Metal Foams as Novel Catalyst Support in Environmental Processes

Metal foams are considered as promising catalyst carriers due to their high porosity, large specific surface area, and satisfactory thermal and mechanical stability. The study presents heat transfer and pressure drop experiments performed for seven foams of different pore densities made from diverse metals. Mass transfer characteristics are derived using the Chilton–Colburn analogy. It was found that the foams display much more intense heat/mass transfer than a monolith, comparable to packed bed. Next, the foams’ efficiencies have been compared, using 1D reactor modeling, in catalytic reactions displaying either slower (selective catalytic reduction of NOx) or faster kinetics (catalytic methane combustion). For the slow kinetics, the influence of carrier specific surface area at which catalyst can be deposited (i.e., catalyst amount) was decisive to achieve high process conversion and short reactor. For this case, monolith appears as the best choice assuming it’s the lowest pressure drop. For the fast reaction, the mass transfer becomes the limiting parameter, thus solid foams are the best solution.


Introduction
It seems usually acceptable that the catalyst is a key element of the catalytic reactor. Indeed, the catalyst enables enhanced reaction kinetics, thus, the reaction rate may be significantly increased when comparing with that of noncatalytic reactions. However, only as many molecules may react as reach the catalyst surface. Hence, the reaction rate depends on the substrate concentration at the catalyst surface (more exactly, at the active centers), not on the concentration in the bulk reactants stream. The concentration at the surface depends, in turn, on the reaction kinetics and the mass transfer coefficient. In fact, the mass transfer rate is as important as the kinetics, being a possible limitation of the process yield. Mass transfer is strictly bound with the heat transfer by the Chilton-Colburn analogy: Nu Pr 1/3 = Sh Sc 1/3 (1) In the literature, many correlations describing the heat (e.g., [15][16][17][18]) and mass transfer coefficient (e.g., [1,[19][20][21]) for solid foams can be found. A comparison between experimental results in terms of Nu/Pr 1/3 (according to the Chilton-Colburn analogy) and calculated based on the selected literature correlations for heat transfer for Al 10 ( Figure 2a) and Ni 0610 (Figure 2b) is presented. For the same foams, a similar comparison of mass transfer coefficient obtained experimentally (i.e., based on the Nu number using Chilton-Colburn analogy) and calculated using selected literature correlations is presented in Figure 3 in the form of Sh/Sc 1/3 . Because literature correlations describing heat and mass transfer coefficient defined dimensionless number (Re, Nu, Sh) with different characteristic dimensions, therefore they were recalculated using strut diameter, ds, (see Section 4 Materials and Methods) as characteristic one. As can be noticed, for both, the heat ( Figure 2) and the mass (Figure 3), when a given correlation describes quite well the results obtained for one foam, it very often fails for the others [22]. A similar situation was also observed for flow resistance [23,24].  In the literature, many correlations describing the heat (e.g., [15][16][17][18]) and mass transfer coefficient (e.g., [1,[19][20][21]) for solid foams can be found. A comparison between experimental results in terms of Nu/Pr 1/3 (according to the Chilton-Colburn analogy) and calculated based on the selected literature correlations for heat transfer for Al 10 ( Figure 2a) and Ni 0610 (Figure 2b) is presented. For the same foams, a similar comparison of mass transfer coefficient obtained experimentally (i.e., based on the Nu number using Chilton-Colburn analogy) and calculated using selected literature correlations is presented in Figure 3 in the form of Sh/Sc 1/3 . Because literature correlations describing heat and mass transfer coefficient defined dimensionless number (Re, Nu, Sh) with different characteristic dimensions, therefore they were recalculated using strut diameter, d s , (see Section 4 Materials and Methods) as characteristic one. As can be noticed, for both, the heat ( Figure 2) and the mass (Figure 3), when a given correlation describes quite well the results obtained for one foam, it very often fails for the others [22]. A similar situation was also observed for flow resistance [23,24]. Nu/Pr 1/3 (describing the heat transfer) and in equivalent mass transfer term (Sh/Sc 1/3 ), according to the Chilton-Colburn analogy (equation (1)).This approach is applied in this paper. Because, for comparison, the results for monolith and packed bed are also presented in Figure 1, therefore, the hydraulic diameter, dh, for all presented catalyst carriers was chosen as the characteristic one. As can be seen, the heat and mass transport properties for solid foams are comparable with packed bed and much higher than for monolith. In the literature, many correlations describing the heat (e.g., [15][16][17][18]) and mass transfer coefficient (e.g., [1,[19][20][21]) for solid foams can be found. A comparison between experimental results in terms of Nu/Pr 1/3 (according to the Chilton-Colburn analogy) and calculated based on the selected literature correlations for heat transfer for Al 10 ( Figure 2a) and Ni 0610 (Figure 2b) is presented. For the same foams, a similar comparison of mass transfer coefficient obtained experimentally (i.e., based on the Nu number using Chilton-Colburn analogy) and calculated using selected literature correlations is presented in Figure 3 in the form of Sh/Sc 1/3 . Because literature correlations describing heat and mass transfer coefficient defined dimensionless number (Re, Nu, Sh) with different characteristic dimensions, therefore they were recalculated using strut diameter, ds, (see Section 4 Materials and Methods) as characteristic one. As can be noticed, for both, the heat ( Figure 2) and the mass (Figure 3), when a given correlation describes quite well the results obtained for one foam, it very often fails for the others [22]. A similar situation was also observed for flow resistance [23,24].   The heat transfer for solid foams is very often described by the correlation of the form: that originally was proposed for the bundle of tubes [25], where coefficient a and exponent b depends on the Reynolds number value. As can be seen in Figure 1, all experimental results of heat/mass transfer of solid foams tested are similar. Therefore, for all the foams', tested parameters a and b from equation (1) were estimated, based on experimental results, obtaining a = 0.489 and b = 0.552. Because heat transfer for the solid foams depends mainly on the specific surface area and strut diameter [15], therefore strut diameter was chosen as the characteristic diameter in the definition of the Reynolds and Nusselt number. The correlation describes the experimental results with average relative error, ey ≈ 9.3%, as presented in Figure 4.

