Mixing of Stratified Miscible Liquids in an Unbaffled Tank with

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Mixing of Stratified Miscible Liquids in an Unbaffled Tank with Application in High Concentration Protein Drug Product Manufacturing Zhao Yu, Brian A Finch, and Dean A Hale Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04618 • Publication Date (Web): 09 Feb 2018 Downloaded from http://pubs.acs.org on February 10, 2018

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Industrial & Engineering Chemistry Research

Mixing of Stratified Miscible Liquids in an Unbaffled Tank with Application in High Concentration Protein Drug Product Manufacturing Zhao Yu*1, Brian A Finch2, Dean A Hale1

1

Bioproduct Development, Lilly Research Laboratories, Eli Lilly and Company, Indianapolis,

Indiana 46285 2

Tech Services/Manufacturing Science, Eli Lilly and Company, Indianapolis, Indiana 46285

KEYWORDS Mixing, stratification, drug product formulation, viscosity, density, computational fluid dynamics, monoclonal antibody

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ABSTRACT During high-concentration protein drug product compounding, the property difference between the drug substance solution and the buffer excipient solution can potentially cause the formation of stratified layers, which may prohibit effective mixing. In this study, mixing of two stratified liquids in an unbaffled tank with an angle-mounted impeller was investigated using both experiments and computational fluid dynamics (CFD) simulations. The results revealed that the mixing time under the stratified conditions could be over an order of magnitude longer than that predicted by a commonly used blend time correlation. Further analysis showed that the observed long mixing time occurred when the buoyancy force due to density difference between the liquids was dominant over the impeller stir, and was correlated with high Richardson number. The study also looked into the impact of factors such as liquid height and impeller size, and a new correlation was proposed based on the experimental data.


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INTRODUCTION Mixing two miscible liquids in a mechanically agitated tank is a common operation involved in many industrial processes. For example, in biopharmaceutical industry, manufacture of typical therapeutic protein drug products involves a formulation compounding step, where a buffer excipient solution is added into a drug substance solution and the two are mixed until homogeneity is achieved to make the final drug product formulation. Depending on their differences in physical properties as well as the addition procedure, the two liquids could form two stratified layers inside the tank. Once formed, such stratification has the potential to negatively impact the effectiveness of the mixer, and cause unexpectedly long mixing times. Particularly, some practical considerations in biopharmaceutical manufacturing may lead to operating conditions that differ from those recommended for good mixing, and can thus increase the propensity of stratification between the two liquid components. For instance, accommodating different batch sizes in the same vessel will lead to variable liquid heights, which may change the flow pattern and mixing efficiency. In addition, for products for which sensitivity to an air-liquid interface is a concern, a reduced impeller speed could be used to minimize air entrainment at the liquid surface, resulting in mixing being conducted in the transitional rather than turbulent regime. Combination of those complexities with liquid stratification has created challenges for some practical mixing applications, but unfortunately there is very limited relevant information available in the literature. The need to develop robust manufacturing processes for high value products such as biopharmaceuticals thus calls for good fundamental understanding of mixing under those challenges.

Liquid mixing in stirred tanks has been studied extensively over the past several decades, and many best practices have been established and are available in the literature.1 However, most of the knowledge and tools for mixing time predictions are generated from “standard” tank configurations, in which an impeller is vertically mounted in the center of a fully baffled tank, and the liquid height is approximately equal to the tank diameter. In practice, many formulation tanks such as those used in parenteral drug product 3 ACS Paragon Plus Environment


manufacturing are typically without baffles due to their simplicity and ease of cleaning. However, lack of baffles in a cylindrical vessel with a centrally mounted impeller could result in vortexing and partially segregated zones. Consequently, mixing times in unbaffled tanks are found to be 2–3 times larger than those pertaining to baffled tanks under the same power input, unless the surface vortex approaches the impeller plane.2 To compensate for the lack of baffles, the impeller can be mounted at an angle in order to reduce the solid-body rotation. Information about mixing in unbaffled tanks with angle-mounted impellers is scarce in the literature. Among the very few studies that exist for such systems, one reported that, in the turbulent regime, the nondimensional mixing time (Nt) in an unbaffled tank with an angled Lightnin A310 impeller is similar to that in a standard baffled tank with the same impeller installed vertically.3 Another work suggested that the power numbers of angle-mounted axial flow impellers in unbaffled tanks are similar to or slightly lower than their corresponding value for standard baffled tanks.4 Both studies were performed for simple liquid blending under turbulent conditions, and did not involve the effect of liquid height or contrast in liquid properties. In the laminar regime, both CFD simulations and experiments have shown that blending in unbaffled tanks can be enhanced by an inclined impeller, as it breaks the symmetry and reduces the isolated mixing zones in the vessel.5 Besides using an angled impeller, another commonly used approach to improve mixing in an unbaffled tank is to mount the impeller vertically at eccentric locations, and it has been proven effective for laminar, transitional, as well as turbulent regimes.6,7,8

