U.S. patent application number 13/649278 was filed with the patent office on 2013-02-07 for methods of modeling physical properties of chemical mixtures and articles of use.
This patent application is currently assigned to Aspen Technology, Inc.. The applicant listed for this patent is Aspen Technology, Inc.. Invention is credited to Chau-Chyun Chen, Yuhua Song.
Application Number | 20130035923 13/649278 |
Document ID | / |
Family ID | 34861720 |
Filed Date | 2013-02-07 |
United States Patent
Application |
20130035923 |
Kind Code |
A1 |
Chen; Chau-Chyun ; et
al. |
February 7, 2013 |
Methods Of Modeling Physical Properties Of Chemical Mixtures And
Articles Of Use
Abstract
Included are methods for modeling at least one physical property
of a mixture of at least two chemical species. One or more chemical
species of the mixture are approximated or represented by at least
one conceptual segment. The conceptual segments are then used to
compute at least one physical property of the mixture. An analysis
of the computed physical properties forms a model of at least one
physical property of the mixture. Also included are computer
program products and computer systems for implementing the modeling
methods.
Inventors: |
Chen; Chau-Chyun;
(Lexington, MA) ; Song; Yuhua; (Somerville,
MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Aspen Technology, Inc.; |
Burlington |
MA |
US |
|
|
Assignee: |
Aspen Technology, Inc.
Burlington
MA
|
Family ID: |
34861720 |
Appl. No.: |
13/649278 |
Filed: |
October 11, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12655988 |
Jan 11, 2010 |
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13649278 |
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10785925 |
Feb 24, 2004 |
7672826 |
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12655988 |
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Current U.S.
Class: |
703/12 |
Current CPC
Class: |
G16C 20/30 20190201 |
Class at
Publication: |
703/12 |
International
Class: |
G06G 7/58 20060101
G06G007/58 |
Claims
1. A computer system for modeling at least one physical property of
a mixture of at least two chemical species, the computer system
comprising: a) a user input means for determining chemical data
from a user; b) a digital processor coupled to receive determined
chemical data from the input means, wherein the digital processor
executes a modeling system in working memory, wherein the modeling
system: i) uses the chemical data to determine at least one
conceptual segment for each of the at least two chemical species,
including, for each conceptual segment, defining an identity and an
equivalent number for the conceptual segment; ii) uses the
determined at least one conceptual segment to compute at least one
physical property of the chemical mixture; and iii) provides an
analysis of the computed at least one physical property, the
analysis forms a model of the at least one physical property of the
mixture; and c) an output means coupled to the digital processor,
the output means provides to the user the formed model of the at
least one physical property of the chemical mixture.
2. The computer system of claim 1, wherein the computer system
enables transmission of some portion of at least one of chemical
data as the formed model over a global network.
3. The computer system of claim 1, wherein the computer system
enables transmission of some portion of at least one of the
chemical data and the formed model over a global network.
4. A pharmaceutical compound manufactured by a process that
includes a modeling method, wherein the modeling method models at
least one physical property of a mixture of at least two chemical
species and comprises the computer implemented steps of: a)
determining at least one conceptual segment for each of the at
least two chemical species, including defining an identity and an
equivalent number of each of the at least one conceptual segment;
b) using the determined at least one conceptual segments, computing
at least one physical property of the mixture; and c) providing an
analysis of the computed physical property, wherein the analysis
forms a model of the at least one physical property of the
mixture.
5. A method of modeling at least one physical property of a mixture
of at least two chemical species using a modeler, the method
comprising the computer implemented steps of: a) providing at least
one conceptual segment, instead of a molecular structural segment,
to a modeler, the modeler during execution being formed of (i) a
databank of conceptual segments of chemical species, and (ii) a
calculator of physical properties of the mixture, the modeler being
configured to be executable by a processor; b) in response the
modeler using the at least one conceptual segment to compute at
least one physical property of the mixture, including any one of
vapor pressure, solubility, boiling point, freezing point,
octanol/water partition coefficient, or a combination thereof; c)
analyzing the computed at least one physical property using the
modeler, in a comparison to the computed at least one physical
property of other mixtures of at least two chemical species, and
forming therefrom a model of the at least one physical property of
the mixture; and d) outputting the formed model from the modeler to
a computer display monitor.
Description
RELATED APPLICATION
[0001] This application is a divisional of U.S. application Ser.
No. 12/655,988, filed Jan. 11, 2010, which is a divisional of U.S.
application Ser. No. 10/785,925, filed Feb. 24, 2004, issued as
U.S. Pat. No. 7,672,826 on Mar. 2, 2010. The entire teachings of
the above applications are incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] Modeling physical properties of chemical mixtures is an
important task in many industries and processes. Specifically, for
many processes, accurate modeling of physical properties for
various mixtures is crucial for such areas as process design and
process control applications. For example, modeling physical
properties of chemical mixtures is often useful when selecting
suitable solvents for use in chemical processes.
[0003] Solvent selection is an important task in the chemical
synthesis and recipe development phase of the pharmaceutical and
agricultural chemical industries. The choice of solvent can have a
direct impact on reaction rates, extraction efficiency,
crystallization yield and productivity, etc. Improved solvent
selection brings benefits, such as faster product separation and
purification, reduced solvent emission and less waste, lower
overall costs, and improved production processes.
[0004] In choosing a solvent, various phase behavior
characteristics of the solvent-solute mixtures are considered. For
example, vapor-liquid equilibrium (VLE) behavior is important when
accounting for the emission of solvent from reaction mixtures, and
liquid-liquid miscibility (LLE) is important when a second solvent
is used to extract target molecules from the reaction media. For
solubility calculations, solid-liquid equilibrium (SLE) is a key
property when product isolation is done through crystallization at
reduced temperature or with the addition of anti-solvent.
[0005] For many applications, hundreds of typical solvents, not to
mention an almost infinite number of mixtures thereof, are
candidates in the solvent selection process. In most cases, there
is simply insufficient phase equilibrium data on which to make an
informed solvent selection. For example, in pharmaceutical
applications, it is often the case that phase equilibrium data
involving new drug molecules in the solvents simply do not exist.
Although limited solubility experiments may be taken as part of the
trial and error process, solvent selection is largely dictated by
researchers' preferences or prior experiences.
[0006] Many solubility estimation techniques have been used to
model the solubility of components in chemical mixtures. Some
examples include the Hansen model and the UNIFAC group contribution
model. Unfortunately, these models are rather inadequate because
they have been developed mainly for petrochemicals with molecular
weights in the 10s and the low 100s daltons. These models do not
extrapolate well for chemicals with larger molecular weights, such
as those encountered in pharmaceutical applications.
Pharmaceuticals are mostly large, complex molecules with molecular
weight in the range of about 200-600 daltons.
[0007] Perhaps, the most commonly used methods in solvent selection
process are the solubility parameter models, i.e., the regular
solution theory and the Hansen solubility parameter model. There
are no binary parameters in these solubility parameter models and
they all follow merely an empirical guide of "like dissolves like."
The regular solution model is applicable to nonpolar solutions
only, but not for solutions where polar or hydrogen-bonding
interactions are significant. The Hansen model extends the
solubility parameter concept in terms of three partial solubility
parameters to better account for polar and hydrogen-bonding
effects.
[0008] In his book, Hansen published the solubility parameters for
over 800 solvents. See Hansen, C. M., HANSEN, SOLUBILITY
PARAMETERS: A USER'S HANDBOOK (2000). Since Hansen's book contains
the parameters for most common solvents, the issue in using the
Hansen model lies in the determination of the Hansen solubility
parameters from regression of available solubility data for the
solute of interest in the solvent selection process. Once
determined, these Hansen parameters provide a basis for calculating
activity coefficients and solubilities for the solute in all the
other solvents in the database. For pharmaceutical process design,
Bakken, et al. reported that the Hansen model can only correlate
solubility data with .+-.200% in accuracy, and it offers little
predictive capability. See Bakken, et al., Solubility Modeling in
Pharmaceutical Process Design, paper presented at AspenTech User
Group Meeting, New Orleans, La., Oct. 5-8, 2003, and Paris, France,
Oct. 19-22, 2003.
[0009] When there are no data available, the UNIFAC functional
group contribution method is sometimes used for solvent selection.
