SolidâLiquid Suspension in Pilot Plants: Using Engineering Tools to

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Organic Process Research & Development

Solid-Liquid Suspension in Pilot Plants: Using Engineering Tools to Understand At-Scale Capabilities Anne E. Mohan*, Joseph Kukura, Glenn Spencer, James Ulis Merck & Co., Inc. 126 East Lincoln Ave. Rahway, NJ 07065

*[email protected]

ACS Paragon Plus Environment

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For Table of Contents Use Only


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ABSTRACT: To address time lost due to inadequate assessment and understanding of solids suspension issues, empirical studies were conducted at pilot scale using a calcium carbonate and de-ionized water (DIW) system. Three tools were used and evaluated to understand suspension status: (1) turbidity meter response, (2) off-line sample analysis, and (3) difference between baffle and bottom temperatures. The data from these studies demonstrated that the most effective tool that also required the least effort was the difference between baffle and bottom temperatures. A standardized experimental procedure was developed and can be used to gain empirical suspension data at scale for any desired solid-liquid system. This procedure involved performing temperature adjustments in the vessel and observing the associated baffle/bottom temperature changes for varying agitator speeds.

KEYWORDS: Solid-liquid mixing; Solid suspension, Pilot plant mixing


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INTRODUCTION:

The efficiency with which insoluble solids can be suspended in liquid is pertinent to the pharmaceutical industry during several critical unit operations including but not limited to reactions, carbon treatments, crystallizations, and filtrations. Effective solid-liquid suspension is crucial to ensure that heat and mass transfer within an operation meet process requirements. Many of the factors which affect solids suspension, such as solid and liquid densities, vessel and agitator geometries, and solids loading, are unique and therefore challenging to characterize through fundamental or theoretical analysis. Additionally, empirical data can be challenging to generate as there are numerous permutations of these factors that can be difficult to mimic at small scale. For these reasons, there is often a lack of empirical data for solids suspension capabilities, causing it to be a pain point for pilot plant operations, as the resulting vessel characterizations and defined capabilities influence process fits. In order to address all these complexities, the methodologies commonly used to ascertain solids suspension were evaluated, streamlined, and standardized. To support this newly standardized methodology, a large amount of empirical data was gained from multiple vessels, leading to: (1) reduced level of effort for suspension analysis, (2) increased availability of resources to support batch execution, (3) increased ability to generate process knowledge during pilot plant batch processing, and (4) improved plant schedule adherence.


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PROCEDURE AND EQUIPMENT

Several suspension studies were performed at pilot scale for this project using a calcium carbonate and deionized water solid-liquid system (see Table 1 below for physical properties of system). These materials were chosen based on their availability, minimal cost, desirable physical properties, and ease of disposal. The methods and tools used to evaluate and ascertain suspension at various agitator speeds included in-line turbidity meter results, off-line sample analysis, and baffle/bottom temperature tracking. The experimental procedure outlined below was first executed with water in order to ensure that the temperature indicators were responding appropriately, and that the study results were interpreted accurately. Then, this same procedure was used for the solid-liquid system. The complete catalog of testing that was performed is listed in Table 1. In order to provide a comprehensive equipment evaluation, the system was tested in both hastelloy and glass-lined vessels. The vessels used were chosen due to their availability in the pilot plant. As can be expected, equipment is at a premium in the plant and scheduling and processing constraints factored into their use for this project.

Table 1. Physical properties of solid-liquid system used for suspension studies. Note that all properties are given for room temperature, 25oC. Substance Density, Viscosity, Mean Particle g/mL cP Size, µm Deionized Water (liquid) 1.00 0.89 N/A Calcium Carbonate (solid) 2.71 N/A 80

General Procedure Used for Solids Suspension Studies: 1) Charge solid and liquid to vessel at 20oC, and adjust agitation speed to desired value 2) Begin recycle through pedestal pump recycle loop and turbidity meter


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3) Adjust jacket setpoint to 60oC 4) Track baffle and bottom temperatures until a ~10oC increase is observed 5) Adjust jacket setpoint to 10oC 6) Track baffle and bottom temperatures until a ~10oC decrease is observed 7) Return system to zero-state (~20oC) 8) Sample vessel via pedestal pump if necessary (see description below) 9) Adjust agitation speed to next desired test value 10) Repeat steps 2 through 7 as necessary

During each agitation speed, a sample was pulled from the pedestal pump and filtered in the lab. The solids were then vacuum dried and the solids ratio in the sample was determined. The sample solids ratio (kg solids per kg liquid) was then compared to the known solids ratio in the vessel. Low agitator tip speeds will cause the solids to partially settle in the dish of the vessel, and cause non-uniform suspension of the solids throughout the batch. As such, the pedestal pump sampling line, which is a subsurface dip tube, can provide some insight to the level of suspension.

