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Methods for Estimating Supersaturation in Antisolvent Crystallization Systems

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Methods for Estimating Supersaturation in Antisolvent Crystallization Systems Methods for estimating supersaturation in antisolvent crystallization systems The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Schall, Jennifer M., Gerard Mendez, and Allan S. Myerson, "Methods for estimating supersaturation in antisolvent crystallization systems." CrystEngComm 38 (Aug. 2019): p. 5811-17 doi 10.1039/ c9ce00843h ©2019 Author(s) As Published 10.1039/c9ce00843h Publisher Royal Society of Chemistry (RSC) Version Final published version Citable link https://hdl.handle.net/1721.1/124866 Terms of Use Creative Commons Attribution Noncommercial 3.0 unported license Detailed Terms https://creativecommons.org/licenses/by-nc/3.0/ CrystEngComm View Article Online PAPER View Journal Methods for estimating supersaturation in † Cite this: DOI: 10.1039/c9ce00843h antisolvent crystallization systems Jennifer M. Schall, Gerard Capellades and Allan S. Myerson * The mole fraction and activity coefficient-dependent (MFAD) supersaturation expression is the least-as- sumptive, practical choice for calculating supersaturation in solvent mixtures. This paper reviews the basic thermodynamic derivation of the supersaturation expression, revisits common simplifying assumptions, and discusses the shortcomings of those assumptions for the design of industrial crystallization processes. A step-by-step methodology for estimating the activity-dependent supersaturation is provided with focus on ternary systems. This method requires only solubility data and thermal property data from a single differen- tial scanning calorimetry (DSC) experiment. Two case studies are presented, where common simplifications to the MFAD supersaturation expression are evaluated: (1) for various levels of supersaturation of L- asparagine monohydrate in water–isopropanol mixtures and (2) for the dynamic and steady-state mixed- Creative Commons Attribution-NonCommercial 3.0 Unported Licence. suspension, mixed-product removal (MSMPR) crystallization of a proprietary API in water–ethanol–tetrahy- Received 31st May 2019, drofuran solvent mixtures. When compared to the MFAD supersaturation estimation, it becomes clear that Accepted 26th August 2019 errors in excess of 190% may be introduced in the estimation of the crystallization driving force by making unnecessary simplifications to the supersaturation expression. These errors can result in additional parame- DOI: 10.1039/c9ce00843h ter regression errors – sometimes by nearly an order of magnitude – for nucleation and growth kinetic pa- rsc.li/crystengcomm rameters, limiting the accurate simulation of dynamic and steady-state crystallization systems. 1. Introduction while at saturation, denoted by sat, the solute has chemical This article is licensed under a potential of Crystallization is a rate-based process, so establishing accu- rate estimates of crystal growth and nucleation rates governs μsat(T)=μ0(T)+RT ln(asat) (2) 1–3 Open Access Article. Published on 27 August 2019. Downloaded 9/17/2019 3:15:13 PM. successful crystallization process design and optimization. Empirically, crystal growth and nucleation are related to Crystallization can occur when the chemical potential of a supersaturation through power law dependencies, with nucle- species is higher than the chemical potential that species ation generally exhibiting a higher power supersaturation de- would exert at equilibrium. The dimensionless thermody- pendence than growth.4 Incorrect estimates of supersatura- namic expression for supersaturation is calculated from the tion lead to incorrect estimates of crystallization kinetics, difference in chemical potentials as4 which result in erroneous predictions of yield, crystal size dis- tribution, and optimal crystallizer operating conditions. By thermodynamic definition, the driving force for crystal- sat x ln (3) lization or dissolution arises from a difference between the sat sat RT x partial molar Gibbs' free energy of a solute and the chemical potential of the solute at equilibrium. At supersaturated con- ditions, the solute has a chemical potential of For the rest of this manuscript, this expression will be re- ferred to as the mole fraction and activity coefficient- μ μ0 (T)= (T)+RT ln(a) (1) dependent (MFAD) supersaturation expression. In this ex- pression, four quantities are needed to calculate supersatura- tion in the solution: Department of Chemical Engineering, Massachusetts Institute of Technology, 77 1. xsat, the mole fraction of the solute in the saturated Massachusetts Avenue, Cambridge, Massachusetts 02139, USA. solution. This can be calculated from solubility data. E-mail: [email protected] † Electronic supplementary