Scale-Up of Unit Operations
7.1 Critical Success Factors for Unit Operations and Equipment
In scale-up of equipment and unit operations often one or more critical success factors for scale-up play a role. Table 7.1 lists the most common critical factors and their potential risks. It can be used as a checklist for scale-up. By highlighting the potential risks often preventive measures can be taken in the research or development stage.
Table 7.1
Critical Scale-Up Factors of Equipment and Unit Operations
| Critical Scale-Up Factor | Potential Risks |
| RTD | In scale-up often the RTD is affected by fast large scale eddies which may cause shortcut flow and more back-mixing. In reactors it may cause less conversion and more by-product formation. In separations it may cause poorer selectivity. |
| Mixing | Mixing velocity reduces with scale-up and for some reaction types it may reduce selectivity. |
| Mass transfer | Mass transfer across interfaces can be slower with scale-up, due to areas of low turbulent intensity causing bubble or droplet coalescence. |
| Heat transfer | Heat transfer rates at scale-up can be lower due to lower specific surface area. |
| Impulse transfer | Impulse transfer may increase in scale-up due to higher velocities and or longer scales. This in turn can cause breakage of catalyst particles and erosion. |
7.2 Scale-Up Methods for Unit Operations
The major scale-up methods for unit operation and equipment are nowadays:
Other methods proposed in the past such as defining all dimensionless numbers (Zlokarnik, 2002) and keeping the values of those numbers for pilot plant the same as the commercial scale have never been fully applied in industry for two reasons. The first reason is that one could never be certain that all critical phenomena were captured in the dimensionless numbers, and secondly communicating the scale-up method to relevant stakeholders in the company with no formal chemical engineering education was impossible.
The major methods and their application areas are described in the following sections.
7.2.1 Brute Force Scale-Up and Scale-Down Method
The brute force scale-up and scale-down method is based on the principle that the pilot plant is a scale-down version of the commercial scale design in such a way that all critical factors for scale-up (see Table 7.1), Section 7.1 are kept the same for both scales. Unit operations, such as multi-tubular reactors, multi-channel micro-reactors, distillation and reactive distillation, are suitable for this type of scale-up and scale-down, as the governing scale for hydrodynamic flow behaviour, tube diameter and length, packing size and shape can be kept the same and also the hydrodynamic flow velocities can be kept the same for the pilot plant to the commercial scale. If the feed quality of the pilot plant is also the same as to be applied in the commercial scale and the feed distribution of the commercial scale design is ensured to be uniform over the tubes or packing then scale-up is very reliable.
This type of scale-up and scale-down is often applied in the oil refining industry, where scale-up has to be very reliable and detailed kinetic models of all components is often not available.
7.2.2 Model-Based Scale-Up Method
In model-based scale-up the effects of scale-up on the unit operation performance are predicted by models. The models contain all physical, chemical and hydrodynamic effects for the performance.
The models have of course to be validated. This validation should occur on two aspects.
The interaction between the hydrodynamics (RTD, mass transfer, heat transfer, impulse transfer) and the reaction chemistry of the model, as in the case of a reactor performance, has to be validated in a pilot plant. The pilot plant experiments should be such that not only a single point validation is carried out but that experiments are conducted in which critical effects to scale-up such as fluid velocities are varied. So that the model predicted effects are validated with the experimental results.
The effects of much larger dimensions of the commercial scale than the pilot plant scale on the hydrodynamic performance behaviour can be validated in cold-flow models, sometimes also called mock-up models. The residence time distribution (RTD), mass transfer, mixing rate and heat transfer rate of the model can be validated with experiments.
If gas–liquid mass transfer is important then the bubble size, bubble break-up and or coalescence is also important. In the hot pilot plant with the real gas–liquid mixture the bubble size may be derived from the model validation and an indication whether the system is a rapid coalescing or a slow coalescing system may be obtained. The gas–liquid model system should then also be of the same nature. This can be obtained by using distilled water of salty water as the liquid.