A turbidity meter was used for these suspension studies and was placed in-line of the pedestal pump recycle loop as shown in Figure 1. The turbidity response was recorded and any trends were analyzed and correlated to solids suspension. The classical definition of turbidity refers to the attenuation of light as it passes through a transparent medium containing dispersed particles. Turbidity is caused by absorption and scattering mechanisms that reduce the amount of light traveling in a straight line.1 Turbidity meters are typically used to monitor


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crystallizations and determine the “cloud point,” or the point at which crystals begin to form – i.e. when the batch turns from clear to opaque. The meter response is reported as a percentage and represents the amount of backscattered light detected when a light source is transmitted through a given stream. Using these principles, a turbidity meter can be used to ascertain solids suspension.

Figure 1. Typical set up of the turbidity probe with mechanical and electrical highlights.

The amount of solids in the pedestal pump sample stream will vary depending on the vessel geometry and the suspension of the solids in the system. Because the turbidity meter is tied into this pedestal pump sample line, the meter’s response is integrally related to the geometry of the vessel and the location of the sample dip tube in that vessel. There will always be a vertical solids concentration gradient in the system even during “full suspension”, and as such the location of the sample dip tube in relation to this gradient will affect the turbidity meter response.


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Figure 2. Diagram of VESSEL 1 (300 gal, HC) used for suspension studies, with visual markers of liquid levels and associated solids ratios tested. (Note: drawing is not to scale)

Table 2. List of various parameters and ranges tested for VESSEL 1 suspension studies. Solids Ratio (kg solid per kg liquid) 0.08 0.12

H/T (liquid height to tank diameter) 0.27 0.54

0.31

0.27

Agitation Range Tested, rpm

Tip Speed Range Tested, m/s

30 to 90 20 to 70

0.76 to 2.27 0.51 to 1.77

P/V range tested (power [watts], per unit volume [liters]) 0.020 to 0.552 0.006 to 0.269

16 to 90

0.40 to 2.27

0.001 to 0.223


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Figure 3. Diagram of VESSEL 2 (500 gal, GLCS) used for suspension studies, with visual markers of liquid levels and associated solids ratios tested. (Note: drawing is not to scale) Table 3. List of various parameters and ranges tested for VESSEL 2 suspension studies. Solids Ratio (kg solid per kg liquid) 0.11 0.13

H/T (liquid height to tank diameter) 0.61 0.68

0.27

0.29

Agitation Range Tested, rpm

Tip Speed Range Tested, m/s

25 to 70 25 to 70

0.75 to 2.09 0.75 to 2.09

P/V range tested (power [watts], per unit volume [liters]) 0.001 to 0.029 0.001 to 0.026

24 to 70

0.72 to 2.09

0.003 to 0.077

Table 4. Physical dimensions of VESSELS 1 and 2.

22

To reach Baffle TI

6

4bladed pitched blade turbine

To reach sample line

19

Clearance in

D, in

Type

Clearance in

Type

D, in 23

3.63

Volume Required, gal

Clearance in

48

Curved blade turbine

19


Upper Impeller D, in

Vessel 2, 500gal GLCS

48


Middle Impeller

Type

Vessel 1, 300gal HC

Tank D, in

Lower Impeller Tank ID

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


8.88


19

29.88

69

63

41.06

None

N/A

N/A

74

105


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A Dynochem suspension model was used to provide a theoretical evaluation of suspension, and this evaluation was compared to the empirical data gained in the plant. The inputs required for the Dynochem model were the vessel geometries (tank, agitator, and baffling), the solid-liquid system properties (solids ratio, liquid volume, and solid/liquid physical properties) and the operating agitator speed. The model used was based on the Dynochem commercially available suspension model.2 One of the most practical and commonly used equations for solids suspension is the “just suspended” agitator speed, Njs, defined by Eqn. 1 below. The just suspended calculation is used frequently by operations engineers during the development of the process fit. This calculation takes into account the physical properties of the solid-liquid system in addition to the physical dimensions of the agitator and vessel. This equation is referred to as the Zwietering correlation. Zwietering defined the just suspended agitator speed as the minimum stirring speed at which no solid particle remains stationary on the vessel bottom for more than one to two seconds.3 It is advantageous because it is based on a very large number of experiments and is dimensionless. It has also been re-confirmed by a number of researchers during the 20th century. However it should be noted that this is an empirical correlation, and as such has some limitations to its tested parameters.4

where:

S= ν= dp = g= ∆ρ = ρL = X= D=

ࢍ∆࣋ ૙.૝૞ ૙.૚૜ ࡿࣇ૙.૚ ࢊ૙.૛ ࢄ ࢖ ቀ ࣋ ቁ Eqn. 1 ࡸ ࡺ࢐࢙ = ૙.ૡ૞ ࡰ geometrical constant dependent on impeller type, diameter and clearance (-) liquid kinematic viscosity (m2/s) diameter of spherical particles (m) gravitational acceleration (m/s2) density difference between solid and liquid (-) liquid density (kg/m3) mass ratio of solid to liquid = weight of solids/weight of liquid x 100 (-) impeller diameter (m)


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RESULTS AND DISCUSSION Method 1: Turbidity Meter Response In the 300 gallon hastelloy vessel, VESSEL 1, the average turbidity meter response varied as the agitation speed was changed (Figure 4). At agitation speeds below the predicted just suspended value, the turbidity was low. During states of non-suspension solids settled on the dish of the vessel, causing the stream in the pedestal pump dip tube to have fewer solids in it. Fewer solids in the analyzed stream translated to a decrease in the amount of deflected light measured by the turbidity meter, leading to a lower turbidity response.

As the agitation speed was increased, the turbidity response also increased and ultimately plateaued between the predicted just suspended and fully suspended values. However, beyond the fully suspended speed the turbidity response decreased. This decreased response can be attributed to vortexing because the overall batch volume was the minimum required to reach the sample dip tube.

When compared to the modeling results of the Dynochem tool, it was observed that the actual solids suspension performance in VESSEL 1 exceeded the predicted performance for the 0.12 and 0.31 batch solids ratios (green and red trends, respectively, on Figure 4). Even at the “not suspended” agitator speeds, the turbidity response was the same as that of the “just” and “fully” suspended speeds. The 0.08 batch solids ratio (blue trend on Figure 4) turbidity responses corresponded with the modeling results in that the “not suspended” agitator speed correlated with the decrease in turbidity meter response.


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Figure 4. Plot showing the results of the turbidity meter response for VESSEL 1 versus agitator tip speed. Predicted results from the Dynochem suspension model are also shown on this plot. This data shows that the turbidity meter has the potential to help ascertain suspension. In the 500 gallon glass-lined vessel, VESSEL 2, the average turbidity meter response showed no changes with agitation speed (Figure 5). Because of this flat-line response, it was impossible to use the turbidity meter to assess the suspension of the solids in the vessel as the agitator tip speed was altered, and demonstrates the limitations of the technology. The accuracy of the turbidity meter response in assessing solids suspension is critically related to how representative the sample stream is of the actual batch. The amount of solids in the sample stream is dependent on the geometry of the vessel and the vertical solids gradient in the batch. Therefore if the location of the sample dip tube is in an area of high or low relative solids concentration, the turbidity meter response will reflect that, potentially leading to false positives or negatives during suspension assessment (Figure 6).


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While the turbidity meter response did not vary with respect to agitator speed, it did vary with respect to the actual solids ratio in the batch. If it is assumed that the turbidity response during full suspension in VESSEL 1 is accurate, then for a similar batch volume and solids ratio, the turbidity response in VESSEL 2 was lower than expected (Figure 7). Several factors could be responsible for this observed response. For example, the sample dip tube could be located in an area of low solids concentration within the vertical gradient, or nitrogen could be entrained in the sample stream due to vortexing, or there could be differences in probe set-up between the two vessels. Without any supplementary data, the turbidity meter response for VESSEL 2 is not value-added and does not increase the understanding of solids suspension in this vessel. However, it should be noted that since a vertical solids concentration gradient will always exist, “uniformity” must be defined on the basis of the process.5

The predicted values from the Dynochem modeling tool for VESSEL 2 could not be correlated with the turbidity responses due to the lack of change with agitator speed.


