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Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Reducing the Fouling Potential in a Continuous Polymerization Millireactor via Geometry Modification Moritz J. Begall,† Alexandra Krieger,† Sebastian Recker,† Frank Herbstritt,‡ Adel Mhamdi,† and Alexander Mitsos*,† †

Aachener Verfahrenstechnik - Process Systems Engineering (AVT.SVT), RWTH Aachen University, Forckenbeckstraße 51, 52074 Aachen, Germany ‡ Ehrfeld Mikrotechnik GmbH, Mikroforum Ring 1, 55234 Wendelsheim, Germany S Supporting Information *

ABSTRACT: Continuous milli-scale reactors with internal mixing elements are increasingly used in the chemical industry and considered for polymerization processes. Their small scale makes them especially susceptible to fouling. Addressing this problem, this article presents a computational fluid dynamics (CFD) analysis of a Miprowa millireactor channel. The flow field is examined with the finite-element based software package COMSOL Multiphysics to identify areas of low velocity, generally prone to fouling during polymerization reactions. For simplicity, the flow is assumed incompressible and isothermal, using the material properties of water. Three geometry modifications to the mixing elements are proposed. Numerical simulations of the flow field around the proposed mixing elements show a reduction in areas with stagnating flow by 20%, reducing the fouling potential without substantially affecting other metrics such as the pressure loss.

1. INTRODUCTION Millireactors are gaining importance in the chemical industry, facilitating continuous production of low-volume specialty polymers.1−4 While chemicals produced in large volumes have been manufactured by highly efficient continuous flow processes for quite some time, specialty chemical products still rely in large part on batch processing.5 This situation has, however, started to change, as an estimated 50% of reactors in the fine chemical and pharmaceutical industry could benefit from continuous processing.6 Continuous processes follow an approach known as quality by design, meaning the product quality can be guaranteed inherently through process design.7 Often cited advantages of continuous millireactors are an increased selectivity, energy efficiency and yield5 when compared to batch processes. Their small holdup can also provide safety benefits when working with dangerous substances or at high temperatures or pressures.8 Furthermore, their high surface to volume ratio makes them suitable for highly exothermic reactions, which require fast heat removal9 and a tight control of the process parameters.10 This ratio can even be maintained during production scaleup,11 reducing the need for pilot stages. While millireactors possess many advantages, their small size renders them especially prone to fouling12 whenever nonpure flows are involved.13 Fouling can be caused by a variety of factors, such as microparticles contained in process fluids, solidification of materials as a result of chemical reactions, crystallization, corrosion or biological growth.14,15 The unifying © XXXX American Chemical Society

characteristic of all these factors is the unwanted accumulation of material,16 preferentially occurring in areas of stagnating flow.17 Fouling negatively impacts the performance of affected systems18 and can cause major problems in reactors, as it can lead to choking and clogging of the reactor, causing a halt of operations, extensive and time-consuming cleanup, downtime and high costs.19 Research into millireactors and fouling is conducted both experimentally and, increasingly, computationally, including CFD modeling, see, e.g., refs 20−31. One application of CFD modeling is the optimization of reactor design. Simulations provide insights into otherwise inaccessible internal processes within reactors and allow for the quick testing of different design modifications, i.e., rapid prototyping, without the need for actual physical prototypes for each design. In this article, the Miprowa Lab reactor,32,33 developed by Ehrfeld Mikrotechnik, is used as a case study. It is composed of three layers of mixing elements in rectangular reactor channels, which are enveloped by a thermal fluid. The reactor is briefly described in Section 2. Then, the utilization of CFD modeling to conduct simulations to identify its stagnant flow areas, assuming water properties, is discussed extensively. Section 3 gives an overview of the applied modeling equations and Received: January 15, 2018 Revised: April 14, 2018 Accepted: April 16, 2018

