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Computational Fluid Dynamics Modeling of the Catalytic Partial Oxidation of Methane in Microchannel Reactors for Synthesis Gas Production Junjie Chen *

ID

, Wenya Song

ID

and Deguang Xu

ID

Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China; [email protected] (W.S.); [email protected] (D.X.) * Correspondence: [email protected] or [email protected]; Tel.: +86-15138057627 Received: 27 May 2018; Accepted: 29 June 2018; Published: 30 June 2018

Abstract: This paper addresses the issues related to the favorable operating conditions for the small-scale production of synthesis gas from the catalytic partial oxidation of methane over rhodium. Numerical simulations were performed by means of computational fluid dynamics to explore the key factors influencing the yield of synthesis gas. The effect of mixture composition, pressure, preheating temperature, and reactor dimension was evaluated to identify conditions that favor a high yield of synthesis gas. The relative importance of heterogeneous and homogenous reaction pathways in determining the distribution of reaction products was investigated. The results indicated that there is competition between the partial and total oxidation reactions occurring in the system, which is responsible for the distribution of reaction products. The contribution of heterogeneous and homogeneous reaction pathways depends upon process conditions. The temperature and pressure play an important role in determining the fuel conversion and the synthesis gas yield. Undesired homogeneous reactions are favored in large reactors, and at high temperatures and pressures, whereas desired heterogeneous reactions are favored in small reactors, and at low temperatures and pressures. At atmospheric pressure, the selectivity to synthesis gas is higher than 98% at preheating temperatures above 900 K when oxygen is used as the oxidant. At pressures below 1.0 MPa, alteration of the dimension in the range of 0.3 and 1.5 mm does not result in significant difference in reactor performance, if made at constant inlet flow velocities. Air shows great promise as the oxidant, especially at industrially relevant pressure 3.0 MPa, thereby effectively inhibiting the initiation of undesired homogeneous reactions. Keywords: catalytic microreactors; synthesis gas production; partial oxidation; microchannel reactors; reactor design; reaction pathway; hydrogen production; computational fluid dynamics

1. Introduction There has been an increasing interest in the production of synthesis gas through the catalytic partial oxidation of methane [1,2], due to its potential applications in many fields such as fuel cells [3,4] and gas turbines [5,6]. Currently, the primary techniques used in industry to produce synthesis gas from methane are steam reforming [7,8], autothermal reforming [9], and partial oxidation [7]. Steam reforming of methane remains the main commercial process for the production of synthesis gas [7,8]. It is important to develop new reaction routes for the production of synthesis gas from methane. A promising reaction route that has received much attention recently is the catalytic partial oxidation of methane in short contact time reactors in high temperature environment [10–12], where a high yield of synthesis gas (higher than 90%) can be achieved [13]. In comparison with other synthesis gas production routes, this technology shows great promise because higher selectivity and better efficiency can be achieved [14]. Processes 2018, 6, 83; doi:10.3390/pr6070083

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Significant progress has been made recently in the understanding of the mechanism of this reaction [15,16]. The reaction proceeds at a lower temperature than the gas-phase partial oxidation route [17–20], thus offering many advantages such as a reduction of undesired by-products and the ability to control the process temperature [21–24]. The catalysts used for this reaction usually contain group VIII transition metals, such as rhodium [25,26], ruthenium [27,28], platinum [29,30], palladium [31,32], nickel [33,34], iridium [35,36], and cobalt [37,38]. The reaction can proceed in short contact time reactors under high-temperature conditions [39–41]. This technology provides a novel route for the production of synthesis gas from methane [1,2], since the yield of the desired products can be greatly improved under controlled conditions [42,43]. It is important to understand the mechanism of the catalytic partial oxidation reaction to improve the yield of synthesis gas [44,45]. However, the pathways for the reaction are still debated, and the prospect for industrial applications is not yet clear. In the case of noble metal catalysts, both heterogeneous and homogeneous reaction pathways may be significant [46,47]. In addition, homogeneous reactions decrease the yield of synthesis gas, thus seriously hindering reactor performance. It is therefore necessary to understand the competition phenomenon between the two reaction pathways during a catalytic partial oxidation process. Unfortunately, the relative contribution of the two reaction pathways to the formation of synthesis gas has not yet been addressed, and thus further research is needed to clarify the mechanism responsible for improving the yield of synthesis gas in a catalytic partial oxidation system. Microreactor technology is expected to offer many advantages for process development [48,49], especially for fast, exothermic reactions such as catalytic partial oxidation. Precise temperature control is possible, thus significantly reducing the undesirable side reactions occurring during a catalytic partial oxidation process [48,49]. Furthermore, higher yields can be achieved for these processes under well-controlled conditions, by taking advantage of enhanced transport in small dimensions [50,51]. For partial oxidation micro-chemical systems, one of the engineering design challenge is to balance the gains made in heat and mass transfer by going to smaller dimensions against the increases in pressure drop [52,53]. However, microfabrication methods have the potential to realize reactor designs that combine excellent thermal uniformity, enhanced transport rates, and low-pressure drop for a catalytic partial oxidation process [54,55]. The intrinsic kinetics of these partial oxidation processes are typically very fast, and thus the realization of this process technology will require continued advances in the development of microreactors [15,16]. The small dimensions associated with these reactors can effectively inhibit the gas-phase reaction occurring during a catalytic partial oxidation process [56]. It is therefore important to determine the favorable operating conditions under which the yield of desired products can be maximized. In addition to providing an explanation of experimental data, numerical simulations can serve as an efficiency design tool for the development of a catalytic partial oxidation system [56,57]. Iterative, costly experimental design processes can be avoided. Furthermore, numerical simulations are necessary to better understand the operating characteristics of a micro-structured device required to implement a catalytic partial oxidation process, and to evaluate the disadvantages and benefits associated with an innovative design of the process [56,57]. A number of commercial software tools are available, but, unfortunately, none of them is universally applicable. To accurately predict the operating characteristics during the process of a catalytic partial oxidation reaction occurring in microreactors and accurately reflect experimental observations, detailed mathematical modeling is often necessary [58]. Detailed computational fluid dynamics modeling can be used to evaluate design changes, such as geometric parameters, Reynolds numbers, and reaction temperature, during a catalytic partial oxidation process [57]. The main focus of this paper is on determining the favorable operating conditions for the small-scale production of synthesis gas from the catalytic partial oxidation of methane. High transport rates are possible in microchannel reactors, thus allowing the catalytic partial oxidation reaction to be carried out under more favorable conditions. Computational fluid dynamics simulations serve as a means to understand the role of heterogeneous and homogenous reaction pathways in determining

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means to understand the role of heterogeneous and homogenous reaction pathways in determining the distribution of reaction products. The effect of reactor dimension, pressure, mixture composition, the distribution of reaction products. The effectto of better reactorunderstand dimension,the pressure, mixture composition, and preheating temperature was investigated operating characteristics of and preheating temperature was investigated to better understand the operating characteristics of the partial oxidation reactor. The favorable conditions for the production of synthesis gas were the partial oxidation reactor. Theisfavorable conditions the production were determined. The major objective to understand the for relative importanceofofsynthesis differentgas reaction determined.inThe major objective is to understand the relative importance of different reaction pathways pathways determining the distribution of reaction products. Special emphasis is placed on in determining the distribution of reaction products. Special emphasis is placed on identifying identifying favorable operating conditions for the production of synthesis gas in high temperature favorable operating conditions for the production of synthesis gas in high temperature environments. environments.

2. Model Model Development Development 2. 2.1. Reaction System 2.1. Reaction System The reaction system used in the present investigation is the catalytic partial oxidation of methane The reaction system used in the present investigation is the catalytic partial oxidation of methane taking place in a microchannel reactor. For microchannel reactors, the width of each of the channels is taking place in a microchannel reactor. For microchannel reactors, the width of each of the channels about one order of magnitude larger than its height [59,60], and thus the reactor used in this paper is is about one order of magnitude larger than its height [59,60], and thus the reactor used in this paper modeled as a two-dimensional system. A premixed methane and either air or oxygen mixture is fed is modeled as a two-dimensional system. A premixed methane and either air or oxygen mixture is to the reactor, after the reactant stream is preheated to a desired temperature. The reactor contains fed to the reactor, after the reactant stream is preheated to a desired temperature. The reactor contains multiple parallel channels having sub-millimeter dimensions, thus offering advantages from enhanced multiple parallel channels having sub-millimeter dimensions, thus offering advantages from heat and mass transfer [61]. The reactor modeled in this paper is shown schematically in Figure 1. enhanced heat and mass transfer [61]. The reactor modeled in this paper is shown schematically in Unless otherwise specified, the reactor consists of two infinitely wide parallel plates of length 8.0 mm, Figure 1. Unless otherwise specified, the reactor consists of two infinitely wide parallel plates of separated by a gap distance 0.8 mm between the two plates. length 8.0 mm, separated by a gap distance 0.8 mm between the two plates.

