energies
Article A Comparative Thermodynamic Study of Equilibrium Conditions for Carbon Deposition from Catalytic C–H–O Reformates
Zdzisław Jaworski * ID and Paulina Pianko-Oprych
Department of Chemical Technology and Engineering, West Pomeranian University of Technology, Szczecin, 71065 Szczecin, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-91-449-4020
Received: 3 April 2018; Accepted: 2 May 2018; Published: 7 May 2018
Abstract: The importance of carbon deposition occurring during catalytic fuel reforming is briefly described along with former studies on the process. Thermodynamic fundamentals of modeling the critical conditions of the deposition equilibrium are presented. Computational results of ternary C–H–O diagrams with the threshold lines between the carbon deposition and deposition-free regions are discussed for two new pressure levels of 3 and 30 bar and a temperature range from 200 to 1000 ◦C. The process pressure does not affect the temperature range typical for the type of deposited carbon allotrope; either graphite, multi-walled carbon nanotubes, or single-walled carbon nanotubes in bundles. However, pressure has a profound influence on the location of the threshold lines for carbon deposition. Three reforming processes of two hydrocarbon fuels are analyzed; catalytic partial oxidation, and wet and dry reforming. Chord lines representing varied compositions of process mixtures are introduced to the ternary diagrams. The intersection points of the chord lines with the threshold lines are used in a novel interpretation of the functions of the oxygen-to-carbon critical ratio against temperature and pressure, which can be used in avoiding carbon deposition in catalytic reforming of natural gas and liquefied petroleum gas.
Keywords: carbon deposition; hydrocarbon reformates; thermodynamic equilibrium; C–H–O diagrams
1. Introduction The demand for useful energy is systematically growing as the world aims to improve its standard of living. The burning of all fossil fuel forms has serious environmental consequences. A promising alternative of fossil fuels for the future is seen in hydrogen. Energy produced by hydrogen-based fuel cells is characterized as high-quality energy, because of the high conversion efficiency from chemical to electrical energy. The efficiency is almost twice as high compared to internal combustion engines and because of the zero emissions of pollutants and greenhouse gases to the environment, hydrogen fuel cells are currently the promoted form. Hydrogen can be obtained using several technologies: steam reforming (SR) [1]; auto-thermal reforming (ATR) [2]; dry reforming (DR) [3]; or catalytic partial oxidation reforming (CPOX)[4]. Catalytic steam reforming is the most common process due to its high energy efficiency. This technology has been widely applied in chemical industries for large-scale hydrogen production, which accounts for 50% of the hydrogen generated worldwide by using methane from natural gas (NG) as the main hydrocarbon source [5]. It is a well-known process described recently by Adiya et al. [6] and Tuna et al. [7]. The reactions that occur in this process primarily produce H2, CO2, and CO, but there is no set quantity for these compounds. The compounds’ concentrations depend on several factors, such as reagent concentration, temperature, and pressure of the reformer, as well as the physical and
Energies 2018, 11, 1177; doi:10.3390/en11051177 www.mdpi.com/journal/energies Energies 2018, 11, 1177 2 of 12 chemical characteristics of the chosen catalyst. The overall reaction that occurs in the steam reforming ◦ process takes place at temperatures between 650 and 850 C obtaining H2 yields of 60–70% at a H2/CO ratio equal to 3.0 [7]. In addition to the main reforming reaction, other reactions can simultaneously occur and modify the equilibrium conversion of CO2 and CH4. Boudouard’s reaction leads to carbon formation by carbon monoxide decomposition. This reaction is very important for the reforming process since it is responsible for solid carbon deposition in catalysts. It occurs when the decomposition reaction of carbon monoxide, together with the decomposition reaction of methane, are faster than the carbon removal rate [8]. The formation of carbon deposits on catalysts leads to a blockage of catalyst pores by the deposited carbon, separation of the catalyst from its support, and lack of gas flow due to an increase in pressure caused by pore blockage [9]. The carbon formation may take place by three routes that result in different kinds of coke [10]. At low temperatures, less than 500 ◦C, adsorbed hydrocarbons may accumulate on the nickel surface and slowly polymerize into an encapsulating film, blocking and deactivating the nickel surface. At high temperature, above 600 ◦C, pyrolytic coke formed by the thermal cracking of hydrocarbons may encapsulate and deactivate the catalyst particle. At temperatures greater than 450 ◦C, whisker (filamentous) carbon is the principal product of carbon formation via a mechanism involving the diffusion of carbon through nickel crystals, nucleation, and whisker growth with a nickel crystal on the top. The whisker-type carbon does not deactivate the nickel surface, but rather causes a breakdown of the catalyst by pore plugging [10]. Ginsburg et al. [11] calculated the correlation between the CO2/CH4 ratio and the process of carbon formation on the surface of Ni-based catalysts. According to their model, the reactant ratio should be equal to 2 in order to provide less carbon accumulation. The oxidizing system must have an excess of CO2 as an oxidant. The modeling of carbon deposition from lower hydrocarbon fuels at thermodynamic equilibrium was widely discussed by Jaworski et al. [12,13]. A minimization algorithm of the system’s total Gibbs energy was applied using the commercial software HSC for both dry and wet reforming processes within the range of 200 ◦C to 1000 ◦C and for four levels of constant pressure. Five carbon solid allotropes, such as graphite, diamond, amorphous, multi-walled carbon nanotubes (MWCNT), and single-walled nanotubes in bundles (SWCNT), were allowed to appear in the solid phase. However, no indication of deposits of diamond and amorphous carbon were found for the analyzed systems. The computation results of the deposition conditions at thermodynamic equilibrium showed for the wet reforming of NG and LPG that the maximum critical atomic oxygen to carbon (O/C) ratios were found at 2.0, 2.4, 2.7, and 3.2 for pressures of 1, 3, 10 and 30 bar, respectively. It was concluded that higher O/C values to the one used in predictions should be applied to avoid nanotubular carbon depositions [13]. In