This model-based scale-up method is often employed in the bulk chemical industry, for large scale reactors in which the reactor dimensions affect the hydrodynamic behaviour via the reaction conversion and selectivity. Examples are bubble flow reactors with or without internals where the feed mixing rate and/or the RTD is critical to the reaction conversion and selectivity. CFD models are then validated with large scale cold-flow models operated with model gases and liquid at ambient temperature and pressure.
Details of model-based scale-up are found for various unit operations in Section 7.3.
7.2.3 Empirical Scale-Up
In the empirical scale-up method the unit operation is carried out at a number of scales, often 3 or 4 scales. Often the test units at various scales are given specific names such as bench scale test, mini-plant, pilot plant, business development plant and demonstration plant. At each scale the performance of the unit is measured and often certain parameters, such as stirred speed, residence time, pH, chemical additives and/or temperature, are adjusted to obtain the desired performance.
By plotting the required adjustments (to obtain the desired performance) to the experimental scale a graph may be obtained revealing a systematic trend. Using this graph extrapolations are made to the commercial scale. Often also scale-up trend effects of similar processes, including the effect of the commercial scale, are available in the company. If the observed trends are similar to these previously obtained trends of similar processes then some scale-up confidence is obtained.
The empirical scale-up method is not very reliable, as the underlying phenomena causing the scale effects are unknown and also the real critical scale-up parameters are unknown. But if the brute force method cannot be applied and also the model-based approach cannot be employed, because the interactions between the hydrodynamics and the chemical reactions are very complex, then this is the only remaining method. Otherwise the commercial scale design has to be chanced into a design where the brute force scale-up method can be applied.
The empirical scale-up method is often employed for polymerisations and fermentations in mechanically stirred vessels. In most cases the reactors are batch or fed-batch operated.
For polymerisations, micro-reactors instead of the empirical method with mechanically stirred vessels can speed up the research and development enormously, because several development steps are not needed anymore. In Section 7.3 this is further elaborated.
7.2.4 Empirical-Model Hybrid Scale-Up
There is a hybrid version of the empirical scale-up method in which modelling and simulation is carried out to interpret the empirical results and simulate and optimise the next scale-up step. In the next step the empirical results are then used to validate or adjust the model. Again the improved model is used to design the next step. In this way the chances of success are increased.
By changing the commercial scale design from a mechanical stirred vessel to multi-tubular or micro-channel design the brute force scale-up method can be applied. The innovation time from laboratory scale to commercial scale may then be so much shortened by much so much more revenue is generated that it covers the higher investment cost of the micro-channel reactor.
7.2.5 Direct Scale-Up
Direct scale-up means directly design, construct and start-up a novel commercial scale process without prior research and development work. It follows directly from the start-up time correlation of Chapter 6 that the start-up time will be lengthy if the process is complex. Design capacity and product quality may never be reached, not even with additional investments to solve the appearing problems. The chance that the process will be a total failure is considerable (Merrow, 2011). So for complex processes this is a no-go method.
For novel single equipment processes direct scale-up is sometimes tempted by technology providers by testing the equipment at the expense of the client. If it fails they often only will lose their own design effort, but the process capital expenditure will have to be paid by the client. Users of novel equipment or processes from technology providers always should check the (lack of) scale-up and design knowledge of the technology providers. The chance of success for direct scale-up is too small to pursue it. It is far better to follow one of the proven scale-up methods provided in this chapter.
7.3 Scale-Up of Most Used Unit Operations
This section covers several most used unit operations which are critical to scale-up. The reader is referred to other books to obtain a full coverage of all unit operations (Bisio, 1985 Euzen, 1993 Zlokarnik, 2002).