Assessment of Solid Foams as Catalyst Carriers
Solid foams can be adapted to process requirements in terms of amount of catalyst due to the wide range of the specific surface area available. The next important benefit of solid foams is a wide range of porosity that offers relatively low flow resistance. Moreover, the complicated three-dimensional (3D) structure of a foam skeleton ensures intense mixing of the flowing fluids, thus intense heat and mass transfer. The heat transfer for solid foams is very often described by the correlation of the form: that originally was proposed for the bundle of tubes [25], where coefficient a and exponent b depends on the Reynolds number value. As can be seen in Figure 1, all experimental results of heat/mass transfer of solid foams tested are similar. Therefore, for all the foams', tested parameters a and b from Equation (1) were estimated, based on experimental results, obtaining a = 0.489 and b = 0.552. Because heat transfer for the solid foams depends mainly on the specific surface area and strut diameter [15], therefore strut diameter was chosen as the characteristic diameter in the definition of the Reynolds and Nusselt number. The correlation describes the experimental results with average relative error, e y ≈ 9.3%, as presented in Figure 4.  The heat transfer for solid foams is very often described by the correlation of the form: that originally was proposed for the bundle of tubes [25], where coefficient a and exponent b depends on the Reynolds number value. As can be seen in Figure 1, all experimental results of heat/mass transfer of solid foams tested are similar. Therefore, for all the foams', tested parameters a and b from equation (1) were estimated, based on experimental results, obtaining a = 0.489 and b = 0.552. Because heat transfer for the solid foams depends mainly on the specific surface area and strut diameter [15], therefore strut diameter was chosen as the characteristic diameter in the definition of the Reynolds and Nusselt number. The correlation describes the experimental results with average relative error, ey ≈ 9.3%, as presented in Figure 4.

Assessment of Solid Foams as Catalyst Carriers
Solid foams can be adapted to process requirements in terms of amount of catalyst due to the wide range of the specific surface area available. The next important benefit of solid foams is a wide range of porosity that offers relatively low flow resistance. Moreover, the complicated three-dimensional (3D) structure of a foam skeleton ensures intense mixing of the flowing fluids, thus intense heat and mass transfer.

