Rev Chem Eng 2017; 33(3): 217–235
Open Access
Zdzisław Jaworski*, Barbara Zakrzewska and Paulina Pianko-Oprych
On thermodynamic equilibrium of carbon
deposition from gaseous C-H-O mixtures:
updating for nanotubes
DOI 10.1515/revce-2016-0022
Received April 29, 2016; accepted July 29, 2016; previously ­published
online August 26, 2016
Abstract: Extensive literature information on experimental
thermodynamic data and theoretical analysis for depositing carbon in various crystallographic forms is examined,
and a new three-phase diagram for carbon is proposed.
The published methods of quantitative description of
gas-solid carbon equilibrium conditions are critically
evaluated for filamentous carbon. The standard chemical potential values are accepted only for purified singlewalled and multi-walled carbon nanotubes (CNT). Series
of C-H-O ternary diagrams are constructed with plots of
boundary lines for carbon deposition either as graphite or
nanotubes. The lines are computed for nine temperature
levels from 200°C to 1000°C and for the total pressure of
1 bar and 10 bar. The diagram for graphite and 1 bar fully
conforms to that in (Sasaki K, Teraoka Y. E
­ quilibria in fuel
cell gases II. The C-H-O ternary diagrams. J Electrochem
Soc 2003b, 150: A885–A888). Allowing for CNTs in carbon
deposition leads to significant lowering of the critical carbon content in the reformates in temperatures from 500°C
upward with maximum shifting up the deposition boundary O/C values by about 17% and 28%, respectively, at 1
and 10 bar.
Keywords: carbon deposition; C-H-O reformates; CNT
effects; thermodynamic equilibrium.
*Corresponding author: Zdzisław Jaworski, Department of Chemical
Technology and Engineering, West Pomeranian University of
Technology, Szczecin, 71065 Szczecin, Poland,
e-mail: [email protected]
Barbara Zakrzewska and Paulina Pianko-Oprych: Department of
Chemical Technology and Engineering, West Pomeranian University
of Technology, Szczecin, 71065 Szczecin, Poland
1 Introduction
The world energy infrastructure currently uses mainly
fossil fuels such as hydrocarbons and various types of
coal with steadily growing contribution from renewable
energy sources as the energy economy based on hydrogen
as energy carrier is still in its infancy. One of the key problems associated with carbonaceous fuels is unfavorable
deposition of solid carbon from gaseous carbon-hydrogen-oxygen (C-H-O) mixtures met in a range of industrial
processes (Rostrup-Nielsen 1997). The main sources of
depositing carbon were described in the literature as (i)
molecules of elemental carbon created in thermal cracking reactions in gas phase (Jankhah et al. 2008) and (ii)
C-H-O compounds of various proportions of the elements,
decomposed on catalyst surfaces (Chen et al. 2011, Korup
et al. 2012). Carbon deposition in (i) consists in directphase transformation of the element molecules from
gaseous state into the solid form.
Decomposition of several hydrocarbons was often
used to produce the so-called pyrolytic carbon (pyrocarbon), which found significant applications initially in the
space and aircraft industries. Nowadays, carbon nanomaterials are being manufactured mainly in the form of
single- or multi-walled nanotubes (Dasgupta et al. 2011,
Prasek et al. 2011). In contrast, carbon deposition process
(coking, fouling) is highly undesirable in petrochemistry
(Benzinger et al. 1996) at cracking and dehydrogenation
processes and also in the solid oxide fuel cell technology.
Likewise, combustion of carbon containing fuels is frequently accompanied by soot formation due to incomplete oxidation (Wijayanta et al. 2012).
However, this study is focused on conditions of carbon
deposition from reformed fuels that is detrimental mainly
to catalyst surfaces, depending on the morphology of the
surface carbon (Pakhare and Spivey 2014). Therefore, the
phenomenon of solid carbon formation both in syngas production and in preprocessing of fuels for solid oxide fuel
cells (SOFCs) is of profound importance. The presence of
©2016, Zdzisław Jaworski et al., published by De Gruyter.
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218 Z. Jaworski et al.: Carbon deposition: updating for nanotubes
C1 to C4 hydrocarbons and CO in reformate gases was found
to be a major precursor of carbon formation in SOFCs (Bae
et al. 2010). On the other hand, the nucleation of graphite
over a catalyst is extremely sensitive to its nanostructure
(Bengaard et al. 2002). The deposition usually occurs on
solid surfaces, but nuclei of solid carbon may also form in
the fluid phase (Guo et al. 2013, Lemaire et al. 2013).
This review starts from a general description of literature data on deposition of various forms of solid carbon
from gaseous reformate mixtures. Based on the literature
experimental data, an original three-phase carbon diagram
is proposed for a wide P-T range followed by validated mathematical expressions for equilibrium carbon vapor pressure
over carbon solid forms. In the following chapter, quantitative description of thermodynamic equilibrium is included
for a range of allotropic forms of solid carbon, including two
filamentous forms. Then the published models of deposition equilibrium are briefly presented. Based on minimization of the Gibbs energy of the considered C-H-O systems,
it was possible to compute equilibrium phase concentrations and detect the depositing carbon form. Series of such
simulations for varied temperature and pressure allowed to
construct ternary C-H-O plots showing boundaries of both
graphitic and filamentous carbon deposition zones.
2 Carbon deposits
Three major types of industrial reforming of hydrocarbon/alcohol fuels can be distinguished. Those are steam
reforming (SR), catalytic partial oxidation (CPOX), and
dry reforming (DR). While SR and DR are endothermic
and CPOX is exothermic, a combination of SR and CPOX is
named oxidative SR and its specific energy-neutral version
is called autothermal reforming (Diaz Alvarado and Gracia
2012). Depending on the process conditions, all those
reforming processes can result in formation of carbonic
solid. Thermal decomposition of hydrocarbons and alcohols proceeds along complex paths, and the mechanism
details are still searched for (Alberton et al. 2007, Dufour
et al. 2009, Wang et al. 2009). Most of the studies of carbon
deposition indicate formation of elemental carbon in the
reforming reactions as the main source of carbon deposition, however, without supplying a validated mechanism.
Two models were considered for pyrolytic carbon (Zheng
et al. 2013): a deposition droplet model proposed by Shi
et al. (1997) and the combined mechanism of nucleation
on graphene and of carbon growth at the edge of graphene (Hu and Hüttinger 2002). Several carbon containing intermediate species were detected during methane
decomposition at catalyst surfaces, and associated mechanisms of filamentous deposit growth were proposed (de
Bokx et al. 1985, Snoeck et al. 1997a, Wagg et al. 2005).
A range of carbonaceous deposit types, both amorphous and crystalline, was found in broad studies of carbon
deposition. The deposits widely differ in morphology and
reactivity (Bartholomew 2001, Wagg et al. 2005, Diaz Alvarado and Gracia 2012). Carbon deposition can result in che­
mical reactions over a catalyst surface, where several forms
including atomic carbon can appear (Kee et al. 2005), or in
gas phase due to free-radical reactions ultimately forming
polyaromatic compounds (Sheng and Dean 2004). McCarty
and Wise (1997) observed four main types of carbon on a
nickel catalyst. Other early classifications (Rostrup-Nielsen
1979, 1984) proposed three types of solid carbon formed at
reforming of fuels: (i) encapsulating film, (ii) whisker-like
(filamentous), and (iii) pyrolytic carbon. Those carbon
forms were also observed by Sehested (2006). The encapsulating tar-like carbon film (i), according to Rostrup-Nielsen
(1979, 1984), is formed by slow polymerization of higher
hydrocarbon radicals at temperatures below 773 K. According to Sehested (2006), the encapsulating carbon (gum)
deposits consist of a thin film of hydrocarbon or a few layers
of graphite. Formation of the filamentous, graphitic type in
the form of tubular filaments (whiskers, fibers ii) prevails
in the temperature range from 720 K up to 870 K (RostrupNielsen, 1979, 1984), whereas at the latter temperature, the
formation of pyrolytic carbon (soot, iii) begins to predominate as result of thermal cracking of hydrocarbons. The
mechanism of pyrolytic carbon deposition in the range of
1073–1273 K was studied by Zheng et al. (2013). Alstrup et al.
