**4. Modeling physicochemical processes in stirred tank reactor**

**Test parameters Agitation speed**

process.

able elsewhere [40, 41].

operating conditions.

Mean agglomerate diameter, mm 3.8330 3.9182 Mean agglomerate compressive strength, Nm m−2 0.4298 0.4351 Mean strain rate, s−1 0.3639 0.4088 Mean maximum compressive force, N 4.9476 5.2303

**Table 2.** Agglomerate characteristics test properties as a function of the reactor agitation speed in a wet agglomeration

Considering the wide range of options available to select from, optimizing a given physicochemical condition for a particular process reactor under laboratory conditions is a daunting task. Therefore, in optimizing the design and process parameters for a particular reactor, a statistical correlation of these parameters from a data set is often required, depending on the available time and complexity of the problem, to obtain accurate information on the optimum design and process conditions. A number of statistical methods such as the design of experiment and response surface methodology can be applied to a large set of experimental data to obtain the desired optimization points. This will facilitate an understanding of the influence of different process conditions on the reactor performance which will assist in the selection of optimized

In most of the physicochemical processes involving particulate flow either as a colloidal dispersion or granular suspension, the species attributes—mean size, particle concentration and distribution and fractal properties of the resulting agglomerates—are the primary parameters of interest [21]. In this case, an appropriate physicochemical simulation such as a jar or cylinder test is often followed by a parametric analysis to characterize the process performance as a function of species attributes. Several other parameters may be of interest depending on the type of reactor and the required solid-liquid separation method. Such parameters may include aggregate mean size, shape and distribution, aggregate volume concentration, aggregate strength, sludge volume index, silting index, residual supernatant turbidity, absorbance or optical density, electrical conductivity, viscosity, zeta or streaming potential, specific resistance to filtration, capillary suction time, and so on [38, 39]. In the case of chemical optimization, a parametric dose-response curve will give reasonably accurate information on the required chemical dose for a particular process condition [42–45]. **Table 2** and **Figure 5** show a typical correlation of the agglomerate test properties with the process condition—shear rate. However, regardless of the choice of parametric test, an examination of the supernatant, sediment, filtrate and residue will yield some valuable information on the reactor performance under specific process conditions. Such assessment is carried out either by direct *in situ* measurements such as in particle counting, *ex situ* analysis in which the samples are extracted for measurements or by other indirect parametric indicators. A detailed discussion on the practical applications of different dispersed phase measurement techniques is avail-

64 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

**145 rpm 165 rpm**

The use of computational fluid dynamics (CFD) as a research tool to investigate complex fluidparticle interactions has been growing in popularity both in academia and in the industry [46]. CFD provides a powerful alternative and a more robust platform for engineers in the design of equipment and processes involving fluid flow and heat transfer when compared to the classical experimental approach. Nowadays, numerical simulations complement the experimental and analytical techniques and are increasingly being performed in many fluid engineering applications ranging from chemical and mineral processing to civil and environmental process engineering [46]. However, it is worth pointing out that the continual development of reliable empirical, mathematical and computational models relies on a robust and detailed experimental data.

**Tables 3** and **4** provide a list of recent experimentally validated numerical studies focusing on the physicochemical analysis of fluid-particle reactors. The former is focused on the analysis of the mixing phenomena in stirred tanks while the latter deals with the technical application of mixing for several industrial processes. The modeling approach in most of these studies is applicable to mixing tanks and process reactors of various geometric designs. Joshi et al. [47, 48] provide a comprehensive review of CFD applications in a single phase mixing tank hydrodynamic analysis focusing on axial and radial flow impellers in a multitude of flow scenarios. Their two-part study, which is one of the most detailed and comprehensive reviews in this field, summarizes developments in mixing tank modeling by bringing together the results of scientific investigations spanning several decades. Similar reviews focusing on turbulent multiphase flows and multiphase


reactor modelling, and which provide a more comprehensive discussion on the subject matter

**Table 3.** Selected studies on CFD characterization of single phase and multiphase flows in classical stirred tank reactors.

