerates the reaction rate. Thus, the Ro number is an effective tool for engineering reactions where temperature influences the thermal driving force and chemical driving force adversely, i.e., exothermic reactions like the WGS reaction. For those reactions the regime between 0 and ―∞ is of interest with -1 being the ideal value that perfectly balances the driving forces maximizing the reaction kinetics.

3. Model Validation The model was compared with experimental temperature data from an industrial, adiabatic WGS reactor operated at the Buggenum IGCC [50]. To the best of the authors’ knowledge, data on isothermal WGS reactors are not available in open source literature. For the validation reactor number 2 from [50] has been chosen due to sintering problems reported in reactor number 1. The catalyst is an Fe/Cr based catalyst whose intrinsic rate equation has been determined in a lab setup. Details of the test conditions can be found in [50]. Reactor and catalyst sizing data were obtained in personal correspondence with the authors. Physical characteristics of the catalyst used by the authors of [50] are held confidential, however, the authors mention that the values fall within the typical range of open literature values. Thus, the data presented in Table 2 which represent commercially available catalysts [51] have been used for the model validation. Additionally, a sensitivity study has been conducted and a second, smaller pellet size (radius: 2.70 mm, height: 3.60 mm, offered by Katalco as “mini”) has been included. In total 7 operating conditions have been simulated and compared to experimental data. Overall the simulation results show excellent agreement with the experimental data. Figure 3 shows temperature profiles of two different steam to carbon monoxide ratios. The model accurately predicts the temperature increase in the middle section of

Page 9 of 26

Advanced Power and Energy Program Manuscript

Figure 3: Water gas shift reactor model validation for steam to carbon monoxide ratios of 2.5 mol/mol and 3.3 mol/mol. The abbreviation S represents a cylindrical catalyst pellet of radius 2.70 mm and length of 3.60 mm. The abbreviation L represents a cylindrical catalyst pellet of radius 4.25 mm and length of 4.90 mm.

Figure 4:Water gas shift reactor model validation for two different mass flows; 1850 kg/h and 2670 kg/h. The abbreviation S represents a cylindrical catalyst pellet of radius 2.70 mm and length of 3.60 mm. The abbreviation L represents a cylindrical catalyst pellet of radius 4.25 mm and length of 4.90 mm.

the reactor as well as the location where equilibrium is reached inside the reactor. The smaller “mini” catalyst pellet leads to a slightly faster increase in reactor temperature than the standard catalyst pellet due to the larger surface area (including internal surface area) available for reaction. With higher steam to carbon monoxide ratio the equilibrium state shifts to the right while the higher steam content leads to a lower reactor outlet temperature. The model can precisely predict this behavior. Similar conclusions can be drawn from Figure 4. Temperature slopes and equilibrium are well predicted while the smaller “mini” catalyst pellet leads to slightly faster conversion rates. Figure 4 illustrates the temperature profiles for two different mass flows. Thus, the final temperatures are identical (note: the 2670 kg/h case has a slightly higher inlet temperature leading to a slightly higher outlet temperature compared to the 1850 kg/h case) with the difference that the profile of the higher mass flow rate is stretched to the right. The model is able to precisely reflect this characteristic. Figure 5 shows the reactor internal temperature profiles for three different inlet temperatures. Again, the performance of the reactor is well predicted by the model. It is noted that the 360 °C equilibrium temperature is slightly higher than the measurement, however, since the temperatures of the other 6 cases were in good agreement with the experiments it is believed that this small difference has its origin in the measurements.

Figure 5: Water gas shift reactor model validation for three different inlet temperatures; 334 °C, 344 °C and 360 °C. The abbreviation S represents a cylindrical catalyst pellet of radius 2.70 mm and length of 3.60 mm. The abbreviation L represents a cylindrical catalyst pellet of radius 4.25 mm and length of 4.90 mm.

Page 10 of 26

Advanced Power and Energy Program Manuscript

4. Application of the Ro Number The application of the isothermal shift reactor model and the optimization using the proposed Ro number is demonstrated for a syngas application in an IGCC power plant with carbon capture. Typical operating conditions and syngas composition have been established in [24], [25], [52]–[54]. In this scenario 90% of the CO entering the WGS section of the plant has to be shifted to CO2 in order to enable the desired carbon capture goal [24]. The dry syngas composition is: 32.2 mol-% H2, 40.6 mol-% CO, 19.2 mol-% CO2 and 8.0 mol-% others (e.g. N2, Ar, CH4, etc.). The scale simulated represents a nominal 500 MW IGCC with a dry syngas flow rate of 16,250 kmol/h [24]. Since the goal of this optimization work is to reduce the reactor size, and as a consequence the cost as much as possible, the smaller catalyst pellet as presented in section 3 has been selected for this task.

4.1 Adiabatic Reference Case The Optimization II case from [24] will function as adiabatic reference case in this study. The Optimization II case consists of three high-temperature sweet shift stages with intercooling which are optimized to reach a CO conversion of 90% while minimizing steam usage in order to improve the overall plant performance. The Optimization II case has shown superior thermodynamic performance and economic benefits over the standard configuration and the Optimization I case [24]. In order to compare the performance of adiabatic and isothermal reactors this reference case is analyzed first. In [24] it has been determined that it is beneficial to have the inlet temperate of the three reactors set to the same value of 335 °C. Based upon the equilibrium considerations for carbon deposition, a steam to carbon monoxide ratio of 2.09 is used. The temperature profiles of the three reactors are shown in Figure 6. The outlet temperatures of the first, second and third reactor are 491 °C, 367 °C and 341 °C. The shape of the

temperature profile of the first reactor distinguishes from the second and third reactor. The high CO inlet concentration leads to an over proportional increase in temperature which accelerates the reaction kinetics near the reactor inlet of the first reactor. The trend follows an exponential Arrhenius type behavior while the reactant concentration is sufficiently high. Thereafter, the temperature increase starts to slow down as the gas approaches equilibrium. The second and third reactor share the same general behavior of the temperature profile. However, the temperature difference between inlet and outlet is smaller for the third reactor compared to the second reactor due to less conversion. In both cases, the CO concentration in the syngas for the second reactor and the third reactor is so low that the heat release is minor compared to the decrease in CO partial pressure. As a result, a steady decay of the reactor’s temperature slope is observed. The concentration profiles for the three reactors are given in Figure 7. The largest changes in species flows are seen in the first reactor with a conversion of 72.6%. After the second reactor, an overall conversion of 87.4% is reached and after the third reactor 90.1% of the initial CO is converted. The curve shapes of the species profiles of all three reactors follow the shape of the temperature profile of the respective reactor and the same conclusions are valid as for the temperature profile. The plots of catalyst effectiveness and reaction rate are provided in Figure 8. The first shift reactor has a maximum apparent reaction rate of 187 mol/m3/s and a maximum intrinsic reaction rate of 1337 mol/m3/s. The intrinsic reaction rate is the maximum reaction rate without pore diffusion limitations. It is the rate at which the reaction would occur if all the internal surface would be exposed to the bulk gas stream. At the beginning, the intrinsic reaction rate starts at a moderate value and then rapidly accelerates until a reactor length of about 0.4. This increase in reaction rate is driven by the increase in temperature. After the reactor length of 0.4, the reaction rate slows down due to the influence of the reduced chemical driving force.

Figure 6: Temperature profiles of the three shift reactors of the reference case using a high temperature, sweet shift catalyst with system sizing factors of 1.25 (1st shift reactor), 1.1 (2nd shift reactor) and 1.1 (3rd shift reactor).