(1998) found that carbon filaments are formed on nickel
catalysts when hydrogen is present in the gas phase while
encapsulating carbon dominated in pure CO reactions.
Filamentous carbon deposits were detected more
than 120 years ago by Hughes and Chambers (1889) during
their search for carbon filaments for electric lighting. The
finding was confirmed by Davis et al. (1953) by means of
electron micrography. Sehested (2006) underlines the
detrimental role of whisker carbon for catalysts and links
development of pyrolytic carbon with the appearance of
higher hydrocarbons at elevated temperature. Generally
similar results were reported by Alberton et al. (2007) and
He and Hill (2007) indicating the importance of catalyst
type and the highly destructive role of carbon dissolved
within the catalyst structure above 873 K. During catalytic and thermal cracking of ethanol in the temperature
range from 523 K to 1123 K, Jankhah et al. (2008) found
that carbon deposits can be formed as filaments, both
rectilinear and helicoidal. Essentially, carbon nanotubes
(CNTs) are layers of coaxially assembled graphene planes,
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Z. Jaworski et al.: Carbon deposition: updating for nanotubes 219
and their continuous catalytic production was reviewed
by Ying et al. (2011). A variety of CNTs can exist ranging
from single-walled to multi-walled tubes with Young’s
modulus over 1 TPa and tensile strength about 150 GPa
(Paradise and Goswami 2007). According to a thermodynamic analysis carried out by Gozzi et al. (2007), the transformation of solid carbon from graphite to multi-walled
carbon nanotubes (MWCNTs) becomes spontaneous at
the temperature, T, of 704 ± 13 K. The authors also found
that thermal decomposition of methane to form MWCNTs
is thermodynamically favored at T > 809 K. In a following paper (Gozzi et al. 2008), they concluded that carbon
nucleation from gas phase usually results in a mixture of
various nanotubes and also amorphous or/and graphitic
forms. Proportions of those carbon forms depend mainly
on temperature and the catalyst type and its granularity.
Similar conclusions about coexistence of different forms
of solid carbon were drawn by Snoeck and Froment (2002)
and Makama et al. (2014). Thermodynamic data for singlewalled CNTs in bundles were also obtained using an indirect solid galvanic cell method (Gozzi et al. 2009).
A specific two-dimensional form of solid carbon,
called graphene, can also be formed on metal surfaces,
e.g. Ni (Arkatova 2010) and Cu. The properties of graphene
were extensively described by Soldano et al. (2010). Three
methods of graphene preparation were employed: (i) segregation of carbon from the bulk of the metal, (ii) chemical vapor deposition of hydrocarbons, and (iii) carbon
vapor deposition (Xu et al. 2013). Despite intensive investigations, many fundamental aspects of the graphene
nucleation are still not fully understood (Mehdipour and
Ostrikov 2012, Zhang et al. 2012, Kim et al. 2013).
A purely chemical kinetic analysis of pyrocarbon
deposition was performed by the team led by Hüttinger
(Becker and Hüttinger 1998a,b,c,d, Hu and Hüttinger
2002). Kazakov et al. (1995) proposed a model for soot
formation in laminar flames, and Appel et al. (2000) presented a new kinetic model of soot formation in flames.
The kinetics of nucleation and growth of soot particles in
turbulent combustion flames was also numerically analyzed (Zucca et al. 2006, Chernov et al. 2012). A kinetic
expression for the coke formation rate on a nickel catalyst was derived by Ginsburg et al. (2005) and Asai et al.
(2008), and evidence of a prior formation of unstable
carbides was presented by Kock et al. (1985). Based on an
elementary kinetic description presented by Bessler et al.
(2007) for SOFCs, a modeling study for predicting carbon
deposition from reformates was also carried out (Yurkiv
et al. 2013). A review and a thorough discussion of the
present knowledge of the factors controlling coke formation in SOFCs were presented by Wang et al. (2013).
It can be summarized that carbon deposition rate
strongly depends on temperature, gas phase composition,
presence of catalysts, and the type of applied catalyst (Rostrup-Nielsen 1972, de Bokx et al. 1985, Kee et al. 2005, Mallon
and Kendall 2005, Ke et al. 2006, Kim et al. 2006, Chen et al.
2011, Yurkiv et al. 2013). Several authors (­Rostrup-Nielsen
1972, 1984, Jankhah et al. 2008, Cimenti and Hill 2009,
Essmann et al. 2014) highlighted that both the thermodynamic equilibrium conditions and the kinetic rate of all
reactions and phase transitions should be considered in
predictions of carbon deposits. However, Rostrup-Nielsen
and Christiansen (2011) showed that the equilibrium constants for methane decomposition decisively depend on the
metal catalyst type and stated that “[t]he important question is whether or not carbon is formed and not the rate at
which it may be formed.” Therefore, the following chapters
are focused on the analysis of current literature information for temperature-pressure conditions for stable phases,
which were first presented in the form of a gas-liquid-solid
diagram for pure carbon and then in ternary diagrams for
C-H-O reformates in thermodynamic equilibrium.
3 Carbon phase diagram
Carbon is the lightest element of Group IV and can form
allotropes of three different covalent bond formations in
condensed phases: sp3 hybridization (diamond, liquid),
sp2 (graphite, nanotubes, graphene, fullerenes, liquid),
and metastable sp (carbynes) (Ghiringhelli et al. 2008).
Thermal functions for gaseous carbon species C1 to C7 were
published (Lee and Sanborn 1973) over 40 years ago.
The overall graphical form of equilibrium phases is
usually presented as a pressure vs. temperature, P-T, phase
diagram indicating areas of existence of thermodynamically stable forms. Two main points are characteristic for
such diagrams: the triple phase point for the coexistence
of solid, liquid, and gas phases and the critical liquid-gas
point. The two points for carbon appear at high temperatures, above 4000 K. Therefore, experimental investigations of the carbon equilibrium conditions required
applications of special techniques. The published papers
refer to either gas-solid (graphite) equilibrium (Marshall
and Norton 1950, Clarke and Fox 1969, Lee and Sanborn
1973, Leider et al. 1973, Baker 1982, Lee and Choi 1998,
Havstad and Ferencz 2002, Joseph et al. 2002, Miller et al.
2008) or equilibrium for liquid-graphite-diamond (Fried
and Howard 2000, Ghiringhelli et al. 2005, Savvatimskiy
2005, Wang et al. 2005, Ghiringhelli et al. 2008, Yang and
Li 2008, Umantsev and Akkerman 2010). The liquid-gas
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220 Z. Jaworski et al.: Carbon deposition: updating for nanotubes
phase boundary was given little attention with the exception of Bundy et al. (1996). However, research papers
on carbon equilibria were mostly devoted to theoretical
studies rather than to the experimental ones.
3.1 C
arbon solid – liquid and liquid – gas
equilibria
van Thiel and Ree (1989) proposed a phase diagram
of graphite-diamond-liquid for bulk carbon. The P-T
diagram was enhanced for bulk carbon by Bundy et al.
