Oliver L Watson1, Suela Jonuzaj1, John McGinty2, Jan Sefcik2, Amparo Galindo1, George Jackson1, Claire S Adjiman1. 1. Department of Chemical Engineering, Centre for Process Systems Engineering, Institute for Molecular Science and Engineering and EPSRC Future Manufacturing Hub in Continuous Manufacturing and Advanced Crystallisation, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K. 2. EPSRC Future Manufacturing Hub in Continuous Manufacturing and Advanced Crystallisation, Department of Chemical and Process Engineering, University of Strathclyde, 75 Montrose Street, Glasgow G1 1XJ, U.K.
Abstract
Choosing a solvent and an antisolvent for a new crystallization process is challenging due to the sheer number of possible solvent mixtures and the impact of solvent composition and crystallization temperature on process performance. To facilitate this choice, we present a general computer aided mixture/blend design (CAMbD) formulation for the design of optimal solvent mixtures for the crystallization of pharmaceutical products. The proposed methodology enables the simultaneous identification of the optimal process temperature, solvent, antisolvent, and composition of solvent mixture. The SAFT-γ Mie group-contribution approach is used in the design of crystallization solvents; based on an equilibrium model, both the crystal yield and solvent consumption are considered. The design formulation is implemented in gPROMS and applied to the crystallization of lovastatin and ibuprofen, where a hybrid approach combining cooling and antisolvent crystallization is compared to each method alone. For lovastatin, the use of a hybrid approach leads to an increase in crystal yield compared to antisolvent crystallization or cooling crystallization. Furthermore, it is seen that using less volatile but powerful crystallization solvents at lower temperatures can lead to better performance. When considering ibuprofen, the hybrid and antisolvent crystallization techniques provide a similar performance, but the use of solvent mixtures throughout the crystallization is critical in maximizing crystal yields and minimizing solvent consumption. We show that our more general approach to rational design of solvent blends brings significant benefits for the design of crystallization processes in pharmaceutical and chemical manufacturing.
Choosing a solvent and an antisolvent for a new crystallization process is challenging due to the sheer number of possible solvent mixtures and the impact of solvent composition and crystallization temperature on process performance. To facilitate this choice, we present a general computer aided mixture/blend design (CAMbD) formulation for the design of optimal solvent mixtures for the crystallization of pharmaceutical products. The proposed methodology enables the simultaneous identification of the optimal process temperature, solvent, antisolvent, and composition of solvent mixture. The SAFT-γ Mie group-contribution approach is used in the design of crystallization solvents; based on an equilibrium model, both the crystal yield and solvent consumption are considered. The design formulation is implemented in gPROMS and applied to the crystallization of lovastatin and ibuprofen, where a hybrid approach combining cooling and antisolvent crystallization is compared to each method alone. For lovastatin, the use of a hybrid approach leads to an increase in crystal yield compared to antisolvent crystallization or cooling crystallization. Furthermore, it is seen that using less volatile but powerful crystallization solvents at lower temperatures can lead to better performance. When considering ibuprofen, the hybrid and antisolvent crystallization techniques provide a similar performance, but the use of solvent mixtures throughout the crystallization is critical in maximizing crystal yields and minimizing solvent consumption. We show that our more general approach to rational design of solvent blends brings significant benefits for the design of crystallization processes in pharmaceutical and chemical manufacturing.
More
than 80% of small-molecule pharmaceuticals are delivered in
a solid form,[1] such as tablets and aerosols;
because of this, pharmaceutical production is dependent on effective
crystallization systems. The properties of the crystal influence not
only the efficacy of the final drug product—absorption and
bioavailability—but also the degree of downstream processing
required due to the dependence of process performance on solid-state
characteristics such as flowability and compressibility.[2] Experience dictates that the majority of industrial
crystallizers are solvent-based,[3] in particular,
due to the relative ease of operation of such units. Hence, the choice
of solvent, or solvents, can drastically affect the outcome and efficiency
of the crystallization process.Thermodynamically, this impact
is seen in changes to the solubility
of the active pharmaceutical ingredient (API), which affects both
the potential crystal yield of the API and the total volume of solvent
required to perform a crystallization. These effects can be observed
by changing the compound used as a solvent or when solvent mixtures
are employed. Indeed, with binary mixtures, it may be possible to
engineer beneficial properties, such as higher API solubility, that
cannot be achieved in either of the pure solvent alone.[4] Exploiting the enhanced performance of mixtures,
however, raises many challenges for solvent selection.The possibility
of selecting a pair of solvents brings the choice
of crystallization techniques to be considered into question; cooling
crystallization, antisolvent crystallization, hybrid approaches, and
evaporative crystallization can all be practical under the correct
conditions, although the latter is not often utilized for industrial-scale
processes. Which techniques are the potential solvents compatible
with and how does the choice of solvent influence the feasible process
conditions? The solvent mixture cannot be allowed to freeze or evaporate
during crystallization, so bounds must be placed on the range of operating
temperature. Similarly, the formation of two immiscible liquid phases,
which may occur at certain solvent ratios, must be avoided, so the
composition of solvent blends must be appropriately constrained. Beyond
this, there may be health or safety concerns regarding the solvent
choice[5] or impurities within the mixture
that need to be removed.It is estimated that only 1 in every
5000 new API molecules discovered
successfully completes all phases of clinical testing and progresses
to market and only 1 in 25,000 recoups the initial investment.[6] As a consequence, there are cost, material, time,
and human resource constraints to contend with when developing potential
pharmaceutical manufacturing processes. Nevertheless, solvent selection
for crystallization systems is currently performed via time-consuming and expensive experiments, requiring significant
materials and personnel commitments, and is heavily reliant on past
experience and rules of thumb.[7] Consequently,
the full range of solvent mixtures and process conditions cannot be
completely explored, and more effective crystallization systems may
be overlooked.To address these issues, a number of pharmaceutical
companies have
produced solvent selection guides, categorizing solvents based on
health, safety, and environmental (HSE) concerns;[8−10] an assessment
of such guides has been published by the CHEM21 consortium.[11] Whilst this approach has the benefit of being
easily accessible to any scientist in a lab setting, the large volume
of information presented in such documents often makes well-informed
decisions difficult.To overcome this shortcoming, Diorazio et al.(12) have developed a computer-based
tool to account
for process requirements and desired solvent properties, as well as
HSE considerations, ultimately yielding a diverse shortlist of suitable
solvent candidates from a much larger solvent pool. Critically, this
removes some of the human decision-making inherent in previous guides,
and benefits from being able to compare newer, “green”
solvents to those used historically. By using experimental data, supplemented
by property prediction tools, a principal component analysis (PCA)
model has been proposed, providing a more interactive, graphical interface
to visualize correlations between experimental properties and computed
descriptors. However, whilst this approach is superior to previous
solvent-selection guides, the manufacturing process is not modeled
directly, instead relying on the assumption that certain combinations
of physical properties will deliver the desired performance, which
may not always be accurate.[13]Over
the last decades, computer-aided molecular design (CAMD) methods[14,15] have been developed with the aim of guiding lab-based experiments
toward optimal candidate molecules—in this case, crystallization
solvents. These approaches are based on specific, process-derived
objectives, such as maximizing crystal yield[16] or minimizing solvent consumption,[17] rather
than on the physical properties of solvents, removing ambiguity from
the design of solvent systems. Thousands of potential molecular structures
are considered in CAMD problems, providing millions of possible mixture
combinations and often leading to the design of novel molecules and
blends. To avoid being overwhelmed by the number of possible solutions,
decomposition-based solution approaches have been proposed,[18] whereby smaller subproblems are posed and solved
sequentially.In a crystallization context, most existing methodologies
have
utilized a decomposition approach. First, a crystallization technique
is selected, usually limiting the design to cooling crystallization
in a single solvent or antisolvent crystallization operating isothermally.
In both cases, the problem is centered around designing a single solvent—either
the cooling crystallization solvent or the antisolvent given an initial
solvent. Following this, the operating conditions are fixed, reducing
the number of variables considered in the design problem, whilst also
providing a means to reduce the number of solvents being considered
based on their melting and boiling points. Ultimately, the objective
of such an approach is to select or design a single solvent that will
optimize a given criterion, such as crystal yield.[19] Unfortunately, problem decomposition approaches may also
lead to the screening out optimal solvents and solvent blends.[20]More integrated problems, in which cooling
and antisolvent effects
are treated simultaneously and solvent mixtures are considered throughout,[21] have not yet received significant attention.
This is likely due to the complexity of formulating and solving a
mixed-integer optimization problem to represent these design choices;
such problems result in challenging nonconvex feasible regions for
the continuous variables, in addition to the combinatorial growth
in the solution space as more pure solvents and solvent blends are
considered. Nevertheless, investigating such approaches is advantageous
not only because an increased range of solvents is investigated but
also because they offer the opportunity to optimize the process so
that the best possible performance is derived from the solvent.In cooling crystallization, lowering the temperature of the solvent-API
mixture produces the driving force for crystallization. Intuitively,
maximizing the difference between the initial and final operating
temperatures should therefore maximize the reduction in the solubility
of the API, thus leading to the highest possible crystal yield. However,
the temperature range cannot be made arbitrarily large, due to the
freezing and boiling points of the solvents present—their liquid
range. As such, whilst fixing the initial and final temperature of
the system removes two degrees of freedom from the problem, the choice
of fixing the temperature range will also screen out any solvent from
the design problem that has a liquid range outside of the set temperature
range. Because higher process temperatures eliminate the opportunity
to select more volatile, but potentially powerful, solvents, whilst
also leading to higher energy costs, it may not always be optimal
to begin the crystallization at the highest allowable operating temperature;
optimal solutions may be overlooked when fixing the crystallization
temperature during solvent selection.Similarly, the approach
taken in the antisolvent design workflow
may obstruct the useful application of solvent blends and the nonlinear
solubility behavior that they can promote. One such example is the
solubility of paracetamol. It is well understood that paracetamol
is only sparingly soluble in water; despite this, the addition of
water to pure acetone initially increases the solubility of paracetamol
in the mixture.[4] Indeed, whilst the solubility
of paracetamol in pure acetone and pure water is 94.5 and 14.0 g/kg,
respectively, it is possible to achieve a solubility that is at least
4.5 times larger than in pure acetone by considering a 70:30 mixture
by mass of acetone and water (at 296.15 K). If one were to attempt
an antisolvent crystallization process by starting with pure acetone,
as is typical in a decomposition-based approach, a much greater volume
would be required to generate supersaturation; at low water volumes,
the paracetamol would simply be diluted by the addition of water,
resulting in lost capacity of the crystallizer. However, by considering
all possible compositions of acetone and water to dissolve the required
quantity of paracetamol and thus starting from an elevated solubility
of paracetamol, water can then be used as a powerful antisolvent to
achieve both a high crystal yield and a lower solvent consumption.Furthermore, a hybrid crystallization technique that integrates
cooling and antisolvent crystallization can provide additional benefits.
Operating at a higher initial temperature makes use of the higher
API solubility, reducing solvent consumption and increasing crystal
yield following the subsequent reduction in temperature and addition
of antisolvents. As such, the design of integrated crystallization
methods, where cooling and antisolvent techniques can be applied simultaneously,
is important for improving the efficiency of the crystallization process.
