16.1 DRIVERS FOR CONTINUOUS REACTIONS IN DRUG SUBSTANCE MANUFACTURING

Continuous processing applications in the pharmaceutical industry have been increasing in recent years [1]. There are many reasons why an API manufacturer may choose to run chemical reactions in continuous mode instead of batch. Typical drivers for choosing continuous instead of batch reaction are fast kinetics, highly exothermic heats of reaction, hazardous reagents, extreme temperatures and pressures, and high throughput. Yield and selectivity may be better for fast reactions in series with unstable intermediates [2]. Safety may be improved for highly exothermic reactions [3]. Operating ranges may be wider, and safety may be improved for high pressure reactions with hazardous gas reagents such as hydrogenations, hydroformylations, aerobic oxidations, and carbonylations. Operating ranges may be larger, and safety may be improved for reactions at extreme temperatures less than −40 °C or greater than 200 °C or superheated reactions with vapor pressure greater than 50 bar at reaction temperature [4]. There are safety advantages of minimizing volumes and maximizing heat transfer rates for reactions with hazardous reagents, potential for thermal runaway or large exotherms [5]. Safety is improved for reactions with hazardous reagents like reactions with hydrazine, bromonitromethane, diazomethane [6], sodium cyanide, methanesulfonyl cyanide, and cyanogen chloride [7]. If there is an advantage to running with no headspace, such as organic azide or tetrazole formations where hydrazoic acid would partition into the headspace of the batch reactor, then a plug flow reactors (PFR) may be superior to batch because it operates 100% liquid filled [8]. If the impurity profile is improved by all‐at‐once addition, coaddition, fast heat‐up, and/or fast cooldown, then a PFR or a continuous stirred tank reactor (CSTR) may be superior to batch. This depends on the kinetics of the side reactions relative to the main desired reaction. Continuous can provide throughput advantages and debottlenecking for high volume products [9]. End‐to‐end fully continuous processes offer advantages of quality control, extreme operating conditions, telescoping, and introducing excipients further upstream to improve processing API to drug product [10]. The use of continuous reactors in the pharmaceutical industry is rapidly increasing [11]. Product consistency advantages can be achieved via continuous processing because of steady‐state operation, feedback control, and real‐time product quality information by online process analytical technology (PAT). It aligns with quality by design (QbD) principles, and implementation of continuous processes is encouraged and supported by the FDA [12].

There are several additional criteria to look for in the batch reaction that may cause one to think about continuous. Is the yield or impurity profile sensitive to reaction time? Are there significant late‐forming impurities? Is the product unstable to end‐of‐reaction conditions? If the answer is yes to any of these questions, then consider reaction in a plug flow tube reactor (PFR), because reaction time is more scalable, the late‐forming impurities can be avoided by precise control of time in the reactor, and the unstable product can be quenched in‐line immediately after the precisely controlled reaction time. Is the yield or impurity profile sensitive to mixing rate, heat‐up rate, or cooldown rate? Reagent addition time is more scalable in flow than in batch because of in‐line mixing and because the production‐scale reactors are not as large as batch. Heat‐up and cooldown rates are more scalable in continuous than batch. This is because process liquids flow through heat exchangers at the reactor inlet and outlet. Does the yield or impurity profile benefit from all‐at‐once mixing of reagents? If so, then a PFR is a better reactor choice than batch for all‐at‐once stoichiometric reagent mixing because of the ability to control (or remove) heat from an exothermic reaction. Is there a lag time or delayed catalyst initiation time in the batch reactor? In this case, the advantage of a CSTR is that the reaction is always operating at the end‐of‐reaction conditions. Is the product cytotoxic or highly potent? Using continuous processing, cytotoxic API production may be achieved in inexpensive, dedicated, and “disposable” equipment sets for production of low volume (<1000 kg/year) cytotoxic APIs in laboratory fume hoods [13]. Is it difficult to recover a batch in the event of operational problems? For example, if the catalyst deactivates because of something like poor inertion and if it is difficult to recover from this event by simply adding more catalyst, then the flow advantage of the PFR is that there is less material at risk due to the small reactor volume compared with the total production volume (one to one in batch operations).