(1996) up to T = 6000 K and extended for diamond
melting by Wang et al. (2005) above 8000 K and also
refined to account for carbon crystal size by ­Savvatimskiy
(2005), who presented experimental thermodynamic
data for the graphite melting points. The diagram was
further adjusted for carbon nanocrystals of graphite and
diamond by Yang and Li (2008). However, the entire
phase diagram should cover the regions of thermodynamically stable three phases: (i) solid phases of graphite
(G), diamond (D), and CNTs; (ii) gas phase (vapors, V);
and (iii) a single liquid carbon (L) zone since Ghiringhelli
et al. (2008) rejected existence of two phases of liquid
carbon, as suggested elsewhere. The border line between
the G and V areas ends at the triple point G-L-V, which was
assumed according to Leider et al. (1973) for TGLV = 4100 K
and PGLV = 1.12 bar. It should also be mentioned that the
NIST-JANAF tables (Chase 1998) suggest that TGLV = 4765 K
and PGLV = 26.95 bar, and the same temperature value is
suggested for 1 bar by the CRC Handbook (Lide 2005).
Ghiringhelli et al. (2005) established the location of the
second triple point for graphite-diamond-liquid carbon at
TGDL = 4250 K and PGDL = 164,000 bar. It was also found that
the P-T coordinates of the triple point, TGDL, shift to lower
P and T with decreasing carbon nanocrystal size (Yang
and Li 2008).
According to Togaya (1997), the line between the
two triple points, GLV-GDL, has a maximum at the temperature of 4790 K and P = 5.6 GPa. The coordinates of
the critical point, CR, where differences between the
carbon liquid and gas phases vanish was adopted based
on Leider et al.’s (1973) approximation at TCR = 6810 K and
PCR = 2300 bar. The line dividing the gas (V) and liquid (L)
carbon phases was assumed linear between CR and GLV,
and the line between the diamond (D) and liquid (L) areas
was based on Savvatimskiy (2005) and Wang et al. (2005)
phase diagrams. The complete carbon phase diagram
shown in Figure 1 was based on Bundy et al.’s (1996) proposal; however, it was widened to include important gas
range and upgraded using a wide collection of literature
Figure 1: Phase diagram for carbon. D, diamond; G, graphite; CNT,
carbon nanotubes; L, carbon liquid; V, carbon vapors; TGLV, solidliquid-gas triple point; TGDL, graphite-diamond-liquid triple point;
CR, critical point.
data described in the next section. In order to better show
details of the carbon diagram, the axis of equilibrium
carbon pressure, PC∗ , in Figure 1 is presented in the logarithmic scale.
An important issue results from the considerations in
section 3.1 that no stable liquid carbon phase is expected
within the temperature range of T < 3000 K. It follows
from the graph that the lines between G-D and D-L and
L-V areas are of little importance to the deposition equilibrium and only the (de)sublimation lines between carbon
vapors V and either solid graphite G or nanotubes CNT
play significant role.
3.2 Carbon solid – gas equilibria
The graphite-vapor equilibrium was empirically studied
by measuring evaporation rates at temperatures above
2000 K (Marshall and Norton 1950, Lee and Sanborn
1973, Joseph et al. 2002). Carbon vapors were assumed to
contain several polyatomic species (Clarke and Fox 1969,
Leider et al. 1973) ranging from C1 to C7; however, C6 was
later ruled out by Joseph et al. (2002). Careful selection,
tuning, and generalization of available experimental data
for carbon led to establishing approved thermochemical
tables, such as NIST-JANAF data (Chase 1998). Therefore,
the equilibrium line for carbon sublimation that divides
the area of carbonic vapors (V) and graphitic solid (G) in
Figure 1 was based on the NIST-JANAF data presented in
details in the next section.
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Typical temperature of reformate gases ranges from
ambient up to 1500 K; therefore, this range is adopted in
the thermodynamic analysis for carbon solid depositions
of this present study. Thus the following thermodynamic
analysis for reformates refers to relevant gas-solid equilibria in that range, first for graphite and then for other
carbon deposits.
3.2.1 Carbon vapors over graphite
Required conditions for carbon deposition usually refer
to the state of thermodynamic equilibrium of the species
containing carbon in the solid and gas phases. It is therefore essential to apply proper tools of modeling of the
equilibrium for C-H-O species and use current data of
thermodynamic properties of different forms of elemental
carbon both in the gas and solid phases.
The standard thermodynamic approach that assumes
equilibrium of a closed system is generally (e.g. Smith
et al. 2005) characterized by two conditions: a minimum
of the total Gibbs energy at constant temperature and
pressure, G, of the considered system, which consists of a
set of nj moles of species “j”:
G(T , P ,{n j }) = minimum or dG(T , P ,{n j }) = 0 (1)
and also by equality of the partial molar Gibbs energy, μj,
i.e. chemical potential of each species in all phases (Smith
et al. 2005), either gas (g), liquid (l), or solid (s).
µ j (s) = µ j (l) = µ j (g) (2)
For a physical phase transfer or a chemical reaction
between species Aj linked by the stoichiometric e­ quation
∑ νA
j
j
j
= 0 and in the state of their thermodynamic
e­ quilibrium, denoted by “*”, the species system undergoing phase transfer or/and reaction obeys Equation (3).
∑ν µ
j
j
∗
j
= 0. (3)
The chemical potential of a pure species in any phase is
usually presented as a sum of its standard-state value,
µ0j (T ), and the contribution resulting from a ratio of the
species activities in a current state, aj, and in the reference
state, normally the standard state, a0j .
µ j = µ0j + RT ln
aj
a0j
(4)
Equation (4) is valid both for pure species and for species
in a single-phase mixture. The aj activity depends on the
actual temperature, T; pressure, P; and composition of the
considered phase. As accepted by convention (e.g. Atkins
1998), the standard activity of any pure element in its
condensed state is equal to the unit for its stable form in
the standard conditions (pure species under P0 = 0.1 MPa)
using various definitions and units of the activity. In a
similar way, the actual activity can be expressed by means
of various measures of species concentration, such as
pressure, molar ratio, etc. The species activity, aj, for gas
phases is usually termed “fugacity”, fj, and is defined as
a product of the non-dimensional fugacity coefficient, φj,
and a species pressure, Pj:
a j = f j = φ j Pj (5)
In that case, the standard activity of a species, a0j , is also
related to the standard pressure, P0. On the other hand,
for gas species under pressures greatly lower than its
critical pressure and for temperature very much higher
than the species critical temperature, both the species
compressibility factor and fugacity coefficient are close
to 1 (Atkins 1998). Therefore, for the saturated carbon
vapor pressures, PC∗ , below 10−19 bar and the analyzed
temperatures up to 1500 K (cf. Figure 1), one can safely
assume a0 [Ci(g)] = P0 and also a[Ci(g)] = P[Ci(g)]. In addition, the solid-state activities of graphite as the stable
form of solid carbon, both the standard, a0[Cg(s)], and
actual, a[Cg(s)], ones are also very close to 1 at total pressure close to P0.
However, one should distinguish between various
allotropic forms of carbon, appearing both in the gaseous,
Ci(g), and solid, Ck(s), states. Most published gaseous
forms of carbon arising from reformates are Ci(g) for i = 1
up to 8. Solid carbon, Ck(s), can be limited here to four
basic classes: graphitic, k = g, two filamentous k = f, and
amorphous k = a. When necessary, two filamentous forms
will be distinguished, the multi-wall, k = MW, and singlewall, k = SW.