This has been investigated in more general computer-aided mixture/blend
design (CAMbD) formulations, where a “generate-and-test”
methodology has been applied[22] to solve
the problem, screening all possible solvent combinations. Whilst this
improves the likelihood of finding a globally optimal solution to
the solvent design problem, the computational time increases rapidly
with the number of solvent candidates considered; 10 potential solvents
result in only 45 binary solvent mixtures, but a list of 100 solvents
gives 4950 possible combinations. Physical insights could be used
to reduce the number of options, for example, by only pairing solvents
from different families—such as aliphatics, alcohols, and acetates—but
the design space would nevertheless remain intractably large. As such,
“generate-and-test” approaches have limited flexibility
for larger numbers of solvents; trailling a number of different design
objectives, or different process constraints, may not be feasible.Recently, the use of generalized disjunctive programming (GDP)[23] within the CAMbD framework—used
to formulate logical constraints as mathematical expressions in the
optimization problem—has been proposed,[24] showing that solvent blends can provide optimal conditions
to maximize the solubility of active pharmaceutical ingredients.[25] This concept has been further developed by Watson et al.,[21] where integrated techniques
for crystallization have been explored and optimized. The promising
results obtained warrant further development of comprehensive CAMbD formulations.In our current paper, a CAMbD formulation for the design
of integrated crystallization solvent systems (without evaporation)
is proposed, whereby the identities of the solvent and antisolvent
molecules are optimized, alongside their compositions and the process
operating temperatures. This overcomes the potential limitations in
the current decomposition-based approaches. The design formulation
is implemented in gPROMS and applied to the crystallization of lovastatin
and of ibuprofen, whereby the effects of crystallization technique,
process temperature, and solvent specification are explored.
Methodology
The CAMbD problem is based on a generic formulation
for the design of integrated crystallization solvent systems, whereby
optimal solvent and antisolvent molecules (s1 and s2, respectively), their compositions, and the process temperatures
are identified. The approach to design focusses on the thermodynamic,
rather than kinetic, aspects of crystallization, and hence, only information
about the initial and final states of the system is required, as illustrated
in Figure . In the
initial state (Figure a), all of the API, nAPI,0L (mol), is dissolved in the initial solvent
blend, comprising of moles of s1 and moles of s2, at a temperature T0 (K), producing a saturated solution. The process
conditions are adjusted to generate the driving force for crystallization
and reach the final state of the system (Figure b)), assumed to be the point when solid–liquid
equilibrium (SLE) is reached between the nAPIC moles of API
crystals and the remaining API dissolved in the final solvent mixture,
consisting of nAPIL moles of API, moles
of s1, and moles of s2, at a final temperature T. It is assumed that there is no solvent loss so and .
Figure 1
The crystallization process,
as described in the general formulation.
From left to right, the process transitions from (a) the initial state
(subscript 0), where the solvent blend is saturated with the API solute
but no crystals are present, to (b) the final state, generating a
solid phase of API by reducing the operating temperature by ΔT = T0 – T, by introducing additional moles of antisolvent , or by doing both. In (b), the final solvent
mixture is also saturated with the API solute, which is in a state
of solid–liquid equilibrium. Here, niϕ denotes
the moles of component i in phase ϕ ∈{L, C}, where L
and C refer to the liquid and crystal phases, respectively. The API
is assumed to be the only component in solid–liquid equilibrium,
which is a function of temperature T, pressure P, and liquid composition L. Impurities in the mixture are assumed to be negligible.
The crystallization process,
as described in the general formulation.
From left to right, the process transitions from (a) the initial state
(subscript 0), where the solvent blend is saturated with the API solute
but no crystals are present, to (b) the final state, generating a
solid phase of API by reducing the operating temperature by ΔT = T0 – T, by introducing additional moles of antisolvent , or by doing both. In (b), the final solvent
mixture is also saturated with the API solute, which is in a state
of solid–liquid equilibrium. Here, niϕ denotes
the moles of component i in phase ϕ ∈{L, C}, where L
and C refer to the liquid and crystal phases, respectively. The API
is assumed to be the only component in solid–liquid equilibrium,
which is a function of temperature T, pressure P, and liquid composition L. Impurities in the mixture are assumed to be negligible.From this description, two key design objectives—API
crystal
yield and solvent consumption—can be considered, without knowledge
of the specific path taken between the initial and final state. In
the proposed formulation, the use of solvent blends in both the initial
and final states of the system is permitted, provided that the blends
consist of the same two solvent molecules, the “solvent”
s1 and the “antisolvent” s2, in
different proportions. It is then possible to exploit an enhanced
solubility in the initial blend,[4] reducing
the volume of solvent required to dissolve the required quantity of
API, followed by an extreme reduction in API solubility through the
addition of more antisolvent, thus achieving larger crystal yields
than when starting with a pure solvent. Additionally, concurrent cooling
and antisolvent crystallization are permitted within the design, utilizing
the benefits of both crystallization techniques in the optimization,
as well as the potential synergistic interactions between the two
modes of operation.To be readily applicable to the pharmaceutical
industry and to
facilitate the rapid deployment of novel drug molecules, the proposed
methodology is based on a “plug-and-play” approach;
users can input their chosen API, specify lists of potential solvent
candidates, and adjust the objectives of the optimization problem
quickly and easily. The optimization problem can be split into the
three main sections depicted in Figure —model equations, optimization variables, and
the optimization itself—to generate optimal solvent blends
and process conditions to suit the user’s needs.
Figure 2
Overview of
the structure of the solvent design framework. In “Block
I: Optimization variables”, two sets of optimization variables
are defined: the process conditions (operating temperatures and solvent
composition) and the choice of solvent and antisolvent. In “Block
II: Model equations”, the general model is described by five
sets of equations: the objective function; the thermodynamic model
consists of SAFT-γ Mie, to calculate the thermodynamic properties
of the liquid phases, and the SLE model to predict the solubility
of the API; solvent assignment constraints; the process model; and
design constraints that exclude impractical solutions or set design
targets. This information is combined in “Block III: Optimization”
to obtain the MINLP to be solved, outputting the optimal process temperature,
solvent blend, and blend composition for the initial and final state
of the crystallization. Additional calculations are performed in “Block
IV: Post-optimization analysis” to determine whether the resulting
ternary mixture exhibits liquid–liquid equilibria (LLE). If
so, additional process constraints are imposed for that specific solvent
blend and the optimization is re-run.
Overview of
the structure of the solvent design framework. In “Block
I: Optimization variables”, two sets of optimization variables
are defined: the process conditions (operating temperatures and solvent
composition) and the choice of solvent and antisolvent. In “Block
II: Model equations”, the general model is described by five
sets of equations: the objective function; the thermodynamic model
consists of SAFT-γ Mie, to calculate the thermodynamic properties
of the liquid phases, and the SLE model to predict the solubility
of the API; solvent assignment constraints; the process model; and
design constraints that exclude impractical solutions or set design
targets. This information is combined in “Block III: Optimization”
to obtain the MINLP to be solved, outputting the optimal process temperature,
solvent blend, and blend composition for the initial and final state
of the crystallization. Additional calculations are performed in “Block
IV: Post-optimization analysis” to determine whether the resulting
ternary mixture exhibits liquid–liquid equilibria (LLE). If
so, additional process constraints are imposed for that specific solvent
blend and the optimization is re-run.
Block
I: Optimization Variables
The first group of
optimization variables is a set of discrete variables that represent
the selection of the solvent and antisolvent molecules (s1 and s2 respectively) that constitute the solvent blend.
These are chosen from a list of possible solvent candidates supplied
by the user, denoted by the set NS, and
are represented mathematically by the binary (0, 1) variables yii,, where ii is either s1 or s2, and j is selected from NS. During the optimization, each combination
of candidate solvents s1 and s2 can be switched
on or off. For example, if acetone were selected as the solvent, and
water as the antisolvent, this would correspond to ys = 1 and ys = 1, with all other combinations being
switched off (i.e., the relevant binary variables
are set to zero).The remaining variables represent the process
conditions within the crystallizer—the initial and final temperatures
of the crystallization process, T0 and T, respectively, along with the initial and final compositions
of the binary solvent mixture, and ,
where the superscript S refers to the
fact that only the solvent/antisolvent is included in this binary
mixture, and the final number of moles of antisolvent present, . By defining the number
of moles of antisolvent,
in conjunction with the final composition of the binary solvent mixture,
this also defines the total number of moles of solvent in the system.It should be noted that, within the general formulation, there
is no specific variable to represent the selection of a crystallization
technique. Instead, the optimal technique, or combination of techniques,
is an inherent outcome of the optimization problem. For instance,
if a higher crystal yield can be obtained from simply cooling a solvent–API
mixture, compared to cooling and adding antisolvent to the mixture,
then the optimization solver will return cooling crystallization,
and not hybrid crystallization, as a solution: the number of added
moles of antisolvent added, denoted here as , will be zero and the initial and final
temperatures will be different. Thus, there is an opportunity to generate a solution that represents cooling crystallization,
or antisolvent crystallization, or a hybrid of the two techniques,
without the need to specify this a priori. Equivalently,
in situations where the use of a pure solvent outperforms a solvent
mixture, the mole fraction of
the second solvent is found to be zero
throughout the crystallization. If required, the user can introduce
additional constraints to limit the crystallization to a single technique;
these are discussed in the case studies.The composition of
the binary solvent mixture is simply bounded
by the definition of mole fractionwith other constraints ensuring that solvent
s1 is always present.The bounds placed upon the
process temperature are less obviously
defined. In practice, there will always be upper and lower limits
to the operating temperature, Tmax and Tmin:The values of these bounds are set based on
the practicality and feasibility of the given crystallization process.
For example, certain pharmaceutical molecules may degrade at high
temperatures, the safety procedures in place for a crystallization
vessel may not be sufficient for temperatures above a specific threshold,
or it may be too costly to cool the solvent-API mixture below the
temperature of standard cooling water.Whilst there is a clear
physical lower bound to the final number
of moles of antisolvent in the solvent mixture, there cannot be a
negative number of molesit is likely that this value will also be
bounded by the design constraints, such as the maximum or minimum
limit of solvent consumption or the condition preventing evaporative
crystallization (eq ).
Block II: Model Equations
Objective Function
“Block II: Model equations”
in Figure defines
the set of equations that are required to calculate the objective
function—in our work, the focus is on maximizing the crystal
yield of the API, YAPIwhere miϕ refers to the mass of component
i in phase ϕ, either the liquid phase (L) or the crystal phase
(C), and subscript “0” refers to the initial state throughout.The choice of objective of the optimization problem is flexible,
however, and eq can
be interchanged with other functions, such as the minimization of
solvent consumption χs (g of solvent per g of API),
or Vs (mL of solvent per g of API):where the total liquid volume is denoted by VL (in L) and is calculated through the thermodynamic
model.
Thermodynamic Model
So that the objective function
can be computed, the relationship between the properties of interest
and the temperature, pressure, and composition of the liquid mixture
and the API must be determined. Because the API in the liquid phase
is assumed to be at equilibrium with the crystal phase, the thermodynamic
properties of the solvent-API mixture are required in order to predict
the API solubility. In our work, the statistical associating fluid
theory (SAFT) is selected. Specifically, the group-contribution (GC)
version of the equation of state (EoS) based on the Mie potential,
SAFT-γ Mie,[26] is employed. For the
SAFT-γ Mie group parameters used throughout this work, refer
to Tables −10 in the Appendix.