The effect of density and viscosity differences between two liquid components on mixing has been explored by a few studies.9,10 Those studies were focused on adding a very small volume of a second liquid into the bulk liquid while the mixer was in operation. Although they were different from the case of our current work, where mixing starts with two initially stratified liquids, the physics revealed in those studies was relevant. In both scenarios, mixing is affected by the interplay between the buoyancy force caused by the density difference and the flow created by the impeller. Particularly, the earlier studies have 4 ACS Paragon Plus Environment

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identified three regimes for mixing between two miscible liquids with contrasting densities and viscosities. In the “stirrer controlled” regime, the added liquid is transported into the impeller region and rapidly mixes with the bulk liquid. The mixing time follows the correlation for single liquid blending, and is unaffected by the density and viscosity differences. In contrast, in the “gravity controlled” regime, the added liquid forms a separate layer either on the liquid surface or at the bottom of the tank, depending on its density. Mixing between the two liquids is due to the surface renewal mechanism at their interface. Very long mixing time is observed in this case, which can be over ten times longer than that in the “stirrer controlled” regime. Both density and viscosity differences affect the mixing time, but density difference is more likely to cause long mixing time. A third “intermediate” regime has also been found where the added liquid is partially pulled into the impeller region, and large scattering of mixing time data is observed in this region due to the unpredictable nature of the movement of the added liquid. The three regimes can be distinguished on the basis of the dimensionless Richardson number ∆

Ri =

(1)

Although high Richardson number is typically associated with the “gravity controlled” regime, it is not possible to clearly define the boundary between the regimes. Mixing of two different liquids in a vessels agitated by a side-entry impeller was also reported in an experimental study.11 In that case, the flow created by the impeller was mostly parallel to the interface, while the flow discharged by the impeller was mostly perpendicular to the interface for top-entry mixers. Despite the obvious difference in mixing configuration, similar mixing regimes regarding stratification was reported. Fast mixing by convection and turbulent diffusion was observed at high impeller speeds, while mixing under low speeds proceeded through gradual erosion of the interface by interfacial wave and was much slower. Unfortunately, mixing time relations presented in the literature are only applicable to the specific condition (scale, mixer, additional point, etc.) used in those studies, and the scaling rule of mixing time in the gravity controlled regime is yet unknown. In addition, most data in the literature correspond to turbulent conditions, while



mixing of two miscible liquids with differing density and viscosities under laminar or transitional flow regime has not been reported.

Computational fluid dynamics (CFD) simulations have been widely used to characterize the performance of various mixers and to predict mixing times under different operating conditions. While applications of CFD in both laminar and turbulent flow regimes are relatively well established, the transitional regime from laminar to turbulent still poses significant challenges in the theory of fluid mechanics as well as in the development of rigorous modeling approaches. From an engineering application perspective, stirred tanks operated in the transitional regime have been studied with both laminar and RANS models. While all models were reported to give reasonable predictions of the mixing time, there was no clear preference between them.12 RANS models with low Reynolds number correction have been applied in modeling small unbaffled tanks. The mixing time results were in good agreement with the experimental value obtained by discoloration method.13 The velocity profile obtained using low Reynolds number RANS model was also validated by particle image velocimetry.14 For fully turbulent flow in unbaffled tanks, Reynolds-stress turbulent model has been reported to be superior to the shear-stress transport model in predicting velocity components, likely due to the anisotropic swirling flow created by the centrally mounted impeller in the unbaffled vessel.15 It is also noted that mixing time in most CFD simulations are obtained for the conditions where a small amount of a tracer species is added into the bulk liquid. Only a few studies have investigated the time to blend two stratified liquid layers. One study for ethanol-glycerol mixing in an unbaffled tank with an anchor impeller employed the homogeneous multiphase model in the liquid phase. The time evolution of the droplet size of the added liquid had to be specified in order to obtain good agreement between the calculated and measured mixing time.16 For a standard tank configuration with a pitched blade turbine operated under intermediate Reynolds number (~6000), simulations based on the lattice Boltzmann method showed significant increase of mixing time with the


