Kinetics Model for Designing Grignard Reactions in Batch or Flow

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Kinetics Model for Designing Grignard Reactions in Batch or Flow Operations Shujauddin Changi, and Sze Wing Wong Org. Process Res. Dev., Just Accepted Manuscript • DOI: 10.1021/acs.oprd.5b00281 • Publication Date (Web): 29 Oct 2015 Downloaded from http://pubs.acs.org on November 24, 2015

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Organic Process Research & Development

Kinetics Model for Designing Grignard Reactions in Batch or Flow Operations Shujauddin M. Changi * and Sze-Wing Wong Small Molecule Design & Development, Eli Lilly and Company, Indianapolis, IN 46285

*

Corresponding author E-mail address: [email protected]

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Abstract This paper describes the development of a “fit for use” model for a Grignard reaction, which was used to produce an intermediate compound during the manufacture of API for edivoxetine hydrochloride. The model includes three parameters, one (kSLa) representing the mass-transfer component and two (k and Ea) representing the Arrhenius dependent rate constant. Several different experiments under various conditions were conducted to fit the parameters and test the model. The model achieves several goals namely, 1) provides an understanding of the kinetics and mass transfer, useful for designing a batch or continuous process, 2) fits and predicts the mass and energy balance for laboratory data under different conditions of reactant stoichiometry or temperatures for process safety monitoring, 3) successfully predicts process dynamics at different scales of operation, from 0.25 L to 1900 L to minimize uncertainty during scale-up, 4) presents a simple way to tune the model to predict dynamics using different magnesium supplies and, 5) develops a platform for quantifying the kinetics for similar Grignard reactions in the future. This model can serve as a powerful tool to help map out the design space and develop operation strategies for successfully running Grignard reactions in a batch or continuous mode. Keywords Grignard, kinetics, mass-transfer, batch, continuous, model



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1. Introduction Grignard reactions are used in organic synthesis to form carbon-carbon bonds and are an excellent methodology for preparing tertiary alcohols.0 The reaction involves two steps: 1) An alkyl or aryl halide (RX or ArX) reacts with metallic magnesium to form an organomagnesium compound (RMgX or ArMgX), which is nucleophilic and, 2) Addition or substitution reaction of the nucleophile with an electrophile to produce an alcohol or ketone product. In the Rδ-Mgδ+X compound, the bonding electrons between carbon and magnesium are shifted away from magnesium forming a polar bond. This charge distribution facilitates the reaction of Grignard reagents with electrophiles. The pharmaceutical industry is going through a paradigm shift by implementing novel continuous technologies for conducting various synthesis. There have been recent publications with a thrust in application of continuous flow synthesis, some even using microreactors.2-5 Grignard reactions are one such class of reactions that can be executed in both batch and continuous fashion, the latter having significant advantages as discussed later. On a commercial scale, the process is run in a typical setup involving, 1) Grignard formation, 2) Grignard reaction and, 3) Quench by hydrolysis of the reaction mixture.6 It should be clarified that Grignard reagent formation and subsequent reaction with the electrophile are discrete steps unlike the Barbier type approach involving a one-pot synthesis. The equipment can usually be constructed of carbon steel, except for the hydrolysis step, which typically involves a glass-lined vessel to avoid corrosion by aqueous acids. Recently, modifications have been made using continuous technologies and improved reactor designs for increasing the yield and purity of Grignard reagents.1,7-10 Previous articles referenced herein only report equipment and operational details for running Grignard reactions and present no information on kinetics or mass-transfer, which 4 ACS Paragon Plus Environment

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are needed for providing guidelines for designing and running a Grignard process at different scales.

Figure 1: Detailed reaction scheme for manufacture of edivoxetine.HCl The process manufacturing of edivoxetine hydrochloride drug substance (for detailed reaction scheme refer Figure 1) employed a Grignard reaction as an intermediate step (Step 2C), of the main focus in this paper. There were several safety concerns in running this process in manufacturing in a traditional batch setup: 1) The organic halide substrate being used to synthesize the Grignard reagent is a strong lachrymator and a mutagen, 2) Grignard reactions are highly exothermic in nature and potentially violent6 and, 3) Hydrogen evolution occurs during the quench process due to excess magnesium stoichiometry; which all require additional design considerations. At Eli Lilly & Co., the benzyl bromide Grignard chemistry (see Figure 1) has been typically run as a batch process with appropriate engineering controls (from laboratory 5 ACS Paragon Plus Environment


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through 1900 L scale). However, during the planned validation launch campaign at 7500 L scale, decision was made to run the process as a continuous operation to overcome the above mentioned safety concerns: Firstly, the continuous operation would considerably reduce the inventory of active magnesium in the tank after the reaction is complete and also separate the Grignard reaction step from the subsequent coupling and quench reactions, reducing hydrogen evolution considerably. Secondly, the continuous stirred tank reactor (CSTR) would require a single magnesium initiation for the entire campaign. A single initiation will substantially mitigate any possibility of thermal runaway and also any risk of exposure of organic halide. However, to successfully run the operation at scale in CSTR maintaining steady state operation one needs to thoroughly understand kinetics and mass-transfer parameters for the Grignard reactions, which was the motivation for this paper. Grignard reactions are heterogeneous solid-liquid reactions and the mechanism of the product formation has been investigated in various level of details.6,11-18 Although the exact mechanism is still not known, it has been hypothesized that alkyl radicals are involved during the formation of Grignard reagent. Walborsky and Rachon15 and Garst et al.18 have specifically discussed two classes of mechanisms for this kind of heterogeneous reactions namely, D (diffusion) and A (adsorption) model, respectively. Both the models assume alkyl radicals to be formed on the magnesium surface. In the “D” model, the alkyl radicals are assumed to undergo an exchange between the solid and liquid phases and then react, isomerize, or couple in the solution, while in the “A” model, Grignard reagents are formed on the magnesium surface via adsorption. Although Garst et al.18 have provided an analytical solution of the D-model, no kinetics information is reported therein. Additionally, the mathematical treatment is provided only in terms of non-dimensionless scaled parameters, which makes it difficult to independently 6 ACS Paragon Plus Environment

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quantify the physical parameters (diffusivity, boundary-layer thickness, mass-transfer fluxes, etc.). It is extremely challenging to design experiments to estimate these parameters, and the authors have only made educated guesses for them to fit their experimental data. Whitesides and co-authors19-21 have carried out competitive kinetics studies (rates relative to a reference cyclopentyl bromide substrate) using different types of magnesium (turnings or rods or powder) and alkyl and aryl halides substrates. They reported the influence of different substituent and solvent on the relative rates of reactions of aryl halides with magnesium. These authors have considered ten rate- limiting transition states including complexes with magnesium surface and those with magnesium ions. Their analysis of rate-structure profiles ruled out ionic radicals (carbanions, carbocations) and also the likelihood of insertion of magnesium into the carbon-halogen-bond. Based on their results, they proposed two possible rate-determining steps, i.e. either the halogen atom abstraction from the organic halide to generate [R.] or the electron transfer to the organic halide from metal to generate [RX]-. Additionally, they believed that the reaction actually occurred at the magnesium-solution interface. They proved that the rate of disappearance of the halide reagent had a first-order dependency on the concentration of halide substrate and also hypothesized a first order dependency on the surface area of magnesium (SMg). Mathematically, the rate of disappearance of the halide substrate can be given by Eq. (1). −

=

(1),

where, kArX = rate constant of halide substrate disappearance, CArX = Concentration of halide substrate at any time ‘t’ SMg = Surface area of magnesium