addition, the threshold temperature of 431 ◦C or 577 ◦C for the deposition boundaries between graphite and MWCNT or MWCNT and SWCNT were confirmed regardless of pressure. Another available option for hydrogen-rich fuel production beyond steam or CO2 reforming is catalytic partial oxidation (CPOx). A thermodynamic analysis of equilibrium conditions of hydrogen production from natural gas and LPG using the CPOx reformer, with reference to carbon deposition phenomena, was performed by Jaworski and Pianko-Oprych [14]. Methane catalytic reforming in the range of 1 < O/C < 4 resulted in the formation of solid carbon deposits. However, only a single form of depositing carbon was predicted at a time if the O/C ratio fell below the critical value. Depending on the temperature, it was either graphite from 200 to 431 ◦C, or one of the two carbon nanotubes. Multi-walled carbon nanotubes were found most stable in the range from 431 to 577 ◦C and single-walled nanotubes in bundles prevailed from 577 up to 1000 ◦C. The maximum critical O/C ratio was about 2.7 or 2.9 for methane with air or pure oxygen as the oxidant, respectively, while for Liquefied petroleum gas (LPG)–oxidant pairs the O/C maxima were lower by about 0.2 [14]. The presented thermodynamic analyses were carried out for a range of fuels indicating the predominant role of temperature in solid carbon formation. The carbon element had different Energies 2018, 11, 1177 3 of 12 allotropic forms in the gas and solid phases and, therefore, the electrochemical data for both purified single-walled and multi-walled CNTs were critical in predicting the conditions of carbon deposition. The key objective of the paper is to present the development of an integrated approach for understanding the mechanism of carbon deposition from catalytic C–H–O reformates. This is envisaged through a theoretical modeling presented in [12–14] over an extended range of operating conditions. To achieve this objective, a thermodynamic analysis on carbon deposition from C–H–O reformates will be expanded for the total pressure of 3 bar and 30 bar and compared with the previous results [12] obtained for 1 bar and 10 bar. Differences in the deposition boundaries for all solid carbon forms predicted for the catalytic partial oxidation, and dry and wet reforming of the NG and LPG will be explained based on the deposition boundaries in the ternary C–H–O diagrams for different temperatures and pressures. The results of this study will quantify the relationship between carbon formation and reforming system conditions promoting coke deposition. Such a comparative analysis of equilibrium deposition for the CPOx, and dry and wet reforming of lower hydrocarbons in NG and LPG will allow the indication of the critical temperature for the deposition at chosen process pressures and reactant compositions.
2. Results This section presents the computational results of threshold atomic ratios of carbon, oxygen, and hydrogen, which separate regions of single-phase gas mixture concentrations from two-phase regions containing solid carbon deposits under thermodynamic equilibrium. The results are presented in C–H–O ternary diagrams as the isothermal threshold lines for the temperature range from 200 to 1000 ◦C and two process pressures of 3 and 30 bar. The modeling is carried out separately for the deposition of graphite only and when deposition of carbon nanotubes is also allowed. In addition, the diagrams are supplied with chord lines drawn between points representing compositions of two fuels and three oxidants that represent different compositions of reformates. Jointly with the results of our former study [12] of ternary diagrams for 1 and 10 bar, those diagrams are used for the interpretation and discussion of the critical O/C values for the fuel-oxidant pairs in the full temperature and pressure ranges.
2.1. Ternary Diagrams for 3 and 30 Bar Additional modeling, explained in Section4, is carried out to construct the critical lines for the two missing ternary diagrams, for 3 and 30 bar. Like in our previous studies, only three allotropes of solid carbon result from the computations, namely graphite up to 431 ◦C, then multiwalled carbon nanotubes up to 577 ◦C, and from there to 1000 ◦C, only single-walled carbon nanotubes were found. Since this study aims to explain differences in the critical O/C ratios for different fuels and oxidants, their composition points are also shown in the diagrams. It can be observed that the computed threshold lines, for temperatures from 200 ◦C to 1000 ◦C in Figure1a,b, exhibit a similar evolution to that shown in corresponding graphs for 1 and 10 bar, published in [12]. Most pronounced differences, for the tested pressure range, are found for the highest pressure of 30 bar (Figure1b). They are mainly in the region of fuel-oxidant mixtures of low hydrogen content, on the right side of the diagrams, where the temperature effect on the threshold lines is minimal. Two types of fuel: natural gas (containing about 94% of CH4) or liquefied petroleum gas (containing mainly C3H8 and C4H10) are used in this study. Depending on the type of the reforming process, a fuel reacts with one of three types of oxidant; oxygen, O2, from air, water steam, H2O, or carbon dioxide, CO2. The composition of a given mixture of the fuel–oxidant pair is represented in ternary diagrams by points located along the straight line connecting the fuel point at the left triangle edge with the oxidant point located on the opposite side. A crossing point of the fuel-oxidant line with the relevant threshold line determines the critical composition of the mixture in terms of the C, H, and O atomic ratios. Raising the C content in the mixture from the crossing point means entering Energies 2018, 11, 1177 4 of 12 the carbon deposition region. The location of the fuel-oxidant lines relative to the relevant deposition threshold line strongly influences the course of the critical O/C curves versus temperature. Energies 2018, 11, x 4 of 11
0,0 0,0 1,0 200 oC 1,0 300 oC 0,1 0,1 400 oC 0,9 0,9 500 oC 600 oC 0,2 0,2 0,8 700 oC 0,8 800 oC 0,3 0,3 900 oC 0,7 0,7 1000 oC 0,4 0,4 Carbon 0,6 Carbon 0,6 deposition deposition 0,5 0,5 H region 0,5 C H region 0,5 C
0,6 0,6 0,4 0,4 CO 0,7 CO2 0,7 2 0,3 C H +C H 0,3 C3H8+C4H10 3 8 4 10 CH 0,8 CH4 0,8 4 No carbon 0,2 No carbon 0,2 deposition deposition 0,9 0,9 0,1 0,1
1,0 1,0 0,0 0,0 H O O H O O 0,0 0,1 0,2 0,32 0,4 0,5 0,6 0,7 0,8 0,9 1,0 2 0,0 0,1 0,2 0,32 0,4 0,5 0,6 0,7 0,8 0,9 1,0 2 O O (a) (b) Figure 1. Ternary C–H–O diagrams for: (a) pressure of 3 bar; and (b) pressure of 30 bar. Figure 1. Ternary C–H–O diagrams for: (a) pressure of 3 bar; and (b) pressure of 30 bar.