16.2 TWO MAIN CATEGORIES OF CONTINUOUS REACTORS: PFRs AND CSTRs

Continuous reactors fall into two main categories, CSTR and plug flow with dispersion reactor (PFDR) [14]. They are shown schematically in Figure 16.1.

The design equations are derived by solving the material balance for conversion versus mean residence time (τ) or distance after making simplifying assumptions [15]. The design equations relate changes in concentration with time to flow of reacting species in and out of reactor and species formation/disappearance by chemical reaction. The design equation for the CSTR assumes no spatial changes within the reactor and no change with time at steady state. If the mixing time is sufficiently fast compared with the mean residence time, then the entire contents of the reactor remain at outlet concentrations. The simplified design equation for the PFDR assumes no change with time for a given location in the reactor, but change in conversion with distance along the axial direction from reactor inlet to outlet. The PFDRs are commonly called PFRs, but PFR implies perfect mixing in the radial direction and no mixing in the axial direction, which is not true for real reactors. All real reactors have some degree of axial dispersion, especially with laminar flow homogeneous liquids. If the axial dispersion number is small enough so that it has negligible impact on conversion versus τ, then the PFDRs are called PFRs. This chapter contains an example of quantifying axial dispersion and then modeling whether or not it has significant impact on conversion versus time in real rectors. There are many types of PFRs such as:

• Microreactors.
• Static mix tube reactors.
• Open tube or pipe reactors.
• Oscillatory baffled tube reactors.
• Flow tube or structured channel reactors that have alternative energy input like microwave, photo, electro, or sono energy input.

With proper engineering design, each of these variations can be designed to minimize axial dispersion such that highly plug flow profiles result.

Reaction conversion versus τ is different in a CSTR than in a PFR, and the respective residence time distributions (RTD) are also very different. Much longer residence times are required for full conversion in a CSTR compared with a PFR, unless the reaction rate is zero order. Example calculations are shown in this chapter to illustrate this point.

Judging by the number of published examples and the number of commercially available continuous reactor systems, PFRs are more commonly applied than CSTRs. PFRs maximize heat transfer A/V compared with stirred tanks, especially if they are microreactors, i.e. characteristic dimension less than 1 mm. A PFR minimizes total reactor volume and thus τ in the reactor for a given conversion. A PFR minimizes transition time and volume to reach a new steady state after a step change in process parameter because of narrow RTD. The PFR can run 100% liquid filled and as a consequence is the best reactor choice to eliminate headspace. This also helps to minimize equivalents of gas reagent for two‐phase vapor–liquid reactions. The working volume of research‐scale PFRs can be less than 0.1 ml; therefore they minimize materials required for research and development. Compared with CSTRs in series or intermittent flow CSTRs, the PFRs can be lower in complexity and lower in cost. One of the biggest challenges is to maintain solubility of reagents and reaction products in PFRs. Most PFRs are not capable of solids in flow because of fouling or blockage. Solids in packed columns are acceptable, for example, packed catalyst bed reactors, but the particle size of the solids should be greater than 100 μm to minimize pressure drop across the bed.

On the other hand, CSTRs, CSTRs in series, or intermittent flow CSTRs may be selected instead of PFRs in certain circumstances. These reactors are more suitable for heterogeneous systems, including slurry flow such as reactive crystallizations, reaction with solid precipitate, or reaction with solid reagent feeds like Grignard formation reactions with solid magnesium reagent. CSTRs tolerate and buffer out fluctuations and/or pulsing of reagent feeds. In fact, a useful reactor configuration is a small CSTR followed by a PFR, where the CSTR dampens out fluctuations in stoichiometry of two reagents combining prior to entering the PFR. While PFRs need precise flow control especially for multiple reagents, CSTRs are more forgiving of short oscillations in flow control. If stoichiometry is critical and the pump flow rates oscillate, then consider CSTRs. CSTRs can be stopped and restarted without loss of mixing during flow stoppage. Also, mixing is independent of flow rate in CSTRs. CSTRs achieve fast liquid–liquid two‐phase mixing over a wider range of scales and reaction times, for example, a one hour reaction time in production‐scale reactor. CSTRs help to overcome induction time or lag time in reaction kinetics, e.g. autocatalytic reaction, because they operate at “end‐of‐reaction” conditions at steady state. Also, because CSTRs do not run completely liquid filled, it is more feasible to adjust residence time in the reactor without changing liquid flow rate.