Table 8
Like-Group Parameter Values for Use
within the SAFT-γ Mie Group-Contribution Approacha
k
group k
vk
Sk
λkkr
λkka
σkk/Å
(ϵkk/kB)/K
Nst,k
nk,H
nk,e1
nk,e2
1
CH3
1
0.57255
15.050
6.0000
4.0773
256.77
2
CH2
1
0.22932
19.871
6.0000
4.8801
473.39
3
CH
1
0.072100
8.0000
6.0000
5.2950
95.621
4
CH2=
1
0.44890
20.271
6.0000
4.3175
300.90
5
CH=
1
0.20037
15.974
6.0000
4.7488
952.54
6
cCH2
1
0.24751
20.386
6.0000
4.7852
477.36
7*
CH2OH
2
0.58538
22.699
6.0000
3.4054
407.22
2
1
2
0
8*
CHOH
1
0.37926
18.185
6.0000
4.5381
599.66
2
1
2
0
9
COO
1
0.65264
31.189
6.0000
3.9939
868.92
1
0
2
0
10
CH3COCH3
3
0.72135
17.433
6.0000
3.5981
286.02
3
1
1
1
11
H2O
1
1.0000
17.020
6.0000
3.0063
266.68
2
2
2
0
v, S, and σ are the
number of segments in group k, the segment shape
factor, and the segment diameter, respectively;
λkkr and
λa are the repulsive and attractive exponents,
and ϵ is the dispersive energy
of the Mie potential characterizing the interaction of two k groups; Nst, is the number of association site types on group k, and n, n, and n are the numbers
of association sites of types H, e1, and e2,
respectively. Rows marked with an asterisk contain parameter values
introduced in our current work. The parameter values for groups without
an asterisk are taken directly from Dufal et al.(54)
Table 10
Group–Group Association Energies
and Bonding Volume Parameter Values for Use within the SAFT-γ
Mie Group-Contribution Approacha
k
l
group k
site a of group k
group l
site b of group l
(ϵkl,abHB/kB)/K
Kkl,ab/Å3
7*
7
CH2OH
H
CH2OH
e1
2097.9
62.309
7*
8
CH2OH
H
CHOH
e1
2500.0
10.444
7*
8
CH2OH
e1
CHOH
H
1464.1
591.55
7*
10
CH2OH
H
CH3COCH3
e1
1844.8
991.95
7*
10
CH2OH
e1
CH3COCH3
H
686.93
585.99
7*
11
CH2OH
H
H2O
e1
621.28
425.00
7*
11
CH2OH
e1
H2O
H
2153.2
147.40
8*
8
CHOH
H
CHOH
e1
2480.6
8.4740
8*
10
CHOH
H
CH3COCH3
e1
1186.9
731.08
8*
10
CHOH
e1
CH3COCH3
H
1323.1
635.37
8*
11
CHOH
H
H2O
e1
2289.1
63.813
8*
11
CHOH
e1
H2O
H
2140.9
19.478
9
11
COO
e1
H2O
H
1245.81
454.98
10
10
CH3COCH3
H
CH3COCH3
e1
980.20
2865.2
10
11
CH3COCH3
H
H2O
e1
1386.8
188.83
10
11
CH3COCH3
e1
H2O
H
1588.7
772.77
10
11
CH3COCH3
e2
H2O
H
417.24
1304.3
11
11
H2O
H
H2O
e1
1985.4
101.69
ϵHB is the association energy of the Mie potential
characterizing the
interaction of site a of group k and site b of group l, and K is the
bonding-volume parameter for such an interaction. Rows marked with
an asterisk contain parameter values introduced in our current work,
which will be the subject of a future paper. The parameter values
for groups without an asterisk are taken directly from Dufal et al.(54)
The use of GC methods within the thermodynamic model supports a “plug-and-play”
approach, allowing the user to describe the relevant API and solvent
molecules in terms of functional-group “building blocks”.
The thermodynamic model is not necessarily limited to molecules for
which experimental data are readily available. Hutacharoen et al.,[27] Di Lecce et
al.,[28] Febra et al.,[29] and Haslam et al.(30) have recently shown that, thanks to
the rigorous thermodynamic concepts that the SAFT-γ Mie EoS,
the thermodynamic platform can provide high-quality predictions of
the solubility of pharmaceutical compounds in a range of solvents,
as well as liquid–liquid and vapor–liquid equilibria,
all key properties for industrial applications.As the formulation
of the crystallization process is based on an
equilibrium model—both the initial and final states of the
system denote solvent blends saturated with API solute (Figure )—it is necessary to
be able to predict the solubility of the API under all possible process
conditions. It is assumed that only the API undergoes a phase change.
The process operating temperature is prevented from approaching the
melting temperatures of the solvent and antisolvent via constraints specified later in this section, and it is assumed that
no solvates.Thus, the solubility of the API in a solvent blend
is determined
fromwhere
γAPI,0L (γAPIL) is the liquid-phase activity coefficient
of the API in the initial (final) liquid phase, calculated with SAFT-γ
Mie as a function of T0 (T), the initial (final) process operating temperature, P0 (P), the initial (final) pressure,
and xi,0L (xiL), i ∈ {API, s1, s2}, the initial (final) liquid-phase mole fractions; TAPIm is the melting temperature and ΔHAPIm the enthalpy
of melting of the API, which are assumed to be known beforehand, preferably
from experiments; is
the difference in the isobaric specific
heat capacity of the API between the solid and liquid phase.The entropic contribution in the SLE equations, given by the last
term in eqs and 7 and expressed in terms of the heat capacity difference,
is often ignored[16] under the assumption
that the two integrals in eq or in eq are
approximately equal or that the heat capacity difference is close
to zero. However, this contribution has been shown to have a significant
impact in certain cases,[31−33] which cannot necessarily be identified a priori, so we include it here. It can be omitted when
the required heat capacity data are not available.
Solvent Assignment
Constraints
A number of logical
constraints are imposed on the binary variables representing the choice
of solvent, namely:both solvent
and antisolvent should each consist of
one solvent candidate onlyno
solvent candidate should be used as both solvent
and antisolventFurthermore, it is
necessary for the
binary variables yii, to be combined with a description of the candidate molecule, j,
in question. To this end, each solvent candidate is defined as a combination
of functional groups, selected from a database, expressed by the parameter
ν, where k is a functional group
in set NFG. For instance, heptane would
comprise two CH3 groups and five CH2 groups
(νheptane,CH = 2 and νheptane,CH = 5, respectively). The solvents s1 and
s2 are then defined in terms of these functional groups
as followswhere ν̃ii,k is the
number of functional group k present in solvent ii.
Process Model
For a successful crystallization, it
is clear that the mass of the API solute in the final state should
be lower than that in the initial state, in order to transfer solute
into the crystal phase. As such, mass balances are performed on the
initial and final states of the system, subject to the thermodynamic
equilibrium between the solid and liquid phases (eqs and 7). First, the
mole fractions are related to mole numbers as followsNext, the number
of moles of solvents
s1 and s2 in the initial and final states of
the system are connected:The
moles nAPIC of crystal produced can be calculated by taking
the difference between the number of moles of the API solute in the
initial state and in the final state.A simple conversion factor can be used to
determine the crystal mass, mAPIC, by using the molecular weight
of the API in question, MAPI
Design Constraints
Having selected
an objective function,
one can then specify additional constraints on the process and solvents,
beyond those already defined within the process model. For instance,
in an optimization problem aiming to maximize crystal yield of the
API, one may decide to limit the solvent consumption to no more than
a specified level. Alternatively, if the intention of the optimization
is to design a more environmentally sustainable crystallization process,
one could minimize solvent consumption, but ensure that the crystal
yield is greater than a minimum level, for example, 90%. Further heuristic
constraints can be included for this purpose too; for instance, experience
may dictate that operating below 4 mL solvent/(g crystal) is likely
to lead to an inoperable process due to high viscosity and shear forces,
so the specific volume of solvent can be bounded by this value, preventing
the optimization from reducing the total volume of solvent beyond
feasible physical limits.Whilst certain solvent blends may
produce mathematically optimal results with respect to API crystal
yield or solvent consumption, it is also important to understand whether
a solvent pairing is feasible under the selected process conditions.
Three key conditions must be satisfied when choosing solvents for
the crystallization problem: a solvent should not boil or freeze during
the crystallization process and, in the case of solvent mixtures,
the solvents should also be miscible with each other over the process
conditions.Liquid-range constraints are enforced for each solvent
candidate
depending on two optimization variables, the initial and final operating
temperatures, based on the (experimental) melting point of each solvent j, Tm, where all temperatures are assumed
to be in K,and the bubble point of the solvent mixture, Tmixbwhere Tos is a
temperature offset chosen to prevent the process from operating too
close to a solvent phase change.One could widen the feasible
temperature range by calculating the
melting point of the solvent mixture, thereby making it possible to
take advantage of eutectic behavior. This formulation is however not
considered here as a relatively high value of 293.15 K is used as
a lower bound on the crystallization temperature.Using solvent-dependent
bounds for the operating temperatures,
rather than fixed maximum and minimum temperature bounds as in previous
work,[16] avoids the screening out of potentially
effective yet relatively volatile solvents. Additionally, while previous
work in this field has been reliant on the boiling points of pure
solvents to define the upper limit of the liquid range of the mixture,
the bubble point of the liquid mixture is calculated using the SAFT-γ
Mie EoS in our formulation. This ensures that any nonlinearities,
such as the formation of high- or low-boiling azeotropes, are captured
in the optimization. This may allow higher temperatures to be utilized
during operation or conversely limit the highest allowable temperatures
of mixtures of solvents relative to those possible with pure solvents.
Finally, the formulation also includes a buffer (taken as Tos = 10 K in our current work) to avoid cases
where, during operation, disturbances to the process temperature may
otherwise push the system beyond the bubble point or freezing point
of a solvent mixture.To ensure the solvent mixture forms a
single, stable liquid phase,
the miscibility of the solvent blend is assessed by using of the Gibbs
stability criterion[34] for which an explicit
(algebraic) expression exists in the case of binary mixtures. The
stability of the binary solvent–antisolvent mixture (denoted
by adding a superscript S to the mole fractions) is calculated by
examining the derivative of the chemical potential of solvent s2 in the binary solvent mixture, :where the mole fractions
in the binary mixture are defined by the following set of equationsWhilst these constraints provide the necessary and sufficient conditions
to prevent the instability of the solvent pair in both the initial
and final states of the system, it does not necessarily guarantee
the miscibility of the ternary mixture that includes the API. Including
a constraint to ensure the miscibility of the ternary mixtures is
more challenging as there is no explicit criterion in this case. However,
in most cases, the API does not affect the calculated phase stability
significantly, as it is often present in low concentrations relative
to the solvent and antisolvent; its presence is therefore neglected
in the optimization. This assumption is then validated in “Block
IV: Post-optimization analysis”, after a solution to the crystallization
design problem has been found.A final constraint must be included;
as the formulation does not
allow for evaporative crystallization, the antisolvent cannot be removed
from the system. This is accounted for in eq :
Block III: Optimization Solution
The optimization formulation
is solved using an algorithm such as Outer-Approximation[35] or Branch & Bound.[36,37] It is instructive to generate multiple high-performance solutions,
obtained using integer cuts, and to undertake parametric studies,
for example, based on varying the bounds on the operating temperature.
Block IV: PostOptimization Analysis
Once the optimization
(Block III) is complete, a simple analysis of the solutions should
be performed as a final feasibility check to determine whether the
ternary mixture is stable or whether it will separate into two distinct
liquid phases, with the potential for the formation of a solid phase
too. The existence of such LLE for a given ternary mixture composition
is tested within gPROMS.Upon performing this calculation, two
scenarios can arise. First, only one liquid phase is found to exist
for the ternary mixture under the optimal process conditions found
during the optimization solution, validating the assumption that the
liquid phase is stable even when the API is present—in this
case, the solution can be taken to be trailled in an experimental
setting. However, in the second scenario, where the suggested ternary
mixture comprises two distinct liquid phases, the assumption that
the solvent mixture stability is a good indicator of overall mixture
stability is incorrect and should be revisited.There are a
number of approaches available for adjusting the optimization
problem to account for the existence of LLE in the final solution.
