Reduced Microkinetics Model for Computational Fluid Dynamics (CFD

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Reduced microkinetics model for CFD simulation of the fixed bed partial oxidation of ethylene Behnam Partopour, and Anthony G. Dixon Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b00526 • Publication Date (Web): 17 Jun 2016 Downloaded from http://pubs.acs.org on June 19, 2016

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Industrial & Engineering Chemistry Research

Reduced microkinetics model for CFD simulation of the fixed bed partial oxidation of ethylene Behnam Partopour, Anthony G. Dixon* Department of Chemical Engineering, Worcester Polytechnic Institute, Worcester, MA, USA, 01609

Abstract An implementation of a simplified microkinetics model in three-dimensional CFD simulations of an ethylene oxide fixed bed reactor is proposed. An existing microkinetics model in the literature is simplified to a model with general rate expressions to reduce the complexity of the computations. Then it is coupled with CFD simulations of flow in the fixed bed and transport inside the catalyst particles. Illustrative CFD simulations are carried out in a randomly packed bed of 120 spherical particles which take into account surface species under steady state conditions in the particles. The proposed approach represents a practical method to integrate simplified surface chemistry with a realistic scale fixed-bed for more in-depth analysis. It is shown that the surface coverages can be greatly affected by the surrounding flow conditions; furthermore, the effects of transport limitations, products and different inlet compositions on the ethylene oxide selectivity are studied.

* Corresponding Author. Tel. +1 5088315350 E-mail address: [email protected].

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1. Introduction Ethylene oxide is one of the most important petrochemicals, which has wide usage in the production of plastics, glycols, and polyesters.1 Ethylene oxide almost exclusively is produced by partial oxidation of ethylene on silver. The reaction is fast and highly exothermic, and carbon dioxide is a major by-product. Multitubular fixed bed reactors are commonly used for these reactions. Low tube-to-particle-diameter ratios (N) are preferred due to the excessive amount of heat that is generated during the process. In the ethylene oxidation case, regions with high temperature suffer from selectivity loss while low temperatures cause catalyst activity loss. All these parameters add to the complexity of these systems. Therefore, an increase in selectivity toward the desirable product not only reduces greenhouse gases emissions but also results in more efficient use of existing materials and utilities, and eventually a sustainable design. Although these processes have existed for a long time, the optimal design parameters remain unresolved.2 Recent advances in computational chemistry have made it possible to understand heterogeneous catalytic reactions in detail. Consequently, new types of catalysts and kinetics models are discovered for catalytic reactions. These kinetics models which connect the electronic structure of the catalysts with the elementary reaction steps give us new insights into the reaction barriers and selectivity analysis toward the desired product 3. However, the kinetics parameters are highly dependent on the reaction conditions. Therefore, molecular level studies alone cannot address all the issues related to the industrial conditions. Screening important catalytic properties under the operating conditions is a desirable approach.4 Computational fluid dynamics provides us detailed information about transport in the fluid phase, and has become a conventional tool in reaction engineering. However, CFD methods for simulation of fixed beds due to their complex geometry have not been developed until recently.5 Integrating heterogeneous catalytic reaction with CFD has been recently studied in the literature. The “solid particle” method was introduced by our research group to couple three-dimensional intraparticle transport and reaction to the flow field in the fixed bed.6,7 User-defined scalars were used to represent the species mass fractions in the 2 ACS Paragon Plus Environment

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solid phase. Therefore, the particles could be modeled as true solid zones with “no-slip” boundary conditions at solid-fluid interfaces. Global kinetics was used to add the reaction to the solid phase. Global lumped kinetic models which are usually generated using experimental data are only valid under the conditions under which the measurements were performed. Therefore, these models start to deviate under the extreme gradients which can form in a realistic packed bed reactor. On the other hand, microkinetic models are valid under a wide range of conditions, and are suitable for three-dimensional packed bed simulations.8 However, the microkinetics models usually contain many species and elementary reactions which can increase the computational cost of the simulations or lead to unstable solutions. Thus, by using the conventional reaction engineering methods such as quasi-equilibrium and hybrid-steady state a reduced model with many fewer parameters and simpler rate expressions can be obtained without losing the important features of the full reaction mechanism.9 Recently, incorporating detailed surface kinetics with CFD has gained significant importance, since in such simulations the effects of the flow field and transport on elementary reaction steps, and surface site coverages can be studied. With such multiscale approaches it is possible to gain new insight into the development of new catalyst and reactors.10 Wehinger et al.