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To contrast the above work regarding rate-limiting step, Beals et al.22 rejected the hypothesis of electron transfer during the Grignard reagent formation and proposed the reaction of the organohalide with a magnesium atom at the surface to be rate-limiting. They developed a theory that allowed calculation of heterogeneous rate constants by monitoring the rate of growth of individual pits during the reaction and correlating it to the rate of reaction and active surface area. By measuring rate constants over a range of temperatures and computing Arrhenius parameters, they determined enthalpic and entropic barriers to be consistent with their hypothesis. Although their work reports individual rate constants, it is not very practical to implement their methodology in studying the kinetics for a continuous study. Rogers et al.19 also mention the importance of mass transfer (movement of reactant from bulk solution to vicinity of interface) and diffusional transfer (movement of reactants through the stationary fluid boundary layer immediately adjacent to solid surface) for the Grignard heterogeneous system but do not necessarily account for its contributions independent from the kinetics, i.e. since they carried out their study at a fixed stirring rate, the estimates in the rate constants need not be free of mass-transfer effects.19 Yet the competitive rate measurements for different substrates were carried out in similar mass transfer regimes, which allows for a fair comparison relative to each other. To summarize, one can identify two prominent gaps in their work: 1) No absolute rates were reported for a given alkyl or aryl halide disappearance and, 2) No set procedure for delineating the kinetics and mass transfer were reported. After carrying out an exhaustive literature search we found only a few papers that attempt to understand the rates under mass transfer and chemical reaction regime for Grignard reactions.19,21,23,24 All of these authors used a rotating disc of magnesium and obtained reaction rates at different angular velocities. They were able to independently correlate the reaction and 8 ACS Paragon Plus Environment

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mass transfer constants as a function of different angular velocities in their studies. Rogers et al.19 results showed that at low agitation rates, the reaction of bromide substrate with magnesium was mass-transport limited, while improved agitation led to chemical reaction controlled rates. This observation was attributed to a decrease in the boundary layer thickness due to increased agitation, causing an increased rate of mass transfer. Richarz and co-workers23,24 showed that for cylopentylbromide substrate at 25 °C, the overall rate constant was influenced by mass transfer even at higher angular velocities. However, at temperatures below -5 °C and high rotating speeds the overall rate constant was controlled by chemical reaction rate. It can be inferred from their work that temperature and agitation speed have an effect on kinetics and mass-transfer, which needs to be well understood for a given system. Although, the methodology outlined in the above papers is very important to distinguish the effect of mass transfer and chemical reaction on the overall rates, a major gap is that it can only be applied to systems involving a rotating magnesium disc. An actual process in laboratory or plant-scale is typically run using turning, or rasping, or powder form but not very often a rotating disc. To the best of our knowledge, none of the previous works have decoupled the effect of mass transfer and chemical reaction rates using magnesium forms other than a rotating disc. To summarize, the key gaps that exist in literature till date for Grignard reactions is a lack of methodology that provides a simple and effective way of obtaining chemical reaction rates that are free of mass transfer rates. When such a distinction is made in literature, the authors have only used rotating disc of magnesium and neglected other practical types such as, powder, rasping, turnings, etc. Lastly, during the literature review there is no discussion on the design considerations for a batch or a continuous Grignard process. An understanding of the



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fundamental kinetics and mass-transfer interplay, will help us plan the operation strategy for designing a robust Grignard process at a given scale. The aforementioned gap is the main motivation for the work, during the process design for production of an intermediate of edivoxetine.HCl via a benzyl bromide Grignard reaction. The challenge was to obtain kinetics information free of mass-transfer. This challenge was overcome by using a blend of experiments and modeling tools. The goal for the reaction model development is to gain an understanding of the kinetics and mass transfer rates, such that the model can guide process development using simulated conversion and temperature profiles at different scales of operation. A secondary objective for the reaction model is to devise a simple way (e.g. using surface-area measurements) to extend the model to predict the mass balances for Grignard reactions carried out using different kinds of magnesium (granule, turning, rasping). Lastly, it was desired to use the benzyl bromide Grignard reaction as a template for development work on other similar Grignard reactions (e.g. benzyl chloride and 2-bromotoluene). 2. Experimental Description 2.a. Reagents: Benzyl bromide was generated in-situ using bromination chemistry (see Figure 2) as a 26 wt% solution in toluene (II) to minimize handling due to its strong lachrymatory nature. This solution was used directly for the batch experiments. However, for the continuous runs, (II) was diluted further with 2-methyltetrahydrofuran (2-MeTHF) to prepare a single feed bottle such that benzyl bromide concentration was about 10-12 wt% to maintain a constant solvent ratio and dilution as the batch process. The choice of 2-MeTHF was implemented after a comparative solvent screening evaluation because it resulted in a higher a) Grignard product to Wurtz coupling by-product (to be discussed in Section 2.e.) ratio, b) yield, c)


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chemoselectivity, d) higher boiling point reducing the propensity for peroxide formation unlike Et2O.25 All the solvents were purchased either from Fisher Scientific or Sigma Aldrich. Magnesium rasping used for Grignard reagent preparation were purchased from SFM. The reactor was rinsed with 2-MeTHF and then dried using a nitrogen purge before starting a reaction.

Figure 2: Schematic representation of bromination chemistry to prepare benzyl bromide reagent 2.b. Batch reactor details: The batch reactions were performed in a Mettler-Toledo RC1e setup equipped with a 500 mL AP00-0.5-RTC-3w reactor. The agitator and the baffle system in the reactor were modified to have only a single finger baffle. The design of this reactor was geometrically scaled to the plant reactor. A rotary curve impeller (RCI) with 41 mm OD was used. The head of the reactor had 5 ports of which, one was used for a temperature probe, other for agitator shaft, a third for nitrogen vent, fourth for the IR probe and fifth for charging magnesium solids. Mettler Toledo’s iControl RC1e (5.0) software was used to control the agitator motor, jacket temperature, and also record the IR and temperature data during the course of the reaction. 2.c. Continuous reactor details: The continuous experiments were run in two different size of reactors, 0.25 and 2 L. The 0.25 L Chemglass reactor was jacketed with a bottom drain valve. Two side entry ports were specifically fabricated in this reactor (one from the bottom-third of the reactor and other from the top-third of the reactor). The lower port was used for the dip 11 ACS Paragon Plus Environment


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tube to sequester magnesium, while the upper port was used for inserting the IR probe. Thermo Scientific Haake A25 chiller were used to control the reaction temperature, which was usually maintained at 0 °C via a jacket-control operation. The entire operation was kept oxygen and moisture free by using a constant nitrogen purge under a pressure of up to 0.5 – 1 lb. A pitch blade turbine impeller was installed (50 mm diameter, 10 mm shaft opening and 45 ° blade inclination) using a IKA Eurostar motor to control the agitation speed. A baffle cage consisting of four rods and attached to the head of the reactor was used to obtain good mixing. The benzyl bromide stream was fed into the reactor using a peristaltic pump (Cole-Parmer’s Masterflex L/S Easy-Load II Head for Precision Tubing, PPS/SS WE 77200-60), which were equipped with 1/8” Gortex tubing to be compatible with 2-MeTHF solvent. Programmable logic circuit (PLC) interface was installed to control the Horner OCS controllers using the Cscape Envision RV software. The software allowed to alter the feed flow-rates, control the reactor or jacket temperature by allowing inputs for the corresponding thermocouples, and record the weights of feed and collection bottles. Figure 3 depicts the pictorial representation of the setup.