Here, we consider two simple methods that can be quickly implemented
into the generic optimization problem. One option is to remove the
solvent pair that formed the LLE (denoted solvent A and antisolvent
B here) from the optimization problem entirely:The use of the binary variables yii, in this way allows both
candidate solvents, A and B, to be selected with other solvent candidates
but not together.Alternatively, one can introduce constraints
on the binary solvent
composition to avoid the LLE region. In this case, the LLE envelope
first needs to be determined. Because the initial and final states
of the crystallization mixtures are considered to be at SLE, only
two stability limits on the envelope are important for a fixed temperature
and pressure, at the initial and/or final state. This can be understood
by applying the Gibbs phase rule, F = C – P + 2, where the degrees of freedom F of a system can be determined from the number of components, C, and phases, P, present. In the case
of the crystallization process considered in this formulation, there
are three components (s1, s2, and API) and two
phases (liquid and solid), giving three degrees of freedom (temperature,
pressure, and the ratio of the mole fractions). When a second liquid
phase is included, the number of degrees of freedom is reduced to
two, meaning that the compositions of both liquid phases at solid–liquid–liquid-equilibrium
(SLLE) are fixed by setting the temperature and pressure.As
such, the composition of the two liquid phases, denoted here
as α and β, can be found by determining the two points
on the LLE envelope that intersect the API solubility curve. These
limits can then be used to further constrain the optimization problem
to avoid the LLE region:where α is taken to be the antisolvent-rich
phase, whilst β is the solvent-rich phase, and as such, these
constraints hold when .
Because feasible operating points may
exist anywhere outside the SLLE envelope, two revised optimization
formulations should be solved—one in the antisolvent rich region , and one in the solvent rich region It should
be emphasized that the SLLE limits
obtained in this manner are only valid for the chosen temperature,
and any changes to the optimal temperature in subsequent optimizations
would require this process to be repeated.
Results and Discussion
The formulation is implemented in gPROMS version 6.0.2, applying
gSAFT to perform calculations using the SAFT-γ Mie group-contribution
thermodynamic platform. Two case studies are considered, pertaining
to the crystallization of lovastatin and ibuprofen. The effects of
the crystallization technique, the operating temperature range, and
the mass of solvent consumed on the optimal solvent choice, compositions,
and process temperatures are all considered in an integrated manner.
In all cases, the operating pressure is taken to be 1 atm. In order,
to explore fully the range of solvents that maximize crystal yield,
no upper limit is placed on solvent consumption, but this can be easily
implemented to reduce the design space and eliminate potentially impractical
solvent mixtures.
Case Study I: Crystallization of Lovastatin
Lovastatin,
as with all statin medications, is used to lower the levels of low-density
lipoprotein cholesterol in the blood, thus reducing the risk of cardiovascular
disease. Comprising a hydroxylated heterocyclic lactone group, an
unsaturated bicyclic structure and a branched butanoate ester (Figure ), the complex interactions
of the API with solvents make it difficult to predict the phase behavior
of the mixture; following the oft-touted “like-dissolves-like”
heuristic may not yield practical solvent mixtures for crystallization.
The SAFT-γ Mie group-contribution approach has been shown to
yield accurate predictions of the solubility of lovastatin in linear
alcohols and ethyl acetates across a range of temperatures.[38] For the model used here (shown in the Appendix), we find a root-mean-square error in the
logarithm (log10) of 0.30 for the solubility (mole fraction)
of lovastatin in 15 solvents, when comparing experimental data to
the predicted values. Such an accuracy is typically sufficient for
the ranking of solvents. The performance of the approach is particularly
accurate for larger solvents (3 or more carbons), as can be expected
from a group-contribution method.
Figure 3
Chemical structure of lovastatin, the
API considered in Case Study
I.
Chemical structure of lovastatin, the
API considered in Case Study
I.Perhaps the most important use
of a computer-aided approach is
the capacity to identify quickly several high-performance solutions
to the solvent design problem, before trialling them experimentally.
In practice, this should reduce the amount of time and material spent
testing ineffectual crystallization solvent blends. Therefore, the
generic formulation is applied here to rank solvent mixtures, based
on maximizing the crystal yield of lovastatin that can be achieved.
For all solutions, the post-optimization analysis (see Figure ) confirms that there is only
one liquid phase in the initial and final states of the system.
Comparison
of Traditional Approaches and Hybrid Crystallization
Whilst
it is trivial to state that using a hybrid approach (H)
to crystallization can achieve better performance than cooling or
antisolvent crystallization alone, it is important to quantify the
degree of improvement that is possible. The use of solvent mixtures
complicates solvent recycling processes; the blends must first be
separated and purified before being reused. Similarly, combining cooling
and antisolvent crystallization increases the complexity of the crystallization
process, placing greater emphasis on bespoke crystallizer design and
control systems, along with the requirement for a higher level of
operator expertise. Ultimately, one must question whether an improvement
in crystal yield, for example, is worth the additional difficulties
which may arise during other aspects of design and operation.To address this question, the general formulation is adjusted to
account for four possible scenarios: cooling crystallization in a
pure solvent (CP); cooling crystallization in a solvent mixture (CM);
antisolvent crystallization at fixed temperature starting with a pure
solvent in the initial state (ASP); and antisolvent crystallization
at fixed temperature where solvent mixtures are considered in both
the initial and final states (ASM). For the cases including cooling
crystallization (CP and CM), the maximum allowable temperature is
fixed at 373.15 K. Whilst this is also true for the cases involving
antisolvent crystallization, it is expected that lower temperatures
would provide increased crystal yields due to the final solubility
of lovastatin being lower. Due to the additional costs associated
with reducing the operating temperature much below that of cooling
water, the lower temperature limit is fixed at 293.15 K for all of
the design problems.In all scenarios, solvents (and antisolvents)
are selected from
a list of thirteen candidates, shortlisted based on their low toxicity
and the availability of the necessary interaction parameters with
lovastatin within the SAFT-γ Mie framework. Hence, there are
78 unique solvent pairings to select from. Solvent consumption is
also investigated, whereby a lower consumption is preferable, but
with lower limits of 3.5 g solvent/(g crystal) and 4 mL solvent/(g
crystal) to prevent the formation of highly viscous slurries. A summary
of these model inputs can be found in Table .
Table 1
Inputs Required to
Describe the CAMbD Problem for the Crystallization of Lovastatin,
Where Technique-Specific
Constraints are Required to Describe Cooling Crystallization or Antisolvent
Crystallization.a
χs ≥ 3.5 g solvent/(g crystal), Vs ≥ 4.0 mL solvent/(g crystal)
technique-specific constraints
ASM: T = T0
Here, s1, s2, and API refer to
the solvent, antisolvent, and lovastatin, respectively.
The operating temperatures (T0 and T) are bounded by upper and lower limits, Tmax and Tmin, respectively,
whilst the solvent mass is constrained only by lower limits, on a
mass (χs) and a volumetric (Vs) basis. The moles of solvent ii in the liquid phase are represented
by niiL, with the added subscript 0 to denote the initial state of
the system. The sum of binary variables ys represents the presence of an antisolvent
and is set to zero in mode CP to ensure a pure solvent is obtained.
Here, s1, s2, and API refer to
the solvent, antisolvent, and lovastatin, respectively.
The operating temperatures (T0 and T) are bounded by upper and lower limits, Tmax and Tmin, respectively,
whilst the solvent mass is constrained only by lower limits, on a
mass (χs) and a volumetric (Vs) basis. The moles of solvent ii in the liquid phase are represented
by niiL, with the added subscript 0 to denote the initial state of
the system. The sum of binary variables ys represents the presence of an antisolvent
and is set to zero in mode CP to ensure a pure solvent is obtained.A ranked list of optimal solvent
blends and process conditions
is given in Table , where the best solution—that with the highest crystal yield
of lovastatin—is given a ranking of 1. In all relevant design
problems, the final operating temperature is 293.15 K—the lower
temperature limit of the case study. Furthermore, all solutions exist
at the limit of one of the implemented constraints—the solvent
mass limit (χs = 3.5 g solvent/(g crystal)), the
temperature limits (T0 = 293.15 K or T0 = 373.15 K), or the solvent liquid range limit
(T0 = Tmixb – 10)—such that
relaxing these constraints may further improve the crystal yield.
Table 2
Results of the Optimization of Lovastatin
Crystal Yield, YAPI, for Five Crystallization
Methods—Cooling Crystallization with: Only Pure Solvent Allowed
in the Initial State (CP), Mixtures Allowed Throughout (CM); Antisolvent
Crystallization with: Only Pure Solvent Allowed in the Initial State
(ASP), Mixtures Allowed Throughout (ASM); and Hybrid Cooling and Antisolvent
Crystallization (H)a
solvents
method
rank
YAPI/%
χs/(g/g)
T0/K
s1
s2
cooling (CP)
1
97.47
73.02
361.15
1.000
1.000
n-heptane
2
96.33
3.50
368.75
1.000
1.000
isobutyl acetate
3
94.89
3.50
363.35
1.000
1.000
1-pentanol
4
93.46
4.11
356.35
1.000
1.000
isopropyl
acetate
5
92.75
3.50
357.05
1.000
1.000
butyl acetate
cooling (CM)
1
97.47
73.02
361.15
1.000
1.000
n-heptane
2
96.45
3.50
369.15
0.962
0.962
isobutyl acetate
n-pentane
3
94.89
3.50
363.35
1.000
1.000
1-pentanol
4
93.46
4.11
356.35
1.000
1.000
isopropyl
acetate
5
93.36
3.50
358.25
0.915
0.915
butyl acetate
n-pentane
anti-solvent (ASP)
1
92.16
85.84
293.15
1.000
0.158
methyl acetate
n-heptane
2
90.24
109.56
293.15
1.000
0.165
ethyl acetate
n-heptane
3
89.85
78.01
293.15
1.000
0.134
methyl acetate
n-pentane
4
87.22
101.97
293.15
1.000
0.139
ethyl acetate
n-pentane
5
85.62
170.49
293.15
1.000
0.174
propyl acetate
n-heptane
anti-solvent (ASM)
1
93.04
75.80
293.15
0.928
0.157
methyl acetate
n-heptane
2
91.67
63.10
293.15
0.882
0.133
methyl acetate
n-pentane
3
90.24
109.56
293.15
1.000
0.165
ethyl acetate
n-heptane
4
87.40
100.40
293.15
0.955
0.139
ethyl acetate
n-pentane
5
85.62
170.49
293.15
1.000
0.174
propyl acetate
n-heptane
hybrid (H)
1
99.23
7.93
370.35
1.000
0.174
propyl acetate
n-heptane
2
99.16
8.59
373.15
1.000
0.184
butyl acetate
n-heptane
3
98.97
7.25
370.35
1.000
0.145
propyl acetate
n-pentane
4
98.93
10.88
373.15
1.000
0.228
isobutyl acetate
n-heptane
5
98.90
7.77
373.15
0.954
0.154
butyl acetate
n-pentane
For each method, the top five solvent
mixtures are ranked with respect to the crystal yield of lovastatin
achieved. The solvent consumption, χs, initial temperature, T0, and binary solvent compositions in terms
of initial and final mole fractions of solvent s1, and ,
are also given. In all cases, the maximum
allowable temperature is 373.15 K, the minimum solvent mass is 3.5
g solvent/(g crystal), and the final temperature is 293.15 K.
For each method, the top five solvent
mixtures are ranked with respect to the crystal yield of lovastatin
achieved. The solvent consumption, χs, initial temperature, T0, and binary solvent compositions in terms
of initial and final mole fractions of solvent s1, and ,
are also given. In all cases, the maximum
allowable temperature is 373.15 K, the minimum solvent mass is 3.5
g solvent/(g crystal), and the final temperature is 293.15 K.Comparing the two modes of
cooling crystallization, CP and CM,
it can be observed that crystallizing lovastatin from pure n-heptane is predicted to provide the highest crystal yield.