Applying Equations (3–5) and the conventions for
carbon in the gas (j = Ci(g)) or solid (j = Ck(s)) phases in the
state of thermodynamic equilibrium (*), we get:
µ0 [Ci ( g )] + RT ln
a∗[Ci ( g )]
a0 [Ci ( g )]
= µ0 [Ck ( s)],
(6)
and as in the considered cases of carbon deposition below
1500 K, φCi ≅ 1, one can express the equilibrium (saturation) pressure over the graphitic carbon solid phase,
shown by the “/Cg(s)” index as
  µ0 [C ( g )] − µ0 [C ( s)]  
i
g
P ∗[Ci ( g ) / C g ( s)] = P 0 [Ci ( g )]exp − 
.
RT

 

(7)
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222 Z. Jaworski et al.: Carbon deposition: updating for nanotubes
That form is convenient for analyzing the relationship
P*[Ci(g)] using the standard values of the chemical potential for various gaseous carbon molecules, Ci(g), available
either directly or indirectly in the subject literature (Yaws
1995, 2012, Chase 1998, Scientific Group 1999, Lide 2005)
and also in the open source Cantera (Goodwin 2009) or
the commercial software HSC (HSC Chemistry 2014). The
chemical potential of formation of gas carbon molecules
from graphite is equal to the numerator, μ0[Ci(g)] – μ0[Cg(s)]
of Equation (7). Due to the convention used in physical
chemistry, it is often assumed μ0[Cg(s)] = 0 for the basic
solid form of atomic species such as graphite in the reference standard conditions. However, this must be coherent
with parallel assumptions for the standard partial molar
enthalpy, H 0j , and partial molar entropy, S 0j , to comply
with the general relationship G0 = H0 – TS0. One should
also remember that a direct deposition process of carbon
vapors is only possible when the local pressure of carbon
vapors, P[Ci(g)], exceeds the corresponding equilibrium
(saturation) counterpart, P*[Ci(g)], resulting from Equation (7).
The temperature influence on the equilibrium pressure of gaseous carbon allotropes, C1 to C8, over solid
graphite is depicted in Figure 2, as computed with the HSC
software (HSC Chemistry 2014). It shows that the first molecule, C1, exhibits principal contribution to the total equilibrium pressure of gaseous carbon and the contribution
of C4 to C8 molecules can be safely neglected.
The total pressure of carbon vapors over graphite
(/Cg(s)),
8
P ∗[Ctot ( g ) / C g ( s)] = ∑ i=1 P ∗[Ci ( g ) / C g ( s)] (8)
at varied temperature, T, was also computed from two
other literature sources: correlation of Miller et al. (2008),
which is compatible with table data of Chase (1998).
The Miller et al. (2008) correlation for such equilibrium pressures, P* in Pa, against temperature, T in K,
recalculated in SI units can be presented as
 85900 
P ∗[Ctot ( g ) / C g ( s)] = 1.47·1013 exp  −
.

T 
(9)
The dependence is graphically shown for comparison in
Figure 2 as the thin solid line. The relationship of Equation (9) is especially useful for a quick comparison with
the equilibrium pressure of gaseous carbon resulting
from selected reactions of C-H-O reformates. It was also
concluded that the three sources (Chase 1998, Miller
et al. 2008, HSC Chemistry 2014) deliver very similar
parameters of equilibrium conditions for carbon gases
over solid graphite. In addition, a similarly good agreement in the individual equilibrium pressures for C1 up to
C5 over graphite was found when data from Chase (1998)
and (HSC Chemistry 2014) were compared (not shown
here).
Two additional P vs. T lines for CNTs, SWCNT, and
MWCNT are also shown in the figure, and their experimental origin is presented in the next section. The equilibrium
carbon vapor pressures over the nanotubes are not largely
different from the total pressure over graphite within
the investigated temperature ranges, as can be seen in
Figure 2.
In summary, it may be stated that gaseous carbonic
species accompany any solid carbon, although at very low
partial pressures. In addition, surpassing the carbon equilibrium pressures described in Equation (7) creates conditions of supersaturation of carbon vapors and tendency to
solid carbon depositions.
3.2.2 Equilibrium conditions for non-graphitic deposits
Figure 2: Equilibrium partial pressures of gaseous carbon molecules over graphite and nanotubes; MWCNT (Equation 16) and
SWCNT (Equation 17).
As early as 1905, Schenck and Heller (1905a,b) found that
the equilibrium of the Boudouard reaction was influenced
by the catalysts used and the obtained reactant compositions differed from those without presence of a catalyst. A
similar conclusion was drawn by Pring and Fairlie (1912)
in respect to the equilibrium of methane pyrolysis. The
discrepancies were later ascribed to formation of solid
filamentous carbon (Cf(s)), which has the standard chemical potential, μ0[Cf(s)] different from that of graphite. The
values of μ0[Cf(s)] were first estimated by Rostrup-Nielsen
(1972) and de Bokx et al. (1985) resulting in their equality
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Z. Jaworski et al.: Carbon deposition: updating for nanotubes 223
to that for graphite, μ0[Cf(s)] = μ0[Cg(s)], roughly at 950 K
for the selected size of catalyst grains.
Three methods of estimation of the standard chemical
potential were published for solid carbon deposits, (Ck(s)),
other than graphite (Cg(s)). The most accurate type was
based on measuring the standard electromotive force, E0,
of high temperature, solid-state galvanic cells (Jacob and
Seetharaman 1995, Gozzi et al. 2007, 2009) with singlecrystal CaF2 as a solid electrolyte. The virtual, resultant
cell reactions between graphite and purified solid forms of
filamentous or amorphous carbon were Cg(s) = Ck(s). Then
the standard chemical potential change of the “i” reaction
between solid carbon species, Δi μ0[C(s)] was calculated as
a temperature function from the measured standard electromotive force, Ei0 (T ), using Equation (10):
∆i µ0 [C ( s)](T ) = −nFEi0 (T ), (10)
where n is the number of electrons transferred per carbon
atom in the cells and F denotes the Faraday constant. The
investigated chemical potential of the non-graphitic solid
carbon, μ0[Ck(s)], can be then derived from
µ0 [Ck ( s)](T ) = µ0 [C g ( s)](T ) + ∆i µ0 [Ck ( s)](T ). (11)
However, the reference value of μ0[Cg(s)] in Equation (11)
was dependent on the convention used.
Another method of determination of the chemical
potential value for single-walled CNTs, μ0[Cf(s)], is based
on precise oxidation calorimetry (Levchenko et al. 2011)
with entropy changes calculated using heat capacities of
graphite and single-walled CNT.
Yet most published estimates of μ0[Ck(s)] relied on
measuring gas reactant partial pressures at equilibrium
conditions, p∗j , and they were determined either at the
beginning of coking (Bernardo et al. 1985) or more typically at the coking threshold obtained for both growing
and decreasing pressures. Carbon depositions accompanying the Boudouard reaction (21) and methane pyrolysis
(23) were investigated and reported in a wide temperature
range, in most cases, with dispersed nickel as a catalyst.
