Medical, Pharma, Engineering, Science, Technology and Business

**Dmitry Vladimirovich Gradov ^{1*}, Gerardo Del Muro González^{2}, Marko Vauhkonen^{2}, Arto Laari^{1} and Tuomas Koiranen^{1}**

^{1}School of Engineering Science, Lappeenranta University of Technology, Lappeenranta, Finland

^{2}Department of Applied Physics, University of Eastern Finland, Kuopio, Finland

- *Corresponding Author:
- Dmitry Vladimirovich Gradov

School of Engineering Science, Lappeenranta University of Technology

Lappeenranta

Finland

**Tel:**+358465470573

**E-mail:**[email protected]

**Received date: ** July 09, 2017; **Accepted date: ** July 13, 2017; **Published date: **July 22, 2017

**Citation: ** Gradov DV, González GDM, Vauhkonen M, Laari A, Koiranen T (2017) Experimental and Numerical Study of Multiphase Mixing Hydrodynamics in Batch Stirred Tank Applied to Ammoniacal Thiosulphate Leaching of Gold. J Chem Eng Process Technol 8: 348. doi: 10.4172/2157-7048.1000348

**Copyright:** © 2017 Gradov DV, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Hydrodynamics of aerated slurry is studied experimentally and numerically using the example of thiosulphate leaching of gold concentrate. The studied milled concentrate has shear-thinning fluid rheology and it was imitated by water-based solutions of CMC. Presence of electrolytes, as in the case of the leaching slurry, has great influence on bubble size distribution. Primary phase flow is measured by Particle Image Velocimetry. Local gas hold-up in aerated CMC 50000 (0.15 w%) solution is measured by Electrical Impedance Tomography. Volumetric mass transfer is measured by dynamic method in different CMC solutions over a range of operational conditions in absence and presence of electrolytes. The experimental data was used in CFD modelling of the aerated slurry. Single phase hydrodynamics of shear-thinning fluid (CMC 50000 (0.15 w%)) have been modelled and validated against experimental data with reasonable agreement. Multiphase mixing of the thiosulphate slurry was modelled with the assumption of constant bubble size. The results of the simulations and measurements are presented and discussed.

Multiphase flow; Slurry mixing; PIV; EIT; CFD

Thiosulphate leaching is a promising alternative to cyanidation, which is frequently used for selective dissolution of gold from ores and concentrates. Slow kinetics of thiosulphate leaching is often boosted by addition of copper (II). The copper oxidizes metallic gold transforming it to ionic form, which reacts with thiosulphate ligands producing stable gold-thiosulphate complexes. Ammoniacal media is required to prevent passivation by sulfur that might appear from the decomposition of thiosulphate when it reacts with ore [1]. It is suggested that ammonia transports gold ions to bulk solution by being more strongly adsorbed on gold surface [2]. Oxygen is needed to recover copper (II) from copper (I) at a little expense of slow thiosulphate oxidation by molecular oxygen [3]. Overall mechanism of gold leaching with thiosulphate can be briefly summarized by the following reaction [4]:

(1)

Selective dissolution of gold with the above-described reaction usually takes place in aerated stirred tanks. Continuous stirred-tank reactors (CSTR) of various types are frequently used in mining, chemical and biochemical industries to promote reaction by providing intensive mixing and high rate of mass transfer. In many cases, mixing affects conversion and yield of product. Poor mixing might result in stagnant zones. It is important to predict locations of stagnant zones. Providing good mixing benefits rate of mass transfer via effective renewal of fluids contact.

As computational power is constantly growing, numerical simulation of mixing tanks may efficiently reveal stagnant zones and help saving resources and time. In the last two decades, Computational Fluid Dynamics (CFD) has been successfully applied for modelling of multiphase hydrodynamics in stirred reactors of different types and shapes. Promising results in resolving flow fields as well as phase interaction parameters are well-described and analyzed in the review article of Joshi et al. [5]. Even though fluid dynamics modelling has been applied successfully to solve engineering tasks, CFD models of multiphase flows involve numerous empirical coefficients caused by spatial discretization and lack of knowledge about phenomena. This leads to uncertainties limiting application area. Tuning of empirical coefficients is a “compulsory measure” that requires validation procedure against experimental data.

There are many methods that have been designed to study fluid flow experimentally. Intrusive techniques such as Hot Wire Anemometry (HWA) are trustworthy and they can produce accurate results of high temporal and spatial resolution. However, they interfere flow and cannot measure many points synchronously [6]. Visual observations and measurements of hydrodynamics has taken significant place in hydrodynamics studies all along. Optical methods such as point-wise Laser Doppler Anemometry (LDA) and field-wise Particle Image Velocimetry (PIV) methods are extensively used in scientific studies dealing with optically transparent flows in stirred tanks [7-10]. For turbid and non-transparent flows Doppler Ultrasonic Velocimetry (DUV) has been developed. The operating principle of DUV is somewhat similar to PIV and it measures flow characteristics by means of ultrasonic beams reflected from seeding particles [11]. Measurements of Bubble Size Distribution (BSD) in mixed multiphase solution by tomographic PIV is challenging since images, taken in twodimensional space and illuminated by laser pulse, give information on bubble size that is limited to particular area of laser sheet. In addition, local gas hold-up remains unknown in whole reactor. Application of Electrical Impedance Tomography (EIT), which is based on voltage measurements, has shown great potential in studies of multiphase flows for phase visualization in 3D [12-14]. Since conductivity is a function of gas hold-up, it is possible to obtain local void fraction of secondary phase by measuring voltages difference between primary phase alone and multiphase flow. Measuring voltage at several electrodes simultaneously reconstruction of conductivity difference distribution and hence local gas hold-up is possible [15,16].