In comparison to the solubility parameter models, UNIFAC's strength
comes with its molecular thermodynamic foundation. It describes
liquid phase nonideality of a mixture with the concept of
functional groups. All molecules in the mixture are characterized
with a set of pre-defined UNIFAC functional groups. The liquid
phase nonideality is the result of the physical interactions
between these functional groups and activity coefficients of
molecules are derived from those of functional groups, i.e.,
functional group additivity rule. These physical interactions have
been pre-determined from available phase equilibrium data of
systems containing these functional groups. UNIFAC gives adequate
phase equilibrium (VLE, LLE and SLE) predictions for mixtures with
small nonelectrolyte molecules as long as these molecules are
composed of the pre-defined set of functional groups or similar
groups.
[0010] UNIFAC fails for systems with large complex molecules for
which either the functional group additivity rule becomes invalid
or due to undefined UNIFAC functional groups. UNIFAC is also not
applicable to ionic species, an important issue for pharmaceutical
processes. Another drawback with UNIFAC is that, even when valuable
data become available, UNIFAC cannot be used to correlate the data.
For pharmaceutical process design, Bakken et al., reported that the
UNIFAC model only predicts solubilities with a RMS (root mean
square) error on In x of 2, or about .+-.500% in accuracy, and it
offers little practical value. Id.
[0011] A need exists for new, simple, and practical methods of
accurately modeling one or more physical properties of a
mixture.
SUMMARY OF THE INVENTION
[0012] The present invention provides a new system and method for
modeling the physical properties or behavior of chemical mixtures
(e.g., chemical solutions or suspensions). Briefly, the molecular
structure of one or more species in a chemical mixture is assigned
one or more different types of "conceptual segments." An equivalent
number is determined for each conceptual segment. This conceptual
segment approach of the present invention is referred to as the
Non-Random Two-Liquid Segment Activity Coefficient ("NRTL-SAC")
model.
[0013] In some embodiments, this invention features a method of
modeling at least one physical property of a mixture of at least
two chemical species. In one embodiment, the method comprises the
computer implemented steps of determining at least one conceptual
segment for each of the chemical species, using the determined
conceptual segments to compute at least one physical property of
the mixture; and providing an analysis of the computed physical
property. The step of determining at least one conceptual segment
includes defining an identity and an equivalent number of each
conceptual segment. The provided analysis forms a model of at least
one physical property of the mixture.
[0014] In further embodiments, this invention includes a method of
modeling at least one physical property of a mixture that includes
at least three chemical species. In one embodiment, the method
comprises the computer implemented steps of determining at least
one conceptual segment for a first chemical species; determining at
least one conceptual segment for a second chemical species;
determining at least one conceptual segment for a third chemical
species; using the determined conceptual segments for the first
chemical species, the determined conceptual segments for the second
chemical species, and the determined conceptual segments for the
third chemical species to compute at least one physical property of
the mixture; and providing an analysis of the computed physical
property. For each conceptual segment, the steps of determining the
conceptual segments include defining an identity and an equivalent
number of the respective conceptual segment. The analysis forms a
model of at least one physical property of the mixture.
[0015] In another embodiment, this invention features methods of
modeling solubility of a pharmaceutical component of a mixture that
includes at least one pharmaceutical component and at least one
solvent. In one embodiment, the method comprises the computer
implemented steps of determining at least one conceptual segment
for the pharmaceutical component, determining at least one
conceptual segment for the solvent, using the determined conceptual
segment for the pharmaceutical component and the determined
conceptual segment for the solvent to compute solubility of the
pharmaceutical component in the mixture, and providing an analysis
of the computed solubility. The steps of determining the conceptual
segments include defining an identity and an equivalent number of
the respective conceptual segment. The analysis forms a solubility
model of the pharmaceutical component in the mixture.
[0016] In further embodiments, this invention features computer
program products. In one embodiment, the computer program product
comprises a computer usable medium and a set of computer program
instructions embodied on the computer useable medium for modeling
at least one physical property of a mixture of at least two
chemical species. The computer program instructions include the
instructions to determine at least one conceptual segment for each
of the chemical species, use the determined conceptual segments to
compute at least one physical property of the chemical mixture; and
provide an analysis of the computed physical property. The program
instructions for determining conceptual segments include
instructions for defining an identity and an equivalent number of
each conceptual segment. The analysis forms a model of at least one
physical property of the mixture.
[0017] In yet a further embodiment, this invention features a
computer system for modeling at least one physical property of a
mixture of at least two chemical species. In one embodiment, the
computer system comprises a user input means for determining
chemical data from a user, a digital processor coupled to receive
input (determined chemical data) from the input means, and an
output means coupled to the digital processor. The digital
processor hosts and executes a modeling system in working memory.
The modeling system (i) uses the chemical data to determine at
least one conceptual segment for each of the chemical species; (ii)
uses the determined conceptual segments to compute at least one
physical property of the chemical mixture, and; (iii) provides an
analysis of the computed physical property. The modeling system
determines a conceptual segment, in part, by defining an identity
and an equivalent number of each conceptual segment. The analysis
forms a model of at least one physical property of the mixture. The
output means provides to the user the formed model of the physical
property of the chemical mixture.
[0018] In some embodiments, this invention features a
pharmaceutical compound manufactured by a process that includes a
modeling method. The modeling method models at least one physical
property of a mixture of at least two chemical species and
comprises the computer implemented steps of determining at least
one conceptual segment for each of the chemical species, using the
determined conceptual segments to compute at least one physical
property of the mixture; and providing an analysis of the computed
physical property. The step of determining at least one conceptual
segment includes defining an identity and an equivalent number of
each conceptual segment. The provided analysis forms a model of at
least one physical property of the mixture.
[0019] This invention provides for the fast, practical modeling of
physical properties or behaviors of chemical mixtures, even when
there is little or no experimental data to which the behavior of
the mixture can be correlated. The formed models offer improved
accuracy over most or all prior modeling methods. For example, this
invention offers a simple and practical tool for practitioners to
estimate solubility of various components of a chemical mixture
(e.g., a mixture including a pharmaceutical component), even when
there is little or no phase equilibrium data available for the
mixture.
[0020] This invention provides for modeling of mixtures having
significant hydrophobic interactions, significant polar
interactions, and/or significant hydrogen-bonding interactions.
This invention eliminates the need to characterize mixture
constituents with sets of pre-defined functional groups and
provides for the modeling of mixtures comprising large, complex
molecules for which a functional group additivity rule becomes
invalid and/or for which there are a number of un-defined
functional groups.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021] The foregoing and other objects, features and advantages of
the invention will be apparent from the following more particular
description of preferred embodiments of the invention, as
illustrated in the accompanying drawings in which like reference
characters refer to the same parts throughout the different views.
The drawings are not necessarily to scale, emphasis instead being
placed upon illustrating the principles of the invention.
[0022] FIG. 1 is a block diagram of a computer system embodying the
present invention modeling methods.
[0023] FIG. 2 illustrates data flow and process steps for a modeler
of the present invention, such as that employed in the embodiment
of FIG. 1.
[0024] FIG. 3 illustrates data flow and process steps for a
computation by the modeler of FIG. 2.
[0025] FIG. 4 illustrates a graph showing the binary phase diagram
for a water, 1,4-dioxane mixture at atmospheric pressure.
[0026] FIG. 5 illustrates a graph showing the binary phase diagram
for a water, octanol mixture at atmospheric pressure.
[0027] FIG. 6 illustrates a graph showing the binary phase diagram
for an octanol, 1,4-dioxane mixture at atmospheric pressure.
[0028] FIG. 7 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for p-aminobenzoic acid in
various solvents at 298.15K.
[0029] FIG. 8 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for benzoic acid in
various solvents at 298.15K.
[0030] FIG. 9 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for camphor in various
solvents at 298.15K.
[0031] FIG. 10 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for ephedrine in various
solvents at 298.15K.
[0032] FIG. 11 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for lidocaine in various
solvents at 298.15K.
[0033] FIG. 12 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for methylparaben in
various solvents at 298.15K.
[0034] FIG. 13 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for testosterone in
various solvents at 298.15K.
[0035] FIG. 14 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for theophylline in
various solvents at 298.15K.
[0036] FIG. 15 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for estriol in nine
solvents at 298.15K.
[0037] FIG. 16 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for estrone in various
solvents at 298.15K.