Usually, the relevant equilibrium quotients (constants),
Kp,i, used in the subject literature, like those cited in Equations (22), (24), and (26), respectively, for reactions (21),
(23), and (25), were originally calculated as follows:
K p ,21 =
K p ,23 =
∗
pCO
2
∗2
pCO
pH∗2
2
∗
pCH
4
(12)
(13)
K p ,25 =
pH∗ O
(14)
2
∗
pH∗ pCO
2
A number of experimental data for such Kp,i quotients are
available in the subject literature (Bromley and Strickland-Constable 1960, Rostrup-Nielsen 1972, Bernardo
et al. 1985, de Bokx et al. 1985, Tavares et al. 1994, Rostrup-Nielsen et al. 1997, Snoeck et al. 1997a,b, Snoeck and
Froment 2002). Formally, each of the partial pressures in
Equations (12) to (14) should be divided by the reference
pressure, P0 = 1 bar. Therefore, those published quotient
values depend on the pressure units used, and this must
be accounted for when calculating the chemical potential
deviation by means of Equation (15) or more general Equation (19). The “i” subscript denotes a considered transformation reaction between different allotropic forms of
solid carbon, Cg(s) and Ck(s).
RT ln
K p ,i [C g ( s)]
K p ,i [Ck ( s)]
= ∆i µ0 [Ck ( s)]
(15)
That energy difference can be used to determine the
standard chemical potential for deposited non-graphitic
carbon, μ0[Ck(s)], from Equation (11), applying literature
thermodynamic data for graphite, μ0[Cg(s)]. Such method
was already used in 1960 by Bromley and StricklandConstable (1960) and also by the Rostrup-Nielsen group
(­Rostrup-Nielsen 1984, Bernardo et al. 1985). In principle,
it should be possible to derive temperature dependences
of μ0[Cf(s)](T) for filamentous deposits (Ck = Cf ) based on
the equations for threshold constants cited by Snoeck and
co-authors (Snoeck et al. 1997a,b, Snoeck and Froment
2002) for methane cracking and wet reforming of methane.
However, those constants resulted in different standard
enthalpy and entropy values for varied methane partial
pressures (Snoeck et al. 1997a) and also the computed
μ0[Cf(s)] values significantly differed from those published earlier. In addition, one has to conclude that majority of the papers quoting quantitative data for Δi μ0[Ck(s)]
did not clarify how the μ0[Cg(s)] values for graphite were
calculated for determining Kp,i[Cg(s)]. Nevertheless, it is
informative to compare the published temperature functions of the chemical potential deviation, Δi μ0[Ck(s)]=f(T),
and a collection of such plots of black (for CNT) and grey
solid lines is graphically presented in Figure 3 along with
information on data sources. The dotted reference line of
Δi μ0[Cg(s)]=0, for graphite is also shown in Figure 3.
Preferred depositing conditions for filamentous
carbon rather than graphite are those where Δi μ0[Ck(s)] < 0,
and most of the lines in Figure 3 go below the chemical
potential level for graphite (dotted line) at the temperature
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cannot be regarded as a sufficient proof of the deposit
purity. Consequently, it was accepted in this study that
thermodynamic data only for pure forms of filamentous
carbon or graphite should be used in predicting equilibrium conditions of their deposition. Therefore, reliable
experimental data for the purified multi-wall (Gozzi et al.
2007) and bundled single-walled (Gozzi et al. 2009) CNTs,
shown in Figure 3 as black solid lines, are applied with
thermodynamic fundamentals in the following sections
to derive conditions of carbon deposition for various
reformate compositions. Relevant relationships reported
for purified CNTs were published by Gozzi et al. (2007)
for Ck(s) = MWCNT in temperature ranging from 820 K to
920 K:
Figure 3: Plots of literature Gibbs energy differences between
graphite and other solid carbon forms. [1] Snoeck and Froment
(2002); [2] Gozzi et al. (2007); [3] Jacob and Seetharaman (1994);
[4] Rostrup-Nielsen (1972); [5] Gozzi et al. (2009); [6] Bromley and
Strickland-Constable (1960); [7] Bernardo et al. (1985); [8] Lee et al.
(2013).
∆i µ0 [ MWCNT ](T ) = (8250 ± 90) − (11.72 ± 0.9)T [J / mol]
for T [K ]
(16)
and by Gozzi et al. (2009) for bundled SWCNT in the temperature range from 750 K to 1015 K in a polynomial form:
9
0
n
∆i µ [ SWCNT ](T ) = −3 F ∑ n=0 anT [J / mol] for T [K ] (17)
ranging from 430°C to 680°C. It can also be concluded
from Figure 3 that a relatively wide scatter exists between
the direct or calculated data for ∆i µC0 ( s ) , which were published by different authors, and it may be useful to identify
possible sources of such discrepancies. For instance, even
from data in a single paper (Snoeck and Froment 2002),
five different Δi μ0[Ck(s)] values can be derived (1a to 1e in
Figure 3). In the authors’ opinions, two key reasons for the
presented scatter can be indicated: (i) lack of crystallographic purity of the investigated carbon deposits and (ii)
use of different values for the standard chemical potential of graphite, which led to differences in the Kp,i[Cg(s)]
equilibrium quotients. The latter may have stemmed from
different selections of the standard and reference states
used in the published papers. For instance, the standard
entropy value for graphite at 298.15 K is assumed either
about 5.7 J mol−1 K−1, e.g. in Rostrup-Nielsen and Bak
Hansen (1993), Lide (2005), and HSC Chemistry (2014), or
0.0 J mol−1 K−1, e.g. in Chase (1998) and Yaws (1995, 2012).
Moreover, some authors apparently assumed μ0[Cg(s)]=0,
independent of temperature for the graphitic solid carbon,
which is in clear disagreement with the dependence of
both standard enthalpy and entropy on temperature for
every species.
Based on the evidence delivered by Gozzi et al. (2007),
one may expect that usually more than one crystallographic form of solid carbon appears in carbon deposits.
The photographic SEM evidence of presence of filamentous carbon, which was often shown in relevant papers,
where F denotes the Faraday constant.
Latini et al. (2014) reported in 2014 that there were no
articles other than the two by Gozzi et al. (2007, 2009) that
dealt with thermodynamic measurements at high temperature on carbon nanostructures. In the study of Wagg
et al. (2005), an upper bound of the chemical potential of
SWCNT growth threshold was estimated for T > 700°C as
{
}
max ∆i µ∗[ SWCNT ](T ) = 80960 − 116T [J/mol]
for T [°C ],
(18)
which indeed results in significantly higher values than
those calculated from Equation (17).
The necessity and importance of purifying the investigated samples of solid carbon deposits were clearly
explained by Gozzi et al. (2009). Moreover, the authors in a
further study obtained significant differences in the standard enthalpy and entropy even for separated and singlewall-in-bundle carbon nanofibers. A similar rationale can
possibly explain substantial differences in Δiμ0[Ck(s)]=f(T)
for amorphous carbon samples (Jacob and Seetharaman
1994, Terry and Yu 1995). It should also be mentioned that
in another study (Lee et al. 2013), the standard partial
molar enthalpy and entropy of the CNT formation were
estimated as ΔfH0 = 54.46 kJ mol−1 and ΔfS0 = 68.9 J mol−1 K−1
based on literature data of de Bokx et al. (1985) and the
NASA data (McBride et al. 2002) for graphite. The values
were then used to derive C-H-O concentration boundaries
for depositing CNT at varied temperature and resulted in
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the deposition boundary lines in a ternary diagram largely
different (Lee et al. 2013) from the corresponding one
shown in Figure 4B.
Perhaps Diaz Alvarado and Gracia (2012) were the only
authors who concurrently considered published equilibria of various solid carbon forms: graphite, MWCNT, amorphous, and polymeric for glycerol reforming systems. The
authors used data for multi-walled nanotubes based on
Gozzi et al. (2007) and found existence of two regions:
the most favorable carbonaceous solid type was graphite
below 450°C, whereas CNTs were preferred to form above
that threshold temperature. However, the deposition
threshold temperatures determined in this study, shown
by the vertical broken lines in Figure 3, were 431°C for the
graphite-to-MWCNT change (as in Gozzi et al. 2007) and
about 590°C for the MWCNT-to-SWCNT transformation. In
conclusion, it should be stressed that carbon vapors are
always expected in equilibrium over solid graphite or CNT,
however, with a very small partial pressure.
