Metal Foams As Novel Catalyst Support in Environmental Processes

catalysts

Article Metal Foams as Novel Catalyst Support in Environmental Processes

Anna Gancarczyk 1,* , Katarzyna Sindera 1, Marzena Iwaniszyn 1, Marcin Pi ˛atek 1, Wojciech Macek 1 , Przemysław J. Jodłowski 2 , Sebastian Wro ´nski 3, Maciej Sitarz 4, Joanna Łojewska 5 and Andrzej Kołodziej 1,6

1 Institute of Chemical Engineering, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland 2 Faculty of Chemical Engineering and Technology, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland 3 Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland 4 Faculty of Materials Science and Ceramics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland 5 Faculty of Chemistry, Jagiellonian University, Gronostajowa 2, 30-387 Kraków, Poland 6 Faculty of Civil Engineering and Architecture, Opole University of Technology, Katowicka 48, 45-061 Opole, Poland * Correspondence: [email protected]; Tel.: +48-32-234-6915

Received: 11 June 2019; Accepted: 3 July 2019; Published: 5 July 2019

Abstract: 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.

Keywords: metal foams; heat transfer; reactor modelling

1. 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 Sh = (1) Pr1/3 Sc1/3

Catalysts 2019, 9, 587; doi:10.3390/catal9070587 www.mdpi.com/journal/catalysts Catalysts 2019, 9, 587 2 of 13 where dimensionless Sherwood (Sh) and Nusselt (Nu) numbers describe mass and heat transfer, respectively. Therefore, in many cases, the mass transfer characteristic can be derived based on the heat transfer experiments, and vice versa. Based on the Chilton–Colburn analogy, the relationship between heat and mass transfer coeﬃcients (h and kC, respectively) is:

h(Ts T) = k (C C )( ∆H ) (2) − C A − As − R where ∆HR is the reaction enthalpy. It means, that for reactor design the knowledge of the heat and mass transfer characteristics of the reactor internals is as necessary as the kinetics of the reaction. Usually, the better the transport characteristics, the better reactor performance, especially for fast catalytic reactions. Another parameter characterizing the reactor internals, which is very important for the reactor functioning, is the flow resistance. It is not a process limitation, however high pressure drop means high pumping costs. Hence, the ratio of the flow resistance to the transport intensity is an important factor for the catalytic reactor optimization [1,2]. The classic solution in many processes, especially in the area of environmental protection, is a monolith with a catalyst deposited on its surface (usually through an intermediate layer, the “washcoat”). The undoubted advantage of such a solution, in addition to the reproducible structure of the channels, is the low flow resistance and the relative ease of forming and depositing the catalyst. However, serious disadvantages are the low mass and heat transfer rates, which are particularly important for fast catalytic reactions. On the other side is the packed bed characterized by the high mass transfer, but also high flow resistance. Solid, open-cellular foams offer significantly higher mass [3] and heat [2] transfer coefficients compared with those of monoliths and lower pressure drop in comparison with that of the packed bed [2,3]. Moreover, solid foams are being manufactured from diverse materials. Ceramic foams are applied as molten metal filters and high-temperature thermal insulations. Metal foams are used in light constructions, as elements of aircraft, and as absorbers of energy, in heat exchangers (as porous fins) or heat recuperators. Thinner struts of metal foams, measuring less than one millimeter, enable the manufacture of foams of larger specific surface area (over 1000 m2/m3) and higher porosity in comparison with that of ceramic ones. Moreover, metal foams show good mechanical properties, high thermal conductivity, and resistance to thermal and mechanical shocks. The above characteristics make metal solid foams attractive for catalytic applications. They have been studied in, for example, the neutralization of air pollutants from automotive exhaust gases [4], the selective catalytic reduction of nitrogen oxides (SCR deNOx) [5,6], the catalytic oxidation of CO [1,7–10], the catalytic combustion and steam reforming of methane [9,11,12], or the catalytic oxidation of hydrocarbons [13,14]. Because knowledge of the heat and mass transfer parameters is as important as the kinetics, therefore, this study presents the heat transfer experimental results for aluminum (Al), nickel (Ni), nickel–chromium (NC), and Fecralloy foams, differing in the pore densities. Next, in order to check the usefulness of metal foams as the catalyst carriers, NC foams were compared with classical catalyst supports—packed beds and monoliths. The removal of NOx by selective catalytic reduction (SCR deNOx) and the catalytic combustion of methane were chosen as the model processes. These processes display relatively slow and fast reaction kinetics, respectively. In addition, they are very important for environmental protection, hence any improvement in their efficiency is highly desirable.

2. Results

2.1. Heat and Mass Transfer The heat transfer coeﬃcients were experimentally determined for several metal foams, namely aluminum (Al), nickel (Ni), nickel–chromium (NC), and Fecralloy. Moreover, the chosen foams diﬀer in the pore densities (pores per inch, PPI) (see Section4 Materials and Methods). Experimental results of heat and mass transfer for tested metal foams are presented in Figure1, in the term of Catalysts 2019, 9, 587 3 of 13 CatalystsCatalysts 2019 2019, 9, ,9 x, xFOR FOR PEER PEER REVIEW REVIEW 3 3of of 13 13

1/3 1/3 NuNu/PrNu/Pr/Pr11/3/3 (describing(describing(describing thethe the heatheat heat transfer) transfer) transfer) and and and in in equivalentin equivalent equivalent mass mass mass transfer transfer transfer term term term (Sh /(Sh/ScSc (Sh/Sc1/3),1/3 according),), according according to the to to Chilton–Colburnthethe Chilton–Colburn Chilton–Colburn analogy analogy analogy (Equation (equation (equation (1)).This (1)).This (1)).This approach approach approach is applied is isin applied thisapplied paper. in in this Because,this paper. paper. for Because, comparison,Because, for for thecomparison,comparison, results for the monolith the results results and for for packed monolith monolith bed and areand alsopacked packed presented bed bed are are in also Figure also presented presented1, therefore, in in Figure the Figure hydraulic 1, 1, therefore, therefore, diameter, the the hydraulic diameter, dh, for all presented catalyst carriers was chosen as the characteristic one. As can dhydraulich, for all presenteddiameter, d catalysth, for all carriers presented was catalyst chosen carriers as the characteristicwas chosen as one. the characteristic As can be seen, one. the As heat can andbebe seen, massseen, the transportthe heat heat and and properties mass mass transport transport for solid properties properties foams are for comparablefor solid solid foams foams with are are packed comparable comparable bed and with with much packed packed higher bed bed than and and formuchmuch monolith. higher higher than than for for monolith. monolith.