[0038] FIG. 17 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for morphine in six
solvents at 308.15K.
[0039] FIG. 18 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for piroxicam in 14
solvents at 298.15K.
[0040] FIG. 19 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for hydrocortisone in 11
solvents at 298.15K.
[0041] FIG. 20 illustrates a graph showing data of experimental
solubilities vs. calculated solubilities for haloperidol in 13
solvents at 298.15K.
DETAILED DESCRIPTION OF THE INVENTION
[0042] A description of preferred embodiments of the invention
follows.
[0043] The NRTL-SAC model of the present invention follows the
segment contribution concept that was first incorporated into the
NRTL model as a Gibbs energy expression for oligomers and polymers.
While the UNIFAC model of the prior art decomposes molecules into a
large number of pre-defined functional groups, the NRTL-SAC model
of the present invention decomposes or assigns to each molecular
species a few pre-defined conceptual segments. For example, in some
embodiments of the present invention, each molecular species is
assigned three types of conceptual segments: a hydrophobic segment,
a polar segment, and a hydrophilic segment. Each conceptual segment
is then assigned an equivalent number. The equivalent numbers of
these conceptual segments are determined, not from their exact
molecular structure (as are the functional groups of the UNIFAC
model), but from experimental data that reflect on their true
molecular characteristics in the mixture. These equivalent numbers
are used to describe or model how the various molecular species of
a mixture interact with one another. In this manner, the NRTL-SAC
methods of the present invention is able to model one or more
physical properties of a mixture.
[0044] Various NRTL models have been used to model various types of
mixtures. Previous segment-based NRTL models used "segments" to
define the various chemical species of a mixture. Like the UNIFAC
model, these segments were based upon the actual molecular
structure of the various chemical species, while the conceptual
segments of the present invention are defined based upon actual
thermodynamic behavior of the various chemical species.
[0045] The segment contribution approach represents a practical
alternative to the UNIFAC functional group contribution approach.
Industrial practitioners generally have a healthy distrust or
suspicion of "predictive" models, empirical or ab initio. Wherever
possible, they prefer correlative models that allow them to
validate the model with available data, determine the model
parameters from the data, and extrapolate into new conditions with
proper molecular insights and thermodynamic consistency. The
NRTL-SAC model of the present invention offers such a framework,
with molecular descriptors identified by using available
experimental data for the chemical species of a mixture. The
NRTL-SAC model is used to extrapolate to other chemical systems
that are also described in terms of the same or similar set of
molecular descriptors.
[0046] In some embodiments, this invention includes methods of
modeling at least one physical property of a mixture of at least
two chemical species. In one embodiment, the method comprises the
computer implemented steps of (i) determining at least one
conceptual segment for each of the chemical species; (ii) using the
determined conceptual segments, computing at least one physical
property of the mixture; and (iii) providing an analysis of the
computed physical property. The step of determining a conceptual
segment includes defining an identity and an equivalent number of
each conceptual segment. The analysis forms a model of at least one
physical property of the mixture.
[0047] The methods of this invention can model mixtures that
include one or more liquid phases. In some embodiments, at least a
portion of at least one chemical species of the mixture is in at
least one fluid phase (e.g., a vapor phase and/or a liquid phase).
For example, the mixture can include one or more liquid phases
(e.g., two or more liquid solvent phases) and a vapor phase. In
further embodiments, at least a portion of at least one chemical
species of the mixture is in one or more solid phases. In yet
further embodiments, the mixture includes at least one solid phase
and at least one liquid phase. In still further embodiments, the
mixture includes at least one solid phase (e.g., at least 1, 2, 3,
or more than 3 solid phases), at least one liquid phase (e.g., at
least 1, 2, 3, or more than 3 liquid phases), and a vapor
phase.
[0048] The methods of this invention can model a wide range of
chemical mixtures. For example, the chemical mixtures can include
one or more of the following types of chemical species: an organic
nonelectrolyte, an organic salt, a compound possessing a net
charge, a zwitterions, a polar compound, a nonpolar compound, a
hydrophilic compound, a hydrophobic compound, a petrochemical, a
hydrocarbon, a halogenated hydrocarbon, an ether, a ketone, an
ester, an amide, an alcohol, a glycol, an amine, an acid, water, an
alkane, a surfactant, a polymer, and an oligomer.
[0049] In further embodiments, the mixture includes at least one
chemical species which is a solvent (e.g., a solvent used in a
pharmaceutical production, screening, or testing process), a
solute, a pharmaceutical component, a compound used in an
agricultural application (e.g., a herbicide, a pesticide, or a
fertilizer) or a precursor of a compound used in an agricultural
application, a compound used in an adhesive composition or a
precursor of a compound used in an adhesive composition, a compound
used in an ink composition or a precursor of a compound used in an
ink composition. As used herein, a "pharmaceutical component"
includes a pharmaceutical compound, drug, therapeutic agent, or a
precursor thereof (i.e., a compound used as an ingredient in a
pharmaceutical compound production process). In some embodiments,
the mixture includes at least one pharmaceutical component having a
molecular weight greater than about 900 daltons, at least one
pharmaceutical component having a molecular weight in the range of
between about 100 daltons and about 900 daltons, and/or at least
one pharmaceutical component having a molecular weight in the range
of between about 200 daltons and about 600 daltons. In further
embodiments, the mixture includes at least one nonpolymeric
pharmaceutical component.
[0050] In further embodiments, the mixture includes at least one
ICH solvent, which is a solvent listed in the ICH Harmonized
Tripartite Guideline, Impurities: Guideline for Residual Solvents
Q3C, incorporated herein in its entirety by reference. ICH STEERING
COMMITTEE, ICH Harmonized Tripartite Guideline, Impurities:
Guideline for Residual Solvents Q3C, International Conference of
Harmonization of Technical Requirements for Registration of
Pharmaceuticals for Human Use (1997).
[0051] It will be apparent to those skilled in the art that a
component of the mixture can belong to more than one type of
chemical species.
[0052] In accordance with one aspect of the present invention, at
least one conceptual segment (e.g., at least 1, 2, 3, 4, 5, 7, 10,
12, or more than 12 conceptual segments) is determined or defined
for each of the chemical species of the mixture. The conceptual
segments are molecular descriptors of the various molecular species
in the mixture. An identity and an equivalent number are determined
for each of the conceptual segments. Examples of identities for
conceptual segments include a hydrophobic segment, a polar segment,
a hydrophilic segment, a charged segment, and the like.
Experimental phase equilibrium data can be used to determine the
equivalent number of the conceptual segment(s).
[0053] The determined conceptual segments are used to compute at
least one physical property of the mixture, and an analysis of the
computed physical property is provided to form a model of at least
one physical property of the mixture. The methods of this invention
are able to model a wide variety of physical properties. Examples
of physical properties include vapor pressure, solubility (e.g.,
the equilibrium concentration of one or more chemical species in
one or more phases of the mixture), boiling point, freezing point,
octanol/water partition coefficient, lipophilicity, and other
physical properties that are measured or determined for use in the
chemical processes.
[0054] In some embodiments, the mixture includes at least two
liquid phases and the modeled physical property or properties
include the solubility of one or more chemical species in the two
liquid phases. In other embodiments, the mixture includes at least
one liquid phase and at least one solid phase, and the modeled
physical property or properties include the solubility of a
chemical species of the solid phase in the liquid phase.
[0055] Preferably, the methods provide equilibrium values of the
physical properties modeled. For example, a mixture can include at
least one liquid solvent and at least one solid pharmaceutical
component and the methods can be used to model the solubility of
the pharmaceutical component. In this way, the method can provide
the amount (e.g., a concentration value) of the pharmaceutical
component that will be dissolved in the solvent at equilibrium. In
another example, the method could model a mixture that includes a
solid phase (e.g., a solid pharmaceutical component) and at least
two liquid phases (e.g., two solvent that are immiscible in one
another). The model can predict, or be used to predict, how much of
the pharmaceutical component will be dissolved in the two liquid
phases and how much will be left in the solid phase at equilibrium.