Figure 1. Two-dimensional schematic diagram of the microchannel reactor geometry used in Figure 1. Two-dimensional schematic diagram of the microchannel reactor geometry used in computational fluid dynamics. computational fluid dynamics.

The physical properties the walls are the same as those of stainless steel. The rhodium catalyzed The physicalof properties walls are the as those of stainless steel. The rhodium partial oxidation methane the is considered in same the present work, since the catalyst has been catalyzed reported partial oxidation of methane is considered in the present work, since the catalyst has been reported to give a high synthesis gas yield with good long-term stability [25,26]. Additionally, a “base case”, to give a high synthesis gas yield with good long-term stability [25,26]. Additionally, a “base case”, where typical operating conditions and design parameters are considered for the catalytic partial where typical operating conditions and design parameters are considered for the catalytic partial oxidation process, is given in Table 1. In this context, the effect of various operating conditions and oxidation process, can is given in Table 1. In this context, the effect of are various operating and design parameters be easily evaluated. Numerical simulations carried out, andconditions the difference


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design parameters can be easily evaluated. Numerical simulations are carried out, and the difference between a methane–oxygen system and a methane–air system is also investigated. Note that most of the catalyst properties listed in Table 1 are taken from the works related to the reaction mechanism used; the reaction mechanism used in this paper will be described in detail in Section 2.3. Reaction mechanisms. The wash coat thickness is specified based on the reaction system considered. Table 1. Nominal values of the operating conditions and design parameters used for the base case. Parameter

Variable

Value

Geometry l d

8.0 mm 0.8 mm

δ λs

0.8 mm 16 W/(m·K) (300 K)

φ pin Tin uin

2.0 0.1 MPa 300 K 0.8 m/s

δcatalyst dpore εp τp Fcat /geo Γ

0.08 mm 20 nm 0.5 3 8 2.72 × 10−9 mol/cm2

Channel length Channel height Solid wall Thickness Thermal conductivity Gas phase Inlet methane-to-oxygen molar ratio Inlet pressure Inlet temperature Inlet velocity Catalyst Washcoat thickness Mean pore diameter Porosity Tortuosity factor Catalyst/geometric surface area Density of rhodium surface sites

Other conditions Ambient temperature Surface emissivity External heat loss coefficient

Tamb ε ho

300 K 0.8 20 W/(m2 ·K)

2.2. Mathematical Model Since the Reynolds number is less than 380, which implies laminar flow. Therefore, it is possible to fully characterize heat and mass transfer in the system. Detailed reaction mechanisms are necessary to accurately predict the partial oxidation process. A two-dimensional numerical model is developed by using the commercial software ANSYS Fluent® Release 16.0 (ANSYS Inc., Canonsburg, PA, USA) [62]. Detailed reaction mechanisms are handled with related external procedures; please refer to Section 2.3. Reaction mechanisms for more details. The steady-state two-dimensional conservation equations are solved in the gas phase: ∂(ρu) ∂(ρv) + =0 (1) ∂x ∂y ∂(ρuu) ∂(ρvu) ∂p ∂ ∂u 2 ∂u ∂v ∂ ∂u ∂v + + − 2µ − µ + − µ + =0 (2) ∂x ∂y ∂x ∂x ∂x 3 ∂x ∂y ∂y ∂y ∂x ∂(ρuv) ∂(ρvv) ∂p ∂ ∂v ∂u ∂ ∂v 2 ∂u ∂v + + − µ + − 2µ − µ + =0 (3) ∂x ∂y ∂y ∂x ∂x ∂y ∂y ∂y 3 ∂x ∂y ! ! Kg Kg ∂(ρuh) ∂(ρvh) ∂ ∂T ∂ ∂T + + ρ Yk hk Vk,x − λ g + ρ Yk hk Vk,y − λ g =0 (4) ∂x ∂y ∂x k∑ ∂x ∂y k∑ ∂y =1 =1


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. ∂ ∂(ρuYk ) ∂(ρvYk ) ∂ ρYk Vk,y − ω k Wk = 0, k = 1, . . . , K g . + + (ρYk Vk,x ) + ∂x ∂y ∂x ∂y

(5)

The diffusion velocity vector is given as follows [63]: "

→

Yk W V k = − Dk,m ∇ ln Wk

!#

"

+

DkT W

#

ρYk W

∇(ln T )

(6)

The ideal gas equation of state is given by p=

ρRT W

(7)

The caloric equation of state is given by hk = hok ( To ) +

Z T To

c p,k dT.

(8)

The coverage equation of surface species can be expressed as .

sm = 0, m = K g + 1, . . . , K g + Ks . ϑm Γ

(9)

The steady-state energy equation in the walls is given by ∂ ∂ ∂T ∂T λs + λs =0 ∂x ∂x ∂y ∂y

(10)

The gaseous species equation at each of the fluid-washcoat interfaces is specified by the boundary condition taken the form . ρYk Vk,y + ηFcat/geo Wk sk inter f ace = 0, k = 1, . . . , K g . (11) inter f ace

The catalyst/geometric surface area, Fcat / geo , is defined as follows [56]: Fcat/geo =

A0 catalyst A0 geometric

(12)

The effect of diffusional limitation in the catalyst wash coat may be significant [64], and thus included in the model . si,e f f tanh(Φ) η= . = (13) Φ si !0.5 . si γ Φ = δcatalyst (14) Di,e f f Ci,inter f ace γ=

Fcat/geo . δcatalyst

(15)

The effective diffusivity can be written as 1 Di,e f f

τp = εp

1 Di,molecular

+

1 Di,Knudsen

(16)


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The Knudsen diffusivity is defined as Di,Knudsen

d pore = 3

s

8RT . πWi

(17)

The energy equation at each of the fluid wash coat interfaces is specified by the boundary condition taken the form

.

qrad − λ g

∂T ∂y

+ λs inter f ace−

∂T ∂y

Kg

+ inter f ace+

∑

.

sk hk Wk

k =1

inter f ace

= 0.

(18)

For the total heat loss to the surroundings, the equation can be written as 4 4 q = ho ( Tw,o − Tamb ) + εFs−∞ σ Tw,o − Tamb

(19)

The external heat loss coefficient, ho , is assumed to be 20 W/(m2 ·K) [65]. 2.3. Reaction Mechanisms Computational fluid dynamics modeling of the catalytic partial oxidation process is complex [15,16], especially when the role of reaction pathway needs to be determined [66]. Therefore, detailed reaction mechanisms are included in the model. The possible reactions involved in the catalytic partial oxidation process are listed as follows: Partial oxidation CH4 +

1 Θ O2 → CO + 2H2 , ∆r Hm (298.15 K) = −35.7 kJ · mol−1 2

Θ CH4 + O2 → CO + H2 + H2 O, ∆r Hm (298.15 K) = −278 kJ · mol−1

(20) (21)

Total oxidation Θ CH4 + 2O2 → CO2 + 2H2 O, ∆r Hm (298.15 K) = −802.3 kJ · mol−1

(22)

Competition between the two reaction routes is responsible for the distribution of reaction products. However, the highly exothermic total oxidation reaction serves as a heat source to ensure self-sustained operation of the system. Therefore, this reaction route can improve the selectivity towards the desired products. However, the products produced by this route decrease the selectivity. Overall, the final yield of synthesis gas is determined by this competitive effect. Steam reforming Θ CH4 + H2 O → CO + 3H2 , ∆r Hm (298.15 K) = +206.2 kJ · mol−1

(23)

Water–gas shift reaction Θ CO + H2 O → CO2 + H2 , ∆r Hm (298.15 K) = −41.2 kJ · mol−1 ,

(24)

Dry reforming Θ CH4 + CO2 → 2CO + 2H2 , ∆r Hm (298.15 K) = 246.9 kJ · mol−1

(25)

The reaction mechanism has attracted increasing attention recently [15,16,67–69]. The reaction may proceed through a combination of direct partial oxidation and steam reforming [39–41]. Both partial and total oxidation products can be formed [40], and carbon dioxide has little or no role during the