InIn almost almost all all published published results results of of computation computation of of carbon carbon deposition, deposition, graphite graphite was was the the only only solid solid carbon allotrope predicted [12]. [12]. It It is, is, therefore, therefore, in informativeformative to to compare compare the the threshold threshold lines lines for for either either graphite only, oror allall possible possible carbon carbon allotropes allotropes independent independent of of temperature. temperature. The The effect effect of allowingof allowing for forthe the filamentous filamentous forms forms of carbon of carbon deposits deposits is represented is represented in Figure in Figure2a,b for2a,b the for process the process pressure pressure of 3 bar of 3and bar in and Figure in Figure3a,b for 3a,b 30 bar.for 30 The bar. threshold The threshold lines are lines shown are inshown pairs ofin constantpairs of constant temperature, temperature, with the withsolid the lines solid representing lines representing all carbon all forms carbon and forms the broken and the lines broken ascribed lines toascribed graphite. to graphite. Starting fromStarting the ◦ ◦ fromtemperature the temperature of 500 C, of only 500 three °C, pairsonly ofthree temperature pairs of temperature lines with 200 linesC incrementswith 200 °C are increments shown in each are showndiagram, in foreach the diagram, sake of clearfor the presentation. sake of clear presentation.
0.0 0.0 1.0 500 oC All C 1.0 600 oC All C 500 oC Gra 600 oC Gra 0.1 o 0.1 o 0.9 700 C All C 0.9 800 C All C 700 oC Gra 800 oC Gra 0.2 o 0.2 o 900 C All C 0.8 1000 C All C 0.8 o 900 C Gra 1000 oC Gra 0.3 0.3 0.7 0.7
0.4 Carbon 0.4 Carbon 0.6 deposition 0.6 deposition 0.5 region 0.5 region H 0.5 C H 0.5 C
0.6 0.6 0.4 0.4
0.7 CO2 0.7 CO2 0.3 0.3 C3H8+C4H10 C3H8+C4H10 CH 0.8 No carbon 0.8 4 0.2 CH4 No carbon 0.2 deposition deposition 0.9 0.9 0.1 0.1
1.0 1.0 0.0 0.0 H O O O 0.0 0.1 0.2 0.32 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2 0.0 0.1 0.2 0.3H2O 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2 O O (a) (b)
Figure 2. 2. DepositionDeposition threshold threshold lines lines for forthe process the process pressure pressure of 3 bar, of 3separately bar, separately for graphite for graphite only— brokenonly—broken lines, and lines, all andcarbon all carbonallotropes—solid allotropes—solid lines: (a lines:) temperatures (a) temperatures of 500, 700, of 500, and 700, 900 and°C; and 900 (◦bC;) temperaturesand (b) temperatures of 600, 800, of 600, and 800, 1000 and °C. 1000 ◦C.
Energies 2018, 11, 1177 5 of 12 Energies 2018, 11, x 5 of 11 Energies 2018, 11, x 5 of 11 0.0 1.0 500 oC All C 0.0 1.0 o o 0.0 500 o C Gra 0.0 600 C All C 1.0 500 C All C o 0.1 o 1.0 o 700 o C All C 0.1 600600 C AllGra C 0.9 500 C Gra 0.9 o o 800 o C All C 0.1 700 o C Gra 600 C Gra 700 C All C 0.1 o 0.9 o 0.9 800 o C Gra 0.2 900 o C All C 0.2 800 C All C 700 C Gra o 0.8 o 0.8 1000o C All C 900 o C Gra 800 C Gra 0.2 900 C All C 0.2 o 0.8 0.8 1000 o C Gra 0.3 900 oC Gra 0.3 1000 C All C 0.7 0.7 1000 oC Gra 0.3 0.3 0.7 0.4 Carbon 0.4 Carbon 0.7 0.6 0.6 0.4 depositionCarbon 0.4 depositionCarbon 0.5 depositionregion 0.6 0.5 depositionregion 0.6 H 0.5 C H 0.5 C H 0.5 region C H 0.5 region C 0.6 0.5 0.6 0.5 0.4 0.4 0.6 0.6 0.4CO 0.7 0.4CO2 0.7 2 C H +C H 0.3 C H +C H CO0.3 3 8 4 0.710 CO2 3 8 4 0.710 2 0.3 C H +C0.8H 0.3 C3CHH8+C0.84H10 No carbon 3CH84 4 10 No carbon 4 0.2 0.2 deposition CH 0.8 Nodeposition carbon CH4 0.8 No carbon 4 0.2 0.2 0.9 deposition 0.9 deposition 0.1 0.1 0.9 0.9 0.1 1.0 0.1 1.0 0.0 0.0 O H O O 1.0 H2O 2 1.00.0 0.1 0.2 0.32 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2 0.00.10.20.30.40.50.60.70.80.91.00.0 0.0 O H O O H2O 2 0.0 0.1 0.2 0.32 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2 0.00.10.20.30.40.50.60.70.80.91.0 O O O O (a) (b) (a) (b) Figure 3. Deposition threshold lines lines for for the process pre pressuressure of 30 bar, separately for graphite only Figure 3. Deposition threshold lines for the process pressure of 30 bar, separately for graphite only (Gra)—broken lines, and all carbon allotropes (All C)—solid lines: ( a) temperatures of 500, 700, and (Gra)—broken lines, and all carbon allotropes (All C)—solid lines: (a) temperatures of 500, 700, and 900 °C;◦C; and ( b)) temperatures temperatures of 600, 800, and 1000 °C.