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An in-house Python-based
algorithm was developed using
simplified
molecular-input line-entry specification (SMILES) strings and a dipole
moment for estimating the normal boiling point, critical properties,
standard enthalpy, vapor pressure, liquid molar volume, enthalpy of
vaporization, heat capacity, viscosity, thermal conductivity, and
surface tension of molecules. Normal boiling point, critical properties,
and standard enthalpy were estimated by using the Joback group contribution
method. Vapor pressure, liquid molar volume, enthalpy of vaporization,
heat capacity, and surface tension were estimated by using the Riedel
model, Gunn–Yamada model, Clausius–Clapeyron equation,
Joback group contribution method, and Brock–Bird model, respectively.
Viscosities of liquid and gas were estimated by using the Letsou–Stiel
model and the Chapman–Enskog–Brokaw model, respectively.
Thermal conductivities of liquid and gas were estimated by using the
Sato–Riedel model and Stiel–Thodos model, respectively.
Dipole moment was calculated through molecular dynamics simulation
using the MMFF94 force field, performed with Avogadro software. A
case study was conducted with dihydro-2-methyl-3-furanone (DHMF),
2-furaldehyde diethyl acetal (FDA), 1,1-diethoxy-3-methyl butane (DEMB),
glutathione (GSH), vitamin B5 (VITB5), homocysteine (HCYS), and O-acetyl-l-homoserine (AH), which are not present
in the existing property database. Cross-validation indicated that
the developed Python-based algorithm provided pure component model
parameters nearly identical with those obtained with the Aspen Property
Constant Estimation System (PCES) method, except for the enthalpy
of vaporization. The parameters for estimating the enthalpy of vaporization
using the current Python-based algorithm accurately represented the
behavior of the actual substances, as determined using the Clausius–Claperyon
equation. This Python-based algorithm provides a detailed and clear
reference for estimating pure property parameters.
1. Introduction
In recent years, studies
on biobased fuels and chemicals have continued
to increase in an effort to reduce the dependence of chemical industries
on fossil fuels.1,2 Because industrial bioprocesses
are relatively less technologically mature than conventional chemical
processes, modeling and optimizing bioprocesses through technical
economic analysis (TEA) and life cycle assessment (LCA) are significant.3 Determining the pure component properties is
the initial step in the modeling and simulation of bioprocesses for
TEA and LCA.4,5 The pure component properties
can be obtained from existing databases or can be determined through
direct experiments, or predictions.6 If
an existing database is available, then cost and time savings can
be accrued by conducting experiments. Although direct experimentation
is the most precise method, it frequently involves time-consuming
procedures. In some cases, obtaining a pure sample for a property
analysis is expensive or practically impossible. In such cases, the
prediction of the pure component properties is a viable alternative.
Bioethanol is a well-known commercial product prepared through
biological conversion rather than from fossil fuels or platform chemicals
via chemical reactions.7−9 Bioethanol is an attractive alternative energy source
for addressing concerns about the depletion of fossil fuels, climate
change, and environmental pollution. The raw materials for bioethanol
include not only high-purity feedstocks, such as sugar cane and starch,
but also low-purity biomass, such as lignocellulose, which are being
used in diverse fields. As a result, many unfamiliar components have
been identified as impurities in bioethanol products owing to the
diversity of the raw materials.10,11 Recently reported biobased
impurities usually lack a properties database, and obtaining measurement
data through experiments often requires a substantial amount of resources.
Aspen, a commonly used commercial tool for developing bioprocess
models,12 has a comprehensive database
of pure component properties.13 However,
for pure components for which there is no existing database, the properties
need to be predicted using a property prediction algorithm called
the property constant estimation system (PCES) method.14 The PCES method can be easily used for both
industrial and academic purposes with a commercial license fee. However,
as a disadvantage, the complete algorithm has not been published.
In this study, a Python-based open-source algorithm with a reproducibility
similar to that of the PCES method is developed. The current Python-based
algorithm has the advantages of a clear theoretical reference, easy
customization, and no license fee. The pure component properties considered
in this study include the normal boiling point, critical properties,
standard enthalpy, vapor pressure, heat capacity, heat of vaporization,
viscosity, thermal conductivity, and surface tension. These properties
are essential for process simulations. Parameter estimation is automatically
conducted for these properties by entering a simplified molecular-input
line-entry specification (SMILES) string.15
To verify the accuracy of the model, the proposed Python-based
algorithm was cross-validated by using the PCES method as a reference
for various substances. Some impurities in biobased ethanol for which
there is no existing property database, such as dihydro-2-methyl-3-furanone
(DHMF), 2-furaldehyde diethyl acetal (FDA), and 1,1-diethoxy-3-methyl
butane (DEMB), were examined and compared. In addition, biobased active
substances for which there is no existing property database, such
as glutathione (GSH), vitamin B5 (VITB5), homocysteine (HCYS), and O-acetyl-l-homoserine (AH), were examined and compared.