Figure 3: Pictorial representation for continuous Grignard operation 12 ACS Paragon Plus Environment

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The dip tube design was critical and served as a primary containment for magnesium particles. The dip tube comprised of two coaxial tubes, an outer perfluoroalkoxy (PFA) tube with ½” OD and an inner PFA tube with ¼” OD. The outer tube was positioned above the impeller such that it was in a region of downward pumping flow, providing minimum solid carry-over from the reactor to the dip tube (pressure drop profile and fluid flow vector in the reactor was modeled using Fluent).26 The dip tube is also angled to allow the solids enough time to settle down and prevent them from rising inside the inner tube. The inner tube was manually adjusted to control the reactor volume with constant withdrawal rate. The role of the dip tube was to selectively remove the Grignard solution to the collection bottles, while keeping the magnesium particles inside the reactor, hence, keeping the operation continuous. In between the reactor and the collection bottles, the design included a T-shaped glass trap for disengaging the solid-liquid-gas by slowing down the flow. The trap had a hold-up of 510 mL at a given time. Any magnesium which escaped the reactor would settle in the trap and be recirculated back through the head of the reactor periodically. The head of the reactor was specially fabricated in a glass-blowing shop to have five ports similar to the batch reactor for: 1) Thermocouple, 2) Agitator, 3) Recycling of magnesium from the trap, 4) Nitrogen purge, and 5) Magnesium charge port, if needed during the process. The design of the 2L reactor was similar to the 0.25 L reactor except for a few differences. The 2 L reactor did not have any side entry ports but a 25 mm port fabricated in the head for charging magnesium and another 15 mm port for the IR (probe was inserted vertically instead at about 60 degree angle with the agitator shaft, as was the case in 0.25 L). Additionally, the baffle cage was replaced by a single finger baffle. The dip tube was geometrically scaled26 to 13 ACS Paragon Plus Environment


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the proposed design at scale and the outer dip tube was constructed of glass, while the inner dip tube was still made of the PFA tubing. Lastly, a glass rotary curve impeller with a 83 mm OD and flat side blades was used instead of a PBT impeller. Note that the 2 L reactor was geometrically similar to the 0.5 L RC1 batch reactor and the actual reactor at scale. However, we did not invest effort to geometrically scale the 0.25 L reactor because of the difficulty involved in estimating the scaling parameters (power number, flow profile, Sherwood number, etc.) at such a small scale. 2.d. Experiment details: The desired Grignard reaction (see Figure 4) was an intermediate step during the manufacture of edivoxetine.HCl. The benzyl bromide (III) of interest herein, is referred to as benzyl bromide.

Figure 4: Reaction scheme of Grignard reagent formation The procedure for running a batch operation was to first charge 4.5 vol. (1 vol = 1 L per kg of limiting reagent) of 2-MeTHF to a dried reactor. Excess stoichiometric amount of magnesium was charged upfront in the reactor. Diisobutyl aluminium hydride (DIBAL-H) was then added (0.04 eq.) to activate the magnesium and quench excess water in the solvent system.27 Although the actual initiation mechanism with DIBAL-H is not well understood, it is hypothesized that DIBAL-H reacts with moisture and the oxide layer present on the surface of the magnesium rasping, which exposes the active magnesium for the reaction. The activation 14 ACS Paragon Plus Environment

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event was exothermic (an adiabatic temperature rise of 156 °C was obtained for initiation when a 1 : 1 magnesium to benzyl bromide was reacted using a calorimeter) and the system was stirred for 15-20 mins following DIBAL-H addition. The batch experiments were run by charging the benzyl bromide in four to five individual spikes (each spike being ~ 20 to 25 % volume of the total charge). This charging strategy was used because of the high exothermicity of the Grignard reactions (∆Hrxn was determined to be -340 kJ/mol for benzyl bromide Grignard reaction using reaction calorimeter experiment), which would result in a considerable adiabatic temperature rise if the benzyl bromide was charged entirely in one portion. The overall stoichiometry of magnesium to benzyl bromide was set at 1.25:1, which resulted in excess magnesium at the end of the reaction. Furthermore, individual spikes will have a different initial ratio of magnesium to benzyl bromide, e.g. for five spikes of benzyl bromide the initial ratio of magnesium to benzyl bromide at the end of first spike will be close to 6:1, while the ratio for the last spike will be close to 2:1. A conversion profile from a batch process would resemble a series of step changes. For the continuous experiments magnesium was charged upfront and activated using DIBAL-H (0.04 eq.). Once activation of magnesium was complete, the feed pump was started at a desired flow rate. Flow rates of benzyl bromide solution were calculated based on the mean residence time of operation, which is defined as the time required to circulate the entire liquid contents of the reactor once overall. The continuous operation was different from a batch operation in the sense that there was a considerable excess of magnesium charged upfront (typically 6 to 12 turnovers worth of magnesium, a turnover being defined as a the entire reactor contents being circulated once over a given residence time). It typically took 2-3 turnovers for the system to operate at a constant and desired conversion (referred from herein as a “steadystate” although in correct terms a 100% steady-state is not achieved due to continuously 15 ACS Paragon Plus Environment


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changing magnesium concentration). The single feed solution of benzyl bromide/toluene/2MeTHF was continuously pumped in at the set flow rate until all the magnesium was consumed and constant conversion state was lost, resulting in a drop in conversion. A conversion profile from a continuous run will resemble an inverted U-curve. It should be noted that we define Rini denoting the initial molar ratio of magnesium to benzyl bromide. For a batch process Rini will simply be defined as the molar ratio of magnesium to the benzyl bromide either for the overall batch or for each of the individual spikes, as deemed necessary for discussion. However, for continuous process, Rini is defined as the initial ratio of moles of magnesium to the moles of benzyl bromide that flows in the reactor during one turnover. 2.e. Side Reactions: A number of side reactions can contribute to the formation of various impurities during Grignard reactions. One such impurity is the homo-Wurtz coupling impurity (IV), see Figure 5, which can formed due to the reaction of the Grignard substrate with unreacted benzyl bromide. The kinetics for the formation of homo-Wurtz coupling impurity were obtained by conducting batch reactions at 0 and 20 °C using benzyl bromide and benzyl bromide Grignard solutions (data not included herein). As also discussed by Wong et al.26, the kinetics of this impurity formation was found to be three orders of magnitude lower than the Grignard formation rate, under the typical CSTR and batch operating conditions, and it will not be formed unless purposely stressed by perturbing different parameters from their target setpoint. Hence, the quantitation of the homo-Wurtz coupling impurity was not carried out in this work.


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Figure 5: Reaction scheme depicting homo-Wurtz coupling impurity Grignard reagents are also very sensitive to air (or oxygen) and moisture. Intrusion of oxygen can result in the formation of a hydroperoxide, which can subsequently hydrolyze to form the benzyl alcohol (I). Hydrolysis of Grignard reagents can form the dehalogenated or ‘proteo’ (V) impurity (see Figure 6). For all the experiments that were conducted, careful control was maintained of both the oxygen (using a nitrogen blanket in the reactor headspace) and water (ensuring that the KF was less than 500 ppm) levels. Additionally, IR analytical technique was used to obtain the reaction profile and input data for model development (as discussed in the next section), preventing exposure of oxygen or moisture during sampling, unlike the HPLC sampling method. Thus, we will not consider the quantitation or the formation kinetics of impurities (I) and (V). Not considering (I), (IV), and (V) will not affect the overall objectives of this paper.



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Figure 6: Reaction scheme depicting dehalogenated (or proteo) impurity 2.f. Analytical Methods: For analyzing the reaction progress and getting useful kinetics information IR and HPLC tools were used. Although various titration methods have been reported in literature,28,29 we did not use any of these methods to obtain the necessary data for the model development. HPLC was conducted using a Zorbax Bonus RP (75 mm x 4.6 mm x 3.5 µm) Agilent Technologies column for separation. Two mobile phases were prepped: Mobile phase A being 5/95/0.1 (v/v/v) acetonitrile: water : tri-fluoro acetic acid (TFA), and mobile phase B being 75/25/0.1 (v/v/v) acetonitrile : water : TFA. The column was operated at 20 °C with a 10 µL injection volume and total flow-rate of mobile phase set at 1.5 mL/min. A UV photodiode array set at 215 nm was used for detecting the Grignard and benzyl bromide. A gradient-based elution method was used starting with 100 % mobile phase A at time 0 mins, linearly ramping to 100 % mobile phase B till 13 mins, then holding it for another 2 mins (t = 15 mins). This was then quickly followed by a ramp to 100 % mobile phase A in 0.1 mins and then holding it for another 4 mins to give a total run time of 19 mins. Using this method, the retention times of benzyl bromide and Grignard were 10.3 and 9.8 mins, respectively. The challenging part in HPLC sample preparation involved drawing a small part of reactor content using a syringe and then quenching quickly in methanol to minimize oxygen exposure during sampling. After 18 ACS Paragon Plus Environment

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appropriate dilution to fall within linear calibration range, the sample was run on HPLC and Grignard and benzyl bromide were quantified using area %, assuming they had the same response factor. Benzyl alcohol (I) was found to be present in the LC chromatograms, which was attributed to be formed via oxidative decomposition of Grignard reagent due to inadequacies in the sampling technique.