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Figure 5. Plot showing the results of the turbidity meter response for VESSEL 2 versus agitator tip speed. Predicted results from the Dynochem suspension model are also shown on this plot. This data shows that the turbidity meter is not a universally applicable tool to ascertain suspension. For this vessel and solids ratios tested, the turbidity response was the same regardless of tip speed.

Figure 6. Examples of how the vertical solids gradient within the batch and the location of the sample


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dip tube in the vessel could affect the turbidity meter response and associated interpretation of the results.

Figure 7. Comparison of the turbidity responses from VESSEL 2 and VESSEL 1. This plot demonstrates how for similar batch systems during full suspension, the turbidity response in VESSEL 2 was lower than that in VESSEL 1. Method 2: Off-Line Sample Analysis The results of the sample analysis for VESSEL 1 and VESSEL 2 are shown in Figures 8 and 9 at varying agitator tip speeds. Also displayed on the plot are the tip speeds associated with the “not suspended,” “probably suspended,” “just suspended,” and “fully suspended,” values from the Dynochem tool for solids suspension. Similar to the turbidity meter, the pedestal sample analysis method was useful for the evaluation of solids suspension in VESSEL 1. However, the sample analysis flat-lined for VESSEL 2, and was not able to provide any insight to the solids suspension in the glass-lined, larger vessel. This is due to the fact that the extent to which the pedestal sample is representative of the batch is dependent on the dip tube’s location in that batch (refer to Figure 6).


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In VESSEL 1, the sample solids ratio increased with the agitator speed until it plateaued at approximately the actual solids ratio of the batch. The ratio remained at this value even at the highest agitator speeds tested. This is different from the trend of the turbidity meter response, where a significant decrease was seen at the higher agitator speeds due to vortexing. It may initially be expected that the sample solids ratio and the turbidity meter response would demonstrate similar trends because both of these data sets are physically from the same recycle dip tube. However, when nitrogen becomes entrained in the sample stream during vortexing, the amount of deflected light (and thereby the turbidity meter response) is reduced. This nitrogen entrainment does not affect the pedestal sample because the physical batch stream that is pulled into the dip tube is representative of the batch in the vessel.

Figure 8. Plot showing the results of the pedestal pump sample analysis for VESSEL 1 versus agitator tip speed. This data shows that the pedestal sampler has potential to ascertain suspension.


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The off-line sample analysis for the 0.12 and 0.31 batch solids ratios (green and red trends, respectively, in Figure 8) showed that the actual solids suspension performance in VESSEL 1 exceeded the predicted performance of the Dynochem model. Even at the model “not suspended” agitator speeds, the sample analysis was equivalent to the solids ratio of the actual batch. The predicted values for the 0.08 batch solids ratio, however, correlated well with the off-line sample analysis. The model “not” and “probably” suspended agitator speeds agree with the decrease in solids ratio in the pedestal sample. These results are similar to the turbidity responses observed for VESSEL 1.

The sample solids ratio results showed no change with agitation speed (Figure 9) in the 500 gallon glass-lined vessel, VESSEL 2. Similar to the turbidity response for VESSEL 2, it was impossible to use the sample solids ratio to assess the suspension of the solids in that vessel. The flat-line solids ratios of the samples analyzed were all within 0.02 of the actual solids ratio of the batch at the time of the sample. This is different from the flat-line turbidity meter response for VESSEL 2, which was lower than the actual batch value based on the turbidity responses yielded during full suspension in VESSEL 1. When the off-line sample analysis is analyzed in addition to the turbidity meter response, the effect of nitrogen entrainment in the sample stream due to vortexing becomes more clear. While nitrogen entrainment does affect the turbidity meter response, it does not affect the physical sample solids ratio. Therefore, during vortexing in VESSEL 2, the turbidity meter response was lower than the actual expected value for the batch, but the off-line solids ratio analysis was equivalent to the actual solids ratio of the batch.


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The predicted values from the Dynochem modeling tool for VESSEL 2 could not be correlated with the off-line sample analysis results due to the lack of change with agitator speed.