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DOI: 10.1021/acs.iecr.8b00206 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

different fluid elements come in contact with the wall. Further, the mixing elements are available in different shapes, and can easily be exchanged, influencing the flow profile and thus the heat transfer, mixing intensity and pressure loss. To facilitate the insertion and removal of the mixing elements, they are slightly smaller than the channel, leaving a gap of nominally 0.075 mm between the individual elements. The reactor and mixing elements are manufactured from cold rolled sheet metal. According to the needs of the application, high-grade steel (e.g., AISI 316Ti) or nickel-based alloys (e.g., Hastelloy C-22) are utilized. The mixing elements are given a surface finish by grinding or electro-polishing, resulting in very smooth surfaces with an average roughness of Ra ≤ 0.8 μm. The Miprowa Lab reactor has been specifically designed for single- or multiphase liquid−liquid and liquid−gas reactions, and can be operated at temperatures ranging from −20 to +200 °C, at a pressure of up to 30 bar. The reactor has an effective fluid volume of about 30 mL, depending on the inlays, and a typical through-put of 0.6−15 L/h.32 Since all eight reactor channels have the same geometry and consequently exhibit similar flow behavior, only a single channel is considered for the examinations undertaken in this paper. The geometry of the mixing inserts is shown in Figure 3. The distance d between the fins is 2 mm, the thickness b of the ridges is 1 mm and the angle α is 45°.

Section 4 describes the numerical methods. Simulation results for the original reactor geometry are shown in Section 5.1, and areas with low flow velocities, generally prone to fouling during polymerization reactions, are identified. Geometry modifications to the mixing elements are then proposed, and their effect on the flow field examined, in Section 5.2. Section 5.3 reexamines some of the previous configurations, removing the simplifying assumption that no gaps are present between the mixing elements. The improvements to the flow profile and resulting reduction of the fouling potential are discussed in Section 6.

2. MIPROWA LAB REACTOR The Miprowa Lab millireactor was developed and is manufactured by Ehrfeld Mikrotechnik. A photo and cutaway of the reactor are shown in Figure 1.

Figure 1. Left: Picture of the Miprowa Lab reactor without the front headplate, providing a view of the partially inserted inserts. Right: View inside the Miprowa Lab reactor.

The reactor contains eight process channels. The process fluid flows through them in a serial fashion, as depicted in Figure 1. The process fluid enters the first channel through the front headplate, is redirected horizontally in the back headplate at the end of the channel and flows back toward the front headplateplate, where it is then redirected vertically. This pattern is repeated until the fluid has passed through all eight channel segments and exits the reactor through the front headplate. The channels are enclosed by a shell through which a thermal fluid is pumped. The shell also contains baffles that direct the tempering fluid in a meander pattern to ensure good and homogeneous heat transfer. The individual channels have a length of 300 mm, and have a rectangular cross-section with interior dimensions of 12 mm by 1.5 mm. Through the flat form of the channel, heat can be transferred more effectively than with a round or square cross section of the same area due to the larger surface to volume ratio. Inside the channels, mixing elements are inserted in three layers, forming a three-dimensional grid with a periodically repeating pattern, see Figure 2. This design has two distinct advantages: Forcing the periodic splitting and redirection of the fluid stream increases the mixing efficiency and ensures that

Figure 3. Characteristic parameters of the inserts.

3. ASSESSMENT OF FOULING POTENTIAL The goal of this article is to identify areas in millireactors that might be especially prone to fouling, and to reduce those areas, using the Miprowa Lab reactor as an example. As previously mentioned, fouling can have many causes, one of which is the buildup of solid material during polymerization reactions, also known as gelation. However, to actually simulate the polymerization reaction process in the millireactor, it would be necessary to couple the Navier−Stokes equations for mass, momentum and energy with species balances and reaction kinetics including the gelation or fouling. This presents difficulties on two fronts: For one, there are different polymerization mechanisms, namely step-growth and chaingrowth polymerization, which includes free radical, anionic, cationic, group transfer and coordination polymerization,34,35 each with their own kinetics. Furthermore, polymerization can be achieved in a range of processes, e.g. bulk, solution, suspension or emulsion polymerization, all requiring different kinetic models. To the knowledge of the authors, a complete model for most of these cases, in particular for the gelation mechanism of the free-radical polymerization of interest, has not been developed yet. Second, even given a suitable model for a specific polymerization process, the resulting system of equations would be very complex and might not be solvable in a reasonable amount of time, especially for a discretization fine enough to capture the geometric details of the reactor channel.

