From Experiments and Models to Business Decisions: A Scale-up

Article Cite This: Org. Process Res. Dev. XXXX, XXX, XXX−XXX

pubs.acs.org/OPRD

From Experiments and Models to Business Decisions: A Scale-up Study on the Reactive Crystallization of a Crop Protection Agent Venkateswarlu Bhamidi,*,† Kim Dumoleijn,‡ Debangshu Guha,§ Shane K. Kirk,† Alain De Bruyn,‡ and Allison K. Pymer∥ Scale-up and Process Innovation, §Worldwide Engineering & Construction, ∥Corporate Analytical Division, Eastman Chemical Company, PO Box 511, Kingsport, Tennessee 37662, United States ‡ Amines & Formic Acid Technology, Eastman Chemical Company, Pantserschipstraat 207, 9000 Ghent, Belgium Org. Process Res. Dev. Downloaded from pubs.acs.org by UNIV OF TEXAS AT DALLAS on 02/11/19. For personal use only.

†

S Supporting Information *

ABSTRACT: Industrial R&D organizations often operate under a paradigm in which the scope of process research is narrowed significantly to the extent needed to solve the problem that is hindering the business from moving forward. In this work we discuss an R&D effort carried out in such a constrained environment toward assessing the feasibility of commercial manufacturing for a crop protection agent. The work, which started as a “brute-force” search for optimal process scale-up conditions, quickly led us to the realization that the process under consideration is far more complex than it appeared at a first glance. The synthesis of the compound of interest involved a reactive crystallization, and the product exhibited rich and intriguing phase separation phenomena that result in drusy crystals of undesirable particle size distribution. Recognizing the crystal “agglomerates” to originate from liquid−liquid phase separation (LLPS), we adopted a simplified process development approach in which we combined a few key experiments with theoretical and engineering models on LLPS and reactor design to effectively explore the design space. Our approach quickly provided the needed information regarding the economic impact of process conditions suitable for scale-up. These insights enabled the business organization to make an informed decision regarding the pursuit of a business opportunity. This work shows how the often-overlooked “academic” concepts can be leveraged in industrial R&D projects toward fruitful outcomes. KEYWORDS: dithiocarbamate, liquid−liquid phase separation, LLPS, oiling out, spherulites, reactive crystallization

1. INTRODUCTION Dithiocarbamates (DTCs) are an important class of organosulfur compounds that are widely used in agriculture as crop protection agents.1−3 Many DTCs (e.g., ferbam, thiram, zineb) find applications as contact fungicides; that is, they are sprayed on plant leaves to be effective in controlling the plant disease. A few DTCs (e.g., metam sodium) are used as soil fumigants and nematicides.4 In this mode of action DTCs are applied on soil where they react with water and slowly release gases that are toxic to soil fungi, nematodes, and soil-dwelling insects. Due to their reactivity with water, typically these crop protection agents are manufactured as solid active ingredients which later are formulated as aqueous dispersions at the time of application. Recently, a business opportunity arose for Eastman to produce several thousand tons per year of a specific dithiocarbamate, compound Z. Compound Z can be synthesized in a single step by reacting a precursor molecule M with formaldehyde (hereafter referred to as aldehyde A for brevity) (Scheme 1). Eastman already produces compound M

commercially, and hence the proposal to manufacture Z made business sense as a value-adding step to an existing molecule. However, an uncertainty existed in the anticipated market life span for compound Z due to the impending regulatory reviews of environmental and toxicological effects of Z. For this reason, building a new manufacturing plant exclusively for producing Z was not desired. A quick appraisal of the existing manufacturing facilities identified a production unit for another chemical in which compound Z may be campaigned for several months a year. The window of opportunity to decide on the business proposal was short, and the technical team, comprising the authors of this work, was tasked with developing and scaling-up a manufacturing process for Z that could be accommodated in the existing facility. The existing production facility into which the manufacturing process for Z needs to be retro-fitted consists of a continuous stirred tank reactor (CSTR) of 1.6 m3 volume. This CSTR discharges into a rotary vacuum filter that handles the slurry resulting from the reaction. This retrofit unit needs to achieve a desired production rate of at least ∼1.2 tons/h (about 20 kg/ min). Also, the solid product needs to be a powder with a narrow particle size distribution in the range of 100−300 μm with a distribution span (= (D90 − D10)/D50) close to 1.0. High temperature reaction and drying operations are not recom-

Scheme 1. Synthesis Reaction for Compound Z

Received: November 23, 2018

© XXXX American Chemical Society

A

DOI: 10.1021/acs.oprd.8b00384 Org. Process Res. Dev. XXXX, XXX, XXX−XXX

Organic Process Research & Development

Article

interest. This choice reduced the experimental effort needed (as desired by the business organization) to determine the phase boundaries over a narrow composition range of process solvent. The solubility data were obtained using a high-throughput solubility apparatus, Crystal 16.8 In this method, known amounts of the solute and solvent are charged to a small vial (a typical HPLC vial of about 1.5 mL), and the contents of the vial are kept stirred while the vial is slowly heated at a set ramp rate. Light transmittance through the solution is monitored during this temperature ramp, and the “clear point” (solubility temperature) for that composition is determined as the temperature at which the transmittance reaches 100% (indicating that all the solids have dissolved). Multiple data points can be obtained simultaneously by varying the concentration of the solute and the solvent in each vial. In our case, given the possibility of a degradation reaction between the solute Z and water, it was desirable to avoid extended contact between the solute and the solvent at elevated temperatures. For this reason, we used a heating rate of 0.5 °C/min in our experiments. The data collection was also limited to a temperature range of 5−65 °C. As a verification of the accuracy of solubility data, a few data points were also determined using a heating rate of 0.25 °C/min with Crystal 16, and these values were not found to be significantly different from the values obtained using 0.5 °C/min. In addition to determining the solubility boundary, we also have determined the liquid−liquid phase separation (LLPS) boundary through rapid cooling of solutions of compound Z dissolved in the process solvent. Two methods were used for this purpose. At first, we attempted to use a cold-stage method in which a droplet of hot solution was cooled rapidly while being monitored for a phase change under a microscope. We encountered experimental difficulties in this method and could obtain only one reliable data point. The details of this effort are provided in the Supporting Information. As an improvisation, we then used the same Crystal 16 apparatus described above to cool the clear solutions rapidly. These experiments were performed separately from the solubility runs. In these experiments the solute was first dissolved quickly by placing the vials in Crystal 16 bays that were already preheated to an appropriate high temperature (always < 60 °C). These vials were then cooled at 1 °C/min until a phase change was registered by the instrument. During cooling, Crystal 16 detects the onset of a new phase at the “cloud point” temperature through a reduction in light transmittance in the solution. By design, the apparatus cannot distinguish between the onset of crystallization and the onset of a liquid−liquid phase separation. However, we actively monitored the vials during the cooling, and when a reduction in the light transmittance was registered by the instrument, we physically retrieved the vials and examined the contents visually. In solutions with high solute concentration (>1.7% (w/w)), we could distinguish the ephemeral cloudy “oil phase” which would very quickly turn into the “white crystal clusters”. The occurrence of LLPS in solutions with solute concentration < 1.7% (w/w) could not be visually ascertained but could be inferred indirectly through the presence of spherulitic crystals in the end. 2.3. Initial Synthesis Experiments. In the beginning, several process synthesis experiments were performed with an optimistic viewpoint of identifying suitable process scale-up conditions by a rather brute-force search of the parameter space. These experiments also helped us gain familiarity with the