Furthermore, the choice of PFR versus CSTR versus batch depends on the best method of reagent addition. Reaction kinetics will determine the best reactor configuration for maximizing yield and minimizing side reactions and impurities. In any of the reactor configurations (batch, plug flow, continuous CSTRs, or intermittent flow CSTR), one can easily use kinetics from the batch reactions to design and size the continuous reactor for full conversion. The bigger challenge is understanding and predicting the impurity profile for the different reactor configurations. For a reaction A + B → C, if the impurity profile and yield are most favorable when reagent B is added in a slow and controlled manner to a vessel containing reagent A, then batch and intermittent flow CSTR are better reactor choices than a PFR or true CSTR. A PFR with multiple addition points of reagent B along the length of the reactor is an alternative, but it requires more pumps and mass flow controllers. A mathematical example is given in Section 16.5. If impurity profile and yield are best for an all‐at‐once addition, then a PFR is the best choice. Batch is usually not practical for all‐at‐once stoichiometric addition because of safety concerns and heat transfer limitations. If yield and selectivity are most favorable as a result of slow coaddition of both A and B at stoichiometric ratios (i.e. coaddition) while keeping the conversion high in the reactor at all times, then a CSTR is the best reactor choice.

16.3 EXAMPLE OF COILED TUBE PFR FOR TWO‐PHASE GAS–LIQUID REACTIONS

An asymmetric hydrogenation reaction operating at 68 bar hydrogen produced 144 kg of penultimate using a 73 L coiled tube PFR [16]. The reactor and the downstream separations and purification unit operations were run in laboratory facilities at 13 kg/day throughput. The hydrogenation was in a special laboratory facility with all explosion proof equipment, utilities, and lighting, high air volume turnovers, specialized doors, and blowout walls. The reaction scheme is shown below in Scheme 16.1. It was a challenging hydrogenation of a tetrasubstituted enone.

The rhodium and Josiphos homogeneous catalyst ligand system was very oxygen sensitive. Running the reaction continuous rather than batch provided advantages for excluding oxygen, because the reactor only needed to be inerted once at the beginning of the campaign. The catalyst system was also very expensive. To be economically viable, this reaction required a 2000 : 1 substrate to catalyst ratio (S : C) and high pressure hydrogen (68 bar) to maintain a high dissolved H₂ concentration. The enone substrate was 0.15 M in 2.5 : 1 ethyl acetate/methanol, and the dissolved H₂ concentration was expected to be on the same order or magnitude at the elevated pressure. Batch processing is normally the default option, but a 68 bar rated autoclave was not available at the selected manufacturing facility for this product. A capital spend was needed to support either a batch or continuous process.

There are several good references for determining kinetics in continuous reactors [17]. Reaction kinetics were measured in a well‐mixed batch PARR autoclave at research scale. Conversion versus time was measured in the autoclave, and the results are listed in Table 16.1.

Plotting the natural log of C/C_o versus time gives a straight line with slope equal to the reaction rate constant for a first‐order reaction, where C is concentration of starting reagent at time t and C_o is initial concentration.

The rate expression is

(16.1)

where

• k is the first‐order rate constant.

By separating variables and integrating, this becomes

(16.2)

(16.3)

A plot of the natural log of C/C_o versus time is shown in Figure 16.2.

In this example, the product concentration is log linear; therefore the reaction is first order or pseudo first order with k = 0.63/h within the time period investigated. The first‐order reaction rate model with k = 0.63/h is plotted with the actual conversion versus time data in Figure 16.3 and Table 16.1.