Figure 2. Three inserts in a Miprowa channel. B


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4. NUMERICAL SOLUTION The simulations are performed with COMSOL Multiphysics version 5.1,36 using a damped Newton solver with pseudo timestepping, which employs the generalized minimum residual (GMRES) method to solve the linearized subsystems. GMRES is an iterative method for general nonsymmetric linear systems of the form Ax = b. It is one of several methods implemented in COMSOL for the solution of linear systems, the others being the flexible generalized minimum residual method (FGMRES), the conjugate gradient method and the biconjugate gradient stabilized iterative method (BiCGStab). Each method has its advantages and no method can be considered superior in all cases. Here, GMRES is chosen because the flexibility of FGMRES comes with increased memory requirements and is not needed, conjugate gradients require a symmetric matrix, and BiCGStab often has a more irregular convergence behavior and needs two matrix-vector multiplications per iteration instead of one. The meshes for the simulations without the gaps between the mixing elements and the channel walls (Sections 5.1 and 5.2) consist of about 4 × 106 elements. To check for grid convergence, simulations are also conducted with a finer mesh with 9.2 × 106 elements, with matching results. The simulations including the gaps (Section 5.3) are conducted on meshes with about 11 × 106 elements, and again checked for grid convergence by comparing to the results obtained on a 19 × 106 element mesh. The simulations are conducted on a system with an eightcore Intel Xeon E5-2630 v2 CPU and 128 GB RAM, running Windows Server 2008 R2. Computation times vary but generally fall in the range 1.5 to 2 h (wall time), with RAM requirements of approximately 80 GB.

To overcome the challenges, a simplification is performed and only the fluid flow is considered; the key assumption is that regardless of the type of polymerization reaction, fouling will occur preferentially in regions of stagnating flow. Moreover, the fluid is approximated using pure water properties. At room temperature (20 °C), this translates to a density of ρ = 998.2 kg/m3 and a dynamic viscosity of μ = 1.002 mPa·s. In a reacting system, the temperature, density, viscosity and composition of the fluid are all subject to change, which potentially has a large influence on the rate of fouling. Consequently, this approach is not meant to give a close approximation of the polymerization process as such, but rather of the complex flow pattern that forms inside the reactor. By only regarding isothermal singlephase fluid flow, many factors present in reacting systems are neglected. Despite this simplification, the presented analysis does provide beneficial insights. Fluid elements passing through slow moving regions will have a longer residence time in the reactor than the bulk flow. This alone might lead to a broad residence time distribution and reduced product quality. Furthermore, as regions with low flow velocity are a likely origin for fouling, and can act as a seed for further fouling, affecting other areas of the reactor, identifying these areas and ensuring optimal fluid flow is of great importance to prevent or inhibit the initial occurrence of fouling. In the following, regions of low velocity and stagnating flow are defined as having a velocity magnitude of less than 10% and 1%, respectively, of the inlet velocity. To identify these regions, the flow field can be calculated by the Navier−Stokes equations. Since water is nearly incompressible, as common monomer solutions are, compressibility is not considered. Likewise, temperature variations of the process fluid did not influence the results significantly, so isothermal flow is assumed. With these assumptions, the necessary equations can be further simplified: The continuity equation reduces to

∇·u = 0

5. RESULTS 5.1. Flow Profile and Fouling Potential. The flow profile in the Miprowa millireactor was examined to identify regions in the geometry with stagnating flow that are likely to be especially prone to fouling. The geometry of a single Miprowa Lab channel with default mixing elements (d = 2 mm, b = 1 mm, α = 45°, cf. Figure 3) is used. Because the flow field in the channel forms a repeating pattern between the fins of the mixing elements, and is fully developed after just a few ribs, the channel length was shortened to 55.5 mm (62.4 mm including in- and outlet) to reduce the computational time. Furthermore, because the reactor channel and mixing elements are symmetric with respect to a plane passing horizontally through its center (cf. Figure 2), only half the channel was simulated. The gaps between the mixing elements and the channel walls were neglected at this stage, as their inclusion would have led to very narrow geometric features, making the problem a lot more numerically challenging. Simulations including the gaps are presented for comparison for a few chosen cases in Section 5.3. The heat exchanger part of the Miprowa Lab surrounding the reactor channels was ignored. Since the thermal and process fluids are physically separated and their flows do not interact hydrodynamically, including the heat exchanger would only result in a more complex model without any additional benefit for the purpose of this investigation. The original mixing element configuration contains some small “dead zones” where stagnating flow might be expected,