FigureFigureFigure 1.1. 1. HeatHeat Heat andand and massmass mass transfertransfer transfer experimentalexperimental experimental resultsresults results vs.vs. vs. Reynolds Reynolds number number for for tested tested solid solid foams. foams. TheTheThe monolithsmonoliths monoliths andand and packedpacked packed bedbed bed areare are shownshown shown forfor for comparison.comparison. comparison.

InInIn the thethe literature, literature,literature, many manymany correlations correlationscorrelations describing describingdescribing the heat thethe (e.g., heatheat [15 (e.g.,–(e.g.,18]) [15–18]) and[15–18]) mass and transferand massmass coe transferffitransfercient (e.g.,coefficientcoefficient [1,19– 21(e.g., (e.g.,]) for [1,19–21]) [1,19–21]) solid foams for for solid cansolid be foams foams found. can can A be comparisonbe found. found. A A comparison betweencomparison experimental between between experimental experimental results in terms results results of 1/3 Nuinin terms/ Prterms of(according of Nu/Pr Nu/Pr1/31/3 (according to (according the Chilton–Colburn to to the the Chilton–Colburn Chilton–Colburn analogy) and analogy) analogy) calculated and and calculated based calculated on the based based selected on on the the literature selected selected correlationsliteratureliterature correlations correlations for heat transfer for for heat heat for transfer transfer Al 10 (Figure for for Al Al 102 a)10 (Figure and(Figure Ni 2a)0610 2a) and and (Figure Ni Ni 0610 06102b) (Figure is (Figure presented. 2b) 2b) is is presented. For presented. the same For For foams,thethe same same a similar foams, foams, comparison a asimilar similar comparison ofcomparison mass transfer of of mass mass coe ffitran trancientsfersfer obtained coefficient coefficient experimentally obtained obtained experimentally experimentally (i.e., based on (i.e., the(i.e., Nubasedbased number on on the the using Nu Nu number Chilton–Colburnnumber using using Chilton–Colburn Chilton–Colburn analogy) and calculatedanalogy) analogy) and usingand calculated calculated selected literatureusing using selected selected correlations literature literature is 1/3 presentedcorrelationscorrelations in is Figure is presented presented3 in the in in form Fi Figuregure of 3 Sh 3in in/ Scthe the form. form Because of of Sh/Sc Sh/Sc literature1/31/3. Because. Because correlations literature literature describing correlations correlations heat describing anddescribing mass transferheatheat and and coe mass ffimasscient transfer transfer defined coefficient dimensionlesscoefficient defined defined number dime dime (Re,nsionlessnsionless Nu, Sh) withnumber number different (Re, (Re, characteristic Nu,Nu, Sh) Sh) with with dimensions, different different thereforecharacteristiccharacteristic they dimensions, weredimensions, recalculated therefore therefore using they they strut were were diameter, recalculated recalculated ds, (see using using Section strut strut4 Materialsdiameter, diameter, andd ds, s,(see Methods)(see Section Section as 4 4 characteristicMaterialsMaterials and and one. Methods) Methods) As can as be as characteristic noticed,characteristic for both, one. one. the As As heatcan can be (Figure be noticed, noticed,2) and for for the both, both, mass the the (Figure heat heat (Figure3 (Figure), when 2) 2) a and givenand the the correlationmassmass (Figure (Figure describes 3), 3), when when quite a agiven wellgiven thecorrelation correlation results obtained describes describes for quite quite one foam,well well the itthe veryresults results often obtained obtained fails for for thefor one othersone foam, foam, [22 it]. it Averyvery similar often often situation fails fails for for wasthe the others alsoothers observed [22]. [22]. A A similar forsimilar flow situat situat resistanceionion was was [23 also ,also24 ].observed observed for for flow flow resistance resistance [23,24]. [23,24].

(a()a ) (b(b) )

Figure 2. Experimental heat transfer results and those calculated based on the literature correlations forFigureFigure (a) Al 2. 2. 10Experimental Experimental and (b) Ni 0610heat heat foams.transfer transfer results results and and those those calculated calculated based based on on the the literature literature correlations correlations forfor (a ()a Al) Al 10 10 and and (b (b) Ni) Ni 0610 0610 foams. foams.

CatalystsCatalystsCatalysts 2019 20192019,,, 9 99,,, 587 xx FORFOR PEERPEER REVIEWREVIEW 444 of ofof 13 1313

((aa)) ((bb))