Figure 9. Plot showing the results of the pedestal pump sample analysis for VESSEL 2 versus agitator tip speed. This data shows the failures of sample analysis to ascertain suspension. Method 3: Difference Between Baffle and Bottom Temperatures The third tool that was evaluated to ascertain suspension was the difference between the baffle and bottom temperatures (see Table 1). During states of inadequate suspension, solids will settle on the dish of the vessel and coat or cover the bottom temperature probe. When this occurs, the bottom temperature response will lag behind the baffle temperature. This effect is most clearly demonstrated when performing batch temperature adjustments (refer to Figure 10 and 11).


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0.31 Solids Ratio, Pedestal Pump Batch Volume in VESSEL 1 Jacket SP

Baffle T

Bottom T

Figure 10. Example of an expected baffle/bottom temperature trend and turbidity response during inadequate suspension.

Agitator SP

Turbidity

Figure 11. Example of an expected baffle/bottom temperature trend and turbidity response during full suspension.

While there are sensitive chemical processes that require tighter temperature control, the default temperature range given to processes in the pilot plant is 5oC. This range is designated for either the baffle or bottom temperature, with the assumption that the batch is uniform and there is not a significant difference between the two temperature readings. Taking this into account, “acceptable suspension” was defined as systems where the difference between the baffle and bottom temperatures was ≤ 2oC.

The difference between baffle and bottom temperature provided greater granularity into the suspension status of the batch at a given agitator speed than either the turbidity meter or the off-line sample analysis. In VESSEL 1, as the agitator speed was increased, the delta between the two temperature indicators decreased, however the rate of this decrease was dependent on the batch solids ratio and fill level in the vessel as seen in Figure 12. For the 0.08 solids ratio (blue trend) “acceptable suspension” as defined above was not achieved until the just suspended speed was reached, and this result agreed with the associated turbidity and sample analysis for this stream. The 0.12 and 0.31 solids ratios (green and red trends, respectively) showed that


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acceptable suspension was achieved even at the not suspended model agitator speeds. This supported the conclusion from the turbidity and sample analysis of the same streams that the actual suspension performance exceeded the predicted performance of the model. As can be expected, the absolute maximum ∆T was observed for the highest solids ratio stream (0.31 solids ratio), since the most solids settled on the dish of the vessel during periods of nonsuspension for this system.

Figure 12. Plot showing the average absolute difference between baffle and bottom temperatures at varying agitator tip speeds, and compared to modeled values from the Dynochem tool for VESSEL 1. The results from this data agreed well with the associated turbidity and sample analysis conclusions. In VESSEL 2, the ∆T for both the 0.11 and 0.13 solids ratio streams had a flat-line response (blue and green trends in Figure 13, respectively) of < 2oC. As such, it was concluded that full suspension was achieved at all agitator speeds tested for these two streams. This conclusion agreed with the turbidity and sample analysis for these batches.


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However, for the 0.27 solids ratio in VESSEL 2 (red trend in Figure 13), the ∆T varied and was significantly greater than 2oC at agitator speeds lower than the just suspended value. The turbidity meter response and sample analysis had flat-lined for all streams in VESSEL 2, therefore the data from the ∆T between the baffle and bottom temperatures provided insight to the solids suspension status where the turbidity meter and off-line sample analysis could not. In addition to meeting the shortfalls of the other two methods used, the use of the baffle and bottom temperature probes was much more efficient since no extra mechanical set-up was required, and the results could be retrieved and interpreted real-time. These aspects eliminated much of the down time that had been spent on the suspension study for the other two methods.

Figure 13. Plot showing the average absolute difference between baffle and bottom temperatures at varying agitator tip speeds, and compared to modeled values from the Dynochem tool for VESSEL 2. This plot shows how the ∆T can be used to asses solids suspension where turbidity and off-line sample analysis could not.


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RECOMMENDATIONS

In order to minimize unnecessary time spent on solids suspension, the data and information gathered from the studies performed were used to create a standardized workflow for assessing and addressing solids suspension issues in the pilot plant. While the decision flow charts shown in this section are targeted for pilot plant engineers using these vessels, they can be used by anyone looking for guidance on how to handle solid-liquid suspension at scale.

After an initial process fit has been developed and solids suspension raised as a concern, a modeling tool should be used to determine the required agitator speeds for the given batch size and vessel fill. If the required speeds fall outside vessel capabilities and the vessel itself cannot be altered due to other process or building constraints, there are several levers which can be pursued to improve suspension. Some of these levers include mechanically expanding the agitator speed range to reach the required speeds or recycling the batch around the vessel (“external recirculation loop”).