Assessment of Solid Foams as Catalyst Carriers
Solid foams can be adapted to process requirements in terms of amount of catalyst due to the wide range of the specific surface area available. The next important benefit of solid foams is a wide range of porosity that offers relatively low flow resistance. Moreover, the complicated three-dimensional (3D) structure of a foam skeleton ensures intense mixing of the flowing fluids, thus intense heat and mass transfer. Comparison of heat and mass transfer coefficients of solid foams with classic packed bed and monolith, as presented in Figure 1, shows that transport intensity for the foams is close to that of packed bed and much higher than that of the monolith. However, in order to test the applicability of solid foam as a catalyst carrier instead of a monolith or packed bed, the reactor performance was compared for catalytic combustion of methane and SCR deNOx, selected as model catalytic reactions. The catalyst carriers chosen were NC 0610 foam, the 100 cpsi monolith (200 mm long), and packed bed of 3 mm spherical particles (egg-shell type), that displayed a similar specific surface area, defined as the external surface area per unit volume of bed (see Table 1). Moreover, NC 2733 was also taken into account in order to check the effect of foam morphology on the process yield.
The correlations describing the heat, mass transfer, and flow resistance for the solid foams (based on the experimental results), as well as the literature correlation for the monolith [26] and packed bed [27,28], are presented in Table 1. Because the compared catalyst carriers significantly differ in their geometry, therefore the hydraulic diameter was used as the characteristic dimension.
To assist in the evaluation and selection of the most favorable catalyst support for a given catalytic process, different criteria are defined in the literature. The criteria take into account different parameters, such as technological (length of reactor, flow resistance) or process selectivity, yield, etc. Choice of the appropriate criterion depends on which parameter is the most important for the designer (operating cost, selectivity, or conversion), or on the available data. Different criteria commonly yield similar results, which is not surprising, especially given that criteria are usually based on similar dependencies [2].  In this work, the performance for SCR deNOx and the catalytic combustion of methane were modelled using the one-dimensional (1D) plug flow reactor model, in accordance with the procedure checked for n-hexane catalytic combustion [29], assuming steady state conditions: • the material balance in the gas phase: with boundary conditions: z = 0; C A = C A0. • the heat balance for the gas phase: Catalysts 2019, 9, 587 6 of 13 with boundary conditions: z = 0; T = T 0 , and assuming no heat losses. • the material balance at the catalyst surface: • the heat balance at the catalyst surface: • the influence of axial dispersion on the final conversion is neglected [29,30].
Kinetic data for considering processes are presented in Table 2. As can be seen, deNOx reaction displays rather slow kinetics, while methane combustion is a very fast reaction. The modelling was performed in two ways: 1. reaction conversion was calculated along the reactor axis (z) for T = const. and w = const.; 2.
necessary reactor length to reach 90% conversion was calculated for given flow velocity at T = const.
The modelling results for SCR deNOx are presented in Figure 5, and for methane catalytic combustion in Figure 6. • the heat balance for the gas phase: with boundary conditions: z = 0; T = T0, and assuming no heat losses.
• the material balance at the catalyst surface: • the heat balance at the catalyst surface: • the influence of axial dispersion on the final conversion is neglected [29,30]. Kinetic data for considering processes are presented in Table 2. As can be seen, deNOx reaction displays rather slow kinetics, while methane combustion is a very fast reaction. The modelling was performed in two ways: 1. reaction conversion was calculated along the reactor axis (z) for T = const. and w = const.; 2. necessary reactor length to reach 90% conversion was calculated for given flow velocity at T = const. The modelling results for SCR deNOx are presented in Figure 5, and for methane catalytic combustion in Figure 6.    Considering the slow deNOx reaction, carriers of close specific surface area (i.e., NC 0610 foam, a 100 cpsi monolith, and a packed bed of 3 mm grains) achieved similar conversion along the reactor axis ( Figure 5a). Therefore, also the reactor length necessary to achieve 90% conversion is almost the same for them in a wide range of flow velocities (Figure 5b). On the other hand, flow resistances for those carriers differ greatly. The highest pressure drop is always displayed by the packed bed, and the lowest by the monolith. The NC 0610 foam is in between. The NC 2733 foam has achieved higher conversion along the reactor length, so also 90% conversion of NO requires a much shorter reactor. This is the result of a much larger specific surface area of NC 2733 foam available to catalyst deposition, hence the mass of catalyst (assuming the same catalyst layer thickness) in comparison with that of other tested catalyst supports.
For the fast reaction of the methane catalytic combustion, the behavior is quite different ( Figure  6). The lowest conversion is offered by the monolith, somewhat higher is that of NC 0610 foam. Packed bed and NC 2733 foam reach close conversion (Figure 6a), although the NC 2733 foam displays a higher specific surface area. The characteristics presented in Figure 6b are similar: the shortest reactor to achieve 90% conversion is required for packed bed and NC 28733, while the longest one for the monolith. Flow resistance for both the tested foams is similar, and only moderately higher than that of monolith (Figure 6b).