However, due to the low solubility of lovastatin in n-heptane at the maximum allowable temperature, the solvent consumption
is also much higher than in many other solvents—a clear example
of the merit of reviewing both crystal yield and solvent consumption
when looking for optimal solvent blends. In CP mode, three of the
remaining top five solvents, isobutyl acetate, isopropyl acetate,
and butyl acetate, are constrained by the lower limit on solvent use—implemented
to prevent the formation of highly viscous slurries—and therefore
the entire temperature range cannot be utilized for cooling. Such
solutions to the optimization problem would not be feasible had the
temperature range been fixed a priori. For the other
two solutions, n-heptane and 1-pentanol, the solvent
phase limits are active at the solvent boiling point, and thus, the
initial temperature could not feasibly be increased further. Using
the general formulation again allows these volatile solvents to be
found as solutions, rather than removing them based on the boiling
point during a prescreening step.Allowing the cooling crystallization
to utilize solvent mixtures
(CM mode) results in similar solutions, with the same selection of
top tier solvents as those found in the CP mode. However, for solutions
ranked 2 and 5, the crystal yield is increased by introducing a small
amount of n-pentane into the mixture. Although this
reduces the solubility of lovastatin in the initial state, meaning
the mass of solvent required to solubilize the same mass of lovastatin
is greater than in the CP mode, it also provides a means for the final
solubility of lovastatin to be lower. The higher initial temperature
thus maintains the low solvent use. The combination of these two effects
leads to an increase in the crystal yield, maintaining the solvent
use at the lower limit of 3.5 g solvent/(g crystal).The top
five optimal solvent blends for both modes of operation
for antisolvent crystallization, ASP and ASM, are identical, although
their specific rankings are different depending on how the crystallizer
is operated. Three of the solvent mixtures lead to higher crystal
yields when utilizing a solvent mixture in the initial state, also
leading to a decrease in solvent consumption. As such, the blend consisting
of methyl acetate and n-pentane is ranked second
in ASM mode, compared to third in ASP mode. This blend replaces ethyl
acetate and n-heptane at rank 2, for which an initial
state in pure ethyl acetate is optimal. As expected, the final process
temperature is minimized to reduce the solubility of lovastatin and
is therefore 293.15 K in all ten cases. For both modes of operation,
the optimal crystal yields achieved are lower than those found when
employing cooling crystallization. Generally, the solvent consumption
for antisolvent crystallization is an order of magnitude greater than
that of cooling crystallization, although it should be noted that
no upper constraint has been imposed on solvent use.In the
scenarios considering the hybrid technique (H), it is seen
that combinations of acetates and n-heptane or n-pentane, where the latter are added as antisolvent, are
found to provide the highest crystal yields. All five solutions utilize
both cooling and antisolvent crystallization to achieve a significantly
greater crystal yield of lovastatin than any of the solutions based
on standard techniques. Furthermore, solvent mixtures that include
propyl acetate as the operating solvent cannot be operated at the
maximum temperature specified due to the lower bubble point of the
mixture (the constraint on the solvent liquid range); previous CAMbD approaches would have screened out this optimal result.Ultimately, it is predicted that the hybrid technique can significantly
outperform antisolvent crystallization of lovastatin, whilst also
achieving a higher crystal yield than cooling crystallization alone.
Our study suggests that the use of hybrid cooling and antisolvent
crystallization would be beneficial in the production of lovastatin.
Recrystallisation in acetone and water mixtures is typically employed[39] as a purification technique in industry, although
studies into the use of alcohols and homologous acetates have also
been considered.[40] Whilst this work considers
the thermodynamic effects of the choice of solvent on the crystallization
system, the crystal habit can also influence this decision, due to
the propensity of lovastatin to form undesirable needle-like crystals.
The consideration of habit is however beyond the scope of our current
paper and will be the focus of further research.
Effect of
Operating Temperature on the Optimal Solvent Blend
It is
apparent from Table that several optimal solutions result in an initial process
temperature that is lower than the maximum temperature specified,
suggesting that there are effective but volatile solvent blends that
can provide a better performance at lower temperatures, as hypothesized.
To assess further the importance of operating temperature on the outcome
of the crystallization solvent design problem, eight design scenarios
are posed; a different upper temperature limit is used in each, ranging
between 303.15 and 373.15 K. As before, the lower temperature limit
is fixed at 293.15 K. Solvents (and antisolvents) are selected from
the same shortlist of thirteen solvent candidates as before. For each
design problem, a list of the most optimal solvent blends is generated,
ranked by the respective crystal yield of lovastatin (refer to Table ). Again, lower limits
of 3.5 g solvent/(g crystal) and 4 mL solvent/(g crystal) are imposed
on the solvent consumption.
Table 3
Results of the Optimization
of Lovastatin
Crystal Yield, YAPI, for Eight Scenarios
with Different Maximum Temperature Limitsa
solvents
Tmax/K
rank
YAPI/%
χs/(g/g)
T0/K
s1
s2
303.15
1
95.31
49.62
303.15
0.932
0.158
methyl acetate
n-heptane
2
94.31
41.93
303.15
0.907
0.133
methyl acetate
n-pentane
3
93.57
69.61
303.15
1.000
0.165
ethyl acetate
n-heptane
4
91.67
63.40
303.15
0.957
0.139
ethyl acetate
n-pentane
313.15
1
96.75
33.91
313.15
0.934
0.158
methyl acetate
n-heptane
2
95.66
31.54
313.15
0.984
0.133
methyl acetate
n-pentane
3
95.65
46.00
313.15
1.000
0.165
ethyl acetate
n-heptane
4
94.37
41.66
313.15
0.957
0.139
ethyl acetate
n-pentane
323.15
1
97.05
30.65
315.95
0.936
0.158
methyl acetate
n-heptane
2
96.99
31.41
323.15
1.000
0.165
ethyl acetate
n-heptane
3
96.11
28.28
323.15
0.950
0.139
ethyl acetate
n-pentane
4
96.02
28.77
316.45
1.000
0.133
methyl acetate
n-pentane
333.15
1
97.87
22.04
333.15
1.000
0.165
ethyl acetate
n-heptane
2
97.25
19.75
333.15
0.962
0.139
ethyl acetate
n-pentane
3
97.16
29.70
333.15
1.000
0.174
propyl acetate
n-heptane
4
97.05
30.65
315.95
0.936
0.158
methyl acetate
n-heptane
343.15
1
98.44
16.00
342.75
1.000
0.165
ethyl acetate
n-heptane
2
98.03
20.42
343.15
1.000
0.174
propyl acetate
n-heptane
3
97.96
14.51
342.75
1.000
0.139
ethyl acetate
n-pentane
4
97.40
18.70
343.15
0.972
0.145
propyl acetate
n-pentane
353.15
1
98.61
14.27
353.15
1.000
0.174
propyl acetate
n-heptane
2
98.44
16.00
342.75
1.000
0.165
ethyl acetate
n-heptane
3
98.21
18.50
353.15
1.000
0.184
butyl acetate
n-heptane
4
98.18
12.96
353.15
0.954
0.145
propyl acetate
n-pentane
363.15
1
99.01
10.11
363.15
1.000
0.174
propyl acetate
n-heptane
2
98.78
12.57
363.15
1.000
0.184
butyl acetate
n-heptane
3
98.70
9.19
363.15
0.983
0.145
propyl acetate
n-pentane
4
98.44
16.00
342.75
1.000
0.165
ethyl acetate
n-heptane
373.15
1
99.23
7.93
370.35
1.000
0.174
propyl acetate
n-heptane
2
99.16
8.59
373.15
1.000
0.184
butyl acetate
n-heptane
3
98.97
7.25
370.35
1.000
0.145
propyl acetate
n-pentane
4
98.93
10.88
373.15
1.000
0.228
isobutylacetate
n-heptane
For each method, the top four solvent
mixtures are ranked with respect to the crystal yield of lovastatin
achieved. The solvent consumption, χs, initial temperature, T0, and binary solvent composition, , are also given. In
all cases, the minimum
solvent consumption is 3.5 g/g, and the final temperature is 293.15
K.
For each method, the top four solvent
mixtures are ranked with respect to the crystal yield of lovastatin
achieved. The solvent consumption, χs, initial temperature, T0, and binary solvent composition, , are also given. In
all cases, the minimum
solvent consumption is 3.5 g/g, and the final temperature is 293.15
K.As represented in Figure , the combination
of cooling and antisolvent crystallization
leads to high crystal yields for all eight scenarios considered, utilizing
solvent mixtures throughout. As expected, relaxing the upper temperature
limit—that is, allowing the crystallization to operate at higher
initial temperatures—generally leads to a
higher crystal yield. Increasing the upper temperature limit often
leads to a change in the solvent mixture ranking, as more volatile
solvents cannot be utilized at the higher initial temperatures. Furthermore,
extending the temperature range leads to a decrease in the overall
solvent consumption of crystallization. This is due to the higher
solubility of lovastatin at higher temperatures, meaning less solvent
is required to completely solubilize the API initially.
Figure 4
Results of
the optimization of lovastatin crystal yield using hybrid
crystallization, for different maximum operating temperatures, between
303.15 and 373.15 K in 10 K increments. The lower bound on the final
temperature for all crystallizations is 293.15 K, whilst the upper
temperature limit is changed for each design problem, which in turn
affects the initial operating temperature shown in the figure. The
optimal solvent is indicated with the symbols □, ◊,
and △, referring to methyl acetate, ethyl acetate, and propyl
acetate, respectively. In all cases, the optimal antisolvent is n-heptane. (a) Maximum crystal yield and optimal initial
temperatures. In most cases, the optimal initial temperature is at
the temperature upper bound but any crystallization operating at an
initial temperature within the corresponding red shaded region is
predicted to achieve a lower crystal yield relative to the designs
on the vertical dashed lines. (b) The solvent consumption is shown
for each optimal solvent mixture (that which maximizes the crystal
yield) over the temperature range, where the horizontal dashed line
is the lower solvent mass limit, 3.5 g solvent/(g crystal).
Results of
the optimization of lovastatin crystal yield using hybrid
crystallization, for different maximum operating temperatures, between
303.15 and 373.15 K in 10 K increments. The lower bound on the final
temperature for all crystallizations is 293.15 K, whilst the upper
temperature limit is changed for each design problem, which in turn
affects the initial operating temperature shown in the figure. The
optimal solvent is indicated with the symbols □, ◊,
and △, referring to methyl acetate, ethyl acetate, and propyl
acetate, respectively. In all cases, the optimal antisolvent is n-heptane. (a) Maximum crystal yield and optimal initial
temperatures. In most cases, the optimal initial temperature is at
the temperature upper bound but any crystallization operating at an
initial temperature within the corresponding red shaded region is
predicted to achieve a lower crystal yield relative to the designs
on the vertical dashed lines. (b) The solvent consumption is shown
for each optimal solvent mixture (that which maximizes the crystal
yield) over the temperature range, where the horizontal dashed line
is the lower solvent mass limit, 3.5 g solvent/(g crystal).It is, however, not always optimal to begin the
crystallization
at the highest allowable temperature. As depicted in Figure , any crystallization operating
at an initial temperature within a red shaded region is predicted
to achieve a lower crystal yield than either of the optimal solutions
on the boundaries of the region (the vertical dashed lines). Thus,
the red shaded regions indicate suboptimal temperatures. For instance,
in Table , four design
scenarios result in mixtures of methyl acetate and n-heptane being one of the top four most optimal solvent blends; for
three of these cases, this outcome is the highest ranked optimal solution.
