ethylene molecule is created in a random position of the
simulation box, and its potential energy of interaction UðcÞ
1 with
all the other molecules is calculated. The change of configurational
energy for the reaction step in the backward direction is then given
by the expression:
DUðbÞ
t ¼ UðcÞ
1 þ UðcÞ
2 UðdÞ
3 (7)
By setting z = 1, the product in Eq. (1) takes the form:
YC
i¼1
Ni!
ðNi þ nizÞ!
¼ N3
ðN1 þ 1ÞðN2 þ 1Þ (8)
Substitution of n ¼ 1, z = 1, and Eq. (8) into Eq. (1) leads to
the following expression for the probability of acceptance of a
reaction step in the backward (b) direction:
PðbÞ
rx ¼ min 1;
P0
V
kBT
N3
KeqðN1 þ 1ÞðN2 þ 1Þ
exp DUðbÞ
t
kBT
( !)
(9)
where the change of configurational energy DUðbÞ
t is given by
Eq. (7).
For the simulation of the vapor-phase chemical equilibrium of
the ternary system at given values of temperature T and pressure P,
the following four-stage strategy was implemented. In the first
stage, by specifying the ethylene to water feed mole ratio and
defining an initial number of ethanol molecules in the simulation
box equal to zero, the initial numbers of ethylene and water
molecules were defined from a total number of 900 molecules. In
the second stage, an NVT-ensemble simulation (with
N = 900 molecules) was carried out with an arbitrary vapordensity
value and for a total number of 1 106 moves (molecular
displacements and rotations), 60% of which were used to
equilibrate the configurational energy. In the third stage, starting
from the final configuration obtained after the NVT run, an NPTensemble
simulation was carried out for a total number of 3 106
moves (using a ratio of one volume change to N molecular
displacements and rotations), 60% of which were used to
equilibrate the density and the configurational energy. In the
fourth stage, starting from the final configuration obtained after
Fig