◦C. 900 °C; and (b) temperatures of 600, 800, and 1000 °C. It follows from Figures 2 and 3 that the maximum effect of the presence of filamentous carbon, It follows from Figures2 and3 that the maximum effect of the presence of filamentous carbon, as as anIt alternative follows from to solely Figures graphite 2 and 3in that the theequilibrated maximum deposits, effect of wasthe presencecomputed of for filamentous 800 °C or 1000carbon, °C an alternative to solely graphite in the equilibrated deposits, was computed for 800 ◦C or 1000 ◦C for asfor an the alternative pressure ofto 3solely or 30 graphitebar, respectively. in the equilibrated For the purpose deposits, of highlighting was computed that for effect, 800 °Cthe or threshold 1000 °C the pressure of 3 or 30 bar, respectively. For the purpose of highlighting that effect, the threshold lines forlines the for pressure the applied of 3 orpressure 30 bar, levels respectively. are shown For inth Figuree purpose 4a,b, of separately highlighting for thatthe twoeffect, temperatures. the threshold linesfor the for applied the applied pressure pressure levels levels are shown are shown in Figure in Figure4a,b, separately 4a,b, separately for the for two the temperatures. two temperatures. 0.0 0.0 1.0 1.0 1 bar 1 bar 0.0 0.0 3 bar 1.0 13 bar 1.0 1 bar 0.1 0.1 10 bar 0.9 310 bar bar 0.9 3 bar 0.1 30 bar 0.1 30 bar 0.9 10 bar 0.9 10 bar 0.2 0.2 30 bar 0.8 30 bar 0.8 0.2 0.2 0.8 0.3 0.8 0.3 0.7 0.7 0.3 0.3 0.7 0.4 Carbon 0.7 0.4 Carbon 0.6 0.6 0.4 depositionCarbon 0.4 depositionCarbon 0.6 0.6 0.5 depositionregion 0.5 depositionregion H 0.5 C H 0.5 C 0.5 region 0.5 region H 0.5 C H 0.5 C 0.6 0.6 0.4 0.4 0.6 0.6 0.4 0.4 0.7 CO2 0.7 CO2 C H +C H 0.3 0.3 3 8 4 0.710 CO2 C3H8+C4H0.710 CO2 0.3 0.3 C3CHH8+C0.84H10 No carbon C3H8+C0.84H10 4 0.2 CH4 No carbon 0.2 CH 0.8 Nodeposition carbon 0.8 deposition 4 0.2 CH4 No carbon 0.2 0.9 deposition 0.9 0.1 deposition 0.1 0.9 0.9 0.1 0.1 1.0 1.0 0.0 0.0 1.0 H2O O2 1.0 H O O2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.0 0.1 0.2 0.32 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 H O O2 O 0.0 0.1 0.2 0.32 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3H2O 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2 O O O O (a) (b) (a) (b) Figure 4. Deposition threshold lines for the border process pressures of 1 and 30 bar: (a) temperature Figureof 800 °C; 4. Deposition Depositionand (b) temperature threshold threshold oflines 1000 for °C. the border process pressures of 1 and 30 bar: ( a)) temperature temperature of 800 °C;◦C; and and ( (bb)) temperature temperature of of 1000 1000 °C.◦C. A direct conclusion that follows from the examination of the two diagrams is that rising of the A direct conclusion that follows from the examination of the two diagrams is that rising of the reformingA direct pressure conclusion for those that temperatures follows from mostly the examination results in lowering of the two the diagrams critical carbon is that risingatomic of ratio the reforming pressure for those temperatures mostly results in lowering the critical carbon atomic ratio ofreforming the reformed pressure mixture. for those However, temperatures the opposite mostly effe resultsct can in be lowering noticed the for criticalreformed carbon mixtures atomic of ratio a high of of the reformed mixture. However, the opposite effect can be noticed for reformed mixtures of a high hydrogenthe reformed atomic mixture. ratio, However,for about H the > opposite0.66. Therefore, effect can the beeffect noticed of te formperature reformed on mixturesthe critical of values a high hydrogen atomic ratio, for about H > 0.66. Therefore, the effect of temperature on the critical values ofhydrogen the carbon, atomic C, ratio,and oxygen, for about O, H is > not 0.66. monotoni Therefore,c for the the effect wet of reformates. temperature The on thepressure critical effects values are of of the carbon, C, and oxygen, O, is not monotonic for the wet reformates. The pressure effects are smallerthe carbon, for the C, and lower oxygen, limit of O, the is not studied monotonic temperatur for thee, wet i.e., reformates.below 500 °C, The where pressure the effectsmost stable are smaller form smaller for the lower limit of the studied temperature, i.e., below 500 °C, where the most stable form offor carbon the lower is graphite. limit of the studied temperature, i.e., below 500 ◦C, where the most stable form of carbon of carbon is graphite. is graphite.In the following two sections, the detailed explanation is presented for the published [13,14] differentIn the courses following of the two critical sections, O/C theratio detailed for the anexplalyzedanation fuel-oxidant is presented mixtures. for the Thispublished is considered [13,14] differentseparately courses for the of naturalthe critical gas O/C and ratio liquefied for the petr analyzedoleum fuel-oxidantgas. Different mixtures. shapes Thisof the is consideredpublished separately for the natural gas and liquefied petroleum gas. Different shapes of the published