Accounting for the temperature buffer of 10 K, the combination of
methyl acetate and n-heptane cannot be used at temperatures
above 315.95 K because the constraint on the liquid range of the solvent
would be violated (Tmixb = 325.95 K). For the first two design
scenarios (Tmax of 303.15 and 313.15 K),
methyl acetate and n-heptane are the optimal solvent
blend, and the crystallization can be operated at the maximum temperature
limit (T0 = Tmax < Tmixb – 10). However, when the maximum allowable
temperature is fixed at 323.15 K, the optimal solution (YAPI = 97.05%) is again found to be a blend of methyl acetate
and n-heptane with an initial temperature of only
315.95 K, as the next best mixture (ethyl acetate and n-heptane) yields a lower yield (YAPI =
96.99%) despite being able to utilize a further 7.2 K of cooling.This effect is replicated when the maximum temperature limit is
fixed at 343.15 K, where it is found that the optimal result is a
mixture of ethyl acetate and n-heptane, with an initial
operating temperature of 342.75 K, and for the design case with an
upper temperature limit of 373.15 K, for which propyl acetate and n-heptane produce an optimal mixture with an initial operating
temperature of 370.35 K.Examining the 5 top solutions for each
of the eight design scenarios,
there are nine solutions that operate at initial temperatures below
the upper temperature limit. Clearly, maximizing the operating temperature
range, such that T0 – T = Tmax – Tmin, is not always optimal, and this emphasizes the importance
of using a general formulation in which molecular and process decisions
are optimized simultaneously. Furthermore, the bubble points of many
of the optimal mixtures are greater than the normal boiling point
of the most volatile solvent in each blend, highlighting the advantage
of considering the bubble temperature of the mixture rather than the
boiling temperatures of the pure components in such designs.From a practical perspective, the optimal values returned by the
solver are very precise and this precision could not be achieved in
practice. By rounding some of the solutions (e.g., hybrid solutions 1 and 2 in Table ) to the nearest 5 K in temperature and to one significant
figure in mole fraction, we find only a mild effect on the predicted
yield and no change in ranking. A key conclusion is thus that there
are several solvent/process combinations that give very high yields,
albeit with varying levels of solvent consumption.
Reducing
Solvent Consumption during Crystallization
Excessive solvent
use in industrial processes is a well-recognized
problem, with solvents typically accounting for more than 80% of process
mass[41] and the majority of energy use[42] in the production of pharmaceuticals. Whilst
efforts are being made to include and improve solvent recovery systems,
process intensification is a crucial step toward a “greener”
manufacturing process. In addition, reducing the volume of solvent
required on-site can improve the inherent safety of the facility.
As such, it is important to design crystallization processes that
are not only efficient in terms of the API crystal yield, but also
with regards to solvent consumption. To understand the relationship
between crystal yield and solvent use, a multiobjective optimization
formulation is solved, with the simultaneous objectives of maximizing
crystal yield and minimizing solvent consumption, on a mass basis.
This is solved using the ϵ-constraint method, with ten values
of ϵ, so that ten instances of the single-objective, yield-maximization,
optimization problem are solved with a different maximum allowable
solvent consumption imposed for each instance. It should be noted
that the lower solvent consumption limits remain fixed at 3.5 g solvent/(g
crystal) and 4 mL solvent/(g crystal). The same list of thirteen solvents
is available for design, and the upper and lower temperature limits
are fixed at 373.15 and 293.15 K, respectively.For all ten
resulting Pareto points, the optimal solvent mixtures are found to
be blends of propyl acetate and n-heptane in varying
proportions (Table ). It is clear from Figure that there is a trade-off between achieving a high crystal
yield and a low consumption of solvent. From these results, it is
possible to choose a compromise solution, whereby less solvent is
used during the crystallization, but a high crystal yield is still
attained.
Table 4
Results of the Multiobjective Optimization
of Lovastatin Crystal Yield and Solvent Consumption, χsa
solvents
χsmax/(g/g)
YAPI/%
χs/(g/g)
T0/K
s1
s2
Unconstrained
99.23
7.93
370.35
1.000
0.174
propyl acetate
n-heptane
7.49
99.22
7.49
370.35
1.000
0.184
propyl acetate
n-heptane
7.04
99.22
7.04
370.35
1.000
0.196
propyl acetate
n-heptane
6.60
99.21
6.60
370.35
1.000
0.209
propyl acetate
n-heptane
6.16
99.20
6.16
370.35
1.000
0.225
propyl acetate
n-heptane
5.71
99.18
5.71
370.35
1.000
0.242
propyl acetate
n-heptane
5.27
99.15
5.27
370.35
1.000
0.263
propyl acetate
n-heptane
4.83
99.11
4.83
370.35
1.000
0.287
propyl acetate
n-heptane
4.39
99.05
4.39
370.35
1.000
0.316
propyl acetate
n-heptane
3.94
98.97
3.94
370.35
1.000
0.352
propyl acetate
n-heptane
3.50
98.83
3.50
370.35
1.000
0.398
propyl acetate
n-heptane
The solvent consumption, χs, initial temperature, T0, and
binary solvent composition, as initial and final mole fractions of
s1, and ,
are also given. In all cases, the minimum
solvent mass is 3.5 g solvent/(g crystal), the upper temperature limit
is 373.15 K and the final temperature is 293.15 K.
Figure 5
Pareto front for the crystal yield of lovastatin and solvent consumption,
where χs = 7.93 g solvent/(g crystal) corresponds
to an unconstrained solvent consumption. All of the Pareto points
have an optimal initial temperature of 370.35 K and final temperature
of 293.15 K, for lovastatin in a mixture of propyl acetate and n-heptane. The vertical dashed line is the lower solvent
mass limit, 3.5 g solvent/(g crystal).
Pareto front for the crystal yield of lovastatin and solvent consumption,
where χs = 7.93 g solvent/(g crystal) corresponds
to an unconstrained solvent consumption. All of the Pareto points
have an optimal initial temperature of 370.35 K and final temperature
of 293.15 K, for lovastatin in a mixture of propyl acetate and n-heptane. The vertical dashed line is the lower solvent
mass limit, 3.5 g solvent/(g crystal).The solvent consumption, χs, initial temperature, T0, and
binary solvent composition, as initial and final mole fractions of
s1, and ,
are also given. In all cases, the minimum
solvent mass is 3.5 g solvent/(g crystal), the upper temperature limit
is 373.15 K and the final temperature is 293.15 K.When the solvent consumption is
unconstrained, the maximum crystal
yield is found to be 99.23% and the corresponding solvent use is 7.93
g solvent/(g crystal). As the maximum allowable solvent consumption
is reduced via an ϵ-constraint, the optimal
amount of antisolvents to be added to the process decreases. This
has a detrimental impact on the API crystal yield as the mole fraction
of antisolvent, n-heptane, in the final solvent mixture
is reduced and the final solubility of lovastatin is thus increased.
The initial conditions of the crystallization, however, remain unchanged
in all Pareto points. These conditions correspond to the highest possible
solubility of API in the initial solvent mixture and hence the lowest
mass of solvent required to solubilize a given mass of lovastatin.
Case Study II: Crystallization of Ibuprofen
Ibuprofen
is a nonsteroidal anti-inflammatory drug (NSAID), widely used around
the world to manage pain. Whilst the crystallization of this API has
already been thoroughly researched in both academia[24,43,44] and industry,[45−47] with global production
estimated to be greater than 35,000 tonnes per annum,[48] ibuprofen remains an interesting compound to study in the
general crystallization solvent design problem. It is well documented
that ibuprofen crystallizes by forming dimers around the carboxylic
acid functional groups due to hydrogen bonding[49] (Figure ); the presence of dimers in solution can be modeled with the SAFT-γ
Mie group-contribution approach[26]via the introduction of association sites on the carboxyl
functional group,[27] accurately predicting
the solubility of ibuprofen in organic solvents. Specifically, the
root mean squared error in the logarithm (log10) of the
solubility of ibuprofen is found to be 0.12 log units when experimental
data in acetone, n-butanol, water, and n-heptane are compared to the predicted values obtained with the model
used in our current work,[27,30] over a range of temperatures.
The predictions are especially accurate in water, acetone, and n-butanol, while the solubility of ibuprofen in n-heptane is underestimated. In the presence of solvent
molecules, there can be competition between the formation of dimers
and the formation of hydrogen bonds between the carboxylic group and
solvent molecules, making it important to rely on quantitative predictions
of the solubility in crystallization process design.
Figure 6
Chemical structure of
ibuprofen, the API considered in Case Study
II.
Chemical structure of
ibuprofen, the API considered in Case Study
II.The objective of the design problem
considered here is to identify
the optimal solvent blend and process conditions that maximize the
crystal yield of ibuprofen. For all scenarios investigated, the solvents
(and antisolvents) are selected from eight candidate molecules, short-listed
based on their low toxicity and the availability of the necessary
interaction parameters in the SAFT-γ Mie framework. As such,
there are 28 potential binary solvent pairs to select from during
the optimization. For all cases studied, the lower temperature limit
is fixed at 293.15 K, whilst the lower limits of solvent consumption
are set at 3.5 gsolvent/(gcrystal) and 4 mLsolvent/(gcrystal). A summary of these model inputs
can be found in Table .
Table 5
Inputs Required to Describe the CAMbD Problem
for the Crystallization of Ibuprofen, Where Technique-Specific
Constraints are Required to Describe Cooling Crystallization or Antisolvent
Crystallizationa
χs ≥ 3.5 gsolvent gcrystal–1, Vs ≥ 4.0 mLsolvent gcrystal–1
technique-specific constraints
ASM: T = T0
Here, s1, s2, and API refer to
the solvent, the antisolvent, and ibuprofen, respectively.
The operating temperatures (T0 and T) are bounded by upper and lower limits, Tmax and Tmin, respectively,
whilst the solvent mass is constrained only by lower limits, on a
mass (χs) basis and on a volumetric (Vs) basis. The final (initial) moles of solvent ii in the
liquid phase are represented by niiL (nii,0L). The binary
variables ys express the selection of a candidate antisolvent (from the list NS) and are included here to prevent the choice
of antisolvent being a design decision in crystallization mode CP.
Here, s1, s2, and API refer to
the solvent, the antisolvent, and ibuprofen, respectively.
The operating temperatures (T0 and T) are bounded by upper and lower limits, Tmax and Tmin, respectively,
whilst the solvent mass is constrained only by lower limits, on a
mass (χs) basis and on a volumetric (Vs) basis. The final (initial) moles of solvent ii in the
liquid phase are represented by niiL (nii,0L). The binary
variables ys express the selection of a candidate antisolvent (from the list NS) and are included here to prevent the choice
of antisolvent being a design decision in crystallization mode CP.
Comparison of Conventional Approaches and
Hybrid Crystallization
As in the case study for lovastatin,
it is important to compare
the hybrid approach to the standard modes of operation—cooling
or antisolvent crystallization operating independently. As such, five
design scenarios are considered: cooling crystallization in a pure
solvent (CP); cooling crystallization allowing solvent mixtures (CM);
antisolvent crystallization where ibuprofen is initially dissolved
in a pure solvent (ASP); antisolvent crystallization where solvent
mixtures can be used throughout (ASM); and the hybrid technique (H).
In each of these scenarios, the top four optimal solvent blends are
ranked based on the crystal yield obtained, and the maximum allowable
temperature is fixed at 318.15 K. In all solutions, the final temperature
is found to be 293.15 K—the minimum allowable temperature.As shown in Table , for the design scenario considering cooling crystallization from
a pure solvent (CP), n-heptane is found to provide
the best performance. The second-ranked solvent is found to be water;
due to ibuprofen being virtually insoluble in water, the solvent consumption
is very high and the result is highly impractical. Crystal yields
below 50% are obtained in the remaining two solvents (1-pentanol and n-pentane), where the complete temperature range cannot
be utilized because of either the lower limit on solvent consumption
on a mass basis (1-pentanol) or the solvent liquid range constraint
(n-pentane). Overall, these results suggest that
only one of the eight solvents chosen is applicable to cooling crystallization.
