INTRODUCTION
The
research of equation of state (EOS) has always been an important field
in chemical engineering thermodynamics. In general,
EOS
can be divided
into
the
specific
EOS for a given substance and
the
general EOS for many kinds of substances1-3.
Differently,
the latter always
has
a wider range of applications while the precision is less than the
former. Fortunately, some
multi-parameter
EOSs both possess a high calculation precision
and
a wide range of applications4,5,
although
their solution methods with
unknown
multiple-parameters are always very difficult and
time-consuming.
Among
the large number of multi-parameter EOSs, the
Benedict-Webb-Rubin6-8 EOS (B-W-R EOS) and
the
Martin-Hou EOS (M-H EOS)9-12 are very representative
and excellent with significant differences in terms of the precision and
the range of application.
On
the one hand,
the
calculation precision of the two equation in gas-phase state is
approximately equivalent and high
enough
for the practical application while the B-W-R EOS is more
precise
in liquid-phase
state;
On the other hand, the M-H EOS has a much broader scope of applications
for most kinds of substances, even the strong polar substances such as
H2O and NH3 and so on, while the B-W-R
EOS is mainly used to calculate the properties of hydrocarbons.
Moreover, the initial value conditions for the derivation of the unknown
characteristic constants in the M-H EOS are more accessible and easy to
use.
Although the M-H EOS was originally put forward in the form of
an
empirical equation, its theoretical formula had been strictly
proved13,14by
the theory of Hard-particle Perturbation theory15-18.
Nowadays, the main
investigation
of the M-H EOS has changed from
the
theory’s exploration to the application of given substances in different
cases.
First
and foremost, especially in refrigeration
industry19-21, the M-H EOS is widely applied as a
specific EOS for a given substance, such as
H2O22, 23,
CO224, natural gas25and so on26. Second,
the
M-H EOS is extended to achieve diversified
applications27-32, e.g., the crossover multi-parameter
EOS31, 32. Last but not least,
the
combination of the M-H EOS with other
theories
is further developed, which has solved many thorny problems in the
past33-36.
Although many
satisfying
researches have been achieved, the improvement of the M-H EOS itself is
essentially stagnant for the application in liquid-phase state after
the
modified M-H EOS put forward by Hou12. In fact, the
original M-H EOS is not very proper to the calculation in liquid-phase
state9, as the improved formula, Hou’s modified M-H
EOS is also not as satisfactory
as
desired
in
term of the calculation precision. In general, most average deviation by
Hou’s modified M-H EOS is less than 5% in liquid-phase state,
while
partial
maximum deviations are up to
15%~20%12. It is still of great
potential to improve the calculation precision of the M-H EOS in
liquid-phase state.
In
this work, we focus on improving the precision of the M-H EOS in
liquid-phase state. First,
based
on
rigorous
derivation and a large number of literature data analysis, the M-H EOS
is further modified
and
the novel formula will be put forward by introducing an appropriate
revision factor h ; And then, the novel M-H EOS will be applied to
six representative substances to verify
the
generality of the novel EOS and the improvement of calculation precision
in liquid-phase state, all the data calculated by different EOS are
listed in the supporting information. At last, the conclusion is drawn.
In the
appendixes,
the unknown characteristic constants in the novel M-H EOS are derived in
detail.