Figure 3. Experimental mass transfer results and those calculated based on the literature correlations forFigureFigure (a) Al 3.3. 10ExperimentalExperimental and (b) Ni 0610 massmass foams. transfertransfer resultsresults andand thosethose cacalculatedlculated basedbased onon thethe literatureliterature correlationscorrelations forfor ((aa)) AlAl 1010 andand ((bb)) NiNi 06100610 foams.foams. The heat transfer for solid foams is very often described by the correlation of the form: TheThe heatheat transfertransfer forfor solidsolid foamsfoams isis veryvery oftenoften describeddescribed byby thethe correlationcorrelation ofof thethe form:form: Nu = aRebPr1/3 (3) Nu=aReNu=aRebbPrPr1/31/3 (3)(3) thatthatthat originally originallyoriginally was waswas proposed proposedproposed for forfor the the bundlethe bundlebundle of tubes ofof tubestubes [25], where[25],[25], wherewhere coefficient coefficientcoefficient a and exponent aa andand exponentexponent b depends bb ondependsdepends the Reynolds onon thethe Reynolds numberReynolds value. numbernumber As value.value. can be AsAs seen cancan in bebe Figure seenseen1 in,in all FigureFigure experimental 1,1, allall experimentalexperimental results of heat resultsresults/mass ofof transferheat/massheat/mass of solidtransfertransfer foams ofof solidsolid tested foamsfoams are similar. testedtested areare Therefore, similar.similar. for Therefore,Therefore, all the foams’, forfor allall testedthethe foams’,foams’, parameters testedtested parameters aparameters and b from aa Equationandand bb fromfrom (1) equation wereequation estimated, (1)(1) werewere based estimated,estimated, on experimental basedbased onon results,experimentalexperimental obtaining results,results, a = 0.489 obtainingobtaining and b aa= ==0.552. 0.4890.489 Because andand bb == heat0.552.0.552. transfer BecauseBecause for heatheat the transfertransfer solid foams forfor thethe depends solidsolid foamsfoams mainly depedepe onnds thends specificmainlymainly on surfaceon thethe specificspecific area and surfacesurface strut diameterareaarea andand strut [strut15], thereforediameterdiameter strut[15],[15], therefore diametertherefore strut wasstrut chosen diameterdiameter as was thewas characteristic chosenchosen asas thethe diameter characteristiccharacteristic in the diameterdiameter definition inin ofthethe the definitiondefinition Reynolds ofof andthethe Reynolds NusseltReynolds number. andand NusseltNusselt The correlation number.number. TheThe describes correlationcorrelation the experimental describesdescribes thethe resultsexperimentalexperimental with average resultsresults relative withwith averageaverage error, ey 9.3%, as presented in Figure4. relativerelative≈ error,error, eeyy ≈≈ 9.3%,9.3%, asas presentedpresented inin FigureFigure 4.4.

FigureFigureFigure 4. 4.4. Experimentally ExperimentallyExperimentally determined determineddetermined heat heat/massheat/mass/mass transfer transfertransfer and andand that thatthat calculated calculatedcalculated based basedbased on Equation onon equationequation (3) with (3)(3) awithwith= 0.489 aa == 0.4890.489 and b andand= 0.552 bb == 0.5520.552 and d andands as dd characteristicss asas characteristiccharacteristic diameter. diameter.diameter. 2.2. Assessment of Solid Foams as Catalyst Carriers 2.2.2.2. AssessmentAssessment ofof SolidSolid FoamsFoams asas CatalystCatalyst CarriersCarriers Solid foams can be adapted to process requirements in terms of amount of catalyst due to the wide SolidSolid foamsfoams cancan bebe adaptedadapted toto processprocess requirementsrequirements inin termsterms ofof amountamount ofof catalystcatalyst duedue toto thethe range of the specific surface area available. The next important benefit of solid foams is a wide range widewide rangerange ofof thethe specificspecific surfacesurface areaarea available.available. TheThe nextnext importantimportant benefitbenefit ofof solidsolid foamsfoams isis aa widewide ofrangerange porosity ofof thatporosityporosity offers thatthat relatively offersoffers low relativelyrelatively flow resistance. lowlow flowflow Moreover, resistance.resistance. the complicated Moreover,Moreover, three-dimensionalthethe complicatedcomplicated (3D)three-dimensionalthree-dimensional structure of a foam (3D)(3D) skeletonstructurestructure ensures ofof aa foamfoam intense skeletskelet mixingonon ensuresensures of the intenseintense flowing mixingmixing fluids, thusofof thethe intense flowingflowing heat fluids,fluids, and massthusthus intense transfer.intense heatheat andand massmass transfer.transfer.

Catalysts 2019, 9, 587 5 of 13

Comparison of heat and mass transfer coefficients of solid foams with classic packed bed and monolith, as presented in Figure1, 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 Table1). 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 Table1. Because the compared catalyst carriers significantly di ffer 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].

Table 1. Correlations and characteristic parameters for tested catalyst carriers.

2 3 1 Catalyst Support Sv (m /m ) dh (m) Correlations ∆P/L = 443.1w2 + 256.8w NC 0610 1298 2.73 10 3 Nu = 0.489Re0.552 Pr1/3 × − Sh = 0.489Re0.552 Sc1/3 ∆P/L = 1791.9w2 + 2719.4w NC 2733 3616 9.61 10 3 Nu = 0.489Re0.552 Pr1/3 × − Sh = 0.489Re0.552 Sc1/3 0.5 (fRe) = 14.23 1 + 0.045/L+ 3 0.45 monolith [26] 1339 2.15 10− = ( + ) × Nu 3.608 1 0.095/L∗ M0.45 Sh = 3.608 1 + 0.095/L∗

2 µw (1 ε) %w2 (1 ε) ∆P/L = 150 2 −ε3 + 1.75 D ε−3 packed bed [27,28] 3 D 1240 1.23 10− = + 0.6 1/3 × Nu 2 1.1Re Pr Sh = 2 + 1.1Re0.6Sc1/3 1 Deﬁned with dh as the characteristic diameter.

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: •

d(CAw) + Svkc(C C ) = 0, (4) dz A − AS

with boundary conditions: z = 0; CA = CA0. the heat balance for the gas phase: • dT w%cp + Svh(T T ) = 0, (5) dz − S Catalysts 2019, 9, 587 6 of 13 Catalysts 2019, 9, x FOR PEER REVIEW 6 of 13

with• the boundary heat balance conditions: for the z gas= 0; phase: T = T 0, and assuming no heat losses.