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process [39,41]. More importantly, both water-gas shift and carbon dioxide reforming do not contribute to the formation of synthesis gas [39,41]. The detailed heterogeneous reaction mechanism developed by Schwiedernoch et al. [70], as given in Table 2, is included in the model. The mechanism consists of 11 surface-adsorbed species and 6 gaseous species involved in 38-step elementary reactions. Since each of the reactive intermediates and elementary reaction steps involved in the catalytic partial oxidation process is included in the reaction mechanism, the global reactions such as steam and carbon dioxide reforming are automatically accounted for [70]. Note that the symbol * used in Table 2 denotes an adsorbed species or an empty site. Table 2. Heterogeneous reaction mechanism used for the partial oxidation of methane over rhodium. A (cm, mol, s)

Reactions

s

Ea (kJ/mol)

Adsorption 1.0 × 10−2 1.0 × 10−2 8.0 × 10−3 1.0 × 10−1 1.0 × 10−5 5.0 × 10−1

H2 + * + * => H * + H * O2 + * + * => O * + O * CH4 + * => CH4 * H2 O + * => H2 O * CO2 + * => CO2 * CO + * => CO * Desorption 3.0 × 1021 1.3 × 1022 3.0 × 1013 3.5 × 1013 1.0 × 1013 1.0 × 1013

H * + H * => * + * + H2 O * + O * => * + * + O2 H2 O * => H2 O + * CO * => CO + * CO2 * => CO2 + * CH4 * => CH4 + *

77.8 355.2–280ΘO* 45.0 133.4–15ΘCO* 21.7 25.1

Surface reactions H * + O * => OH * + * OH * + * => H * + O * H * + OH * => H2 O * + * H2 O * + * => H * + OH * OH * + OH * => H2 O * + O * H2 O * + O * => OH * + OH * C * + O * => CO * + * CO * + * => C * + O * CO * + O * => CO2 * + * CO2 * + * => CO * + O * CH4 * + * => CH3 * + H * CH3 * + H * => CH4 * + * CH3 * + * => CH2 * + H * CH2 * + H * => CH3 * + * CH2 * + * => CH * + H * CH * + H * => CH2 * + * CH * + * => C * + H * C * + H * => CH * + * CH4 * + O * => CH3 * + OH * CH3 * + OH * => CH4 * + O * CH3 * + O * => CH2 * + OH * CH2 * + OH * => CH3 * + O * CH2 * + O * => CH * + OH * CH * + OH * => CH2 * + O * CH * + O * => C * + OH * C * + OH * => CH * + O *

5.0 × 1022 3.0 × 1020 3.0 × 1020 5.0 × 1022 3.0 × 1021 3.0 × 1021 3.0 × 1022 2.5 × 1021 1.4 × 1020 3.0 × 1021 3.7 × 1021 3.7 × 1021 3.7 × 1024 3.7 × 1021 3.7 × 1024 3.7 × 1021 3.7 × 1021 3.7 × 1021 1.7 × 1024 3.7 × 1021 3.7 × 1024 3.7 × 1021 3.7 × 1024 3.7 × 1021 3.7 × 1021 3.7 × 1021

83.7 37.7 33.5 104.7 100.8 171.8 97.9 169.0 121.6 115.3 61.0 51.0 103.0 44.0 100.0 68.0 21.0 172.8 80.3 24.3 120.3 15.1 158.4 36.8 30.1 145.5

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C * + OH * => CH * + O *

3.7 × 1021

145.5

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Leedsmethane methaneoxidation oxidation mechanism [71,72] is included the model to describe the The Leeds mechanism [71,72] is included in thein model to describe the reaction reaction taking place the gas phase. The mechanism reaction mechanism is also accounted forradical the free radical taking place in the gasinphase. The reaction is also accounted for the free coupling coupling such reactions such as coupling oxidativeof coupling of The methane. The selectivity to C2-hydrocarbons reactions as oxidative methane. selectivity to C2 -hydrocarbons may be as may high be as as high as 20% for the reactionunder proceeded under certainthrough conditions, through reaction a gas-phase 20% for the reaction proceeded certain conditions, a gas-phase routereaction [73,74]. route [73,74]. These C2-hydrocarbons areduring undesirable during the catalytic partial oxidation process, These C2 -hydrocarbons are undesirable the catalytic partial oxidation process, as they can as theythe can cause the problem related to theofformation of coke. cause problem related to the formation coke. CHEMKIN transport transport database database [63] [63] isis used used inin the the model. model. The homogeneous and The CHEMKIN heterogeneous reaction rates are handled through the CHEMKIN [75] and Surface-CHEMKIN [76] respectively. interfaces, respectively.

2.4. 2.4. Computation Computation Scheme Scheme An orthogonal staggered staggered grid grid isisused usedfor forthe thebase basecase, case,consisting consisting axial nodes An orthogonal of of 200200 axial nodes by by 80 80 transverse nodes. Typical fluid node spacing near the catalyst wash coat is 40 µm in the axial transverse nodes. Typical fluid node spacing near the catalyst wash coat is 40 μm in the axial direction direction 5 µm in the transverse direction. For thereactor largest dimension, reactor dimension, a grid consisting of and 5 μmand in the transverse direction. For the largest a grid consisting of 20,000 20,000 nodes is utilized. Adequate grid resolution is verified by doubling the number of grid nodes in totalin is total utilized. Adequate grid resolution is verified by doubling the number of grid points. points. Figure 2 shows the profiles of the hydroxyl radical concentration along the centerline between Figure 2 shows the profiles of the hydroxyl radical concentration along the centerline between the the parallel plates some of the grids used methane–oxygen system. The inlet pressure twotwo parallel plates for for some of the grids used forfor thethe methane–oxygen system. The inlet pressure is is MPa. of the parameters are listed in Table Asgrid thedensity grid density increases, 3.03.0 MPa. TheThe restrest of the parameters usedused herehere are listed in Table 1. As1.the increases, there there is a convergence the solution. The numerical with the coarsest grid, consisting 4000 is a convergence of theof solution. The numerical modelmodel with the coarsest grid, consisting of 4000ofnodes nodes incannot total, cannot accurately capture the hydroxyl concentration the channel and its in total, accurately capture the hydroxyl radicalradical concentration withinwithin the channel and its peak peak location, and thus fails to accurately predict the onset of gas-phase combustion within the system. location, and thus fails to accurately predict the onset of gas-phase combustion within the system. In In contrast, solution obtained numerical model with a grid consisting tens of thousands contrast, thethe solution obtained byby thethe numerical model with a grid consisting of of tens of thousands of of nodes is reasonably accuratefor forthe thebase basecase casegiven givenininTable Table1.1.There Thereisislittle littleor or no no advantage advantage for the nodes is reasonably accurate largest grid density, density, up up to to 32,000 32,000nodes nodesin intotal. total.

Hydroxyl radical mass fraction

0.009 (16000 nodes are used in this paper for the base case)

4000 nodes 8000 nodes 16000 nodes 32000 nodes

0.006

0.003

0.000

0

2

4

6

8

Axial distance (mm) Figure 2. 2. Profiles Profiles of of the the hydroxyl hydroxyl radical radical concentration concentration along along the the centerline centerline between between the the two two parallel parallel Figure plates for some of the grids used for the methane–oxygen system. The inlet pressure is 3.0 MPa. plates for some of the grids used for the methane–oxygen system. The inlet pressure is 3.0 MPa. The The rest rest ofparameters the parameters are listed in Table of the usedused here here are listed in Table 1. 1.

The physical properties of the mixture depend on the local conditions of component and The physical properties of the mixture depend on the local conditions of component and temperature. The physical properties the walls, such as the thermal conductivity and specific heat temperature. The physical properties the walls, such as the thermal conductivity and specific heat capacity, depend on the local temperature. The conservation equations are discretized by using a capacity, depend on the local temperature. The conservation equations are discretized by using a finite-volume method. The momentum, energy, and species equations are discretized by using a twofinite-volume method. The momentum, energy, and species equations are discretized by using a order upwind approximation. The pressure-velocity coupling is discretized using the “SIMPLE” two-order upwind approximation. The pressure-velocity coupling is discretized using the “SIMPLE” method. The convergence criterion is 10−6 by examining the values of the residuals for all of the method. The convergence criterion is 10−6 by examining the values of the residuals for all of the conservation equations. Convergence of the solution is usually difficult due to the inherent stiffness conservation equations. Convergence of the solution is usually difficult due to the inherent stiffness of

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the detailed reaction mechanism used. of the detailed reaction mechanism used.Figure Figure3 3shows showsthe theresiduals residualsfor forthe theconservation conservation equations at the end of each solver iteration. The The residual residual plot plot indicates indicates that that after after approximately approximately 800 800 iterations, iterations, the convergence satisfied. satisfied. Processes 2018, 6, criterion x FOR PEERis REVIEW 9 of 24 of the detailed reaction mechanism used. Figure 3 shows the residuals for the conservation equations at the end of each solver iteration. The residual plot indicates that after approximately 800 iterations, the convergence criterion is satisfied.