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increase of density difference, or equivalently the Richardson number. However, that study was purely computational, and no experimental data were used to validate the model.17

In this work, experimental and computational techniques were used to investigate mixing of two initially stratified liquids in an unbaffled tank. The conditions explored were representative of those in a typical monoclonal antibody drug product manufacturing process, and data from two antibody drug product formulation batches are presented. A series of experiments were also carried out using a surrogate fluid system at 10L and 50L scales. The measured mixing times were compared with the predictions from a commonly used correlation in the literature for single fluid blending, and it was shown that, under certain conditions, the correlation significantly under predicted the actual mixing time. CFD simulations were performed to relate the flow pattern under fast and slow mixing conditions with the measured mixing time and visual observations made during the experiments. Finally, the effects of the Richardson number, the liquid height, and impeller size on mixing of stratified liquids are further discussed. A new correlation is also proposed based on the experimental data obtained in this work.

EXPERIMENTAL MEASUREMENTS Mixing Equipment Mixing experiments were conducted at two different scales to assess the effect of tank geometry on the mixing characteristics. The commercial 50 liter tank had been designed with the following constraints: the tank was not baffled to simplify cleaning operations and a high aspect ratio (H/T) was used to meet sampling requirements and for a floating batch size (25 – 50 liters). The 10 liter scale tank was designed to be s scale-down version of the 50L tank for process development work. Both tanks were set up to be geometrically similar to the extent practical, and their configuration is shown in Figure 1. The impeller 7 ACS Paragon Plus Environment


clearance was defined as the distance from the lowest point of the blade tip to the bottom of the tank. The impeller offset was the distance from the center of the impeller to the centerline of the tank. Agitation was achieved with a Lightnin Labmaster mixer drive (0 – 1800 rpm) equipped with an A310 impeller on a 9.5 mm diameter shaft. The impeller was positioned in the tank offset from center and at a 15° angle from vertical, and operated in the down-pumping mode. All other critical dimensions for the tanks are listed in Table 1.

O

H D

C

T

Figure 1. Schematic of the mixing tank configuration

Table 1. Commercial and scale-down model tank dimensions 10L Vessel 50L Vessel Tank Diameter (T) 0.210 m 0.356 m Maximum Solution Height (Hmax) 0.315 m 0.533 m Impeller Clearance (C) 0.051 m 0.102 m Impeller Offset (O) 0.038 m 0.076 m Impeller Diameter (D) 0.064 or 0.086 m 0.097 or 0.132 m


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Drug Product Batches Two drug product batches were manufactured in this study, both in the 50L tank. Drug product compounding was accomplished by dilution of a concentrated drug substance solution, which contains a monoclonal antibody at approximately 150 mg/mL, with a buffer excipient solution that was chemically identical to the drug substance with the exception of the protein. Drug substance from multiple containers was transferred into the mixing vessel to make up approximately 80% of the final batch weight, followed by the excipient solution which made up the remaining ~20% of the total batch. Both components were added through a diverter tube at the top of the tank to prevent air from being sparged through the solution in the mixing vessel. The drug substance solution has a viscosity of approximately 30 cP, and a density of 1.07 g/mL. It is noted that the antibody formulation in the concentration and shear rate ranges in this study behaved as a Newtonian fluid, which was also reported in other studies in the literature for similar formulations.18,19 The viscosity and density of the buffer excipient solution were similar to those of water. The mixing endpoint for drug product batches was defined as the point at which homogeneity was achieved. Homogeneity was determined by measuring the antibody concentration of the solution via spectrophotometry. Samples of the solution were obtained via a NovaSeptum sampling bag attached to the side of the mixing vessel, close to the bottom tangent line.