mended due to the accelerated decomposition of Z when in contact with water at elevated temperatures. Hence any manufacturing process conceived should produce solids at near-ambient temperature, and these solids should filter well. Even though DTCs have been in agricultural use for several decades, one finds that most of the open literature discusses mainly either the analytical methods that characterize trace levels of these pesticides or the environmental effects of these compounds.5,6 Little information is available on the process design and engineering aspects of the manufacture of these DTCs at an industrial scale, except for select patents that are compound-specific.7 Hence we were in a situation in which the process knowledge essential to assess the economic feasibility needed to be generated from the ground-up. This R&D effort can be a costly venture. Given the uncertainty of the return on investment, the business organization requested the research team minimize the expenditure on the R&D activities and asked us to reach a conclusion within 3 to 6 months. This business rationale dictated the team prioritize a quick techno-economic evaluation of the opportunity rather than an elaborate research program focused on detailed process development. The present work describes our efforts in this context. Here we describe the methodology in which we carried out a few key experimental studies and took advantage of the existing theoretical and engineering models to arrive at a rational business decision.

2. EXPERIMENTAL SECTION 2.1. Materials and Methods. The precursor M used in the experimental studies is a commercial product from Eastman available as a 50−60% (w/w) aqueous solution. Subsequent dilutions of this solution were performed as needed using demineralized water. Aldehyde A was purchased from SigmaAldrich as a nominal 37% (w/w) aqueous solution containing 10−15% (w/w) methanol as a stabilizer. Pure methanol was also obtained from Sigma-Aldrich. The concentrations of M and A in various batches of starting solutions were determined prior to use through high performance liquid chromatography (Agilent HPLC 1260). The concentration of methanol in the purchased reactant A solutions was determined using gas chromatography (Agilent GC 7890). Optical micrographs of the product were collected using a compound microscope (Leica DM750P) equipped with a digital camera (Leica DMC2900). High magnification micrographs of the solid product were obtained using a scanning electron microscope (FEI Quanta 450F SEM). Particle size distributions of the product were determined with a Malvern Mastersizer model 2000. All the computational procedures were implemented in Mathematica (v11.3, Wolfram Research). 2.2. Determination of Solubility and the LLPS Boundary. To understand the liquid−solid phase behavior of compound Z under process conditions, the solubility of Z in the process solvent of interest at various temperatures needed to be determined. As we note from above, both reactant streams (streams of M and A) contain water as a major component. Also, as evident from Scheme 1, the synthesis produces 2 mol of water for each mole of the product Z generated. Process calculations indicated that for the expected concentration ranges of M and A in the reactant streams, the reaction mixture will have ∼96 to 98% (w/w) water and 2 to 4% (w/w) methanol as solvent at full conversion. The solubility of Z and other phase behavior is not expected to vary significantly within this narrow composition range of the “solvent”. Hence, we chose 98% (w/w) water − 2% (w/w) methanol as our representative “process solvent” of B



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2.5. Reactive Crystallization Experiments. These experiments were similar to the synthesis experiments described above and also were carried out in batch mode. However, the objective of these experiments was different. In these experiments we sought to understand the phase transformation process of the product once it forms by chemical reaction. To this end, batch reactive crystallizations were carried out in a 300 mL glass jacketed reactor (Wilmad LabGlass) equipped with process analytical technology (PAT) tools capable of monitoring the crystallization process. This PAT equipment consisted of a focused beam reflectance measurement probe (FBRM Model D600, Mettler-Toledo) and a particle vision and measurement probe (PVM Model V819, Mettler-Toledo) inserted into the reaction mixture. In these experiments the reactor was first loaded with 50% (w/w) aqueous solution of M and was equilibrated to 18 °C. Where needed, additional water was added in required amounts as diluent before equilibration. A stoichiometric amount of aldehyde A (as 33% (w/w) solution) was then charged to the reactor rapidly in one aliquot while stirring the contents of the reactor. Optical micrographs of the solution were collected in situ by the PVM probe, while the FBRM probe tracked the size evolution of particles in the reaction mixture. The brief rise of temperature (despite the cooling provided by the jacketed fluid) was monitored using a thermocouple. We obtained additional optical micrographs of the crystalline particles later at the end of the experiment using an off-line optical microscope. These experiments were carried out with different target product concentrations ranging from 10 to 35% (w/w).

synthesis, identify key variables in the process, and recognize the peculiarities of the phase behavior of Z in the reaction solvent. These preliminary experiments were carried out in a 2 L glasslined jacketed reactor (Büchi Polyclave) with temperature control. The flows of reactants were regulated by Coriolis mass flow meters. We conducted these experiments in semibatch, fed batch, and continuous modes, and characterized the products resulting from various experiments. In the semibatch experiments, first a solution containing aldehyde A (stream A) was charged to the reactor in the required amount. This solution was kept stirred while the solution containing precursor M (stream M) was added slowly to the reactor at a set flow rate. These experiments explored the effect of excess amount of reactant A on the conversion and the physical attributes of the solid product. Additional experiments that probed the effect of temperature on the product characteristics were carried out in a fed-batch mode, in which both reactant streams (equilibrated to the temperature of interest) were added simultaneously to the stirred reactor at set flow rates and the temperature of the mixture was maintained by employing cooling on the jacket. Continuous synthesis experiments were also performed in the same reactor setup and the effects of residence time and target product concentration on the product particle size distribution were studied. 2.4. Reaction Kinetics Experiments. Batch experiments targeted at generating the reaction kinetic data usually involve collecting samples from a reaction batch at various times and determining the concentrations of various species as functions of time. During the preliminary experiments, however, we observed that the reaction between M and A is quite fast, resulting in precipitated solids of the product within seconds after contact between the reactant streams. Thus, it was difficult to perform batch reaction kinetic experiments in the traditional manner. Online reaction monitoring probes capable of resolving ultrafast reaction kinetics may be needed to fully characterize the reaction kinetics, and such equipment were not available. To circumvent these experimental difficulties and yet be able to generate a useful kinetic model, we adopted the following experimental strategy. Apart from being fast, the chemical reaction between M and A is also highly exothermic. Thus, the temperature of an adiabatic reaction mass continuously rises as the reaction progresses. Knowing the physical properties of the reaction mass, one can estimate the heat release as a function of time by tracking the temperature rise during the reaction. This heat release then can be tied to an assumed reaction rate expression, making it possible to generate information on the reaction rate constant and its temperature functionality. This procedure provided us with a working model for estimating the reaction kinetics. Experiments conducted to this end were performed using a 1 L insulated reactor (Berghof HP BR-1000). The thermocouple in the reactor was hooked-up to a computer to record the temperature vs time data at 1 Hz. First, an aqueous solution of M was loaded into the reactor and was equilibrated to the ambient temperature (approximately 21 °C) while stirring. Upon equilibration, preweighed reactant A solution (also at room temperature) was injected into the reactor at once while stirring the reactor contents. The rise of temperature was monitored with time for about an hour. These data were later used to build a working reaction kinetic model. These experiments were carried out at two different target product concentrations of 15 and 25% (w/w).