Figure 3. 3. Residuals Residuals for for the the conservation conservation equations equations at at the the end end of of each each solver solver iteration. iteration. The The mesh mesh used used Figure here consists of 16,000 nodes in total. The parameters used in the numerical simulations conducted here consists of 16,000 nodes in total. The parameters used in the numerical simulations conducted Residuals for the conservation equations at the end of each solver iteration. The mesh used here Figure are the the3.same same as those those adopted in Figure Figure 2. here are as adopted in 2.

here consists of 16,000 nodes in total. The parameters used in the numerical simulations conducted are the same as those adopted in Figure 2. Modelhere Validation

2.5. Model Validation 2.5.

In order order to verify the 2.5. Modelto Validation In verify the model, model, the the experimental experimental results results reported reported in in the the literature literature [77] [77] are are utilized. utilized. The reactor used is made of a quartz tube, and the inside diameter of the reactor is mm, as The reactor used is quartzthe tube, and the inside diameter is [77] 18 mm, as18described In order to made verify of theamodel, experimental results reportedof inthe the reactor literature are utilized. described in the literature [77]. The inlet temperature of a methane and oxygen mixture is 20 °C, ◦ reactor [77]. used The is made a quartz tube, the inside diameter of the is reactor 18 mm, as and in theThe literature inlet of temperature of a and methane and oxygen mixture 20 C,isand the pressure themaintained pressure 0.12 MPa at temperature the outlet. Nitrogen dilution is inlet 30%, and rate the inlet flow describedisin the The inlet of a methane and the oxygen mixture is 20 and rate is atmaintained 0.12literature MPa atat[77]. the outlet. Nitrogen dilution is 30%, and flow is°C, maintained 3/min. A grid consisting of 36,000 nodes in total is used here. Numerical is maintained at 5000 cm 3 the pressure is maintained at 0.12 MPa at the outlet. Nitrogen dilution is 30%, and the inlet flow rate at 5000 cm /min. A grid consisting of 36,000 nodes in total is used here. Numerical simulations are is maintained at 5000 cm3/min. Atested grid consisting 36,000 nodes in total isoperating used here. Numericalgiven simulations forcase the experimental case tested under theand conditions and performed forare theperformed experimental under theof operating conditions design parameters simulations are performed for the experimental case tested under the operating conditions and design parameters in the literature [77].the The results obtained for theconversion selectivityfor and the outlet in the literature [77].given The results obtained for selectivity and the outlet the mixture design parameters given inwith the literature [77]. The results obtained for theto selectivity and the outlet conversion for the mixture different compositions is compared the experimental data in with different compositions is compared to the experimental data in Figure 4. The maximum difference conversion for the mixture with different compositions is compared to the experimental data in Figure 4. the Thenumerical maximum results difference the numerical results and5.6%. the experimental data is about between andbetween the experimental data is about Therefore, the numerical Figure 4. The maximum difference between the numerical results and the experimental data is about 5.6%. Therefore, the numerical results are in consistent with the experimental data. results are in consistent with the experimental data. 100 Lines:numerical numerical results 100 Lines: results Symbols:experimental experimental data Symbols: data 95 95

Selectivity (%)

Selectivity (%)

95 95

90 90

85

90 90

85

80

80

Outlet methane conversion (%)

100100

85

Hydrogen selectivity

1.5

1.5

Hydrogen selectivity Carbon monoxide selectivity Carbon monoxide selectivity Outlet methane conversion Outlet methane conversion

1.6 1.7 1.8 1.9 2.0 Inlet methane-to-oxygen molar 1.6 1.7 1.8 1.9 ratio2.0

2.1

85

80

2.1


5.6%. Therefore, the numerical results are in consistent with the experimental data.

80

Inlet methane-to-oxygen molar ratio Figure 4. Comparison between the numerical results and the experimental data obtained for a Figure 4. Comparison between the numerical results and the experimental data obtained for a methane methane and oxygen between mixture with various compositions. The experimental data aredata taken from the for a Figure 4. Comparison numerical results and the experimental obtained and oxygen mixture with variousthe compositions. The experimental data are taken from the previous previous work of Bodke et al. [77]. A grid consisting of 36,000 nodes in total is used here. methane and oxygen mixture with variousof compositions. experimental data are taken from the work of Bodke et al. [77]. A grid consisting 36,000 nodesThe in total is used here. previous work of Bodke et al. [77]. A grid consisting of 36,000 nodes in total is used here.


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3. Results and Discussion Processes 2018, 6, x FOR PEER REVIEW

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In the following sections, the reactor performance in terms of conversion, selectivity, 3. Results and Discussion and temperature under various operating conditions is discussed in detail, and the relative importance of different pathways in determining the distribution of reaction products is investigated. In reaction the following sections, the reactor performance in terms of conversion, selectivity, and Additionally, comparisons areoperating made in terms of reactor performance between the results obtained temperature under various conditions is discussed in detail, and the relative importance of for different reaction pathways in determining the system. distribution of reaction products is investigated. a methane–oxygen system and for a methane–air Additionally, comparisons are made in terms of reactor performance between the results obtained

3.1. Base for aCase methane–oxygen system and for a methane–air system. For the base 3.1. Base Case case given in Table 1, a methane-to-oxygen molar ratio of 2.0, i.e., a stoichiometric mixture for the production of synthesis gas, is used. This ratio is ideal for the downstream For the base case given in Table 1, a methane-to-oxygen molar ratio of 2.0, i.e., a stoichiometric processing such as in the synthesis of methanol and in the production of Fischer-Tropsch products. mixture for the production of synthesis gas, is used. This ratio is ideal for the downstream processing The temperature is set as 300 K at the inlet for the base case, thus effectively avoiding gas-phase such as in the synthesis of methanol and in the production of Fischer-Tropsch products. The combustion; please theKSection Further Discussion forthus more details. avoiding gas-phase temperature is refer set asto300 at the 4. inlet for the base case, effectively Figure 5 shows contour plots of the methane and carbon monoxide concentrations and combustion; please refer to the Section 4. Further Discussion for more details. temperature within the fluid in the methane–oxygen system. Despite the small dimension involved, Figure 5 shows contour plots of the methane and carbon monoxide concentrations and temperatureand within the fluid in the methane–oxygen system. Despite the of small dimension involved, the temperature species gradients change significantly in the vicinity reaction region. This can be the temperature and species gradients change significantly in the vicinity of reactionand region. This can attributed to the difference in the time scale between the heterogeneous reaction the heat transfer attributeddirection. to the difference in the time scale in between the heterogeneous reaction and themay heat need in thebe transverse The significant change both temperature and species gradients in the transverse direction. Thefluid significant change in both andof species gradients to usetransfer a two-dimensional computational dynamics model, astemperature axial diffusion species and energy may need to use a two-dimensional computational fluid dynamics model, as axial diffusion of species is not negligible. Furthermore, mass-transfer limitations, typical characteristics of a catalytic partial and energy is not negligible. Furthermore, mass-transfer limitations, typical characteristics of a oxidation reaction, are observed here, despite the small dimension involved. Accordingly, the effect of catalytic partial oxidation reaction, are observed here, despite the small dimension involved. transport phenomena willof betransport discussed in the following sections.in the following sections. Accordingly, the effect phenomena will be discussed

Figure 5. Contour plots of the methane and carbon monoxide concentrations and temperature within

Figure 5. Contour plots of the methane and carbon monoxide concentrations and temperature within the fluid in the methane–oxygen system. The operating conditions and design parameters used are the fluid in the methane–oxygen system. The operating conditions and design parameters used are listed in Table 1. listed in Table 1.