information (ESI) available: Summary of gPROMS 2. x, the mole fraction of the solute in the supersaturated model equations, parameters and variables. Error propagation study. See DOI: solution. This can be calculated from mother liquor 10.1039/c9ce00843h concentration data. This journal is © The Royal Society of Chemistry 2019 CrystEngComm View Article Online Paper CrystEngComm 3. γsat, the activity coefficient of the solute in the saturated will have a significantly different density and average molec- solution. This can be calculated from the generalized ular weight than the supersaturated system, and the ratio of solubility equation.4 concentrations will not be equivalent to the ratio of molar 4. γ, the activity coefficient of the solute in the supersatu- fractions. rated solution. Simplifications 2 and 3 may also be flawed in highly Unfortunately, it is extremely challenging to measure the supersaturated systems. As the system further deviates from solute activity coefficient at supersaturated conditions be- ideality, the activity coefficient ratio deviates further from cause the system is not at an equilibrium state.5 For this rea- one. This scenario is frequently encountered during batch son, the thermodynamic expression for supersaturation is crystallization and many transient continuous systems. Thus, not immediately useful in industrial settings. This has tradi- accounting for the solute activities is often critical for a good tionally led to the use of simplifying assumptions to approxi- prediction of these processes, as well as for the calibration of mate the true supersaturation of a solution. For example, in mathematical models that account for significant variations dilute systems, the ratio of the solute mole fraction in the in supersaturation between experiments. This limitation is supersaturated and saturated phases is close to the ratio of more restrictive for antisolvent crystallization, where the ac- the solute molar concentrations in the supersaturated and tivity coefficient ratio quickly deviates from unity even at low saturated phases. This allows to simplify the supersaturation supersaturations. expression as To circumvent the difficulties in measuring the activity co- efficient at supersaturated conditions, an estimation method 7 c was recently proposed by Valavi, Svärd, and Rasmuson. In Simplification 1: ln sat sat (4) that method, the activity coefficient in the supersaturated bi- c nary solution is assumed to be the same as the activity coeffi- cient in a saturated binary solution of the same composition, This simplification of using concentrations instead of Creative Commons Attribution-NonCommercial 3.0 Unported Licence. allowing the activity coefficient to be approximated using mole fractions is common practice, as it eliminates the need only solubility data and the generalized solubility equation. to convert high performance liquid chromatography (HPLC) For these cases, the underlying assumption is that the activity or other mass-based concentration measurements to solute coefficient is a strong function of composition but a weak mole fractions. If the system is also ideal, the activity coeffi- function of temperature. cients are unity, and the supersaturation expression can be In this manuscript, we first present a step-by-step proce- simplified even further as dure, which builds on the method proposed by Valavi et al.,7 to estimate the MFAD supersaturation in ternary systems. c The presented method can also be used for binary systems, Simplification 2: ln sat (5) This article is licensed under a c although it is especially important for calculating supersatu- ration during antisolvent crystallization, where both kinetics This simplified expression is also acceptable near equilib- and thermodynamics are strongly affected by solvent compo- 8 Open Access Article. Published on 27 August 2019. Downloaded 9/17/2019 3:15:13 PM. rium when the ratio of the activity coefficient at supersatu- sition. With this method, activity-dependent supersaturation rated and saturated conditions is close to unity. For special estimates may be obtained by pairing solubility data with σ ≪ cases where the supersaturation is also very low ( 1) such thermodynamic data from a single differential scanning calo- σ σ that ln( +1)= , the dimensionless chemical potential dif- rimetry (DSC) experiment. In the second half of the manu- ference can be approximated by a dimensionless concentra- script, we present two case studies to quantify the differences tion difference amongst simplifications 1–3, and demonstrate the need for using proper supersaturation estimates. cc sat Simplification 3: (6) csat 2. Methods This is generally a poor approximation at σ > 1,6 but it is 2.1 Method for estimating MFAD supersaturation in a solvent still normally used despite including the
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