4 P
ublished models of deposition
equilibrium
Several proposals for quantitative description of equilibrium conditions for carbon deposition from gaseous
reformates have already been published, and an early
communication in 1972 was delivered by Rostrup-Nielsen
(1972). In the paper, formation of whisker carbon was evidenced, and the equilibrium constants for actual reaction with carbon deposition, Kp,observed, were compared
to the theoretical equilibrium constant computed for
graphite, Kp,graphite. Higher CH4 or CO concentrations were
detected (Rostrup-Nielsen 1979) before carbon formation
on catalysts than for non-catalyzed graphite deposition,
which implies smaller constants, Kp,observed, than those for
graphite, Kp,graphite, at a given temperature (Rostrup-Nielsen
1984). The excess chemical potential, Δμ[Ck(s)], of the
deposited carbon compared to that based on graphite was
estimated (Rostrup-Nielsen 1972) on the basis of the two
constants, Equation (19).
∆µ[Ck ( s)] = ∆µ0actual − ∆µ0graphite = RT ln
K p ,graphite
K p ,observed
(19)
That approach was further developed by the introduction of the so-called principle of equilibrated gas
(­
Rostrup-Nielsen 1984), which states “[c]arbon formation is to be expected if the gas shows affinity for carbon
after the establishment of the methane reforming and
the shift equilibria.” In that case, Kp,observed > Kp,equilibrium and
Δμ[Ck(s)] < 0, and it is true except for noble metals as catalysts (Rostrup-Nielsen and Christiansen 2011). The steadystate activity of solid carbon, a[Ck(s)], was also defined
based on a kinetic analysis (Rostrup-Nielsen 1984). The
principle of actual gas was presented by Rostrup-Nielsen
and Christiansen (2011) and has been often used to assess
the risk of carbon formation in a non-equilibrium, steadystate process. In that case, the quotient, Kp,observed, should
be calculated for actual, non-equilibrium concentrations.
In an early study, de Bokx et al. (1985) concluded
that the deposited filamentous carbon in the presence of
catalysts is a metastable carbide intermediate of a higher
chemical potential than that of graphite but is not decomposed to graphite due to a high activation barrier for the
homogeneous nucleation of graphite, which causes a very
low rate of the nucleation. It also implies that almost filament-free operation is possible for more carbon bearing
gases than it results from graphite equilibria.
A thermodynamic analysis of carbon deposition
accompanying methane SR (Xu and Froment 1989) was
carried out using a ratio, Vi, of the pressure quotient of the
actual partial pressures of species “j”, pj, to the quotient
for equilibrium conditions of the “i” reaction, the latter
being the equilibrium constant, Kp,i, for that reaction.
(∏ p )
V=
νj
j
i
j
K p ,i
(20)
i
That approach was also applied by Hou and Hughes (2001)
for methane reforming. Magnitude of the ratio indicates
whether a reaction goes to the right (Vi < 1) or to the left
(Vi > 1) or remains at equilibrium (Vi = 1). A related presentation of the conditions of carbon deposition was used
in an analysis for catalyzed reforming of methane (Ginsburg et al. 2005), in a SOFC fueled by sewage biogas (van
Herle et al. 2004), and also when the fuel cell was fed with
methane (Klein et al. 2007).
One of the similar approaches (Tsiakaras and Demin
2001) was based on consideration of the Boudouard reaction of carbon disproportionation, Equation (21).
2CO = CO2 + C (21)
The relevant equilibrium constant of Equation (21), Kp,21,
for species pressures, pi, was used (Tsiakaras and Demin
2001) to define the carbon activity, a[Ck(s)],21, which is a
reciprocal of Vi.
a[Ck ( s)],21 =
2
K p ,21 pCO
pCO
2
(22)
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It was commonly assumed that the carbon activity
equals 1 at the thermodynamic equilibrium, and solid
carbon formation is possible only when a[Ck(s)],21 > 1
(­Assabumrungrat et al. 2004, Tsiakaras and Demin 2001).
That analysis was also extended by considering carbon
activities resulting from other reactions (Assabumrungrat
et al. 2005, Sangtongkitcharoen et al. 2005, Assabumrungrat et al. 2006): methane pyrolysis (23) and reverse gasification (25)
CH4 = 2H2 + C (23)
a[Ck ( s)],23 =
pH2
(24)
4
2
CO + H2 = H2O + C (25)
a[Ck ( s)],25 =
K p ,23 pCH
K p ,25 pCO pH
pH O
2
(26)
2
In seven further studies (Sangtongkitcharoen et al. 2005,
Klein et al. 2007, Nikooyeh et al. 2008, da Silva et al. 2009,
Vakouftsi et al. 2011, Nematollahi et al. 2012, Trabold
et al. 2012), the same or slightly transformed definitions,
as those in Equations (22), (24), and (26), were applied
to determine values of the solid carbon activity, a[Ck(s)].
The calculations were based on minimization of the Gibbs
energy using either commercial software or thermodynamic data from literature.
Other types of carbon deposition analyses were
based on the C-H-O diagrams, and they were relatively
often quoted in the subject literature. Bartholomew
(1982) was perhaps the first to publish equilibrium isotherms at 450°C and 1.4 atm both for graphite and amorphous carbon plotted in a C-H-O ternary diagram. The
isotherm lines were based on literature experimental
data and clearly showed the deposition region for amorphous carbon was smaller than that for graphite, i.e. its
boundary was shifted towards higher C content of C-H-O
mixtures. Eguchi et al. (2002) possibly pioneered systematic application of that approach supported by commercial software for computing the equilibrium phase
contents with assumed temperature, pressure, and input
moles. The boundaries were also presented in a ternary
C-H-O diagram. A comprehensive study by Sasaki and
Teraoka (2003b) led to detail boundaries of graphitic
carbon deposition for equilibrium temperature ranging
from 100°C to 1000°C. Essentially the same approach
was reported in several other papers (Koh et al. 2001,
2002, Sasaki and Teraoka 2003a, Sasaki et al. 2004, Kee
et al. 2008, Aravind et al. 2009, Chen et al. 2011, Lee et al.
2013, Liu et al. 2013) using various software codes. Determination of the carbon deposition boundary was based
on assumption of a very small but non-zero amount of
solid carbon in equilibrium (Koh et al. 2002) or a fraction
of 10−6 of the total carbon amount (Sasaki and Teraoka
2003a). A similar criterion of the minimum carbon fraction, xC,min, for carbon deposition to occur was proposed
by Heddrich et al. (2013) as xC,min=10−4, which resulted
from the thermodynamic equilibrium concentrations
computed by minimizing the Gibbs energy of reacting
systems.
In another study, Jankhah et al. (2008) performed a
thermodynamic analysis for DR of ethanol and also for
its thermal cracking based on a commercial software that
uses the Gibbs energy criterion, Equation (1). Minimum
temperatures for thermodynamic exclusion of carbon
formation at various oxidant/ethanol ratios were determined. Later on, Wang and Cao (2010) assumed, in their
analysis of the conditions for solid carbon formation,
that the partial molar Gibbs energies both of gas carbon
and solid carbon, μ[C(g,s)], have zero value independent of temperature. This assumption may have caused
significant impact on the authors’ assessment of critical
temperatures above which coke is not formed. A two-case
limit model for the driving force of graphene deposition
from hydrocarbons was proposed by Lewis et al. (2013) for
a hot wall reactor. Case 1 corresponded to thermodynamic
equilibrium of chemical reactions of hydrocarbons in the
gas phase, and a separate Case 2 considered the solid-gas
phase equilibrium composition over a growing graphene
film.