Energies 2018, 11, 1177 6 of 12
In the following two sections, the detailed explanation is presented for the published [13,14] differentEnergies 2018 courses, 11, x of the critical O/C ratio for the analyzed fuel-oxidant mixtures. This is considered6 of 11 separately for the natural gas and liquefied petroleum gas. Different shapes of the published threshold O/Cthreshold curves O/C can curves be justified can be byjustified comparing by comparing the crossing the crossing points of points the critical of the temperature critical temperature lines in thelines ternary in the diagramternary diagram with a chord with a relevant chord relevant to the fuel–oxidant to the fuel–oxidant pair. For pair. instance, For instance, the chord the line chord for Cline3H 8for+ C43H810 +(LPG) C4H10 –(LPG) CO2 –runs CO across2 runs theacross diagram the diagram almost almost horizontally, horizontally, which meanswhich themeans critical the carboncritical ratio,carbon C, ratio, is then C, roughly is then constant. roughly However, constant. theHowever, critical oxygen the critical atomic oxygen ratio, O,atomic increases ratio, with O, increasingincreases with temperature. increasing In temperature. that case of the In dry that LPG case reforming, of the dry the LPG critical reforming, O/C ratio the lowers critical with O/C rising ratio temperature.lowers with Onrising the temperature. contrary, the chordOn the lines contrary for wet, reformatesthe chord runlines in for the wet diagrams reformates from the run two in fuelthe pointsdiagrams (CH from4 or LPG)the two to “Hfuel2O”, points through (CH4high or LPG) atomic to “H ratios2O”, of through hydrogen, high H, atomic and are ratios almost of hydrogen, parallel to theH, and threshold are almost lines parallel of low temperatureto the threshold range lines from of 200low to temperature 400 ◦C. range from 200 to 400 °C.
2.2. Natural Gas Reformates A cumulative graph is presented in Figure5 5aa forfor threethree reformatesreformates ofof naturalnatural gasgas (NG):(NG): fromfrom catalytic partial oxidation [[13],13], water steam reforming, and carbon dioxide [[14].14]. Computed data for two border levels of the process pressure,pressure, either 1 bar (solid lines) or 30 bar (broken lines), are chosen for comparison.
1 bar CPOx 4 1 bar CPOx 4 30 bar CPOx 30 bar CPOx 1 bar wet refor. 1 bar wet refor. 30 bar wet refor. 30 bar wet refor. 1 bar dry refor. 1 bar dry refor. 3 30 bar dry refor. 3 30 bar dry refor.
2 2 O/C atomic ratio O/C atomicratio 1 GRAPHITE MW CNT SW CNT 1 GRAPHITE MW CNT SW CNT
0 0 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 700 800 900 1000
o o Temperature [ C] Temperature [ C] (a) (b)
Figure 5. Critical O/C lines for the catalytic partial oxidation reforming (CPOx), wet and dry Figure 5. Critical O/C lines for the catalytic partial oxidation reforming (CPOx), wet and dry reformates of:reformates (a) natural of: gas;(a) natural and (b )gas; liquefied and (b petroleum) liquefied gas.petroleum gas.
In the range of graphite deposition, pressure has almost no effect on the threshold O/C values for theIn theCPOx range or dry of graphite reforming deposition, of natural pressure gas, as has shown almost in noFigure effect 5a. on This the thresholdis a consequence O/C values of only for the CPOx or dry reforming of natural gas, as shown in Figure5a. This is a consequence of only small small differences in the critical line locations in the ternary diagrams for temperatures below◦ 500 °C differencesand the hydrogen in the criticalatomic lineratio locations H < 0.6, inirrespective the ternary of diagramsthe process for pressure. temperatures This conclusion below 500 isC valid and thefor low-hydrogen hydrogen atomic reformates ratio H
Energies 2018, 11, 1177 7 of 12
2.3. Liquified Petroleum Gas Reformates A similar collective graph of equilibrium conditions for three reformates of liquefied petroleum gas (LPG) is presented in Figure5b. A considerable similarity in the shape of the O/C threshold lines to those of NG reformates (Figure5a) can be noticed for the CPOx and dry reforming types. However, the critical lines for the wet reforming of LPG have different shapes than those of NG for the deposition regions of graphite and multi-walled carbon nanotubes, i.e., for temperatures lower than 577 ◦C. They start at 200 ◦C from about O/C = 1.9 then decrease to a minimum at roughly 400 ◦C, and start growing with increasing temperature in the area of MWCNT deposition and the beginning of the SWCNT. In the region of SWCNT deposition from LPG wet reformates, the O/C curves show maxima dependent on the process pressure with a close similarity to their equivalents for NG wet reformates.