2. Methods
2.1. Chemicals
The
properties of substances
not present in the Aspen Property Database, including DHMF, FDA, DEMB,
GSH, VITB5, HCYS, and AH, were examined. The chemical formulas, SMILES
strings, and Chemical Abstracts Service (CAS) numbers of these chemicals
are summarized in Table 1. Because almost all of these chemicals are synthesized through biological
processes, racemic compounds were not considered.
Table 1. Summary of Data for Chemicals Covered
in This Study.
Aspen covers a wide range
of property models, and its built-in templates have different unit
systems, which can lead to confusion. Table 2 provides a summary of the unit systems based
on the property models and Aspen models,14 to prevent confusion. Because industrial bioprocesses are performed
in aqueous solutions, a unit system of the Aspen electrolyte template
was used in this study. Although the unit system used the Aspen electrolyte
template, the models employed in this study do not include pure property
predictions for ionic species. The proposed algorithm in this study
operates only for molecular species, similar to the Aspen PCES method.
Table 2. Summary of Unit Systems for Reference
Models and Aspen Models Based on Properties.
property
reference
model
model in Aspen electrolyte template
with their
identifiers
normal boiling
temperature, Tb
Joback group
contribution method in eq 1 with temperature in K.
scalar property, TB, with temperature in °C.
critical temperature, Tc
Joback group contribution method in eq 2 with temperature in K.
scalar property, TC, with temperature in °C.
critical pressure, Pc
Joback group contribution method in eq 3 with pressure in bar.
scalar property, PC, with pressure in bar.
critical volume, Vc
Joback
group contribution method in eq 4 with volume in cm3 mol–1.
scalar property, VC, with volume
in cm3 mol–1.
enthalpy of formation of ideal gas at 298 K, ΔfHig298
Joback group contribution method in eq 5 with enthalpy in kJ mol–1.
scalar property, DHFORM, with enthalpy
in kcal mol–1.
dipole moment, μ
dipole moment in Debye is calculated based on an electric charge
and an energy-optimized molecular structure, and a molecular dynamics
simulation using the MMFF94 force field is performed with Avogadro
software.
scalar property, MUP, with dipole moment in
Debye.
vapor pressure, P
Riedel model in eq 9 with dimensionless reduced
temperature, Tr, and dimensionless reduced
pressure, Pr.
extended Antoine
equation, PLXANT, in eq 18 with pressure in bar and temperature in
°C. If any of CP,5–CP,7 has a nonzero value, the temperature unit of CP,1–CP,7 is changed to K.
liquid molar volume, Vl
Gunn–Yamada model in eq 28 with volume in m3 kmol–1, temperature in K, and pressure in bar.
Rackett model with scalar property,
RKTZRA, in eq 35 with
volume in cm3 mol–1, temperature in K, and pressure in
bar.
enthalpy of vaporization, ΔvapH
Clausius–Clapeyron
equation in eq 37 with
enthalpy in kJ mol–1, temperature in K, pressure in bar,
and volume in m3 kmol–1.
Watson model, DHVLWT, in eq 41 with enthalpy in kcal mol–1 and temperature in °C.
ideal gas heat capacity, Cigp
Joback group contribution method in eq 42 with heat capacity in J mol–1 K–1 and temperature in K.
Aspen ideal gas heat capacity
polynomial model, CPIG, in eqs 47 and 48 with heat capacity in cal mol–1 K–1 and temperature in °C.
If any of CCp,10 and CCp,11 has a nonzero value, the temperature unit of CCp,9–CCp,11 is changed to K.
liquid viscosity, ηl
Letsou–Stiel model in eq 64 with viscosity in cP, temperature in K, and pressure in bar.
Andrade model,
MULAND, in eq 68 with
viscosity in cP and temperature in °C. If
any Cη,2 and Cη,3 has a nonzero value, the temperature unit of Cη,1–Cη,3 is changed to K.
gas viscosity, ηg
Chapman–Enskog–Brokaw model in eq 69 with viscosity in cP, dipole moment
in Debye, temperature in K, and volume
in m3 kmol–1.
the same method as the reference model with viscosity
in cP.
liquid thermal conductivity, λl
Sato–Riedel model in eq 76 with thermal conductivity in kcal m h–1 m–2 K–1 and temperature in K.
DIPPR eq 100 model, KLDIP, in eq 77 with thermal conductivity in kcal m h–1 m–2 K–1 and temperature in K.
gas thermal conductivity, λg
Stiel–Thodos model in eq 78 with thermal conductivity in W m–1 K–1, heat capacity
in J mol–1 K–1, and viscosity in cP.
the same method as the reference
model with thermal conductivity
in kcal m h–1 m–2 K–1.
surface tension, σl
Brock–Bird
model in eq 79 with
surface tension in dyne cm–1, temperature in K, and pressure in
bar.
DIPPR eq 106 model, SIGDIP, in eq 81 with surface tension in dyne cm–1 and temperature in °C.
