ช่วยแปลหน่อยนะคะ เยอะมากเรย
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7.1. Base case
In order to establish a reference point, optimization is carried
out for a base case and the operating conditions used for
both sides of the reactor are given in Tables 7 and 8. Operating
conditions for the methanol synthesis side are similar
to those used by Rahimpour et al. [33]. The inlet composition
of the methanol synthesis reaction is typical of industrial
methanol synthesis process. It corresponds to a hydrogen:
carbon dioxide ratio of 7 having small amount of CH3OH,
CO and H2O together with inert gases of CH4 and N2. On the
endothermic side, the inlet mole fraction of cyclohexane that
is diluted with argon is the same as that presented by
Kusakabe et al. [52]. Thus, the base case aims to investigate
the situation when the cyclohexane dehydrogenation is used
for the consumption of the generated heat from methanol
synthesis and to cool down it, resulting in a higher temperature
at first parts of exothermic side for higher kinetics
constants and then reducing temperature gradually at the
end parts of reactor for increasing thermodynamics equilibrium
which is similar to the temperature profile along a tube
filled with catalyst within a methanol conventional reactor.
This allows comparison of the methanol synthesis process in
the optimized thermally coupled reactor (OTCR) with
conventional methanol reactor (CMR) for similar thermal
behavior. The optimization and simulation results of the
reactor in the endothermic side are not compared with any
7.2. Simulation and optimization
With due attention to subjects of Section 5, the optimization
approach is to find optimal temperature profiles along
the exothermic and endothermic sides to maximize methanol
and benzene mole fractions through the optimization
of initial molar flow rate of endothermic stream and inlet
temperature of exothermic and endothermic sides. Differential
evolution method is applied to determine the optimal
reactor operating conditions for methanol and benzene
production process in a thermally coupled reactor. Figs. 4
and 5 show profiles of objective function in terms of inlet
temperature of exothermic and endothermic sides in the
thermally coupled reactor, respectively. As shown in these
figures, the objective function is maximized in one point.
This means there is an optimal inlet temperature of
exothermic and endothermic sides and their values are
527.8 and 423.0 K, respectively. Also Fig. 6 shows variation
of objective function in term of initial molar flow rate of
endothermic stream in thermally coupled reactor. As it can
be seen in this figure, the optimum value of initial molar
flow rate of endothermic stream is 0.111 mol s_1. The
results of the optimization (using differential evolution
method and MATLAB programming) are summarized in
Table 9.
The simulation of thermally coupled reactor is carried
out using optimization results in Table 9 and the results of
this simulation are shown in several figures. Fig. 7(a)(e)
shows the comparison of mole fraction of components in
exothermic side of optimized thermally coupled reactor
(OTCR) with conventional methanol reactor (CMR). Fig. 7(a)
illustrates the mole fraction profile of methanol along the
reactor, at steady-state for exothermic side of OTCR and
CMR. Fig. 7(b)(e) presents similar results for other components.
The important point as illustrated in these figures is
a reaction kinetic controlling in the upper sections of
reactor while in other sections, the rate of reactions has
decreased to its equilibrium value and equilibrium is
controlling.
As it can be seen in Fig. 7(a), the comparison of methanol
mole fraction in exothermic side of OTCR with CMR shows
that the methanol mole fraction in output of OTCR is
increased by 3.67%, although, the profiles of methanol mole
fraction along the upper sections of reactor have the same
patterns in the both reactor under steady-state conditions.
Fig. 8 is simultaneous plots of mole fraction for cyclohexane,
benzene and hydrogen in the endothermic side of OTCR
along the reactor axis. The mole fraction of hydrogen and
benzene is increased and cyclohexane is decreased. As the
reaction scheme for cyclohexane dehydrogenation indicates,
the increase of hydrogen mole fraction is higher than
benzene.
Fig. 9(a) and (b) shows axial temperature profiles in the
exothermic and endothermic sides of OTCR and CMR. In
addition, the highest temperature is observed at the
exothermic side, since this is where heat is generated. Part of
this heat is used to drive the endothermic reaction and the
rest to heat the reaction mixtures in both sides. The
temperature of the dehydrogenation side is always lower
than that of the exothermic side in order to make a driving
force for heat transfer from the solid wall. Along the
exothermic side, temperature decreases rapidly and a cold
spot develop as demonstrated in Fig. 9(a), then increases and
make a hot spot, afterward the temperature decreases to
505 K. At the entrance of dehydrogenation side, the temperature
increases rapidly and a hot spot form and then the
temperature decreases.
Fig. 10(a) shows the variation of rate of reaction for both
sides of OTCR. Near the reactor entrance, the cyclohexane
dehydrogenation is fast. Comparing the values for the reaction
rates present in the exothermic side, it can be seen that the
predominant reactions are hydrogenation of CO and hydrogenation
of CO2; however, water-gas shift reaction can be
neglected, its contribution being significant. Fig. 10(b) illustrates
the variation of the generated and consumed heat flux in
the exothermic and the endothermic reaction, respectively,
and transferred heat from the solid wall along the reactor for
OTCR. In the first half of the reactor, methanol reaction
proceeds rapidly and as a result much heat is produced by the
exothermic reaction. In this section, the transferred heat from
the solid wall is higher than generated heat in the exothermic
side (dimensionless length ผ 00.05 in Fig. 10(b)) and consequently
the temperature in exothermic side decreases as
illustrated by the temperature profile in Fig. 9(a).
Afterward, the generated heat in the exothermic side is
higher than the transferred heat from the solid wall and
therefore the excess heat raises the temperature of the system
in the first half of the reactor (dimensionless lengthผ 0.050.3
in Fig. 9(a)). In this region, the generated heat flux is higher
than the consumed one. The system heats up and a peak in
the generated heat flux is observed (Fig. 10(b)). Afterward, the
generated heat flux decreases smoothly, mainly due to fuel
depletion. The opposite situation occurs when the consumed
heat flux is higher than the generated one. If the consumed
heat flux is higher than the generated one, the system starts to
cool down resulting to low temperature, which in turn
decreases both reaction rates. Thus, after a certain position
along the reactor (dimensionless length ผ 0.3 in Fig. 10(b)) the
generated heat flux becomes lower than the consumed one,
which coincides with a hot spot development (see Fig. 9(a)). As
the reactions in the second half of the reactor, are equilibrium
limited, so the lower temperature enhances the equilibrium
conversion (see Fig. 7).
An increase in the reaction heat flux consumed is observed
near the reactor entrance, and is associated to the relatively
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