Figure 7: Waterfall plot of reaction spectra. The Benzyl Bromide addition point along with the Benzyl Grignard formation was clearly tracked from the MIR spectra data Reaction progress was quantified in situ using FTIR with DSHFP-9-305-2-6994 AgX DiComp Probe and Mettler Toledo’s iC IR 4.3 software. Significant absorbance band shifts between 1200 cm-1 and 1220 cm-1 (corresponds to C6H5-C stretches) during the course of the reaction enabled mid-IR (MIR) to differentiate among benzyl bromide Grignard (III) (1207 cm-1) , benzyl bromide (II) (1229 cm-1), and even the quenched Grignard as toluyl species (V) (1216 cm-1) in solution. To account for a small amounts of peak shifts under different reaction conditions, benzyl bromide was actually selected using height to single point baseline at 1229 cm-1 and baseline point at 1235 cm-1, Grignard was selected from 1206-1210 cm-1 and baseline



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point chosen at 1193 cm-1 and toluene solvent was identified from 726 to 736 cm-1. See Figure 7 for a waterfall plot distinguishing between the benzyl bromide and the Grignard reagent. A calibration curve was setup for the Grignard and benzyl bromide to quantify the molar concentrations of Grignard and benzyl bromide in the reaction mixture. For generating the calibration curve of the Grignard, a batch experiment was conducted with five individual spikes (~ 20 % benzyl bromide each time) using an overall Rini of 1.2:1. The IR signal intensities were recorded for the Grignard for each spike and correlated to the concentration computed from stoichiometry. A linear calibration curve was obtained, which was used for all other batch and continuous experiments to back-calculate the concentration of Grignard using the raw IR data. For benzyl bromide, however, there was interference from toluene at the wave numbers chosen. A constant shift in the baseline of benzyl bromide was obtained, once all of it had reacted at the end of each spike, providing evidence of an interference. To overcome this problem and still be able to quantify the benzyl bromide, baseline correction with different solvent ratios was needed. A separate experiment was conducted without any magnesium by adding five individual spikes of benzyl bromide/toluene solution of known concentrations and recording the IR signals for the benzyl bromide and toluene for each spike. This experiment was used to develop a linear calibration curve for toluene wt % and toluene IR signal. Next, the batch experiments at 30 °C (described in Section 4.a) was used to determine the benzyl bromide baseline shift for each individual spike. A linear correlation was obtained for this baseline shift to the corresponding toluene wt % present for each individual spike, the latter determined from the toluene-calibration curve. The baseline shifts were determined for each spike and added to the raw IR signal. A final calibration curve was generated for the baseline corrected IR signal and the concentration of benzyl bromide during each spike of the second experiment.


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3. ‘Dissolution-Reaction’ Model For a classical heterogeneous solid-liquid reacting system two processes are involved, solid and/or liquid transfer to the reacting boundary (mass-transfer contribution) and reaction of solid – liquid molecules (chemical reaction contribution). This section will describe a “fit for use” model for Grignard reaction that distinguishes the chemical reaction and mass-transfer rates. It is emphasized that this model does not attempt to capture the mechanism of Grignard reactions. The “fit for use” modeling approach is simple to implement and can be used to obtain the mass and energy balances under different conditions of reactant stoichiometry or temperatures and help predict process dynamics during scale-up. Additionally, the model could serve as a platform for quantifying Grignard reactions in general and also predict process dynamics using different supplies of magnesium, which in turn can help save time and efforts running experiments for characterization of similar Grignard reactions.

Figure 8: Pictorial representation of ‘dissolution-reaction’ model The model can be pictorially represented as shown below in Figure 8, wherein at time t = 0 there is diffusion of benzyl bromide (BnBr) species from the bulk liquid to the magnesium surface. Both magnesium and BnBr species then diffuse to the thin liquid film, where the actual reaction happens to form the product Grignard, the latter then diffuses out of the reaction boundary layer. The reaction will continue until either BnBr or magnesium is consumed. 21 ACS Paragon Plus Environment


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3.a. Rate of Mass-Transfer The rate of diffusional mass-transfer for magnesium can be mathematically defined as in Eq.(2). This rate is a product of diffusional mass-transfer coefficient (kSL), the interfacial area for mass transfer (a), and the concentration driving force (C* - C), with C* and C being the concentrations of magnesium particles at the solid surface and in the bulk of the liquid, respectively. Note that we fit C* = 10 mol/L to provide consistency across different magnesium loadings, which is apparently the same order of magnitude as starting magnesium concentration. On analogy, one can write a similar rate of mass-transfer for benzyl bromide, however, one needs to replace and re-estimate kSLa with kLLa because the diffusion of benzyl bromide is from bulk liquid to boundary layer liquid film instead of it being from solid to the boundary liquid film. dC Mg dt

(

* = k SL a C Mg − C bulk Mg

)

(2)

The speed of agitation only affects the diffusion controlled process and hence can be correlated to the kSLa.30-34 Figure 9 shows a typical variation in mass transfer rates with agitation speeds. As the rate of agitation is increased, the mass-transfer coefficient will increase and the overall process is mass-transfer controlled. However, beyond a just suspended speed (Njs), the observed mass-transfer coefficient may not increase with increasing agitation, indicating the process is bulk reaction controlled. Although, correlations exists for determining Njs [Zwitering correlation, Eq. (3)] or the regime for mass-transfer and reaction control, the specific impact of agitation (i.e. the geometrical constant, s) should be determined experimentally for the system of interest. N JS = sv 0.1 (

g∆ρ

ρL

) 0.45 X 0.13 d p D − 0.85 0.2


(3),

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where, s = geometrical constant, a function of impeller type, D/T, CT, vessel base v =kinematic viscosity of liquid (m2/s) = µL/ρL g = acceleration due to gravity (m/s-2) ρL = liquid density (kg/m3) ∆ρ = density difference between solid and liquid (kg/m3) X = mass ratio of solid to liquid (%) dp = particle size (m) D = impeller diameter (m)

Figure 9: Typical graphical relationship between agitation rates and the rate of mass transfer (measured as a function of the mass transfer coefficient) The surface area component in the rate of mass-transfer continuously changes over time. The ‘shrinking core model’ was assumed to correlate these changes, mathematically described as in Eq.(4).35,36 To simplify the model, magnesium particles were assumed to be uniformly spherical, with an understanding that this does not truly reflect reality. In Eq.(4), a0Mg represents the initial specific surface area determined from BET (Brunauer-Emmett-Teller) measurements, while Mgst=t, and Mgst=0 are concentrations of solid magnesium at any instant ‘t’ and starting time (t=0), respectively.