Table 6
Results of the Optimization of Ibuprofen
Crystal Yield, YAPI, for Five Crystallization
Methods—Cooling Crystallization with: Only Pure Solvent Allowed
in the Initial State (CP), Mixtures Allowed Throughout (CM); Antisolvent
Crystallization with: Only Pure Solvent Allowed in the Initial State
(ASP), Mixtures Allowed Throughout (ASM), and Hybrid Cooling and Antisolvent
Crystallization (H)a
solvents
method
rank
YAPI/%
χs/(g/g)
T0/K
s1
s2
cooling (CP)
1
87.18
11.02
318.15
1.000
1.000
n-heptane
2
78.96
3498.90
318.15
1.000
1.000
water
3
44.97
3.50
307.65
1.000
1.000
1-pentanol
4
35.41
55.49
298.65
1.000
1.000
n-pentane
cooling (CM)
1
90.07
3.50
318.15
0.133
0.133
ethanol
n-heptane
2
90.00
3.50
318.15
0.147
0.147
1-propanol
n-heptane
3
89.90
3.50
318.15
0.166
0.166
1-butanol
n-heptane
4
89.77
3.50
318.15
0.191
0.191
1-pentanol
n-heptane
anti-solvent (ASP)
1
99.83
8.64
293.15
1.000
0.040
ethanol
water
2
99.78
10.77
293.15
1.000
0.027
acetone
water
3
99.71
14.42
293.15
1.000
0.027
1-propanol
water
4
99.51
23.74
293.15
1.000
0.020
1-butanol
water
anti-solvent (ASM)
1
99.83
8.64
293.15
1.000
0.040
ethanol
water
2
99.81
9.19
293.15
0.641
0.027
acetone
water
3
99.71
14.42
293.15
1.000
0.027
1-propanol
water
4
99.52
23.25
293.15
0.624
0.020
1-butanol
water
hybrid (H)
1
99.94
4.00
318.15
0.475
0.021
acetone
water
2
99.92
4.09
318.15
0.517
0.040
ethanol
water
3
99.90
4.80
318.15
0.423
0.027
1-propanol
water
4
99.88
5.78
318.15
0.438
0.020
1-butanol
water
For each method, the top four solvent
mixtures are ranked with respect to the crystal yield of ibuprofen
achieved. Solvent consumption, χs, initial temperature, T0, and binary solvent composition, , are also given. In
all cases, the maximum
allowable temperature is 318.15 K, the minimum solvent mass is 3.5
g solvent/(g crystal), and the final temperature is 293.15 K. Italicized
solutions are optimal mixtures with additional composition constraints,
to prevent the occurrence of LLE.
For each method, the top four solvent
mixtures are ranked with respect to the crystal yield of ibuprofen
achieved. Solvent consumption, χs, initial temperature, T0, and binary solvent composition, , are also given. In
all cases, the maximum
allowable temperature is 318.15 K, the minimum solvent mass is 3.5
g solvent/(g crystal), and the final temperature is 293.15 K. Italicized
solutions are optimal mixtures with additional composition constraints,
to prevent the occurrence of LLE.However, expanding the design space to include solvent
mixtures
(CM) improves the usefulness of the primary alcohols; the combination
of primary alcohols with n-heptane leads to an absolute
increase in crystal yield of at least 2.5%, whilst achieving the minimum
allowable solvent consumption for the process. Taking the case of
ibuprofen dissolved in an n-heptane-rich mixture
with a primary alcohol, it is clear from Figure that the solubility of ibuprofen increases
at a much greater rate, relative to the composition of alcohol, at
higher temperatures. Hence, by blending small proportions of the selected
alcohol with n-heptane, a higher initial solubility
is achieved relative to pure n-heptane, reducing
the mass of the solvent required to completely dissolve ibuprofen.
Upon cooling the solution to 293.15 K, the high levels of n-heptane in the mixture cause a significant drop in the
solubility of ibuprofen, leading to a higher crystal yield. The merit
of using solvent mixtures in the cooling crystallization framework
is evident in both improving crystal yield and reducing solvent consumption
in the crystallization of ibuprofen.
Figure 7
Predicted solubility of ibuprofen, xibuprofen*, as a
function of the mole fraction of alcohol in binary solvent mixtures
of primary alcohols and n-heptane at 293.15 K (solid
curve) and 318.15 K (dashed curve): (a) ethanol, (b) 1-propanol, (c)
1-butanol, and (d) 1-pentanol. In mode CM, the mixture marked with
a red cross is cooled, reducing the solubility of ibuprofen as indicated
by the red arrows. The solubilities are calculated using the SAFT-γ
Mie group-contribution approach in gPROMS.
Predicted solubility of ibuprofen, xibuprofen*, as a
function of the mole fraction of alcohol in binary solvent mixtures
of primary alcohols and n-heptane at 293.15 K (solid
curve) and 318.15 K (dashed curve): (a) ethanol, (b) 1-propanol, (c)
1-butanol, and (d) 1-pentanol. In mode CM, the mixture marked with
a red cross is cooled, reducing the solubility of ibuprofen as indicated
by the red arrows. The solubilities are calculated using the SAFT-γ
Mie group-contribution approach in gPROMS.The two design scenarios considering antisolvent crystallization,
ASP and ASM, differ only marginally in results, producing very high
crystal yields. In all eight solutions, water is selected as the optimal
antisolvent, whilst the operating temperature is fixed at the lower
limit of 293.15 K. Whilst allowing the use of solvent mixtures throughout
the crystallization (mode ASM) can improve the crystal yield and reduce
solvent consumption in two of the top-ranked cases, the change is
minimal.Similar to the results for lovastatin, the solutions
for the design
scenario considering the hybrid technique (H) show that the combined
use of cooling and antisolvent crystallization leads to greater crystal
yields of ibuprofen compared to any of the standard techniques. Furthermore,
solvent mixtures are utilized in all stages of operation, highlighting
the benefit of employing the hybrid technique. In comparison to the
results for the cooling crystallization design problems (modes CP
and CM), using the hybrid technique achieves a crystal yield which
is more than 11% higher, whilst also maintaining a low solvent consumption.
Although the crystal yield of mode H is fractionally higher compared
to the antisolvent designs (modes ASP and ASM), and the solvent consumption
is between two and five times lower, this difference may not warrant
the use of a more complicated hybrid system. Nevertheless, being able
to investigate these different modes of operation allows the rapid
planning of experimental campaigns, eliminating poor-performing crystallization
techniques before time and material are spent testing them.It should be noted that three of the solvent mixtures used with
the hybrid technique (H) are initially found to exhibit liquid–liquid
equilibrium; these pairs are identified by italics in Table . As a result, additional constraints
(eqs and 23) have been included on the binary solvent composition.
For each of the three pairs of binary solvents, a different constraint,
derived from the stability limits of this specific pair, is used.
Effect of Operating Temperature on the Optimal Solvent Blend
Although the crystal yield of the four top-ranked optimal solutions
are very similar, it is important to understand the effect of operating
temperature on the design of the crystallization solvent blend. As
such, five design scenarios are posed; in each, the upper temperature
limit is different, ranging between 298.15 and 318.15 K, and the lower
temperature limit is fixed at 293.15 K. Solvent consumption is also
examined, whereby a lower consumption is preferable, but the lower
limits are set at 3.5 gsolvent/(gcrystal) and
4 mLsolvent/(gcrystal). It should also be noted
that several of the solutions of the initial optimization problem
are found to exhibit LLE when considering the ternary solvent-antisolvent-API
mixture—this is even the case for mixtures containing acetone
and water, which are miscible in all proportions for the given temperature
range, but where the presence of ibuprofen induces phase separation.
Once again, additional constraints are placed upon the optimization
problem for those cases, as described in eqs and 23; this has a
negligible impact, and does not result in a change in the ranking
of solutions with only a decrease in crystal yield by less than 0.01%
in absolute terms. However, it is worth noting that the miscibility
limits on solvent composition are active in these solutions, and thus,
small perturbations may result in an unstable mixture. As such, an
additional buffer-zone could be included in eq to move the operating conditions sufficiently
outside the LLE envelope.As represented in Figure , combined cooling and antisolvent
crystallization is an effective way to use solvent mixtures, leading
to a very high crystal yield, which is only marginally improved by
relaxing the upper temperature limit; from the results presented in Table it is evident that
the principal driving force is from the addition of water as an antisolvent.
In contrast to the case of lovastatin, there are no areas of suboptimal
temperatures for this crystallization (no red shaded regions as in Figure ); it is important
to note that within the range of operating temperatures considered
here, none of the four most optimal solvent blends are at their respective
liquid range limit; all four blends are feasible across the entire
temperature range. Despite this, the optimal solvent changes from
ethanol to acetone at temperatures higher than 303.15 K. This highlights
that it is crucial not to extrapolate results from one operating temperature
to another, even for temperatures that lie within the liquid range
of the solvent.
Figure 8
Results of the optimization of the ibuprofen crystal yield
for
different operating temperatures. The final temperature for all crystallizations
is fixed at 293.15 K, whilst the upper temperature limit is changed
for each design, which in turn affects the initial operating temperature.
The optimal solvents, ethanol and acetone, are indicated by the symbols
□ and ◊, respectively. In all cases, the optimal antisolvent
is water. (a) The maximum crystal yield is expressed for initial temperatures
between 298.15 and 318.15 K. (b) The solvent consumption is shown
for each optimal solvent mixture (the mixture which maximizes the
crystal yield) over the temperature range, where the horizontal dashed
line is the lower solvent volume limit, 4.0 mL/g.
Results of the optimization of the ibuprofen crystal yield
for
different operating temperatures. The final temperature for all crystallizations
is fixed at 293.15 K, whilst the upper temperature limit is changed
for each design, which in turn affects the initial operating temperature.
The optimal solvents, ethanol and acetone, are indicated by the symbols
□ and ◊, respectively. In all cases, the optimal antisolvent
is water. (a) The maximum crystal yield is expressed for initial temperatures
between 298.15 and 318.15 K. (b) The solvent consumption is shown
for each optimal solvent mixture (the mixture which maximizes the
crystal yield) over the temperature range, where the horizontal dashed
line is the lower solvent volume limit, 4.0 mL/g.Relaxing the upper temperature limit may have a limited impact
on the crystal yield in this case, but it leads to significant improvements
in the overall solvent consumption. One reason for this is made apparent
from the relationship between solubility and temperature—increasing
the upper temperature limit makes it possible to employ a higher initial
operating temperature, meaning less solvent is required to completely
dissolve the ibuprofen initially. However, there is a second effect
that compounds this benefit and only arises due to the use of solvent
mixtures.In Table , the
initial mole fraction of solvent in the binary solvent mixture is
listed for each solvent design problem; the higher the initial temperature,
the lower the initial composition of solvent s1 in the
crystallizer and the higher the initial composition of antisolvent
s2. It should be noted that the definition of antisolvent
here is based on the solubility of ibuprofen in the pure solvent,
rather than the solvent mixture; ibuprofen is practically insoluble
in pure water, but mixing water with other solvents can significantly
increase the solubility of the API relative to the pure solvent. By
studying the solubility curves in Figure , it is seen that an increase in operating
temperature leads to a relative shift of the solubility curve, such
that the greatest drop in ibuprofen solubility occurs at a higher
composition of antisolvent. Though at low temperatures the effect
of unfavorable interactions between the API and antisolvent is so
great that even a small addition of water leads to a considerable
drop in solubility, at high temperatures these effects are reduced;
the system requires considerably more water to reduce the solubility
of ibuprofen significantly. As such, at higher initial temperatures,
more antisolvents can be present in the initial mixture without negatively
impacting the initial solubility of API, and therefore, less additional
water is required to achieve the final, low-solubility composition
at 293.15 K. It is clear that the integration of cooling and antisolvent
crystallization techniques is critical in allowing nonlinear interactions
such as these to occur. Such gains are not observed for all APIs;
this phenomenon is not present in the case of lovastatin, where the
solubility curve shifts in the opposite direction when the temperature
is increased. Given the range of possible behaviors, the proposed
general approach provides the opportunity for optimal scenarios to
be discovered. Indeed, the differences between the two APIs considered
highlight the key benefits of CAMbD and the importance
of applying a general approach to solvent design.