the material balance at the catalyst surface:dT • wρc + S hT-T = 0, (5) p dz v S kc(CA CAS) = η( RA) = ηkrCAS, (6) 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: • kcCA-CAS = η-RA = ηkrCAS, (6) h(TS T) = ∆HRη( RA), (7) • the heat balance at the catalyst surface:− − −

the influence of axial dispersion on thehT final-T = conversion -ΔH η-R is neglected, [29,30]. (7) • S R A Kinetic• the datainfluence for considering of axial dispersion processes on are the presented final conversion in Table is2. neglected As can be [29,30]. seen, deNOx reaction displaysKinetic rather data slow for kinetics,considering while processes methane are combustion presented isin aTable very fast2. As reaction. can be seen, deNOx reaction displays rather slow kinetics, while methane combustion is a very fast reaction. Table 2. Catalyst preparation and kinetic data. Table 2. Catalyst preparation and kinetic data. Pre-Exponential Activation Energy, Effectiveness Catalyst Metal Content (wt %) Factor, k (m/s) ActivationEa, (kJ/ mol) Factor, η 1 Metal Content Pre-Exponential∞ Effectiveness Catalyst Energy, Ea, Cu/USY/s [31] 3.70(wt0.04 %) Factor, k 3.32∞ (m/s) 36.21Factor, η1 1 ± 10 (kJ/mol) Pd/Al2O3 [2] 3.43 0.9 1.07 10 110.4 0.32 Cu/USY/s [31] 3.70± ± 0.04 3.32× 36.21 1 1 calculated for 723 K and catalyst layer thickness l = 20 µm. Pd/Al2O3 [2] 3.43 ± 0.9 1.07 × 1010 110.4 0.32 1 calculated for 723 K and catalyst layer thickness l = 20 µm. The modelling was performed in two ways:

1. Thereaction modelling conversion was performed was calculated in two along ways: the reactor axis (z) for T = const. and w = const.; 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 2. necessary reactor length to reach 90% conversion was calculated for given flow velocity at T T = const. = const. The modelling results for SCR deNOx are presented in FigureFigure5 5,, andand forfor methane methane catalyticcatalytic combustion in Figure6 6..

(a) (b)

Figure 5. Modelling results for SCR deNOx process in T = 723 K. (a) Conversion and pressure drop proﬁlesFigure 5. along Modelling the reactor results length for forSCR w deNOx= 2 m/s, process (b) Reactor in T length= 723 K. and (a) corresponding Conversion and pressure pressure drop drop for assumedprofiles along conversion the reactor X = 90%. length SCR for deNOx: w = 2 m/s, selective (b) Reactor catalytic length reduction and corresponding of nitrogen oxides. pressure drop for assumed conversion X = 90%. SCR deNOx: selective catalytic reduction of nitrogen oxides.

CatalystsCatalysts2019 2019,,9 9,, 587 x FOR PEER REVIEW 77 ofof 1313

(a) (b)

Figure 6. Modelling results for CH4 combustion process in T = 773 K. (a) Conversion and pressure dropFigure profiles 6. Modelling along the results reactor for length CH4 combustion for w = 2 m process/s, (b) Reactor in T = length773 K. and(a) Conversion corresponding and pressurepressure dropdrop forprofiles assumed along conversion the reactor X =length90%. for w = 2 m/s, (b) Reactor length and corresponding pressure drop for assumed conversion X = 90%. Considering the slow deNOx reaction, carriers of close specific surface area (i.e., NC 0610 foam, a 100Considering cpsi monolith, the and slow a packeddeNOx bed reaction, of 3 mm carriers grains) of achievedclose specific similar surface conversion area (i.e., along NC the0610 reactor foam, axisa 100 (Figure cpsi monolith,5a). Therefore, and a alsopacked the bed reactor of 3 lengthmm grains) necessary achieved to achieve similar 90% conversion conversion along is almost the reactor the sameaxis (Figure for them 5a). in Therefore, a wide range also of the flow reactor velocities length (Figure necessary5b). Onto achieve the other 90% hand, conversion flow resistances is almost for the thosesame carriersfor them di inffer a greatly.wide range The of highest flow velocities pressure drop (Figure is always 5b). On displayed the other by hand, the packed flow resistances bed, and thefor lowestthose carriers by the monolith.differ greatly. The The NC highest 0610 foam pressure is in between. drop is always The NC displayed 2733 foam by hasthe achievedpacked bed, higher and conversionthe lowest by along the monolith. the reactor The length, NC 0610 so also foam 90% is conversionin between. ofThe NO NC requires 2733 foam a much has achieved shorter reactor. higher Thisconversion is the result along of the a much reactor larger length, specific so also surface 90% area conversion of NC 2733 of NO foam requires available a much to catalyst shorter deposition, reactor. henceThis is the the mass result of catalystof a much (assuming larger thespecific same surface catalyst area layer of thickness) NC 2733 infoam comparison available with to catalyst that of otherdeposition, tested catalysthence the supports. mass of catalyst (assuming the same catalyst layer thickness) in comparison withFor that the of fastother reaction tested ofcatalyst the methane supports. catalytic combustion, the behavior is quite different (Figure6). The lowestFor the conversion fast reaction is oofff eredthe methane by the monolith, catalytic somewhatcombustion, higher the behavior is that of is NC quite 0610 different foam. Packed(Figure bed6). The and lowest NC 2733 conversion foam reach is offered close conversion by the monolith, (Figure somewhat6a), although higher the NCis that 2733 of foamNC 0610 displays foam. aPacked higher specificbed and surface NC 2733 area. foam The characteristicsreach close conversion presented in(Figure Figure 66a),b are although similar: thethe shortestNC 2733 reactor foam todisplays achieve a 90%higher conversion specific surface is required area. for The packed characteristics bed and NC presented 28733, whilein Figure the longest6b are onesimilar: for thethe monolith.shortest reactor Flow resistance to achieve for 90% both conversion the tested foams is required is similar, for andpacked only bed moderately and NC higher 28733, than while that the of monolithlongest one (Figure for 6theb). monolith. Flow resistance for both the tested foams is similar, and only moderately higher than that of monolith (Figure 6b). 3. Discussion 3. Discussion For processes characterized by rather slow kinetics (SCR deNOx), the conversion achieved (FigureFor5a) processes and the reactor characterized length (Figure by rather5b) is slow proportional kinetics to(SCR the surfacedeNOx), area the of theconversion catalyst carriers,achieved thus(Figure to the 5a) catalyst and the mass, reactor therefore, length NC (Figure 2733 shows 5b) is muchproportional higher conversion to the surface and mucharea shorterof the catalyst reactor lengthcarriers, needed thus toto achievethe catalyst 90% conversion.mass, therefore, This results NC 2733 from shows the slow mu kineticsch higher of theconversion reaction. and For allmuch the carriersshorter considered,reactor length the needed mass transfer to achieve is much 90% more conver intensesion. thanThis theresults reaction from rate. the Thus,slow kinetics the process of the is strictlyreaction. kinetic For all dependent. the carriers In suchconsidered, a situation, the mass the rational transfer choice is much of carrier more fromintense among than those the reaction having arate. comparable Thus, the S vprocessis, of course, is strictly a monolith, kinetic dependent. with the lowest In such flow a situatio resistancen, the and rational reactor choice length of similar carrier tofrom the among others. those The samehaving results a comparable were also Sv obtained is, of course, for the a monolith, methane combustionwith the lowest carried flow out resistance on the palladiumand reactor catalyst length prepared similar byto thethe incipientothers. The wetness same method, results displayingwere also “slow”obtained kinetics for the [2]. methane combustionFor processes carried with out fast on kinetics the palladium (catalytic combustioncatalyst prepared of methane), by the the incipient reaction iswetness strongly method, limited bydisplaying insufficient “slow” mass kinetics transfer [2]. rate. In this case, the mass transfer becomes the limiting factor for the processFor yield. processes Specific with surface fast areakinetics and catalyst(catalytic amount comb playustion less of important methane), roles. the Therefore,reaction is foams strongly and packedlimitedbed by insufficient needed much mass shorter transfer reactor rate. than In monoliththis case, (Figurethe mass6b), transfer especially becomes for higher the limiting fluid velocity. factor Thatfor the agrees process with yield. theresults Specific presented surface area in Figure and catalyst1: transport amount intensity play less for important foams and roles. packed Therefore, bed is closefoams and and much packed higher bed needed than for much monolith. shorter The reactor consequence than monolith is not only(Figure shorter 6b), especially reactor (the for smaller 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