3. RESULTS 3.1. Batch Experiments. The initial experiments that followed a brute-force approach (Section 2.3) toward finding optimal process conditions uncovered several important concerns toward scale-up of the synthesis. First, the reaction appeared to be quite fast as evidenced by a rapid precipitation of the product solids upon contact between the reactants. Analysis of the liquid phase soon after the addition of reactants showed that the reaction typically occurs to near 100% conversion with negligible impurity generation. In addition, we observed that the reaction is highly exothermic. This large heat of reaction raised concerns over the cooling requirements for the reactor at scale. The most troubling aspect identified in these experiments, however, was a “sticky” crystallization and the resulting unacceptable particle size distribution of the final product, which became the focus of the search for scalable process conditions afterward. The product specification mandates a solid with particles mainly in the size range of 200 to 300 μm, with particles 35 °C are not recommended in the final process due to the accelerated reaction between Z and water leading to C



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Table 1. Effect of Excess Equivalents of A and the Rate of Addition of Stream M on the PSD of the Product at 30 °Ca mole ratio (A/M)

rate of M (g/h)

D10 (μm)c

D50 (μm)

D90 (μm)

Spanb

3.0 2.7 2.3 2.3

200 200 200 1000

3.4 3.7 2.3 4.8

115.0 136.9 123.3 151.1

521.7 728.7 510.2 307.5

4.507 5.296 4.119 2.003

Table 3. Effect of Mean Residence Time (τ) and Target Product Concentrationb on the PSD during the Continuous Synthesis of Compound Za

a

Used reactant concentrations in streams A and M were 10% and 30% (w/w), respectively. bSpan, a measure of the spread of the distribution, is defined here as (D90 − D10)/D50. cThe size reported by the PSD instrument is a volume-averaged equivalent spherical diameter.

D10

D50

D90

(°C)

(μm)

(μm)

(μm)

10 30 50

206 341 397

455 641 888

825 1185 1492

τ (h)

D10 (μm)

D50 (μm)

D90 (μm)

Span

7.5 7.5 15.0 15.0

0.5 1.0 0.5 1.0

257 121 264 242

627 281 533 502

1089 533 1044 910

1.34 1.47 1.46 1.33

a The molar ratio of A/M used in these experiments was 1.9. Reactant concentrations in streams A and M were 10% and 32% (w/w), respectively. The reactor was maintained at 20 °C during the experiments. bThis concentration (Czo) represents a theoretical maximum concentration of the product upon complete conversion of the reactants to Z before a phase split.

Table 2. Effect of Reaction Temperature on the PSDa temp.

target product conc. (%(w/w))

these batch and continuous mode experiments were rarely unimodal. Most of the experiments resulted in particles with bimodal, trimodal, and even quadrimodal distributions with no particular trend. Such multimodal wide PSDs are unacceptable. At this point, it became clear to the technical team that a bruteforce search was unlikely to result in scalable process conditions. It was imperative that the specifics of both reaction and crystallization processes involved in the synthesis need to be understood for further progress. While the business interests urged the team to minimize the R&D expenditure, we felt that additional time and resources invested in understanding the fundamentals of the process were more likely to provide a success than an arbitrary search of the design space. Thus, hereafter the team focused on understanding the dynamics of reaction and crystallization steps involved in the synthesis of compound Z. 3.3. Particle Characteristics and Link to Phase Behavior. All the “brute-force” experiments typically produced a granular material that was somewhat “sticky” before it was dried. While these “granules” were desirable from a filtration perspective, they were prone to handling difficulties after filtration and exhibited unacceptable particle size distributions. Figure 1 shows the scanning electron micrographs (SEMs) of the particles produced in a continuous (CSTR) synthesis that targeted a Czo of 15% (w/w) in the reactor. At low magnification the particles appear to be random agglomerates (Figure 1a). However, the high magnification image in Figure 1b indicates the product granules to be drusy, with several tiny crystallites encrusting what appear to be central crystalline cores. The systematic radial orientation and the roughly equal size of the “spikes” suggest that these crystal granules could not have formed through the agglomeration of individual primary particles; rather these spikes may have originated from a central core simultaneously and have grown into each other. This mode of “spherulitic” crystal growth is typically observed in large molecules such as proteins9,10 and is thought to be related to the liquid−liquid phase separation (LLPS, also known as oiling out) phenomenon that manifests in some solute−solvent systems.11−13 To verify our hypothesis that indeed the product granules resulted from a metastable liquid−liquid phase separation, we carried out a reactive crystallization study in which we monitored the solution reacting at various conditions using FBRM/PVM instruments (Section 2.5). Figure 2a shows an image from the reacting solution obtained by PVM approximately a minute after the rapid addition of the aldehyde A solution to the precursor M solution. This batch experiment targeted a Czo of 35% (w/w). Immediately following

Span 1.360 1.316 1.233

a The molar ratio of A/M used in these experiments was 2.3. Reactant concentrations in streams A and M were 10% and 30% (w/w), respectively. The rates of addition for streams A and M were 142 and 192 g/h, respectively.

the decomposition of Z. Another aspect observed from Tables 1 and 2 is that for the same reaction temperature (30 °C) and the same molar ratio of A/M (2.3), PSDs of the resulting solid particles were widely different depending on the mode of solution addition. This result highlights that mixing of the streams and the target concentration of the product in the reaction can strongly influence the physical properties of the resulting solid. Also, rapid precipitation of product upon contacting the reactant streams indicated that the synthesis involves a reactive crystallization, and the individual time scales of product formation (reaction) and phase transformation (crystallization) govern the product particle size distribution. 3.2. Continuous Synthesis Experiments. In these experiments, we investigated the effect of the mean residence time (τ) and the product concentration (Czo) at the reactor outlet on the size distribution of the resulting particles. In this context, Czo denotes a target value, a theoretical maximum that may be realized upon a complete conversion of the reactants to Z. High product concentrations in the reactor effluent stream are desirable from a plant throughput perspective, and hence concentrations lower than 7% (w/w) were not explored (in this phase of the study). The results from these experiments are tabulated in Table 3. Intuitively, one expects crystal nucleation and growth to be influenced significantly by the concentration of solute at the onset of crystallization (supersaturation) and the time available for growth. Nevertheless, we did not observe any obvious correlation between the characteristics of the PSD and τ or target product concentration. Additional experiments performed to explore longer residence times and higher concentrations than shown in Table 3 were not successful due to experimental difficulties. In all these continuous mode synthesis experiments, we observed serious solid build up on the reactor internals, agitator blades, and connected tubing over time. This is of great concern if the process were to be scaled-up, as these observations point to a reactive crystallization that is prone to coat the surfaces. Moreover, the size distributions observed on particles from all D



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Figure 1. Scanning electron micrographs (SEMs) of the granular particles. (a) The particles at low magnification may appear as random agglomerates, but (b) high magnification images emphasize the drusy, spherulitic nature of the particles. These granular particles typically resulted from experiments that targeted a high product concentration in solution.