Overall gas–liquid mass transfer coefficient, k_La, was the order of 0.01–0.1/s; therefore conversion versus time was likely not mass transfer rate limited. The kinetic data informs the choice of reactor type: batch versus PFR versus CSTR. The rate data was used to predict how long the reaction must run to reach a desired 99.9% conversion level in batch mode and what is the required reaction time to reach the same conversion in the PFR or CSTR.

In the PFR, the reagent solution, catalyst solution, and reagent gas flowed cocurrently through the coiled tubes. A simplified schematic of the reactor system is shown in Figure 16.6.

Photographs of the 73 L reactor are shown in Figure 16.7. The overall height and diameter of the cylindrical coiled tubing assembly was designed to fit inside an existing 0.91 m diameter jacketed single plate filter that was used as a constant temperature bath, also shown in Figure 16.7.

The PFR was constructed of 316 L stainless steel tubing with outer diameter (o.d.) = 19.1 mm, inner diameter (i.d.) = 16.5 mm, and L = 340 m. Overall L/d was about 20 600, which is unusually large for tubular reactor designs. This is because the reactor was designed for 12 hours τ and flow was in the laminar regime. Reynolds number was about 250 in the flow tube reactor. In the laminar regime, the larger the L/d, the lower the overall reactor axial dispersion number [18]. Due to the low linear velocity because of the 12 hours τ, the reactor operated with pressure drop of only about 10 psi; thus the pressure drop was not problematic. Reactor cost and ease of fabrication were the practical limitations on higher L/d in this case. The tubing was formed into eight concentric cylindrical coils 0.53 m tall and ranging from 0.36 to 0.80 m diameter as pictured in Figure 16.7. Vapor and liquid flowed cocurrently through each of the eight coils in series in the uphill direction starting with the outside coil. These individual coils were linked by down‐jumper tubes constructed from 316 L stainless steel tubing with o.d. = 6.35 mm and i.d. = 4.57 mm. The reactor was designed with these narrow diameter down‐jumpers to maintain greater than 99% of the total reactor volume in the uphill flow direction, which helped the reactor run more liquid filled in the forward direction. This also made it possible to almost completely empty the reactor by pushing with nitrogen in the reverse direction at the end of the production. There was no mechanical mixing of the hydrogen and liquid throughout the length of the tube. Gas–liquid mixing was sufficient so that conversion versus time was the same as in a well‐mixed batch reactor.

The reactor was designed to be low cost so that it was dedicated to this specific chemistry and this rhodium catalyst and then disposed when no longer needed for the product. This reduced the cleaning burden, eliminated the possibility of cross‐contamination, and eliminated other metal catalyst from the possibility of catalyzing undesired side reactions. The 73 L coiled tube PFR in this example cost $16 000.

Using the PFDR model, vessel dispersion number D/uL can be calculated by fitting experimental F‐curve data to the basic differential equation representing dispersion by numerically solving for D/uL and θ as shown in the following equation:

(16.14)

• D = Taylor longitudinal dispersion coefficient that incorporates the effect of both diffusion and convection
• u = average flow velocity
• L = vessel length
• C = concentration
• θ = dimensionless time (t/τ), where τ is mean residence time
• Z = dimensionless length (x/L)

From θ and the recorded time for each data point, we can calculate τ. The C‐curve characterizes spreading of a pulse tracer injection into the inlet of a flow tube reactor as it travels along the length of the reactor, also known as residence time distribution. See chemical engineering textbooks for details on the methods and analyses [15]. For small extents of dispersion, D/uL < 0.01, the basic differential equation representing dispersion can be solved analytically to give the following symmetrical C‐curve:

(16.15)

Given that the F‐curve is the integral of the C‐curve, this equation was used to quantify D/uL and θ for the experimental F‐curve using a simple Excel^® spreadsheet.