Catalysts 2019, 9, x FOR PEER REVIEW 8 of 13

(theCatalysts smaller2019, 9 volume),, 587 but also lower catalyst mass. In this case, the rational choice is the solid foam8 of 13 offering shorter reactor and low flow resistance, that is only slightly higher compared to the monolith.volume), but also lower catalyst mass. In this case, the rational choice is the solid foam offering shorter reactorImportance and low flowof the resistance, heat transfer that is is equal only slightlyfor both higher the fast compared and slow toreactions. the monolith. Each of them brings Δ a certainImportance energetic of theeffect, heat thus transfer the reaction is equal forheat both (or theenthalpy fast and H slowR) has reactions. to be transferred Each of them between brings catalyst surface and the bulk reactant stream. The problem is of special importance for highly a certain energetic effect, thus the reaction heat (or enthalpy ∆HR) has to be transferred between exothermic reactions like, for example, catalytic combustion. Insufficient heat transfer can lead to the catalyst surface and the bulk reactant stream. The problem is of special importance for highly catalyst overheating. This can be avoided by lowering process temperature or substrate exothermic reactions like, for example, catalytic combustion. Insufficient heat transfer can lead to the concentration, according to Equation (2), but also, to some extent, by choosing (or designing) the catalyst overheating. This can be avoided by lowering process temperature or substrate concentration, reactor internal characterized by desirable heat and mass transfer characteristics. according to Equation (2), but also, to some extent, by choosing (or designing) the reactor internal characterized by desirable heat and mass transfer characteristics. 4. Materials and Methods 4. Materials and Methods 4.1. Foam Morphology 4.1. Foam Morphology The commercially available metal foams used in this study were made of aluminum (ERG MaterialsThe commercially and Aerospace available Corp., metal Oakland, foams usedCA, US in thisA), studynickel were and madenickel–c of aluminumhromium (ERG(Recemat Materials BV, Dodevaard,and Aerospace The Corp., Netherlands), Oakland, CA,and USA),Fecralloy nickel (Good andfellow nickel–chromium Cambridge (RecematLtd., Huntingdon, BV, Dodevaard, England) The withNetherlands), pore density and from Fecralloy 10 to (Goodfellow40 PPI (pores Cambridge per inch). Ltd., Huntingdon, England) with pore density fromThe 10 to porosity 40 PPI (poresand specific per inch). surface area for the foams were obtained using X-ray microcomputed tomographyThe porosity (micro-CT). and specific The foam surface samples area for had the a foams cylindrical were obtainedshape with using a height X-ray and microcomputed diameter of abouttomography 10 mm. (micro-CT). For aluminum The foam samples(Al), nickel had a(Ni), cylindrical and nickel–chromium shape with a height (NC) and diameterfoam, the of microtomographyabout 10 mm. For aluminummeasurements (Al), nickelwere performed (Ni), and nickel–chromium using a SkyScan (NC)1172 foam,micro-CT the microtomography scanner (Bruker, Kontich,measurements Belgium), were while performed for the using Fecralloy a SkyScan foam, 1172 the micro-CT“nanotom scanner 180N” (Bruker,(GE Sensing Kontich, & Inspection Belgium), Technologieswhile for the Fecralloy phoenix|X-ray foam, the Gmbh) “nanotom was 180N” used. (GE Duri Sensingng the & scanning Inspection process Technologies of each phoenix foam,|X-ray the sampleGmbh) wasrotated used. slowly During and the projection scanning images process were of each acquired foam, for the each sample rotation rotated angle. slowly The and obtained projection 2D shadowimages were projections acquired were for eachpreprocessed rotation angle. using TheiMorph obtained software. 2D shadow First, using projections the global were preprocessedthresholding method,using iMorph binarization software. was First, performed using (Figure the global 7A). thresholding Next, to exclude method, potential binarization internal wasdiscontinuities performed in(Figure the foam7A). Next,skeleton, to exclude which can potential cause internallarge errors discontinuities in the designated in thefoam external skeleton, porosity which accessible can cause for fluidlarge flow errors and in the external designated surface external on which porosity the accessiblecatalyst may for be fluid deposited, flow and th thee dilatation external (Figure surface 7B) on andwhich erosion the catalyst (Figure may 7C) be operations deposited, thewere dilatation performed (Figure for7 B)the and selected erosion region (Figure of7C) interest operations (ROI) were (for detailsperformed see [22,32]). for the selectedFor such region postprocessed of interest images, (ROI) (fora 3D details reconstruction see [22,32 of]). the For ROI such was postprocessed carried out (Figureimages, 7D) a 3D and reconstruction porosity and of specific the ROI surface was carried area were out (Figure determined.7D) and The porosity procedure and is specific schematically surface presentedarea were determined.in Figure 7. The procedure is schematically presented in Figure7.