Page 11 of 26

Advanced Power and Energy Program Manuscript

Figure 7: Species profiles of the three shift reactors of the reference case using a high temperature, sweet shift catalyst with system sizing factors of 1.25 (1st shift reactor), 1.1 (2nd shift reactor) and 1.1 (3rd shift reactor).

The apparent reaction rate shows a very similar behavior and after a reactor length of about 0.7 both reaction rates drop below a value 5 mol/m3/s. The difference in the reaction rates between the apparent and intrinsic reaction rates is due to pore diffusion inside the catalyst pellet. Diffusion limits the internal surface penetration with reactants and slows down the process of product removal from the reaction site. An increase in temperature has only a small impact on the effective diffusivity which leads to the conclusion that the observed increase in apparent reaction rate is mostly due to the increase in intrinsic reaction rate. This means that when increasing the temperature, more reaction will occur closer to the pore entrance. Thus, less reactants can diffuse all the way into the pore, which reduces the active reaction surface significantly and widens the gap between the apparent and intrinsic reaction rate. A measure of this phenomenon is the catalyst effectiveness, which is the ratio between the intrinsic and apparent reaction rate. Thus, the catalyst effectiveness is the lowest when the intrinsic reaction rate is the highest and vice versa. For all reactors, the catalyst effectiveness approaches 100% towards the end of the reactor, which indicates that the reaction

proceeds at very low speed and the gas composition is close to equilibrium. For the first reactor, this value is reached earlier as a higher system sizing factor is used. The left-shift in the location of the maximum reaction rate of the apparent reaction rate compared to the intrinsic reaction rate is due to internal pore transport phenomena. The average species concentration of CO inside the pore is lower than in the bulk phase. Thus, the effective CO concentration for the apparent reaction rate is lower and leads to a faster decay in the reaction rate, which ultimately leads to this left-shift of the maximum value of the apparent reaction rate (the intrinsic reaction rate is determined based upon the surface concentration). In the second reactor, the reaction rates decrease monotonically. The CO concentration after the first shift reactor is not high enough to lead to an increase in reaction rate in the second reactor indicating that the reaction rate is controlled by equilibrium driving forces rather than thermal driving forces. However, a change in curvature indicates that the influence of temperature is still present at the reactor inlet. The maximum apparent and intrinsic reaction rates are: 15 mol/m3/s and 24 mol/m3/s. When the syngas enters the third shift reactor, the CO

Figure 8: Catalyst effectiveness, intrinsic ration rate and apparent reaction rate of the three shift reactors of the reference case using a high temperature, sweet shift catalyst with system sizing factors of 1.25 (1st shift reactor), 1.1 (2nd shift reactor) and 1.1 (3rd shift reactor).

Page 12 of 26

Advanced Power and Energy Program Manuscript concentration is so low that the maximum apparent and intrinsic reaction rates are 2.1 mol/m3/s and 3.0 mol/m3/s and follow an exponential decay throughout the catalyst bed. Due to the slow reaction rates a higher catalyst effectiveness is reached in the third shift reactor. Because of the extremely high reaction rate in the first reactor, external mass and heat transport have an influence on the chemical conversion of CO. The external transfer coefficients can be increased by lowering the crosssectional area and increasing the gas velocity, but the associated pressure drop would become too large. For the second and third stage external mass and heat transport are negligible. The strongest limitations result from the internal diffusion which limits the apparent reaction rate and can lead to an extremely low catalyst effectiveness. However, the internal heat transfer modulus is still below its critical value of 0.1 which ensures the validity of the assumption of an isothermal catalyst particle in all three reactors. Furthermore, plug flow conditions and neglecting axial dispersion are valid based on criteria defined in Section 2.2.2. The catalyst requirement for the first, second and third reactor are 13.7 m3, 51.4 m3 and 64.2 m3 (with diameters of 2.79 m, 3.30 m and 3.56 m) totaling to 129.3 m3. The respective pressure drops associated with the shift reactors are 1.00 bar, 1.23 bar and 1.01 bar. All reactors in this scenario use an Fe-based catalyst and require evaluation of the Fischer-Tropsch liquid formation. In the first reactor the RFT values are 0.89 at the inlet and 1.49 at the reactor outlet. The second reactor has RFT values of 1.46 and 1.71 at inlet and outlet. The third shift reactor has RFT values of 1.70 and 1.71 which means that Fischer-Tropsch liquids are not a concern during normal operation.

order to reduce the amount of shift steam required. Because of the higher operating temperature in this case compared to conventional isothermal shift reactors a less reactive high temperature sweet shift catalyst based upon Fe/Cr has to be used. Under isothermal conditions a reactor outlet temperature of 340 °C is needed to obtain the desired CO conversion. With 336 °C being the lowest temperature in the reactor, a steam to carbon monoxide ratio of 2.09 is needed to avoid carbon deposition onto the catalyst. The heat exchanger employed in the isothermal reactor has a specific surface area of 5.7 m2/m3reactor with a volume fraction of 7.1%. The isothermal reactor is designed with an adiabatic section before the heat exchanger coils, which includes a guard bed which accounts for 5% of the total catalyst volume, and an adiabatic section after the heat exchanger where only catalyst is present. The adiabatic section at the reactor outlet is needed to equilibrate the gas mixture inside the reactor. Reactor cooling moves the gas mixture faster way from equilibrium than the kinetics approach equilibrium and thus a higher conversion at a given temperature can be achieved by using an adiabatic outlet section where the gas mixture can equilibrate; however, this creates a temperature dip in the middle of the reactor which determines the steam addition to control carbon deposition. The temperature and cooling profiles of the isothermal shift reactor are plotted in Figure 9.

4.2 Isothermal – IP Steam Case Although this reactor type is commonly called an isothermal shift reactor, the temperature profile of the syngas inside the reactor is not truly isothermal. Boiler feed water is introduced into the tube side of the reactor at its saturation temperature and provides a constant temperature heat sink. However, the heat transport trough the tube is determined by the temperature gradient and heat transfer coefficient (the specific exchanger surface area does not change in axial direction) and the gas will not reach thermal equilibrium in the short time the syngas is in contact with the heat exchange surface. Thus, a rate-based temperature change of the syngas will occur governed by the heat transfer rate and the heat generation rate. Current offerings of isothermal shift reactors are based on IP steam generation (typical operating range of isothermal shift reactors is 250-300 °C). In this study IP steam is generated at 237 °C (based upon integration with the IGCC steam cycle) which is used as coolant in the isothermal shift reactor. Since the temperature gradient between the desired outlet temperature and the coolant is large (resulting in efficient cooling), it is desirable to introduce the syngas at the same temperature as the outlet gas in

Figure 9: Temperature profile and cooling load of the isothermal IP shift reactor using a HT sweet shift catalyst, IP steam generation and a system sizing factor of 1.1.

At the adiabatic inlet, the temperature profile has a negative curvature which changes as soon as the gas enters the exchanger coil section and its associated heat transfer starts. Nevertheless, the temperature keeps increasing for a short distance but quickly reaches its maximum and starts decreasing. After the cooling section, the temperature rise remains low since most of the reactants have already reacted and a state close to equilibrium is reached at the end of the adiabatic outlet section.