 Mg ts=t  0   a = aMg  Mg st =0   

2

3


(4)


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3.b. Rate of Chemical Reaction For a reactive diffusion system, once the magnesium has diffused into the reacting boundary, it undergoes reaction with the benzyl bromide. The Grignard reaction is assumed to be an elementary reaction such that the reaction rate is directly proportional to the concentrations of magnesium and benzyl bromide with individual orders being unity for each reactant. Eq.(5) represents mathematically the rate of formation of Grignard reagent, where ‘kr’ is the chemical reaction rate constant, and CBnBr is the concentration of the benzyl bromide at a given time. rGrignard = k r (C Mg )(C BnBr )

(5)

To summarize, there are two competing rates for the Grignard reaction as described above. The start of the reaction will have a high concentration ratio of magnesium to benzyl bromide and the rate of mass transfer will be controlling. Towards the end of the reaction, the concentration of magnesium will become comparable to the benzyl bromide and chemical reaction will be rate-limiting. Values of kSL, and kr need to be determined in the model to capture the complete dynamics throughout the reaction. 3.c. Energy Balance Energy balance was another critical component of the model that provides the capability to predict the reaction temperature profile. In order to do so, Eqs. (2), (4), and (5) can be simultaneously solved to obtain the reaction conversion. Reactor temperature can be subsequently estimated using Eq. (6). The heat transfer coefficient (UA) was determined experimentally by measuring the reactor temperature for a set jacket temperature program ramp. Q = UA(T j − Tr ) = ∆Hr.C BnBr ,initial . X BnBr 24 ACS Paragon Plus Environment

(6)

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where, Q = heat duty (W) UA=heat transfer coefficient (W/K) Tj =jacket temperature (K) Tr = reactor temperature (K) ∆Hr = Heat of reaction (J/mol) CBnBr, initial = initial concentration of benzyl bromide (mol/s) XBnBr = conversion of benzyl bromide

4. Experimental Design to Estimate Model Parameters A number of carefully thought out experiments were designed and executed to estimate the desired parameters and use the model to make predictions for a large number of situations and gain confidence in the model’s predictive capability. This section will discuss the rationale behind the experimental plan for estimating the model parameters. One of the main goal of this paper was to obtain the kinetics information free of masstransfer to design the Grignard reaction to run in a batch or continuous fashion. Two aspects were considered in the experimental plan: a) Operation – batch versus continuous and, b) Process variables – temperature, initial magnesium loading, and speed of agitation, to ensure that the effect of all the key variables and different regime of operations are covered in the model parameter estimates.

4.a. Operation: As mentioned previously in the experimental section, the batch experiments were run by loading entire amount of magnesium upfront but charging the benzyl bromide in five individual portions (each spike being ~ 20 % volume of the total charge). Three batch experiments were run to estimate the model parameters: two were run at 0 °C and 30 °C at 500 rpm, and the third one at 0 °C and 300 rpm. For the continuous operation, various amounts of magnesium were charged upfront in the reactor but the flow rates of benzyl bromide were determined based on the residence time of operation (ζ). Three experiments were executed as 25 ACS Paragon Plus Environment


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continuous operation: two were run at a ζ = 15 mins, 0 °C and Rini = 12:1 but at agitation speeds of 400 and 600 rpm, while the third experiment was ran at a ζ = 60 mins, 0 °C, Rini = 6:1, and agitation speed of 400 rpm. As will be discussed in the next section, the combination of these experiments considered effect of different variables.

4.b. Process Variables: Batch experiments at 0 and 30 °C were conducted to capture the temperature dependency on activation energy (Ea). One can obtain Ea for a batch process, by fitting the conversion-time profile for only two temperature runs, whereas, the continuous mode requires additional steady-state conversion values corresponding to each temperature. Continuous experiments were run at two different magnesium loadings, i.e. Rini of 6:1 (ζ = 60 mins) and 12:1 (ζ = 15 mins) to capture effects of residence time and higher magnesium to benzyl bromide loading in the model parameter estimates. Lastly, the just suspended speed (Njs) for the batch reactor (0.5 L) was determined to be 300 rpm via observation. Note that for the continuous reactor (2 L), Njs was visually determined to be at 200 rpm. Zwitering’s correlation (Eq.3) was also used to correlate Njs using a solid loading value (X) of 13 % and value of the geometrical constant, ‘s’ as 6.3 for the 2 L reactor based on spherical magnesium particle assumption, but it over-predicted the Njs. Constant movement of all particles from the tank bottom could be achieved at lower speeds, likely due to the impact of lift associated with fluid flowing around the flat magnesium shavings. A ‘s’ value of 2.64 was estimated based on experimental observation for obtaining Njs = 200 rpm for the 2 L run. These ‘s’ and ‘X’ values were used in the model prediction for other geometric similar scales. Most of the continuous experiments were run at 400 rpm, where the regime was assumed to be free of mass transfer since it is above Njs. A continuous experiment was also run under similar conditions but at 600 rpm to compare the reaction profile with 400 rpm experiment. 26 ACS Paragon Plus Environment

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Additionally, to correlate the effect of the agitation rate on mass-transfer coefficient (similar to Figure 9) batch experiments were carried out at 300 and 500 rpm. We preferred batch over continuous operation for obtaining this correlation because of the geometric similarity of the batch reactor with the reactor at scale, enabling us to directly correlate the kSL obtained using laboratory data with scale-up performance. Table 1 summarizes the experimental design for estimating the necessary model parameters.

Table 1: Summary of experimental design for estimating model parameters Operation

Scale (mL)

Variable Change

Range

Goal

Batch

500

Temperature

0 & 30 °C

Ea dependency on T

CSTR

250

Rini

12:1 & 6:1

Effect of ζ and Mg loading

CSTR

250

Agitation

400 & 600 rpm

Correlate kSL to rpm

Batch

250

Agitation

300 & 500 rpm

Correlate kSL to rpm

5. Results and Discussions 5.a. Model Parameters Fit DynoChem (version 2.0) was used to determine the model parameters. Dynochem fits reaction rate constant using Arrhenius functionality (Eq. (7)) at a reference temperature (chosen as 0 °C for this study). Note that in Eq. (7), Ea is the activation energy, R is the universal gas constant, Tref is the reference temperature, T is the desired temperature at which rate constant is to be determine, k is the pre-exponential factor for the reaction and kr is the actual rate constant at the temperature T. Thus, one now need to estimate kSL, k, and Ea from the experimental data. This section describes in detail the process that was followed to estimate the parameters.  E 1 1 k r = k . exp − a  −  R  T Tref  

    


(7)


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It should be noted that almost identical concentration-time profiles via IR were obtained experimentally, overlaying within 2-3 mins of each other, for the continuous runs carried out at 400 and 600 rpm (ζ = 15 mins, Rini = 12:1), Figure 10. Thus, it can be concluded that the kinetics obtained at both of these agitation speeds were relatively free of mass-transfer effects and the small difference in reaction profile could be attributed to the inherent variability in the IR data or experimental errors.

Figure 10: Graphs comparing fit of experimental concentrations ( Grignard and BnBr) with model concentrations ( Grignard and BnBr) at different times, for continuous runs carried under conditions: a) Rini = 12:1 and agitation speed = 400 rpm, b) Rini = 12:1 and agitation speed = 600 rpm and, c) Rini = 6:1 and agitation speed = 400 rpm


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The model parameters were optimized by regressing simultaneously the concentrationtime data for benzyl bromide (reactant) and Grignard (product) for the continuous experiments carried at: a) 400 rpm, ζ = 15 mins, Rini = 12:1, b) 600 rpm, ζ = 15 mins, Rini = 12:1 and, c) 400 rpm, ζ = 60 mins, 0 °C, Rini = 6:1 and for batch experiments conducted at d) 0 °C and 500 rpm and, e) 30 °C and 500 rpm. An overall kSL = 5.7x10-5 m/min, k = 1.25x10-2 L/mol/s, and an Ea = 12.2 kJ/mol was obtained. Given that the initial specific area for the SFM grade magnesium particles from BET measurements, a0Mg = 26,100 m2/m3, kSLa was calculated for our system to be 1.5 min-1. One can compute the Damkohler number at the initial conditions of reaction, which is defined as the ratio of the reaction rate over diffusion rate, i.e. kCMg, ini / kSLa. For our case, the Damkohler number was 3.4, confirming the fact that mass-transfer is controlling at the start of the reaction. Table 2 summarizes the final parameters estimated for the model.