Figure 7. Region of interest (ROI) after (A) binarization, (B) dilatation operation, (C) erosion operation, Figure 7. Region of interest (ROI) after (A) binarization, (B) dilatation operation, (C) erosion (D) three-dimensional (3D) reconstruction. operation, (D) three-dimensional (3D) reconstruction. The strut diameter (i.e., solid elements of foam skeleton, depicted in Figure7D) was determined The strut diameter (i.e., solid elements of foam skeleton, depicted in Figure 7D) was determined using optical microscopy. The results are presented in Table3. using optical microscopy. The results are presented in Table 3.

Catalysts 2019, 9, 587 9 of 13 Catalysts 2019, 9, x FOR PEER REVIEW 9 of 13

Table 3. Table 3. Morphological parameters of foams tested. 1 2 3 Foam Foam PPIPPI 1 dss (m) dh d (m)h (m) ε εSv (mS2/vm(m3) /m ) −4 −3 3 Al 10Al 10 10 10 4.49 4.49 × 1010− 4.124.12 × 1010 − 0.890.89 860.98 860.98 × −4 × −3 3 Al 20Al 20 20 20 3.73 3.73 × 1010− 3.943.94 × 1010 − 0.910.91 926.49 926.49 × −4 × −3 3 Al 40Al 40 40 40 3.04 3.04 × 1010− 3.193.19 × 1010 − 0.910.91 1139.6 1139.6 2 × 4 × 3 FecralloyFecralloy 20 208 PPC 8 PPC 2 2.17 2.17 × 1010−−4 1.551.55 × 1010−3 − 0.830.83 2084.63 2084.63 × 4 × 3 Ni 0610Ni 0610 6 ... 6…1010 4.71 4.71 × 1010−−4 4.054.05 × 1010−3 − 0.920.92 908.73 908.73 × 4 × 3 NC 0610NC 0610 6 ... 6…1010 5.29 5.29 × 1010−−4 2.732.73 × 1010−3 − 0.880.88 1297.72 1297.72 × 4 × 3 NC 2733 27 ... 33 1.35 10 −4 9.61 10−3 0.87 3615.7 NC 2733 27…33 1.35× × 10− 9.61 × ×10 − 0.87 3615.7 1 Pores1 Pores per per inch, inch, acco accordingrding to producer.2 2Pores Pores per per centimeter centimeter

4.2. Heat and Mass Transfer The experimentalexperimental setup setup is is shown shown in in Figure Figure8. The8. The main main part part is the is heatthe heat exchanger, exchanger, in which in which the foam the samplesfoam samples were tested. were tested. The foam The specimen, foam specimen, placed in plac theed central in the part central of the part exchanger, of the exchanger, had a rectangular had a shaperectangular (45 mm shape 30(45 mm) mm × and 30 mm) was and oriented was oriented perpendicular perpendicular to the air to the flow air direction. flow direction. Metal Metal foam × samplesfoam samples were heatedwere heated by the by current the current flowing flowing directly directly through through the foam the foam body body (Imax (Imax150 ≈ 150 A A0.1 ± 0.1 A). ≈ ± TheA). temperaturesThe temperatures of the of foam the sample foam andsample the flowingand the gas flowing were measured gas were by measured means of thermocouplesby means of placedthermocouples on the inlet placed and on outlet the sideinlet ofand the outlet sample side and of heatthe sample exchanger, and respectively. heat exchanger, Air flowrespectively. velocity wasAir flow changed velocity in the was velocity changed range in the of 0.2–11velocity m /rangs (fore moreof 0.2–11 details m/s see (for [22 more,33]). details see [22,33]).

Figure 8. Experimental setup: 1—blower, 1—blower, 2—rotameter, 2—rotameter, 3—reactor, 4—electric power generation and control system, 5—solid foam, 6—thermocouple,6—thermocouple, 7—data7—data acquisitionacquisition system.system.

The heat transfer coecoefficient,ﬃcient, h,h, andand NusseltNusselt number,number, Nu,Nu, werewere determineddetermined as:as: QQ h =h = (8) FF·∆∆TT · hh·ddh NuNu= = · h (9) kk where the hydraulichydraulic diameterdiameter isis deﬁneddefined as:as: 4ε4ε dhd=h = (10) SvSv

Mass transfertransfer coe coefficientsfficients were were not not determined determin experimentally.ed experimentally. According According to the Chilton–Colburnto the Chilton– analogy,Colburn theanalogy, mechanism the mechanism of heat and of mass heat transferand mass are transfer essentially are theessentially same (see the Equation same (see (1)). Equation (1)). This analogy was experimentally confirmed for solid foams [15,21]. Therefore, for the purpose of this work,This analogy mass transfer was experimentally coefficients were confirmed calculated for based solid onlyfoams on [15,21]. the heat Therefore, transfer experiments. for the purpose of thisMoreover, work, mass flow transfer resistance coefficients experiments were calcul for theated foams based were only also on the performed. heat transfer The experiments. results were correlatedMoreover, for each flow foam resistance separately experiments (Table1). for the foams were also performed. The results were correlated for each foam separately (Table 1).

Catalysts 2019, 9, 587 10 of 13

4.3. Kinetic Tests First, the appropriate catalysts were prepared. For selective catalytic reduction of NO with NH3 (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 CH4 combustion, a palladium catalyst (Pd/ZrO2) 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 NH3, and 25,000 ppm of O2 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 CH4/Air [35].