Page 13 of 26

Advanced Power and Energy Program Manuscript The cooling load is mostly determined by the temperature difference between the syngas and the IP boiler feed water which is constant throughout the tube. IP boiler feed water is only partially evaporated and recirculated to minimize fouling (build-up of minerals) inside the tubes. Higher heat fluxes result primarily from higher gas temperatures since the heat transfer coefficient remains essentially constant throughout the reactor. The heat exchange surface area in this type of reactor is engineered to be essentially constant in the axial direction and has no influence on the heat flux as a function of the axial distance. Thus, the heat flux and cooling load are strongly influenced by the gas side temperature and consequently follow the gas temperature profile. In the adiabatic inlet section, the chemical reaction proceeds fast and leads to a steep increase in temperature. After cooling comes into effect, the temperature increase can be reduced and after a reactor length of 0.09 the cooling load matches the heat released by the chemical reaction and a maximum temperature of 483 °C is reached. After that, the kinetics are too slow, because of the lower reactant concentration, and the syngas starts cooling down. While cooling down, the syngas moves away from its chemical equilibrium and the reaction kinetics are too slow to counter this process. Hence, the gas mixture is not in equilibrium. In order to reach the desired carbon monoxide conversion, the syngas temperature would have to drop significantly below the stable gas temperature since a much lower temperature would be needed compared to a gas mixture that is in equilibrium. As a result, an adiabatic outlet section is used to equilibrate the gas mixture and increase the lowest reactor temperature. The temperature increase in the adiabatic section is approximately 4 °C. With a required equilibrium outlet temperature of 340 °C, this means that after the cooling section a temperature of 336 °C is needed. This is not much different than the inlet temperature in the reference case and ultimately results in no savings in shift

steam. The molar flows of reactants and product species are plotted in Figure 10. The molar flows of the species in the adiabatic inlet section behave very similarly to the temperature profile and general explanations as discussed before also apply here. However, after the maximum temperature is reached, there is a sudden change in the slope of the molar flows and the conversion continues at a much slower rate. This is due to the reduction of temperature by cooling and the continuous removal of reactants which both together result in a sharp decrease in the conversion of reactants. Throughout the cooling section a moderate slope is maintained, as cooling drives the reaction away from its equilibrium, and levels off in the adiabatic section where equilibrium is reached eventually. The catalyst effectiveness, intrinsic reaction rate and apparent reaction rate are shown in Figure 11. As discussed before, most of the conversion occurs at the inlet section of the reactor. The maximum reaction rates of 1314 mol/m3/s (intrinsic) and 180 mol/m3/s (apparent) are comparable to the reaction rates of the first shift reactor of the reference case. However, cooling starts right before the maximum temperature is reached, which is why the reaction rates in this Isothermal – IP Steam case are slightly lower. Because of this high reaction rate, the catalyst effectiveness goes down quickly at the inlet section but recovers in the heat exchange section. In the heat exchange section, cooling drives the reaction as the mixture is constantly moved away from its equilibrium composition. In the adiabatic outlet section the reaction rate levels off as it approaches equilibrium and the catalyst effectiveness moves towards a value of 100%.

Figure 10: Species profiles of the isothermal IP shift reactor using a HT sweet shift catalyst, IP steam generation and a system sizing factor of 1.1.

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Advanced Power and Energy Program Manuscript The catalyst requirement for the isothermal shift reactor is 112.1 m3 with a reactor diameter of 3.66 m. This represents a catalyst reduction of 13.3% compared to the reference case. Most of the reaction occurs in the adiabatic section where this Isothermal – IP Steam case and the reference cases have similar reaction rates. Thus, external mass and heat transfer impacts the reaction kinetics in that section. The syngas is then cooled, externally in a separate exchanger in the reference case while internally in this Isothermal – IP Steam case. External cooling introduces the gas into the second reactor at a lower temperature and the mixture heats up while reacting. Internal cooling slowly reduces the gas temperature while it is still reacting which leads to an overall higher average gas temperature and a reduction in the catalyst requirement. Throughout the cooling section and adiabatic outlet section only internal diffusion limitation plays a role. As in the reference case, assumptions made with respect to plug flow conditions and neglecting axial dispersion and temperature gradients within the catalyst pellet are confirmed to be valid. The pressure drop associated with the reactor is 1.50 bar. Since an Fe-based catalyst is used in the isothermal shift reactor it has to be verified that the formation of Fischer-Tropsch liquids is not a concern. With RFT of 0.82 and 1.84 at reactor inlet and outlet, it may be concluded that the reactor can operate without producing Fischer-Tropsch liquids.

4.3 Isothermal – HP Steam Case The production of only IP steam can have negative impact on the overall plant performance. Even the adiabatic scenarios discussed in [24] enable HP steam generation to some extent. From that perspective it might be desirable to produce HP steam in the isothermal shift reactor to enable a better heat integration. However, HP steam is generated at a temperature of 337 °C while as mentioned previously, an equilibrated gas mixture at a temperature of 340 °C is needed to enable CO conversion of 90%. Thus, the temperature gradient across the heat exchanger wall is not sufficient for an economic design of the shift reactor. To increase the pinch temperature to a more practical 11 °C, it is necessary to increase the gas side temperature which requires an increase in the amount of steam addition to drive the reaction equilibrium towards the product side so that the same CO conversion may be achieved as in the previous cases. Identical to the Isothermal - IP Steam case, the heat exchanger embedded in the catalyst bed in this Isothermal – HP case has a specific surface area of 5.7 m2/m3reactor with a volume fraction of 7.1%. The adiabatic guard bed at the reactor inlet accounts for 5% of the total catalyst volume. The temperature and cooling load profiles are shown in Figure 12. The temperature increase in the guard bed is higher than in the Isothermal - IP Steam case. Due to the overall larger reactor size in this Isothermal – HP Steam case, the reaction in the adiabatic inlet section almost reaches

Figure 12: Temperature profile and cooling load of the isothermal HP shift reactor using a HT sweet shift catalyst, HP steam generation and a system sizing factor of 1.1.

Figure 11: Catalyst effectiveness, intrinsic reaction rate and apparent reaction rate of the isothermal IP shift reactor using a HT sweet shift catalyst, IP steam generation and a system sizing factor of 1.1.

equilibrium before the cooling section starts. The heat removal rate in this scenario is lower than in the previous scenario as a result of the higher exchanger feed water temperature required to raise HP steam. Thus, cooling over a longer range is needed to achieve the same heat removal as in the Isothermal – IP Steam case. Having less cooling per unit volume leads to the gas mixture being closer to its thermodynamic equilibrium state at the end of the cooling section compared to the Isothermal – IP Steam case (the kinetics are too slow/rate limiting and cannot reach equilibrium while cooling). As a result, the length of the adiabatic section at the reactor outlet, where the syngas equilibrates, is decreased in the Isothermal – HP Steam case. The temperature increase in the adiabatic outlet section is approximately 1 °C.

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Advanced Power and Energy Program Manuscript The profiles of the flow rates of the different species are plotted in Figure 13.

Figure 13: Species profiles of the isothermal HP shift reactor using a HT sweet shift catalyst, HP steam generation and a system sizing factor of 1.1.

As mentioned previously, the reaction in the adiabatic inlet section proceeds very fast at the prevailing temperatures and results in a large difference between the intrinsic and apparent reaction rate (max. intrinsic 1214 mol/m3/s, max. apparent 176 mol/m3/s). Due to this fast reaction rate, the reaction temporarily approaches a state of equilibrium before it enters the cooling section and the kinetics start slowing down at a reactor length of approximately 0.05. As a result, the catalyst effectiveness goes up to a value of almost 100% and drops to about 85% at the beginning of the cooling section. The reaction rates in the cooling section are between 5 mol/m3/s and 1 mol/m3/s before they start approaching zero in the adiabatic section. Assumptions made with respect to plug flow, axial dispersion and isothermality of the catalyst pellet are again valid for this case. External mass and heat transport limitations only exist at the adiabatic inlet section of the reactor. The catalyst volume required is 204.8 m3 with a diameter of 3.66 m. This is a substantial increase over the Isothermal – IP Steam case especially because of the

Most of the species conversion is achieved in the adiabatic inlet section where the temperature increase helps to accelerate the reaction rate. After cooling starts, the increasing chemical potential difference drives the conversion to higher values. Eventually, the species profiles level off as the reactant concentrations and the lower temperature hinder the reaction from proceeding at high rates. In the adiabatic outlet section, the gas mixture nearly reaches equilibrium and no significant change in the species flow profiles is observed. The catalyst effectiveness together with intrinsic and apparent reaction rate are shown in Figure 14.