Table 2: Summary of Model Parameter Estimates Parameter

Value

Units

k

0.0125 ± 0.0001

L/mol/s

Ea

12.2 ± 0.4

kJ/mol

kSLa

1.5 ± 0.06

min-1

Figure 10 shows the model fit to the concentration-time data for the continuous experiments used to estimate the parameters. Overall the model fit visually appears to be in excellent agreement with the experimental data. To confirm that the model fit is indeed good and acceptable, RMSE was calculated [using the definition in Eq. (8), where Cexp and Cmodel are concentrations of BnBr or Grignard determined experimentally and by the model, and Ndata,total is the total number of data points under consideration] to be ± 1.6 mmol for BnBr and ± 2.4 mmol for Grignard, i.e. only within 3-4 % of the experimental concentrations.



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RMSE =

∑#!" ∑ !" $%%,'%(

(8)

Another goal of this project was to estimate the effect of the agitation rate on kSLa. As mentioned previously, batch experiments (300 rpm, corresponding to the Njs, and 500 rpm) were used because of the geometric similarity of the batch reactor with the tank geometry at scale. The model accurately predicted the concentration-time changes for the Grignard and BnBr for the batch run carried at N = 500 rpm, using the parameter estimates in Table 2 because the kinetics under these conditions are relatively free of mass-transfer. However, at N = 300 rpm, kSL had to be refit using the corresponding concentration-time data to provide a new value of kSLa = 0.17 ± 0.005 min-1 for a good fit. Table 3 summarizes the variation in kSLa with agitation rate, while Figure 11 shows the model fit to the experimental data for the two cases.

Figure 11: Graphs comparing fit of experimental concentrations ( Grignard and BnBr) with model concentrations ( Grignard and BnBr) at different time for batch runs carried under conditions: a) Rini = 1.5:1, T = 0 °C and agitation speed = 500 rpm with kSLa = 1.5 min-1 and, b) Rini = 1.5:1, T = 0 °C and agitation speed = 300 rpm with kSLa = 0.17 min-1 Table 3: Correlation of kSLa with agitation rate (rpm)


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N (rpm)

kSLa (min-1)

Condition

300

0.17 ± 0.005

= Njs

500

1.5 ± 0.06

> Njs

For our purposes, the experiments were conducted at N = Njs or N > Njs. One can conduct additional experiments between 300 and 500 rpm to correlate the kSLa as a function of agitation speed. At the plant scale, typical operation speeds are Nplant > Njs. The Nplant value can be easily converted to a corresponding agitation rate at the laboratory scale (N) using any particular criteria (same power per unit volume draw, same impeller tip speed, same Reynold’s number, Sherwood’s number, etc.). A suitable kSLa can be obtained for the plant process using the correlation. Thus, by determining kSLa at different agitation speed for a given geometry, a database can be created for all other similar heterogeneous system. This methodology provides a simple way to predict the process dynamics at different scales only by knowing a suitable kSLa corresponding to the agitation speed with geometrically similar reactors.

5.b. Model Validation and Predictive Capability Having obtained the model parameters using the procedure outlined in the previous section, our next goal was to verify the model by predicting the system behavior under different conditions. The model was used to predict the mass and energy balance or more explicitly, the temperature and also the concentration-time data for BnBr and Grignard for a number of experiments ranging from laboratory to plant scale. This section describes the experiments and the results of the model’s predictive capability.



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5.b.i. Batch run with a large Rini: A batch experiment was conducted but with a higher magnesium loading upfront such that the initial ratio of magnesium to the first addition of BnBr was 12:1. This experiment was conducted at 0 °C and 600 rpm. In all there were four additions of BnBr, such that at the last spike the molar ratio of magnesium to BnBr was 6:1. Note that the overall Rini was 2:1 for the complete run. The goal of this experiment was to test the model’s capability to predict the performance of a batch run with a high initial magnesium loading, mimicking the CSTR conditions. We wanted to test whether there was any effects of masstransfer when using the model to predict the batch process, giving that it was operating at a much lower overall Rini compared to continuous run. As can be seen from Figure 12, the model successfully predicted the concentrations of both the BnBr and the Grignard species very well (RMSE was calculated using (Eq. (8)) to be ± 2.8 mmol for BnBr and ± 1.5 mmol for Grignard), indicating that the model is fairly robust even under these conditions.

Figure 12: Model’s prediction capability for batch run conducted at 0 °C and 600 rpm with first spike Rini = 12:1 for a) Experimental ( ) and Model ( ) concentrations of the Grignard profile and, b) Experimental ( ) and Model ( ) concentrations of the BnBr profile


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5.b.ii. Continuous run with low Rini: Although a continuous process typically operates at a desired conversion, it is a mandatory aspect of process development to understand the effect of process disturbances on the reaction impurity profile and subsequent downstream operations to be able to define the overall control strategy of the process. A pharmaceutical process involves rigorous studies to design the control strategy to minimize impurity formation and understand its fate of rejection. An integration of continuous process and appropriate control strategies can guarantee that the critical quality attributes (CQA) of the final product are met.37 Therefore, defining the operation ranges for process parameters and process dynamics must be fully understood to design control strategies to ensure product quality. During the process development for the API under interest (edivoxetin.HCl), we conducted different stress studies to map out the operation space for a robust process. These studies were designed to intentionally stress the Grignard reactions by manipulating key variables at once to produce high amounts of impurities. This stressed Grignard product was then forward-processed to form the intermediate and the rejection of the impurities downstream was tested to ensure that the CQAs were met with. One can refer to Wong et al.26 for additional details and rationales of these studies. The mathematical model came in very handy to design the experimental conditions that would in turn give the desired outcome of maximized impurity formation, i.e. the model explicitly helped determine the appropriate reaction temperature, magnesium recharge amount and frequency. Without the model, one would have to do a trial-and-error approach which would be time and resource intensive. Each of the these stressed studies were conducted in a continuous mode of operation maintaining a Rini between 1.2:1 to 2.8:1 and recharging magnesium when there was deviation from steady-state conversion. The deviation from steady-state was confirmed by IR measurements showing a drop in conversion. 33 ACS Paragon Plus Environment


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Based on the understanding of the chemistry for this system, key variables were changed to have deliberate process disturbances from steady-state.26 The goal was to use the model and test against these experiments, which when successful could provide additional validation of the model during the continuous operation even with a low Rini. Additionally, one can now optimize the operation space to run the process at a desired conversion and minimize the impurities.

Figure 13: Model’s prediction capability for Grignard concentrations ( Experimental and Model), BnBr concentrations ( Experimental and Model) and Mole % Grignard in CSTR ( HPLC, IR, and Model) for different stress studies carried in CSTR a) Study 1 conducted at 25 °C, 400 rpm, ζ = 30 mins, and Rini = 1.2:1, b) Study 2 conducted at 0 °C, 400 rpm, ζ = 60 mins, and Rini = 2.8:1, c) Study 3 conducted at 0 °C, 400 rpm, ζ = 60 mins, and Rini = 2.0:1 and, d) Study 4 conducted at 0 °C, 400 rpm, ζ = 180 mins, and Rini = 1.8:1 34 ACS Paragon Plus Environment

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Figure 13 shows the model’s prediction results for concentrations of Grignard and BnBr and also the mole % of Grignard as validated from IR and HPLC measurements (manual samples were drawn and diluted by quenching in methanol and then run on LC) for these stress studies. The model qualitatively and quantitatively predicts the IR and/or HPLC data, proving its robustness in predicting the outcomes of these experiments. This exercise provides additional confidence in the model for its use in mapping out the design space producing quality material.