Surrogate Solution Batches Due to the cost and availability of drug substance solution, most of the experimental batches were conducted with surrogate solutions. The drug substance solution was simulated with an aqueous solution of 11% (by weight) sodium chloride (CAS Number 7647-14-5) and 0.6% (by weight) sodium carboxymethylcellulose (CAS Number 9004-32-4). These concentrations had been selected to achieve a solution density and viscosity of 1.08 g/ml and approximately 50 cP, respectively. Although these values



were slightly higher than those expected for the drug substance, they represent a reasonable worst case approximation. The drug substance surrogate solution was formulated in the mixing vessel immediately prior to each experiment batch. The surrogate solution was formulated to 80% of the total volume for each condition. Agitation was halted and purified water was transferred into the mixing vessel to simulate the remaining 20% of the volume as the buffer surrogate. The water was transferred slowly into the vessel to minimize the disturbance in the interface between the two surrogate solutions. The mixing endpoint was determined by measuring the refractive index of samples periodically taken from the top surface at every 5 to 120 seconds depending on the expected blend time. The refractive index is a material property that determines how the light path is bent (refracted) when light enters the material. Here it was measured in Brix unit, which is proportional to the salt content in the solution. Zero Brix corresponded to the refractive index of water, while 10 Brix corresponded to a solution with roughly 8.6% sodium chloride. The refractive index was measured with a hand-held refractometer (Fisher Scientific, Model Number FS1394621). The mixing time was defined as the time when the variation of the refractive index was within 5% of the final steady value. Visual observation was also used to confirm that stratification was no longer present at the mixing endpoint. A total of 30 runs were performed with surrogate solutions, including 23 batches in the 10L tank and 7 batches in the 50L tank.

COMPUTATIONAL FLUID DYNAMICS MODELING A computational model was constructed to simulate the flow and mass transport in the tank. The transient flow model includes the continuity equation and momentum equations for an incompressible fluid. The fluid was treated as mixture of two miscible species, and its density and viscosity vary as a function of local species concentration through the coupling with the mass transfer model. The effect of impeller rotation was treated using the multiple reference frame approach without actual mesh motion during the 10 ACS Paragon Plus Environment

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simulation. The entire fluid domain was divided into two zones. The impeller zone was a cylindrical region with 1.25 times the impeller diameter and 2.8 times the impeller height. It enclosed the impeller and was aligned with the shaft. Equations for the impeller zone were solved in a rotational reference frame while equations for the rest of the tank were solved in a stationary reference frame, and the two zones were coupled at their interface through a coordinate transformation for the variables. The Reynolds number was defined based on the impeller speed and initial properties of the drug substance as: =

(2)

The calculated Re values indicated that the flow in all cases in this study was in the laminar to transitional flow regime. Therefore the laminar flow model was applied in this work, as previous studies in the literature indicated it was able to give reasonable prediction of the mixing behavior in both regimes.12 The mass transfer model included the contributions from both convection and diffusion. In Equation (3) the second term on the left hand side accounted for the convection contribution, and the right hand side represented the diffusion contribution, with Dm being the molecular diffusivity. +

∇ ∙ = ∇ ∙ ∇Y

(3)

A diffusivity value of 10-10 m2/s was used in the simulation, which is slightly higher than the reported value of 4×10-11 m2/s for an IgG antibody in water.20 For stirred tank under laminar or transitional regimes, the blending time (macro mixing) was mostly influenced by the convection mechanism that distributed the species throughout the tank. At a smaller length scale, molecular diffusion became relevant for mass transport within and across the fluid elements. The simulation started with two stratified layers, and the initial distributions of the two miscible liquids as well as their respective properties were specified. The gravitational force was included in the model to account for the buoyancy effect caused by the density difference in the two liquids. At the top boundary, a rigid flat surface with free-slip condition was assumed due to relative low impeller speed and little deformation on the liquid surface. The liquids were



initially at rest. When the simulation started, the flow equations and the mass transfer equation were solved simultaneously. In all cases, the mass fraction of the species was monitored at five representative locations distributed throughout the tank at five vertical levels. Two were in the top region, including one close to the center near the liquid surface, one close to the tank wall at about 90% of the liquid height. They were in the region initially in the buffer solution, and represented the last points to mix. Two probes were at about 30% and 60% of the liquid height, about 0.8 tank radius from the centerline. They represented the condition in the bulk of the liquid domain. The last probe was about one impeller radius below the impeller, and represented the condition in the impeller discharge zone and near the bottom of the tank. The probes were positioned in regions with representative mixing conditions in the tank. Therefore, together they provided comprehensive information of the mixing progress toward homogeneity. The computation continued until the concentration in the tank reached homogeneity. The mixing time in the simulation was obtained from the time when concentration variations at the five monitored locations were all within 5% of the final uniform concentration, and homogeneity was confirmed from the concentration contour plots. The geometric model for the tank configuration including the impeller in each case was constructed in a commercial software package SpaceClaim®. The geometry was then exported to Ansys Mesher to create the computational mesh used in the simulation. A typical mesh contained about 0.8 million computational cells, with refined mesh sizes near the impeller. Simulation results for different cases obtained using mesh size ranging from 0.75 million to 1.2 million cells appeared to be consistent, and such resolution was also considered to be sufficient in similar CFD studies reported in the literature.15,21,22 The governing equations were solved in a commercial CFD code Ansys Fluent® v15.0 with 4 parallel processes on a desktop computer. The computation in each case took from a few hours to a few days, depending on the duration of the actual mixing times under the condition being simulated.


