(690d) Elucidating Design and Operational Impact on Dissolution Kinetics in Mixing Vessels through CFD Modelling

In the manufacture of many pharmaceutical products, the essential unit operations are designed on a lab-scale and then are used to scale-up. The dissolution of solids in a liquid phase is one of these essential unit operations. Conventionally, these unit operations have been subjected to empirical techniques rather than numerical approaches to be optimized during the scale-up process.

This has changed in recent years though. Many studies have been focusing on analyzing the hydrodynamics of the agitated vessels with numerical methods. This includes varying the flow regimes and minimizing the vortex formation to better mix and enhance dissolution processes. To be able to model these phenomena through Computational Fluid Dynamics (CFD) there are several turbulence models and different model approaches to consider the impeller rotation and resolve the hydrodynamics present in the agitated vessels [1].

Many investigations have provided sufficient evidence that modeling solid-liquid mixing through CFD can have great advantages [2], [3], [4], [5], [6], [7]. Numerous configurations and arrangements can be modelled in less time and with a high accuracy. These advantages can lead to better scale-ups while reducing experimental costs [8]. However, dissolution kinetics are not explicitly included in these studies which are an important parameter to see the impact of underlying hydrodynamics.

The objective of this investigation is to combine the CFD hydrodynamics with the dissolution kinetics in an agitated vessel and provide insights about impact of design and operational configuration on the dissolution. To accomplish this, at first a CFD model is developed using Euler-Euler multiphase model together with dissolution kinetics and is followed up by simulating several scenarios to elucidate the impact of design and operational configurations on dissolution.

Methods

A CFD model is developed to investigate the dissolution kinetics of solute (NaCl) in water when mixed in a stirred vessel with a 50L volume. The model is transient, incompressible and multiphase. A two-phase Euler-Euler model was used to model the solute transport in the water. The impeller rotation was described by the Multiple Reference Frame (MRF) model [1]. The model was developed in Ansys Fluent 2019 R1^©.

The dissolution rate was included explicitly in the model. This rate is function of the equilibrium solubility of the solute, the specific surface of the particles, the concentration of the dissolved material, the diffusion constant in the liquid phase, and the relative velocities of the particles and the fluid [8]. The equation 1 describes the dissolution rate [8]:

Whereas, is the dissolution rate of one particle, is the molar mass, is the diffusion coefficient, is the particle surface, is the diameter, is the gradient between the local liquid concentration and is the saturation concentration in the specified liquid [8].

The Sh is Sherwood number and is a function of Reynolds and Schmidt numbers (eq. 2) [8]:

Six different scenarios are modelled to assess the impact of operational and design configurations on the dissolution rate. The base case was designed to have the initial results and behavior of the dissolution kinetics and serve as a base line to compare with the rest of the scenarios. This base case was done in the 50L volume stirred tank and the solute was simply placed at the bottom of the tank. Scenario 1 has the same volume as the base case and the same mass, but the solute was introduced from the top by a single inlet. Scenario 2 is almost identical to scenario 1 but the solute is introduced through two inlets instead of one.

In scenario 3 a solute (Glucose) with lower diffusion coefficient is modelled with the same configuration as of Scenario 1. Scenario 4 is the scale-up scenario going from the initial 50L volume to 1000L volume. The final scenario, scenario 5, has the same configuration as scenario 1 with the only difference of change of the impeller location in the mixing vessel. The summary of the scenarios can be seen in the table 1.

Figure 1 shows the geometry used for scenario 1. A polyhedral mesh of size 800k was created to solve the continuity equations and the kinetics involved in the dissolution process.

Results

Figure 3 shows the volume fraction of solutes at 2 s in different scenarios. Different distributions in these scenarios shows the impact of different flow conditions arising due to different configurations. These different configurations lead to different dissolution times and hence shows the importance of design and operational conditions on the eventual dissolution.

Figure 4 shows mass of the solute in the solid state and Figure 5 shows the conc. of solute in the liquid. It is visible, that the base case has a longer dissolution time compared to scenario 1 and 2. This shows solute introduction method has a significant impact on the dissolution rate. However, the scenario 1 and 2 have almost the same dissolution rate of the solute in the mixing vessel. This demonstrates that in such configurations, one or two inlets have a small impact on the dissolution time. This could be attributed to the fact that inlets are close to central vortex that is formed due to stirring. Scenario 3 has the longest time due to the change in solute (from NaCl to glucose) and this change will affect the dissolution process because of the difference in the diffusion coefficient. It takes at least 120 s more than in scenario 1 for the solute to be completely dissolved.

Scenario 5 shows how the dissolution of the mass of the solute is affected when mixer location is changed. In Scenario 5, it takes a longer time to dissolved with the same amount of energy and for the same size of vessel (approximately 40s more). This reveals that the mixer location is crucial for the hydrodynamics and dissolution kinetics in the mixing vessels.

For scenario 4 the mass of solute is linearly scaled-up to be able to compare it with scenario 1 and it is seen that it has different dissolution performance. In this case scenario 4 takes a longer time for the solute to be dissolved in comparison with scenario 1. This can be explained due to the non-linearity of the scale-up process. This conclusion is also supported by plotting the average concentration of the solute in the solvent as mentioned before. This provides insight of how the variation between scenarios is and how important is to study and model the scale-up of a dissolution process. The study of the scale-up system will bring insights of how to introduce the solute and how it will behave in the stirred reactor to obtain similar results as in lab-scale testing.

Conclusion

This study presented a developed CFD model that can describe the kinetics of a dissolution process. It shows how changes in solute, design or operation have a direct impact on the dissolution kinetics in a mixing vessel. It also shows the benefits of virtual piloting to scale-up because it will give confidence to the decision makers to take the correct steps to do it. With the calculated variables process engineers will be capable of comparing a multitude of stirring equipment and its parameters. This could lead to optimize systems without the high costs of physical piloting.

References

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