5.b.iii. Scale-up dynamics: To test the model’s predictive capability for scale-up operations, a continuous experiment was designed and executed at a 2L scale, which was geometrically similar to the batch RC1 reactor (0.5 L). The just suspended speed (Njs) for magnesium particles for the 2L reactor was determined visually to be 200 rpm. The rationale for choosing to run at Njs was that if we run at different scales but at their respective Njs, we should get similar kSLa (as in Table 3), since the latter depends only on agitation rate. IR was used to obtain concentration-time information from the 2L run and then refit the kSL keeping the kinetics parameters (k, Ea) fixed. The model predicted a kSLa of 0.164 min-1, which is in excellent agreement with the kSLa of 0.166 min-1 for a smaller scale reaction (0.5 L). Figure 14 shows the model prediction to be in excellent agreement with the scale-up run (RMSE in mole % Grignard prediction for steady-state operation was very tight being only ± 3.5 %).



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Figure 14: Model’s prediction for scale-up 2 L run conducted at 0 °C, 200 rpm (Njs), ζ = 60 mins, and Rini = 1.9:1for a) BnBr concentrations ( Experimental and Model) and Mole % Grignard in CSTR ( HPLC, IR, and Model) and, b) Grignard concentrations ( Experimental and Model) As a second test for the model’s ability for predicting scale-up behavior, the model was run to successfully predict an actual Grignard run done at a 1900 L scale during one of the API campaigns as a batch operation with benzyl bromide solution added over 2.5 hour. Since the operation was conducted at a speed much greater than Njs, kSLa was assumed to be 1.5 min-1 (from Table 3). With the established understanding of kinetics and mass-transfer, the model provided accurate predictions with the Grignard concentration data obtained at scale (determined using a IR probe), see Figure 15. Note that time t = 0 is defined herein as the start time at which initiation was complete, thus the Grignard concentration does not really start at zero.


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250 Concentration (mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


200 150 100

Grignard (Model) Grignard (Exp)

50 0 0

50

100 150 Time (min)

200

250

Figure 15: Experimental ( ) and model ( ) Grignard concentrations for a 1700 L scaleup Grignard reaction during one of the campaigns run at kinetics free of mass-transfer, hence a kSLa of 1.5 min-1 was used for making predictions Thus, the above examples are conclusive that the model is capable to obtain process dynamics at scale, something not reported previously in literature for Grignard reactions.

5.b. iv. Reaction temperature: To test the model’s predictive capability for reaction temperatures, Eq. (6) was used. UA values for the laboratory reactor was estimated to be 4.5 W/K, while that at the plant scale (950 L) was estimated to be 100 W/K as determined from the solvent run. Figure 16 shows an excellent fit within ± 0.5 °C for the experimental and model. It should be noted that a constant UA has been assumed for simplicity, which in theory should change as the magnesium loading is varied in the reactor. For instance, especially for the continuous run, magnesium loading will be typically varied from 15-20 turnovers to 2-3 turnovers before a recharge, thereby significantly affecting the solid-liquid fill in the reactor and hence the UA. Future work can incorporate an estimate of UA as a function of solid-liquid loading, but the model does a reasonably good job in predicting the energy balances as is.



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(a)

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(b)

Figure 16: Model’s prediction for reaction temperature ( Experimental and Model)for a) Laboratory continuous run conducted at 25 °C, 400 rpm, ζ = 30 mins, and Rini = 1.2:1 with UA = 4.5 W/K, and b) Plant scale batch run conducted at 950 L scale with UA = 100 W/K 5.b.v. Different magnesium supplies: As a last test of the model, we wanted to test the model’s ability in predicting mass balances using different suppliers of magnesium. Grignard reactions were carried out using Aldrich granules, Timinco grade, and BASF grade and measured the concentration of Grignard and BnBr using IR. Note that magnesium purity was still > 99 % grade for all these supplies. Each of these experiments was executed in batch mode at -10 °C and 400 rpm, with five individual spikes of BnBr solution, such that overall Rini was 1.2:1. The only change that needed to be made to the model was re-defining the specific surface area based on the BET measurements for different magnesium (a0Mg), see Table 4.

Table 4: Specific surface area for different supplies of magnesium particles Mg Suppliers

Specific surface area (a0Mg) m2/m3

SFM

26,100

Aldrich granules

205,320

Timinco

123,530

BASF

125,380


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Figure 17: Model prediction for Grignard concentrations ( Experimental and Model) and BnBr concentrations ( Experimental and Model) for batch experiments conducted at -10 °C, 400 rpm, and overall Rini = 1.2:1 for different supplies of magnesium such as: a) Aldrich granules, b) Timinco and, c) BASF The model was then used with all other parameters kept fixed and it predicted the mass balances reasonably well for all the cases under consideration, see Figure 17. The deviation seen in case of fitting the Grignard concentration (for BASF) is probably due to a calibration issue of the IR signal. Note that one calibration model was used for converting the raw data to concentrations for all of these experiments, which may not be representative across different systems. Additionally, while performing that experiment, there was a potential ingress of oxygen 39 ACS Paragon Plus Environment


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lowering the total Grignard concentration. However, the theoretical concentrations obtained using stoichiometry matched very well with the model predictions. Thus, there is no systematic error in the model and one should get confidence that the deviation seen in this case is only due to random errors. The above results indicate a strong capability of the model in extending it to different supplies of magnesium with different surface area (and purity > 98%), without necessarily carrying out additional experiments. The only information that is needed to implement the model for predicting the process dynamics is the specific surface area information for the magnesium of interest. Thus, the model does an excellent job in predicting process dynamics within and at times even outside the parameter space. This section highlighted the model’s predictive results under different scenarios to provide confidence in using the model for such cases. To summarize, the model was successfully applied to predict batch and continuous mode of operations with various loadings of magnesium and various process disturbances, scale-up dynamics from 0.25 L to 1900 L, and mass balances for different supplies of magnesium.

6. Platform for Similar Grignard Reactions With the results in the previous section, we were motivated to extend the methodology as a template for obtaining reaction kinetics that would help design processes for other similar Grignard reactions. We applied the same approach to benzyl chloride Grignard (bromide in BnBr

replaced by chloride) and 2-bromotoluene Grignard (

). Both these Grignard processes


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were directly relevant to benzyl bromide process: the former was considered as an alternative to BnBr, while the latter was used in a clean-up step to consume unused magnesium and minimize the usage of BnBr given its lachrymator property. For benzyl chloride Grignard, two batch experiments were conducted at 20 and 40 ° C and 500 rpm in the RC1 (0.5 L) reactor. The aryl chloride was spiked in four shots (first two being 20 % vol. and next two being 30 % vol.) such that overall Rini was 1:1. To increase the parameter space, two additional continuous runs were done at Rini of 12:1 and 6:1 at ζ of 15 mins and 400 rpm in the 250 mL continuous reactor setup. These experimental data were fit keeping the same kSLa of 1.5 min-1, as determined for the benzyl bromide, to obtain a k = 0.0075 L/mol/s and Ea of 13.3 kJ/mol. The model was validated to successfully predict the batch experiment run at 40 °C and at 400 rpm (Figure 18.a).

Figure 18: a) Model prediction for benzyl chloride Grignard concentrations ( Experimental and Model) and BzCl concentrations ( Experimental and Model) for batch experiments conducted at 40 °C, 400 rpm, and overall Rini = 1:1, b) Comparison of experimental ( ) and model ( ) steady-state mole % for 2-bromotoluene Grignard carried out in continuous run with Rini = 6:1, 400 rpm and ζ1 = 60 mins and then changing to ζ2 = 30 mins after 240 mins of the run



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For 2-bromotoluene, batch RC1 reaction was run with overall Rini of 0.6 : 1 at 25 °C and 500 rpm. However, Ea could not be determined because a batch experiment was not run at another temperature. An activation energy same as determined for the benzyl chloride was used and the RC1 data was fit to obtain a k = 0.006 L/mol/s (assuming Tref = 25 °C). This model was validated by conducting a continuous run with Rini = 6:1, 400 rpm, and ζ1 = 60 mins and then changing to ζ2 = 30 mins after 240 mins of the run. The experimental steady-state conversion was 98 % and 92 % at ζ1 and ζ2, which were consistent with model predicted conversion of 98.5 % and 91.4 % (see Figure 18.b). Thus, the model predicted the continuous profile fairly well using kinetics determined from batch measurements. Having obtained the kinetics information, one can now compare the three Grignard reactions qualitatively and quantitatively, using the model-estimated mass-transfer rates (See Table 5). This approach can be used to appreciate the Grignard’s reaction rates relative to different substrates. The benefit of such a comparison is to quantify the risk of scale-up with potential mass-transfer concerns. One could also use either the batch or continuous experiments for parameter estimates and then successfully predict the conversion profile at scale-up (e.g. 2bromotoluene). Thus, one can design Grignard processes using either operation mode and the approach outlined in this paper with less than five experiments, saving considerable development efforts.