Studying of mixing hydrodynamics facilitates finding local k_{L},
which is needed to evaluate specific volumetric interfacial mass transfer
rate in CSTR. Based on Higbie’s penetration theory Kawase et al. [17,18]
showed that mass transfer coefficient in liquid film for viscous fluids can
be expressed through local energy dissipation:

(2)

where ε is the turbulence energy dissipation rate, m^{2}/s^{3}, DL is the
gas diffusivity in liquid, m^{2}/s, *ρ* is the liquid density, kg/m^{3}, K is the
consistency index, Pa∙sn, n is the dimensionless flow behavior index,
C is the proportionality coefficient. The effect of gas bubbles to the
mass transfer coefficient is taken into account with the proportionality
coefficient. The value of 0.301 for the coefficient, proposed by Kawase
[18], has been tested by Garcia-Ochoa and Gomez [19] and was found to
produce accurate results for gas-liquid mass transfer in stirred reactors.

In addition to local mass transfer coefficient, local interfacial area
is also needed to evaluate local k_{L}a. Measured locally distributions of
bubble sizes and gas void fraction can provide information about local
interfacial area between gas and liquid.

The idea of the current work is to acquire sufficient experimental data in order to be able to connect hydrodynamics of stirred multiphase flow to reaction kinetics. Thiosulphate leaching of gold in ammoniacal solution with the presence of copper (II) in stirred reactor was studied experimentally first and then simulated by means of CFD in order to get distribution of local mass transfer rate of oxygen into solution. The data presented in this study are useful for multiphase flows of finely-milled concentrate as well as for shear-thinning fluids agitated by Rushton turbine in aerated baffled reactors.

**Object of study**

The process of gold leaching with thiosulphate in ammoniacal solution, studied earlier [20] in a lab-scale batch STR, was taken as an example of typical multiphase pulp mixing process frequently encountered in mining and pharmaceuticals industries. The reaction proceeds under almost ambient conditions (atmospheric pressure and 30°C).

A lab-scale baffled stirred reactor, equipped with standard sixblade
Rushton turbine, was investigated in the current research. A
schematic representation of the vessel geometry and its dimensional
parameters are presented in **Figure 1**. The impeller clearance was set at
the distance equal to its diameter from the bottom of the tank. The gas
sparger is a perforated metal pipe mounted at the bottom of the tank.
The tank, made out of plexiglass, was designed and constructed in two
versions. EIT uses controlled current injections to measure responding
voltages at electrodes placed around the flow. Therefore, the vessel,
meant to be used in EIT experiments, was equipped with electrodes
on the walls arranged in rows. In particular, an arrangement of 4 rows
consisting of 16 electrodes, made out of stainless steel, was mounted
on perimeter of the reactor wall. Thus, approximate resolution of the
spatial reconstruction is roughly 2 cm^{3}. Another tank of the same size
was encased inside a rectangular plexiglass container to be filled with
liquid of the same refractive index as the studied solution in order to
eliminate visual distortions.

The power input per volume of fluid that was used in the reaction kinetics research was scaled via the known power number of the dual impeller to the reactor scale used in the current work. The scaled power input corresponds to the mixing rate of around 400 rpm.

**Experimental techniques**

**Rheology study:** The mean diameter of the gold concentrate particles
used by Lampinen et al. [20] was 7 μm. [21] Having measured the total
heat production in calorimeter (universal Calvet calorimeter С80 CS
Evolution of SETARAM Instrumentation with reversing mechanism)
as the function of solids content, and the maximum value corresponded
to 30% of solids content, which was suggested to be optimal in the
leaching solution. The range of the shear rate in the pulp mixing with
the four different impeller speeds was roughly estimated using the
PIV data (Figure 6) and the CFD model. Single phase mixing of the
above-mentioned reactor was simulated in Fluent 16 and the results
are summarized in **Table 1**. Looking ahead, rheological measurements
of the gold concentrate suspended in water revealed shear-thinning
behavior (Figure 4). The suspension used in the leaching experiments is
non-transparent. Therefore, it is not suitable for hydrodynamics study
by PIV. Suspended solids may also cause some bias when measured by

Impeller speed, rpm |
γs-1 | Method of determination | ||
---|---|---|---|---|

Minimum | Maximum | Volume average d | ||

100 | 0.002 | 350 | 2 | CFD |

200 | 0.005 | 708 | 5 | CFD |

400 | 0.012 | 1443 | 12 | CFD |

400 | 0 | 70 | 8 | 2DPIV plane (Figure6) |

600 | 0.024 | 2186 | 19 | CFD |

**Table 1:** Range of shear rate in the reactor.

EIT due to conductivity difference between solids and liquid. For that reason, it was decided to imitate the solution experimentally by using Sodium Carboxy Methyl Cellulose (CMC) dissolved in water. Water solutions of CMC also have shear-thinning behavior and effect of CMC to rheological properties depends on molecular length. Two CMC powders were tested: CMC 30 and CMC 50000. The number going after CMC denotes viscosity of 2 % water-based solution measured at 25°C [22].

Dynamic Mechanical Analysis of the leaching pulp and waterbased CMC solutions was performed using Anton Paar Modular Compact Rheometer 302. By means of swirling cone-analyzer (standard measuring cylinder CC27/T200/AL) the effective viscosity was measured in the shear rate range from 1 to 200 s-1. Suspended solids in the leaching pulp had a tendency to sedimentate. Therefore, the pulp viscosity was measured additionally with a stirrer-sensor (ST24-2D/2V/2V-30/109). Measurements made by the cone and the blade analyzers produced similar results meaning that sedimentation for such tiny particles is a relatively slow process. Thus, the cone mixersensor was used alone in all the experiments in further.