If any Cσ,1–Cσ,5 has a nonzero value,
the temperature unit of Cσ,1–Cσ,5 is
changed to K.
The term “scalar
property” refers to properties that are independent of temperature
or pressure, and this term is used in Aspen software to collectively
describe such properties. In the Aspen PCES method, various scalar
properties are estimated using the Joback group contribution method.16
1
2
3
4
5
where Tb, Tc, Pc, Vc, and ΔfHig298 are the normal boiling temperature, critical temperature,
critical
pressure, critical volume, and enthalpy of formation of the ideal
gas at 298 K, respectively. Tb,i, Tc,i, Pc,i, Vc,i, and ΔfHig298 are the
values for each property associated with a specific functional group. Na is the total number of atoms in the molecule,
excluding hydrogen. The number of functional groups was estimated
using an automated algorithm in the JRgui software proposed by Shi
and Borchardt.17
The Pitzer acentric
factor, ω, was calculated according to the following definition:18
6
7
8
where P, T, Pr, and Tr are the vapor pressure,
temperature, reduced vapor pressure,
and reduced temperature, respectively. The method for predicting Pr is described in Section 2.4.
The dipole moment, μ, was
estimated by molecular dynamics
simulation using Avogadro software.19 The
molecular structure was built from SMILES strings by using the built-in
function in Avogadro software. The molecular structure was optimized
using the MMFF94 force field, known for its high accuracy for analyzing
organic compounds.20 For the geometry optimization,
a number of steps of 500, the steepest descent algorithm, and a convergence
of 10–7 options were used. μ was automatically
calculated from the electric charge and the optimized molecular structure.
2.4. Vapor Pressure
The reference value
for P was predicted by using the Riedel model.21
9
10
11
12
13
14
15
16
17
where Tbr denotes the reduced boiling temperature. A, B, C, D, Q, αc, Ψb, and K are parameters of the Riedel model. K depends on the type of material, and 0.0838 is recommended for general
purposes.21
The extended Antoine
equation model was used to simulate P in the PCES
method and the current Python-based algorithm.
18
where CP,1, CP,2, CP,3, CP,4, CP,5, CP,6, CP,7, CP,8, and CP,9 are parameters
of the extended Antoine equation. If
the temperature is out of bound, linear extrapolation is conducted
up to 7 + ln P at T = CP,9 where the slope is determined by ln P versus 1/T; beyond this limit, the vapor pressure
remains constant. The Riedel model parameters can be analytically
converted into extended Antoine equation parameters as follows:
19
20
21
22
23
24
25
26
27
where the temperature boundary
between CP,8 and CP,9 was defined according to the PCES method.
2.5. Liquid Molar Volume
The reference
liquid molar volume for the pure component was predicted by applying
the Gunn–Yamada model.22
28
29
30
31
32
33
34
where Vl is the volume of the pure liquid. δ, V(0)r, ZSC, and VSC are
parameters of the Gunn–Yamada model. R is
the ideal gas constant, and a value of 0.0831446 m3 bar
K–1 kmol–1 was used in eqs 28–34.
The Rackett model was used to simulate Vl using the PCES method and the current Python-based algorithm.23
35
where ZRA is the parameter of the Rackett model. For the PCES method,
a value of 83.1446 m3 bar K–1 kmol–1 was used for R in eq 35. If Tr is greater than 0.99, a special form of extrapolation is used to
obtain a smooth curve according to the PCES method.24 The Gunn–Yamada and Rackett models are analytically
inconsistent. A detailed document explaining the clear algorithm used
to evaluate ZRAin PCES could not be found.
Instead, the empirical correlation for the critical compressibility
factor proposed by Gunn and Yamada was applied to estimate ZRA.22
36
2.6. Enthalpy of Vaporization
The reference
value for the enthalpy of vaporization was predicted by applying the
Clausius–Clapeyron equation:25
37
where ΔvapH is the enthalpy of
vaporization. Vg is the volume of the
pure gas. P and Vl can
be obtained from eqs 18 and 35, respectively.
dP/dT was obtained by numerical
differentiation with 1 × 10–5 dT. Vg was obtained by PCES using the Redlich–Kwong
equation of state (RKEOS):26
38
39
40
where a and b are the RKEOS parameters. Vg under the given T and P conditions
was determined by using the well-known Newton–Raphson method.
An objective function that involves multiplying both terms of eq 37 by was used, along with the initial value
of RT/P.