Figure 2. Images of the reacting solution captured by the PVM probe before the onset of crystallization. (a) The dense liquid droplets resulting from the liquid−liquid phase separation (LLPS) of compound Z, and (b) the same droplets a few seconds after their first appearance. The coalescence and “hardening” of droplets on their way to forming the granular crystals is rapid, as captured by these images.

Figure 3. Optical micrographs of compound Z crystals grown from lean liquid phases resulting from the LLPS. The crystals shown here were produced from batch experiments that targeted a product concentration of (a) 13.9% with 98% water−2% methanol in the solvent phase and (b) 36.8% with 93% water−7% methanol in the solvent phase. All the percentages are on mass basis. The higher concentration of methanol in the solvent phase in case (b) may have given rise to crystals that look quite different from those in case (a). Note the difference in scale between the images.

sticky phase. In our experiments, both the FBRM and PVM probes fouled quickly after the observation of this liquid−liquid phase separation, and the trends and images collected afterward were not useful. For this reason, the FBRM trends are not presented here. Other batch experiments carried out with product concentration in the range of 10 to 35% (w/w) also exhibited similar phase behavior during the reactive crystallization, revealing the origins of the sticky granules to lie in the LLPS phenomenon.

the solution addition, the temperature of the batch pulsed quickly from 18 to 53 °C due to the reaction exotherm before falling due to the cooling provided by the jacket. The image in Figure 2a was collected when the temperature of the solution was around 50 °C. The LLPS and the resulting “oil” droplets are clearly visible in this image. Figure 2b shows another image from the same solution obtained 10 s later than the image in Figure 2a. This image already shows a degree of “hardening” and coalescence of the droplets into forming “jelly-beads” and a E



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3.4. Particles from Dilute Solutions. During the liquid− liquid phase separation, the solute partitions into two solutions, one a “dense” liquid phase with a high solute concentration, seen as “oil” droplets in Figure 2a, and the other a “lean” liquid phase which forms the continuous medium in which the dense phase is dispersed. Both these liquid phases are metastable with respect to the solid−liquid equilibrium condition. In other words, the lean liquid also produces crystals, typically much later than the dense phase. However, the supersaturation sustained by the lean liquid is significantly low, and hence the particles that nucleate and grow from this lean liquid are expected to be more “regular” and less prone to agglomeration. Indeed, when we collected the clear solutions from these experiments (the solutions remaining in the reactor soon after LLPS has occurred and most of the reactor internals were coated), these solutions produced the primary particles shown in Figures 3a and 3b. 3.5. Phase Boundaries. To understand this reactive crystallization mediated through LLPS, we determined the solubility and the LLPS boundaries of the system as described in Section 2.2. The solubility data obtained from experiments are shown in Figure 4 along with the LLPS data points. As

which we could visually confirm the occurrence of LLPS. These results support the hypothesis that the same physical mechanism of LLPS must have caused the eventual crystallization in all cases, even though LLPS could not be ascertained visually for data points with low solute concentrations.

4. DISCUSSION The observation that compound Z produces “regular” crystals with a uniform particle size distribution (Figure 3) in lean solutions rather than the sticky granules (Figure 1) points to a strategy of controlling the reactive crystallization by operating the CSTR under dilute conditions. However, running the CSTR with a low target product concentration results in a low commercial production rate given that the process must leverage an existing reactor of a fixed size. Such a scale-up condition may be uneconomical. The other option is to run the reaction in a methanol-rich solvent phase or in another solvent. But this option is not practical from safety and waste treatment perspectives due to the design of the existing production facility. To choose economical reaction conditions rationally and to overcome the operational difficulties, it is necessary to completely characterize the phase boundaries and reaction kinetics of compound Z. This need has led us to further investigations as described below. 4.1. Understanding LLPSBinodal and Spinodal. When a system that contains a dissolved solute is cooled rapidly (i.e., quenched), the system can become unstable with respect to the existing single-phase composition and can undergo an LLPS through a spinodal decomposition mechanism before it can nucleate crystals.14 The locus of the temperature and composition points at which the system becomes unstable is given by the “spinodal” curve. The locus of the temperatures and compositions at which the system exists in a local equilibrium of two liquid states (the dense and lean liquids) is specified by the “co-existence curve”, also known as the “binodal”. The binodal curve envelopes the spinodal on a temperature vs composition diagram (see below). When a clear solution of compound Z with a fixed solute concentration is cooled rapidly beyond the solubility temperature, it is possible to drive the system inside the binodal before crystallization can occur. However, it is more difficult to drive the system all the way inside the spinodal envelope. That effort typically requires a fast quench and high heat removal rate from a bulk. Thus, in our experiments with Crystal 16 that used a moderate cooling rate of 1 °C/min, LLPS may have occurred as soon as the temperature decreased below the binodal temperature rather than after the system penetrated the spinodal. Hence the locus of the LLPS points observed with Crystal 16 provide a good estimate for the location of the lean-liquid branch of the binodal. However, to understand the bounds on product concentration from a CSTR operation-perspective, one also needs to characterize the dense liquid branch of the binodal and preferably the spinodal curve as well. Experimental determination of the spinodal envelope and the dense liquid branch of the binodal is a nontrivial task, and such efforts were out of the scope of the current business-driven project. In this constrained situation, we resorted to using the existing theoretical models to complete the characterization of phase boundaries. 4.1.1. Prediction of the Binodal and Spinodal Curves. The various mechanisms through which liquid−solid phase separation occurs have been the intense focus of many theoretical and experimental investigations over the past several decades.15−18 Studies exist in the literature that discuss the prediction of the

Figure 4. Phase boundaries determined experimentally using Crystal 16 apparatus for compound Z in 98% water−2% MeOH. The circles indicate the solubility data, and the squares show the LLPS points. The single LLPS data point shown with a plus (+) is the data point obtained with the cold-stage method. See the Supporting Information for details of this measurement. The line through the circles is the fit to the solubility data by the model discussed in Section 4.1.1. The line through the squares is the binodal curve “calculated” (i.e., not fit) using the model parameters obtained from the solubility data.

mentioned earlier, the LLPS could be visualized only in solutions with high solute concentration (>1.7% (w/w)). This result is expected, because at low solute concentration (before the phase split) the second (dense) liquid phase resulting from the LLPS will have a higher supersaturation than that produced at a high concentration. This dense phase can nucleate crystals rapidly, thus reducing the lifetime of the metastable oil phase. Also, the relative amounts of the dense and lean phases are governed by the “lever rule”. The amounts of dense and lean liquids are comparable at elevated temperatures, whereas at low temperatures only a small amount of the dense phase forms. Such a small amount of the dispersed “oil” may not be obvious to the human eye and even may be difficult for the instrument detector to distinguish. As seen in Figure 4, all the data points obtained for the “cloud point” follow a single trend that agrees with the data point obtained from the cold stage experiment in F