7.3.1 Adiabatic Fixed Bed Reactors
7.3.1.1 Design of Fixed Bed Laboratory Reactors
Laboratory fixed bed reactors can be designed in such a way that nearly all critical scale-up factors have the same effect on the reactor performance on the laboratory scale and the commercial scale even if the capacity scale-up is by a factor 105 or more. The only critical scale-up factors that cannot be kept at the same effect have to do with the catalyst used on the small scale. This catalyst is in general made in the laboratory as well, while at commercial scale the catalyst is made in a commercial scale catalyst plant. This catalyst performance can then be different at commercial scale and therefore this catalyst performance of the commercial scale has to be tested later separately in a pilot plant.
Laboratory reactor design parameters are the following:
7.3.2 Space Velocity
In the absence of effects of RTD, heat transfer and mass transfer on reactor performance the reactor performance on conversion and selectivity is governed by the space velocity (Levenspiel, 1999) only. The space velocity is defined by
(7.1)
There are other space velocity definitions such as weight hourly space velocity in which the feed flow is expressed in kilogramme per hour and the catalyst amount in kilogramme. Sometimes this type is expressed as liquid hourly space velocity (LHSV) or gas hourly space velocity (GHSV) and often only the resulting dimension (L/h) is given. Often also kinetic rate constants are directly determined from conversions and space velocities. The reader should be aware that the resulting rate constant values then only have a meaning in relation to these space velocity definitions.
By keeping the space velocity in the laboratory reactor the same as the commercial scale design, the laboratory reactor will show the same performance as the commercial scale reactor. These conditions then also allow an experimental reactor optimisation study with the laboratory reactor using the space velocity, temperature and feed concentrations as optimisation variables.
Often however companies use the constant space velocity as the only scaling up rule and don’t pay attention to the potential effects of residence distribution, heat transfer and mass transfer. In the section laboratory reactor sizing these effects will be treated.
7.3.3 Catalyst Sample Representativeness
By taking a very small catalyst sample it may well be that the sample is not representative of the whole catalyst amount, because there will always be inhomogeneity in catalyst particles impregnation. Gierman provides a graph where for the following types of test reactors the maximum allowable deviation between the ratio between more active particle catalytic rate and the less active catalyst rate is given and the required sample size fraction, for the criterion that the standard deviation for repeated experiments is less than 5%. For a bench scale reactor the sample size of 10% is sufficient if the activity ratio is 5 (Gierman, 1988; Table 7.2).
7.3.4 Catalyst Loading
The catalyst must be loaded such that the particles are uniformly placed in the reactor, without empty pockets. If a mixture of catalyst particles and inert particles are used then the mixture must be loaded without segregation of the two types of particles. This can be obtained by alternate feeding of small portions of catalyst and inert particles. Premixing and loading often results in segregation during the loading process and is therefore not recommended.
7.3.5 Initial Feed Distribution
The feed fluid distribution over the fixed bed catalyst must be even. This can be obtained by an inert layer in front of the fixed bed. The length of this inert layer is so long that after that layer a uniform flow is obtained. This is obtained when Ldistr>5× reactor diameter (Gierman, 1988).
7.3.6 Reactor Diameter
The void fraction of particles near the reactor wall is much higher than in the rest of the fixed bed. This can cause shortcutting fluid flow along the wall. This effect is minimised by a high reactor diameter relative to the bed particles. Vortmeyer proved experimentally that this effect is minimal by having Dreactor>25 dp.
This can be obtained by the size of the reactor diameter relative to the catalyst particle diameter. It can also be obtained by changing the effective average particle diameter by mixing in inert small particles with the catalyst particles. The average particle size of a mixture is best determined from the Sauter diameter dpav:
(7.2)
7.3.7 Length of Catalyst Bed
The length of the catalyst bed can have a strong effect on the RTD and the external mass transfer at a fixed space velocity. The effect of the RTD on the reactor conversion becomes negligible when
(7.3)
in which Pe is the Peclet number:
(7.4)
The axial dispersion Dax is obtained from the Bodenstein number (Bo):
(7.5)
This can then be rewritten as
(7.6)
From Gierman (1988) correlations of Bo with the Reynolds number are available.