(1)

with the velocity vector u. The momentum equation can be written as ⎛ p⎞ ∂u + (u ·∇)u − ν∇2 u + ∇⎜ ⎟ = 0 ∂t ⎝ ρ⎠

(2)

with the pressure p and the kinematic viscosity ν. The only acting body force, gravity, is ignored, because its influence is minor and not of relevance. Because the density ρ is assumed constant, and assuming also constant viscosity ν, the equations decouple from the energy equation, and since isothermal flow is considered, the energy equation can be dropped completely. The only remaining variables are u and p, therefore eqs 1 and 2 are sufficient for their evaluation. Standard velocity-inlet and pressure-outlet boundary conditions are used. Setting a uniform velocity over the inlet cross section is reasonable, because the flow has sufficient opportunity to develop before reaching the domain of interest, eliminating entry effects and making more intricate boundary conditions unnecessary. This is a common approach and has the advantage that no information other than the inlet velocity has to be known. The back pressure can be set to an arbitrary value, which together with the computed corresponding inlet pressure gives the pressure loss. C


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to create a first variant, because this leads to perfect alignment of the mixing elements at the fin tip side of the channel. The second variant was obtained by moving the mixing element 0.6 mm to the right, aligning the elements at the spine side (see Figure 7). The pattern created by the mixing elements repeats every 4.24 mm. This means that shifting an element more than that will not yield any configurations that would not be attainable with a smaller shift. It also implies that the 0.43 mm shift to the left of the first modification is equivalent to a 3.81 mm shift to the right. For shifts of the central mixing element in the range of −1.2 to +0.59 mm (negative values indicating a shift to the left), dead zones of varying size remain at the spine side of the fluid domain. A parameter study was conducted to identify other favorable mixing element offsets. The displacement yielding the largest improvement, i.e., the smallest amount of stagnating flow, was selected for further examination, giving the third modification. To obtain a fourth modification, in addition to shifting the central mixing element, the angle α (cf. Figure 3) of all elements was changed from 45° to 44.8°, aligning them at both the spine and fin tip side of the channel. Figure 6 shows the respective ratios of slow moving and stagnating flow for all cases. For the investigated part of the reactor channel (excluding the in- and outlet areas), Figure 6 gives the volumes of areas with a velocity magnitude of less than 20%, 10%, 5% and 1% of the inflow velocity as a ratio of the total volume of the channel part. The individual mixing element configurations and the resulting channel geometries of the four selected cases are shown in Figure 7. As is obvious from the displacements given above, the changes to the mixing elements are rather small. This has two advantages: For one, manufacture of the modified elements poses no additional challenges. Second, the flow fields only differ locally, at the spine and fin tips of the mixing elements, but otherwise retain their characteristics (cf. Table 1). The selected modifications were analyzed in the same manner as before. The top row of Figure 8 compares the areas

see Figure 4. Computing a stationary flow field yields the results shown in Figure 5.

Figure 4. On the left, the mixing element configuration as specified by the manufacturer is shown. The middle depicts the corresponding fluid domain, which is part of the channel volume not taken up by the mixing elements. On the right is a close-up of some of the “dead edges” where stagnating flow is to be expected.