Overall gas hold-up measurements: Gas hold-up measurements were made based on visual observation of liquid surface level of the agitated solutions. The reliability of the measurements was compromised by surface fluctuations and appearance of foam. In order to reduce uncertainties, the rise of the surface level Δh was measured at two positions: between the baffles next to the vessel wall. In each experiment, the agitated solution was allowed to reach equilibrium and then 10 readings from each point were made and averaged. The overall gas hold-up was computed based on the following equation:

(3)

where ε_{Δh} the overall gas hold-up, h_{gassed} and h_{ungassed} are the heights
of the mixed solutions with and without gas introduction correspondingly.

EIT: The EIT set-up used in the experiments involved a signal generator, receiver, controller, and computer. The purpose of the signal generator is to produce current pulses of constant voltage to the solution according to a predefined scheme of pulses order. There are two different scenarios for the order of current injections that can be applied. Voltage injections can be sent pair-wise e.g., adjacent pairs of electrodes or multiple electrodes simultaneously. In both scenarios, voltages are measured at all electrodes. Then, obtained signal goes to demodulation process, where input voltage is decomposed into real and imaginary parts that are needed to get phase and amplitude according to the following formulations [23]:

(4)

(5)

(6)

(7)

where N is the number of electrodes, v(i) is the measured voltage
at i-th electrode, V, V_{real} is the real part of measured voltage, V, V_{image} is
the imaginary part of measured voltage, V, φ and A are the signal phase
and amplitude correspondingly.

Finding a conductivity distribution out of measured voltage outcomes of preset current injections represents itself an inverse problem. Computation of conductivity distribution is a challenging task to solve, since even a slight shift of voltages may be a result of significant change of conductivity distribution in solution, meaning that the “equation” might have several solutions. Therefore, some additional information about object of study is needed to solve the inverse problem. Prior information on conductivity distribution may be achieved statistically and used as a reference [23,24].

The difference method exploits measurements of non-gassed mixed solution as a reference in order to get gas void fraction distribution in the reactor. The conductivity distribution is the function of fluid resistance, and hence, local gas hold-up could be found as follows [23]:

where σ1 is the conductivity distribution of liquid phase, S/m, σ2 is the conductivity distribution of dispersed gas phase, S/m. Thereby, the difference method automatically removes the influence of nonconductive parts of the vessel such as baffles and impeller.

Many researches describe successful applications of the technique for stirred tanks to measure local gas hold-up [13,14,25-28]. Value of current injections value is dictated by conductivity of the studied solution. The higher the solution conductivity, the higher the current injections are required in order to increase sensitivity of the system.

PIV: Particle Image Velocimetry was used to study the hydrodynamics of the liquid phase agitated in multiphase mixing. The PIV technique measures velocity flow fields by capturing the movement of tracing particles, which are small enough not to interfere the flow. By slicing the flow with a laser sheet, PIV can produce a two-dimensional picture of the fluid motion within the laser sheet of illumination. A vector velocity field is constructed based on spatial shift of tracer-particles between a pair of laser pulses emitted consecutively in accordance with a preset time delay. The PIV set-up included a double-pulsed Nd:Yag laser and two Charge-Coupled Device (CCD) cameras of the following resolution 1600 × 1200 pixels. The laser and the cameras were managed by Davis 7.2 PIV software. The imaging of tracers shift was carried out by two CCD cameras which were synchronized with laser pulsing. Thus, velocity vector fields of axial and radial components were measured in 2D space.

In order to measure liquid phase flow, fluorescent particles of size 20 – 50 μm, made of polyamide, were used as tracers. The fluorescent tracers emit light at different wavelength than the laser. This property facilitates getting images with uniformly illuminated background.

High bandpass filters (Light red bandpass filter: BP635) were installed on the CCD cameras to separate light within the wavelength range 615 – 645 nm to filter out the green light coming from light-reflecting surfaces of the reactor [29]. Gas bubbles pictures were made using the light reflected from bubbles. In this case, a camera was capped with a grey filter (B+W, 52 103 ND 0.9 8x) only to reduce intensity of the reflected light.

The laser sheet in the reactor was positioned vertically near the
baffle and 2 mm behind the vertical axe of the shaft. The reason for
this positioning was to remove as many visual obstacles and strong
reflections as possible. Size of single frame taken (measurement
window) depends on camera resolution and focal length of objective. A
typical size of the measurement frame was 127 × 100 mm. Such frames
were processed twice via cross-correlation algorithm. At first, the frame
square is split by the PIV software into interrogation areas of 128 × 128
pixels to search vectors. Then, interrogation areas were decreased to
64 × 64 pixels with 50% overlap and the frame was treated in similar
way to search for tracers shift with higher precision. The final PIV
results have resolution of 2.2 mm. A sample of the taken frames and
the resulting vector field of instantaneous and average velocities are
presented in **Figure 3**. In order to get a full picture of the reactor, it was
necessary to take three frames at different heights along the vertical axe
with 50 mm overlapping (**Figure 2**). Thus, when the captured frames
were assembled, a full image of the reactor, from the tank wall to the
shaft, of size 127 × 200 mm could be obtained. The resolution of postprocessed
and vertically combined frames was 51 × 79 vectors. Totally
1000 frames were taken and processed in order to obtain time-averaged
results.

**k _{L}a measurements:** Volumetric mass transfer coefficient was
measured via “gassing-out” dynamic method by using dissolved oxygen
meter MARVET BASIC. All the experiments were performed at 20°C.
The reactor was at first bubbled with nitrogen until dissolved oxygen
concentration reached its minimum. Then a valve of nitrogen pipe
line was closed and air was introduced. The evolution of the changing
oxygen concentration was recorded until it reached its maximum value.
The data was analyzed by parameter estimation software MODEST
[30] and the volumetric mass transfer rate was calculated using Eq. 10.