In yet a further embodiment, the methods can be used to predict the
behavior of a mixture after a change has occurred. For example, if
the mixture includes two liquid phases and one solid phase, and an
additional chemical species is introduced into the mixture (e.g., a
solvent, pharmaceutical component, or other chemical compound),
additional amounts of a chemical species are introduced into the
mixture, and/or one or more environmental conditions are changed
(e.g., a change in temperature and/or pressure), the method can be
used to predict how the introduction of the chemical species and/or
change in conditions will alter one or more physical properties of
the mixture at equilibrium.
[0056] The models of the physical property or properties of the
mixture are produced by determining the interaction characteristics
of the conceptual segments. In some embodiments, the
segment-segment interaction characteristics of the conceptual
segments are represented by their corresponding binary NRTL
parameters. Given the NRTL parameters for the conceptual segments
and the molecular descriptors for the molecules, the NRTL-SAC model
computes activity coefficients for the segments and then for the
various molecules in the mixture. In other words, the physical
properties or behavior of the mixture will be accounted for based
on the segment compositions of the molecules and their mutual
interactions. The activity coefficient of each molecule is computed
from the number and type of segments for each molecule and the
corresponding segment activity coefficients.
[0057] In further embodiments, this invention includes a method of
modeling at least one physical property of a mixture that includes
at least three chemical species. In one embodiment, the method
comprises the computer implemented steps of (i) determining at
least one conceptual segment for a first chemical species; (ii)
determining at least one conceptual segment for a second chemical
species; (iii) determining at least one conceptual segment for a
third chemical species; (iv) using the determined conceptual
segments for the first chemical species, the determined conceptual
segments for the second chemical species and the determined
conceptual segments for the third chemical species (e.g., a
pharmaceutical component), computing at least one physical property
of the mixture; and (v) providing an analysis of the computed
physical property. Each step of determining the conceptual segments
includes defining an identity and an equivalent number of the
respective conceptual segment. The analysis forms a model of at
least one physical property of the mixture.
[0058] In further embodiments, this invention features methods of
modeling solubility of a pharmaceutical component of a mixture that
includes at least one pharmaceutical component and at least one
solvent. The methods comprise the computer implemented steps of (i)
determining at least one conceptual segment for the pharmaceutical
component; (ii) determining at least one conceptual segment for the
solvent; (iii) using the determined conceptual segment for the
pharmaceutical component and the determined conceptual segment for
the solvent, computing solubility of the pharmaceutical component
in the mixture; and (iv) providing an analysis of the computed
solubility. The analysis forms a solubility model of the
pharmaceutical component in the mixture.
[0059] In some embodiments, this invention features computer
program products. The computer program products comprise a computer
usable medium and a set of computer program instructions embodied
on the computer useable medium for modeling at least one physical
property of a mixture of at least two chemical species. Included
are (a) instructions to determine at least one conceptual segment
for each of the chemical species; (b) instructions to use the
determined conceptual segments to compute at least one physical
property of the chemical mixture; and (c) instructions to provide
an analysis of the computed physical property, wherein the analysis
forms a model of at least one physical property of the mixture.
[0060] Referring now to FIG. 1, illustrated is a computer system 10
embodying the present invention modeling methods mentioned above.
Generally, computer system 10 includes digital processor 12 which
hosts and executes modeler 20. Modeler 20 comprises the modeling
method of the invention in working memory. Input means 14 provides
user selectable/definable chemical data (e.g., data relating to, or
useful for, modeling a mixture that includes a pharmaceutical
component) from a user of computer system 10. Input means 14 can be
implemented as any of various in-put/out-put devices, programs, or
routines coupled to computer system 10.
[0061] Responsive to input means 14 is user interface 22. User
interface 22 receives user input data from input means 14 and
provides input data for processing by modeler 20. Modeler 20
determines at least one physical property of a mixture that
includes at least one user input compound. Modeler 20 further
provides an analysis of the determined physical properties and thus
outputs a model 16 of the determined physical property. As such,
output 16 is a model of at least one physical property of a mixture
(e.g., a mixture including one or more pharmaceutical components)
derived based on the chemical data from input 14.
[0062] In one embodiment, computer program product 80, including a
computer readable medium (e.g., a removable storage medium such as
one or more DVD-ROM's,
[0063] CD-ROM's, diskettes, tapes, etc.) provides at least a
portion of the software instructions for modeler 20, user interface
22, and/or any of component of modeler 20 or user interface 22.
Computer program product 80 can be installed by any suitable
software installation procedure, as is well known in the art. In
another embodiment, at least a portion of the software instructions
may also be downloaded over a wireless connection. Computer program
propagated signal product 82 embodied on a propagated signal on a
propagation medium (e.g., a radio wave, an infrared wave, a laser
wave, a sound wave, or an electrical wave propagated over a global
network such as the Internet, or other network(s)) provides at
least a portion of the software instructions for modeler 20, user
interface 22, and/or any component of modeler 20 or user interface
22.
[0064] In alternate embodiments, the propagated signal is an analog
carrier wave or digital signal carried on the propagated medium.
For example, the propagated signal may be a digitized signal
propagated over a global network (e.g., the Internet), a
telecommunications network, or other network. In one embodiment,
the propagated signal is a signal that is transmitted over the
propagation medium over a period of time, such as the instructions
for a software application sent in packets over a network over a
period of milliseconds, seconds, minutes, or longer. In another
embodiment, the computer readable medium of computer program
product 80 is a propagation medium that the computer system 10 may
receive and read, such as by receiving the propagation medium and
identifying a propagated signal embodied in the propagation medium,
as described above for computer program propagated signal product
82.
[0065] FIGS. 2 and 3 illustrate data flow and process steps for a
modeler performing the methods of the invention, such as modeler 20
of FIG. 1. With reference to FIG. 2, chemical data describing one
or more chemical species of the mixture and/or environmental
conditions (e.g., pressure and/or temperature) is entered at step
105 of the modeler process. Step 110 uses that data to determine at
least one conceptual segment for each chemical species of the
mixture. The determined conceptual segments are used to compute at
least one physical property of the mixture during step 115. The
computed physical properties are analyzed to form a model of at
least one physical property of the mixture (e.g., solubility of one
or more chemical species in one or more phases of the mixture) in
step 120. The model information is then given as output at step
125. The output can take the form of data or an analysis appearing
on a computer monitor, data or instructions sent to a process
control system or device, data entered into a data storage device,
and/or data or instructions relayed to additional computer systems
or programs.
[0066] FIG. 3 illustrates in more detail the computation at step
115 in FIG. 2. Step 115 begins with the receipt of determined
conceptual segments for each chemical species of the mixture. The
determined conceptual segments and the equation:
ln .gamma. m lc = j x j G jm .tau. jm k x k G k m + m ' x m ' G m m
' k x k G k m ' ( .tau. m m ' - k x k G k m ' .tau. k m ' k x k G k
m ' ) ##EQU00001##
are used to compute at least one physical property of the mixture
during step 215. The computed physical properties are provided as
output 220 from computation step 215. In step 220, the computed
physical properties are passed to step 120 of FIG. 2 for forming a
model of the physical property of the mixture as described
above.
[0067] According to the foregoing, in some embodiments, the
invention features a computer system for modeling at least one
physical property of a mixture of at least two chemical species.
The computer system is formed of a user input means for determining
chemical data from a user, a digital processor coupled to receive
input from the input means, and an output means coupled to the
digital processor. The digital processor hosts and executes a
modeling system in working memory. The modeling system (i) uses the
chemical data to determine at least one conceptual segment for each
of the chemical species; (ii) uses the determined conceptual
segments to compute at least one physical property of the chemical
mixture; and (iii) provides an analysis of the computed physical
property. The analysis forms a model of the at least one physical
property of the mixture. The output means provides to the user of
the formed model of the physical property of the chemical
mixture.
[0068] In some embodiments, this invention features a
pharmaceutical compound manufactured by a process that includes a
modeling method. The modeling method models at least one physical
property of a mixture of at least two chemical species and
comprises the computer implemented steps of determining at least
one conceptual segment for each of the chemical species, using the
determined conceptual segments to compute at least one physical
property of the mixture; and providing an analysis of the computed
physical property. The step of determining at least one conceptual
segment includes defining an identity and an equivalent number of
each conceptual segment. The provided analysis forms a model of at
least one physical property of the mixture.
[0069] The following Examples are illustrative of the invention,
and are not meant to be limiting in any way.
