2228 Russ. Chem. Bull., Int. Ed., Vol. 67, No. 12, December, 2018
Katsman et al.
Table 4. Unambiguosly estimated parameters and parametric
functions (complexes) of kinetic models, their values and errors
of calculations
intermediate, the kinetics of an admixture Kn formation
cannot be adequately described.
As it was found earlier, an unusual behavior of nickel
sulfide catalysts involves an increase in heptadecene se-
lectivity with increasing hydrogen pressure.3—7 This is
associated with the known ability of metal hydrides, in-
cluding nickel and silver, to inhibit the chain polymeriza-
tion/oligomerization of olefins, in particular, the radical-
chain (thermal) polymerization.3—7 This feature of hydride
behavior is consistent with the empirical kinetic equation
of the corresponding step 8 (see Table 3), which contains
negative orders of 0.5 for the catalyst and hydrogen con-
centrations.
In the group of nickel sulfide catalysts for decarbonyl-
ation of fatty acids, an unusual tendency is observed: the
loss of heptadecenes due to a secondary hydrogenation
with heptadecane formation decreases with increasing
hydrogen pressure. This was typical of the undoped cata-
lyst; however, this effect is even more pronounced in the
presence of a silver promoted catalyst. Kinetic modeling
provides a rational explanation for this fact. As follows
from the composition of the adsorption complex I (see the
scheme presented above), the target decarbonylation step
(1) is sharply accelerated and up to the third order of
magnitude with increasing pressure of hydrogen, which is
not consumed at this step. The reason is that with in-
creasing pressure of hydrogen the quasi-equilibrium
concentration of the above mentioned complex involved
in decarbonylation increases. In agreement with the com-
position of the corresponding adsorption complexes III
and VI, an increase in the rate of secondary hydrogenation
steps 2 (1) and 2 (2) is less strong. Thus, an increase in
hydrogen pressure does not only inhibit the side reaction
of oligomerization of target heptadecenes,3—7 but also
increases the rate of formation of the target heptadecenes
relative to their consequent hydrogenation. The total effect
becomes apparent in an increase in olefin selectivity with
increasing hydrogen pressure.
Line
Parametric
function
Numerical
value
Logarithmic calcul-
ation error ( )
a
b
c
d
e
f
g
h
i
KIV/(KVIk2(2)
)
4.67•100
4.84•10–1
1.59•10–3
4.93•10–1
1.22•10–4
3.32•10–4
1.09•100
1.91•10–3
1.40•10–1
3.78•100
2.51•100
0.08
0.08
0.05
0.10
0.11
0.12
0.14
0.24
0.46
0.46
0.68
k1KI/(KVIk2(2)
)
k4
k3KII/(KVIk2(2)
)
k8
k6K4
k2(1)KIII/(KVIk2(2)
)
k5
KV/(KVIk2(2)
)
j
k
K2
K5
but only some packages of parameters, the nonlinear
parametric functions (NPF), can be unambiguously de-
termined (calculated and represented in the form of "mean
error"). If the parameter value is calculated unambigu-
ously, such an estimate is referred to as "unmixed".8—10
Table 4 represents six uniquely estimated NPFs of our
kinetic model, their corresponding values (lines a, b, d, f,
g, i) and "unmixed" estimates of the sought for parameters
of the kinetic model (lines c, e, h, j, k).
The unambiguously estimated nonlinear parametric
functions ("packages", lines a, b, d, f, g, i in Table 4) include
the products of adsorption equilibrium constants and the
rate constants of the decomposition of the corresponding
adsorption complexes, as well as the ratio of adsorption
equilibrium constants. Evidently, the NPFs include several
parameters of the model, between unknown values of
which a functional relationship exists. The inevitability of
the appearance of such NPFs is associated, firstly, with
the construction of a kinetic model based on the Langmuir
mechanism which includes the assumption of a quasi-
equilibrium of the adsorption steps. Secondly, a very small
fraction of unoccupied catalytic sites must be taken into
account. It is in the last case when the contribution of
occupied sites is governed by the ratios of the adsorption
equilibrium constants rather than by the values of these
constants. Therefore, a direct comparison of the values of
model parameters for unpromoted and silver promoted
catalysts is not informative and, as a result, inadvisable.
An unambiguously determined NPF (line f in Table 4)
corresponds to the case of a quasi-equilibrium shifted to
the left (formation of stearic anhydride), which is well-
known in formal chemical kinetics, followed by the de-
composition of its product (decarboxylation of the anhy-
dride to diheptadecyl ketone). An attempt to substitute
steps 4 and 6 by a single common step, made in elaborat-
ing the hypothesis, did not result in an adequate model.
Hence, without the assumption of anhydride of St as an
Now we can try to explain why the contribution of the
side reaction of hydrogenation of olefins over a silver-
promoted catalyst is not as high as found with an unpro-
moted system. As can be seen in the diagram reflecting the
results of kinetic modeling, adsorption complex I contains
an additional hydrogen molecule as compared to the
complex formed in the presence of the unpromoted cata-
lyst. Incorporation of hydrogen in the adsorption com-
plexes formed by the active sites of the catalyst may indicate
that in the absence of hydrogen the activity of these sites
in decarbonylation is low or not evident. It is possible that
hydrogen bonding disorders the structure of the active
sites and thus contributes into an enhancement of the
catalytic activity.
Silver and nickel in silver promoted nickel sulfide
catalyst are found in supported particles of different nature,
the average size of which is 11.9 2.8 nm, and the smallest