8,11,12

have made several studies on the detailed numerical simulation of catalytic fixed

beds. In their approach microkinetics models are coupled with the CFD simulation as a boundary condition for the external surfaces of the catalyst particles. In other words, they neglected the reaction inside the solid particles. Furthermore, the computational times for these studies were high (several days on a cluster). Maffei et al.13 recently developed a multi-region method to couple reaction with CFD in both solid and fluid phases under transient conditions; therefore, the reactor could not be studied directly under the steady state conditions. The computational time is not reported in that study; however, for coupling kinetics and transport under transient conditions, the time step needs to be significantly small. Therefore, it can be assumed that such simulations are computationally very expensive. The complexity



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of the nonlinear systems and high computational cost of these simulations can be regarded as drawbacks for using them as a fixed bed design tool, and for parameter studies. Reducing microkinetic models to general rate expression models is a convenient approach to overcome the complexity of the reaction scheme and to obtain better understanding of the mechanism. Mhadeshwar et al.14 performed a comprehensive analysis to generate a reduced microkinetic model for the water-gas shift reaction on Pt. They showed that the reduced model is dependent on the reaction conditions, and effective reaction orders can change. However, the mechanism was significantly simplified while the important features were reproduced by the reduced model. Recently, a method was proposed by Karst et al.15 for microkinetic model reduction, with emphasis on the sensitivity analysis of the overall model to certain elementary reaction steps. The proposed method provides rate expressions for the mechanism while those expressions are valid through a wide range of operating conditions. This is helpful for computationally expensive simulations such as reaction conditions optimization. Here we propose a method to study surface kinetics coupled with CFD based on reduced microkinetics to simplify the complexity of the computation, and minimize the computational time. 1.1 Partial oxidation of ethylene The standard overall kinetics of the partial ethylene oxidation on silver is described as 1 + ↔ ∆ = −105 / 2

+ 3 ↔ 2 + 2 ∆ = −1327 kJ/mol

5 + ↔ 2 + 2 ∆ = −1223 / 2

A 17-step microkinetics model involving two active sites was introduced by Stegelmann et al.,16 for ethylene oxidation on silver (Table 1). Three of the elementary steps contribute to the parallel combustion of ethylene. It is stated that these elementary steps are not important under industrial reaction conditions. It is also mentioned that acetaldehyde will only form in the absence of oxygen. Oxametallacycle


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(CH2CH2O) is isomerized through different pathways to ethylene oxide (7) and acetaldehyde (8) which is rapidly oxidized to carbon dioxide. Adsorbed oxygen forms an active site on which surface reactions for ethylene oxidation and combustion take place. Adsorbed ethylene on a silver site, on the other hand, does not participate in any reactions; however, it is important to study due to the site blocking. The model was validated with experimental data over a wide range of different conditions. Selectivity toward ethylene oxide for unpromoted silver is reported to be 55% and decreases in the presence of the product.

2- Methods 2-1 Simplifying microkinetics The proposed method for incorporating microkinetics into CFD is not limited to our particular generated reduced microkinetics model, and can be applied to other ones. There are different methods, such as DeDonder relations, reaction route graphs, and degree of rate control (DRC) for studying the reaction mechanism9,17,18. Each method has its own advantages and drawbacks depending on the mechanism that is being studied. Campbell has done a comprehensive comparison between DeDonder relations and DRC, and has shown that DRC is powerful and easy to implement for more complex mechanisms. Reaction route graphs enable us to make a detailed analysis of the mechanism based on Kirchhoff’s law, however, due to the existence of the two active sites (surface oxygen and metal sites) it can lead to very long and complex rate expressions which will not be productive for further CFD simulations. The procedure for reducing the microkinetics model involves several steps. The first and key step is to find the rate-determining elementary steps (RDS). Here we found Campbell’s degree of rate control (DRC)19 more suitable to analyze the reaction scheme and find the RDS (equation 1). In reaction mechanisms with multiple reactions usually there is more than one RDS. In this situation the hybrid steady state assumption (HSSA)9 along with other methods should be used to simplify the kinetics. In this approach steady state balances are written for the RDS while all the other steps are assumed to be at quasi



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equilibrium (QE). It is important to notice that all of these analyses are dependent on operating conditions, and under different reaction conditions the RDS might change.