EXAMPLE 1
Modeling a Mixture of Nonelectrolyte Chemical Species
[0070] A study was performed to determine how well the NRTL-SAC
models the solubility of mixtures comprising a solid organic
nonelectrolyte.
[0071] The solubility of a solid organic nonelectrolyte is
described well by the expression:
ln x I SAT = .DELTA. fus S R ( 1 - T m T ) - ln .gamma. I SAT
##EQU00002##
for T.ltoreq.T.sub.m and where the entropy of fusion of the solid
(.DELTA..sub.fusS) is represented by:
.DELTA. fus S = .DELTA. fus H T m ##EQU00003##
x.sub.l.sup.SAT is the mole fraction of the solid (the solute)
dissolved in the solvent phase at saturation, .gamma..sub.l.sup.SAT
is the activity coefficient for the solute in the solution at
saturation, R is the gas constant, T is the temperature, and
T.sub.m is the melting point of the solid. Given a polymorph,
.DELTA..sub.fusS and T.sub.m are fixed and the solubility is then a
function of temperature and activity coefficient of the solute in
the solution. The activity coefficient of the solute in the
solution plays the key role in determining the solubility. In
general, the activity coefficient of the solute in the solution is
usually calculated from a liquid activity coefficient model.
[0072] Except for the ideal solution model, an activity coefficient
model is often written in two parts as such:
ln.gamma..sub.1=ln.gamma..sub.l.sup.C+ln.gamma..sub.l.sup.R
.gamma..sub.l.sup.C and .gamma..sub.l.sup.R are the combinatorial
and residual contributions to the activity coefficient of component
I, respectively.
[0073] In NRTL-SAC, the combinatorial part, .gamma..sub.l.sup.C, is
calculated from the Flory-Huggins term for the entropy of mixing.
The residual part, .gamma..sub.l.sup.R, is set equal to the local
composition (lc) interaction contribution,
.gamma..sub.l.sup.lc:
ln .gamma. I R = ln .gamma. I lc = m r m , I [ ln .gamma. m lc - ln
.gamma. m lc , I ] ##EQU00004##
with
ln .gamma. m lc = j x j G jm .tau. jm k x k G k m + m ' x m ' G m m
' k x k G k m ' ( .tau. m m ' - k x k G k m ' .tau. k m ' k x k G k
m ' ) , ln .gamma. m lc , I = j x j , I G jm .tau. jm k x k , I G k
m + m ' x m ' , I G m m ' k x k , I G k m ' ( .tau. m m ' - k x k ,
I G k m ' .tau. k m ' k x k , I G k m ' ) , x j = J x J r j , J I i
x I r i , I , x j , I = r j , I j r j , I , ##EQU00005##
where i,j,k,m,m' are the segment-based species index, I,J are the
component index, x.sub.j is the segment-based mole fraction of
segment species j, and x.sub.j is the mole fraction of component J,
r.sub.m,l is the number of segment species m contained in component
I,.gamma..sub.m.sup.lc is the activity coefficient of segment
species m, and .gamma..sub.m.sup.k,l is the activity coefficient of
segment species m contained only in component I. G and .tau. are
local binary quantities related to each other by the NRTL
non-random factor parameter .alpha.:
G=exp(-.alpha..tau.)
[0074] The equation:
ln .gamma. I R = ln .gamma. I lc = m r m , I [ ln .gamma. m lc - ln
.gamma. m lc , I ] ##EQU00006##
is a general form for the local composition interaction
contribution to activity coefficients of components in the NRTL-SAC
model of the present invention. For mono-segment solvent components
(S), this equation can be simplified and reduced to the classical
NRTL model as follows:
ln .gamma. I = S lc = m r m , S [ ln .gamma. m lc - ln .gamma. m lc
, S ] ##EQU00007##
with
r.sub.m,S=1, ln .gamma..sub.m.sup.lc,S=0.
[0075] Therefore,
ln .gamma. I = S lc = j x j G jS .tau. jS k x k G kS + m x m G Sm k
x k G k m ( .tau. Sm - k x k G k m .tau. k m k x k G k m ) ,
##EQU00008##
where
G.sub.iS=exp(-.alpha..sub.jS.tau..sub.jS),
G.sub.Sj=exp(-.alpha..sub.jS.tau..sub.Sj).
This is the same equation as the classical NRTL model.
[0076] Three conceptual segments were defined for nonelectrolyte
molecules: a hydrophobic segment, a polar segment, and a
hydrophilic segment. These conceptual segments qualitatively
capture the phase behavior of real molecules and their
corresponding segments. Real molecules in turn are used as
reference molecules for the conceptual segments and available phase
equilibrium data of these reference molecules are used to identify
NRTL binary parameters for the conceptual segments. Preferably,
these reference molecules possess distinct molecular
characteristics (i.e., hydrophobic, hydrophilic, or polar) and have
abundant, publicly available, thermodynamic data (e.g., phase
equilibrium data).
[0077] The study was focused on the 59 ICH solvents used in
pharmaceutical process design. Water, triethylamine, and n-octanol
were also considered. Table 1 shows these 62 solvents and the
solvent characteristics.
TABLE-US-00001 TABLE 1 Common Solvents in Pharmaceutical Process
Design Solvent Solvent (Component 1) .tau..sub.12.sup.a
.tau..sub.21.sup.a .tau..sub.12.sup.b .tau..sub.21.sup.b
.tau..sub.12.sup.c .tau..sub.21.sup.c characteristics ACETIC-ACID
1.365 0.797 2.445 -1.108 Complex ACETONE 0.880 0.935 0.806 1.244
Polar ACETONITRILE 1.834 1.643 0.707 1.787 Polar ANISOLE
Hydrophobic BENZENE 1.490 -0.614 3.692 5.977 Hydrophobic 1-BUTANOL
-0.113 2.639 0.269 2.870 -2.157 5.843 Hydrophobic/ Hydrophilic
2-BUTANOL -0.165 2.149 -0.168 3.021 -1.539 5.083 Hydrophobic/
Hydrophilic N-BUTYL-ACETATE 1.430 2.131 Hydrophobic/Polar
METHYL-TERT-BUTYL- -0.148 0.368 1.534 4.263 Hydrophobic ETHER
CARBON-TETRACHLORIDE 1.309 -0.850 5.314 7.369 Hydrophobic
CHLOROBENZENE 0.884 -0.194 4.013 7.026 Hydrophobic CHLOROFORM 1.121
-0.424 3.587 4.954 Hydrophobic CUMENE Hydrophobic CYCLOHEXANE
-0.824 1.054 6.012 9.519 Hydrophobic 1,2-DICHLOROETHANE 1.576
-0.138 3.207 4.284 2.833 4.783 Hydrophobic 1,1-DICHLOROETHYLENE
Hydrophobic 1,2-DICHLOROETHYLENE Hydrophobic DICHLOROMETHANE 0.589
0.325 1.983 3.828 Polar 1,2-DIMETHOXYETHANE 0.450 1.952 Polar
N,N-DIMETHYLACETAMIDE -0.564 1.109 Polar N,N-DIMETHYLFORMAMIDE
1.245 1.636 -1.167 2.044 Polar DIMETHYL-SULFOXIDE -2.139 0.955
Polar 1,4-DIOXANE 1.246 0.097 1.003 1.010 Polar ETHANOL 0.533 2.192
-0.024 1.597 Hydrophobic/ Hydrophilic 2-ETHOXYETHANOL -0.319 2.560
-1.593 1.853 Hydrophobic/ Hydrophilic ETHYL-ACETATE 0.771 0.190
0.508 3.828 Hydrophobic/Polar ETHYLENE-GLYCOL 1.380 -1.660
Hydrophilic DIETHYL-ETHER -0.940 1.400 1.612 3.103 Hydrophobic
ETHYL-FORMATE Polar FORMAMIDE Complex FORMIC-ACID -0.340 -1.202
Complex N-HEPTANE -0.414 0.398 Hydrophobic N-HEXANE 6.547 10.949
6.547 10.949 Hydrophobic ISOBUTYL-ACETATE Polar ISOPROPYL-ACETATE
Polar METHANOL 1.478 1.155 0.103 0.396 Hydrophobic/ Hydrophilic
2-METHOXYETHANOL 1.389 -0.566 Hydrophobic/ Hydrophilic
METHYL-ACETATE 0.715 2.751 Polar 3-METHYL-1-BUTANOL 0.062 2.374
-0.042 3.029 -0.598 5.680 Hydrophobic/Hydrophilic
METHYL-BUTYL-KETONE Hydrophobic/Polar METHYLCYCLOHEXANE 1.412
-1.054 Polar METHYL-ETHYL-KETONE -0.036 1.273 0.823 2.128 -0.769
3.883 Hydrophobic/Polar METHYL-ISOBUTYL-KETONE 0.977 4.868
Hydrophobic/Polar ISOBUTANOL 0.021 2.027 0.592 2.702 -1.479 5.269
Hydrophobic/ Hydrophilic N-METHYL-2-PYRROLIDONE -0.583 3.270 -0.235
0.437 Hydrophobic NITROMETHANE 1.968 2.556 Polar N-PENTANE 0.496
-0.523 Hydrophobic 1-PENTANOL -0.320 2.567 -0.029 3.583
Hydrophobic/ Hydrophilic 1-PROPANOL 0.049 2.558 0.197 2.541
Hydrophobic/ Hydrophilic ISOPROPYL-ALCOHOL 0.657 1.099 0.079 2.032
Hydrophobic/ Hydrophilic N-PROPYL-ACETATE 1.409 2.571
Hydrophobic/Polar PYRIDINE -0.665 1.664 -0.990 3.146 Polar
SULFOLANE 1.045 0.396 Polar TETRAHYDROFURAN 0.631 1.981 1.773 0.563
Polar 1,2,3,4- 1.134 -0.631 Hydrophobic TETRAHYDRONAPHTHALENE
TOLUENE -0.869 1.292 4.241 7.224 Hydrophobic 1,1,1-TRICHLOROETHANE
0.535 -0.197 Hydrophobic TRICHLOROETHYLENE 1.026 -0.560 Hydrophobic
M-XYLENE Hydrophobic WATER 10.949 6.547 Hydrophilic TRIETHYLAMINE
-0.908 1.285 1.200 1.763 -0.169 4.997 Hydrophobic/Polar 1-OCTANOL
-0.888 3.153 0.301 8.939 Hydrophobic/ Hydrophilic Wherein: 1.