Figure 16.8 shows the experimental F‐curve data collected during startup transition of the 73 L coiled tube reactor. The reactor initially started filled with solvent. At time zero, the reagent solution with enone, the dissolved catalyst + ligand solution, and hydrogen gas started flowing into the reactor. The figure plots product concentration at the reactor exit versus normalized time, t/τ. t/τ = 1 corresponds to 11.8 hours.

In this example, the axial dispersion number, D/uL, was 0.000 12, and τ was 11.8 hours (Figure 16.8). Thus, the continuous reactor exhibited nearly ideal plug flow characteristics. This is a remarkably low axial dispersion number given that the reactor is in the laminar regime. Reynolds number in the reactor was only about 250 (liquid density 0.9 g/ml, internal diameter 16 mm, linear velocity 8 mm/s, viscosity about 0.45 cp). The gas + liquid two‐phase flow decreases axial dispersion compared with liquid‐only flow because the gas bubbles disrupt the parabolic velocity profile and cause some mixing in the radial direction [16]. Even without the gas, however, axial dispersion would be low in this reactor at Reynolds number about 250 because of the extremely high length to diameter ratio, as explained elsewhere [16]. Steady state was achieved in this example after about 1.03 × τ during startup transition from a solvent‐filled reactor, as shown in Figure 16.8. Target reaction τ was 12 hours, but actual was 11.8 hours. This emphasizes the value of measuring and modeling the startup transition curve, because it quantifies the actual τ. In addition to many other things, τ depends on % vapor space in the reactor, which is difficult to predict because it depends on relative gas versus liquid linear velocities. This makes it difficult to know actual τ without measuring the startup transition curve. A nonreactive tracer could also be used, but this was a production run for a pharmaceutical intermediate, so any extra additives are scrutinized.

Numerical modeling of the one‐dimensional convective diffusion equation was performed to illustrate the effects of dispersion in the 73 L PFR. The partial differential equation was solved using gPROMS custom modeler [19] discretizating along the length of the tube reactor. Backward finite differences were used, and a Danckwerts boundary condition was employed [20]. Numerical diffusion dictated the number of discretization points needed in order to simulate very low D/uL scenarios. Approximately 10 000 discretization grid points were needed to ensure numerical diffusion was small relative to the diffusion expected for a D/uL of 1.2e‐4. Analytical expressions were used for the simulation of ideal PFR and CSTR cases.

First the effect of dispersion on the steady‐state conversion at the exit of the tube reactor was examined. The numerical results of the model are shown in Figure 16.9. The limiting conversion at low D/uL is due to the residence time needed to achieve the design criteria of 99.9% conversion. At high D/uL the limiting case for an ideal CSTR is obtained. The conversion is insensitive to dispersion for D/uL < 1e‐3.

Next the steady‐state fractional conversion was simulated as a function of distance along the PFR for several representative values of D/uL, and the results are shown in Figure 16.10. At a D/uL of 1e‐4, the concentration profile is virtually indistinguishable from the ideal PFR curve. For an ideal CSTR (infinitely high D/uL), the concentration at L = 0 drops (instantaneously) to the steady‐state conversion of a CSTR with 11.8 hours τ.

Figure 16.11 shows the comparison of ideal PFR and the real PFR with D/uL = 0.000 12 for the last 10 m of the reactor. The difference in conversion versus distance along the reactor is quantifiable but negligible for this low value of axial dispersion. The ideal PFR curve was done analytically, and the plug flow with dispersion curve was done using the gPROMS numerical solver and 10 000 grid points. The simulations show that conversion versus distance is slightly less for the reactor with dispersion but clearly negligible for practical purposes.

To illustrate the effect of dispersion when not at steady state, concentration profiles along the length of the PFR are shown in Figure 16.12 for time = 1 hour after switch to the reactive feeds. For an ideal PFR the step change is infinitely narrow; however for larger values of dispersion, the step change gradually broadens out.

16.4 EXAMPLE OF CSTR FOR GRIGNARD FORMATION REACTION WITH SEQUESTERED Mg SOLIDS

A continuous Grignard formation reaction was run in a CSTR with sequestered magnesium solids for reasons of safety and minimizing key impurities. The reaction is shown below in the Scheme 16.2.