The Watson model
was used to simulate ΔvapH in both
the PCES method and the current Python-based algorithm:27
41
where CWT,1, CWT,2, CWT,3, CWT,4, and CWT,5 are the parameters of the Watson model. If the temperature
condition is out of bound, linear extrapolation is performed. Previously,
in PCES, the Clausius–Clapeyron equation was used as a reference
model to estimate the parameters in eq 41.14 However, a detailed
explanation of the algorithm could not be found. In this study, CWT,1 was determined as ΔvapH at Tb by using eq 37. CWT,2 was determined as Tb. CWT,3 and CWT,4 were
determined through regression analysis of the results obtained from eq 41. These results were
simulated at 10 uniformly spaced intervals between Tb and Tc using eq 37. The Nelder–Mead method
was employed for the regression analysis with a reflection parameter
of 1, an expansion parameter of 2, a contraction parameter of 0.5,
a shrink parameter of 0.5, an initial simplex parameter for nonzero
values of 5 × 10–2, and an initial simplex
parameter for zero values of 2.5 × 10–4.28 The initial values of CWT,3 and CWT,4 for the Nelder–Mead
method were analytically determined and used to interpolate the two
points dividing the temperature range between Tb and Tc into thirds according
to eq 37. CWT,5 was determined by multiplying Tb by 0.4, according to the PCES method.
2.7. Ideal
Gas Heat Capacity
The reference
ideal gas heat capacity was simulated using the Joback group contribution
method:16
42
43
44
45
46
where is the ideal gas heat capacity. , , , and are the ideal gas
heat capacities associated
with a specific functional group. , , , and are parameters of the Joback ideal gas
heat capacity model, which is the sum of the values corresponding
to the functional groups.
In both the PCES method and the current
Python-based algorithm, was simulated using the following empirical
equation, known as the Aspen ideal gas heat capacity polynomial model:
47
48
where CCp,1, CCp,2, CCp,3, CCp,4, CCp,5, CCp,6, CCp,7, CCp,8, CCp,9, CCp,10, and CCp,11 are parameters of the Aspen ideal gas
heat capacity polynomial model. If the temperature condition is out
of bound, then a linear extrapolation is performed. The Joback model
parameters can be analytically converted into the Aspen ideal gas
heat capacity polynomial model parameters. A conversion factor of
4.1868 for converting the units from calorie to Joule was obtained
from the International Standard.29
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
Eqs 49 and 52 are the unit
conversion for the heat capacity from
J mol–1 K–1 to cal mol–1 K–1. Note that the temperature unit of CCp,1 – CCp,8 in eqs 47, 48, and 53–63is °C whereas the temperature unit for CCp,9 – CCp,11 is K.
The temperature boundary between CCp,7 and CCp,8 was defined according to the
PCES method.
2.8. Viscosity
The
reference liquid viscosity
was simulated using the Letsou–Stiel model:30
64
65
66
67
where η and M are the liquid viscosity and molecular weight, respectively.
(ηξ)(0), (ηξ)(1), and
ξ are the parameters of the Letsou–Stiel model. ω
can be calculated by using eq 6.
The Andrade model was used to simulate ηl in both the PCES method and the current Python-based algorithm:31
68
where Cη,1, Cη,2, Cη,3, Cη,4, and Cη,5 are parameters of the
Andrade model. If the temperature condition is out of bound, linear
extrapolation is conducted with a slope determined by ln ηl versus 1/T. It was not possible to find
a detailed explanation of the algorithm used to evaluate Cη,1, Cη,2, and Cη,3 in the PCES method. Cη,4 was determined as Tb according to the PCES method. Cη,5 was determined as 0.99Tc according to
the PCES method. Cη,1, Cη,2, and Cη,3 values
were determined through regression analysis of the results obtained
from eq 68. These results
were simulated at 10 uniformly spaced intervals between Tb and 0.99Tc using eq 64. The well-known ordinary
least-squares regression method was employed for regression analysis.
The Chapman–Enskog–Brokaw model was used to simulate
the gas viscosity in the PCES method and the current Python-based
algorithm.32,33
69
70
71
72
73
74
75
where ηg is the gas viscosity. δ and Vb are the polarity parameter and gas volume at Tb, respectively. σ is a dimensional parameter related
to the intermolecular potential. ϵ and kB are energy parameters related to the intermolecular potential
and Boltzmann constant (1.38 × 10–18 erg/K),
respectively. These parameters were used directly in the form of the
Lennard-Jones energy parameter (ϵ/kB) without the requirement of separate calculations. T* is the reduced temperature defined in the model. Ω2,2p and Ω2,2n are the polar
Lennard-Jones (12–6) potential and nonpolar Lennard-Jones (12–6)
potential, respectively. μ was calculated using molecular dynamics,
as described in Section 2.3. When μ is small, it is anticipated that Aspen will
employ a different model or algorithm to calculate the gas viscosity.
However, a clear reference specifying the exact model to be used could
not be found.
2.9. Thermal Conductivity
The reference
liquid thermal conductivity was simulated using the Sato–Riedel
model:34
76
where λl is the thermal
conductivity of the pure liquid.
The Design
Institute for Physical Properties (DIPPR) eq 100 model was employed
to simulate λl in the PCES method and the current
Python-based algorithm.
77
where Cλ,1, Cλ,2, Cλ,3, Cλ,4, Cλ,5, Cλ,6, and Cλ,7 are parameters
of the DIPPR eq 100 model. Linear extrapolation is conducted for T outside the range Cλ,6 to Cλ,7. Cλ,6 was determined as Tb according
to the PCES method. Cλ,7 was determined
as 0.99Tc according to the PCES method.