5. 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.

Author Contributions: Conceptualization, A.G.; Investigation, K.S., M.I., M.P., W.M., P.J. and S.W.; Methodology, P.J., S.W., M.S. and J.Ł.; Supervision, A.G. and A.K.; Writing—original draft, A.G.; Writing—review & editing, A.K. Funding: The research was supported by the National Science Centre (Projects No. DEC-2011/03/B/ST8/05455, DEC-2016/21/B/ST8/00496, and DEC-2016/23/B/ST8/02024). Conﬂicts of Interest: The authors declare no conﬂict of interest.

List of Symbols

3 CA reagent concentration in gas stream, mol/m cp specific heat, J/(kg K) · D diameter, m 2 DA diffusivity, m /s dc cell diameter, m dh hydraulic diameter, m ds strut diameter, m Nuexp Nucorr 100 Pn | − |· ey i>1 Nuexp average relative error, = n ,% F heat transfer area, m2 2 f ∆P = ρw Fanning friction factor, L 2 f ε2D h heat transfer coefficient, W/(m2 K) · k thermal conductivity, W/(m K) · kC mass transfer coefficient, m/s kr reaction rate constant Catalysts 2019, 9, 587 11 of 13 k pre-exponential coefficient in Arrhenius equation, m/s ∞ L bed or channel length, m L+ dimensionless length for the hydrodynamic entrance region, = L/(D Re) · L* dimensionless length for the thermal entrance region, = L/(D Re Pr) · · L*M dimensionless length for the mass transfer entrance region, = L/(D Re Sc) · · Nu Nusselt number, = h D/k · Pr Prandtl number, = Cp µ/k · Q heat flow rate, W ( R ) reaction rate, mol/(m2 s) − A · Re Reynolds number, = w D %/(µ ε) · · · Sc Schmidt number, = µ/(% D ) · A Sh Sherwood number, = kC D/DA · 2 3 Sv specific surface area (external surface area per unit volume of bed) m /m T temperature, K w superficial velocity, m/s ∆HR standard heat of reaction, J/mol ∆P pressure drop, Pa logarithmic mean temperature difference between gas and structure surface at the inlet ∆T and outlet sides z reactor axis, m ε porosity η effectiveness factor for catalyst µ dynamic viscosity (Pa s) · % density (kg/m3)

Subscripts ds based on strut diameter s refers to the catalyst surface

References

1. Giani, L.; Groppi, G.; Tronconi, E. Mass-transfer characterization of metallic foams as supports for structured catalysts. Ind. Eng. Chem. Res. 2005, 44, 4993–5002. [CrossRef] 2. Gancarczyk, A.; Iwaniszyn, M.; Piatek, M.; Korpys, M.; Sindera, K.; Jodlowski, P.J.; Lojewska, J.; Kolodziej, A. Catalytic combustion of low-concentration methane on structured catalyst supports. Ind. Eng. Chem. Res. 2018, 57, 10281–10291. [CrossRef] 3. Patcas, F.C.; Garrido, G.I.; Kraushaar-Czarnetzki, B. Co oxidation over structured carriers: A comparison of ceramic foams, honeycombs and beads. Chem. Eng. Sci. 2007, 62, 3984–3990. [CrossRef] 4. Pestryakov, A.N.; Yurchenko, E.N.; Feofilov, A.E. Foam-metal catalysts for purification of waste gases and neutralization of automotive emissions. Catal. Today 1996, 29, 67–70. [CrossRef] 5. Ochońska-Kryca,J.; Iwaniszyn, M.; Pi ˛atek,M.; Jodłowski, P.J.; Thomas, J.; Kołodziej, A.; Łojewska, J. Mass transport and kinetics in structured steel foam reactor with cu-zsm-5 catalyst for scr of nox with ammonia. Catal. Today 2013, 216, 135–141. [CrossRef] 6. Liu, Y.; Xu, J.; Li, H.R.; Cai, S.X.; Hu, H.; Fang, C.; Shi, L.Y.; Zhang, D.S. Rational design and in situ fabrication

of MnO2@NiCO2O4 nanowire arrays on ni foam as high-performance monolith de-nox catalysts. J. Mater. Chem. A 2015, 3, 11543–11553. [CrossRef]

7. Giani, L.; Cristiani, C.; Groppi, G.; Tronconi, E. Washcoating method for pd/γ-Al2O3 deposition on metallic foams. Appl. Catal. B 2006, 62, 121–131. [CrossRef]

8. Cimino, S.; Lisi, L.; Totarella, G.; Barison, S.; Musiani, M.; Verlato, E. Highly stable core–shell pt-CeO2 nanoparticles electrochemically deposited onto fecralloy foam reactors for the catalytic oxidation of co. J. Ind. Eng. Chem. 2018, 66, 404–410. [CrossRef] 9. Cimino, S.; Gerbasi, R.; Lisi, L.; Mancino, G.; Musiani, M.; Vázquez-Gómez, L.; Verlato, E. Oxidation of co and ch4 on pd–fecralloy foam catalysts prepared by spontaneous deposition. Chem. Eng. J. 2013, 230, 422–431. [CrossRef] Catalysts 2019, 9, 587 12 of 13