The key impurities are shown below.

The Wurtz coupling impurity was minimized by maintaining a high stoichiometric ratio of magnesium to aryl bromide starting material, the proteo impurity was reduced by minimizing water, and phenol was decreased by minimizing oxygen. Control of each of these impurities was easier to accomplish in a continuous reactor compared with batch. Oxygen and water are easier to minimize in a continuous reactor versus batch because the reactor is inerted and dried once and then remains inert and dry at steady state. The explanation for why the CSTR maintained high stoichiometric ratio of magnesium to aryl bromide starting material is given in the following discussion.

Liquid solutions were continuously pumped into the reactor containing a large molar excess of a solid activated magnesium metal, while liquid product solution was continuously pumped out, with the solid magnesium being sequestered in the reactor. Solid magnesium particles were periodically added once every four hours at an average rate equal to the molar feed rate of the starting material. In other words, Mg solids were added at a rate to match consumption. The magnesium was added in a very simple way. In a 6 L pilot‐scale reactor, a 2 in diameter cap was removed from a nozzle on the top of a glass reactor, and the Mg was poured into the vessel from a beaker through a funnel. In a 100 L manufacturing reactor, the port on the Hastelloy reactor was removed, and Mg was poured into the vessel from 1 gal wide‐mouth containers inside a glove bag. The freshly added metal rapidly activated when it mixed with the existing Grignard solution without the need for any additional activating agent. The kinetics of the Grignard formation reaction were extremely fast, achieving greater than 99% conversion in a single CSTR with a 1 hour mean residence time. This corresponds to a batch reaction with 99% conversion in 26 seconds, as described later in this section. A simplified schematic of the reactor system is shown in Figure 16.13.

Keeping solid magnesium particles in the CSTR was a key operational challenge. The two main methods/devices used to prevent magnesium from exiting the system were the settling pipe in the CSTR and the magnesium settling trap immediately downstream from the CSTR. These are described in more detail in the literature [21]. A 6 L pilot‐scale reactor operated at the 4.5 L fill level and a 100 L manufacturing‐scale reactor operated at the 45 L fill level. The 100 L CSTR was used to generate 4000 L of 0.85 M Grignard reagent solution for an API starting material. Forward processing of the Grignard reagent into a coupling reaction and subsequent workup and isolation were done in batch 8000 L vessels. There were significant safety advantages of running the reaction in a 100 L CSTR instead of 8000 L batch reactor. The Grignard formation reaction was highly exothermic, initiation was difficult, and the reaction had runaway potential; therefore minimizing the size of the reactor minimized the safety risks. The Grignard initiation was confirmed in the CSTR by stopping flow of aryl bromide after five minutes and quantifying the exotherm before continuing. The Grignard was first initiated batch but only at 250 ml reactor scale. A 250 ml CSTR produced enough active Grignard reagent to initiate a 6 L CSTR, and the 6 L CSTR produced enough active Grignard reagent to initiate a 100 L CSTR.

The number of molar equivalents of magnesium in the reactor relative to substrate oscillated. The goal was to keep at least 4 M equiv. Mg in the CSTR relative to substrate, which was greater than 99% Grignard reagent rather than aryl bromide at any time. Therefore, the CSTR started with 8 M equiv., and the first Mg recharge was done after four reactor volume turnovers. Plotting the instantaneous molar equivalents of magnesium in the reactor results in a sawtooth plot over the 96 turnover manufacturing campaign (Figure 16.14). Observe that the Grignard reaction maintained high instantaneous magnesium equivalents (4–8) while achieving usage of 1.04 equiv. of magnesium overall for the manufacturing campaign. This can be compared with 1.5 equiv. of magnesium that would have been used in the batch campaign. This is probably the main reason why the CSTR approach gave less Wurtz coupled impurity compared with the batch reaction approach. In addition, a batch reaction with 1.5 M equiv. of Mg would have resulted in more magnesium to quench at the end, compared with the CSTR manufacturing that used 1.04 M equiv. overall. The magnesium quench liberates hydrogen; therefore the continuous process generated less hydrogen than the batch counterpart would have generated, which was a safety advantage of the CSTR approach.