Figure 15: Ro numbers of the adiabatic shift reactors, the isothermal IP shift reactor, the isothermal HP shift reactor, the Ro-optimized shift reactor and the rate-optimized shift reactor.

reduced cooling density. The pressure drop associated with the shift reactor is 2.88 bar. The RFT values at reactor inlet and outlet are 0.79 and 1.66 which is safely below the critical value of 1.9.

4.4 Isothermal – Ro Optimized Case

Figure 14: Catalyst effectiveness, intrinsic reaction rate and apparent reaction rate of the isothermal HP shift reactor using a HT sweet shift catalyst, HP steam generation and a system sizing factor of 1.1.

Introducing the concept of the Ro number can help reactor designers to address issues of underperforming sections inside the reactor. In the case of the WGS reaction it is desirable to obtain a Ro number of -1 throughout the reactor in order to maximize the kinetics. A value between -1 and ―∞ indicates that the temperature is too low and a value between -1 and 0 indicates that the temperature is too high. However, from a system integration point of view

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Advanced Power and Energy Program Manuscript a value of -1 does not necessarily represent the most efficient system solution, e.g. preheating the syngas to extremely high reactor inlet temperatures in order to increase the Ro number to a value of -1. Rather it is important to avoid unnecessary reheating and reduce the steam requirement. With this in mind it is best to have an adiabatic inlet section where cooling starts when a Ro value of -1 is reached (an adiabatic inlet section is also favorable with respect to guard bed catalyst replacement). After the value of -1 is reached the cooling load has to be adjusted to maintain the Ro number at -1. Since the coolant temperature is constant, this will dictate the required surface area needed in this section of the reactor (note that the heat transfer coefficient also varies slightly with the axial position). Thus, the heat exchanger geometry in this case is tailored to match the cooling load. A comparison of the different WGS reactor configurations including the Ro number optimized case are presented in Figure 15. For the adiabatic case the three reactors have been plotted in series to enable a better comparison. The first reactor of the adiabatic case shows a large variation of the Ro number. A majority of the reactor at the inlet section is not hot enough to reach the maximum reaction rate due to the excessive amount of reactants. However, preheating the reactor to very high temperatures is not necessarily desirable with respect to catalyst stability, metallurgy, balance of plant heat integration and CO conversion in the case of an adiabatic reactor. On the other hand, the remainder of the reactor experiences severe overheating with respect to the optimum reaction rate. The second reactor shows a similar trend, however, not as pronounced as in the first reactor. Initially the reactor temperature could be higher but very quickly enters a region where lower temperatures would be desirable. The third reactor exhibits such low reactant concentrations that cooling would be beneficial throughout the entire reactor. At the reactor inlet of the Isothermal – IP Steam case, the Ro number is two orders of magnitude more negative than the optimum value of -1. After that the Ro number rapidly increases to a value of -0.026 before it decreases to a value of almost -1 and increases again. At the inlet, the chemical potential is so large that addition of heat would lead to a significant acceleration of the kinetics. Thus, having an adiabatic inlet helps to improve the reaction kinetics. Later when most of the reactants are consumed the Ro number decreases to -1 indicating that cooling is needed to increase the chemical potential in order to accelerate the reaction rate. Cooling starts before the local minimum at the reactor length of 0.05 but is only able to provide enough cooling to accelerate the reaction after a reactor length of 0.10. At a reactor length of 0.53 a Ro-value of -0.86 is reached, however, in order to achieve the desired conversion without lowering the gas temperature too much, a large section without cooling is needed. This adiabatic outlet section leads to an increase in the Ro number which represents the slowdown of the reaction in the approach to equilibrium whereby the chemical potential is decreasing.

The Ro number of the Isothermal – HP Steam case shows that the provided cooling density inside the reactor is not sufficient throughout the entire cooling section and leads to an increase in the required catalyst volume. Compared to the Isothermal – IP Steam case it becomes obvious that the Ro number levels off much sooner and never reaches a value close to -1 (except in the adiabatic inlet section where the Ro number increases rapidly in the approach to equilibrium). Although the heat exchanger design is identical to the Isothermal – IP Steam case, the higher temperature at which HP steam is generated lowers the heat flux substantially. For most of the reactor, the reaction kinetics are inhibited from proceeding faster due to insufficient cooling. Only at the adiabatic inlet where a large chemical potential difference is present higher temperatures are favorable. From a reactor length of 0.04 (which is in the adiabatic bed) cooling would help to accelerate the kinetics and ultimately reduce cost. Using the proposed Ro number and adjusting the reactor design to achieve a Ro value of -1 can help to optimize the reaction kinetics in the reactor. As before, the initial Ro value in the reactor is -295 and increases as the gas temperature increases in the adiabatic section. The reactor is designed to cool the syngas as soon as a Ro value of -1 is reached at a reactor length of 0.15 and the heat exchanger surface is adjusted to maintain this value until the desired conversion is obtained. In comparison to the Ro-optimized case, also an apparent reaction rate optimized case is shown in Figure 15. Although severe internal diffusion limitations and mild external mass and heat transfer limitations exists, the Ro-number is able to accurately predict the maximum reaction rate. Deviations of the Ro-number in the apparent reaction rate optimized case range from 0.013-0.040 over the range of the cooling section. The resulting maximum difference in CO conversion for a given location in the reactor is always less than 0.01%. The resulting temperature profile and cooling load from the Ro optimization are shown in Figure 16.

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Figure 16: Temperature profile and cooling load of the Rooptimized shift reactor using a HT sweet shift catalyst and a system sizing factor of 1.1.

Advanced Power and Energy Program Manuscript The catalyst effectiveness is a measure of how effectively the internal surface area of the pellet is used, or in other words how much catalyst is not being used but needs to be paid for. The Ro number on the other hand optimizes the turnover (the number of molecules that can undergo chemical conversion per reaction site per unit time) that can be achieved under certain operating conditions.

5. Conclusion

Figure 17: Catalyst effectiveness, intrinsic reaction rate and apparent reaction rate of the isothermal Ro-optimized shift reactor using a HT sweet shift catalyst and a system sizing factor of 1.1.