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RESULTS AND DISCUSSION Observed mixing time The first drug product batch in which the stratified mixing effects were observed was at full volume in the 50L tank (H/T = 1.5). This batch was mixed initially at 130 rpm (initial Re =1160) for 10 minutes and did not meet the criteria for homogeneity. Mixing time was extended to a total of 60 minutes and the batch still tested as heterogeneous. Mixing was extended for additional time at successively higher mixing speeds before homogeneity was achieved. Visual observations during the batch indicated two stratified layers in the tank with minimal disturbance of the interface until the mixing speed had been increased. A subsequent full volume drug product batch was executed at a higher impeller speed (180 rpm, initial Re = 1600). Homogeneity was achieved within 15 minutes for this batch. Visual observations again indicated the presence of stratified layers, although the interface was significantly distorted throughout the run. Variations of the protein concentration in the solution samples from the two batches can be found in Figure 2, and they exhibit the mixing progress under those conditions.



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Figure 2. Mixing time in 50L drug product formulation batches For both batches, the observed mixing times were found to be significantly longer than what was predicted by typical blend time correlations. In general, mixing time in a typical mechanically stirred tank in the transitional regime can be predicted by23 !"#$ =

%&'

/* ( +,

. 0

- /

(4)

In above equation, Np is the impeller power number. For the A310 impeller under the condition investigated, its value was approximately 0.3. Such correlation would predict a mixing time of 4.1 minutes at 130 rpm, and 2.1 minutes at 180 rpm. The observed mixing time was over 15 times higher than the prediction for the 130 rpm batch, and 7 times higher for the 180 rpm batch.


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Additional experiments with surrogate solutions showed similar discrepancy between the observed mixing time and the mixing time predicted by Equation (4). Figure 3 shows a subset of the surrogate solution experiment where the impeller to tank diameter ratio D/T was fixed at 0.41. The dimensionless mixing time Nt decreases with increasing Reynolds number Re, indicating that conditions investigated corresponded to the transitional regime from laminar to turbulent. Note that in unbaffled tanks with centrally mounted impeller, abrupt drop of Nt instead of a constant has also been observed at higher Re numbers in the turbulent regime.2 But that is attributed to the change in circulation flow pattern with the variation in vortexing depth under those conditions. In each of the H/T ratios in Figure 3, the slope of observed Nt against Re in the log-log plot appeared to be much steeper than that suggested by Equation (4). In some cases with low Reynolds numbers, the observed mixing time could be more than an order of magnitude higher than the prediction. The trend applied to all aspect ratio conditions, although higher H/T ratio seemed to deviate more from the prediction. There are several factors that could have contributed to the significant difference between the predicted and measured mixing times. First, it was noted that the correlation was generated from experimental data obtained in baffled tanks with a centered vertical impeller, and thus strictly speaking does not directly apply to the unbaffled tank with an angled impeller, which is the equipment used in this study. However, past experience indicated that the correlation could at least give a reasonable estimation for the current setup, and was not expected to result in an order of magnitude difference. Second, the correlation does not include the effect of liquid height, as most mixing tanks typically operate with a liquid height approximately equal to the tank diameter. In the two drug product batches described above, the liquid height to tank diameter ratio (H/T) is about 1.5. Higher H/T ratio could negatively impact the mixing performance. The Fluid Mechanics Processing (FMP) consortium provided another proprietary correlation that considered the effect of H/T in the transitional regime. This correlation was able to predict a longer mixing time, which was about 40% higher than the result given by Equation. (4), but it was still significantly less than the measured value. Another work by Myers et al suggested that for down-pumping



axial impellers in baffled tanks, the turbulent blend time increased rapidly when H/T became greater than 1.25. At H/T=1.5, the blend time with a down-pumping HE-3 impeller was over 2.5 times of that at H/T=1.24 Our internal data for simple liquid blending using angled impellers also showed important impact of H/T on mixing time in the range 1

Mixing of Stratified Miscible Liquids in an Unbaffled Tank with

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