In case of the current Python algorithm, Cλ,1, Cλ,2, Cλ,3, Cλ,4, and Cλ,5 were determined using the well-known
ordinary least-squares regression with 10 temperature points uniformly
distributed between Cλ,6 and Cλ,7.
The Stiel–Thodos model
was employed to simulate the gas
thermal conductivity using both the PCES method and the current Python-based
algorithm:35
78
where λg is the gas thermal conductivity. Cigp values can be
obtained using eqs 47 and 48. A value of 8.134 J mol–1 K–1 was used for R in eq 78 to obtain a reference
value of λg in W m–1 K–1. In the Aspen electrolyte template, because the units of the gas
thermal conductivity and heat capacity are kcal m h–1 m–2 K–1 and cal mol–1 K–1, respectively, the reference value of λg must be converted by applying 3.6/4.1868.
2.10. Surface Tension
The reference liquid
surface tension for the pure component was simulated using the Brock–Bird
model:36,37
79
80
where σl is the liquid surface tension. Yc is
a parameter of the Brock–Bird model.
The DIPPR eq 106
model was employed to simulate the liquid surface tension in both
the PCES method and the current Python-based algorithm:
81
where Cσ,1, Cσ,2, Cσ,3, Cσ,4, Cσ,5, Cσ,6, and Cσ,7 are parameters
of the DIPPR eq 106 model. Linear extrapolation is conducted for T outside the range Cσ,6 to Cσ. Because the DIPPR 106 model
and Brock–Bird models have mathematically identical structures,
the parameters can be obtained analytically; the relationships are
as follows:
82
83
84
85
86
87
88
where the temperature boundary
between Cσ,6 and Cσ,7 was defined according to the PCES method.
2.11. Python-Based Algorithm Code
In this
study, a Python-based algorithm code for estimating the property parameters
was developed. SMILES arbitrary target specification (SMARTS) codes
corresponding to each functional group proposed in JRgui software
were applied.17 The open-source Chemoinformatics
package RDKit automatically detects and counts functional groups.38 The Numpy package was used for array calculations.39 All of the algorithms introduced in this study
were developed in Python; the source codes are provided in the Supporting Information.
3. Results and Discussion
3.1. Scalar Properties
Table 3 lists the
calculated data for
the scalar properties. The percent absolute residuals between the
PCES method and the current Python-based algorithm for Tb are 0.13, 0.09, 0.11, 0.03, 0.04, 0.07, and 0.06% for
DHMF, FDA, DEMB, GSH, VITB5, HCYS, and AH, respectively. The percent
absolute residuals between the PCES method and the current Python-based
algorithm for Tc are 0.08, 0.07, 0.08,
0.02, 0.03, 0.05, and 0.05% for DHMF, FDA, DEMB, GSH, VITB5, HCYS,
and AH, respectively. There were slight differences in the cases of Tb and Tc because
the first parameter in eq 1 was set to 198.0 instead of 198.2 in the PCES method. In the original
study, a value of 198.2 was used as the first parameter.16 The current Python-based algorithm used the
same values as in the original study. The simulated values of Pc, Vc, , and ω were all the same
regardless
of the method used. Therefore, the percent absolute residuals are
zero for all of these properties.
Table 3. Estimated Scalar
Properties from the
PCES Method and the Current Python-Based Algorithm.
The extended Antoine
equation parameters for the vapor pressure model were analytically
derived from the Riedel model using the values of Tb, Tc, and Pc listed in Table 3. The values of all parameters were similar for both the PCES
and the current Python-based algorithms, as listed in Table 4. Slight differences were observed
in CP,2, CP,6, CP,8, and CP,9 owing to variations in Tb and Tc, as mentioned in Section 3.1. The percent mean absolute residuals between
the PCES method and the current Python-based algorithm for P are 0.47, 0.44, 0.46, 0.34, 0.60, 0.67, and 0.53% for
DHMF, FDA, DEMB, GSH, VITB5, HCYS, and AH, respectively.
Table 4. Estimation of Extended Antoine Equation
Parameters Using the PCES Method and the Current Python-Based Algorithm.
For the current
Python-based algorithm, ZRA was obtained
from the empirical model of eq 36 proposed by Gunn and Yamada. However, there is no clear published
algorithm for estimating ZRA for the PCES
method. Nevertheless, the PCES method and the current Python-based
algorithm yielded similar results, as shown in Table 5. This example demonstrates the versatility
of the empirical model proposed by Gunn and Yamada (eq 36) for obtaining the Rackett parameter. Figure 1 shows the calculated
liquid molar volumes for FDA and HCYS, demonstrating that the simulation
results were almost identical. The calculation results for the liquid
molar volume of all substances can be seen in Figure S1 in the Supporting Information. The percent mean
absolute residuals between the PCES method and the current Python-based
algorithm for Vl are 0.48, 0.89, 0.66,
0.62, 0.61, 0.78, and 1.14% for DHMF, FDA, DEMB, GSH, VITB5, HCYS,
and AH, respectively.