10. Ambrosetti, M.; Balzarotti, R.; Cristiani, C.; Groppi, G.; Tronconi, E. The influence of the washcoat deposition process on high pore density open cell foams activation for co catalytic combustion. Catalysts 2018, 8, 510. [CrossRef] 11. Podyacheva, O.Y.; Ketov, A.A.; Ismagilov, Z.R.; Ushakov, V.A.; Bos, A.; Veringa, H.J. Metal foam supported perovskite catalysts. React. Kinet. Catal. Lett. 1997, 60, 243–250. [CrossRef] 12. Balzarotti, R.; Beretta, A.; Groppi, G.; Tronconi, E. A comparison between washcoated and packed copper foams for the intensification of methane steam reforming. React. Chem. Eng. 2019.[CrossRef] 13. Pestryakov, A.N.; Fyodorov, A.A.; Shurov, V.A.; Gaisinovich, M.S.; Fyodorova, I.V. Foam metal catalysts with intermediate support for deep oxidation of hydrocarbons. React. Kinet. Catal. Lett. 1994, 53, 347–352. [CrossRef] 14. Pestryakov, A.N.; Fyodorov, A.A.; Gaisinovich, M.S.; Shurov, V.P.; Fyodorova, I.V.; Gubaydulina, T.A. Metal foam catalysts with supported active phase for deep oxidation of hydrocarbons. React. Kinet. Catal. Lett. 1995, 54, 167–172. [CrossRef] 15. Giani, L.; Groppi, G.; Tronconi, E. Heat transfer characterization of metallic foams. Ind. Eng. Chem. Res. 2005, 44, 9078–9085. [CrossRef] 16. Das, S.; Deen, N.G.; Kuipers, J.A.M. Direct numerical simulation for flow and heat transfer through random open-cell solid foams: Development of an ibm based cfd model. Catal. Today 2016, 273, 140–150. [CrossRef] 17. Calmidi, V.V.; Mahajan, R.L. Forced convection in high porositymetal foams. J. Heat Transf. 2000, 122, 557–565. [CrossRef] 18. Mancin, S.; Zilio, C.; Diani, A.; Rossetto, L. Air forced convection through metal foams: Experimental results and modeling. Int. J. Heat Mass Transf. 2013, 62, 112–123. [CrossRef] 19. Huu, T.T.; Lacroix, M.; Huu, C.P.; Schweich, D.; Edouard, D. Towards a more realistic modeling of solid foam: Use of the pentagonal dodecahedron geometry. Chem. Eng. Sci. 2009, 64, 5131–5142. [CrossRef] 20. Garrido, G.I.; Kraushaar-Czarnetzki, B. A general correlation for mass transfer in isotropic and anisotropic solid foams. Chem. Eng. Sci. 2010, 65, 2255–2257. [CrossRef] 21. Groppi, G.; Giani, L.; Tronconi, E. Generalized correlation for gas/solid mass-transfer coefficients in metallic and ceramic foams. Ind. Eng. Chem. Res. 2007, 46, 3955–3958. [CrossRef] 22. Gancarczyk, A.; Iwaniszyn, M.; Pi ˛atek,M.; Sindera, K.; Korpy´s,M.; Jodłowski, P.J.; Łojewska, J.; Kołodziej, A. Interfacial heat and momentum transfer relation for porous media. Int. J. Therm. Sci. 2018, 132, 42–51. [CrossRef] 23. Gancarczyk, A.; Piatek, M.; Iwaniszyn, M.; Jodlowski, P.J.; Lojewska, J.; Kowalska, J.; Kolodziej, A. In search of governing gas flow mechanism through metal solid foams. Catalysts 2017, 7, 124. [CrossRef] 24. Piatek, M.; Gancarczyk, A.; Iwaniszyn, M.; Jodlowski, P.J.; Lojewska, J.; Kolodziej, A. Gas-phase flow resistance of metal foams: Experiments and modeling. ALChE J. 2017, 63, 1799–1803. [CrossRef] 25. Žkauskas, A. Heat transfer from tubes in crossflow. Adv. Heat Transf. 1987, 18, 87–159. 26. Hawthorne, R.D. Afterburner catalysis—Effects of heat and mass transfer between gas and catalyst surface. ALChE Symp. Ser. 1974, 70, 428–438. 27. Bird, R.B. Transport Phenomena; Wiley: New York, NY, USA, 1960; 780p. 28. Wakao, N.; Kaguei, S. Heat and Mass Transfer in Packed Beds; Gordon and Breach Science Publisher: New York, NY, USA, 1982. 29. Kołodziej, A.; Łojewska, J.; Tyczkowski, J.; Jodłowski, P.; Redzynia, W.; Iwaniszyn, M.; Zapotoczny, S.; Ku´strowski, P. Coupled engineering and chemical approach to the design of a catalytic structured reactor for combustion of vocs: Cobalt oxide catalyst on knitted wire gauzes. Chem. Eng. J. 2012, 200, 329–337. [CrossRef] 30. Kolodziej, A.; Lojewska, J. Prospect of compact afterburners based on metallic microstructures. Design and modelling. Top. Catal. 2007, 42, 475–480. [CrossRef] 31. Jodlowski, P.J.; Kuterasinski, L.; Jedrzejczyk, R.J.; Chlebda, D.; Gancarczyk, A.; Basag, S.; Chmielarz, L. Deno(x) abatement modelling over sonically prepared copper usy and zsm5 structured catalysts. Catalysts 2017, 7, 205. [CrossRef] 32. Leszczyński,B.; Gancarczyk, A.; Wróbel, A.; Pi ˛atek,M.; Łojewska, J.; Kołodziej, A.; P˛edrys,R. Global and local thresholding methods applied to x-ray microtomographic analysis of metallic foams. J. Nondestruc. Eval. 2016, 35, 35. [CrossRef] Catalysts 2019, 9, 587 13 of 13

33. Kołodziej, A.; Łojewska, J.; Ocho´nska,J.; Łojewski, T. Short-channel structured reactor: Experiments versus previous theoretical design. Chem. Eng. Process. 2011, 50, 869–876. [CrossRef] 34. Jodlowski, P.J.; Jedrzejczyk, R.J.; Chlebda, D.K.; Dziedzicka, A.; Kuterasinski, L.; Gancarczyk, A.; Sitarz, M. Non-noble metal oxide catalysts for methane catalytic combustion: Sonochemical synthesis and characterisation. Nanomaterials 2017, 7, 174. [CrossRef][PubMed] 35. Jodłowski, P.J.; J˛edrzejczyk,R.J.; Gancarczyk, A.; Łojewska, J.; Kołodziej, A. New method of determination of intrinsic kinetic and mass transport parameters from typical catalyst activity tests: Problem of mass transfer resistance and diﬀusional limitation of reaction rate. Chem. Eng. Sci. 2017, 162, 322–331. [CrossRef]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).