Discussion
For processes characterized by rather slow kinetics (SCR deNOx), the conversion achieved ( Figure 5a) and the reactor length (Figure 5b) is proportional to the surface area of the catalyst carriers, thus to the catalyst mass, therefore, NC 2733 shows much higher conversion and much shorter reactor length needed to achieve 90% conversion. This results from the slow kinetics of the reaction. For all the carriers considered, the mass transfer is much more intense than the reaction rate. Thus, the process is strictly kinetic dependent. In such a situation, the rational choice of carrier from among those having a comparable Sv is, of course, a monolith, with the lowest flow resistance and reactor length similar to the others. The same results were also obtained for the methane combustion carried out on the palladium catalyst prepared by the incipient wetness method, displaying "slow" kinetics [2].
For processes with fast kinetics (catalytic combustion of methane), the reaction is strongly limited by insufficient mass transfer rate. In this case, the mass transfer becomes the limiting factor for the process yield. Specific surface area and catalyst amount play less important roles. Therefore, foams and packed bed needed much shorter reactor than monolith (Figure 6b), especially for higher fluid velocity. That agrees with the results presented in Figure 1: transport intensity for foams and packed bed is close and much higher than for monolith. The consequence is not only shorter reactor Considering the slow deNOx reaction, carriers of close specific surface area (i.e., NC 0610 foam, a 100 cpsi monolith, and a packed bed of 3 mm grains) achieved similar conversion along the reactor axis ( Figure 5a). Therefore, also the reactor length necessary to achieve 90% conversion is almost the same for them in a wide range of flow velocities (Figure 5b). On the other hand, flow resistances for those carriers differ greatly. The highest pressure drop is always displayed by the packed bed, and the lowest by the monolith. The NC 0610 foam is in between. The NC 2733 foam has achieved higher conversion along the reactor length, so also 90% conversion of NO requires a much shorter reactor. This is the result of a much larger specific surface area of NC 2733 foam available to catalyst deposition, hence the mass of catalyst (assuming the same catalyst layer thickness) in comparison with that of other tested catalyst supports.
For the fast reaction of the methane catalytic combustion, the behavior is quite different (Figure 6). The lowest conversion is offered by the monolith, somewhat higher is that of NC 0610 foam. Packed bed and NC 2733 foam reach close conversion (Figure 6a), although the NC 2733 foam displays a higher specific surface area. The characteristics presented in Figure 6b are similar: the shortest reactor to achieve 90% conversion is required for packed bed and NC 28733, while the longest one for the monolith. Flow resistance for both the tested foams is similar, and only moderately higher than that of monolith ( Figure 6b).

Discussion
For processes characterized by rather slow kinetics (SCR deNOx), the conversion achieved ( Figure 5a) and the reactor length (Figure 5b) is proportional to the surface area of the catalyst carriers, thus to the catalyst mass, therefore, NC 2733 shows much higher conversion and much shorter reactor length needed to achieve 90% conversion. This results from the slow kinetics of the reaction. For all the carriers considered, the mass transfer is much more intense than the reaction rate. Thus, the process is strictly kinetic dependent. In such a situation, the rational choice of carrier from among those having a comparable S v is, of course, a monolith, with the lowest flow resistance and reactor length similar to the others. The same results were also obtained for the methane combustion carried out on the palladium catalyst prepared by the incipient wetness method, displaying "slow" kinetics [2].
For processes with fast kinetics (catalytic combustion of methane), the reaction is strongly limited by insufficient mass transfer rate. In this case, the mass transfer becomes the limiting factor for the process yield. Specific surface area and catalyst amount play less important roles. Therefore, foams and packed bed needed much shorter reactor than monolith (Figure 6b), especially for higher fluid velocity. That agrees with the results presented in Figure 1: transport intensity for foams and packed bed is close and much higher than for monolith. The consequence is not only shorter reactor (the smaller volume), but also lower catalyst mass. In this case, the rational choice is the solid foam offering shorter reactor and low flow resistance, that is only slightly higher compared to the monolith.
Importance of the heat transfer is equal for both the fast and slow reactions. Each of them brings a certain energetic effect, thus the reaction heat (or enthalpy ∆H R ) has to be transferred between catalyst surface and the bulk reactant stream. The problem is of special importance for highly exothermic reactions like, for example, catalytic combustion. Insufficient heat transfer can lead to the catalyst overheating. This can be avoided by lowering process temperature or substrate concentration, according to Equation (2), but also, to some extent, by choosing (or designing) the reactor internal characterized by desirable heat and mass transfer characteristics.