In the adiabatic inlet section, the temperature rises to a maximum value of 484 °C before the cooling section starts at a reactor length of 0.15. In order to maintain the Ro number at a value of -1 most of the cooling is needed at the peak temperature and as the reaction proceeds, less and less cooling is needed to keep the reaction rate at its optimum value. The reason for this is that as the reaction proceeds, less and less carbon monoxide is converted, and less heat of reaction has to be removed per volume of catalyst. By adjusting the heat transfer area in the catalyst bed accordingly, it can be ensured that the chemical potential driving force and the thermal driving force are well balanced, and that the reaction proceeds as fast as possible. The intrinsic and apparent reaction rates as well as the catalyst effectiveness are shown in Figure 17. The reaction rates in the adiabatic section including the maximum reaction rates remain unchanged. However, at the beginning of the cooling section the apparent reaction rate is about 15 times faster than in the previous case with Ro number ≠ -1. Since the cooling section was the part where the reaction was operated far away from its ideal condition this acceleration of the reaction kinetics has a significant impact on the overall catalyst volume. In the optimized case with Ro number equal to -1 the catalyst volume is reduced from 129.3 m3 (adiabatic), 112.1 m3 (Isothermal – IP Steam), 204.8 m3 (Isothermal – HP Steam) to 54.9 m3. This is an effective reduction of 57.5% versus the adiabatic case, 51.0% versus the Isothermal – IP Steam case and 73.2% versus the Isothermal – HP Steam case. A faster reaction rate ultimately leads to a reduced catalyst effectiveness as the reaction occurs closer to the pore mouth and less reactants diffuse all the way into the pore. Application of the proposed Ro number along with a knowledge of catalyst effectiveness provides a useful method for the reactor design engineer to optimize the reaction kinetics and minimize catalyst requirement and reactor volume.

A new simplified model for using power law kinetics has been demonstrated and shown to deliver results that are in good agreement with the performance of industrial scale WGS reactors. Furthermore, an approach for simulating real isothermal shift reactors has been presented. Isothermal shifting can reduce reactor size, catalyst volume and operating cost. Important for the economic performance of an isothermal WGS reactor is the cooling load. The case studies of the Isothermal – IP Steam and Isothermal – HP Steam cases have shown that most of the reactor volume is needed to sufficiently cool the syngas. Furthermore, the analysis revealed that after the adiabatic inlet section intensive cooling is desirable to increase the chemical driving force and accelerate the kinetics. Both effects together can lead to a reduction of reactor cost, catalyst cost and operating cost. In the reference case with 3 adiabatic high temperature reactors the total catalyst volume is 129.3 m3 whereas the catalyst volume in the Isothermal – IP Steam case is 112.1 m3 (without optimization of the Ro number). In the Isothermal – HP Steam case the catalyst requirement increased to 204.8 m3 due to the slow heat removal and the insufficient chemical potential. With optimized Ro number the catalyst volume can be reduced to 54.9 m3. Using the Ro Number in the reactor design leads to a significant reduction in reactor size. The here introduced Ro number which compares the impact of temperature on the thermal driving force to the chemical driving force can help reactor engineers to make effective use of the catalyst. For the WGS reaction, a value of -1 represents the optimum reaction rate. By designing the heat exchanger in the isothermal shift reactor in accordance with the Ro number a reduction of the required catalyst volume from initially 129.3 m3 to 54.9 m3 was possible. The optimization with the Ro number has shown that most of the cooling is needed after a certain adiabatic inlet length and the ideal cooling profile follows an exponential decay along the reactor axis. Furthermore, the Ro number approach has shown to be highly accurate even under external heat and mass transport limitations and even severe internal mass transport limitations. Future studies should address the turn down potential and part load behavior of isothermal shift reactors and possible designs for the heat exchanger design in the Rooptimized case e.g. using tubes of different lengths in combination with fins.

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Advanced Power and Energy Program Manuscript

Acknowledgements The authors wish to acknowledge DOE’s U.S. - China Clean Energy Research Center for Water and Energy Technologies program under whose sponsorship this work was conducted by the University of California, Irvine. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.

Nomenclature Roman Symbols a a ac A b Bi c C Ca cp d dk dpore D D12 Dax Deff DK EA F h JD JH k k0 kB K

Reaction Constant (-) Equilibrium Correction Factor (-) Specific External Surface Area of Catalyst (m2/g) Surface Area (m2) Reaction Order Exponent (-) Biot Number Concentration (mol/m3) Cross-Sectional Area (m2) Carberry Number (-) Heat Capacity at Constant Pressure (kJ/mol/K) Catalyst Pellet Diameter (m) Molecules Kinetic Diameter (m) Pore Diameter (m) Reactor Diameter (m) Binary Diffusivity (m2/s) Axial Dispersion (m2/s) Effective Diffusivity (m2/s) Knudsen Diffusivity (m2/s) Activation Energy (kJ/kg/K) Pressure Correction Factor (-) Reaction Enthalpy (kJ/mol) Colburn Factor Mass Transport (-) Colburn Factor Heat Transport (-) Reaction Constant (mol kPam+n+o+p/gcat/s) Frequency Factor (mol kPam+n+o+p/gcat/s) Boltzmann Constant (J/K) Equilibrium Constant (-)

Kn L m M 𝑀 n 𝑛 𝑁 o p p Pe 𝑄 rg rv R R RFT Re Ro S Sc Sh T Tm u v V Vpellet 𝑉 X y z

Knudsen Number (-) Length (m) Carbon Monoxide Reaction Order (-) Molecular Weight (g/mol) ave. Molecular Weight (g/mol) Water Reaction Order (-) Molar Flux (mol/m2/s) Molar Flow Rate (mol/s) Carbon Dioxide Reaction Order (-) Hydrogen Reaction Order (-) Pressure (bar) Peclet Number (-) Energy Flow (kW) Gravimetric Reaction Rate (mol/gcat/s) Volumetric Reaction Rate (mol/m3cat/s) Gas Constant (kJ/kg) Radius (m) Fischer-Tropsch Criterion (-) Reynolds Number Rate Optimization Number Catalyst Pellet Surface Area (m2) Schmidt Number Sherwood Number Temperature (K) Equilibrium Temperature Approach (K) Superficial Velocity (m/s) Velocity (m/s) Volume of Element (m3) Volume of Catalyst Pellet (m3) Volumetric Flow Rate (m3/s) Conversion (-) Mole Fraction (-) Direction of Reactor Axis (m)

Greek Symbols α β Γ Δc Δp Δx Δy Δx εbed εpellet ζ η μ π ρ Σv τbed τpellet τ Φb Φg Χ

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Heat Transfer Coefficient (W/m2/K) Mass Transfer Coefficient (m/s) Mears Modulus for Intra-Particle Heat Transfer (-) Concentration Change (mol/m3) Pressure Drop (Pa) Height of Volume Element (m) Width of Volume Element (m) Depth of Volume Element (m) Bed Void Fraction (-) Catalyst Porosity (-) Friction Coefficient (-) Catalyst Effectiveness (-) Kinematic Viscosity (Pa s) Circle Constant (-) Density (kg/m3) Diffusion Volume (-) Catalyst Bed Tortuosity (-) Catalyst Pellet Tortuosity (-) Residence Time (s) Thiele Modulus (-) Generalized Thiele Modulus (-) Shape Factor (-)

Advanced Power and Energy Program Manuscript Ψ Ω

Weisz-Prater Modulus (-) Mears Modulus for Extra-Particle Heat Transfer (-)

[10]

Subscripts C H D q i j

Carbon Species Hydrogen Species Difference between H and C Species Volume Element q Species i Species j

[11]

[12]

Abbreviations HP IGCC IP PIS WGS

[13]

High-pressure Integrated Gasification Combined Cycle Intermediate Pressure Process Intensification Strategy Water Gas Shift

[14]

References [1] [2] [3] [4] [5]

[6]

[7]

[8]

[9]

[15]

