# EuroScale – a Logical Approach to Mixing

Euromixers EuroScale design procedure has been developed to help relate mixing problems to the required level of agitation in a way that is simple and quantifiable.

The applications covered include fluid motion to promote contact of a liquid, solid or gas phase with a continuous liquid phase.
The differences in the ways each of these phases interact with the continuous liquid phase forms the basis for the three main categories of mixing.

## Liquid blending

Liquid-Liquid
contact for all liquid phase mixing

## Solids suspension

Liquid-solids
contact for suspending solids in a liquid phase

## Gas dispersion

Liquid-gas
contact for gas dispersion in a liquid phase

EuroScale procedures involve – Identifying the mixing objective, analysis of relevant process data and optimising the mixing solution utilising a combination of specialist software developed in-house and practical experience. The main categories are summarised below together with the definition, difficulty parameter and the process data required for a complete description of the mixing problem.

## Liquid blending

Mixing two or more miscible liquid components into a more uniform composition. The difficulty of a mixing problem can be qualified by disparities between component liquid viscosities and component liquid specific gravities. Process data required to calculate blend time and provide the mixing solution include:

1. Batch size and tank dimensions.
2. Component liquid viscosities.
3. Component liquid specific gravities.
4. Ratio or relative quantity of liquid components.
5. Euro-scale mixing level.

## Solids suspension

Suspending of solid particles in a liquid to form a slurry. The difficulty of a mixing problem can be qualified by the solids settling rate in the liquid. Process data we require to calculate the settling rate and provide the mixing solution include:

1. Batch size and tank dimensions.
2. Specific gravities of liquid and solid.
3. Liquid viscosity.
4. Weight % of solids in the slurry.
5. Average particle size.
6. Euro-scale suspension level.

## Gas dispersion

Dispersing gas in a liquid to form a gas dispersion.
The difficulty of a mixing problem can be qualified by the gas sparging rate in the liquid. Process data we require to calculate the sparging rate and provide the mixing solution include:

1. Batch size and tank dimensions.
2. Specific gravities of liquid and gas.
3. Liquid viscosity.
4. Volume of gas input in L/s or m3/hr.
5. Gas-Liquid reaction rate, if known.
6. Euro-scale dispersion level.

Batch size – is defined as the working volume of liquid in tank, this may vary over time such as during filling or emptying of a vessel normally a minimum batch height to tank height ratio >0.2 is recommended. It’s also important to know the tank orientation and geometry to further help determine the ideal impeller type, number, size and location for the application. Operating data such as temperatures and pressures also need to be specified to accurately evaluate and render a machine selection that will help maintain the critical process conditions. In many applications, all three phases liquid, solids, and gas will be in contact with another liquid, in such cases Euro-scale can be utilised for each category and the most difficult and hence controlling mixing problem used for equipment selection.

## EuroScale – Explained

When solving any mixing problem, it is essential that to achieve the desired process result. However, it is often difficult to state this with accuracy or relate it to a specific impeller, hence, before considering the various mixer options a suitable process response is needed to serve as a basis for determining the optimal mixing solution.

Liquid blending – The intensity of mixing is related to the superficial fluid velocity in a batch, this is an average velocity value used in calculations of fluid flow due to the complexity of velocity distribution in a batch mixing system.

The superficial velocity can be calculated as follows:

Where

$Latex formula$

Vb (m/min) – Superficial velocity of the fluid batch
Q (m3) – Volumetric flowrate of the fluid batch
A(m3) – Cross sectional area of the fluid batch

Considering theoretical analysis, experimental results and extensive practical experience, we also know that mixing intensity and hence fluid velocity as a variable for scale up produces >90% success on production scale. Therefore, the process response for liquid blending is based on the superficial velocity in the batch. The greater the disparity in liquid component viscosities and specific gravities, the higher the superficial velocity and the higher the mixing scale.

EuroScale is a 1-10 scale, developed to help customers quantify the required level and mixing intensity in a way that is simple and quantifiable.

The volumetric discharge rate of an Impeller operating at a given speed measured at the impeller divided by the total working volume of product in-tank (Q/V) quantifies the level of mixing in terms of tank turnovers. This is a simple yet widely used criterion for mixer sizing within the industry and is defined as the number of times the entire liquid contents of a tank is completely circulated throughout the batch volume per unit of time. From turnover, the blend time can be derived, or the mixing time required before the batch reaches complete homogeneity for miscible liquid systems. Now the essential mixing parameters have been identified the table below demonstrates the relation of superficial velocity to EuroScale level and how mixing performance can be described as the scale increases.

Tank turnovers and blend times have also been calculated at selected mixing scales for an example set of conditions including working volume, SG & viscosity.

Example based on:

• Tank 1500mm diameter with a working volume of 3m3.
• Based on two component liquid system.
• Concentration ratio of low viscosity to high viscosity component is 5:1.
• Mid-range SG’s & viscosities have been used for each Euro-scale level.
EuroScale Superficial velocity (m/min) Process Performance Turnover (min-1) Blend time (min)
1 1.8 Mild Blending
Very slow to mind flow with miscible components.Flat surface motion.Process objective:Blend to complete homogeneity.Limiting range:Differences in SG < 0.1Viscosity ratios < 100
Example for Mixing Scale 2:
Average SG = 1.05Average viscosity = 50cPQ / V = 2.4
5
2 3.7
3 5.5 Medium Intensity Mixing
Medium flow with typical average viscosities.Sufficient for the widest range of applications in the process industries. Rippling surface motion at low viscosities.Process objective:Blend to complete homogeneityLimiting rangeLimiting range:Differences in SG < 0.4Viscosity ratios < 7,500
Example for Mixing Scale 4:
Average SG = 1.2Average viscosity = 740cPQ / V = 4.1
15
4 7.3
5 9.2
6 11.0 High Intensity Mixing
High flow with difficult to mix components.Fast an rippling surface motion at low viscosities.Process objective:Blend to complete homogeneityLimiting rangeLimiting range:Differences in SG<0.6Viscosity ratios<50,000
Example for Mixing Scale 7:
Average SG = 1.3Average viscosity = 4,250cPQ / V = 5.3
25
7 12.8
8 14.6
9 16.5 Violent Agitation
Extremely high flow for very difficult applications.Surging surface motion at low viscosities.Process objective:Blend to complete homogeneityLimiting rangeLimiting range:Differences in SG < 1.0Viscosity ratios < 100,000
Example for Mixing Scale 9:
Batch volume = 3m³Average SG = 1.5Average viscosity = 15,000cPQ/ V = 3.6
65
10 18.3

## Table key with definitions

Process objective:
Achieve the desired process result.

Complete Homogeneity:
The degree of homogeneity we define as ‘complete’ is based on an empirically derived equation that calculates the time taken to blend fluids to within 5% of the final concentration i.e. to >95% homogeneity.

Limiting Range:
Based on multi component liquid system with differences in SG and viscosity ratios that fall within the limits for each scale.

As you can see from the example above, as the intensity of mixing increases; from increasing mixing scale; the turnover will generally increase due to an increase in momentum of the fluid inside the tank. However, the increase in average viscosity reduces the ability of the impeller to effectively pump the fluid and this ultimately results in a lower turnover for the 15,000cP case.

Hence it is worth noting that the number of tank turnovers depends on the quantity of mixer action rather than mixing intensity, where slow speed mixing with a large impeller can produce a higher turnover than high speed mixing with a small impeller. The transition to slow speed mixing becomes increasingly important for blending higher viscosity fluids in the laminar regime that may be sensitive to shear including fluids with complex rheology’s often a combination of each type of mixing is required in a single batch system; macro-scale mixing for bulk fluid motion and micro-scale mixing for high shear homogenisation. It is deduced that the blend time, which is derived from turnover, will increase due to the increase in viscosity. It is worth noting that allowable blend times are typically longer for higher viscosity mixing, so the aim of the mixing scale here is to keep the blend time within a reasonable limit for maximum output whilst avoiding an impractical & over-sized mixer selection. Ultimately, the answer we must lend from a mixer application engineer’s practical experience with a wide range of process applications, or in the case of a novel mixing process, pilot testing may form the basis for equipment selection and scale up.

## Solids Suspension

The process response for solids suspension is relatively easy to quantify and can be defined in terms of suspension levels and solids distribution in a liquid batch. There is a distinct level at which most of the solids are lifted within the fluid; this is known as the cloud height and is expressed as a percentage of the liquid batch height. The liquid below this height is solids-rich, while above it is sparsely populated by a few solid particles. Now that we have identified the essential mixing parameters, in the table below we will demonstrate the relation of cloud height to EuroScale level and how mixing performance can be described as the scale increases. Turnover has been calculated for the example set of conditions as a point of comparison.

EuroScale – Example based on:
Tank 2500mm diameter with a working volume of 8.8m3 with 5% solids with average particle size = 100um.
Liquid SG taken as 1.0, Solid SG taken as 3.0, and Viscosity of liquid as 1cP.
Impeller speed is the only variable where impeller diameter is recommended at D/T = 0.3 for the liquid viscosity.

EuroScale Suspension level Cloud Height (%) Turnover (min-1)

1

On bottom suspension

For use in applications where little suspension is required. Mainly used to keep the solids moving to prevent accumulation at the bottom of the tank.

41.6

2.2

2

3

Off bottom suspension

Sufficient for the widest range of solids suspension applications where all solids are to be completely suspended off the tank bottom.

59.4

3.1

4

5

6

Off bottom 80% homogeneity

For applications where a greater height of suspension relative to the batch height is required.

80.2

4.2

7

8

9

Off bottom 100% homogeneity

For applications where solids need to be suspended uniformly within the whole batch volume.

100

5.3

10

As you can see from the example above, as the intensity of mixing increases; from increasing mixing scale; the speed of agitation increases in order that solids are suspended at greater cloud heights. This in turn increases the turnover due to an increase in momentum of the fluid inside the tank.

It can be deduced from further testing that:

• When the percentage of solids and the particle size increases, a greater speed of agitation is required to achieve the required level of suspension.
• When the batch volume increases, the agitation speed will remain constant to achieve the required level of suspension, however this results in a lower turnover.
• When viscosity of the liquid increases, the agitation speed increases to combat the greater resistance to flow. Hence, the turnover increases as more turnovers are now required for the same level of suspension.

## Gas dispersion

The process response for gas dispersion is relatively easy to quantify and can be based on the superficial gas velocity of the batch, calculated by taking the gas volumetric flow rate and dividing it by the cross-sectional area of the tank.

The process objective is typically mass transfer. The batch cycle time for complete dispersion can be controlled by producing a required bubble size which will affect the mass transfer rate. This will determine the gas-liquid reaction time where a finer dispersion i.e. smaller bubbles is required for slower reactions.

We have three simple categories to describe the process response for gas dispersion:

• Low Gas Dispersion – Impeller is flooded and there is little dispersion as gas flows through the impeller.
• High Gas Dispersion – Gas is fully dispersed to the tank wall.
• Uniform Gas Dispersion – Gas is fully dispersed to the tank wall and circulated under the impeller.

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