Table 5. Estimation of Rackett
Model Parameters
from the PCES Method and the Current Python-Based Algorithm.
Simulation of liquid molar volume for FDA (a) and HCYS (b) using
the Rackett model with parameters estimated by the PCES method and
the current Python-based algorithm.
3.4. Enthalpy of Vaporization
As shown
in Table 6, the values
of CWT,1, CWT,3, and CWT,4 estimated by using the PCES
method and the current Python-based algorithm were significantly different. CWT,1 can be derived from the enthalpy of vaporization
at Tb by using the Clausius–Clapeyron
equation (eq 37). Figure 2 shows the results
for DHMF and GSH obtained with the Clausius–Clapeyron equation,
calculated by using both Aspen software and the current Python-based
algorithm. The calculation results for the Clausius–Clapeyron
equation of all substances can be seen in Figure S2 in the Supporting Information. Both algorithms yielded the
same results. Nevertheless, the estimated value of CWT,1 was different, although the exact cause could not
be analyzed, owing to a lack of a clear reference. CWT,3 and CWT,4 are parameters
that represent the influence of ΔvapH on the temperature; the difference between the PCES method and the
current Python-based algorithm is more pronounced for these parameters. Figure 3 shows the ΔvapH for DHMF and GSH, simulated using the
Watson model with the parameters estimated using the PCES method and
the current Python-based algorithm. The calculation results for the
ΔvapH of all substances can be seen
in Figure S3 in the Supporting Information. In the case of the PCES method, CWT,4 had a significantly negative value. As a result, in some cases (including
for GSH), ΔvapH reached a maximum
value at a certain temperature and tended to decrease as the temperature
decreased. For common substances (such as water, ethyl alcohol, carbon
disulfide, ethyl ether, n-pentane, and sulfur dioxide),
the heat of vaporization gradually decreases with increasing temperature
until it approaches zero near the critical temperature. This phenomenon
is consistent with predictions based on the Clausius–Clapeyron
equation.40 As mentioned earlier, in the
case of the PCES method, there are regions that do not align with
the trends predicted by the Clausius–Clapeyron equation. However,
the results obtained with the Watson model using the parameters estimated
from the current Python-based algorithm exhibited the typical behavior
wherein ΔvapH does not decrease,
but the slope of ΔvapH versus temperature
decreased as the temperature decreased. The percent mean absolute
residuals between the Clausius–Clapeyron equation and the PCES
method for ΔvapH are 6.82, 7.15,
7.53, 7.42, 7.38, 6.43, and 6.86% for DHMF, FDA, DEMB, GSH, VITB5,
HCYS, and AH, respectively. The percent mean absolute residuals between
the Clausius–Clapeyron equation and the current Python-based
algorithm for ΔvapH are 0.20, 0.24,
0.25, 0.31, 0.32, 0.22, and 0.19% for DHMF, FDA, DEMB, GSH, VITB5,
HCYS, and AH, respectively. Based on the results, it can be asserted
that the regression using this Python-based algorithm shows better
alignment with the Clausius–Clapeyron equation. The value of P in the Clausius–Clapeyron equation can be obtained
from the extended Antoine equation (eqs 26 and 27); the extended
Antoine equation performs extrapolation beyond the Tb and Tc ranges. Anticipating
the potential for heightened physical inconsistency, simulations of
the Clausius–Clapeyron equation and regression with the Watson
model were performed within the temperature range of Tb to Tc.
Table 6. Data Estimated by Applying the Watson
Model Using Parameters from the PCES Method and the Current Python-Based
Algorithm.
Enthalpy
of vaporization for DHMF (a) and GSH (b) simulated
using
the Watson model with parameters estimated by the PCES method and
the current Python-based algorithm.
3.5. Ideal Gas Heat Capacity
Table 7 presents the results
of the analytical conversion of the ideal gas heat capacity model
parameters obtained through the Joback method into the Aspen ideal
gas heat capacity polynomial model parameters. The results obtained
with PCES and the current Python-based algorithm were identical. Therefore,
the percent mean absolute residuals are zero.
Table 7. Data Estimated
by Applying an Aspen
Ideal Gas Heat Capacity Polynomial Model with Parameters from the
PCES Method and Current Python-Based Algorithm.
Table 8 lists the
parameters of the Andrade liquid
viscosity model estimated using the PCES method and the current Python-based
algorithm. Although the exact algorithm for the PCES method is unknown,
the values were nearly identical to the results obtained with the
Python-based algorithm. As shown in Figure 4, the simulations employing the Andrade model
with the parameters obtained from the PCES method and the current
Python-based algorithm yielded nearly identical results for DEMB and
HCYS. The calculation results for the liquid viscosity of all substances
can be seen in Figure S4 in the Supporting Information. The percent mean absolute residuals between the PCES method and
the Python-based algorithm for ηl are 1.05, 1.06,
1.08, 1.04, 1.08, 1.06, and 1.07% for DHMF, FDA, DEMB, GSH, VITB5,
HCYS, and AH, respectively.