For single-phase flow and very low velocities; Reynolds number <10, Bo=2.
For gas–liquid trickle flow and Reynolds number for liquid <10, Bo=2×10−2.
With these values the minimal catalyst bed length to avoid RTD effects can now be determined using expression (7.6).
7.3.8 Mass Transfer Limitations
Avoiding mass transfer limitations at the outside of catalyst particles is in general easily obtained, because the diffusion through the mass transfer layer at the outside of the particle is in general faster than the diffusion through the catalyst pores. The reason for this is twofold. The diffusion coefficient in the pores is at least a factor 4 lower than at the outside of the particle and the diffusion layer at the outside (δ) is thinner than the diffusion length inside the particle (which is 0.5 dcat).
Only in cases where diffusion limitations inside the catalyst play a role (Thiele modulus larger than 0.2) outside mass transfer limitations also can play a role.
Gierman discusses correlations of mass transfer in trickle flow but states that none of these are accurate at low Reynolds numbers, so are of little use. Still how to avoid external mass transfer limitations is shown in the following sections.
For trickle beds a particular type of mass transfer limitation can occur when not all catalyst particles are irrigated by the liquid. The irrigation of all particles is obtained when the wetting number (We)
(7.7)
exceeds a minimum value (Gierman, 1988). For hydrocarbon–hydrogen trickle flow systems complete irrigation is obtained when (Gierman, 1988):
(7.8)
For other liquid–gas flow combinations the critical wetting number value is best obtained by performing laboratory reaction experiments at the same space velocity but at increasing superficial velocities and in the absence of RTD effects (criterion (7.6)). As soon as the conversion reaches a constant value the wetting criterion will be fulfilled and then also the criterion of no external mass transfer limitation.
This criterion of complete wetting and no external mass transfer limitation can be fulfilled even in very small reactors by adding first of all inert very fine particles to reduce the average particle size and second by choosing the reactor length such that the superfacial velocity vsup becomes large enough.
7.3.9 Pilot Plan Design Adiabatic Fixed Bed Reactors
The pilot plant will be a downscaled version of the commercial scale design using the brute force scale-up method. To ensure that the axial adiabatic temperature profile of the pilot plant is the same as the commercial scale the pilot plant diameter has to exceed a certain minimum, such that heat loss to the wall is negligible. Alternatively the reactor wall can be divided into several sections and each section has controlled wall heating such that not net heat is flowing to the wall.
7.3.10 Multi-Tubular Heat Exchange Fixed Bed Reactor
In multi-tubular heat exchange fixed bed reactors the reactors are cooled or heated via the reactor wall. The brute force scale-up method can be easily applied by designing the pilot plant with a few tubes. The reason for selecting a few tubes is that also the proof of proper filling of the tubes with catalyst and the proof of proper feed distribution over the tubes is also taken into account. The minimum number of tubes to determine meaningful standard deviations is 3.
7.3.11 Micro-reactors
For micro-reactors the brute force scale-up method is applicable in the same way as for multi-tubular heat exchanger reactors. The even feed distribution over the micro-channels is however here an even more critical aspect (Harmsen, 2013b). Investment cost can be quickly estimated using the method of Harmsen (2013a).
7.3.12 Single-Phase Tubular Reactors
For single-phase reactors and Newtonian fluids the hydrodynamics for RTD, mass transfer and heat transfer are well known. If the reaction kinetics are well known as well then model-based scale-up is the obvious choice. The model can be validated with a pilot plant operating in the same flow regime (laminar or turbulent) as the commercial scale.
If however micro-mixing effects in particular in combination with non-Newtonian behaviour are relevant for the reactor performance then a brute force pilot plant scale-up method is a more reliable method. If feasible and affordable the commercial scale diameter and length may be design such that the downscaled pilot plant can easily be based on the brute force scale-up method.