3. Discussion In the modeling of carbon deposition, the same computing methodology as that published in former papers [12–14] is applied to predict conditions of the thermodynamic equilibrium of reformates. Unchanged chemical potential data from the literature are also applied for considered forms of solid carbon allotropes. The C–H–O ternary diagrams for two previous levels of process pressure, 1 and 10 bar [12], are now extended to 3 and 30 bar. It follows from the comparative analysis of those diagrams that the flow of the threshold lines, between the deposition and deposition-free regions, continues the trends found earlier [12], both for the process temperature and pressure. In particular, the ranges of deposition temperature for three carbon allotropes; graphite, and multi-walled and single-walled nanotubes, were independent of pressure. The maximum differences between the threshold lines are found at higher temperatures than formerly in [12], i.e., about 800 ◦C and 1000 ◦C for the pressure of 3 and 30 bar, respectively. The ternary diagrams are now also equipped with chord lines indicating the compositions of possible fuel-oxidant mixtures. The crossing points of the chord and threshold lines correspond to relevant points of the O/C critical lines for a given fuel-oxidant pair. The points are used in the interpretation and explanation for the critical lines in the function of temperature and pressure in our former results [13,14]. Six types of reformed mixtures of fuel-oxidant are considered using two fuels (NG or LPG) and three oxidants: air in CPOx reforming [13] and water (wet reforming) or carbon dioxide (dry reforming) in [14]. The non-monotonic influence of both process temperature and pressure on the computed critical O/C lines is easily explained by referencing to the distribution of the relevant threshold and chord lines in the ternary diagram. Detail explication of the specific O/C functions of temperature and pressure are presented in Sections 2.2 and 2.3. It is explained in reference to appropriate—for the analyzed fuel-oxidant mixtures—threshold and chord lines in ternary diagrams.
4. Materials and Methods
4.1. Basic Reactions and Energy Effects The reforming reactions depend on the type of fuel and on the reforming reactant. They are usually carried out in the gas phase to obtain hydrogen, H2, and carbon monoxide, CO. This study concerns lower, i.e., C1 to C4, saturated hydrocarbons, which are the most popular and still low-cost fossil fuels. Those fuels can be reformed in reactions with an oxygen-carrying reactant, such as water steam (H2O), carbon dioxide (CO2), or oxygen (O2). Basic reactions, (a) to (c), of the hydrocarbon fuels with the reforming reactants are presented in the summary forms in Table1. The number of carbon atoms in the fuel molecules is equal to “n”. The reaction equations are followed by associated standard 0 0 values of the reaction enthalpy, ∆Hi , and chemical potential, ∆µi , at the temperature of 298 K. The data were obtained from the recognized database [15]. The wet and dry reforming reactions, respectively (a) and (b), are highly endothermal, whereas the partial oxidation reaction (c) is exothermal. Energies 2018, 11, 1177 8 of 12
Table 1. Basic reactions and their standard thermodynamic data.
Energies 2018, 11, x 0 −1 −1 8 of 11 Equation ∆Hi (298) kJ mol kJ mol Reaction (i) ∼ ∼ CnH2n+2 + nH2O(g) = nCO + (2n + 1)H2 =56.4 + 148.4 n =61.6 + 79.6 n (a) carbonaceous deposits can be computed from∼ compositions of the reacting∼ fuel–oxidant mixtures at CnH2n+2 + nCO2 = 2nCO + (n + 1) H2 =56.4 + 189.6 n =61.6 + 108.2 n (b) the coking threshold. This was already reviewed∼ in our previous study∼ [12] with the conclusion that CnH2n+2 + n/2O2 = nCO + (n + 1) H2 =56.4 − 93.4 n =61.6 − 149.0 n (c) the wide scatterCH4 =of C the(g) + chemical 2H2 potential estimate791.2s resulted most probably 721.8 from deriving (d) them for different mixtures2CO = Cof(g) the+ CO crystallog2 raphic forms of544.2 the carbonic deposits 551.2in relevant experiments. (e) The pentagon COshown + H2 by= Cthe(g) +blue H2O lines in Figure 6 show585.4s the range of estimates 579.8 of the standard (f) chemical potential2H of2 filamentous+ CO2 = C(g) +carbon 2H2O deposits, as determined626.5 from the coking 608.5 threshold compositions (g) in m C(g) = m Cg(g) −716.7 m −671.2 mΔμ 0 (h) several reforming reactions. The estimates are presented as their difference, Cs(), from the μ 0 standard chemical potential of graphite, Cg() s , which is assumed to be 0 for any temperature, Substrates andEnergies products 2018, 11, ofx the basic reactions can further react to form also vapors of carbon,8 of 11 C(g), asaccording shown in to reactions the convention (d) to (g). applied The thermodynamicin physical chemistry. effects of the deposition of m atoms of carbon carbonaceous deposits can be computed from compositions of the reacting fuel–oxidant mixtures at vapors to form solid graphite, Cg(s), are also included in Table1. the cokingTable threshold. 