(9)

where c_{sat} is the saturated oxygen concentration in water, mol/m^{3},
c_{liquid} is the oxygen concentration in liquid, mol/m^{3}, at t_{1} and t_{2}.

Time constant shows how quickly a measuring probes responses
to a sudden step change of oxygen concentration. In order to expect
accurate results the value of the time constant should be lower than
k_{L}a^{-1} [31,32]. The response time constant τ of the probe was measured
separately for each solution studied. In the experiments, the oxygen
probe was placed between baffles where the mixing is vigorous and
the bulk solution around the probe is constantly renewed by the flow.
Otherwise, the probe might consume all the oxygen presented in the
bulk around at some moment and further measurements become
inaccurate.

**Modelling theory**

**Multiphase fluid flow:** The Stoke’s number (Eq. 11) for the studied
system is more than 1, meaning that the secondary phase influence
onto the primary phase is not negligible and it has to be taken into
account.

(10)

Where Ԏ_{q} and Ԏ_{p} are the relaxation time of primary phase and

bubble, s, dp is the bubble diameter, m,ε is the energy dissipation, m^{2}/

s3, ν is the kinematic viscosity, m^{2}/s.

Therefore, in the gas-liquid modelling, Eulerian-Eulerian multiphase approach was used, in which gas and liquid phases are considered as interpenetrating continua. A set of conservation equation is solved for each phase (Eq. 13 and 14). Additionally, volume fraction is introduced (Eq. 12).

(11)

(12)

(13)

where αi is the phase volume fraction, u - phase velocity, m/s, is
the pressure, Pa, μ _{turb} is the turbulent viscosity, Pa∙s.

**Suspended solids:** The tiny milled concentrate was used in the
original leaching tests with mean size of 7 μm. Pulp flow can be modeled
via effective viscosity [33]. Rheology of the leaching slurry has been
measured experimentally and modeled via power law model (Eq. 23).

**Turbulence:** In CFD modelling, available computing power
and acceptable simulation time were limited, for which reason it
was decided to apply a Reynolds-Averaged Navier-Stokes (RANS)
turbulence model in the current simulations. Turbulence formulation
in RANS models are based on statistical analysis rather than on actual
physical phenomena. By contrast, the Large Eddy Simulation (LES)
model is based, at least partially, on resolving turbulence fluctuations.
Approximations such as the Boussinesq hypothesis can lead to
mismatches with real flow behavior due to turbulence isotropy and
homogeneity. As a result, empirical constants are introduced to tune
the model (Eq. 15 and 16). In the current work, it was decided to
evaluate the suitability of the most frequently applied RANS models
rather than attempt to implement a novel turbulence model by tuning
the model constants for the hydrodynamics of the specific stirred
tank. In our previous work [34], three popular models in the RANS
family were tested, namely the Realizable k-ε model, the Shear Stress
Transport k-ω model, and the Reynolds Stress Model (RSM). The
Realizable k-ε model produce the most accurate results for single and
multiphase mixing in round bottom STR. The Realizable k-ε model is a
recent model with an improved computational mechanism preventing
turbulence energy from being negative. Such energy is not physical but
can occur using the Standard k-ε model.

(14)

(15)

where k is the turbulence kinetic energy, m^{2}/s^{2}. Production P
includes one more constant.

Dispersed turbulence formulation model was used since the secondary phase is dilute and fluctuating quantities of the gaseous phase may be found as the function of the mean terms of the liquid phase. At first, turbulence terms k and ε are first computed for primary phase. Then, secondary phase turbulence terms are found and exchange of turbulence momentum between phases is computed based on Tchentheory [35].

Phase interaction: Momentum conservation equation (Eq. 17) includes cumulative force (Eq. 18) acting on primary phase. The cumulative force comprises several forces occurring in multiphase interaction, including drag, virtual mass, lift, wall lubrication, turbulence diffusion forces etc.

(16)

(17)

where is the external body force,the lift force, is the wall lubrication force is the virtual mass force, and is the turbulence diffusion force.

Different drag models can be found in published literature. The most popular model, proposed by Schiller and Naumann [36] in Eq. 19, is a drag model suitable for rigid spherical particles.

(18)

where ρ_{P} is the particle density, kg/m^{3} D C is the drag coefficient, A_{i} is the relative Reynolds number, and A_{i} is the interfacial area, m^{2}. The
drag force coefficient is the function of Re according to the following
formulation:

(19)

The drag force model is based on bubble rise velocity measured in stagnant fluids, which is higher than rise velocity in turbulent flow. A model correcting drag force coefficient for turbulence was proposed by Brucato et al. [37]. This turbulence modification factor concept (Eq. 21) changes stagnant fluid drag force to make it suitable for adoption in turbulent multiphase flow simulation Later, Lane et al. [24] critically considered Brucato’s formulation and found that ratio of slip and terminal velocity as a function of bubble size and Kolmogorov length scale does not take into account particle density or density difference between phases. Having pointed out this deficiency in Brucato’s model, Lane et al. suggested a new correlation (Eq. 22) for turbulence modification factor that is based on ratio of stagnant to turbulent terminal velocity to be correlated with ratio of particle relaxation time to integral time scale of turbulence (Eq. 23).

(20)

Where η is the turbulence modification factor, K= 6.5∙10-6, λ is the Kolmogorov length scale, m.

(21)

(22)

Gradov et al. showed that the Schiller-Naumann drag force model in conjunction with Lane’s turbulence modification factor gave the most accurate results for air-water mixing in stirred tank at the assumption of constant bubble diameter equal 1 mm. Also, the effect of non-drag forces was found to be insignificant air-water mixing simulations. Therefore, in order to reduce computational complexity and promote solution stability the above mentioned combination of models was used to simulate drag force, while other forces models were ignored [34].