7.3.13 Reactive Distillation
For reactive distillation in the oil refining the brute force scale-up method is in general applied. Many industrial cases are provided for reactive distillation for hydrogenations of refinery streams (Harmsen, 2007, 2013b).
For applications in the chemical industry the model-based method is applied. The model is validated by well-designed pilot plant tests (Harmsen, 2007, 2013b).
7.3.14 Distillation
For distillation the same brute force scale-up can be applied. However, model-based scale-up is in general chosen in the industry. The physical properties are in general well known. Also tray or packing models for mass transfer and RTDs are available. A rate-based distillation model can then directly be validated with a well-designed pilot plant distillation column. If model predictions deviate from the pilot plant results then foaming or frothing may be the cause of the deviation. The use of anti-foam additives may solve the problem.
Often the rate-based model has also been validated for commercial scale distillation for similar products as the new design case. So that the risk of scale-up using the model is greatly reduced.
Dividing wall column distillation scale-up has a few extra scale-up risks. The risks are vapour flow distribution over the sections is different from model prediction, process control is different from classic distillation control and mechanical integrity of the dividing wall. The first two risks can be mitigated by a dynamic flow model validated by a pilot plant or by a commercial scale divided wall in operation. Mechanical integrity can be obtained from an engineering contractor with experience in construction large scale dividing wall column distillations.
7.3.15 Mechanically Stirred Reactors
Mechanically stirred reactors are mainly applied in the pharmaceutical and fermentation industries. The reason for the choice of this type of reactor is that the stirrer speed can be varied in the operation by which the phenomena, mixing, mass transfer and heat transfer can be changed and in this way the desired reactor performance can be obtained, often in combination with changing other conditions.
The scale-up of this reactor type, when mixing rates or mass transfer rates are important for the reactor performance, is however very difficult as the turbulent field is very inhomogeneous. Near the impeller high shear rates and high turbulence occur, while further away the turbulence is less intense. Upon scale-up these local areas of high and low turbulent intensity change. This often causes unpredictable scale-up effects. What is adding to the complexity is that there are many geometrical aspects of impellers and baffles, namely the shape, the length, the height and thickness. Upon scale-up all these aspects change, while their effect on the local turbulence is not completely known.
For processes like emulsion and suspension polymerisation where the droplet size formation determines the product quality the scale-up is very difficult and the empirical scale-up method is here in general applied.
7.3.16 Bubble Flow Reactors
Bubble flow reactors are often employed for gas–liquid systems where mass transfer between the phases is needed. For cases where the mass transfer is not the limiting step and the degree of back-mixing is not very critical for the reaction conversion and selectivity they are a low-cost option and scale-up is not difficult.
However if mass transfer is the limiting step and the commercial scale size is in the order of 100 m3 or more then reliable scale-up is hard, as the effect of the reactor size on the mass transfer performance is underestimated in all empirical correlations determined on small scales only. The reason for this underestimation is that in the larger scale the vertical liquid recirculation velocity is much higher, causing the bubbles to rise faster through the column, which in turn means a lower bubble hold-up and thereby a lower mass transfer rate. Scale-up is then only reliable by oversizing the bubble column. CFD modelling can help to indicate the increased circulation rate of the large scale and so the required oversizing can be estimated.
If the liquid RTD is important for the reactor performance then often a cross-flow bubble reactor can be employed. The column is then placed horizontally. The liquid flows horizontally through the reactor, while the gas still flows vertically through the reactor. In the reactor baffles are placed to reduce back-mixing. By using CFD the liquid RTD of the commercial scale can be predicted and the baffle geometry and sizing be optimised. In this respect special attention should be paid to shortcutting of tiny parts of the flow, if a deep conversion is required. This shortcutting flow easily occurs and causes less deep conversion. A specific internal geometry to prevent shortcutting flow is provided by Harmsen (2009).