1. Basic reactionsThis was already and their reviewed standard in our previousthermodynamic study [12] withdata. the conclusion that Reliable thermodynamicthe wide scatter data of the for chemical carbon potential nanotubes estimate ats the resulted reference most probably temperature from deriving of 298 them K cannot for be different mixtures of the crystallog0raphic forms of the carbonic deposits0 in relevant experiments. The found in the subject literature. However,Δ severalH ()298 values kJ mol of the−1 chemicalΔμ ()298 potential kJ mol of−1 the carbonaceous Equationpentagon shown by the blue linesi in Figure 6 shows the range ofi estimates of the standardReaction chemical (i) deposits can be computed from compositions of the reacting fuel–oxidant mixtures at the coking CnH2n+2 + nH2O(g)potential = nCO of+ (2nfilamentous + 1)H2 carbon deposits,≅56.4 + as148.4 determined n from the≅61.6 coking + threshold79.6 n compositions(a) in threshold. This wasseveral already reforming reviewed reactions. in The our estimates previous are studypresented [12 as] withtheir thedifference, conclusion Δμ 0 , thatfrom thethe wide CnH2n+2 + nCO2 = 2nCO + (n + 1) H2 ≅56.4 + 189.6 n ≅61.6 + 108.2 n Cs() (b) scatter of the chemicalstandard potential chemical estimatespotential of resultedgraphite, μ most0 , which probably is assumed from to derivingbe 0 for any them temperature, for different CnH2n+2 + n/2O2 = nCO + (n + 1) H2 ≅56.4 − 93.4Cg() s n ≅61.6 − 149.0 n (c) mixtures of the crystallographicaccording to the convention forms of applied the carbonic in physical deposits chemistry. in relevant experiments. The pentagon CH4 = C(g) + 2H2 791.2 721.8 (d) shown by the blue lines in Figure6 shows the range of estimates of the standard chemical potential 2CO = C(g) + CO2 Table 1. Basic reactions544.2 and their standard thermodynamic551.2 data. (e) of filamentous carbon deposits, as determined from the coking threshold compositions in several CO + H2 = C(g) + H2O 585.4ΔH 0 ()298 −1 Δμ 0 ()298579.8 −1 (f) Equation i kJ mol i 0 kJ mol Reaction (i) reforming reactions. The estimates are presented as their difference, ∆µ ( ), from the standard chemical 2H2 + CO2 = Cn(g)H 2n+2+ 2H+ nH2O2O (g) = nCO + (2n + 1)H2 626.5≅56.4 + 148.4 n ≅61.6C 608.5s + 79.6 n (a) (g) 0 potential of graphite,m C(g) = µmCCgn HC(2n+2g(g)s) +, whichnCO2 = 2nCO is assumed + (n + 1) H2 to−716.7 be≅ 056.4 form + 189.6 any temperature,n ≅61.6−671.2 + according108.2 m n to the(b) convention(h) applied in physical chemistry.CnH2n+2 + n/2O2 = nCO + (n + 1) H2 ≅56.4 − 93.4 n ≅61.6 − 149.0 n (c) CH4 = C(g) + 2H2 791.2 721.8 (d)
2CO10000 = C(g) + CO2 544.2 551.2 (e) CO + H2 = C(g) + H2O 585.4 Data 579.8[16] (f) 2H2 + CO2 = C(g) + 2H2O 626.5 Extrapolation608.5 (g) Linearized [17] m C(g) = m Cg(g) −716.7 m −671.2 m (h) 5000 Δμ0 C(s) 10000 [J/mol] Data [16] GRAPHITEExtrapolation 0 Linearized [17] 5000 Δμ0 C(s) MWCNT [J/mol] GRAPHITE 0 -5000 MWCNT SWCNT -5000
-10000 SWCNT 400 500 600 700 -10000 o 400 500T [ C] 600 700 o T [ C] FigureFigure 6. 6.Chemical ChemicalFigure potential potential 6. Chemical of of the the potential formation formation of the of formation of carbon carbon of deposits carbon deposits deposits relative relative relative to graphite.to graphite. graphite. represents represents represents the 0 0 Δμ Δμ 0 the range of Csthe() range for carbonof Cs() nanotubes for carbon nanotubes (CNTs) (CNTs) [12] [12]estimated estimated from from thethe compositions compositions in the in the range of ∆µC(s) for carbon nanotubes (CNTs) [12] estimated from the compositions in the literature at theliterature coking at threshold. the cokingliterature threshold. at the coking threshold. Chemical potential data for the carbon nanotubes, CNT, should be obtained for their purified ChemicalChemical potentialpotentialforms, either datadata multi-walled, forfor thethe carbon carbon MWCNT, nanotubes, nanotubes, or single-walled CNT,CNT, in bundles, should should SWCNT. be be obtained obtained Such data for for for their elevatedtheir purified purified forms,forms, either either multi-walled, multi-walled,temperatures MWCNT, MWCNT,is available from or or single-walled elsingle-walledectrochemical measurements inin bundles, bundles, publis SWCNT.SWCNT.hed by Gozzi Such Such et dataal. data [16,17]. for for For elevated elevated measurements with the multi-walled CNT and in temperature ranging from 820 K to 920 K, the temperaturestemperatures isis availableavailableauthors [16] from from obtained el electrochemicalectrochemical the following relationship: measurements measurements publis publishedhed by by Gozzi Gozzi et al. et [16,17]. al. [16,17 For]. Formeasurements measurements with with the themulti-walled multi-walled Δ=−CNTμ 0 CNT ()and and in temperature in temperature ranging ranging from from 820 820K to K 920 to 920K, the K, MWCNT TT8250 11.72 (J/mol) for T (K). (1) theauthors authors [16] [16 obtained] obtained the the following following relationship: relationship: This relationship is graphically shown in Figure 6 by the dark blue solid line, which is also Δ=−μΔ=0 μ 0 extrapolated to Cs() ()0TT, to represent8250 11.72its chemical (J/mol) potential equal for to thatT (K). of graphite, which occurs ∆µ0 MWCNT(T) = 8250 − 11.72T (J/mol) for T(K). (1)(1) at about 431MWCNT °C. Results of similar measurements carried out for bundled single-walled carbon This relationship is graphically shown in Figure 6 by the dark blue solid line, which is also Δ=μ 0 extrapolated to Cs() 0 , to represent its chemical potential equal to that of graphite, which occurs at about 431 °C. Results of similar measurements carried out for bundled single-walled carbon
Energies 2018, 11, 1177 9 of 12
This relationship is graphically shown in Figure6 by the dark blue solid line, which is also 0 = extrapolated to ∆µC(s) 0, to represent its chemical potential equal to that of graphite, which occurs at about 431 ◦C. Results of similar measurements carried out for bundled single-walled carbon nanotubes [17], in the temperature range from 750 K to 1015 K, were presented in the form of the 9th degree polynomial: 9 0 n ∆µSWCNT(T) = ∑ anT . (2) n=0 A piecewise approximation of that function is presented in Figure6 by the red line. The common point of Equations (1) and (2) occurs at a temperature of about 577 ◦C. Such temperature functions of the chemical potentials of the MWCNT and SWCNT were used in calculations of the equilibrium concentrations of the gas and solid phases with the HSC software [18]. The calculations were based on the principles of the thermodynamic equilibrium, which are briefly described in the following section.