**Modelling strategy:** In the gas-liquid flow simulations, the gas was introduced into converged liquid flow field in order to reduce
computational instabilities. In the CFD simulations, the stirred tank
can be considered as a semi-batch system with gas is supplied via
sparger and exit through liquid surface. The gas phase was introduced
in a transient manner at 0.02 s time step until mass flow rate balance
was reached and stabilize within 5% deviation. Under relaxation
factors for pressure and velocity were reduced up to 0.15 and 0.35
correspondingly to facilitate convergence. Second order discretization
scheme was applied to all the parameters. Convergence criterion was
set at 10-4 for all the variables to be simulated. When multiphase flow
hydrodynamics have been computed, mass transfer was calculated on
top of multiphase results according to Eq. 2. The operational conditions
simulated and models used in single phase and multiphase mixing
simulations are summarized in **Tables 2 and 3**.

Operational conditions | Modelled phenomenon | Model used |
---|---|---|

400 rpm | Turbulence | k-ε Realizable |

Shear-thinning rheology of mixed fluid | Power-law model | |

Flow near the solid walls | Standard wall function |

**Table 2:** Summarized conditions for single phase mixing simulations.

Operational conditions | Modelled phenomenon | Model used |
---|---|---|

400 rpm | Turbulence | k-ε Realizable |

Shear-thinning rheology of mixed fluid | Power-law model | |

1.25 L/min of air flow rate |
Flow near the solid walls | Standard wall function |

Bubble size | Constant db=1.5 mm |

**Table 3:** Summarized conditions for multiphase mixing simulations.

**Experimental results**

**Rheology:** The rheology of the leaching suspension as well as the
water solutions of CMC 50000 (0.15 w%) and CMC 30 (1.8 w%) were
measured and shown in **Figure 4**. The presented data was plotted in
log-log scale, and the rheological parameters were found from the
Ostwald-de Waele power law [38]:

(23)

The viscosity of all the solutions approach constant level as the
shear rate is increased. However, only the solution of short molecular
chain CMC 30 shows insignificant shear-thinning rheology. Therefore,
only CMC 50000 (**Figure 11**) has been used in further as an imitation
model of leaching suspension. It is advisable to set limits for the
effective viscosity when modelling non-Newtonian hydrodynamics in
order to avoid numerical errors. Calculated power law parameters are
summarized in **Table 4**.

Solution | n | K, Pa∙s^{n} |
µ_{min}, Pa∙s |
µ_{max}, Pa∙s |
---|---|---|---|---|

Thiosulphate slurry | 0.200 | 0.044 | 0.02 | 0.40 |

CMC 50000 (0.15 w%) | 0.746 | 0.086 | 0.02 | 0.09 |

**Table 4:** Power law model parameters.

**Gas hold-up:** Measurement of gas hold-up in STR by level
difference has better accuracy at high gas hold-ups. Gas hold-up has
linear dependence on superficial velocity as described by Rewatkar et
al. [39] numerically and approved experimentally experimentally later by Kraume and Zehner [40] for glass beds suspended in water and by
Laakkonen [41] for Xanthan solutions. In the current study, gas holdup
was measured over the range of gas flow rates from 1 to 10 L/min at
constant impeller speed of 400 rpm. The results are plotted in **Figure 5**.

The obtained results show almost linear dependence of gas hold-up from gas flow rate. It is necessary to use relatively low gas flow rate in PIV measurements to ensure good optical transparency of solution and reduce impact of gas bubbles onto laser intensity. Therefore, gas flow rate could be safely reduced to 1.25 L/min.

**EIT:** Increased viscosity promotes growth of bubble size due to
increased coalescence rate. However, it is also known that presence of
electrolytes in solution inhibits bubble coalescence [42]. At sufficiently
high salt concentrations, bubbles, covered by ion layer, repel each
other. The total optimal concentration of salts for thiosulphate leaching
was found to be 0.4 mol/L [20]. Unfortunately, the EIT set-up loses its
sensitivity at high conductivity of solution since the maximum current was limited to 6.5 mA. For that reason, the salt concentration had to be
reduced to lower value, where a compromise between the similarity in
the multiphase solution properties compared to the original solution
and the set-up limits could be met. It can be concluded, that significant
amount of ions in liquid suppresses the bubble-growing effect
generated by higher viscosity. The influence of the salt concentration
on gas phase can also be tested indirectly by measuring the power draw
of the impeller. Impeller torque was measured as salts were added stepwise
(0.05 mol/L per step). The results (**Figure 9**) show that 0.05 mol/L
of salts was enough to effectively cover the major part of the bubbles
surface in the solution. Further addition of salts has insignificant effect
on the mixing power and hence on the gas hold-up. However, the power
draw is manly driven by the average density of the multiphase solution,
and it is little influenced by the distribution of bubble size which has,
however, significant influence on the contact surface area between the
phases. Therefore, the overall k_{L}a was also measured at different salt
concentrations, as depicted in **Figure 9** (left plot). The slow increase of the overall mass transfer is an evidence of the ongoing shift in the BSD
towards small bubbles. At concentration 0.1 mol/L, with a conductivity
of 7.9 mS/m (which is within the maximum conductivity limit of the
EIT), the k_{L}a value is 91% of the maximum k_{L}a value at concentration
0.4 mol/L. Therefore, this concentration was selected as a reasonable
compromise and was used in all the experiments.

In order to evaluate the performance of the EIT set-up, several
experiments were made at three gas flow rates without mixing. The
obtained local gas hold-ups are illustrated in **Figure 10**. The resolution
of the resulting images was around 2 cm^{3}. It is clear that at large flow
rates, the contrast in gas-liquid conductivity is high and the EIT results
of gas-liquid mixing become more reliable.

The local gas hold-ups of the water-based solution of CMC 50000
mixed at 200, 400 and 600 rpm over the range of gas flow rates from 1
to 2 L/min are presented in **Figures 13-15**.