,! =

! $" ( ) " $! &' ,()

(1)

The RDS analysis was carried out for inlet and average gas compositions in the reactor which is the conventional approach in reduced microkinetics model construction.9,14 The RDS did not change under these conditions. The analysis for the two different compositions was carried out for inlet temperatures up to 650 K since at temperatures over 650 K the ethylene combustion becomes dominant which is avoided in practice. Figure 1 shows the DRC analyses for the EO mechanism under the average gas composition in the reactor. To obtain numerical values of the DRC, the reaction mechanism is solved as a system of nonlinear equations at steady state. It can be seen that steps 2, 5, 7 and 8 are the rate determining steps as was predicted for a differential reactor by Stegelmann et al.16 Table 2 shows the QE and HSSA balances for the ethylene oxidation mechanism. Since O* participates in many elementary steps, it is impossible to deduce a general rate expression for the mechanism.12 However, for certain reaction conditions, and using stricter assumptions such as non-reversible steps20 overall rate expressions for the mechanism can be obtained. For further analyses a reversibility parameter is defined.14 Ф!

=

+,! +,! + +-!

(2)

Ф! values close to 0.5 indicate that step i is at equilibrium while values close to 1 indicate that the forward reaction controls the step i reaction rate. Reversibility analyses for steps 2, 5, 7 and 8 are done for inlet

and average gas composition (Figure 2 (a) and (b), respectively). It is observed that under these operating conditions except for step 7 at high conversion, the rates of all the other steps are controlled by the forward reaction. Therefore, using the equations in Table 2 we can derive equations that correlate fractions of oxametallacycle, oxygen, and empty surface sites. 6 ACS Paragon Plus Environment

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.//0/0 =

.//0/0 =

123,4 567, 8/ (567,9 80 ):.4 .0 + 36 8/0 .0 123,= + 123,?

2123, 567,@ 80 . ∗ 123,4 567, 8/ (567,9 80 ):.4 .0 + 6123,? 6123,?

(3)

(4)

Equations (3) and (4) are obtained by solving equations (9) and (10) in Table 2, respectively. Now, these two equations give two separate expressions for .//0/0 . Using equations (3) and (4) we can write the following for .0 and . ∗:

2123, 567,@ 80 . ∗ 123,4 567, 8/ (5679 80 ):.4 123,4 567, 8/ (567,9 80 ):.4 +C − D .0 6123,? 6123,? 123,= + 123,? =

36 8/0 . 123,= + 123,? 0

(5)

The right hand side term in equation (5) is very small, especially at low conversion, compared to the other terms. Therefore, the following can be written (surface sites can only have positive values)

.0 =

H F F

K F F

2123, 567,@ 80 .∗ 123,? G6 J :.4 :.4 − 123,4 567, 8/ (567,9 80 ) F F F 123,4 567, 8/ (567,9 80 ) F 123,= + 123,? E I

(6)

By substituting equation (6) in equation (3), using equations (1-8) in Table 2 and the surface site coverage balance L .! = 1

(7)

a quadratic equation based on . ∗ is obtained. The positive root of the equation gives the expression for

the empty surface sites based on partial pressures, rate and equilibrium constants.



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O O 80 .4 .4 . ∗ = N0.25 ∗ N−1 − 1.41 ∗ Q123, ∗ 567,@ ∗ R − 567,@ ∗ 80 − 1.41 ∗ S567,9 ∗ 80 T N M

M

∗ Q123, ∗ 567,@ ∗

80 .4 80 .4 R − 1.41 ∗ 567, ∗ 8/ ∗ Q123, ∗ 567,@ ∗ R − 1.41

∗ 567,> ∗ 8/0 ∗ Q123, ∗ 567,@ ∗

∗ W8/0 ∗

80 .4 R − 567,@@ ∗ 8/ − 1.189

80 .4 Y Z − 8/0 − 80 567,@ ∗ 567,@ 567,@ 567,@9

X123, ∗ 567,@ ∗

.4

80 .4 O .4 + NO1 + 1.41 ∗ Q123, ∗ 567,@ ∗ R + 567,@ ∗ 80 + 1.41 ∗ S567,9 ∗ 80 T M M ∗ Q123, ∗ 567,@ ∗

80 .4 80 .4 R + 1.41 ∗ 567, ∗ 8/ ∗ Q123, ∗ 567,@ ∗ R + 1.41

∗ 567,> ∗ 8/0 ∗ Q123, ∗ 567,@ ∗

80 .4 R + 567,@@ ∗ 8/ + 1.189

8 .4 X123, ∗ 567,@ ∗ 0 Y Z + 8/0 + 80 ] + 8 ∗ W[6 ∗ 567,@ ∗ 567,@ 567,@ 567,@9 \ .4

∗ Q123, ∗ 567,@ ∗ ∗

(8)

.4

80 @.: 8/ ] ]] .4 ^ R ∗ 123,4 ∗ 567, ∗ S567,9 ∗ 80 T ∗ 123,= + 123,? ^ ^^ 123,= + 123,?