Foam Morphology
The commercially available metal foams used in this study were made of aluminum (ERG Materials and Aerospace Corp., Oakland, CA, USA), nickel and nickel-chromium (Recemat BV, Dodevaard, The Netherlands), and Fecralloy (Goodfellow Cambridge Ltd., Huntingdon, England) with pore density from 10 to 40 PPI (pores per inch).
The porosity and specific surface area for the foams were obtained using X-ray microcomputed tomography (micro-CT). The foam samples had a cylindrical shape with a height and diameter of about 10 mm. For aluminum (Al), nickel (Ni), and nickel-chromium (NC) foam, the microtomography measurements were performed using a SkyScan 1172 micro-CT scanner (Bruker, Kontich, Belgium), while for the Fecralloy foam, the "nanotom 180N" (GE Sensing & Inspection Technologies phoenix|X-ray Gmbh) was used. During the scanning process of each foam, the sample rotated slowly and projection images were acquired for each rotation angle. The obtained 2D shadow projections were preprocessed using iMorph software. First, using the global thresholding method, binarization was performed ( Figure 7A). Next, to exclude potential internal discontinuities in the foam skeleton, which can cause large errors in the designated external porosity accessible for fluid flow and the external surface on which the catalyst may be deposited, the dilatation ( Figure 7B) and erosion ( Figure 7C) operations were performed for the selected region of interest (ROI) (for details see [22,32]). For such postprocessed images, a 3D reconstruction of the ROI was carried out ( Figure 7D) and porosity and specific surface area were determined. The procedure is schematically presented in Figure 7. (the smaller volume), but also lower catalyst mass. In this case, the rational choice is the solid foam offering shorter reactor and low flow resistance, that is only slightly higher compared to the monolith. Importance of the heat transfer is equal for both the fast and slow reactions. Each of them brings a certain energetic effect, thus the reaction heat (or enthalpy ΔHR) has to be transferred between catalyst surface and the bulk reactant stream. The problem is of special importance for highly exothermic reactions like, for example, catalytic combustion. Insufficient heat transfer can lead to the catalyst overheating. This can be avoided by lowering process temperature or substrate concentration, according to Equation (2), but also, to some extent, by choosing (or designing) the reactor internal characterized by desirable heat and mass transfer characteristics.

Foam Morphology
The commercially available metal foams used in this study were made of aluminum (ERG Materials and Aerospace Corp., Oakland, CA, USA), nickel and nickel-chromium (Recemat BV, Dodevaard, The Netherlands), and Fecralloy (Goodfellow Cambridge Ltd., Huntingdon, England) with pore density from 10 to 40 PPI (pores per inch).
The porosity and specific surface area for the foams were obtained using X-ray microcomputed tomography (micro-CT). The foam samples had a cylindrical shape with a height and diameter of about 10 mm. For aluminum (Al), nickel (Ni), and nickel-chromium (NC) foam, the microtomography measurements were performed using a SkyScan 1172 micro-CT scanner (Bruker, Kontich, Belgium), while for the Fecralloy foam, the "nanotom 180N" (GE Sensing & Inspection Technologies phoenix|X-ray Gmbh) was used. During the scanning process of each foam, the sample rotated slowly and projection images were acquired for each rotation angle. The obtained 2D shadow projections were preprocessed using iMorph software. First, using the global thresholding method, binarization was performed ( Figure 7A). Next, to exclude potential internal discontinuities in the foam skeleton, which can cause large errors in the designated external porosity accessible for fluid flow and the external surface on which the catalyst may be deposited, the dilatation ( Figure 7B) and erosion ( Figure 7C) operations were performed for the selected region of interest (ROI) (for details see [22,32]). For such postprocessed images, a 3D reconstruction of the ROI was carried out ( Figure 7D) and porosity and specific surface area were determined. The procedure is schematically presented in Figure 7. The strut diameter (i.e., solid elements of foam skeleton, depicted in Figure 7D) was determined using optical microscopy. The results are presented in Table 3. The strut diameter (i.e., solid elements of foam skeleton, depicted in Figure 7D) was determined using optical microscopy. The results are presented in Table 3.