The reaction achieved 99.9% conversion with a 60 minute residence time in a single CSTR operating at 41 °C. Assuming pseudo first‐order reaction process, the rate constant can be calculated:

(16.12)

• k = 16/minute

Conversion for different τ can be predicted once the rate constant is known. For example, if the residence time is reduced to 30 minutes, then conversion would drop to 99.8%:

One can calculate what the reaction time would be for 99.9% conversion if the reaction was run isothermally batch. Of course, it is not possible to run this reaction isothermally batch because of the large exotherm and the unrealistically high heat removal rate that would be required:

(16.5)

• t = 0.43 minutes

It is important to note that it is not practical to measure this rate constant by running a batch reaction. The adiabatic temperature rise was 130 °C; therefore it would not be possible to keep the reactor temperature at 40 °C during a 26 second reaction. Performing this reaction in batch would also have mass transfer limitations. Therefore running this reaction in a CSTR is a more effective way to experimentally quantify the true kinetics for this fast exothermic reaction.

At pilot scale, the automation system monitored the process with a real‐time energy balance in the 6 L CSTR campaign, in order to prove the reaction was operating at a high conversion. At steady state, the heat removal rate by the cooling jacket was 188 W:

(16.16)

Increasing the incoming feed from room temperature to the reaction temperature consumed 26.4 W:

The steady‐state heat generation rate from reaction was 208 W:

(16.17)

The heat loss to surroundings was assumed zero since the reactor jacket was room temperature.

Real‐time energy balance was 103%, because total heat removed was 214 W and heat generated was 208 W. This real‐time energy balance was an important safety feature of the process, and it was constantly calculated and monitored by the distributed control system (DCS). Automated shutoffs were in place to stop the reagent feeds if the real‐time energy balance was below a limit, preventing the possibility of unreacted aryl bromide reagent accumulating to unsafe levels in the Grignard reactor.

16.5 NUMERICAL MODELING TO SELECT THE BEST REACTOR TYPE FOR MINIMIZING IMPURITIES

A simple hypothetical series–parallel reaction is used next to illustrate that there can be significant differences in impurity profiles for the same reaction depending on the reactor choice (PFR vs. batch with controlled addition vs. CSTR). The reaction and the kinetics (at 25 °C) in this example are

where

• A and B are reactants.
• P is the product.
• Imp is an undesired impurity.

The details of the governing equations and the parameters used in this illustration are listed in Table 16.2. The governing equation for PFR is the same as batch with all‐at‐once addition, because time variable in batch translates to residence time along the reactor for a PFR.

PFR (Batch with All‐at‐Once Addition)	Controlled Addition (Semi‐batch)	Three CSTRs in Series
Inlet concentration of species j to reactor cj: Concentration of species j along the reactor (at residence time t) rj: rate of formation per unit volume of species j	Initial concentration of species j cj: Concentration of species j at time t vf: Ratio of volumetric flow rate of addition stream to volume of reactor Species j concentration in addition stream rj: Rate of formation per unit volume of species j	Inlet concentration of species j to CSTR 1 : Concentration of species j in CSTR 1, 2, and 3, respectively τ: Residence time in each CSTR rj: Rate of formation per unit volume of species j
Reaction Rate Expressions	rA =  − k1cAcB
PFR Inlet concentration: Residence time: 1 h
Controlled Addition (Semi‐batch) Initial concentration in reactor: Addition stream concentration: Addition stream flow rate:4 L/h, initial reactor volume: 3 L, and dosing time: 30 min Reaction time: 1 h
CSTR: (Three CSTRs in Series with Equal Residence Time) Inlet concentration to CSTR 1: Residence time of each CSTR: 1 h

The concentrations after all reagents are mixed (if there was no reaction) would be the same in all three cases in the table. For the batch with controlled addition over 30 minutes, c_A after mixing would be 2 × 3/(3 + 4 × 0.5) = 1.2 M, and c_B after mixing would be 4 × 4 × 0.5/(3 + 4 × 0.5) = 1.6 M.