The overall gas hold-ups increase as the gas flow rate is increased with all the impeller speeds tested. Unfortunately, the poor resolution of the EIT set-up does not capture small bubbles present in high quantities in the most agitated region around the impeller. At low gas flow rates and high impeller speeds conditions are challenging when bubbles are smaller and distributed more uniformly in the volume of the reactor. Decreased and evenly distributed gas void fraction allows electrical current bypassing small bubbles especially at high loads of electrolytes in the solution. The measured zero value of gas hold-up around the impeller indicates narrow size distribution of small bubbles. The bubbles become traceable only in the region of low turbulence intensity where bubble coalescence takes place. The regions of bubble growth are most distinct at low ratio of impeller speed to gas superficial velocity. It can be noticed that bubble size grows in radial direction towards the wall. Below the impeller, a down pumping circulation loop generates a stagnant zone where the retention time of bubbles is bigger. Meanwhile, bubbles, escaping the loop, gravitate to the free surface and move into less turbulent region where they coalesce. In addition, intensive foaming takes place when the CMC-water-thiosulphate solution is mixed which facilitates accumulation and growth of bubbles near the free surface. As a result, high local gas hold-up next to the surface is formed which is also presented in all the figures.

**PIV:** PIV results of CMC 50000 (0.15 w%), showing contours of
the averaged velocity vector field and the r.m.s instantaneous velocity
field, are shown in Figure 5. The averaged velocity vector field is a
great source of information. The spatial velocity gradients may give
information about the range of shear rate in the 2D slice of the flow
(**Figure 6**). That information was used to define the range of shear rate
in the rheology study of the suspension and the CMC water-based
solutions. When studying the shear rate distribution in the PIV plane
more closely one may notice that the agitated flow is rapidly attenuated
in the viscous solution. It can be clearly seen that the visible stable
streams which have shear rates of 70 s^{-1} are pushed by the agitator and
dissipated into the bulk solution where the initial shear rate is reduced
to around 10 s^{-1}.

Salts free single phase mixing of the CMC solution at 400 rpm (Figures 5 and 6) at 1.25 L/min were measured by the PIV and used for validation of CFD results.

As it was stated earlier, the leaching solution used in the original
tests of thiosulphate leaching of gold [20] had high salts concentration.
In the PIV tests, CMC 50000 (0.15 w%) solution with 0.1 mol/L
concentration of sodium thiosulphate was used to study gas bubbles.
Presence of salts has significant impact onto BSD. Ions of the same sign
cover surface of gas bubbles and block coalescence rate by repelling
mechanism. As a result, one may notice narrow distribution of gas
bubbles in **Figure 7**.

Bubble size distribution is almost uniform in the most turbulent region next to the impeller as well as also elsewhere in the image. Bubble size varies from 1 mm to 1.8 mm as it is seen in the zoomed picture. The bubbles are densely populated in the plane of measurement. However, it should be mentioned that only those bubbles that are in focus were considered when evaluating the bubble size.

Such a narrow range of BSD may be approximated as a constant bubble size (1.5 mm) throughout the reactor under the current conditions. Considering CFD modelling this approximation greatly simplifies modelling and use of Population Balance Model (PBM) can be avoided.

**Overall k _{L}a:** Two water-based solutions of CMC 30 (1.8%) and
CMC 50000 (0.15%) were used to measure the volumetric mass transfer
coefficient at three impeller speeds and the range of gas flow-rates with
and without addition of salts. The results are presented in Figure 14.

The volumetric mass transfer rate is proportional to interfacial contact area and mixing intensity. At mixing speed 600 rpm k_{L}a grows
as gas flow rate is increased. However, at lower mixing speeds k_{L}a
increases up to some point and then goes down with the increase of
gas input. The reason for this behavior is the contact area that drops if
mixing intensity is not enough to keep the bubble size small. Without
salts both CMC solutions have similar mass transfer due to similar
apparent viscosity. Presence of ions in water-based solution of CMC
30 does not lead to significant drop of viscosity and the similar mass
transfer can be observed. However, ion presence affects CMC 50000
so that the long chain molecules are broken and the apparent viscosity
of solution is decreased. Low viscosity and high content of ions in the
solution give nearly constant and small bubble size that results in high
values for k_{L}a.

**Numerical results**

Grid independence test: Spatial discretization influences results of numerical simulation. Five different grids have been tested. Water mixing simulations were used in grid independence study. Reactor geometry was meshed with almost doubling factor relatively one another and scaling uniformity was maintained as well. Re number differs significantly within the vessel therefore 14 sampling points of velocity have been defined in the reactor domain. A normalized root mean square error index (NRMSE) was employed as a criterion for grid independency validation [43]. Its formulation is as follows:

(24)

where N is number of cells in a grid (it is advised to keep grid size ratio above 1.3 corresponds to order of discretization, n is number of samples, φ1 and φ2 are predictions on coarse and fine grids accordingly.

According to the authors, grid difference might be considered
negligible if NRMSE value is less than 10%. During mesh sizing
independence tests simulations were performed with second order
discretization scheme. Results presented in **Table 5** clearly indicate grid
4 to be optimal one for the needs of the current study.