B. Smith R J, M. Loganathan, and M. S. Shantha, “A Review of the Water Gas Shift Reaction Kinetics,” Int. J. Chem. React. Eng., vol. 8, no. 1, 2010. S. Fail, “Biohydrogen Production Based on the Catalyzed Water Gas Shift Reaction in Wood Gas,” Diss. Tech. Univ. Wien, 2014. A. Plaza et al., “Apparent kinetics of the catalyzed water–gas shift reaction in synthetic wood gas,” Chem. Eng. J., vol. 301, pp. 222–228, 2016. C. R. F. Lund, “Microkinetics of Water - Gas Shift over Sulfided Mo/Al2O3 Catalysts,” Ind. Eng. Chem. Res., vol. 35, no. 8, pp. 2531–2538, 1996. S. S. Hla, G. J. Duffy, L. D. Morpeth, A. Cousins, D. G. Roberts, and J. H. Edwards, “Investigation into the performance of a Co-Mo based sour shift catalyst using simulated coal-derived syngases,” Int. J. Hydrogen Energy, vol. 36, no. 11, pp. 6638–6645, 2011. S. S. Hla et al., “Kinetics of high-temperature watergas shift reaction over two iron-based commercial catalysts using simulated coal-derived syngases,” Chem. Eng. J., vol. 146, no. 1, pp. 148–154, 2009. H. A. J. Van Dijk, K. Damen, M. Makkee, and C. Trapp, “Water-gas shift (WGS) operation of precombustion CO2 capture pilot plant at the Buggenum IGCC,” Energy Procedia, vol. 63, pp. 2008–2015, 2014. Y. Choi and H. G. Stenger, “Water gas shift reaction kinetics and reactor modeling for fuel cell grade hydrogen,” J. Power Sources, vol. 124, no. 2, pp. 432–439, 2003. N. A. Koryabkina, A. A. Phatak, W. F. Ruettinger, R. J. Farrauto, and F. H. Ribeiro, “Determination of kinetic parameters for the water-gas shift reaction on copper catalysts under realistic conditions for fuel cell applications,” J. Catal., vol. 217, no. 1, pp.

[16]

[17]

[18]

[19]

[20]

[21]

[22] [23]

Page 20 of 26

233–239, 2003. D. Mendes, V. Chibante, A. Mendes, and L. M. Madeira, “Determination of the Low-Temperature Water-Gas Shift Reaction Kinetics Using a CuBased Catalyst,” Ind. Eng. Chem. Res., vol. 49, pp. 11269–11279, 2010. C. V. Ovesen et al., “A microkinetic analysis of the water-gas shift reaction under industrial conditions,” J. Catal., vol. 158, no. 1, pp. 170–180, 1996. J. M. Moe, “Design of water-gas shift reactors,” Chem. Eng. Prog., p. 33, 1962. R. L. Keiski, T. Salmi, and V. J. Pohjola, “Development and verification of a simulation model for a non-isothermal water-gas shift reactor,” Chem. Eng. J., vol. 48, no. 1, pp. 17–29, 1992. J. A. Francesconi, M. C. Mussati, and P. A. Aguirre, “Analysis of design variables for water-gas-shift reactors by model-based optimization,” J. Power Sources, vol. 173, no. 1, pp. 467–477, 2007. P. Giunta, N. Amadeo, and M. Laborde, “Simulation of a low temperature water gas shift reactor using the heterogeneous model/application to a PEM fuel cell,” J. Power Sources, vol. 156, no. 2, pp. 489– 496, 2006. M. Levent, “Water-gas shift reaction over porous catalyst: Temperature and reactant concentration distribution,” Int. J. Hydrogen Energy, vol. 26, no. 6, pp. 551–558, 2001. W. H. Chen, M. R. Lin, T. L. Jiang, and M. H. Chen, “Modeling and simulation of hydrogen generation from high-temperature and low-temperature water gas shift reactions,” Int. J. Hydrogen Energy, vol. 33, no. 22, pp. 6644–6656, 2008. T. A. Adams and P. I. Barton, “A dynamic twodimensional heterogeneous model for water gas shift reactors,” Int. J. Hydrogen Energy, vol. 34, no. 21, pp. 8877–8891, 2009. P. Mobed, J. Maddala, R. Rengaswamy, D. Bhattacharyya, and R. Turton, “Data reconciliation and dynamic modeling of a sour water gas shift reactor,” Ind. Eng. Chem. Res., vol. 53, no. 51, pp. 19855–19869, 2014. N. M. Musich and R. S. Nataraja, “Process and System for Conductiong Iso-thermal Lowtemperature Shift Reactor using a Compact Boiler,” US 2010/0176346 A1, 2010. D. Xie, “ISOTHERMAL CONVERSION REACTOR WITH HIGH CO AND HIGH CONVERSION RATE, AND PROCESS THEREFOR,” US 2016/0200572 A1, 2016. Linde Group, “Hydrogen Brochure,” www.the-lindegroup.com, 2016. C. Higdon, A. Anderson, and T. Jakubowski, “Innovative Integration & High Availability at Air Products ’ Baytown , TX Polygeneration Syngas Plant,” in Gasification Technologies Conference, 2008.

Advanced Power and Energy Program Manuscript [24]

[25]

[26]

[27]

[28]

[29]

[30] [31] [32] [33] [34] [35] [36] [37] [38] [39]

[40]

F. Rosner, Q. Chen, A. Rao, S. Samuelsen, A. Jayaraman, and G. Alptekin, “Thermo-economic analyses of IGCC power plants employing warm gas CO2 separation technology,” Energy, vol. 185, pp. 541–553, Oct. 2019. F. Rosner, Q. Chen, A. Rao, S. Samuelsen, A. Jayaraman, and G. Alptekin, “Process and Economic Data on the Thermo-Economic Analyses of IGCC Power Plants Employing Warm Gas CO2 Separation Technology,” Data Br., no. 104716, 2019. S. Bac, S. Keskin, and A. K. Avci, “Modeling and simulation of water-gas shift in a heat exchange integrated microchannel converter,” Int. J. Hydrogen Energy, vol. 43, no. 2, pp. 1094–1104, 2017. G. Kim, J. R. Mayor, and J. Ni, “Parametric study of microreactor design for water gas shift reactor using an integrated reaction and heat exchange model,” Chem. Eng. J., vol. 110, pp. 1–10, 2005. T. Baier and G. Kolb, “Temperature control of the water gas shift reaction in microstructured reactors,” Chem. Eng. Sci., vol. 62, pp. 4602–4611, 2007. E. V Rebrov, S. A. Kuznetsov, M. H. J. M. De Croon, and J. C. Schouten, “Study of the water-gas shift reaction on Mo2C/Mo catalytic coatings for application in microstructured fuel processors,” Catal. Today, vol. 125, pp. 88–96, 2007. J. W. Colton, “Pinpoint Carbon Deposition,” Hydrocarb. Process., 1981. W. Kast, H. Nirschl, E. S. Gaddis, K.-E. Wirth, and J. Stichlmair, VDI Wärmeatlas - L1 - Einphasige Strömungen. 2013. A. Rao, “Sustainable Energy Conversion for Electricity and Coproducts,” Wiley, 2015. M. E. Davis and R. J. Davis, “Fundamentals of Chemical Reaction Engineering,” McGraw-Hill, pp. 184–239, 2013. W. He, W. Lu, and J. H. Dickerson, “Gas Transport in Solid Oxide Fuel Cells,” Springer, pp. 9–17, 2014. H. R. Perry, Perry’s Chemical Engineers’ Handbook, 7th ed., vol. 19, no. 9. 1997. B. E. Poling, J. M. Prausnitz, and J. P. O’Connell, “THE PROPERTIES OF GASES AND LIQUIDS,” McGraw-Hill, 2004. J. B. Rawlings and J. G. Ekerdt, “Chemical Reactor Analysis and Design Fundamentals,” Nob Hill Publ. LLC, 2015. H. S. Fogler, “Elements of Chemical Reaction Engineering,” Prentice-Hall, 2004. P. N. Dwivedi and S. N. Upadhyay, “Particle-Fluid Mass Transfer in Fixed and Fluidized Beds,” Ind. Eng. Chem. Process Des. Dev., vol. 16, no. 2, pp. 157– 165, 1977. J. Pérez-Ramírez, R. J. Berger, G. Mul, F. Kapteijn, and J. A. Moulijn, “Six-flow reactor technology a review on fast catalyst screening and kinetic studies,” Catal. Today, vol. 60, no. 1, pp. 93–109,