4.2. Thermodynamic Equilibrium The basic postulate of chemical statics, for the thermodynamic equilibrium (*) to occur [19], is the reaction system reaches then a minimum of its total Gibbs energy, G (J):
∗ ∗ n ∗o dG T , P , nj = 0 (3)
The chemical potential of a species “j”, µj (J/mol), is the partial molar Gibbs energy of the system for constant temperature and pressure: " # ∂G = µj (4) ∂nj T,P
In a homogeneous mixture of many species, the chemical potential can be expressed as the sum 0 of its standard value (for pure species “j”), µj , and a contribution of the ratio of the species activity in 0 the mixture, aj, to its value in the standard state, aj : a = 0 + j µj µj RT ln 0 (5) aj
When dealing with gas phase mixtures, the species activity is usually expressed as a product of the species partial pressure, Pj, and the fugacity coefficient, ϕj:
aj = ϕjPj (6)
The fugacity coefficient practically equals 1.0 [19] when the species partial pressure, Pj, is significantly lower than its critical pressure and also the process temperature is much higher than the species critical temperature. In the state of thermodynamic equilibrium, denoted by “*”, the species chemical potential should be constant in all phases containing the species: solid (s), liquid (l), and gas (g):
∗ ∗ ∗ µj(s) = µj(l) = µj(g) (7)
Consequently, in the case of chemical reactions between species in a given phase, the postulate of Equation (3) leads to Equation (8), which is valid for constant temperature and pressure:
∗ ∑ νj,i·µj = 0 (8) j Energies 2018, 11, 1177 10 of 12
The stoichiometric coefficients, νj,i, of the j-th reactant, that participates in the i-th reaction, are negative for substrates and positive for products. The standard enthalpy and chemical potential of a chemical reaction “i” are calculated in a similar way, accounting for contributions from substrates and products:
0 0 ∆Hi (T) = ∑ νj,i·Hj (T) (9) j
0 0 ∆µi (T) = ∑ νj,i·µj (T) (10) j Their values for relevant reactions are quoted in Table1. The conditional minimum of the total Gibbs energy, expressed in Equation (3), can be computed in several ways [20]. This leads to the determination of the composition of each phase at the thermodynamic equilibrium for the prescribed initial mole number of substrates and the final phase species, temperature, and pressure. Those computations can be carried out with the help of a commercial package, such as HSC [18], which was used in this study.
4.3. Modeling Procedure and Scope The modeling of equilibrium conditions of C–H–O mixtures was specifically directed to detect the beginning of the formation of solid carbon. Two types of such computations were applied in our former studies [12–14] and they were based on the principles presented in the previous section. Details of the computing procedure were also described there and the interested reader is referred to those open access papers. The relationship (Equation (1)) for MWCNT was directly applied to widen the 0 HSC databank. However, the ∆µSWCNT function of temperature, Equation (2), was piecewise linearly 0 approximated for ∆µSWCNT < 0 and then introduced to the HSC software database. The approximation 0 lines are presented in Figure6, with the extrapolation of Equation (1) to the level of ∆µMWCNT = 0 shown by the broken line. The border temperatures of 431 and 577 ◦C were found independent of the process pressure in the equilibrium calculations. They correspond to the crossing points of the pairs of lines in Figure6: graphite–MWCNT and MWCNT–SWCNT. The depositing type of carbon is characterized in the thermodynamic equilibrium by the lowest value of its standard chemical potential. Our former paper [12] reported details on the critical C, O, and H atomic fractions around which a step change from none to a detectable amount of solid carbon occurs. This allowed for determining critical lines, which divide in ternary C–H–O diagrams the carbon deposition area from the deposition-free area. However, only two levels of the total pressure, i.e., 1 bar and 10 bar, of the equilibrated mixture of carbon-, hydrogen-, and oxygen-containing compounds were applied in [12]. This present study is aimed at a comparison and discussion of the critical deposition lines presented for the CPOx reforming in [13] and for the wet and dry reforming in [14]. Those two papers discussed the critical O/C atomic ratios against temperature for two types of hydrocarbon fuels, NG and LPG, and three types of oxygen-containing reforming oxidants; O2 from air, H2O, and CO2. Four levels of constant pressure: 1, 3, 10, and 30 bar, were used in [13,14], while only two of them, i.e., 1 and 10 bar, were applied in [12] Therefore, the former computational results are supplemented in this study by new data for C–H–O ternary diagrams for the pressure of 3 and 30 bar, as presented in Section2.
Author Contributions: Z.J. and P.P.-O. designed the study; Z.J. designed and performed the computations, Z.J. analyzed a majority of the data; P.P.-O. contributed to analyses of the data and wrote the main part of the Introduction; and Z.J. wrote the rest of the paper. Funding: This research was funded by [European Union’s Seventh Framework Programme] grant number [FP7/2007–2013], [Fuel Cells and Hydrogen Joint Undertaking (FCH JU)] grant number [621213] and [Polish research funds] grant number [3126/7.PR/2014/2]. Energies 2018, 11, 1177 11 of 12
Acknowledgments: The research program leading to these results received funding from the European Union’s Seventh Framework Programme (FP7/2007–2013) for the Fuel Cells and Hydrogen Joint Undertaking (FCH JU) under grant agreement no. 621213 with the STAGE-SOFC acronym. Information contained in the paper reflects only the view of the authors. The FCH JU and the Union are not liable for any use that may be made of the information contained therein. The work was also financed from the Polish research funds awarded for project no. 3126/7.PR/2014/2 of international cooperation within STAGE-SOFC in the years 2014–2017. The authors received funds from FCH JU for covering the costs to publish in open access. Conflicts of Interest: The authors declare no conflict of interest.
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