Table 8. Data Estimated by
Applying Andrade
Model with Parameters from the PCES Method and Current Python-Based
Algorithm.
Liquid viscosity for
DEMB (a) and HCYS (b) simulated using the
Andrade model with parameters estimated by the PCES method and the
current Python-based algorithm.
The dipole moment is essential for calculating
the gas viscosity
by using the Chapman–Enskog–Brokaw model. Figure 5 shows the vector of the dipole
moment and the energy-optimized molecular structures of DEMB and HCYS
obtained by using Avogadro software. The calculation results for the
dipole moment of all substances can be seen in Figure S5 in the Supporting Information. Table 9 summarizes the dipole moments
predicted by using Avogadro software. The PCES method does not include
an algorithm for estimating the dipole moments; therefore, unless
the user provides this value, the dipole moment is treated as zero.
Group contribution methods are available for calculating dipole moments,41,42 but relatively low accuracy is expected owing to the three-dimensional
characteristics of the dipole moment. Therefore, free software, such
as Avogadro, which can simulate three-dimensional structural information
using molecular dynamics, may be a useful alternative for calculating
dipole moments. Figure 6 shows the gas viscosities of DEMB and HCYS simulated by using the
Chapman–Enskog–Brokaw model. The calculation results
for the gas viscosity of all substances can be seen in Figure S6 in the Supporting Information. The
results obtained with PCES and the current Python-based algorithm
are identical. The percent mean absolute residuals between the PCES
method and the current Python-based algorithm for ηg are 0.40, 0.67, 0.66, 0.48, 0.61, 0.79, and 0.98% for DHMF, FDA,
DEMB, GSH, VITB5, HCYS, and AH, respectively.
Dipole moment
vector with energy-optimized molecular structure
for DEMB (a) and HCYS (b) simulated using Avogadro software. Light
gray, dark gray, red, blue, and yellow spheres indicate hydrogen,
carbon, oxygen, nitrogen, and sulfur atoms, respectively. Red arrow
indicates the vector of the dipole moment.
Table 9. Dipole
Moments Obtained by Molecular
Dynamics Simulation Using Avogadro Software.
Gas viscosity
for DEMB (a) and HCYS (b) simulated by using
the
Chapman–Enskog–Brokaw model.
3.7. Thermal Conductivity
Table 10 lists the DIPPR equation with
100 model parameters obtained from the Sato–Riedel model. Although
the exact data interval, quantity, and data-fitting method used by
the PCES algorithm remain undisclosed, the values were almost identical
to the results obtained using the current Python-based algorithm.
As shown in Figure 7, the liquid thermal conductivity data from the DIPPR eq 100 model
using the parameters estimated by the PCES method and the current
Python-based algorithms were almost identical for DHMF and AH. The
calculation results for the liquid thermal conductivity of all substances
can be seen in Figure S7 in the Supporting Information. Figure 8 shows the
gas thermal conductivities of DHMF and HCYS simulated by using the
Stiel–Thodos model. The results from the PCES method and the
current Python-based algorithm are almost identical. The calculation
results for the gas thermal conductivity of all substances can be
seen in Figure S8 in the Supporting Information. The percent mean absolute residuals between the PCES method and
the current Python-based algorithm for λl are 0.21,
0.21, 0.23, 0.15, 0.17, 0.19%, and 0.19% for DHMF, FDA, DEMB, GSH,
VITB5, HCYS, and AH, respectively. The percent mean absolute residuals
between the PCES method and the current Python-based algorithm for
λg are 0.72, 0.93, 0.93, 0.80, 0.89, 0.97, and 1.32%
for DHMF, FDA, DEMB, GSH, VITB5, HCYS, and AH, respectively.
Table 10. Estimation of DIPPR Equation 100
Liquid Thermal Conductivity Model Parameters Using the PCES Method
and the Current Python-Based Algorithm.
Liquid thermal
conductivity for DHMF (a) and AH (b) simulated using
the DIPPR eq 100 model with parameters estimated by the PCES method
and the current Python-based algorithm.
Gas thermal
conductivity for DHMF (a) and AH (b) simulated
by using
the Stiel–Thodos model.
3.8. Surface Tension
Table 11 shows the DIPPR eq 106 model
parameters estimated from the PCES method and the current Python-based
algorithm. Notably, the PCES method and the current Python-based algorithm
yielded different results, with a notable difference in Cσ,1. In the current Python-based algorithm, Cσ,1 was analytically determined using eq 82; therefore, the aforementioned
difference may be attributed to Yc in eq 80. Equation 80 is an empirical expression proposed by Miller
and Thodos37 based on experimental data
from various substances and was not directly proposed by Brock and
Bird.36 Unfortunately, a model for Yc that predicts the same Cσ,1 as the PCES method could not be found. Nevertheless,
as shown in Figure 9, the surface tension data simulated by using the parameters obtained
from the PCES method and the current Python-based algorithm were almost
identical. The calculation results for the surface tension of all
substances can be seen in Figure S9 in the Supporting Information. The percent mean absolute residuals of the PCES
method and the current Python-based algorithm for σ are 2.76,
2.76, 2.88, 2.51, 2.59, 2.63, and 2.66% for DHMF, FDA, DEMB, GSH,
VITB5, HCYS, and AH, respectively.