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3.2. Effect of Preheating for Oxygen Feed 3.2. Effect of Preheating for Oxygen Feed Figure 6 shows the influence of preheating temperature on the performance of the methane– Figure 6 shows the influence of preheating temperature on the performance of the methane–oxygen oxygen system. As the pressure increases, there is a sharp drop in the selectivity to synthesis gas system. As the pressure increases, there is a sharp drop in the selectivity to synthesis gas (Figure 6a,b) (Figure 6a,b) and conversion (Figure 6c), but a sharp rise in wall temperature (Figure 6d). This sharp and conversion (Figure 6c), but a sharp rise in wall temperature (Figure 6d). This sharp drop implies drop implies the initiation of the total oxidation reaction occurring in the gas phase. After the the initiation of the total oxidation reaction occurring in the gas phase. After the initiation of gas-phase initiation of gas-phase combustion, the contribution of heterogeneous reactions is still considerable, combustion, the contribution of heterogeneous reactions is still considerable, as indicated by the as indicated by the selectivity to synthesis gas at high pressures (Figure 6a,b), but there is lack of selectivity to synthesis gas at high pressures (Figure 6a,b), but there is lack of oxygen for the catalytic oxygen for the catalytic partial oxidation reaction. partial oxidation reaction. 100 300 K 500 K

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Figure 6. Influence of preheating temperature on the selectivity, conversion, and maximum wall Figure 6. Influence of preheating temperature on the selectivity, conversion, and maximum wall temperature in the methane–oxygen system. Hereafter, all other parameters are kept at their base case temperature in the methane–oxygen system. Hereafter, all other parameters are kept at their base values shown in Table 1. The sharp drop in selectivity and conversion indicates the initiation of gascase values shown in Table 1. The sharp drop in selectivity and conversion indicates the initiation phase combustion. (a) Selectivity to carbon monoxide; (b) selectivity to hydrogen; (c) outlet of gas-phase combustion. (a) Selectivity to carbon monoxide; (b) selectivity to hydrogen; (c) outlet conversion; conversion; (d) (d) maximum maximum wall wall temperature. temperature.

At atmospheric pressure, the selectivity to synthesis gas (Figure 6a,b) and the conversion (Figure At atmospheric pressure, the selectivity to synthesis gas (Figure 6a,b) and the conversion 6c) increase with increasing preheating temperature. Very high selectivity to synthesis gas (>98%) is (Figure 6c) increase with increasing preheating temperature. Very high selectivity to synthesis possible at atmospheric pressure when the preheating temperature is above 900 K. At atmospheric gas (>98%) is possible at atmospheric pressure when the preheating temperature is above 900 K. pressure, the main product is synthesis gas, and the catalytic partial oxidation reaction is favored at At atmospheric pressure, the main product is synthesis gas, and the catalytic partial oxidation high temperatures. On the other hand, gas-phase combustion is favored at high temperatures, at reaction is favored at high temperatures. On the other hand, gas-phase combustion is favored at which the initiation of the combustion reaction is possible at lower pressures. For example, as the high temperatures, at which the initiation of the combustion reaction is possible at lower pressures. inlet temperature increases from 300 to 900 K, the initiation pressure decreases from about 2.5 to 0.7 For example, as the inlet temperature increases from 300 to 900 K, the initiation pressure decreases MPa. At high pressures, the catalytic partial oxidation reaction is favored at low temperatures. The from about 2.5 to 0.7 MPa. At high pressures, the catalytic partial oxidation reaction is favored at low situation is the reverse of the results obtained at atmospheric pressure. In all of the cases examined here, the selectivity to synthesis gas (Figure 6a,b) and the conversion (Figure 6c) decrease with


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temperatures. The situation is the reverse of the results obtained at atmospheric pressure. In all of the cases examined here, the selectivity to synthesis gas (Figure 6a,b) and the conversion (Figure 6c) increasing pressure. After the initiation of gas-phase combustion, however, the pressure has little or decrease with increasing pressure. After the initiation of gas-phase combustion, however, the pressure no effect on the conversion. Furthermore, the loss in conversion at between atmospheric pressure and has little or no effect on the conversion. Furthermore, the loss in conversion at between atmospheric the highest pressure is almost the same. pressure and the highest pressure is almost the same. On the other hand, as the pressure increases, there is a transition of primary reaction pathway On the other hand, as the pressure increases, there is a transition of primary reaction pathway from catalytic partial oxidation to gas-phase combustion, as depicted by the inflection point in the from catalytic partial oxidation to gas-phase combustion, as depicted by the inflection point in the conversion profile (Figure 6c). After the reactants have been ignited in the gas phase, there is a conversion profile (Figure 6c). After the reactants have been ignited in the gas phase, there is a significant drop in conversion. This is due to lack of oxygen for the gas-phase combustion reaction, significant drop in conversion. This is due to lack of oxygen for the gas-phase combustion reaction, despite the fact that a stoichiometric methane–air mixture is used for the production of synthesis gas despite the fact that a stoichiometric methane–air mixture is used for the production of synthesis gas from the catalytic partial oxidation reaction. Please refer to the stoichiometric coefficients described from the catalytic partial oxidation reaction. Please refer to the stoichiometric coefficients described in in the chemical Equations (20)–(22) for more details. the chemical Equations (20)–(22) for more details.

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3.3. Effect of Preheating for Air Feed 3.3. Effect of Preheating for Air Feed One of the major challenges during the catalytic partial oxidation process is a reduction of the One of the major challenges during the catalytic partial oxidation process is a reduction of the cost cost of pure oxygen separation [15,16], since the production of pure oxygen is highly expensive. The of pure oxygen separation [15,16], since the production of pure oxygen is highly expensive. The reaction reaction system in the presence of a catalyst can be operated at much milder conditions as compared system in the presence of a catalyst can be operated at much milder conditions as compared to the to the gas-phase partial oxidation system, which can effectively inhibit the formation of nitrogen gas-phase partial oxidation system, which can effectively inhibit the formation of nitrogen oxides in oxides in the gas phase, making it possible to use air instead of pure oxygen [15,16]. This shows great the gas phase, making it possible to use air instead of pure oxygen [15,16]. This shows great promise promise for the catalytic partial oxidation process. for the catalytic partial oxidation process. Figure 7 shows the effect of preheating temperature on the performance of the methane–air Figure 7 shows the effect of preheating temperature on the performance of the methane–air system. The pressure has a small effect on the selectivity to synthesis gas, but with a tendency to shift system. The pressure has a small effect on the selectivity to synthesis gas, but with a tendency to shift towards a higher yield of synthesis gas as the pressure decreases, as shown in Figure 7a,b towards a higher yield of synthesis gas as the pressure decreases, as shown in Figure 7a,b Additionally, Additionally, high preheating temperatures tend to improve the yield of synthesis gas. Therefore, the high preheating temperatures tend to improve the yield of synthesis gas. Therefore, the production of production of synthesis gas is favored at low pressures and high temperatures. In this context, the synthesis gas is favored at low pressures and high temperatures. In this context, the outlet concentration outlet concentration of carbon dioxide is very low (Figure 7a), but the small amount of carbon dioxide of carbon dioxide is very low (Figure 7a), but the small amount of carbon dioxide must be removed to must be removed to meet the downstream processing requirements [15,16]. The amount of the total meet the downstream processing requirements [15,16]. The amount of the total oxidation products oxidation products and C2-hydrocarbons increases with increasing pressure, leading to a decrease in and C2 -hydrocarbons increases with increasing pressure, leading to a decrease in both conversion and both conversion and the selectivity to synthesis gas. On the other hand, the conversion is favored at the selectivity to synthesis gas. On the other hand, the conversion is favored at high temperatures and high temperatures and at low pressures, as shown in Figure 7c. In contrast, the maximum wall at low pressures, as shown in Figure 7c. In contrast, the maximum wall temperature increases with temperature increases with increasing pressure, especially at high preheating temperatures (Figure increasing pressure, especially at high preheating temperatures (Figure 7d) where the total oxidation 7d) where the total oxidation reaction is favored. In comparison with the results obtained for the reaction is favored. In comparison with the results obtained for the methane–oxygen system (Figure 6), methane–oxygen system (Figure 6), the initiation of gas-phase combustion is impossible for the the initiation of gas-phase combustion is impossible for the methane–air system, and the contribution methane–air system, and the contribution of homogeneous reactions is small. of homogeneous reactions is small.