Grid name | Number of elements | Torque, mNm | ∫kdvm2/s2 ∙ 10-5 |
εdV, m2/s3 ∙ 10-5 | NRMSE u̅ % |
---|---|---|---|---|---|

1 | 108 276 | 54.0 | 9.9 | 139.2 | 20 |

2 | 269 654 | 56.0 | 10.8 | 161.2 | 13 |

3 | 464 532 | 56.6 | 10.7 | 166.4 | 15 |

4 | 754 056 | 65.6 | 13.0 | 209.1 | 9 |

5 | 1 969 376 | 64.4 | 12.6 | 208.5 | NaN |

Measured experimentally | 65 ± 3 |

**Table 5:** Grid test results of water mixing at 400 rpm in STR.

Shear-thinning fluid mixing: To reduce numerical instability the gas-liquid multiphase simulation strategy included two steps. The gas-liquid simulations were made in two-way coupling. At first, primary phase flow has been resolved, converged solution results of which were used as initial data before activation of secondary phase. It is important to resolve primary phase accurately because primary phase hydrodynamics has great impact onto secondary phase. Before gas phase introduction in a transient manner, the simulation results of mixed non-Newtonian solution were validated against experimental results.

Qualitative analysis was performed by comparison of the velocity
contour fields in vertical 2D plane sampled at the identical spatial
position and it is shown in Figure 2. Particle Image Velocimetry
used in this work measured only two velocity components out of
three. Therefore, the velocity contour of CFD simulation results was
adjusted for qualitative comparison and includes only radial and axial
components. The tip speed of the Rushton turbine rotating at 400 rpm
is 1.57 m/s (**Figure 12**). Radial and tangential at the tip of impeller can
be equaled. However, accurate measurements of impeller jet-stream
are complicated by rotating blades of the turbine and slight swinging
of the shaft. That makes slight underprediction of maximum radial
velocity component in the impeller region in PIV measurements.

Overall velocity distribution profiles look quite similar between CFD and PIV results. Both circulations taking place above and below jet-stream are captured at the same locations and in similar manner. However, jet-stream velocity field profile is a bit thicker in CFD contour. It could be explained by isotropic turbulence being used by the turbulence model, while the flow turbulence produced by a Rushton turbine is anisotropic [44,45].

Since velocity filed contours comparison might be biased, the
velocity components normalized with the tip speed were validated
against experimental results in radial profiles (**Figure 16**). In order to
sample hydrodynamics at different regions of the reactor, the profiles
were taken at three vertical positions 30, 80 and 150 mm starting from the bottom. The simulation of shear-thinning flow agitated by the
Rushton turbine describes the flow accurately.

Power draw was found experimentally by measuring torque via
on-shaft torque transducer. The measured and simulated torque of
single phase mixing of CMC 50000 (0.15 w%) and the leaching slurry
are presented in **Table 6**. As expected, the reduction of power draw
is observed in case of gas-liquid mixing, because average density of
multiphase solution is lower than of single phase. The torque of mixed
CMC 50000 was simulated accurately (**Figure 17**).

Flow type | Torque, mN∙m | ||
---|---|---|---|

Experimental | CFD | ||

Single phase | CMC 50000 (0.15 w %) | 68 ± 3 | 65.6 |

Thiosulphate slurry | - | 103.0 | |

Multiphase | Thiosulphate slurry | - | 101.2 |

**Table 6:** Simulated VS experimental torque.

**Aerated slurry mixing:** When the solution of the leaching slurry
mixing has reached convergence, air has been introduced via velocity
inlet in transient manner with 0.02 s as time step. The simulation lasted
until the balance of air mass flow rate was observed. Average density of
the suspension (30 w%) is 1570 kg/m^{3}.

Average velocity field of the mixed slurry is presented in **Figure 18**.
Maximum value of velocity magnitude is around tip speed. One may
notice velocity contour of the air jet supplied via sparger.

As it was found during the gas bubbles study in PIV section, the BSD is very narrow in presence of electrolytes (0.1 mol/L). Therefore, 1.5 mm bubble size was used in the simulations. Specific volumetric surface area of secondary phase can be found as follows:

(25)

where ε_{p} is the volume fraction of secondary phase, fraction.

The volume fraction and specific surface area of gas phase in the
mixed slurry are shown in Figure 18. On one hand, high apparent
viscosity of the leaching slurry increases dissipation rate of energy and power draw growth as a result. On other hand, higher viscosity hinders
rise velocity of gas bubbles that leads to higher gas hold up almost twice
up to 1.35% (**Figure 8**). Being small the bubbles follow the flow of the
primary phase. The flow pattern of the radial impeller has two loops
of circulation. Following radial jet-flow of Rushton turbine they are
dragged into down circulation while only small portion of gas goes
up. The upper loop can also be distinguished since some amount of air
bubbles are accumulated there. Total interfacial area is 0.26 m^{2}.

Mass transfer: Mass transfer has been modeled using Eq. 2.
Diffusivity of oxygen in liquid depends on physical properties of
solution. According to Hung and Dinius [46] increase of electrolytes
concentration drops oxygen diffusivity. Diffusion coefficient of oxygen
was calculated based on measured values of D_{L}(O_{2}) in water with
presence of sodium sulphate. Linear interpolation from the above
mentioned work resulted in D_{L}(O_{2})=1.65 × 10-9 m^{2}/s. Influence of
suspended solids interaction with gas bubbles onto diffusion coefficient
is unknown and neglected in this work since particles are finely milled.
Theoretically, tiny particles can partially cover gas-liquid interface
and cause some decrease of oxygen mass transfer into the liquid
phase. However, overall kLa reduction should not be significant since
interfacial area was increased drastically due to small bubbles. The
distributions of specific volumetric mass transfer coefficient and mass
transfer rate of oxygen are presented in **Figure 19**.

As it can be noticed from the distribution of specific mass transfer,
the rate of mass transfer is higher in the regions where gas hold-up
and energy dissipation rate are high. Therefore, the most intensive
mass transfer is in the radial jet created by Rushton turbine. However,
high gas hold-up of small bubbles, which do not coalesce, in the lower
loop promotes mass transfer. Also, the region of moderate k_{L}a value,
caused by bubble retention in the upper circulating loop can be seen.
Overall simulated mass transfer in mixed thiosulphate slurry is 0.0183
s^{-1}, which is 30% higher compared to the mass transfer measured in the mixed CMC 50000 (0.15%) solution under analogous operational
conditions [47,48].