The left side of Figure 5 shows areas with a velocity magnitude of less than 10% of the inflow velocity. This limit might seem arbitrary, however, qualitatively similar results are obtained with other limits, as shown later on (cf. Figure 6). The result of the simulation is in agreement with the initial assumption that the flow is slowest in the corners of the channel. A second study was performed using COMSOL’s particle tracking module. 2000 tracers were tracked from the inlet through the already computed flow field. The image on the right of Figure 5 shows these paths, colored by velocity magnitude. The tracers basically follow the local velocity vectors at each point on their path. It is evident that the particles do not enter the dead corners at both the top and the bottom of the channel. This suggests that the bulk of the flow does not pass through these areas. 5.2. Investigation of Mixing Element Modifications. In an effort to reduce the stagnant zones of the original channel geometry, modifications were made to the mixing elements. The first two modifications were obtained by shifting the central mixing element with respect to the outer mixing elements. The mixing element was moved 0.43 mm to the left

Figure 5. Original mixing element configuration. The left image highlights areas with a velocity magnitude |u| < 0.1 · uinlet, which amount to 8.61% of the reactor volume. The inlet velocity in this case is 13.1 mm/s. The average velocity in the reactor is 17 mm/s, which with a hydraulic diameter of dh = 1.2 mm corresponds to a Reynolds number of Re = 20.4. Simulations with higher inlet velocities show qualitatively similar results. The right image shows tracers, colored by velocity magnitude. D


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Figure 6. Reactor volume ratios [%] with |u| < x·uinlet. Modifications 1−3 are indicated. In the case of Modification 4, an offset cannot be given, because the geometry was altered more profoundly. Nevertheless, the corresponding values are given for comparison as open dots. See Table S1 for the raw data.

Figure 7. In the top row, the modified mixing element configurations are shown. The bottom row depicts the corresponding fluid domains. The first three Modifications were obtained by shifting the central mixing element with respect to the outer elements. For Modification 4, the fin angle was changed.

Comparing the tracer streamlines (bottom row of Figure 8), it is obvious that for the first modification, the tracers do not pass through the dead corners at the spine side of the channel. For the second and fourth modifications, no such dead zones are present, and they are considerably less pronounced in Modification 3. At the fin tip side of the channel, Modification 3 seems to yield the best results, since all other cases have corners that no tracers, and in turn no significant flow, pass through. In fact, these corners are present in Modification 3 as well, but comparatively small and difficult to discern, because they are masked by other areas containing tracers that lie in front or behind them. Both the graphical evaluation and the quantified findings in Figure 6 reveal that Modifications 3 and 4 are the most promising candidates for better avoiding fouling of the mixing elements. Specifically, the areas of stagnating flow (|u| < 0.01 · uinflow) are reduced by 40% for Modification 4, and by 65% in the case of Modification 3. The pressure loss was not significantly affected by the modifications. Table 1 gives the average pressure loss per mm of reactor channel. 5.3. Influence of the Gaps between Inserts. In the previous sections, the small gaps between the mixing elements

Table 1. Average Pressure Loss, for an Average Inflow Velocity of 13.1 mm/s Mixing elements Original Modification Modification Modification Modification

1 2 3 4

Pressure loss [Pa/mm] 1.22 1.22 1.19 1.07 1.24

with a velocity magnitude of less than 10% of the inflow velocity, corresponding to the left side of Figure 5. The first geometry modification had even larger stagnant areas at the spine side of the mixing elements than those previously observed, but smaller ones at the fin tip side. The second modification lead to significantly improved flow at the spine side of the mixing elements. Modification 4 combines these benefits: Whereas Modifications 1 and 2 yielded improvements at either the spine or fin tip side of the mixing elements, while negatively impacting the flow at the other side, changing the angle of the mixing elements resulted in an overall improvement. E


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Figure 8. Top row depicts areas with |u| < 0.1 · uinflow, the bottom row tracer streamlines.

and the channel walls, which have a width of nominally 0.075 mm and are present in the real reactor channel geometry, have been neglected to simplify the computations. To investigate their effects on the results obtained in the previous section, simulations including the gaps were conducted on a 28 mm long channel section for the original geometry and Modifications 3 and 4. Figure 9 shows a section of the fluid domain for Modification 3. The narrow layers, which form due to the gaps, are clearly visible.