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Figure 7. Effect of preheating temperature on the selectivity, conversion, and maximum wall Figure 7. Effect of preheating temperature on the selectivity, conversion, and maximum wall temperature in the methane–air system. (a) Selectivity to carbon monoxide and carbon dioxide; (b) Figure 7. Effect preheating temperature selectivity, and maximum wall temperature temperature in of the methane–air system. on (a)the Selectivity toconversion, carbon monoxide and carbon dioxide; (b) selectivity to hydrogen and water; (c) outlet conversion; (d) maximum wall temperature. in the methane–air system. (a) Selectivity to carbon monoxide and carbon dioxide; (b) selectivity to selectivity to hydrogen and water; (c) outlet conversion; (d) maximum wall temperature. hydrogen and water; (c) outlet conversion; (d) maximum wall temperature.

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3.4. Effect of Reactor Dimension for Oxygen Feed 3.4. Effect of Reactor Dimension for Oxygen Feed The reactor dimension 3.4. Effect of Reactor Dimensioncan for significantly Oxygen Feed affect the effect of mass transfer [78]. For the system The reactor dimension can significantly affect the effect of mass transfer [78]. For the system examined here, it is unclear whether there is an optimal dimension in which the yield of synthesis The reactor significantly the effect of mass [78]. Forofthe system examined here, itdimension is unclear can whether there is affect an optimal dimension intransfer which the yield synthesis gas can be maximized. To provide a way to reduce the contribution of homogeneous reactions, the examined it is unclear whetherathere optimal in which the yield of reactions, synthesis gas gas can behere, maximized. To provide way is toan reduce thedimension contribution of homogeneous the effect of reactor dimension is investigated. can beof maximized. To provide a way to reduce the contribution of homogeneous reactions, the effect effect reactor dimension is investigated. Figure 8 presents the results obtained for the selectivity, conversion, and maximum wall of reactor dimension is investigated. Figure 8 presents the results obtained for the selectivity, conversion, and maximum wall temperature at different dimensions of the methane–oxygen system. The selectivity to synthesis gas Figure 8atpresents results obtained for the selectivity, conversion, and maximum temperature differentthe dimensions of the methane–oxygen system. The selectivity to synthesiswall gas is favored in smaller reactors, as shown in Figure 8a,b. The dimension has little effect on the reactor temperature at different dimensions of in theFigure methane–oxygen system. has Thelittle selectivity synthesis is favored in smaller reactors, as shown 8a,b. The dimension effect ontothe reactor performance at low pressures, where the system is operated in a surface kinetically-controlled regime gas is favoredat inlow smaller reactors, as shown in Figure 8a,b. The has little effect on the regime reactor performance pressures, where the system is operated indimension a surface kinetically-controlled and the yield of synthesis gas is excellent. At high pressures, however, both mass-transfer limitations performance at low pressures, where the system is operated in a surface kinetically-controlled regime and the yield of synthesis gas is excellent. At high pressures, however, both mass-transfer limitations and homogeneous reactions become significant. For the smallest reactor studied, the dominant and the yield of synthesis gas is excellent. At high pressures, however,reactor both mass-transfer homogeneous reactions become significant. For the smallest studied, the limitations dominant chemistry is heterogeneous at all of the pressures examined. At the highest pressure examined, the and homogeneous reactionsatbecome significant. For the smallest reactor pressure studied, examined, the dominant chemistry is heterogeneous all of the pressures examined. At the highest the selectivity to synthesis gas is quite high in the smallest reactor, but drops sharply in the largest chemistry all ofhigh the pressures examined. Atbut thedrops highest pressure examined, selectivity is to heterogeneous synthesis gas isatquite in the smallest reactor, sharply in the largest reactor. Furthermore, the yield of synthesis gas is favored in smaller reactors, in which the dominant the selectivity to synthesis gas is highgas in the smallest dropsinsharply in the largest reactor. Furthermore, the yield of quite synthesis is favored inreactor, smaller but reactors, which the dominant chemistry is heterogeneous, as discussed above. Therefore, the design shows great promise for the reactor. Furthermore, the yield synthesisabove. gas is Therefore, favored in smaller reactors, which the dominant chemistry is heterogeneous, as of discussed the design showsingreat promise for the production of synthesis gas, but only at low pressures. To achieve a high yield of synthesis gas at chemistry heterogeneous, above. Therefore, the design shows great promise for productionisof synthesis gas, as butdiscussed only at low pressures. To achieve a high yield of synthesis gasthe at high pressures, the reactor dimension must be carefully designed to reduce the mass-transfer production of synthesis gas, but only at low pressures. To achieve a high to yield of synthesis gas at high high pressures, the reactor dimension must be carefully designed reduce the mass-transfer limitations. pressures, limitations.the reactor dimension must be carefully designed to reduce the mass-transfer limitations.

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Figure 8. Effect of reactor dimension on the selectivity, conversion, and maximum wall temperature 8. Effect of reactor dimension on the selectivity, andcarbon maximum wall (b) temperature inFigure the methane–oxygen system. (a) Selectivity to carbonconversion, monoxide and dioxide; selectivityin the methane–oxygen system. (a) Selectivity to carbon monoxide and carbon dioxide; (b) selectivity to hydrogen and water; (c) total selectivity to C2 products; (d) outlet conversion and maximum wall to hydrogen and water; (c) total selectivity to C products; (d) outlet conversion and maximum 2 temperature. wall temperature.

Figure 8a,b also shows the selectivity to the total oxidation products. For the largest dimension Figure 8a,bthe alsoamount shows the to the totalproducts oxidationisproducts. For the largest dimension examined here, of selectivity the total oxidation considerable, especially at high examinedas here, the amount the total oxidation is increases considerable, especially atdue high pressures, shown in Figureof8a,b. In this context,products there is an in temperature topressures, the heat as shown Figure In this reaction context, there is an in temperature due toofthe heat released released byinthe total8a,b. oxidation Figure 8d,increases thus increasing the amount undesired byby the total oxidation reaction Figure 8d, thus of undesired by-products such as products such as C2-hydrocarbons (Figure 8c). increasing Therefore,the theamount contribution of homogeneous reactions 8c). Therefore, the contribution homogeneous reactions at high pressures atChigh pressures is(Figure considerable for the largest dimension of examined. After the initiation of gas-phase 2 -hydrocarbons is considerable largest dimension examined. After the initiation of gas-phase combustion, combustion, therefor is the a sharp drop in conversion for the moderate to large reactors studied, as shown is a8d. sharp in conversion moderate to largewith reactors studied,the as reactor shown in Figure 8d. inthere Figure Thedrop inflection point offor thethe pressure decreases increasing dimension. Themaximum inflection point the pressureincreases decreaseswith withincreasing increasingpressure. the reactor dimension. The maximum The wall of temperature This is mainly due to the wall temperature with increasing This is mainly due to the increased of the increased amount increases of the reactants. A sharp pressure. rise in temperature represents initiation amount of gas-phase reactants. A as sharp rise in represents initiation wall of gas-phase combustion, as shown combustion, shown in temperature Figure 8d. Finally, thethe maximum temperature levels off at highin pressures. yield of synthesis gas is favored low for theOverall, methane–oxygen Figure 8d.Overall, Finally, the maximum wall temperature levelsatoff at pressures high pressures. the yield of synthesis gas is favored at low pressures for the methane–oxygen system. system.

3.5.Effect EffectofofReactor ReactorDimension Dimensionfor forAir AirFeed Feed 3.5. Asdiscussed discussed above, significantly affect the performance of theofmethane–oxygen As above, the thedimension dimensioncan can significantly affect the performance the methane– system operated at high pressures. To gain a better understanding of the design described in this paper, oxygen system operated at high pressures. To gain a better understanding of the design described in the paper, effect ofthe reactor investigatedisfor the methane–air system operatedsystem at various pressures. this effectdimension of reactorisdimension investigated for the methane–air operated at Figure 9 presents the results obtained for the selectivity, conversion, and maximum wall various pressures. temperature different dimension has little no effect on the Figure 9 at presents thereactor resultsdimensions. obtained forThe thereactor selectivity, conversion, andor maximum wall selectivity toat synthesis (Figure 9a,b) under conditions studied here. orThe temperature different gas reactor dimensions. The the reactor dimension has little no production effect on theof C -hydrocarbons is favored in lager reactors (Figure 9c). On the other hand, the reactor dimension 2 selectivity to synthesis gas (Figure 9a,b) under the conditions studied here. The production of C2has little effect on the conversion (left vertical axis, Figure 9d), and the maximum wall temperature hydrocarbons is favored in lager reactors (Figure 9c). On the other hand, the reactor dimension has (right vertical axis, Figure 9d). expected, dominant is heterogeneous in all(right of the little effect on the conversion (leftAs vertical axis, the Figure 9d), andchemistry the maximum wall temperature cases under the conditions studied here, and the initiation of gas-phase combustion is impossible vertical axis, Figure 9d). As expected, the dominant chemistry is heterogeneous in all of the casesin the methane–air system examined. under the conditions studied here, and the initiation of gas-phase combustion is impossible in the methane–air system examined.