.tau..sub.12.sup.a and .tau..sub.21.sup.a are NRTL binary .tau.
parameters for systems of the listed solvents and hexane. NRTL
non-random factor parameter, .alpha., is fixed as a constant of
0.2. In these binary systems, solvent is component 1 and hexane
component 2. .tau.'s were determined from available VLE & LLE
data. 2. .tau..sub.12.sup.b and .tau..sub.21.sup.b are NRTL binary
.tau. parameters for systems of the listed solvents and water. NRTL
non-random factor parameter, .alpha., is fixed as a constant of
0.3. In these binary systems, solvent is component 1 and water
component 2. .tau.'s were determined from available VLE data. 3.
.tau..sub.12.sup.c and .tau..sub.21.sup.c are NRTL binary .tau.
parameters for systems of the listed solvents and water. NRTL
non-random factor parameter, .alpha., is fixed as a constant of
0.2. In these binary systems, solvent is component 1 and water
component 2. .tau.'s were determined from available LLE data.
[0078] Hydrocarbon solvents (aliphatic or aromatic), halogenated
hydrocarbons, and ethers are mainly hydrophobic. Ketones, esters
and amides are both hydrophobic and polar. Alcohols, glycols, and
amines may have both substantial hydrophilicity and hydrophobicity.
Acids are complex, with hydrophilicity, polarity, and
hydrophobicity.
[0079] Also shown in Table 1 are the available NRTL binary
parameters (.tau.) for various solvent-water binary systems and
solvent-hexane binary systems. Applicants obtained these binary
parameters from fitting selected literature phase equilibrium data
and deliberately ignoring the temperature dependency of these
parameters. These values illustrate the range of values for these
binary parameters. Note that many of the binary parameters are
missing, as the phase equilibrium data is not found in the
literature or simply has never been determined for that solvent
mixture. Also note the sheer number of binary parameters needed for
the prior art NRTL models for even a moderately sized system of
solvents. For example, to model 60 solvents with the NRTL model,
60x60 NRTL binary parameters would be needed. Table 1 shows that,
for the NRTL binary parameters determined from VLE and LLE data for
hydrophobic solvent (1)/water (2) binaries, all hydrophobic
solvents exhibit similar repulsive interactions with water and both
.tau..sub.12 and .tau..sub.21 are large positive values for the
solvent-water binaries. When the hydrophobic solvents also carry
significant hydrophilic or polar characteristics, .tau..sub.12
becomes negative while .tau..sub.21 retain a large positive
value.
[0080] Table 1 also illustrates that similar repulsive, but weaker,
interactions between a polar solvent (1) and hexane (2), a
representative hydrophobic solvent. Both .tau..sub.12 and
.tau..sub.21 are small, positive values for the solvent-hexane
binaries. The interactions between hydrophobic solvents and hexane
are weak and the corresponding NRTL binary parameters are around or
less than unity, characteristic of nearly ideal solutions.
[0081] The interactions between polar solvents (1) and water (2)
are more subtle. While all .tau..sub.21 are positive, .tau..sub.12
can be positive or negative. This is probably due to different
polar molecules exhibiting different interactions, some repulsive
and others attractive, with hydrophilic molecules.
[0082] Hexane and water were chosen as the reference molecule for
hydrophobic segment and for hydrophilic segment, respectively. The
selection of reference molecule for polar segment requires
attention to the wide variations of interactions between polar
molecules and water. Acetonitrile was chosen as the reference
molecule for a polar segment, and a mechanism was introduced to
tune the way the polar segment is characterized. The tuning
mechanism, as shown in Table 2, allows tuning of the interaction
characteristics between the polar segment and the hydrophilic
segment. In other words, instead of using only one polar segment
("Y"), two polar segments ("Y-" and "Y+") were used. The difference
between Y- and Y+ is the way they interact with the hydrophilic
segment.
[0083] The chosen values for the NRTL binary interactions
parameters, .alpha. and .tau., for the three conceptual segments
are summarized in Table 2.
TABLE-US-00002 TABLE 2 NRTL Binary Parameters for Conceptual
Segments in NRTL-SAC Segment (1) X (hydrophobic X (hydrophobic Y-
(polar Y+ (polar X (hydrophobic segment) segment) segment) segment)
segment) Segment (2) Y- (polar Z (hydrophilic Z (hydrophilic Z
(hydrophilic Y+ (polar segment) segment) segment) segment) segment)
.tau..sub.12 1.643 6.547 -2.000 2.000 1.643 .tau..sub.2l 1.834
10.949 1.787 1.787 1.834 .alpha..sub.12 = .alpha..sub.21 0.2 0.2
0.3 0.3 0.2
[0084] As a first approximation, the temperature dependency of the
binary parameters was ignored.
[0085] The binary parameters for the hydrophobic segment
(1)--hydrophilic segment (2) were determined from available
liquid-liquid equilibrium data of hexane-water binary mixture (see
Table 1). .alpha. was fixed at 0.2 because it is the customary
value for a for systems that exhibit liquid-liquid separation. Here
both .tau..sub.12 and .tau..sub.21 are large positive values
(6.547, 10.950). They highlight the strong repulsive nature of the
interactions between the hydrophobic segment and the hydrophilic
segment.
[0086] Determining a suitable value for .alpha. is known in the
art. See J. M. PRAUSNITZ, ET AL., MOLECULAR THERMODYNAMICS OF
FLUID-PHASE EQUILIBRIA 261 (3d ed. 1999).
[0087] The binary parameters for the hydrophobic segment (1)--polar
segment (2) were determined from available liquid-liquid
equilibrium data of hexane--acetonitrile binary mixture (see Table
1). Again, a was fixed at 0.2. Both .tau..sub.12 and .tau..sub.21
were small positive values (1.643,1.834). They highlight the weak
repulsive nature of the interactions between hydrophobic segment
and polar segment.
[0088] The binary parameters for the hydrophilic segment (1)--polar
segment (2) were determined from available vapor-liquid equilibrium
data of water--acetonitrile binary mixture (see Table 1). .alpha.
was fixed at 0.3 for the hydrophilic segment--polar segment pair
because this binary does not exhibit liquid-liquid separation.