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simultaneously eqs 2 and 3 for the two liquid phases (Phase I and Phase II). For this calculation, one uses the required conditions of mechanical and chemical equilibria as PI = PII and μIL = μIIL at a given temperature T to obtain the volume fractions φI and φII of the solute in the two liquid phases at equilibrium. This solution procedure can be tricky because of the existence of a trivial solution at φI = φII. The spinodal curve may be obtained by solving (∂μL/∂φ)T = 0. Equations 2−4 thus form the basis for predicting the phase diagram as a function of the strength ε and range λ of molecular interaction. In our case, we do not know the values for ε and λ that represent the intermolecular interactions of compound Z in the process solvent (98% (w/w) water −2% (w/w) methanol). However, since the experimental solubility data are available, we can follow the reverse procedure and determine the values for ε and λ that best describe the experimental data. Once we obtain these parameters by regressing the solubility data, the other LLPS phase boundaries (binodal and spinodal) can be calculated independently. Details of the procedure used here are provided in the Supporting Information. The results of these calculations are shown in Figure 5. The final parameter values that predict the phase diagram shown in

metastable liquid−liquid equilibrium boundaries from the knowledge of intermolecular interactions.19−21 Here, we leverage these studies and predict the LLPS phase boundaries for compound Z in the process solvent of interest following the generalized phase diagram method.22,23 In this method, we assume that the interactions between the molecules of Z can be represented by a square-well potential, which expresses the pair interaction energy U(r) as l ∞, o o o o −ε , U (r ) = o m o o o o o n 0,

r≤σ σ < r ≤ λσ r > λσ

(1)

Equation 1 assumes the molecules to be spheres of diameter σ. These spheres experience a constant attractive interaction of strength ε when they are separated by a center to center distance of r in the range of σ to λσ. As r → 0 (i.e., when the molecular “spheres” touch), they experience an infinite repulsion. The molecules do no interact when they are separated by a distance that exceeds λσ. Thus, eq 1 characterizes the intermolecular interactions in terms of a strength parameter ε and a range parameter λ. The equation of state (EOS) for such a square-well fluid may be expressed as a semiempirical relation through eq 2:20,22 ζ=

6φ(ε /kT )f bφ 4πPa3 =1+ + 2 3φkT π (1 − φ /φb)3 (1 − φ /φ0)

(2)

in which ζ is the compressibility factor, P is the pressure, a is the radius of the molecule (= σ/2), φ is the molecular volume fraction, b and φ0 are constants (= 4.0 and 0.8404, respectively), k is the Boltzmann’s constant, and T is the absolute temperature of the system. Note that it is customary to normalize the strength of molecular interaction ε to the thermal energy of the system kT. The constants f and φb in eq 2 are functions of the range of interaction λ that fits the fluid thermodynamic properties to the results from numerical simulations (see Supporting Information for more details). For species that behave as a square-well fluid whose EOS is expressed through eq 2, the chemical potentials in the liquid phase, μL, and that in the solid phase, μS, are given respectively as19,22,24 (μL /kT ) =

∫

0

φ

Figure 5. Phase boundaries for compound Z determined from the generalized phase diagram method. The symbols indicate the experimental data points, and the lines are predictions from the models. Curve A is the solubility line, obtained by fitting the experimental data to μL = μS (eqs 3 and 4). This fitting procedure provided the molecular interaction parameters (λ = 1.315, ε/k = 713.88−0.816 T, where T is the temperature in kelvin) necessary for the prediction of the other curves. Curves B and C are the calculated binodal and spinodal lines, respectively. The binodal and spinodal meet at the critical point at 24.45% (w/w) and 102.9 °C. The parameters ε and λ, obtained from the solubility fit, automatically predicted a binodal that passes through the experimental data points (squares and plus). Curve D is the gelation boundary calculated from eq 5. For a close-up view of the experimental data with respect to the calculated models, see Figure 4.

yz dφ′ ij 4πPa3 4πPa3 z jj jj 3φ′kT − 1zzz φ′ + 3φkT + ln(φ) − 1 { k

(3)

(μS /kT ) = − (ns /2)(ε /kT ) − 3 ln(λ − 1)

(4)

In these equations, φ′ is the (dummy) variable of integration representing φ, and ns is the coordination number, i.e., the number of nearest neighbors for a molecule in the crystal lattice. The coordination number ns is a phenomenological constant, and here we considered ns = 12 following the discussion in refs 19 and 23. The true value for ns is not known, as the crystal structure for compound Z is not available. At solid−liquid equilibrium, the chemical potentials of the solute in the solid and liquid phases are equal. For this case, if ε and λ are known, one can solve μL = μS at a given temperature T to obtain the equilibrium volume fraction (solubility) φ. Assuming the solid to be incompressible, the other condition for equilibrium, the equality of pressures, can be ignored. The coexistence curve (binodal) may be obtained by solving

Figure 5 are λ = 1.315, α0 = 713.88 ± 44.67, and α1 = −0.816 ± 0.137, where α0 and α1 are related to ε through ε/k = α0 + α1T (see the Supporting Information). Note that the calculations of the solubility curve (solid−liquid equilibrium boundary) and the binodal curve (liquid−liquid equilibrium boundary) are independent. Here we found the parameters that fit the solubility data by curve-fit, and these parameters in turn predicted the LLPS curve that agreed with the LLPS data very well (without a need to fit the LLPS data). This result gave us confidence that we have a working predictive model for the three phase boundaries−solid−liquid equilibrium (solubility), liquid−liquid equilibrium (binodal), and the instability boundary (spinodal). G



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4.1.2. Prediction of the Gel Boundary. Our experiments also indicated the appearance of an undesirable sticky-gel phase during the reactive crystallization. In fact, in Figure 2, we have seen experimental evidence for the possible gelation of the dense liquid droplets resulting from the LLPS. The solute concentrations at which the system may undergo such a liquid to gel transition may also be estimated for a square-well fluid. On the basis of the mode-coupling theory arguments, Bergenholtz et al. have derived an analytical expression for the location of the liquid-gel boundary as a solution of the equation21,25 12 φ (λ − 1)(e ε / kT − 1)2 = 1.42 π2 g

reaction that forms the product, and possible side reactions that give rise to the trace impurities are neglected. The differential and algebraic eqs 6−8 may be solved simultaneously using the known initial values of species concentrations and temperature as the initial conditions. Using eqs 6−8 in a nonlinear regression procedure, one can fit the T vs t data to obtain the three adjustable parameters k0, Ea, and −ΔHr. However, mathematical considerations do not recommend fitting all three parameters simultaneously for the data.26,27 For this reason, we preassigned a value of 13000 cal/mol for the activation energy, and estimated only k0 and −ΔHr. This choice of Ea = 13000 cal/mol was motivated by the rule of thumb that the rate of reaction typically doubles for every 10 degrees rise in temperature (in the temperature range of interest). The reader is referred to the Supporting Information for further details. The rate parameters estimated from the experimental T vs t data are tabulated in Table 4. We note from Table 4 that the

(5)

in which φg is the volume fraction at which the solute may form a gel. Using the ε and λ values obtained above, one can solve eq 5 for the gelation concentration φg at a given temperature T. The gel boundary thus estimated is also shown in Figure 5. 4.2. Reaction Kinetics Model. A reaction kinetic model is essential for determining reactor productivity and for the rational selection of reaction conditions. Also, the manipulation of the size distribution of particles resulting from a reactive crystallization is greatly benefited by the knowledge of the rate of reaction and the rate of increase of product (solute) concentration in solution. To this end, a working kinetic model was obtained as discussed below using the temperature vs time data collected from the calorimetric experiments (Section 2.4). We note that reaction and crystallization processes are difficult to separate in our experiments. However, during the initial times of the reaction the product (solute) concentration is still increasing and may not exceed the threshold for LLPS or crystallization. Thus, we have used in the analysis only the first 1 min of data collected in each experiment. This consideration addresses another concern regarding the dataif phase separation is not significant, the temperature rise during the initial reaction period can entirely be attributed to the heat of reaction. A reaction kinetic model under these assumptions can be formulated using standard reaction engineering arguments. During the initial time, we express the change in the molar concentration Ci of species i, as dCi = νir dt