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Figure 9. Effect of dimension on the performance of the methane–air system operated at various Figure 9. Effect of dimension on the performance of the methane–air system operated at various pressures. (a) Selectivity to carbon monoxide and carbon dioxide; (b) selectivity to hydrogen and pressures. (a) Selectivity to carbon monoxide and carbon dioxide; (b) selectivity to hydrogen and water; water; (c) total selectivity to C2 products; (d) outlet conversion and maximum wall temperature. (c) total selectivity to C2 products; (d) outlet conversion and maximum wall temperature.

3.6. Effect of Nitrogen Diluent 3.6. Effect of Nitrogen Diluent For the design examined, the onset of gas-phase combustion can be inhibited by utilizing a For the design examined, the onset of gas-phase combustion can be inhibited by utilizing a methane–air system (Figures 7 and 9), while a methane–oxygen system (Figures 6 and 8) will allow methane–air system (Figures 7 and 9), while a methane–oxygen system (Figures 6 and 8) will allow the gas mixture to be ignited at a certain pressure, as discussed above. It is therefore important to the gas mixture to be ignited at a certain pressure, as discussed above. It is therefore important to determine the critical dilution to reduce the contribution of the reaction occurring in the gas phase. determine the critical dilution to reduce the contribution of the reaction occurring in the gas phase. Figure 10 shows the influence of nitrogen diluent on the performance of the reactor operated at Figure 10 shows the influence of nitrogen diluent on the performance of the reactor operated at preheating temperature 700 K. The contribution of homogeneous reactions is small, but considerable preheating temperature 700 K. The contribution of homogeneous reactions is small, but considerable under certain conditions. At high pressures, the methane–air system has the advantage of reducing under certain conditions. At high pressures, the methane–air system has the advantage of reducing undesired by-products and improving the selectivity to synthesis gas, as shown in Figure 10a,b. At undesired by-products and improving the selectivity to synthesis gas, as shown in Figure 10a,b. At the the highest pressure examined, there appears to be an optimal dilution ratio, of about 38% nitrogen highest pressure examined, there appears to be an optimal dilution ratio, of about 38% nitrogen in the in the mixture, which exhibits the maximum yield of synthesis gas. The methane–air system suffers mixture, which exhibits the maximum yield of synthesis gas. The methane–air system suffers a slight a slight drop in conversion (Figure 10d), but offers an economical solution to the production of drop in conversion (Figure 10d), but offers an economical solution to the production of synthesis gas synthesis gas (Figure 10a,b). At moderate pressure 1.5 MPa, only 8% nitrogen diluent is needed to (Figure 10a,b). At moderate pressure 1.5 MPa, only 8% nitrogen diluent is needed to avoid the initiation avoid the initiation of the combustion reaction occurring in the gas phase. At atmospheric pressure, of the combustion reaction occurring in the gas phase. At atmospheric pressure, the contribution of the contribution of homogeneous reactions is rather small, and thus nitrogen dilution has little or no homogeneous reactions is rather small, and thus nitrogen dilution has little or no effect on the yield effect on the yield of synthesis gas. At moderate to high pressures, there exists a sharp rise in the yield of synthesis gas. At moderate to high pressures, there exists a sharp rise in the yield of synthesis of synthesis gas, as shown in Figure 10. The inflection point of the nitrogen diluent increases with gas, as shown in Figure 10. The inflection point of the nitrogen diluent increases with increasing increasing pressure. For the methane–air system, the yield of synthesis gas also increases with pressure. For the methane–air system, the yield of synthesis gas also increases with increasing pressure. increasing pressure. For the system operated at moderate to high pressures with a low dilution, the For the system operated at moderate to high pressures with a low dilution, the initiation of gas-phase initiation of gas-phase combustion is possible, and both the amount of C 2-hydrocarbons and the maximum wall temperature increases with increasing pressure, as shown in Figure 10c,d.


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Figure Figure 10. 10. Effect Effectof of nitrogen nitrogen diluent diluenton on the the selectivity, selectivity, conversion, conversion, and and maximum maximum wall wall temperature temperature at different pressures when the reactor is operated at preheating temperature 700 K. at different pressures when the reactor is operated at preheating temperature 700 K. (a) (a) Selectivity Selectivityto to carbon monoxide and carbon dioxide; (b) selectivity to hydrogen and water; (c) total selectivity to C carbon monoxide and carbon dioxide; (b) selectivity to hydrogen and water; (c) total selectivity to C22 products; products; (d) (d) outlet outlet conversion conversion and and maximum maximum wall wall temperature. temperature.

3.7. Air Feed Versus Oxygen Feed 3.7. Air Feed Versus Oxygen Feed Comparisons are made between the results obtained for the two systems operated at Comparisons are made between the results obtained for the two systems operated at atmospheric atmospheric pressure. Figure 11 shows the influence of preheating temperature on the performance pressure. Figure 11 shows the influence of preheating temperature on the performance of the two of the two systems operated at atmospheric pressure. Both the selectivity to synthesis gas (Figure systems operated at atmospheric pressure. Both the selectivity to synthesis gas (Figure 11a,b) and the 11a,b) and the outlet conversion (Figure 11c) are higher for the methane–oxygen system than for the outlet conversion (Figure 11c) are higher for the methane–oxygen system than for the methane–air methane–air system, especially at lower temperatures. For both systems, the production of synthesis system, especially at lower temperatures. For both systems, the production of synthesis gas is favored at gas is favored at high preheating temperatures, but the methane–air system can benefit more from high preheating temperatures, but the methane–air system can benefit more from preheating, as shown preheating, as shown in Figure 11. Therefore, the effect of preheating is more pronounced for the in Figure 11. Therefore, the effect of preheating is more pronounced for the methane–air system. methane–air system. For each of the two systems, the maximum wall temperature increases with For each of the two systems, the maximum wall temperature increases with increasing preheating increasing preheating temperature under the conditions examined here (Figure 11c). As expected, the temperature under the conditions examined here (Figure 11c). As expected, the maximum temperature maximum temperature within the walls is higher for the methane–oxygen system than for the within the walls is higher for the methane–oxygen system than for the methane–air system. methane–air system.

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Oxyg

10

5

en fee d

80 300


(a)

0 900

(b) 100


15

1400

d en fee

90

Oxyg

80

Air

1300

feed 1200

ed en fe Oxyg 70

1100

eed Air f 60 300



Air


Oxygen

100


20



100

17 17 of of 24 24

1000 900

(c) Figure 11. Comparisons the methane–air methane–air system system operated operated Figure 11. Comparisons between between the the methane–oxygen methane–oxygen system system and and the at atmospheric pressure. (a) Selectivity to carbon monoxide and carbon dioxide; (b) selectivity to at atmospheric pressure. (a) Selectivity to carbon monoxide and carbon dioxide; (b) selectivity to hydrogen and water; water; (c) (c) outlet outlet conversion conversion and and maximum maximum wall wall temperature. temperature. hydrogen and