.tau..sub.12 was fixed at a positive value (1.787) and .tau..sub.21
was allowed to vary between -2 and 2. Two types of polar segments
were allowed, Y- and Y+. For Y- polar segment, the values of
.tau..sub.12 and .tau..sub.21 were (1.787, -2). For Y+ polar
segment, they were (1.787, 2). Note that both Y- polar segment and
Y+ polar segment exhibited the same repulsive interactions with
hydrophobic segments as discussed in the previous paragraph. Also,
ideal solution was assumed for Y- polar segment and Y+ polar
segment mixtures (i.e., .tau..sub.12=.tau..sub.21=0).
[0089] Table 2 captures the general trends for the NRTL binary
parameters that were observed for a wide variety of hydrophobic,
polar, and hydrophilic molecules.
[0090] The application of the NRTL-SAC model requires a databank of
molecular descriptors for common solvents used in the industry. In
this example, each solvent was described by using up to four
molecular descriptors, i.e., X, Y+, Y-, and Z. So, using four
molecular descriptors to model a system of 60 solvents, a set of up
to 4x60 molecular descriptors would be used. However, due to the
fact that these molecular descriptors represent certain unique
molecular characteristics, often only one or two molecular
descriptors are needed for most solvents. For example, alkanes are
hydrophobic and they are well represented with hydrophobicity, X,
alone. Alcohols are hybrids of hydrophobic segments and hydrophilic
segments and they are well represented with X and Z. Ketones,
esters, and ethers are polar molecules with varying degrees of
hydrophobic contents. They are well represented by X and Y's.
Hence, the needed set of molecular descriptors can be much smaller
than 4x60.
[0091] Determination of solvent molecular descriptors involves
regression of experimental VLE or LLE data for binary systems of
interested solvent and the above-mentioned reference molecules
(i.e., hexane, acetonitrile, and water) or their substitutes.
Solvent molecular descriptors are the adjustable parameters in the
regression. If binary data is lacking for the solvent with the
reference molecules, data for other binaries may be used as long as
the molecular descriptors for the substitute reference molecules
are already identified. In a way, these reference molecules can be
thought of as molecular probes that are used to elucidate the
interaction characteristics of the solvent molecules. These
molecular probes express the interactions in terms of binary phase
equilibrium data.
[0092] Table 3 lists the molecular descriptors identified for the
common solvents in the ICH list.
TABLE-US-00003 TABLE 3 Molecular Descriptors for Common Solvents.
Solvent name X Y- Y+ Z ACETIC-ACID 0.045 0.164 0.157 0.217 ACETONE
0.131 0.109 0.513 ACETONITRILE 0.018 0.131 0.883 ANISOLE 0.722
BENZENE 0.607 0.190 1-BUTANOL 0.414 0.007 0.485 2-BUTANOL 0.335
0.082 0.355 N-BUTYL-ACETATE 0.317 0.030 0.330
METHYL-TERT-BUTYL-ETHER 1.040 0.219 0.172 CARBON-TETRACHLORIDE
0.718 0.141 CHLOROBENZENE 0.710 0.424 CHLOROFORM 0.278 0.039 CUMENE
1.208 0.541 CYCLOHEXANE 0.892 1,2-DICHLOROETHANE 0.394 0.691
1,1-DICHLOROETHYLENE 0.529 0.208 1,2-DICHLOROETHYLENE 0.188 0.832
DICHLOROMETHANE 0.321 1.262 1,2-DIMETHOXYETHANE 0.081 0.194 0.858
N,N-DIMETHYLACETAMIDE 0.067 0.030 0.157 N,N-DIMETHYLFORMAMIDE 0.073
0.564 0.372 DIMETHYL-SULFOXIDE 0.532 2.890 1,4-DIOXANE 0.154 0.086
0.401 ETHANOL 0.256 0.081 0.507 2-ETHOXYETHANOL 0.071 0.318 0.237
ETHYL-ACETATE 0.322 0.049 0.421 ETHYLENE-GLYCOL 0.141 0.338
DIETHYL-ETHER 0.448 0.041 0.165 ETHYL-FORMATE 0.257 0.280 FORMAMIDE
0.089 0.341 0.252 FORMIC-ACID 0.707 2.470 N-HEPTANE 1.340 N-HEXANE
1.000 ISOBUTYL-ACETATE 1.660 0.108 ISOPROPYL-ACETATE 0.552 0.154
0.498 METHANOL 0.088 0.149 0.027 0.562 2-METHOXYETHANOL 0.052 0.043
0.251 0.560 METHYL-ACETATE 0.236 0.337 3-METHYL-1-BUTANOL 0.419
0.538 0.314 METHYL-BUTYL-KETONE 0.673 0.224 0.469 METHYLCYCLOHEXANE
1.162 0.251 METHYL-ETHYL-KETONE 0.247 0.036 0.480
METHYL-ISOBUTYL-KETONE 0.673 0.224 0.469 ISOBUTANOL 0.566 0.067
0.485 N-METHYL-2-PYRROLIDONE 0.197 0.322 0.305 NITROMETHANE 0.025
1.216 N-PENTANE 0.898 1-PENTANOL 0.474 0.223 0.426 0.248 1-PROPANOL
0.375 0.030 0.511 ISOPROPYL-ALCOHOL 0.351 0.070 0.003 0.353
N-PROPYL-ACETATE 0.514 0.134 0.587 PYRIDINE 0.205 0.135 0.174
SULFOLANE 0.210 0.457 TETRAHYDROFURAN 0.235 0.040 0.320
1,2,3,4-TETRAHYDRONAPHTHALENE 0.443 0.555 TOLUENE 0.604 0.304
1,1,1-TRICHLOROETHANE 0.548 0.287 TRICHLOROETHYLENE 0.426 0.285
M-XYLENE 0.758 0.021 0.316 WATER 1.000 TRIETHYLAMINE 0.557 0.105
1-OCTANOL 0.766 0.032 0.624 0.335
[0093] Among the ICH solvents, the molecular descriptors identified
for anisole, cumene, 1,2-dichloroethylene, 1,2-dimethoxyethane,
N,N-dimethylacetamide, dimethyl sulfoxide, ethyl formate, isobutyl
acetate, isopropyl acetate, methyl-butyl-ketone, tetralin, and
trichloroethylene were questionable, due to lack of sufficient
experimental binary phase equilibrium data. In fact, no public data
for methyl-butyl-ketone (2-hexanone) was found and its molecular
descriptors were set to be the same as those for
methyl-isobutyl-ketone.
[0094] The NRTL-SAC model with the molecular descriptors
qualitatively captures the interaction characteristics of the
solvent mixtures and the resulting phase equilibrium behavior.
FIGS. 4 to 6 contain three graphs illustrating the binary phase
diagrams for a water, 1,4-dioxane, and octanol system at
atmospheric pressure. The graphs illustrate the predictions of both
the NRTL model with the binary parameters in Table 1 and NRTL-SAC
models with the model descriptors of Table 3. FIG. 4 illustrates
the water, 1,4-dioxane mixture; FIG. 5 illustrates the water,
octanol mixture; and FIG. 6 illustrates the octanol, 1,4-dioxane
mixture. The predictions with the NRTL-SAC model are broadly
consistent with the calculations from the NRTL model that are
generally understood to represent experimental data within
engineering accuracy.
EXAMPLE 2
Model Prediction Results
[0095] Data compiled by Marrero and Abildskov provides a good
source of solubility data for large, complex chemicals. Marrero, J.
& Abildskov, J., Solubility and Related Properties of Large
Complex Chemicals, Part 1: Organic Solutes Ranging from C.sub.4 to
C.sub.40, CHEMISTRY DATA SERIES XV, DECHEMA, (2003). From that
applicants extracted solubility data for the 8 molecules reported
by Lin and Nash. Lin, H.-M. & R. A. Nash, An Experimental
Method for Determining the Hildebrand Solubility Parameter of
Organic Electrolytes, 82 J. PHARMACEUTICAL SCI. 1018 (1993). Also
tested, were 6 additional molecules with sizable solubility data
sets.
[0096] The NRTL-SAC model was applied to the solvents that are
included in Table 3. The molecular descriptors determined for the
solutes are summarized in Table 4. During the data regression, all
experimental solubility data, regardless of the order of magnitude,
were assigned with a standard deviation of 20%. The comparisons
between the experimental solubility and the calculated solubility
are given in FIGS. 7 to 20, which illustrate phase diagrams for the
systems at 298.15K and atmospheric pressure.