Thermodynamic properties of metallurgical coke
formation were also investigated and discussed (Terry
and Yu 1991, Jacob and Seetharaman 1994, Jacob and
Seetharaman 1995, Terry and Yu 1995). A decrease of
solid carbon amount resulting from application of
the amorphous carbon properties instead of those for
graphite was verified by Cimenti and Hill (2009) in their
thermodynamic calculations. They also found that due
to a higher energy of the amorphous form than that for
graphite, a joint use of properties of the two carbon
forms results in the same equilibrium composition as
that for graphite.
It follows from the literature presented in this section
that the thermodynamic equilibrium is one of the key
factors controlling the formation of carbon deposits
during reforming of C-H-O mixtures. The thermodynamic
analyses carried out for a range of oxidized fuels indicated
the predominant role of the mixture composition and temperature in solid carbon formation. The boundaries of nodeposition operational regimes were determined using
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different thermodynamic criteria and properties. In the
majority of the published thermodynamic approaches,
different authors considered solid carbon and typically
neglected existence of carbon vapors in their thermodynamic calculations. However, the carbon element is
known of having different allotropic forms both in the
gas and solid phases and their thermodynamic equilibria
may be critical in understanding the conditions of carbon
deposition. Those aspects are considered in the following
chapter.
5 T
hermodynamic equilibrium for
C-H-O mixtures
5.1 T
emperature dependence of carbon
deposition equilibrium
Carbonaceous depositions can occur as a result of side
reactions in reforming popular hydrocarbons such as
methane from natural/bio gas, propane with butane from
LPG, or higher hydrocarbons from diesel fuel. The preceding section on gas-solid carbon equilibrium clearly quantified the equilibrium partial pressures of carbon vapors,
which exist over different crystallographic forms of solid
carbon. However, most authors who analyzed thermodynamic conditions of carbon deposition neglected the presence of carbon vapors in Equations (22), (24), and (26),
assuming perhaps that all atomic carbon was completely
transferred to the solid phase and therefore did not influence the reaction equilibrium. The importance of carbon
gas pressure was explicitly found in only two papers
(Bromley and Strickland-Constable 1960, da Silva et al.
2009); however, the solid carbon activity was used there
in calculations of the reaction constants. Critical compositions of C-H-O mixtures for carbon deposition to occur
were usually studied with the help of commercial software
based on principles expressed in Equations (1) to (7).
Several papers (Bartholomew 1982, Koh et al. 2001,
Eguchi et al. 2002, Koh et al. 2002, Sasaki and Teraoka
2003a,b, Sasaki et al. 2004, Kee et al. 2008, Aravind et al.
2009, Chen et al. 2011, Lee et al. 2013, Liu et al. 2013)
reported C-H-O equilibrium calculations and their comprehensive presentation in ternary diagrams. Most of the
published studies considered only the graphitic form of
solid carbon. However, the thermodynamic data for CNTs
by Gozzi et al. (2007, 2009), respectively, for the multiwall and single-wall in bundles are also considered in this
section. As already mentioned, the authors of this study
decided that only the galvanic cell data (Gozzi et al. 2007,
2009) for filamentous carbon can be regarded as trustworthy and useful in the thermodynamic analysis. By analogy
to approaches applied by other authors (Diaz Alvarado
and Gracia, 2012), the chemical potential dependence
on temperature by Gozzi et al. (2007) was assumed valid
down to 600 K (inclined dotted line in Figure 3). In addition to graphite data as a reference, table data for diamond
and experimental data for the chemical potential of formation of amorphous carbon (Jacob and Seetharaman
1994) were also added and applied in the HSC software
(HSC 2014). However, the amorphous data along with that
for diamond did not turn out significant within the ranges
considered in this study, i.e. temperature between 200°C
and 1000°C and pressure of 1 and 10 bar.
5.2 Numerical predictions of C-H-O equilibria
A wide series of computations of equilibrium phase concentrations of C-H-O reformates were performed with
finding of the depositing carbon form, for varied temperature between 200°C and 1000°C with 100°C increments and two pressure levels of 1 bar and 10 bar. Based
on those results, boundary lines between the deposition
and no deposition zones were drawn in ternary diagrams
and their selection is presented in Figures 4–7. In order to
verify the simulation procedure, such boundary plots for
1 bar and graphite only in the solid phase (Figure 4A) were
first compared with the original ternary plots published
by Sasaki and Teraoka (2003b) (not shown here) and the
two line sets turned out practically identical within the
temperature range from 200°C to 1000°C.
The effect of adding Δi μ0[Cf(s)] data for filamentous carbon, either MWCNT [Equation (16)] or SWCNT
[­Equation (17)], as a thermodynamic equilibrium alternative to graphite is visually presented in Figure 4. In the
performed calculations, the most stable forms of solid
carbon were generally graphite for temperatures from
200°C to 431°C; MWCNT from 431°C up to about 577°C; and
above it, the SWCNT prevailed. Therefore, corresponding
boundary lines for a given temperature are identical up to
400°C, as only graphite was computed in the solid phase,
and differ significantly for higher temperatures where filamentous carbon was predicted. Based on the presented
results, it may be stated that by the time new reliable
thermodynamic data for the chemical potential of filamentous carbon are published, the boundary lines shown
in Figure 4B should be used as reference in reforming
processes with nickel catalyst where filamentous carbon
deposits may be formed.
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228 Z. Jaworski et al.: Carbon deposition: updating for nanotubes
Figure 4: Ternary plots for solid phase of graphite only (A) and all carbon allotropes (B) at P = 1 bar.
Figure 5: Deposition boundaries for graphitic carbon (
) and all solid forms (
For clearer viewing of the differences in the boundary lines, two diagrams for the total pressure of 1 bar are
shown in Figure 5. Each of them presents three pairs of
corresponding temperature lines either for graphite only
(broken lines) or for all considered carbon solid forms
(solid lines). Extension of the carbon deposition regions
towards lower C concentration, with reference to those
for graphite, is due to accounting also for the filamentous
carbon forms and is illustrated in Figure 5 by grey shading.
One can conclude that the deposition boundary lines for
P = 1 bar differ mainly for the reformate temperature close
to 800°C and the line differences decrease towards the
limits of the studied range from 500°C to 1000°C.
) at 1 bar.
5.3 P
ressure effect on carbon deposition
equilibrium
The course of deposition boundary lines was found
dependent also on the total pressure, P, of the C-H-O
mixtures. A visual comparison of ternary plots with the
equilibrium boundary lines computed for 10 bar, separately for graphite and for all considered solid carbon
allotropes, is shown in Figures 6A and B, respectively. The
equilibrium simulations were done for the same temperature range from 200°C to 1000°C as before for 1 bar. For
that elevated pressure, the conditions of carbon deposition also significantly depended on the solid carbon
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Z. Jaworski et al.: Carbon deposition: updating for nanotubes 229
Figure 6: Ternary plots for solid phase of graphite only (A) and all carbon allotropes (B) at P = 10 bar.
Figure 7: Deposition boundaries for graphitic carbon (
) and all solid forms (
allotropes considered. Identical to the threshold temperatures at 1 bar, graphite was in solid phase for temperatures
from 200°C to 431°C, while MWCNT formed solid phase
from 431°C up to about 577°C, and above it, the SWCNT
prevailed.