4. Further Discussion 4. Further Discussion The results presented above indicate that the design shows great promise for the production of The results presented above indicate that the design shows great promise for the production of synthesis gas from methane. When the dominant chemistry is heterogeneous, the effect of pressure synthesis gas from methane. When the dominant chemistry is heterogeneous, the effect of pressure is is small. In contrast, when the gas-phase chemistry is considerable, the pressure can significantly small. In contrast, when the gas-phase chemistry is considerable, the pressure can significantly affect affect the reactor performance such as the yield of synthesis gas. In this context, the initiation of gasthe reactor performance such as the yield of synthesis gas. In this context, the initiation of gas-phase phase combustion is possible, the temperature is high, the amount of undesired by-products is combustion is possible, the temperature is high, the amount of undesired by-products is relatively relatively large, and the out conversion is low, as shown in Figure 8. For the base case, a stoichiometric large, and the out conversion is low, as shown in Figure 8. For the base case, a stoichiometric mixture mixture for the production of synthesis gas is utilized. In this context, homogeneous reactions can for the production of synthesis gas is utilized. In this context, homogeneous reactions can lead to a lead to a lower outlet conversion, because they tend to consume more amount of oxygen than lower outlet conversion, because they tend to consume more amount of oxygen than heterogeneous heterogeneous reactions, which leads to lack of oxygen. reactions, which leads to lack of oxygen. At the highest pressure examined, it may be difficult to optimize operating conditions of the At the highest pressure examined, it may be difficult to optimize operating conditions of methane–oxygen system. This is because high preheating temperatures increase the outlet the methane–oxygen system. This is because high preheating temperatures increase the outlet conversion, but decrease the selectivity to synthesis gas, as shown in Figure 6. Furthermore, the conversion, but decrease the selectivity to synthesis gas, as shown in Figure 6. Furthermore, the selectivity to synthesis gas is not high enough, at all of the preheating temperatures examined for the selectivity to synthesis gas is not high enough, at all of the preheating temperatures examined for the methane–oxygen system. The selectivity to synthesis gas decreases with increasing the preheating methane–oxygen system. The selectivity to synthesis gas decreases with increasing the preheating temperature, as shown in Figure 6. However, smaller reactors show great promise, since they can temperature, as shown in Figure 6. However, smaller reactors show great promise, since they can delay the initiation of gas-phase combustion, as shown in Figure 8. delay the initiation of gas-phase combustion, as shown in Figure 8. At high pressures, the methane–air system has the advantage of reducing the contribution of At high pressures, the methane–air system has the advantage of reducing the contribution of homogeneous reactions, as shown in Figures 6 and 7. At low pressures, the dimension has little or no homogeneous reactions, as shown in Figures 6 and 7. At low pressures, the dimension has little or effect on the performance of each of the two systems, as shown in Figures 8 and 9. At all of the no effect on the performance of each of the two systems, as shown in Figures 8 and 9. At all of the pressures examined here, the dimension has little effect on the performance of the methane–air system, and the contribution of homogeneous reactions is negligible, as illustrated in Figure 9. For


18 of 24

pressures examined here, the dimension has little effect on the performance of the methane–air system, and the contribution of homogeneous reactions is negligible, as illustrated in Figure 9. For the mixture of methane and oxygen diluted with a large amount of nitrogen, the collision between the reactant molecules becomes less frequent, which can greatly reduce the contribution of homogeneous reactions, as shown in Figure 10. However, the contribution may still be considerable at high pressures, as shown in Figure 10, because mass-transfer limitations are significant under the conditions examined here. At the highest pressure examined here, the methane–air system can offer a good yield of synthesis gas, especially at high preheating temperatures, as shown in Figure 7. For each of the two systems, the yield of synthesis gas decreases with increasing pressure, as shown in Figures 6 and 7. At high pressures, the production of synthesis gas is favored at low preheating temperatures for the methane–oxygen system (Figure 6), but at high preheating temperatures for the methane–air system (Figure 7). At atmospheric pressure, the use of oxygen and the use of preheated air have the similar effect on the reactor performance, due to the negligible contribution of homogeneous reactions (Figure 11). At high pressures, however, the effect played by the above two feeding methods is quite different from each other, because in this context the contribution of homogeneous reactions is considerable. For each of the two systems, the outlet conversion decreases with increasing pressure due to the mass-transfer limitations and the possible occurrence of gas-phase combustion, especially in larger dimensions. The mass-transfer effect is more pronounced at high pressures, as shown in Figures 7 and 8. As the dimension of the methane–oxygen system increases, the outlet conversion drops sharply (Figure 8), because in this context the mass-transfer effect may be important [79,80] and the initiation of gas-phase combustion is possible. 5. Conclusions Catalytic partial oxidation of methane in microchannel reactors in high temperature environments was studied numerically. This investigation provided knowledge on how reaction conditions affect the operating characteristics and the distribution of reaction products in the reactor. Comparisons were made with published results, suggesting that the model developed in this paper is reliable and helpful to the design of the system. Furthermore, the catalytic partial oxidation process under extremely short contact time conditions can be accurately described by the model via the combination of detailed heterogeneous and homogenous reaction mechanisms. The results have shown that the relative role of heterogeneous and homogeneous reaction pathways depends strongly upon the operating conditions. The distribution of reaction products depends upon a number of factors, such as the reactor dimension, pressure, temperature, and feed composition. The operating temperature can significantly affect the yield of synthesis gas. Undesired homogeneous reactions are favored in large reactors, and at high temperatures and pressures. It is more economical to utilize air instead of oxygen as the oxidant. Such an arrangement is particularly beneficial, since the onset of homogeneous reactions can thereby be inhibited or avoided. It is necessary to use the reactant mixture diluted with a sufficient amount of nitrogen to avoid homogenous reactions at high pressures. When air is used as the oxidant, preheating is needed, and the production of synthesis gas is practically favored at high pressures. The use of air as the oxidant is preferred at industrially relevant pressure 3 MPa, at which the contribution of undesired homogeneous reactions is usually small. Further research is needed on the principles underlying the catalytic partial oxidation process. Catalyst deactivation may be an important risk factor, which is not addressed in this paper. This deactivation can significantly decrease the yield of synthesis gas, thus reducing the performance of the system. There are potential solutions to this issue, such as process control to maintain the temperature below a certain damaging threshold, non-uniform catalyst distribution, and thicker catalyst layers. Furthermore, the success of microchannel reactors is highly dependent on the robust catalysts suitable for the operating conditions of these small-scale chemical systems. On the other hand, high temperatures obtained within the system may destroy the catalyst wash coat employed


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and impose severe constraints on the materials used. Lower reactor temperatures are essential for the stability of the catalyst and materials used. The problem related to the materials stability limit is also not addressed in this paper. A temperature threshold should be well defined in the practical design, which will be the subject of future work. Author Contributions: Conceptualization, J.C.; Methodology, J.C.; Software, W.S.; Validation, W.S.; Formal Analysis, J.C. and D.X.; Investigation, J.C. and W.S.; Resources, D.X.; Supervision, J.C.; Project Administration, J.C. and D.X.; J.C. conceived and designed the analyses and simulations; W.S. implemented the C code for the ANSYS Fluent program; D.X. contributed to concepts and notebooks; J.C. and D.X. provided chemical expertise and insight; J.C. wrote the paper. Funding: This research was funded by the National Natural Science Foundation of China (No. 51506048) and the Fundamental Research Funds for the Universities of Henan Province (No. NSFRF140119). Acknowledgments: J.C. is grateful for financial support from the National Natural Science Foundation of China and the Henan Polytechnic University. The authors would also like to acknowledge the DETCHEM website for their computing resources. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature A A0 C c D DT Deff Dm d dpore Ea Fcat/geo F Θ ∆r Hm h ho Kg , Ks l m p q R . s s T, To u, v

pre-exponential factor surface area concentration specific heat capacity diffusivity thermal diffusivity effective diffusivity mixture-averaged diffusivity channel height mean pore diameter activation energy catalyst/geometric surface area view factor standard molar enthalpy of reaction specific enthalpy external heat loss coefficient number of gaseous species and number of surface species length total number of gaseous and surface species pressure heat flux ideal gas constant rate of appearance of a heterogeneous product sticking coefficient absolute temperature and reference temperature streamwise and transverse velocity components

V, V

diffusion velocity and diffusion velocity vector

W, W x Y y

relative molecular mass and relative molecular mass of the mixture

→

→

streamwise coordinate mass fraction transverse coordinate


20 of 24

Greek variables γ surface area per unit catalyst volume ε emissivity δ thickness εp catalyst porosity λ thermal conductivity η effectiveness factor µ dynamic viscosity ρ density σ Stefan-Boltzmann constant ϑ site occupancy τp catalyst tortuosity factor φ inlet molar ratio . ω rate of appearance of a homogeneous product Γ site density Θ surface coverage Φ Thiele modulus Subscripts amb ambient eff effective g gas i, k, m species index, gaseous species index, and surface species index in inlet o outer rad radiation s solid w wall x, y streamwise and transverse components

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Computational Fluid Dynamics Modeling of The Dalles Project ...

Computational fluid dynamics (CFD)

Computational Fluid Dynamics

Computational fluid dynamics

Applied Computational Fluid Dynamics

Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD)

COMPUTATIONAL FLUID DYNAMICS SIMULATION OF

COMPUTATIONAL FLUID DYNAMICS SIMULATION OF ...

Forebay Computational Fluid Dynamics Modeling for The Dalles ...