Table 5: Qualitative comparison of rates for different Grignard reactions BnBr Grignard

BnCl Grignard

2-bromotoluene Grignard

Rate constant @ 25 °C

0.020

0.012

0.006

Comparison

-

1.6 times slower

3.3 times slower


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To sum up, the experimentation and modeling approach presented herein has several applications and benefits. One can use the approach to aid in the process development work for designing either a batch or a continuous Grignard process at a given scale. The model can help define the operation space for obtaining the desired product quality. Lastly, the model can also aid in conducting failure mode and effect analysis (FMEA) and devising operation strategies by simulating potential failure scenarios and estimating the risk associated in the likelihood of an unexpected event, thereby, allowing to evaluate the safety consequences associated with that event (will be discussed in more detail in Wong et al.26)

7. Conclusion The paper describes a “fit for use” model to obtain kinetics free of mass transfer and help in scale up for Grignard reactions using either a batch or continuous mode of operation. The mass transfer rates depend on the agitation speed and magnesium type used. The effect of agitation rate is captured by the mass-transfer coefficient (kSL), which varies linearly until the just suspended speed (Njs) is reached and then remains fairly constant at speeds much greater than Njs. An order of magnitude difference is obtained when fitting the kSL at Njs compared to speeds much greater than Njs for the reactor configuration described. Having established the kSL values at Njs and above allows us to scale-up appropriately with the estimated kinetics parameters. The effect of magnesium type was captured by redefining only the initial specific area of the particles used. The model predicted the mass and energy balances for Grignard and benzyl bromide as verified with three supplies of magnesium (Aldrich turnings, Timinco, and BASF) with specific surface areas varying from 2.5x104 to 2x105. The model can also be effectively used to predict scale-up data and serve as a platform for running similar Grignard reactions in the future. 43 ACS Paragon Plus Environment


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8. Acknowledgements The authors thank the Edivoxetine.HCl development team and management of Eli Lilly and company for their support. The authors specifically acknowledge inputs and help received from Martin Johnson, Wei-Ming Sun, Jeffrey Lewis, Timothy Braden, and Michael Kopach for the model development.

9. References 1. Kopach, M.E., Roberts, D.J., Johnson, M.J., Groh, J.G., Adler, J.J., Schafer, J.P., Kobierski, M.E., and Trankle, W.G. Green Chem. 2012, 14, 1524-1536 2. Mason, B.P., Price, K.E., Steinbacher, J.L., Bogdan, A.R., and McQuade, D.T., Chem. Rev. 2007, 107, 2300–2318 3. Ahmed-Omer, B., Brandt, J.C., and Wirth, T., Org. Biomol. Chem. 2007, 5, 733–740. 4. Perazzo, A., Tomaiuolo, G., Sicignano, L., Toscano, G., Meadows, R.E., Nolan, S.P., and Guido, S. RSC Advances, 2015, 5, 63786-63792 5. Malet-Sanz, L. and Susanne, F. Journal of Chemical Chemistry 2012, 55, 4062-4098 6. Silverman, G.S., and Rakita P.E., Handbook of Grignard Reagents; CRC Press, 1996 7. Hirsch, A., US Patent 2464685, 1949 8. Jennings, J.R., J. Organometallic Chem. 1987, 325, 25-29 9. Klokov, B.A., Org. Process Res. Dev. 2000, 4, 122-128 10. Klokov, B.A., Org. Process Res. Dev. 2001, 5, 234-240 11. Gomberg, M., Bachmann, W.E., J.Am.Chem.Soc. 1927, 49, 236-257 12. Bodewitz, H.W.H.J., Blomberg, C., and Bickelhaupt. Tetrahedron Letters 1975, 24, 20032006 13. Lawrence, L.M., and Whitesides, G.M., J. Am. Chem. Soc. 1980, 102 , 2493-2494 14. Ashby, E.C., and Oswald, J., J. Org. Chem. 1988, 53, 6068-6076 15. Walborsky, H.M., and Rachon, J., J. Am. Chem. Soc. 1989, 111, 1897-1900 16. Walborsky, H. M., Acc. Chem. Res. 1990, 23, 286-293 17. Garst, J.F., and Swift, B.L., J. Am. Chem. Soc. 1989, 111, 241-250 18. Garst, J.F., Swift, B.L., and Smith, D.W., J. Am. Chem. Soc. 1989, 111, 241-250 19. Rogers, H.R., Deutch, J., and Whitesides, G.M., J. Am. Chem. Soc. 1980, 102, 226-231 20. Rogers, H.R., Rogers, R.J., Mitchell, H.L., and Whitesides, G.M., J. Am. Chem. Soc. 1980, 102, 231-238 21. Root, K.S., Deutch, J., and Whitesides, G.M., J. Am. Chem. Soc. 1981, 103, 5475-5479 22. Beals, B.J., Bello, Z.I., Cuddihy, K.P., Healy, E.M., Koon-Church, S.E., Owens, J.M., Teerlinck, C.E., and Bowyer, W.J. J. Phys. Chem. 2002, 106, 498-503 23. Hasler, Ph. and Richarz, W., Ind. Eng. Chem. Res. 1989, 28,38-43 24. Hammerschmidt, W.W., and Richarz, W., Ind. Eng. Chem. Res. 1991, 30, 82-88 25. Kadam, A., Nguyen, M., Kopach, M., Richardson, P., Gallou, F., Wan, Z-K., and Zhang, W., Green Chem. 2013, 15, 1880-1888


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26. Wong, S.Z., Changi, S., Shield, R., Bell, W., McGarvey, B., Johnson, M.D., Sun, W-M., Braden, T.M., Kopach, M.E., Spencer, R.D., Flanagan, G., and Murray, M. Org. Process Res. Dev. 2015, Submitted to OPRD 27. Tilstam, U., and Weinmann, H., Org. Process Res. Dev. 2002, 6, 906-910 28. Lin, H-S., and Paquette, L.A., Synth. Commun. 1994, 24, 2503-2506 29. Vlismas, T., Parker, R.D., J. Organomet. Chem. 1967, 10, 193-196 30. Nienow, A.W., Chem. Eng. J. 1975, 9, 153-160 31. Nienow, A.W., and Miles, D., Chem. Eng. J. 1978, 15, 13-24 32. Chaudhari, R.V., AIChE J. 1980, 26, 177-201 33. Conti, R., and Sicardi, S., Che. Eng. Commun. 1982, 14, 91-98 34. Atiemo-Obeng, V.A., Penney, W.R., and Armenante, P., Handbook of Industrial Mixing: Science and Practice, Chapter 10, John Wiley & Sons, 2004 35. Levenspiel, O., Chemical Reaction Engineering, John Wiley & Sons, 3rd Edition 36. Nativ, M., Goldstein, S., and Smuckler, G. J., Inorg. Nucl. Chem. 1975, 37, 1951–1956 37. ICH Guidance for Industry, Q8 (R2) Pharmaceutical Development, 2009


Kinetics Model for Designing Grignard Reactions in Batch or Flow

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