**Experimental validation method**

Hydrodynamic Characterization of Physicochemical Process in Stirred Tanks and Agglomeration Reactors

consumption, solids concentration measurements

conductometry

Cylindrical tank Pitched-blade turbine PEPT Fluent/MRF k-ω, k-ε, RSM [79]

PIV, critical impeller speed measurements

Solids concentration measurements

Cylindrical tank Rushton turbine 2D PIV, LDA Fluent/sliding mesh DES [73] Cylindrical tank Double Rushton turbine LDA CFX/MRF k-ε [74]

Cylindrical tank Rushton turbine LDV Fluent/MRF k-ε [78]

Cylindrical tank Rotor-stator mixer PIV Fluent/MRF/sliding

Cylindrical tank Rotor-stator mixer LDA Fluent/sliding mesh k-ε [83]

**Numerical code/ modeling approach**

CFX/MRF/sliding

Fluent/MRF k-ε [76]

Fluent/MRF k-ε [77]

Fluent/MRF k-ε [80]

grid

DPIV Fluent/MRF k-ε [81]

mesh

**Turbulence models**

67

k-ε [75]

http://dx.doi.org/ 10.5772/intechopen.77014

k-ε, k-ω [82]

Regardless of the specific focus of each study, most of the studies differ only in terms of stirrer-vessel configurations, experimental validation methods and the choice of modeling approach. In terms of the stirrer-vessel configuration, there is a wide variety of flow inducers available for fluid flow investigation, each with different power demands and flow patterns. In addition to well-established impeller designs employed in most of the studies—Rushton turbine, pitched-blade turbine, propeller, and so on, a few innovative designs have been used with good results [52]. The turbulence models of choice in most of the investigations are the two equation eddy viscosity models such as k-ε and k-ω, and RSM models which are quite efficient in handling rotating flows in stirred tanks and multiphase reactors. The dominant modeling approaches for rotating flow problems are the MRF and sliding mesh. The former is suitable for steady-state problems while the latter is employed for transient calculations. Despite the technical limitations of some of the experimental flow measurement techniques, reasonable agreement was obtained in most of the studies between the experimental data and numerical simulation. In a few of the studies, the model predictions were not quite robust enough when compared to the experimental data set partly due to the complexity of the flow

are available elsewhere [19, 49–51].

**Reactor configuration Fluid agitator/**

Cylindrical tank Pitched-blade turbine,

Cylindrical tank Rigid, rigid-flexible and

Cylindrical tank Flat blade impeller,

impeller

**application**

Cylindrical tank Rushton turbine Mixing time, power

Cylindrical tank Rushton turbine Particle size analysis,

double disc impeller

punched rigid-flexible

angle pitch impeller

scenario being modeled.

Hydrodynamic Characterization of Physicochemical Process in Stirred Tanks and Agglomeration Reactors http://dx.doi.org/ 10.5772/intechopen.77014 67


**Reactor configuration Fluid agitator/**

Cylindrical tank Grid disc impeller, solid

Cylindrical tank Foil impeller, Rushton turbine

Cylindrical tank Pfaudler retreat curve impeller

Cylindrical tank Rushton turbine, pitched

Cylindrical tank Flat blade turbine,

Cylindrical tank Rushton turbine, disc

blade turbine

pitched blade turbine, Rushton turbine

turbine, elliptical blade

disc turbine

Cylindrical tank Rushton turbine,

**application**

66 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

disc, propeller

flotation impeller

Square tank Rushton turbine Power consumption

Cylindrical tank Rushton turbine Solids concentration

**Experimental validation method**

for several industrial processes. The modeling approach in most of these studies is applicable to mixing tanks and process reactors of various geometric designs. Joshi et al. [47, 48] provide a comprehensive review of CFD applications in a single phase mixing tank hydrodynamic analysis focusing on axial and radial flow impellers in a multitude of flow scenarios. Their two-part study, which is one of the most detailed and comprehensive reviews in this field, summarizes developments in mixing tank modeling by bringing together the results of scientific investigations spanning several decades. Similar reviews focusing on turbulent multiphase flows and multiphase

Cylindrical tank Grid disc impeller LDA CFX/MRF k-ε [53]

Cylindrical tank Rushton disc impeller LDA Fluent/snapshot k-ε [55] Cylindrical tank Rushton turbine LDA Fluent/MRF k-ε, DES [56]

Cylindrical Tank Pitched-blade turbine PEPT CFX/MRF k-ε [58] Cylindrical tank Rushton turbine LDV Fluent/MRF k-ε [59, 60] Cylindrical tank Rushton turbine PLIF Fluent/MRF k-ε [61]