Common questions that should be asked to determine suspension sensitivity and if empirical data is required to ensure batch success are shown in the flow chart in Figure 14. This flow chart is not meant to be prescriptive and the questions listed are not the only questions that should be asked. These questions should be adjusted and expanded based on the individual process needs. An important question which should always be asked when ascertaining suspension is, “what is/are the consequence(s) of failure?” This question prompts the development of a mitigation plan in the event of suspension failure, streamlining the decisionmaking process during processing, and improving the overall timecycle of the batch. The answer


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to this question could also potentially initiate a process fit change depending on the severity of the failure to either the building or the process.

Figure 14. Decision flow chart for the initial assessment of solids suspension needed for batch processing. This should be used while assembling the process fit. If a solids suspension study is deemed necessary for batch success, the experimental description described by Figure 15 should be used to evaluate the suspension performance. A solvent baseline should always be conducted prior to any solids suspension experiment for


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multiple reasons. Firstly, in order to ensure that the temperature indicators are functioning properly. Secondly, because the suspension methodology utilizes heat transfer principles, it is critical to understand the effects of the heat transfer properties of the neat process solvent on the temperature responses.

In addition to the experimental methodology in Figure 15, the following recommendations are put forward for achieving optimal suspension: (1) Because the difference between the baffle and bottom temperatures is the most effective and lowest effort tool to evaluate suspension, it is recommended that this tool is the only one used. The turbidity meter and/or off-line sample analysis should only be used if deemed critical by the project team for further knowledge capture. a. In the event that the batch level will not reach the baffle temperature probe, heat transfer modeling should be used to predict the time required for a given temperature adjustment. The required time for the bottom temperature change from the empirical data can then be compared with the modeled predicted time. If the actual time required was much longer than the predicted time, it can be assumed that solids have settled on the bottom of the dish, impeding the heat transfer and the bottom temperature probe readout. (2) Depending on solids properties, it is beneficial to increase agitation quickly, rather than gradually, so as to incorporate solids into a mixture as rapidly as possible and prevent build up along the vessel walls. (3) Solids charged via multiple small charges are more adequately brought into solution due to the gradual addition that this type of charge entails. Single large solids charges may be


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required in some cases, but if these charges are substantial it is pivotal to address other aspects of the process further downstream such as agitation and incorporation.

Figure 15. Recommended methodology for conducting a solids suspension study at scale.

CONCLUSIONS The results observed from the calcium carbonate – DIW system suspension studies provide several valuable conclusions. Although the turbidity meter and sample analysis can potentially provide insight to solids suspension in a vessel, their dependency on the vertical concentration gradient and physical geometry of that vessel limit them from being universally advantageous across vessel types and solid-liquid systems. The difference between baffle and bottom temperatures can provide useful data regardless of the vertical solids gradient. Additionally, the use of the baffle/bottom temperature probes is much more efficient than the turbidity meter or sample analysis because no extra mechanical setup is required and the data can be obtained real-time.


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The proposed standardized workflow for assessing suspension and, where applicable, executing empirical studies, can reduce the overall timecycle by a minimum of 33% and a maximum of 80% (via theoretical implementation of workflow using Six Sigma DMAIC methodologies).6 This would lead to a significant reduction in time lost to suspension issues, as well as an improvement in building metrics and customer satisfaction.

ACKNOWLEDGMENT This project was made possible by the support and execution of the Merck Rahway MSO pilot plant staff: Khalif Rashid, Adam Lukaszewski, Bruce Hrynyk, Mark Morgan, Barbara Figurski, and John Nolan.

REFERENCES 1

Harner R. S., Ressler R. J., Briggs R. L., Hitt J. E., Larsen P. A., Frank T. C., Org. Process

Res. Dev., 2009, 13, 114-124. 2

DynoChem Resources, www.scale-up.com, “Solid-Liquid_DB.xls”

3

Zwietering T. N., Chem. Eng. Sci., 1958. 8, 244–253.

4

Mak A.T-C., Solid-Liquid Mixing in Mechanically Agitated Vessels. Ph.D. Dissertation,

University College London, 1992. 5

Fluid Mixing in Pharmaceutical Processes, Armenante P.M., NJIT 2012

6

Six Sigma Methodologies, www.6sigma.us


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SolidâLiquid Suspension in Pilot Plants: Using Engineering Tools to

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