Table 7
Comparison of Ranked Solvent Blends
for Integrated Cooling and Antisolvent Crystallization of Ibuprofena
solvents
T0/K
rank
YAPI/%
Vs/(mL/g)
s1
s2
298.15
1
99.85
7.82
1.000
0.040
ethanol
water
2
99.84
7.90
0.603
0.027
acetone
water
3
99.74
12.72
1.000
0.027
1-propanol
water
4
99.61
18.72
0.556
0.020
1-butanol
water
303.15
1
99.87
6.93
1.000
0.040
ethanol
water
2
99.87
6.57
0.580
0.027
acetone
water
3
99.77
11.28
0.679
0.027
1-propanol
water
4
99.70
14.65
0.497
0.020
1-butanol
water
308.15
1
99.89
5.28
0.553
0.027
acetone
water
2
99.88
6.07
1.000
0.040
ethanol
water
3
99.82
9.09
0.559
0.027
1-propanol
water
4
99.77
11.07
0.486
0.020
1-butanol
water
313.15
1
99.92
4.01
0.519
0.027
acetone
water
2
99.90
5.23
1.000
0.040
ethanol
water
3
99.86
6.92
0.471
0.027
1-propanol
water
4
99.84
7.92
0.467
0.020
1-butanol
water
318.15
1
99.94
4.00
0.475
0.021
acetone
water
2
99.92
4.13
0.517
0.040
ethanol
water
3
99.90
4.80
0.423
0.027
1-propanol
water
4
99.88
5.78
0.438
0.020
1-butanol
water
In all cases, T0 = Tmax, and the final temperature
is 293.15 K. Italicized solutions are optimal mixtures with additional
composition constraints, to account for the presence of LLE.
Figure 9
Predicted solubility
of ibuprofen, xibuprofen*, on a
molar basis, in mixtures of ethanol and water at 293.15 K (solid line)
and 318.15 K (dashed line), calculated using the SAFT-γ Mie
group-contribution approach in gPROMS. xwaterS refers to
the mole fraction of water in the binary solvent mixture.
Predicted solubility
of ibuprofen, xibuprofen*, on a
molar basis, in mixtures of ethanol and water at 293.15 K (solid line)
and 318.15 K (dashed line), calculated using the SAFT-γ Mie
group-contribution approach in gPROMS. xwaterS refers to
the mole fraction of water in the binary solvent mixture.In all cases, T0 = Tmax, and the final temperature
is 293.15 K. Italicized solutions are optimal mixtures with additional
composition constraints, to account for the presence of LLE.
Conclusions
A
general formulation has been presented based on a CAMbD
framework, with an aim to guide experiments toward the identification
of optimal solvent blends for the crystallization of pharmaceutical
compounds, reducing the time and costs typically associated with solvent
selection. By using this general approach, the optimal solvent and
antisolvent molecules, their compositions, and the process temperatures
required to maximize the crystal yield of a given API can be identified
simultaneously, for both the initial and final states of crystallization.The general formulation has been applied successfully to the crystallization
of lovastatin, where optimal solvent mixtures are determined and ranked
for several operating temperature ranges, process conditions, and
crystallization techniques. Furthermore, we show that constraining
the mass of solvent utilized during crystallization can lead to compromise
solutions, where a small decrease in crystal yield makes it possible
to achieve a more environmentally desirable design. The formulation
has also been applied to the crystallization of ibuprofen, under similar
conditions, expressing the versatility of the general approach. Whereas
it was found that integrating cooling and antisolvent crystallization
can significantly improve the crystal yield of lovastatin, this hybrid
approach and antisolvent crystallization is seen to offer similar
performance in the case of ibuprofen. Furthermore, the solubilities
of the two APIs, in the respective optimal solvent mixtures, have
different responses to a change in temperature; for ibuprofen, the
solubility curve shifts to improve the crystal yield and solvent consumption,
whilst for lovastatin, the opposite is true. As such, the general
methodology proposed in our current work is particularly powerful
in highlighting optimal solutions across a range of API molecules
and conditions, taking into account the subtle impacts of different
chemistries.The simultaneous design of the solvent mixture
and operating temperature
led to improvements compared to those achieved when the temperature
range is fixed. Moreover, it was shown that maximizing the temperature
range may not always result in the optimal operating conditions—the
application of powerful but volatile solvents or antisolvents can
instead improve the outcome of a crystallization, whilst reducing
the initial operating temperature. In both case studies, a better
performance is also found for the hybrid cooling and antisolvent crystallization
techniques compared to standalone methods. Permitting the use of solvent
mixtures throughout the entire crystallization introduces the possibility
for the process to utilize all regions of the API solubility curve,
potentially increasing crystal yield and reducing solvent consumption.
Additionally, the proposed method is applicable to any number of mixture
components and could thus be expanded to model ternary solvent mixtures,
such as those where residual water may still be present following
upstream solvent swaps or to model the impact of impurities, provided
their molecular structure is known. Because the proposed approach
is derived from the generic multicomponent framework of Jonuzaj et al.,[24] it is in fact possible
to optimize the identity of additional components. Finally, we find
it remarkable that high performance (high yields and low solvent consumption)
can be achieved using a relatively limited number of solvents. This
may be due to some extent to the fact that the solvents considered
cover several chemical classes. As more group-interaction parameters
are developed for the SAFT-γ Mie equation of state,[30] the range of solvents can be expanded further.Because of the necessity to produce a flexible framework for solvent
design in the pharmaceutical industry, other considerations are required
to expand this type of study. Whilst the toxicity of solvents is used
to shortlist candidates initially for the case studies explored here,
it is important to consider other HSE aspects, such as the flammability
or reactivity of solvents. This can be achieved by including additional
GC methods in the formulation,[16] selecting
solvents based on the ICH classification[50] or by applying safety indicators[11] to
the list of candidate solvents to screen them;[17] Jonuzaj et al.(51) have recently investigated the effects of such a choice on crystallization
metrics. Furthermore, although it is important to design efficient
crystallization processes, problems can arise downstream from the
morphology of the final crystal form, such as needle- or plate-like
particles inhibiting filtration systems. This has been the subject
of earlier work,[16] which concentrated on
the correlation between solubility parameters and crystal growth rates,
but would benefit from a more mechanistic description of solvent effects
on shape. Finally, it would be advantageous to take into the account
wider process impacts of the use of solvents. This includes capital
and operating costs—for instance, energy costs arising from
solvent recovery and waste treatment—which may result in different
cooling/antisolvent crystallization designs. It also includes broadening
the scope of the processing steps considered to take into account
isolation[51] as well as synthesis, which
has typically been considered separately from crystallisation.[52,53]
Table 9
Group–Group Dispersive Interaction
Energies and Repulsive Exponents for Use within the SAFT-γ Mie
Group-Contribution Approacha
k
l
group k
group l
(ϵkl/kB)/K
λklr
k
l
group k
group l
(ϵkl/kB)/K
λklr
1
1
CH3
CH3
256.77
15.050
4*
7
CH2=
CH2OH
375.51
CR
1
2
CH3
CH2
350.77
CR
4*
8
CH2=
CHOH
449.83
CR
1
3
CH3
CH
387.48
CR
4
9
CH2=
COO
CR
CR
1
4
CH3
CH2=
333.48
CR
4*
10
CH2=
CH3COCH3
288.20
CR
1
5
CH3
CH=
252.41
CR
4*
11
CH2=
H2O
387.25
94.463
1
6
CH3
cCH2
355.95
CR
5
5
CH=
CH =
952.54
15.974
1*
7
CH3
CH2OH
333.20
CR
5
6
CH=
cCH2
398.35
CR
1*
8
CH3
CHOH
479.38
CR
5*
7
CH=
CH2OH
414.91
CR
1
9
CH3
COO
402.75
CR
5*
8
CH=
CHOH
540.83
CR
1
10
CH3
CH3COCH3
233.48
14.499
5*
9
CH=
COO
818.79
CR
1
11
CH3
H2O
358.18
100.00
5*
10
CH=
CH3COCH3
437.75
CR
2
2
CH2
CH2
473.39
19.871
5*
11
CH=
H2O
332.21
17.309
2
3
CH2
CH
300.07
CR
6
6
cCH2
cCH2
477.36
20.386
2
4
CH2
CH2=
386.80
CR
6*
7
cCH2
CH2OH
CR
CR
2
5
CH2
CH=
459.40
CR
6*
8
cCH2
CHOH
554.50
CR
2
6
CH2
cCH2
469.67
CR
6
9
cCH2
COO
498.60
CR
2*
7
CH2
CH2OH
423.17
CR
6*
10
cCH2
CH3COCH3
352.19
CR
2*
8
CH2
CHOH
517.64
CR
6*
11
cCH2
H2O
347.48
28.497
2
9
CH2
COO
498.86
CR
7*
7
CH2OH
CH2OH
407.22
22.699
2
10
CH2
CH3COCH3
299.48
11.594
7*
8
CH2OH
CHOH
389.23
CR
2
11
CH2
H2O
423.63
100.00
7*
9
CH2OH
COO
CR
CR
3
3
CH
CH
95.621
8.0000
7*
10
CH2OH
CH3COCH3
338.47
CR
3
4
CH
CH2=
426.77
CR
7*
11
CH2OH
H2O
353.37
CR
3
5
CH
CH=
502.99
CR
8*
8
CHOH
CHOH
599.66
18.185
3
6
CH
cCH2
570.45
CR
8*
9
CHOH
COO
CR
CR
3*
7
CH
CH2OH
329.22
CR
8*
10
CHOH
CH3COCH3
340.81
CR
3*
8
CH
CHOH
0.00
CR
8*
11
CHOH
H2O
479.16
CR
3*
9
CH
COO
353.65
CR
9
9
COO
COO
868.92
31.189
3
10
CH
CH3COCH3
637.29
CR
9*
10
COO
CH3COCH3
547.44
CR
3
11
CH
H2O
275.75
CR
9*
11
COO
H2O
396.81
15.140
4
4
CH2=
CH2=
300.90
20.271
10
10
CH3COCH3
CH3COCH3
286.02
17.433
4
5
CH2=
CH=
275.75
CR
10
11
CH3COCH3
H2O
287.26
CR
4
6
CH2=
cCH2
CR
CR
11
11
H2O
H2O
266.68
17.020
λr is the repulsive exponent
and ϵ is the dispersive energy
of the Mie potential characterizing the interaction of two groups k and l. CR refers to parameter values
that are determined using combining rules (see Dufal et al.(54)). Rows marked with an asterisk contain
parameter values introduced in our current work, which will be the
subject of a future paper. The parameter values for groups without
an asterisk are taken directly from Dufal et al.(54)
Authors: Heiko Struebing; Zara Ganase; Panagiotis G Karamertzanis; Eirini Siougkrou; Peter Haycock; Patrick M Piccione; Alan Armstrong; Amparo Galindo; Claire S Adjiman Journal: Nat Chem Date: 2013-09-22 Impact factor: 24.427
Authors: Andrew R Bogdan; Sarah L Poe; Daniel C Kubis; Steven J Broadwater; D Tyler McQuade Journal: Angew Chem Int Ed Engl Date: 2009 Impact factor: 15.336
Authors: Vasileios Papaioannou; Thomas Lafitte; Carlos Avendaño; Claire S Adjiman; George Jackson; Erich A Müller; Amparo Galindo Journal: J Chem Phys Date: 2014-02-07 Impact factor: 3.488
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9