.4 8 @.: X123, ∗ 567,@ ∗ 0 Y ∗ 123,4 ∗ 123, ∗ S567,9 ∗ 80 T ∗ 8/

\ \\

where m is =

6123,? 123,4 567, (567,9 80 ):.4 8/ − 123,4 567, (567,9 80 ):.4 8/ 123,= + 123,?


(9)

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Furthermore, similar expressions for the other surface species can be obtained by simply substituting θ* in the other equations in Table 2. Rate expressions for steps 2, 5, 7, and 8 based on partial pressures and kinetics parameters can then be derived. 2-2 One-dimensional model governing equations

A 1D plug flow reactor is described by the following ordinary differential equations _` _`de

ab! = "! ac

af = L "! ! ac

(10)

(11)

where _ is density, ` is interstitial velocity, and b! and "! are mass fraction and the production

rate of species i, respectively. It is important to note that the 1D model is just used for comparison of the reduced and the original microkinetics models, and it is not intended to be compared to the CFD simulations. The density is calculated by the ideal gas law, cp is assumed to be constant (2200 J/kg.K). Inlet temperature is set to 500 K, and interstitial velocity to 0.5 m/s. 2-3 CFD governing equations The conventional governing equations are the conservation equations of mass, momentum and energy that are well described in any CFD references. The solid particle method6 is used for modeling reaction and

scalar transport in both the solid and fluid phases. ghe − 1 scalars (i( ) are defined that are representing mass fraction of the jk species. Under steady-state conditions, assuming the fluid phase to be isotropic

the jk scalar satisfies

∇. S_mi( − Γ( ∇i( T = 0

for = 1,2, … ghe − 1. In the solid phase i( satisfies


(12)


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−∇. (Γ( ∇i( ) = pqr

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(13)

again for = 1,2, … ghe − 1. pqr is the generation term for the jk scalar due to the reaction. In both

phases the equations above are supplemented by

stu v@

istu = 1 − L i( (w@

(14)

Diffusivity terms for the fluid and solid phase are given by

_y(6 (z{a) |j Γ( = x _y( + (}m{a) pdj

(15)

The fluid value is the sum of molecular and turbulent diffusivities, and the solid value is evaluated using the Dusty Gas Model from Hite and Jackson21

stu 1 g ∑w@ ( − ( ) 1 ∆( g( = stu g y(6 1 − ( ∑w@ g(

1 1 1 = 6 + 6 6 ∆( y( y y ∑ 6 &( & y&

(16)

(17)

Molecular diffusivities are calculated by the Fuller, Schettler, and Giddings correlation22. Knudsen diffusivity is defined by y& =

ae 8"f 3

(18)

In this method it is assumed that pressure variations inside the particle are small compared to total fluid pressure, without assuming that the pressure is constant. To evaluate the ratios of the fluxes in equation (16) it is necessary to assume a dominant reaction and Nl/Nk = αl/αk, the ratio of the stoichiometric coefficients. The ethylene epoxidation, which is assumed as the dominant reaction, is indeed dominant through the reactor length, however, for some regions of the reactor in which combustion speeds up the parallel reaction can become dominant. To overcome this problem for species that do not exist in the epoxidation reaction an effective binary diffusion coefficient between those and the inlet species is considered .7 It is reported that catalyst pore diameter can affect the internal mass diffusion in a study on 10 ACS Paragon Plus Environment

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washcoat.23 However, here we used an average pore diameter for the catalyst since there is not enough experimental data available for the current reaction. The source term for mass transfer is calculated by: g"

pq' = L _z ({ + ){ =1

(19)

where _h is the catalyst density, ! is the stoichiometric coefficient of species { in reaction , + is the rate of reaction , and ! is the molecular weight of species {.

Heat generation is calculated by:

s

where −∆ is heat of reaction .

= L _h + (−∆ ) w@

(20)

The solid particle method was previously validated by comparison to experiment for methane steam reforming reaction conditions.24 2-4 Geometry and computational domain A randomly packed bed of 120 spherical particles with N = 5.04 is used for the simulations (Figure 3). Particles are 6 mm in diameter. Particle-particle and particle-wall contact points are handled with the bridges method.25 In this method small cylinders (rb = dp/10) are placed at the 384 contact points to overcome mesh generation difficulties. 70 of these cylinders are located at the particle-tube contact points. An effective thermal conductivity is defined to model the heat transfer between the particles and tube wall as the solid bridge replaces a combination of particle and stagnant gas fillet. Two boundary layers are used for both inside and outside of the particles to capture the sharp local gradients in those regions. Since we include diffusion and reaction of species inside the catalyst pellets, it is necessary to have a refined mesh inside the particle near the surface where there are strong gradients in composition. Furthermore, mesh refinement procedure is carried out similar to a previous study.26 Prism