Table 4. Estimates for the Reaction Kinetic Parametersa

(7)

k r = k 0e−Ea / RT

−ΔHrc

(% w/w)

(J/mol)

(m3 mol−1 s−1)

(J/mol)

15 25

54392 54392

1.614 ± 0.128 1.259 ± 0.063

63662.4 ± 3497.5 67652.6 ± 2102.5

values of k0 and −ΔHr obtained from the two experiments are close to each other. As an additional confirmation, we have also estimated separately the heat of reaction from the adiabatic temperature rise observed in each of these experiments and verified that the values of −ΔHr shown in Table 4 are as expected. Thus, the simplified kinetic description represented by eqs 6−8 with the averages of fitted parameters in Table 4 provided us a reasonable kinetic model in the temperature range of interest. 4.3. Reactor Model. To further assess the feasibility of a scaled-up process, an isothermal CSTR model was developed with the available reaction kinetics information using the following assumptions: (i) the solid phase in the reactor consists only of product Z, (ii) solids do not slip in the reactor and flow homogeneously with the liquid phase (i.e., the solid holdup in the outlet stream is the same as that in the reactor), (iii) the outlet liquid phase is saturated with respect to Z, and (iv) the density of the liquid phase, which largely is water, does not change significantly from the inlet to the outlet of the reactor. With these assumptions, the mass balance for the reactant M is expressed as

in which −ΔHr is the molar heat of reaction, and ρ and C̅ p are the density and the average specific heat capacity of the solution, respectively. Note that eq 7 considers C̅ p to remain constant in the range of temperatures experienced by the reaction mixture. We assume the reaction to be elementary, and the reaction rate r to follow first order kinetics in each species, and express r as with

k0 × 10−10c

The activation energy given here is a pre-assigned value of 13000 cal/mol. bThe solute concentration represents the maximum product concentration possible in the reaction mixture assuming a complete conversion of reactants into the product and includes the product in both the solid and liquid phases. cThe uncertainty represents a 95% confidence interval for the estimated parameter.

in which the variable t represents time, νi is the stoichiometric coefficient of species i, and r is the rate of reaction. The rate of change of temperature T of the system is given by the energy balance equation

r = k rCmCa

Ea

a

(6)

−ΔHr dT =r dt ρCp̅

Solute Conc.b

Q inCmin − Q L,outCmout − k rCmoutCaoutVr(1 − ηs) = 0

(9)

in which Qin is the total volumetric flow rate into the reactor, Cinm is the molar concentration of M at the reactor inlet, QL,out is the volumetric flow rate of the liquid phase at the reactor outlet, Cout m and Cout are the concentrations of unreacted M and A, a respectively, in the outlet liquid stream, kr is the reaction rate constant (see eq 8), Vr is the volume of the reactor, and ηs is the solids holdup (volume fraction) in the reactor. The solids holdup ηs is defined as

(8)

in which k0 is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and Cm and Ca are the molar concentrations of reactants M and A, respectively. In this simplified reaction scheme, we have considered only a single H


Organic Process Research & Development ηs =

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effluent stream (QL,out) goes as a waste stream, and assigning a waste treatment cost of $0.04x/kg, we can estimate the waste treatment cost per unit time. The gross margin on the product ($/kg Z produced) under the reactor operating condition is then defined as

(ṁ s /ρs ) (ṁ s /ρs ) + Q L,out

(10)

In eq 10, ṁ s is the mass flow rate of solid Z (crystallized product) at the reactor outlet, and ρs is the density of the solid. Also, based on the reaction stoichiometry, moles of A reacted must be equal to twice the moles of M reacted. Similarly, moles of product Z formed must be equal to the moles of M reacted. These considerations provide two more relations Q inCain − Q L,outCaout = 2(Q inCmin − Q L,outCmout)

(11)

(ṁ s /M z) + Q L,outCzeq = Q inCmin − Q L,outCmout

(12)

Ä ij 1 yzÅÅÅij product payback yz j z zz gross margin = jj zzÅÅÅÅjj j ṁ s zÅÅk time { k {Ç ÉÑ ij reactant cost + waste treatment cost yzÑÑÑ zzÑÑ − jj time k {ÑÑÖÑ

(16)

Note that several other costs, such as utilities and labor, need to be factored into a rigorous economic analysis. We neglected such indirect costs for our first pass economic feasibility calculations. The viability and capacity aspects of the existing wastewater treatment facility to handle streams containing excessive amounts of reactants are also neglected at this stage of analysis. 4.4. Search for Optimal Scale-up Conditions. The viability of an industrial process may be assessed primarily through two aspects, viz, (i) the productivitythe (technological) ability to produce the material of interest with a given throughput, and (ii) the economicsthe prospect of the process to be profitable. In the present case we also consider a third aspect, operabilitythe ability to run the process without operational difficulties and downtime. In fact, the operability aspect underlies the other two aspects, but for the sake of clarity of thought, let us consider it separately here. The current project is limited by the need to fit the process into an existing production facility which has a CSTR of a fixed size (1.6 m3) and associated capital assets. Hence, the available degrees of freedom for scale-up of the process are reduced to the choice of operating conditions of the CSTR, such as the volumetric flow rates of the reactant streams (Qmi and Qai), the molar excess ratio of reactants ξ at the reactor inlet, the target conversion β, and the temperature of the reaction Tr. Given the process safety concerns due to the possible product decomposition at elevated temperatures, which results in the release of a toxic gas, a Tr of 35 °C was deemed the maximum safe operating temperature for the CSTR. The feed streams to the process are expected to be 50% aqueous solution of precursor M and 37% aqueous solution of aldehyde A (with about 13% methanol, all percentages are on mass basis). The total volumetric flow rate of the reactants Qin (= Qmi + Qai) is fixed by the mean residence time τ, which is linked to the process throughput through conversion of the reactants achieved in the CSTR. Any unreacted M and A in the reactor outlet liquid stream cannot be recycled for two reasons: (i) the product slowly reacts with water and hence its contact with aqueous medium should be minimizedbut a recycle stream always brings back some dissolved product, and (ii) the process will be a retrofit and relevant unit operations to separate M, A, and Z from the reactor effluent liquid do not exist. The goal of the feasibility exercise then becomes finding under these constraints a right combination of ξ and τ that results in an economical and operable process which produces Z at the desired throughput of 20 kg/min. The theoretical maximum gross margin, calculated just from the raw material costs alone, is $1.48x/kg of Z produced. For business attractiveness the chosen process conditions should also result in a gross margin as close as possible to this value.

in which Cina is the molar concentration of reactant A at the inlet, Ceq z is the molar solubility of Z in the process solvent, and Mz is the molecular weight of Z. The overall mass balance relation can be expressed as Q in ρL = Q L,out ρL + ṁ s