Cylindrical tank Pitched-blade turbine 2D PIV Fluent/sliding mesh k-ε [63] Cylindrical tank Rushton turbine CARPT Fluent/MRF k-ε [64]

Square tank Rotating cylinder LDA Fluent/MRF k-ε [67]

Cylindrical tank Rushton turbine LDV Fluent/MRF k-ε, LES [69]

Cylindrical tank Rushton turbine LDV Fluent/MRF RSM [71]

measurements

measurements

2D PIV, laser granulometry, nephelometry

**Numerical code/ modeling approach**

LDA CFX/MRF k-ε [52]

2D PIV Fluent/MRF k-ε [54]

Image analysis PHOENICS/MRF k-ε [57]

RPT, LDA Fluent/MRF k-ε [68]

LDV Fluent/MRF k-ε [70]

SPIV Fluent/sliding mesh k-ε, LES [72]

Fluent/MRF RSM [62]

CFX/MRF k-ε [65]

Fluent/sliding mesh k-ε [66]

**Turbulence models**

**Table 3.** Selected studies on CFD characterization of single phase and multiphase flows in classical stirred tank reactors.

reactor modelling, and which provide a more comprehensive discussion on the subject matter are available elsewhere [19, 49–51].

Regardless of the specific focus of each study, most of the studies differ only in terms of stirrer-vessel configurations, experimental validation methods and the choice of modeling approach. In terms of the stirrer-vessel configuration, there is a wide variety of flow inducers available for fluid flow investigation, each with different power demands and flow patterns. In addition to well-established impeller designs employed in most of the studies—Rushton turbine, pitched-blade turbine, propeller, and so on, a few innovative designs have been used with good results [52]. The turbulence models of choice in most of the investigations are the two equation eddy viscosity models such as k-ε and k-ω, and RSM models which are quite efficient in handling rotating flows in stirred tanks and multiphase reactors. The dominant modeling approaches for rotating flow problems are the MRF and sliding mesh. The former is suitable for steady-state problems while the latter is employed for transient calculations. Despite the technical limitations of some of the experimental flow measurement techniques, reasonable agreement was obtained in most of the studies between the experimental data and numerical simulation. In a few of the studies, the model predictions were not quite robust enough when compared to the experimental data set partly due to the complexity of the flow scenario being modeled.


**5. Conclusions and future perspectives**

indispensable well into the foreseeable future.

Benjamin Oyegbile\* and Guven Akdogan

\*Address all correspondence to: oyegbile@sun.ac.za

**Acknowledgements**

ment number UID: 105553.

**Author details**

**References**

jece.2017.04.016

A review of recent advances in the experimental analysis and numerical modeling of physicochemical processes in stirred tanks and agglomeration reactors have been presented. This review briefly summarizes important findings and major contributions from numerous publications in this field. This short review of the developments in this field clearly shows that significant progress has been made over the past decade in the understanding of complex physicochemical phenomena that are vital for many industrial and environmental processes, especially from experimental and theoretical perspective. However, there is still a gap in knowledge especially in the suitability of the existing mathematical models to accurately predict the reactor performance in a wide range of existing and emerging processes. This clearly calls for a numerical code programming and development to form an integral part of the engineering training and curriculum in future. The successful design, development and optimization of agglomeration units depend on the robustness of the experimental data, mathematical models and simulation tools. This short review is by no means an exhaustive one, and readers are advised to consult other multitudes of scientific publications on the subject matter. In conclusion, numerical modeling along with robust experimental data will continue to be highly

Hydrodynamic Characterization of Physicochemical Process in Stirred Tanks and Agglomeration Reactors

http://dx.doi.org/ 10.5772/intechopen.77014

69

The authors would like to acknowledge the financial support from the National Research Foundation (NRF) and The World Academy of Sciences (TWAS) under the funding instru-

Department of Process Engineering, Stellenbosch University, Stellenbosch, South Africa

[1] Oyegbile B, Hoff M, Adonadaga M, Oyegbile B. Experimental analysis of the hydrodynamics, flow pattern and wet agglomeration in rotor-stator vortex separators. Journal of Environmental Chemical Engineering. 2017;**5**:2115-2127. DOI: 10.1016/j.

**Table 4.** Selected studies on CFD characterization of hydrodynamics and physicochemical processes in field-assisted process reactors.