[0097] Good representations for the solubility data was obtained
with the NRTL-SAC model. The RMS errors in ln x for the fits are
given in Table 4.
TABLE-US-00004 TABLE 4 Molecular descriptors for solutes. RMS # of
error on Solute MW solvents T (K) X Y- Y+ Z lnK.sub.sp ln x
p-Aminobenzoic 137.14 7 298.15 0.218 0.681 1.935 0.760 -2.861 0.284
acid Benzoic acid 122.12 7 298.15 0.524 0.089 0.450 0.405 -1.540
0.160 Camphor 152.23 7 298.15 0.604 0.124 0.478 0.000 -0.593 0.092
Ephedrine 165.23 7 298.15 0.458 0.068 0.000 0.193 -0.296 0.067
Lidocaine 234.33 7 298.15 0.698 0.596 0.293 0.172 -0.978 0.027
Methylparaben 152.14 7 298.15 0.479 0.484 1.218 0.683 -2.103 0.120
Testosterone 288.41 7 298.15 1.051 0.771 0.233 0.669 -3.797 0.334
Theophylline 180.18 7 298.15 0.000 0.757 1.208 0.341 -6.110 0.661
Estriol 288.38 .sup. 9.sup.a 298.15 0.853 0.000 0.291 1.928 -7.652
0.608 Estrone 270.37 12 298.15 0.499 0.679 1.521 0.196 -6.531 0.519
Morphine 285.34 6 308.15 0.773 0.000 0.000 1.811 -4.658 1.007
Piroxicam 331.35 14.sup.b 298.15 0.665 0.000 1.803 0.169 -7.656
0.665 Hydrocortisone 362.46 11.sup.c 298.15 0.401 0.970 1.248 0.611
-6.697 0.334 Haloperidol 375.86 13.sup.d 298.15 0.827 0.000 0.000
0.131 -4.398 0.311 .sup.aWith THF excluded. .sup.bWith 1,2
dichloroethane, chloroform, diethyl ether, and DMF excluded.
.sup.cWith hexane excluded. .sup.dWith chloroform and DMF
excluded.
[0098] K.sub.sp, the solubility product constant, corresponds to
the ideal solubility (in mole fraction) for the solute. The quality
of the fit reflects both the effectiveness of the NRTL-SAC model
and the quality of the molecular descriptors identified from the
limited available experimental data for the solvents.
[0099] FIGS. 7, 8, 9, 10, 11, 12, 13, and 14 include graphs
illustrating the experimental solubilities vs. calculated
solubilities for p-aminobenzoic acid, benzoic acid, camphor,
ephedrine, lidocaine, methylparaben, testosterone, and
theophylline, respectively, in various solvents at 298.15K. The
various solvents used were selected from a group of 33 solvents,
including acetic acid, acetone, benzene, 1-butanol, n-butyl
acetate, carbon tetrachloride, chlorobenzene, chloroform,
cyclohexane, 1,2-dichloroethane, dichloromethane,
1,2-dimethoxyethane, N,N-dimethylformamide, dimethyl-sulfoxide,
1,4-dioxane, ethanol, 2-ethoxyethanol, ethyl acetate, ethylene
glycol, diethyl ether, formamide, n-heptane, n-hexane, isopropyl
acetate, methanol, methyl acetate, 1-pentanol, 1-propanol,
isopropyl alcohol, tetrahydrofuran, toluene, water, and 1-octanol.
The experimental solubility data was represented well with the
NRTL-SAC model.
[0100] FIG. 15 includes a graph illustrating the experimental
solubilities vs. calculated solubilities for estriol in 9 solvents
at 298.15K. The experimental solubility data was represented well
with the NRTL-SAC model. The data for tetrahydrofuran is found to
be a very significant outlier and it is not included in the 9
solvents shown in FIG. 15.
[0101] FIG. 16 includes a graph illustrating the experimental
solubilities vs. calculated solubilities for estrone in various
solvents at 298.15K. The experimental solubility data was
represented well with the NRTL-SAC model.
[0102] FIG. 17 includes a graph illustrating the experimental
solubilities vs. calculated solubilities for morphine in 6 solvents
at 308.15K. Cyclohexane and hexane were outliers. They are very low
solubility solvents for morphine and the quality of the data is
possibly subject to larger uncertainties.
[0103] FIG. 18 illustrates a graph of the experimental solubilities
vs. calculated solubilities for piroxicam in 14 solvents at
298.15K. 1,2-dichloroethane, chloroform, diethyl ether, and
N,N-dimethylformamide (DMF) were found to be major outliers and are
not included in the 14 solvents shown in FIG. 18. Interestingly,
Bustamante, et al. also reported 1,2-dichloroethane, chloroform,
and diethyl ether as outliers in their study based on solubility
parameter models. P. Bustamante, et al., Partial Solubility
Parameters of Piroxicam and Niflumic Acid, 1998 INT. J. OF PHARM.
174, 141.
[0104] FIG. 19 illustrates a graph of the experimental solubilities
vs. calculated solubilities for hydrocortisone in 11 solvents at
298.15K. Hexane is excluded because of the extreme low solubility
of hydrocortisone in hexane which could possibly subject the data
to larger uncertainty.
[0105] FIG. 20 illustrates a graph of the experimental solubilities
vs. calculated solubilities for haloperidol in 13 solvents at
298.15K. Haloperidol showed unusually high solubilities in
chloroform and DMF and these two solvents are not included in the
13 solvents.
[0106] The average RMS error on ln x for the predictions vs.
experimental solubility data in Table 4 is 0.37. This corresponds
to about .+-.45% accuracy in solubility predictions.
[0107] Experiment 3: Comparison of NRTL-SAC Model to Prior Art
Methods for Pharmaceutical Components
[0108] The solubilities of various pharmaceutical compounds was
modeled with the NRTL-SAC approach of the present invention as well
as some prior art models (e.g., the Hanson model and the UNIFAC
model) to compare their relative accuracies. The pharmaceutical
compounds used included VIOXX.RTM., ARCOXIA.RTM., Lovastatin,
Simvastatin, FOSAMAX.RTM.. (Available from Merck & Co., Inc.,
Whitehouse Station, N.J.). The solvents used included water,
N,N-Dimethylformamide ("DMF"), 1-propanol, 2-propanol, 1-butanol,
toluene, Chloro-benzene, acetonitrile, ethyl acetate, methanol,
ethanol, heptane, acetone, and triethylamine (TEA).
[0109] Saturated solutions of the compounds in the solvents were
allowed to equilibrate for at least 48 hours. Supernatant fluid was
filtered and diluted, and a high pressure liquid chromatography
(HPLC) concentration analysis was performed to compare the
predicted solubility values with actual solubility values.
[0110] The NRTL-SAC model of the present invention gave a RMS error
on ln x of about 0.5 (i.e., an accuracy and predictive capability
of .+-..about.50%), while the Hansen model had a RMS error on ln x
of more than 0.75 and the UNIFAC model had a RMS error on In x of
more than 1.75. Additional comparisons were made for
dual-solvent/pharmaceutical systems, and acceptable predictions
were obtained from the NRTL-SAC model of the present invention.
[0111] These experiments show that the NRTL-SAC model is a simple
correlative activity coefficient equation that requires only
component-specific molecular descriptors (i.e., conceptual
segments). Conceptually, the approach suggests that a practitioner
account for the liquid ideality of both small solvent molecules and
complex pharmaceutical molecules in terms of component-specific
molecular descriptors (e.g., hydrophobicity, polarity, and
hydrophilicity). In practice, these molecular descriptors become
the adjustable parameters that are determined from selected
experimental data. With the development of molecular descriptors
for solvents and organic solutes, engineering calculations can be
performed for various phase equilibrium studies, including
solubilities in solvents and solvent mixtures for solvent
selection. The NRTL-SAC model provides good qualitative
representation on phase behaviors of organic solvents and their
complex pharmaceutical solutes and it offers a practical predictive
methodology for use in pharmaceutical process design.
[0112] While this invention has been particularly shown and
described with references to preferred embodiments thereof, it will
be understood by those skilled in the art that various changes in
form and details may be made therein without departing from the
scope of the invention encompassed by the appended claims.
* * * * *