The model for this example was implemented using DynoChem [22]. The governing equations are different between PFR, batch with controlled addition, and CSTRs in series. Even though the kinetics are the same, the impurity profiles are different for the three different reactors. In this example, the PFR with residence time of 1 hour results in 96% in situ yield and 2.5% Imp. Controlled addition of B over 30 minutes, followed by 30 minutes of additional reaction mixing time, results in 94% in situ yield and 1.8% Imp. If this reaction is run using three CSTRs each with 1 hour residence time, an in situ yield of 94% can be achieved, but the impurity level at steady state is 5%. Figure 16.15 shows the impurity level versus conversion of A for (i) a PFR, (ii) batch with controlled addition, and (iii) three equal volume CSTRs in series.

In this case, a controlled addition (semi‐batch) gives a lower impurity level than a PFR because it keeps the concentration of B lower. CSTRs give the highest level of impurities in this case because they are operating at steady‐state conditions with P and B together for longer times. B is at low levels, but P is always at high concentration levels, and contact time is 3 hours in the three CSTRs in series. The figure also shows two additional scenarios that begin to mimic batch with controlled addition in a PFR. Reagent B is added at multiple points along the PFR. The normal PFR has one addition point, which is at the inlet to the tube. The PFR with one side stream has two addition points, one at the inlet and one 1/3 of the way down the reactor length. Half of the reagent B feed solution was added at each location. The PFR with two side streams has three addition points. One is at the inlet, the second is at a distance 1/6 of the way down the reactor length, and the third is at a distance 1/3 of the way down the reactor length. Reagent B feed solution was added in three equal portions at the three locations. Interestingly, the impurity level in the PFR with multiple addition points matched batch reactor with controlled addition, even with only one side stream. Practically speaking, the cost of running a PFR with side streams is that another pump or control valve with mass flow control is needed for each additional side stream. This may be low cost compared to the benefit in yield and selectivity. Clearly, the numerical modeling is useful for reactor design and selection provided that the kinetics of the main reaction and of the unwanted side and series reactions are known. It is especially important when the impurities are difficult to reject and/or could be reactive downstream.

16.6 WHAT CAN BE DONE BATCH BEFORE RUNNING CONTINUOUS REACTION EXPERIMENTS?

Much of the experimental work to generate the data needed to develop a continuous flow process can actually be accomplished more quickly and efficiently in batch equipment. The impact of different reagents, solvents, and catalysts can often be run using less material in batch. In addition, batch experiments do not have the transitional waste produced in flow experiments to achieve steady state after changing an operational parameter. One may observe reaction characteristics in batch (such as solid precipitation) that will influence the eventual choice of flow reactor type or even advise when a flow process undesirable. Table 16.3 is a guide to what can be done batch to help design the continuous reaction before running continuous flow experiments.

16.7 WHAT IS DIFFICULT TO PREDICT FROM BATCH EXPERIMENTS?

Table 16.4 lists information that is best obtained in the actual flow chemistry experiments because it is difficult to predict from batch experiments.

ACKNOWLEDGMENTS

Mark Kerr was the process chemist for the continuous Grignard formation reaction in the 100 L CSTR, and Sylvia Nwosu was the engineer on the scale‐up project. The third‐party CMO who did the scale‐up manufacturing work did an outstanding job and are largely responsible for the success of the project. Ed Deweese, Paul Milenbaugh, and Rick Spears of D & M Continuous Solutions constructed and operated the hydrogenation PFR system. Jake Remacle, Miguel Gonzales, Wei‐Ming Sun, and Nick Zaborenko developed the 73 L coiled tube PFR for hydrogenation, and the chemistry was designed and developed by Joel Calvin. We thank Bret Huff for initiating, leading, and sponsoring the continuous reaction design and development work at Eli Lilly and Company.

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