Heat and Mass Transfer
The experimental setup is shown in Figure 8. The main part is the heat exchanger, in which the foam samples were tested. The foam specimen, placed in the central part of the exchanger, had a rectangular shape (45 mm × 30 mm) and was oriented perpendicular to the air flow direction. Metal foam samples were heated by the current flowing directly through the foam body (I max ≈ 150 A ± 0.1 A). The temperatures of the foam sample and the flowing gas were measured by means of thermocouples placed on the inlet and outlet side of the sample and heat exchanger, respectively. Air flow velocity was changed in the velocity range of 0.2-11 m/s (for more details see [22,33]

Heat and Mass Transfer
The experimental setup is shown in Figure 8. The main part is the heat exchanger, in which the foam samples were tested. The foam specimen, placed in the central part of the exchanger, had a rectangular shape (45 mm × 30 mm) and was oriented perpendicular to the air flow direction. Metal foam samples were heated by the current flowing directly through the foam body (Imax ≈ 150 A ± 0.1 A). The temperatures of the foam sample and the flowing gas were measured by means of thermocouples placed on the inlet and outlet side of the sample and heat exchanger, respectively. Air flow velocity was changed in the velocity range of 0.2-11 m/s (for more details see [22,33]). The heat transfer coefficient, h, and Nusselt number, Nu, were determined as: where the hydraulic diameter is defined as: Mass transfer coefficients were not determined experimentally. According to the Chilton-Colburn analogy, the mechanism of heat and mass transfer are essentially the same (see Equation (1)).
This analogy was experimentally confirmed for solid foams [15,21]. Therefore, for the purpose of this work, mass transfer coefficients were calculated based only on the heat transfer experiments.
Moreover, flow resistance experiments for the foams were also performed. The results were correlated for each foam separately (Table 1). The heat transfer coefficient, h, and Nusselt number, Nu, were determined as: where the hydraulic diameter is defined as: Mass transfer coefficients were not determined experimentally. According to the Chilton-Colburn analogy, the mechanism of heat and mass transfer are essentially the same (see Equation (1)).
This analogy was experimentally confirmed for solid foams [15,21]. Therefore, for the purpose of this work, mass transfer coefficients were calculated based only on the heat transfer experiments.
Moreover, flow resistance experiments for the foams were also performed. The results were correlated for each foam separately (Table 1).

Kinetic Tests
First, the appropriate catalysts were prepared. For selective catalytic reduction of NO with NH 3 (SCR deNOx), ultrastabilized Y-type zeolite (USY) was synthesized under rigorous conditions, then subjected to the sonochemical irradiation with 0.5 M aqueous copper nitrate solutions (for details see [31]), denoted as Cu/USY/s. For CH 4 combustion, a palladium catalyst (Pd/ZrO 2 ) was prepared by impregnation, also using a sonochemically irradiated catalyst precursor (for details see [34]). Kinetic tests for both catalysts were performed using a Catlab (Hiden Analytical, Warrington, UK) fixed-bed quartz tubular test reactor. For SCR deNOx, the experiments were carried out at atmospheric pressure within a temperature range of 50-550 • C using a gas mixture containing 2500 ppm of NO, 2500 ppm of NH 3, and 25,000 ppm of O 2 balanced by helium, with a total flow rate of 40 mL/min [31]. For methane catalytic combustion tests, the temperature ranged from 100 • C to 550 • C and gas composition was set to 2000 ppm CH 4 /Air [35].

Conclusions
The experimental results show that the heat/mass transfer intensity for solid foams is much more intense than that of monoliths and similar to that of packed beds. In turn, performance modelling indicated that, for slow kinetics, when the impact of mass transfer intensity is weak; specific surface area (or catalyst amount) is the decisive factor. For fast kinetics, mass transfer plays a more important role, being the limiting parameter of the process. For carriers of intense mass transfer, such as solid foams, the reactor length is much shorter than for the others and flow resistance can be much lower due to reactor shortening.
Depending on the reaction enthalpy, inlet concentration, and temperature, heat transfer rate between catalyst surface and the bulk reactant stream may be insufficient. The remedy is lowering inlet temperature or substrate concentration, as well as the selection of the catalyst carrier with the most favorable transport parameters. As was presented, the heat and mass transport properties of solid foams are comparable to packed bed and much higher than those of monoliths. Moreover, solid foams offer much lower flow resistance than packed bed. Therefore, solid foams are very promising catalyst carriers, especially for fast reaction.

Conflicts of Interest:
The authors declare no conflict of interest.