[41] [42] [43] [44]

[45] [46]

[47] [48]

[49] [50]

[51] [52]

[53]

[54]

[55] [56]

Page 21 of 26

2000. C.-H. Li and B. A. Finlayson, “Heat transfer in packed beds - A reevaluation,” Chem. Eng. Sci., vol. 32, pp. 1055–1066, 1977. C. F. Chu and K. M. Ng, “Flow in packed tubes with a small tube to particle diameter ratio,” AIChE J., vol. 35, no. 1, pp. 148–158, 1989. D. E. Mears, “The role of axial dispersion in trickleflow laboratory reactors,” Chem. Eng. Sci., vol. 26, no. 9, pp. 1361–1366, 1971. R. S. Abdulmohsin and M. H. Al-Dahhan, “Axial dispersion and mixing phenomena of the gas phase in a packed pebble-bed reactor,” Ann. Nucl. Energy, vol. 88, pp. 100–111, 2016. J. M. P. Q. Delgado, “A critical review of dispersion in packed beds,” Heat Mass Transf., vol. 42, no. 4, pp. 279–310, 2006. P. Y. Lanfrey, Z. V. Kuzeljevic, and M. P. Dudukovic, “Tortuosity model for fixed beds randomly packed with identical particles,” Chem. Eng. Sci., vol. 65, no. 5, pp. 1891–1896, 2010. D. E. Mears, “Diagnostic criteria for heat transport limitations in fixed bed reactors,” J. Catal., vol. 20, no. 2, pp. 127–131, 1971. F. Yoshida, D. Ramaswami, and A. Hougen, “Termperatures and Partial Pressures at the Surfaces of Catalyst Particles,” A.I.Ch.E. J., vol. 8, no. 1, pp. 5–11, 1962. T. Bergman, A. Lavine, F. Incropera, and D. Dewitt, “Fundamentals of Heat an Mass Transfer,” John Wiley + Sons, 2011. H. A. J. van Dijk, D. Cohen, A. A. Hakeem, M. Makkee, and K. Damen, “Validation of a water-gas shift reactor model based on a commercial FeCr catalyst for pre-combustion CO2 capture in an IGCC power plant,” Int. J. Greenh. Gas Control, vol. 29, pp. 82–91, 2014. Johnson Matthey, “Katalco Brochure: delivering world-class hydrogen plant performance,” www.matthey.com, 2007. U.S. Department of Energy/NETL, “Cost and Performance Baseline for Fossil Energy Plants Volume 3a: Low Rank Coal to Electricity: IGCC Cases,” DOE/NETL-2010/1399, 2011. F. Rosner, Q. Chen, A. Rao, and S. Samuelsen, “Thermo-economic analyses of concepts for increasing carbon capture in high-methane syngas integrated gasification combined cycle power plants,” Energy Convers. Manag., vol. 199, p. 112020, Nov. 2019. Fabian Rosner, “Techno-Economic Analysis of IGCCs Employing Novel Warm Gas Carbon Dioxide Separation and Carbon Capture Enhancements for High-Methane Syngas,” Thesis. Univerity of California, Irvine, 2018. Johnson Matthey, “HiFUEL® Base Metal Water Gas Shift Catalysts Catalogue,” www.alfa.com, 2016. H. Bohlbro, E. Mogensen, M. Jørgensen, and K. Søndergaard, “An Investigation on the Kinetics of

Advanced Power and Energy Program Manuscript

[57] [58]

[59]

[60]

[61]

[62]

[63]

[64] [65]

[66]

the Conversion of Carbon Monoxide with Water Vapour Over Iron Oxide Based Catalysts,” Gjellerup, 1969. “Personal Correspondence with Ashok Rao, Ph.D., P.E.,” 2017. G. Alptekin, “Investigation of Effects of Coal and Biomass Contaminants on the Performance of Water-Gas- Shift and Fischer-Tropsch Catalysts,” in Progress Review for DE-PS26-08NT00258-03, Morgantown, USA, 2011. B. Liu, Q. Zong, X. Du, Z. Zhang, T. Xiao, and H. Almegren, “Novel sour water gas shift catalyst (SWGS) for lean steam to gas ratio applications,” Fuel Process. Technol., vol. 134, pp. 65–72, 2015. K. Antoniak-Jurak et al., “Sulfur tolerant Co-Mo-K catalysts supported on carbon materials for sour gas shift process - Effect of support modification,” Fuel Process. Technol., vol. 144, pp. 305–311, 2016. F. Meshkani and M. Rezaei, “High temperature water gas shift reaction over promoted iron based catalysts prepared by pyrolysis method,” Int. J. Hydrogen Energy, vol. 39, no. 29, pp. 16318–16328, 2014. X. Lin et al., “The role of surface copper species in Cu-Fe composite oxide catalysts for the water gas shift reaction,” Int. J. Hydrogen Energy, vol. 40, no. 4, pp. 1735–1741, 2015. F. Meshkani, M. Rezaei, and M. H. Aboonasr Shiraz, “Preparation of high temperature water gas shift catalyst with coprecipitation method in microemulsion system,” Chem. Eng. Res. Des., vol. 113, pp. 9–16, 2016. Clariant, “Catalysts for SYNGAS,” www.catalysts.clariant.com, 2010. N. D. Ågren, M. O. Westermark, M. a. Bartlett, and T. Lindquist, “First Experiments on an Evaporative Gas Turbine Pilot Power Plant: Water Circuit Chemistry and Humidification Evaluation,” ASME J. Eng. Gas Turbines Power, vol. 124, no. 1, pp. 96– 102, 2002. E. Lorenz, F. Wodtcke, F. L. Ebenhoech, and E. Giesler, “Catalytic Reaction of Carbon Monoxide with Steam,” US 1970/3529935, 1970.

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Appendix 𝑟 = 300

Water Gas Shift Catalysts The WGS reaction is a mildly exothermic reaction at standard conditions with a net enthalpy of -41 kJ/mol and can be represented by the overall reaction: CO + H2O ⇌ CO2 + H2

(72)

Depending on the application, a certain species ratio or maximum CO conversion might be desirable. Based on these objectives and the other syngas components (especially impurities), various options for syngas shifting are available ranging from sweet and sour shifting to high and low temperature shifting. Temperature plays a key role for the WGS reaction as it not only dictates the reaction kinetics but also impacts the equilibrium and thus the CO conversion. Thus, high temperature shifting is often used for bulk CO conversion and low temperature shifting for yield optimization. An important side reaction that can occur on shift catalysts is the deposition of elemental carbon. By maintaining a certain minimum steam to carbon ratio, the formation of solid carbon can be prevented. The concept of a steam to carbon ratio is mostly used in reforming where a feedstock with a defined C:H ratio is used. In the context of syngas, a more sophisticated approach is needed to determine a stable gas operating regime as H-atoms and Oatoms also contribute to the equilibrium (this will be discussed in detail in Section 2.2.1). Furthermore, the formation of Fischer-Tropsch liquids and/or methanol is critical for the operation of sweet shift reactors and will be discussed in the following section. Depending on the trace component present in the gas stream the catalyst life typically varies between 2-6 years, however, catalyst deactivation is an important aspect when evaluating the reactor performance. In order to account for catalyst deactivation and middle of run condition in steady state simulations a 13.9 °C equilibrium temperature approach is adopted in this work. 2.1.2 Sweet Water Gas Shift Reactors Sweet shifting refers to the shifting of CO in the absence of sour gases like H2S and COS and is typically conducted downstream of a desulfurization unit. Sweet shifting is divided into adiabatic high temperature shifting, low temperature shifting, medium temperature shifting and isothermal shifting. For high temperature shifting, temperature resistant Fe/Cr-based catalysts are used as the operating temperature typically ranges from 300-500 °C. High temperature sweet shifting will be the focus of this study and study scenarios are conducted with the same catalyst in order to provide a fair comparison between the various scenarios investigated. In this study, the following intrinsic rate equation of a commercially available high temperature shift catalyst was employed [3].