Table 11. Estimation Results
of DIPPR Equation
106 Surface Tension Model Parameters Using the PCES Method and the
Current Python-Based Algorithm.
Surface tension of DHMF (a) and AH (b) simulated
using the DIPPR
eq 106 model with parameters estimated by the PCES method and the
current Python-based algorithm.
3.9. Comparative Summary and Future Work
The
primary objective of this study is to compare the PCES method
with the current Python-based algorithm and to make it available to
the public. It was found that the various scalar properties, vapor
pressure, liquid molar volume, ideal gas heat capacity, viscosity,
thermal conductivity, and surface tension predicted by both methods
show almost identical results. However, as seen in Figure 3, the results predicted for
the enthalpy of vaporization by these two methods differed from each
other. Although the current Python-based algorithm more accurately
matched the Clausius–Clapeyron equation compared to the PCES
method, this does not necessarily prove that it is more consistent
with the actual experimental results.
If experimental values
for the properties of pure substances can be obtained, then comparing
them with simulation results is the most useful method for demonstrating
accuracy. While the original works for each pure property were developed
based on the experimental values of various substances,22 the value of such comparative studies remains
valid for newly predicted substances. Unfortunately, as mentioned
in the introduction, the substances applied in our study make it challenging
to obtain pure substances through experiments. Our future plans involve
developing an in-house Python-based algorithm for the mixture model
of the Aspen electrolyte template. Through this study, several binary
mixture simulation results will be compared with various binary mixture
experimental values, such as density, heat capacity, viscosity, and
thermal conductivity.43
Additionally,
we compared the experimental values of the well-known
enthalpy of vaporization for ethanol44−46 with the predictions
made by the PCES method and the current Python-based method, as shown
in Figure 10. The
percent mean absolute residuals for the vaporization enthalpy predicted
by the PCES method and the current Python-based algorithm were 14.7
and 10.4%, respectively. This suggests that the current Python-based
algorithm can be expected to predict acceptable results. Although
comparison with experimental data for more substance would be useful
in generalizing, it is beyond the scope of this study.
Enthalpy
of vaporization for ethanol simulated using the PCES model
and the current Python-based algorithm with the experimental data.
4. Conclusions
The
Aspen PCES method and
an in-house Python-based algorithm were
compared to estimate the parameters of the pure component property
models for substances not registered in the Aspen software. The impurities
found in biobased ethanol (DHMF, FDA, and DEMB) and biobased active
substances (GSH, VITB5, HCYS, and AH) were analyzed and compared.
The estimated parameters for the normal boiling point, critical properties,
standard enthalpy, vapor pressure, liquid molar volume, heat capacity,
viscosity, thermal conductivity, and surface tension models were nearly
identical with those of the PCES method and the current Python-based
algorithm. In the case of the enthalpy of vaporization, the current
Python-based algorithm estimated parameters that exactly matched the
Clausius–Clapeyron equation but yielded different results from
the PCES method. The current Python-based algorithm accurately represented
the temperature dependence of the enthalpy of vaporization for common
substances. Furthermore, the dipole moment was determined using the
Avogadro software, and it was verified that the gas viscosity could
be calculated using this calculated value. The methods presented in
this study provide detailed and clear references for estimating the
parameters of pure component property models.
Acknowledgments
This work is supported by the CJ BIO Research Institute,
CJ CheilJedang, South Korea. Thanks are given to CJ CheilJedang for
granting permission to publish this article.
An in-house Python-based
algorithm capable of estimating
the properties of pure components (ZIP)
A comparative graph of property simulations
using parameters
estimated by the PCES method and the current Python-based
algorithm for seven substances—dihydro-2-methyl-3-furanone,
2-furaldehyde diethyl acetal, 1,1-diethoxy-3-methyl butane, glutathione,
vitamin B5, homocysteine, and O-acetyl-l-homoserine (PDF)
The
authors declare no
competing financial interest.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
was used, along with the initial value
of RT/P.
is the ideal gas heat capacity. 
, 
, 
, and 
are the ideal gas
heat capacities associated
with a specific functional group. 
, 
, 
, and 
are parameters of the Joback ideal gas
heat capacity model, which is the sum of the values corresponding
to the functional groups.
was simulated using the following empirical
equation, known as the Aspen ideal gas heat capacity polynomial model:
, and ω were all the same
regardless
of the method used. Therefore, the percent absolute residuals are
zero for all of these properties.