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layer thicknesses are dp/1000 and dp/833 for inside the particles, and dp/1000 for outside. A relatively fine mesh with 20.1 million cells is used where the cell size is dp/25. Ethylene oxide fixed bed simulation is carried out under laminar flow conditions. To maintain in this condition the inlet velocity is set to a constant value of 0.075 m/s (" =

8/0 .0 5. ./ = 567,@@ 8/ .∗ 8/0 6. .0/ = ( ):.4 .0 567,@ 567,@ 8/0 7. ./0 = ( ). 567,@ ∗ 80 8. .0 = ( ). 567,@9 ∗ 9. 2+ + +4 − 6+@: = 0 10. +4 − += − +? = 0 11. +? − +@: = 0

Table 2. QE and HSSA balances for ethylene oxidation mechanism


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Relative Difference with

Relative Difference with

EO * 10 6 (kg/s)

case 1

CO2 * 10 6 ( kg/s)

case 1

case 3

1.7824596

0.11195234

3.737338

0.16085945

case 2

1.7350676

0.08238777

3.5721158

0.10953956

case 1

1.603

-

3.2194578

-

Table 3. Net production of ethylene oxide and CO2 for different inlet ethylene compositions



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Figure captions Figure 1. Degree of rate control for different elementary reaction steps at average gas composition. 80 = 0.4, 8 / = 2, 80 = 0.01, 80 = 1, and 8/ 0 = 0.01 atm. Figure 2. Reversibility parameter values for rate determining steps at (a) inlet composition (b) average gas composition

Figure 3. Illustrative geometry of randomly packed bed of 120 spherical particles.

Figure 4. Comparison between (a) the ethylene oxidation TOF, (b) the surface site coverages obtained by reduced microkinetics and full numerical solution of the mechanism under the operating conditions.

Figure 5. Comparison between reduced microkinetics and (a) Grant and Lambert experiments, (b) Campbell experiments.

Figure 6. Parity plot of the gas composition along a 10 cm reactor using an isothermal one-dimensional model

Figure 7. Contour plots of (a) temperature (K), (b) oxygen mass fraction, (c) EO mass fraction, and (d) &2 reaction rate ( .h6 ) on mid-plane through the bed. Figure 8. Contour plots of (a) empty, (b) oxametallacycle, (c) EO, and (d) ethylene surface sites coverages on mid-plane through the bed.

Figure 9. Contour plots of ethylene for (a) case 1 (b) case 2 and (c) case 3 on mid-plane through the bed.

Figure 10. Contour plots of EO for (a) case 1 (b) case 2 and (c) case 3 on mid-plane through the bed.


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Figure 1. Degree of rate control for different elementary reaction steps at average gas composition. 0.4, PC2H4 = 2, PEO = 0.01, PCO2 = 1, and PH2O = 0.01 atm. 338x190mm (300 x 300 DPI)

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PO2 =


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Figure 2. Reversibility parameter values for rate determining steps at (a) inlet composition (b) average gas composition 338x190mm (300 x 300 DPI)


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Figure 3. Illustrative Geometry of randomly packed bed of 120 spherical particles. 338x190mm (300 x 300 DPI)



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Figure 4. Comparison between (a) the ethylene oxidation TOF, (b) the surface site coverages obtained by reduced microkinetics and full numerical solution of the mechanism under the operating conditions. 338x190mm (300 x 300 DPI)


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Figure 5. Comparison between reduced microkinetics and (a) Grant and Lambert experiments, (b) Campbell experiments. 338x190mm (300 x 300 DPI)



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Figure 6. Parity plot of the gas composition along a 10 cm reactor using an isothermal one-dimensional model 338x190mm (300 x 300 DPI)


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Figure 7. Contour plots of (a) temperature (K), (b) oxygen mass fraction, (c) EO mass fraction, and (d) reaction rate (Kmol/(m3.sec) ) on mid-plane through the bed. 338x190mm (300 x 300 DPI)



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Figure 8. Contour plots of (a) empty, (b) oxametallacycle, (c) EO, and (d) ethylene surface sites coverages on mid-plane through the bed. 338x190mm (300 x 300 DPI)


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Figure 9. Contour plots of ethylene for (a) case 1 (b) case 2 and (c) case 3 on mid-plane through the bed. 338x190mm (300 x 300 DPI)



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Figure 10. Contour plots of EO for (a) case 1 (b) case 2 and (c) case 3 on mid-plane through the bed. 338x190mm (300 x 300 DPI)


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Reduced Microkinetics Model for Computational Fluid Dynamics (CFD

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