(13)

where ρL is the density of the liquid phase in the reactor. The five equations, eq 9−13, can be solved simultaneously to obtain the out five unknown variables Q L,out, Cout a , Cm , ηs, and ṁ s for any specified molar excess ξ of the limiting reagent and the desired mean residence time τ. This is so, because a specified ξ determines the ratio of flow rates of streams M and A. Similarly, the total volumetric flow rate is constrained by the reactor volume and the specified τ. Thus, the volumetric flow rates of individual streams (Qmi and Qai for reactants M and A, respectively) are constrained in their ratio (Qmi/Qai) by ξ and in their sum (Qmi + Qai) by τ. 4.3.1. Definition of Critical Variables. Once the primary variables are determined for a given set of ξ and τ, additional functions that help characterize the reactor performance may be defined. Here, a fractional conversion β for a limiting reagent is calculated as in out in β = (Q inC lm − Q L,outC lm )/(Q inC lm )

(14)

in which the subscript “lm” denotes the limiting reagent (M or A). The overall product concentration at the outlet, Czo, is expressed as in Czo = βC lm /( −νlm)

(15)

Note that by convention the stoichiometric coefficient ν for the reactants is negative. Also, since the variable Czo is solely determined by the chosen reactant conversion, it cannot account for the phase separation of the product. Hence Czo characterizes the product Z in both the solid and the liquid phases, as discussed earlier in Section 3.2. Assuming no filtration and other handling losses, the solid flow rate ṁ s may be considered as the production rate resulting from the CSTR. The product that does not crystallize but stays dissolved in the liquid stream becomes part of the waste stream. 4.3.2. Cost Margin. To assess the economics of the process, we define a gross cost margin on the product by considering a cost basis of $x/kg for the raw material M. On this basis, the reactant A costs $0.75x/kg. Knowledge of the reactant inlet concentrations Cinm and Cina and the total volumetric flow rate Qin then allows us to calculate the reactant consumption cost per unit time. Given the product selling price ($ 2.30x/kg of Z) and the production rate ṁ s, we calculate the product payback per unit time. Assuming that the entire liquid portion of the reactor I



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Figure 6. Predicted effect of mean residence time τ and molar excess ξ on the conversion when the CSTR is run at 35 °C with (a) aldehyde A being the excess reagent and (b) precursor M being the excess reagent. The percentages indicate the molar percent excess based on reaction stoichiometry. The conversions achieved for the limiting reagent in both cases appear to be about the same for a given set of ξ and τ.

Figure 7. Gross margin vs production rate plots for various molar excesses ξ of (a) aldehyde A and (b) precursor M. The gross margins in both (a) and (b) are expressed relative to the base cost of $x/kg. As we observe, operating the reactor with excess A is more economical than operating it with excess M. For the desired production rate of 20 kg/min, the reactor may be operated between 0 and 10% molar excess of A and achieve a payback of $1.32x/kg of Z produced.

4.4.1. Productivity and Economics. The analysis below discusses a scenario in which Tr = 35 °C, although similar analysis can be carried out at other meaningful CSTR operating temperatures. Figures 6a and 6b show the effect of mean residence time τ on the molar conversion β of reactants M and A, respectively, for various molar excesses ξ of A and M, respectively, at the reaction temperature. As expected, an increase in τ increases β for any degree of ξ in both cases. Moreover, these plots indicate that running the reactor with just stochiometric equivalents of the reactants is sufficient to achieve a conversion between 90 and 95% within a reasonable residence time of 1 h. On the basis of these results alone, one may be tempted to interpret that (i) more or less the same production rate may be achieved for a given mean residence time regardless of which reactant is chosen to be fed in excess, and (ii) any excess reactant fed to the reactor may be a waste of money, because a good conversion can be achieved just with stoichiometric amounts of reactants. However, the gross margin vs the production rate plots shown in Figures 7a and 7b indicate that this is not the case. Figures 7a and 7b show that operating the CSTR with an excess reactant A is always more economical than otherwise. This counterintuitive result may be understood as follows. Each mole of M reacts with 2 mol of A. Thus, when excess M is fed to the reactor, the reactor contents get depleted in A at a rate faster

than the rate with which M gets depleted when A is fed in excess. The net result is that in the excess M case, despite an increase in conversion, a lower production per unit time is achieved due to the shortage of reactant A. Also, Figure 7a shows that a molar excess A between 0 and 10% has no significant impact on the gross margin near the desired production rates, whereas this is not to be the case when excess M is fed to the reactor. Figures 7a and 7b also highlight that one cannot increase the gross margin by attempting to increase the conversion of the reactants (and thus the production rate) in this retrofit scenario. This result is expected, because increased conversion is typically achieved with increased mean residence time, and a high residence time reduces the amount of product coming out of the reactor per unit time, i.e., productivity. This is a direct consequence of attempting to fit the process in an existing reactor of a fixed size. This kind of retrofit will drastically reduce the earnings from the sale of Z if in future the demand for Z increases and a higher production rate becomes necessary. The above analysis suggests that running the CSTR at 35 °C with 0 to 10% excess A at a mean residence time of 27 min (corresponding to the desired production rate of 20 kg/min, with a conversion β from 90 to 94%) may be an optimal scale-up condition for the process. However, only two aspects of process viabilityproductivity and economicsare considered thus far. The third essential aspect, operability, which ensures that the J



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process produces a sellable product without downtime and operational difficulties, has not been addressed yet. It is here that the knowledge of the phase behavior of compound Z at process conditions becomes vital. 4.4.2. Productivity and Operability. Key to the success of the operation is the choice of conditions for the reactive crystallization. To assess the operability of the chosen process conditions (ξ = 0% A, τ = 27 min, Tr = 35 °C), we plot together the gross margin and production rate as functions of the corresponding product concentration Czo expected in the reactor. Figure 8 shows that plot. From this plot we note that,

region and becomes unstable. The resulting dense liquid phase will have an estimated dense binodal concentration of Z at 52.7% (w/w), which is far beyond the expected gelation concentration of 34.7% (w/w). The net result is that with the most economic condition that produces Z at the required rate, a part of the product generated by the reaction at any given time can potentially transform into a gel phase soon after its generation. This LLPS and gelation not only produce large spherulitic crystals with multimodal and broad size distributions, but also will lead to significant operational problems. To ensure a trouble-free operation that produces an acceptable product, one needs to operate the process at a Czo that is significantly away from the spinodal region, and also preferably away from the binodal region. This requires the CSTR to be operated ideally at a Czo ≤ 1.6% (w/w) or at least at a Czo ≪ 9.6% (w/w). Operating the reactor at such dilute conditions can increase the productivity greatly (due to the short residence time needed for the low conversion) but will decrease the gross margin equally sharply (due to the wasted reactants, the excessive volume of the waste stream to be treated, and the loss of dissolved product in that waste stream). The above considerations indicate that operating the CSTR at 35 °C is troublesome. After carefully examining the other possible reactant stream concentrations and reaction temperatures in light of the phase diagram, it became evident to us that a scale-up condition that satisfies all three criteriaproductivity, economics, and operabilitydoes not exist within the constraints under which the process needs to operate. This realization led us to conclude that the process should not be scaled up under the process retrofit business scenario. For a trouble-free and economic operation, a different reaction solvent that can significantly change the phase diagram and/or a different reactor size may be needed. Efforts to identify a suitable solvent and design a proper reactor will incur significant additional R&D costs. Also, any optimized process toward scaleup will require major changes to the exiting operating unit considered for retrofit. The technical team communicated these concerns to the business organization, which then made a rational decision of not pursuing the business opportunity further.