Figure 10. Images at the top depict areas with |u| < 0.1 · uinflow. The bottom images show the corresponding tracer streamlines.

Table 2. Reactor Volume Ratio [%] with |u| < x·uinlet x [%]

Figure 9. Left: Part of the fluid domain. The narrow fluid layers between and around the mixing elements are visible. Right: Flow in three cutplanes perpendicular to the main flow direction.

Mixing Elements

Figure 10 shows the regions of low flow velocity, as well as tracer streamlines, in analogy to Figure 8. The streamlines show similar behavior as before, avoiding the dead zones in the original geometry. The regions of slow moving fluid have enlarged as a result of the gaps. Looking at Table 2, we observe that the improved mixing elements still lead to a reduction in stagnating flow by 19% for Modification 3, and 21% for Modification 4. Hence, Modification 4 can be regarded as the best option for reducing the fouling potential by modifying the mixing element geometry, at the cost of a slightly larger pressure loss (cf. Table 3). Modification 3 offers a trade-off between reducing the pressure loss and the fouling potential. The improvements are less pronounced than those achieved neglecting the gaps (cf. Figure 6), which is plausible, because the gaps allow the fluid to more easily enter and leave the dead edges. The trend is still present, however, emphasizing the benefit of the improved mixing elements.

Original Modification 3 Modification 4

20

10

5

1

21.7 18.1 20.0

14.7 12.7 13.0

8.98 8.16 7.81

1.68 1.35 1.32

Table 3. Average Pressure Loss, for an Average Inflow Velocity of 11.5 mm/s Mixing elements

Pressure loss [Pa/mm]

Original Modification 3 Modification 4

0.89 0.85 0.99

6. CONCLUSIONS Fouling is a common and important problem in the chemical industry, and should thus be prevented as far as possible. In particular for millireactors, fouling can significantly impact process performance and lead to clogging of the entire reactor. This is especially true for chemical reaction fouling, which can occur during polymerization reactions, since it can manifest very rapidly and to an extend that halts the whole process. For this reason, the flow fields in the Miprowa Lab millireactor were F


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Industrial & Engineering Chemistry Research examined with CFD to identify stagnating flow zones, assuming these to be a starting point for the occurrence of fouling. Areas with slow moving flow were identified and could be reduced by geometric modifications to the mixing elements. In a first step, neglecting any gaps between the mixing elements, four different modifications to the original mixing elements were examined. This study leads to a reduction of slow moving flow regions, defined as regions with less than 10% of the inflow velocity, of up to 39%, and of stagnating flow, defined as less than 1% of the inflow velocity, of up to 65%. This analysis was then repeated taking into consideration the gaps for the original elements and Modifications 3 and 4, resulting in a reduction of stagnating flow of 21% in the case of Modification 4. These results clearly show that CFD can be a useful tool in the development and design of millireactors. The mixing elements resulting from the most promising fourth modification have been manufactured by Ehrfeld Mikrotechnik and are currently being examined experimentally to validate the findings. While the modifications examined here were selected manually, employing a shape optimization procedure might yield even better mixing element geometries. However, care has to be taken to respect possibly competing objectives. For example, reducing stagnant flow regions should not negatively impact the mixing or other reactor properties. More importantly, the CFD approach followed thus far has to be coupled to the kinetics of one or more selected polymerization reactions to get a more thorough understanding not just of the fluid flow, but of the whole reaction process inside the reactor.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b00206. Table giving the reactor volume ratios corresponding to Figure 6 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*A. Mitos. E-mail: [email protected]. ORCID

Alexander Mitsos: 0000-0003-0335-6566 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work presented in this article was conducted as a part of the KoPPonA project, a research project concerned with the development of an efficient overall concept for continuously operated processes for specialty polymer production. The support of the German Federal Ministry for Economic Affairs and Energy (BMWi) under grant number 03ET1183C is gratefully acknowledged. For more information, see http:// enpro-initiative.de/en/KoPPonA.html. We thank the colleagues in the KoPPonA project for useful discussions, especially Dr. Christian Schwede, Dr. Omar Naeem and Prof. Ulrich Nieken.

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REFERENCES

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