mol kPa gcat s

―102

1.33

 𝑒

kJ mol

𝑅 𝑇

 

(

1 𝑝CO2 𝑝H2 0.23 ―0.16 ―0.11 𝑝1.37 ⋅ 1― ⋅ CO  𝑝H2O  𝑝CO2  𝑝H2 𝐾 𝑝CO 𝑝H2O

(73)

)

Critical for the operation of Fe-based shift catalysts is the formation of Fischer-Tropsch liquids. In order to avoid formation of Fischer-Tropsch liquids, the following criterion is applied [55]. 𝑅FT =

𝑦CO + 𝑦H2 𝑦CO + 𝑦H2O

∙

𝑝 < 1.9 26 bar

(74)

𝑦 in this equation is expressed in species vol-% and the total

pressure p in bar. Physical properties and other specifications from the supplier of the catalyst described above are not available and the following values from literature have been assumed. Table 2: Physical Catalyst Properties – High Temperature Sweet Shift Catalyst

Specification Pellet Radius Pellet Height Solid Density Bed Void Volume Porosity Tortuosity Pore Diameter Thermal Conductivity

Unit m m kg/m3 nm W/m/K

Value 0.00425 0.0049 4650 0.36 0.59 3 50 1.7

Source [51] [51] [56] [56] [57] [10]

The bed void volume is calculated based on the bed bulk density provided in [51] which is given as 1220 kg/m3. For the pore diameter a medium value of 50 nm has been assumed based on literature values for various shift catalysts which typically range from 10 – 100 nm [58]–[63]. The thermal conductivity is estimated with a value from a Cu-based catalyst which is acceptable considering that the bulk of the catalyst pellet is made up by the support material common to the two catalysts. Low temperature sweet shifting mostly relies on more reactive Cu-based catalysts and operates around 180250 °C. Commercial low temperature Cu catalysts are often combined with Zn (Cu/Zn) and supported on alumina. A concern with Cu-based catalysts is the formation of methanol; especially at temperatures below 200 °C, the equilibrium concentration of methanol becomes important. Thermodynamic equilibrium concentrations of methanol produced from the syngas are shown in Figure 18.

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Advanced Power and Energy Program Manuscript contrast to adiabatic reactors where chemical reaction and cooling are sequential. Having the heat exchanger embedded in the catalyst bed poses challenges for filling the reactor and replacing the catalyst. Thus, isothermal reactors are preferred in sweet shifting applications where the catalyst lifetime is typically longer than for sour shift applications 2.1.2 Sour Water Gas Shift Reactors

Figure 18: Methanol equilibrium concentrations derived from syngas for various temperatures as function of steam to carbon monoxide ratio.

The plot in Figure 18, shows that with increasing steam to carbon ratio, the formation of methanol can be suppressed. However, for very low temperatures, e.g. 175200 °C, the dew point of the gas mixture is reached before the methanol formation can be pushed below 0.1%. Nevertheless, catalyst promotors added to modern catalyst can suppress the formation of methanol by as much as 95% [44]. The dew point is another critical value for the operation of catalytic processes. The syngas entering the reactor should contain enough superheat to avoid pore condensation. A value of 15 °C superheat is recommended. Typical shift catalyst properties are summarized in Table 3. Table 3: Physical Catalyst Properties – Low Temperature Sweet Shift Catalyst

Specification Pellet Radius Pellet Height Solid Density Bed Void Volume Porosity Tortuosity Pore Diameter Thermal Conductivity

Unit m m kg/m3 nm W/m/K

Value 0.0024 0.0032 4133 0.4 0.25 3 50 1.7

Source [64] [64] [57] [57] [57] [57] [58] [10]

Sour shifting refers to the shifting of CO in the presence of sour gases like H2S and COS. This has implications for the reactor vessel metallurgy which needs to be able to withstand the sour gases’ corrosion behavior. Common sour gas WGS catalysts consists of Mo/Co supported on alumina whereby MoS2 represents the active species [65]. Thus, a minimum partial pressure of the sulfur components is required in order to maintain the catalyst in its active state. Typically, the reaction rate even improves with higher sulfur content. This is contrary to sweet shift catalysts where sulfur compounds act as catalyst poison and leads to its deactivation. The lifetime of sour shift catalysts ranges from 2-4 years depending on the trace components present in the syngas. In addition to the WGS reaction, the sour shift catalyst supports hydrolysis reactions, e.g. of COS, making the hydrolysis reactor in certain application redundant. COS + H2O ⇌ CO2 + H2S

(75)

HCN + H2O ⇌ NH3 + CO

(76)

Sour shift catalysts are used for high temperature shifting as well as low temperature shifting, however, the activity of sour shift catalyst suffers significantly at low temperatures. A summary of the typical properties of sour shift catalysts is provided in Table 4. Table 4: Physical Catalyst Properties - Sour Shift Catalyst

Specification Pellet Radius Pellet Height Solid Density Bed Void Volume Porosity Tortuosity Pore Diameter Thermal Conductivity

The pore diameter is an estimated value between fresh catalyst and used catalyst [58]. Medium temperature shifting is less prominent compared to high and low temperature shifting and typical operating temperatures range between 200-350 °C. Often this medium temperature range is used for isothermal shifting, however, isothermal in this context does not mean that the temperature throughout the reactor remains constant. Isothermal shifting refers to a specific reactor design where a heat exchanger is embedded in the catalyst bed to constantly remove heat from the reaction while minimizing the overall bed temperature rise. This is in

Unit m m kg/m3 nm W/m/K

Value 0.0015 0.0065 4753 0.45 0.60 3 50 1.7

Source [2] [2] [60] [57] [10]

The solid density is based upon the composition of the sour shift catalyst disclosed in BASF's patent [66] and the bed void volume has been calculated based on the bed bulk density disclosed in the same document which is given as 1050 kg/m3. Catalyst pore data are difficult to obtain, and the pore diameters changes with aging of the catalyst. A medium pore diameter of 50 nm seems reasonable based on literature values which range from 14-79 nm [59], [60]. The thermal conductivity again is estimated using the value for Cu-based catalyst due to limited availability of data while noting that shift catalysts are typically supported on

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Advanced Power and Energy Program Manuscript an alumina support making the conductivity of the pellet relatively insensitive to the actual catalytic compound.

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HIGHLIGHTS

   

Simplified integration of power law kinetics into reactor model Simulation of isothermal WGS with internal heat transfer and steam generation Dimensionless number for optimizing reaction rates even under transport limitations Isothermal WGS can reduce catalyst volume by 57.5% versus adiabatic WGS

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

+ Corresponding Author: Tel.: +1 949 824 7302; Fax: +1 949 824 7423

E-mail address: [email protected]