A graphical presentation of the effect of considering
either graphite only or filamentous carbon allotropes in
the equilibrium simulations is shown in Figure 7 for the
total pressure of 10 bar, which is qualitatively similar to
that in Figure 5 for 1 bar. One can notice that both at the
total pressure of 1 bar and 10 bar of the C-H-O mixtures,
carbon deposition can occur when C > 0.5, independent
of the H and O atomic ratios. When considering all solid
carbon forms, the maximum shift of the equilibrium
boundary line relative to that for graphite was found for
) at P = 10 bar.
the reformate temperature of about 900°C, i.e. somewhat
higher than for the total pressure of 1 bar.
The character of temperature influence on the course
of the deposition boundary lines depends on the hydrogen concentration; for low H values, an increase in temperature lowers the critical C value, whereas for high
hydrogen concentration (lower left part of diagrams), the
temperature effect is opposite. Those effects are qualitatively similar for the two considered pressure values of 1
and 10 bar and either carbon deposit.
The effect of total pressure on the studied equilibrium
conditions can also be assessed by comparing locations of
the corresponding pairs of boundary lines in Figures 4A and
6A for graphite only and those in Figures 4B and 6B for all
solid carbon forms. Two other ternary graphs were prepared
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230 Z. Jaworski et al.: Carbon deposition: updating for nanotubes
(not shown here) for all carbon solid forms with boundary
line pairs for 1 and 10 bar and for three temperature levels
in each diagram, similarly to those in Figures 5 and 7. From
their analysis, it was concluded that the maximum divergence in the lines, i.e. the strongest pressure effect, was in
the temperature range from 700°C to 800°C when graphite
was the only solid form allowed. However, the temperature
range of the maximum influence of pressure was shifted up
by about 100°C when all solid carbon allotropes were considered in equilibrium simulations for the total pressure of
10 bar, compared to those for 1 bar.
6 Concluding remarks
The Gibbs and activation energies of chemical reactions
and physical phase transformations are dependent on
temperature; therefore, both the equilibrium conditions and kinetics of the relevant carbon phase changes
are also temperature sensitive, which was confirmed by
several researchers. Carbon can deposit in variety of crystallographic forms on different catalysts, including singlewalled and multi-walled nanotubes (Jankhah et al. 2008,
Gozzi et al. 2008, Makama et al. 2014). Although thermodynamic criteria indicate either graphite or fibrous carbon
as stable solid forms at T < 1500 K, the kinetics of their
mutual direct transformation can be extremely slow and
difficult to detect.
Wide literature information on both theoretical and
experimental studies on carbon deposition from C-H-O
reformates was examined in this review. Based on the
analysis of published models, it was concluded that the
thermodynamic conditions for deposition of various
carbon allotropes require stringent specification. In the
first step, the three-phase carbon diagram was updated
for only graphite and diamond in the solid phase. It was
confirmed that within the temperature and pressure
ranges up to 1500 K and 10 bar, respectively, the carbon
equilibrium should be considered between only the gas
and solid phases.
Physical chemistry fundamentals along with relevant experimental data for filamentous carbon were
reviewed in Section 3. Significant differences were found
in the standard chemical potentials estimated from the
literature equilibrium concentrations for carbon deposition reactions. The lack of crystallographic purity of the
carbonaceous deposits was suggested as the major cause
of the discrepancy. Therefore, only the electrochemical measurement data for purified both single-walled an
multi-walled CNTs (Gozzi et al. 2007, 2009) were accepted
for filamentous carbon in the thermodynamic analysis
presented in Sections 3 and 4. Verified table data for the
chemical potential of other solid forms, such as graphite,
diamond, and amorphous carbon, were also used in the
computations.
C-H-O atomic concentration diagrams with equilibrium ternary plots for deposition boundaries of the carbon
form, characterized by a minimum of its Gibbs energy
(Equation (1)), were constructed for varied temperature
and pressure. The obtained diagram for graphite as the
single solid carbon was practically identical with that
published by Sasaki and Teraoka (2003b). Within the analyzed ranges of T-P, only either graphite and or one of the
two nanotube types turned out as the depositing carbon
form. The following threshold temperatures were estimated for carbon allotropes in solid phase: 431°C for the
transition of graphite to multi-walled nanotubes, which
is similar to conclusions of Diaz Alvarado and Gracia
(2012). A higher threshold at about 580°C was found for
SWCNT replacing MWCNT, independent of pressure at 1
and 10 bar. The thresholds are shown by dotted lines in
Figure 3. Consideration of the chemical potential data
for filamentous carbon in addition to that for graphite
resulted in shifting the deposition boundary lines towards
lower carbon ratio in C-H-O reformates for temperatures
above 431°C. This was valid independent of pressure, P,
at constant temperature and of temperature for constant
pressure. The strongest effect of the presence of filamentous carbon on lowering the critical carbon atomic ratio,
C, was found for reformates without hydrogen, i.e. for
H = 0. The maximum shift in the boundary molar C ratio
was estimated as ΔC1,G-CNT = −0.042 for nearly 800°C at 1 bar
and as ΔC10,G-CNT = −0.052 for nearly 900°C at P = 10 bar. The
two shift values corresponded to an increase in the critical
oxygen-to-carbon atomic ratio, O/C, by about 17% or 28%
for 1 bar and 10 bar, respectively.
It is also envisaged that similar analyses focused on
practical fuel reformates from different reforming methods
will be presented as a follow-up in a separate paper.
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 STAGESOFC in the years 2014–2017.
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Z. Jaworski et al.: Carbon deposition: updating for nanotubes 231
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Bionotes
Zdzisław Jaworski
Department of Chemical Technology and
Engineering, West Pomeranian University
of Technology, Szczecin, 71065 Szczecin,
Poland,
[email protected]
Zdzisław Jaworski, DSc, PhD, has been employed as an academic
teacher since 1980 and, from 2004, has held a professor position
of Chemical Engineering at the West Pomeranian University of Technology, Szczecin. His research interest was focused on numerical
modeling of transport processes, mixing and reaction technology,
heat transfer, multiphase fluid flow, rheology, thermodynamics,
multi-scale modeling, and fuel cell technology. He has led several
research projects, both national and European, and published over
150 refereed papers.
Barbara Zakrzewska
Department of Chemical Technology and
Engineering, West Pomeranian University
of Technology, Szczecin, 71065 Szczecin,
Poland
Barbara Zakrzewska has been employed as an academic teacher
since 1996 at the West Pomeranian University of Technology,
­Szczecin. She was awarded a PhD with distinction in 2003. Her
research interest was focused on CFD modeling of transport
processes in mixing technology and application of artificial neural
network in reactor modeling, and currently, she is involved in
multi-scale modeling in chemical and process engineering and fuel
cell technology. She has participated in several national and three
European research projects.
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Z. Jaworski et al.: Carbon deposition: updating for nanotubes 235
Paulina Pianko-Oprych
Department of Chemical Technology and
Engineering, West Pomeranian University
of Technology, Szczecin, 71065 Szczecin,
Poland
Paulina Pianko-Oprych was awarded her PhD with distinction in
2005, and in 2016, she received the DSc degree. She has been a
lecturer since 2008 at the West Pomeranian University of Technology, Szczecin. Her research results were published in 70 papers.
With over 16 years of experience in CFD applications, she is involved
in fuel cell modeling and the creation of BoP system models using
process simulator tools. She is now a research-team leader and
project manager in two EU projects.
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