Figure 8. Influence of product concentration at reactor outlet on the productivity and economics. Gross margin is expressed relative to the base cost of $x/kg. Curve A (green) shows that as Czo increases, gross margin increases. Curve B (red) indicates that the production rate sharply decreases as Czo increases within a narrow range. The crossover point for the two lines indicates a production rate above which the process quickly becomes uneconomical. The shaded area shows the range of Czo enveloped by the spinodal. The dotted arrows suggest that for the desired production rate of 20 kg/min the reactor needs to be operated at a Czo of 33.5 wt %, and the operation can result in a gross margin of $1.32 x/kg of Z. However, this Czo is not only deep inside the spinodal but also close to the gelation region. Operating the process at such a high Czo results in LLPS of Z due to thermodynamic instability, and the dense liquid phase generated can quickly gel and coat the reactor internals.

5. CONCLUDING REMARKS This work describes a process development effort for a crop protection agent that was focused on finding the right scale-up conditions toward retrofitting the process in an existing production facility. Initial experiments carried out with a hope of finding the appropriate scale-up conditions by an arbitrary search of the design space were not successful. While these experiments were fraught with operational difficulties and produced a product with unacceptable physical attributes, they helped the team identify the critical aspect of the process to be a reactive crystallization mediated through liquid−liquid phase separation. Subsequent work focused on understanding the dynamics of reaction and crystallization involved in the synthesis led the technical team on the right path. These insights enabled the team to conclude that a satisfactory design space does not exist for this process within the constraints dictated by the business scenario. This work thus helped the business organization make an informed decision to not pursue the business opportunity. Reactive crystallizations often exhibit a rapid generation and subsequent precipitation of the product due to its poor solubility in the reaction medium. Particle size control in such scenarios

with increasing Czo at the reactor outlet, the production rate decreases, whereas the gross margin increases. For maximum economic gain per kg of Z produced (i.e., $/kg), one needs to operate the reactor with a high Czo. Such a condition sharply decreases the productivity (i.e., kg/min), because high Czo can only be achieved with a high conversion, which requires a high mean residence time. Thus, with a high Czo the overall economics over a given operational period ($/total campaign time) become unfavorable. Also, as Figure 8 indicates, for the desired production rate of 20 kg/min, the scale-up conditions chosen above require one to operate the reactor at a Czo of 33.5% (w/w). From the phase diagram in Figure 5, we note that at 35 °C the range of Czo enveloped by the binodal is 1.6−52.7% (w/w), and that enveloped by the spinodal is 9.6−43.8% (w/w). Thus, the chosen reaction condition, which satisfies the productivity and economic criteria, places the solution in the reactor deep inside the spinodal region! Moreover, given that the gel boundary at 35 °C is estimated to be at 34.7% (w/w), the reaction condition also places Czo in the vicinity of the expected gelation concentration. Since the reaction is quite fast, the solution entering the reactor very quickly gets quenched into the spinodal K



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can be difficult if one lacks understanding of the thermodynamics and kinetics of crystallization involved in the process of interest. One expects that manipulation of the PSD for primary particles obtained at low supersaturations is relatively easier than that for the granules resulting from the LLPS. When a crystallization is mediated through LLPS, the PSD is affected strongly by an uncontrolled and random coalescence of the dense droplets turning into jelly beads of broad size distribution. In our case the very dilute solutions required for producing the primary particles with controllable PSD result in poor and uneconomical throughput for the process, which must leverage an existing reactor of a fixed size. As illustrated by these experimental results, an understanding of the phase boundaries and reaction kinetics is critical to a rational choice of process conditions that produce the compound of interest through reactive crystallization. Process development efforts in industrial R&D are frequently limited to those critical studies that involve minimal time and resources yet pave the way to profitable business decisions. Often project teams are required to find solutions to problems through a random search of the design space (an approach that is presumed to be fast and inexpensive) rather than following a systematic approach that thoroughly characterizes the various aspects of the process. However, in following these “short-cut” approaches, often the important “show-stopping” aspects of the problem are missed. For example, without focusing on and exploring the thermodynamic aspects of the phase separation, the team would have spent a great deal more time trying to search for the elusive optimum design space and would have missed the critical insights on the role of LLPS in dictating the process outcome. Worse yet, the team would have assumed a seemingly reasonable process condition to be a satisfactory solution and would not have found the subtle, yet serious, problems with the solution. For instance, the reaction kinetic analysis in this work provided a counterintuitive insight that operating the reactor with a high conversion in this case does not necessarily result in a high net payback from the process. Also, if one attempts to increase the productivity by decreasing the residence time, one may actually end-up with less product. This is so because only the crystallized product is recoverable. Large volumes of waste streams (resulting from reduced residence time) carry with them a large amount of dissolved product to waste. Another nonobvious key insight the team gained from the thermodynamic and reaction kinetic studies is that the profitability of a retrofit option goes down if the production rate needs to be increased due to an increased market demand for compound Z. These results indicate that time and resources invested in understanding the fundamentals of a process, although not necessarily to an academic rigor, are rewarding. The mechanisms through which phase separations occur are of great interest to academic scientists from various disciplines, and several advances have been made in academia in recent times in characterizing the phase behavior of compounds. However, typically these studies do not find active application in industrial problem solving. Our study leveraged important concepts from colloidal and phase transformation sciences and effectively employed the models from academia in conjunction with a few key experiments to arrive at rational business decisions. This work also suggests a methodology toward understanding and improving reactive crystallizations that often occur in industrial processes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.oprd.8b00384.

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(i) Description of the cold-stage experiments toward determining the LLPS boundary, (ii) explanation on the equation of state (EOS) for the square-well fluid, (iii) details of the phase diagram calculations, and (iv) details of the reaction kinetic model development. (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Venkateswarlu Bhamidi: 0000-0003-1875-0574 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This publication has been approved for external use by Eastman. We thank Ir. Alexis Henricot (Eastman-Ghent) for his contribution toward the experiments during the initial stages of the project. We greatly appreciate the support of Dr. Peter Roose (Eastman-Ghent) and Dr. Kristof Moonen (EastmanGhent) for establishing the technical team to work on this interesting problem and for encouraging the publication of the work. The help of Dr. Jane Zhu (Eastman-Kingsport) in collecting the SEM images is acknowledged. V.B. is grateful to Dr. Brendan Abolins (Eastman-Kingsport) for stimulating conversations regarding the computational physical chemistry and theoretical models, and to Dr. Scott D. Barnicki (EastmanKingsport) for providing critical comments on the manuscript. High quality graphics in this work were generated using Daniel’s XL Toolbox (v 7.3.2) add-in, a free utility created for Microsoft Excel by Daniel Kraus, Würzburg, Germany.

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REFERENCES

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