During this work mixing of aerated slurry on the example of thiosulphate leaching has been studied experimentally and simulated numerically. Rheology of the suspended solids was measured and found similar to those of shear-thinning fluids, which can be described by power-law model. Therefore, the slurry was imitated with waterbased Carboxy Methyl Cellulose solutions (CMC 30 and CMC 50000) in order to study mixing hydrodynamics experimentally. Velocity vectors and shear rate fields of CMC 50000 (0.15 w%), mixed at 400 rpm were measured by stereoscopic PIV in vertical 2D plane.

Volumetric mass transfer was measured by dynamic method in the
CMC solutions over the range of operational conditions in absence and
presence of electrolytes. Presence of electrolytes promotes mass transfer
of oxygen. Electrolytes decrease viscosity by breaking molecular chains
of CMC that increases mass transfer coefficient. Bubbles coalescence
blockage causes significant growth of surface area. Measurements of
volumetric mass transfer at constant operational conditions were made
with stepwise addition of electrolytes. The study revealed that decrease
of bubble size is dominating factor upon kLa because viscosity drop
takes place at lower salt amount. When level of electrolytes saturation
is reached slight decrease of mass transfer was found at (**Figure 9**) at
stable power draw. It could be due to contamination of the gas-liquid
interfacial area.

Local gas hold-up in the aerated CMC 50000 (0.15 w%) solution was measured by EIT. Potentially the technique is capable to measure local gas hold-up in slurry. However, the sensitivity of the set-up was not enough to measure gas hold-up distribution of dispersed phase in electrolyte solution accurately.

The achieved experimental data was used in CFD modelling of the aerated slurry. Single phase non-Newtonian fluid mixing, modelled via effective viscosity, was validated against the PIV measurements of velocity components in vertical plane. Simulated and measured power consumptions of the CMC mixing at 400 rpm were in reasonable agreement. In the presence of electrolytes (0.1 mol/L) the bubble size in the CMC solution (400 rpm and 1.25 L/min) was found to be almost constant (1.5 mm). Multiphase mixing hydrodynamics of the thiosulphate slurry was modeled at the assumption of constant bubble size. Results of the simulation were presented and discussed. The simulated kLa in the leaching pulp was compared to the measured one in CMC 50000 (0.15 w%) under analogous operating conditions. It was found that bigger density of the leaching slurry caused higher global gas hold-up and hence oxygen mass transfer rate [49].

The authors are grateful to the Finnish Funding Agency TEKES and, in particular, to Outotec Finland Oy collaborating under FERMATRA project (908/31/2016 and 958/31/2016), for active supervision and financial support. Also, the work of Marko Vauhkonen and Gerardo Del Muro González was supported by the Academy of Finland (Project 250215 Finnish Center of Excellence in Inverse Problems Research).

Symbols | Meaning | Units |
---|---|---|

A | Signal amplitude | - |

A_{i} |
Interphase surface area | m^{2} |

C_{i} |
Empirical coefficient | - |

CD | Drag force coefficient | - |

c_{gas} |
Oxygen concentration in gas phase | mol/m^{3} |

c_{liquid} |
Oxygen concentration in liquid phase | mol/m^{3} |

db | Bubble diameter | m |

DL | Diffusivity in liquid phase | m^{2}/s |

Force | N | |

h_{gassed} |
Surface level in gassed reactor | m |

h_{ungassed} |
Surface level in non-gassed reactor | m |

K | Consistency index | Pa∙sn |

K_{pq} |
Interphase exchange coefficient | - |

k | Turbulence kinetic energy | m^{2}/s^{2} |

k_{L} |
Mass transfer coefficient in liquid phase | m/s |

k_{L}a |
Volumetric mass transfer coefficient | s^{-1} |

N_{fine} |
Number of cells in fine grid | - |

N_{coarse} |
Number of cells in coarse grid | - |

n | Dimensionless flow behavior index | - |

NRMSE | Normalized root mean square error | % |

Pressure | Pa | |

P* | Order of discretization | - |

Re | Reynold’s number | - |

St | Stoke’s number | - |

T_{L} |
Turbulence length scale | m |

t | Time | s |

U_{T} |
Particle terminal velocity in turbulent flow | m/s |

U_{S} |
Particle terminal velocity in stagnant flow | m/s |

Mean velocity | m/s | |

u_{r} |
Radial velocity component | m/s |

u_{z} |
Axial velocity component | m/s |

V | Volume of reactor | m^{3} |

v_{image} |
Imaginary part of measured voltage | V |

v_{real} |
Real part of measured voltage | V |

Greek letters | Meaning | Units |
---|---|---|

α_{i} |
Phase volume fraction | - |

ε | Turbulence kinetic energy dissipation rate | m^{2}/s^{3} |

ε_{EIT} |
Global gas hold-up measured by EIT | - |

ε_{Δh} |
Global gas hold-up measured by level differencing | - |

ε_{i,EIT} |
Local gas hold-up in element i, measured by EIT | - |

μ | Dynamic viscosity | Pa∙s |

μ_{eff} |
Effective viscosity | Pa∙s |

μ_{turb} |
Turbulent viscosity | Pa∙s |

η | Turbulence modification factor for drag force | - |

ρ | Density | kg/m^{3} |

σ_{1} |
Conductivity distribution of non-gassed mixing | S/m |

σ_{2} |
Conductivity distribution of gas-liquid mixing | S/m |

τ | Time constant | s |

τ_{b} |
Relaxation time of bubble | s |

τ_{q} |
Relaxation time of primary phase | s |

ν | Kinematic viscosity | m^{2}/s |

γ | Shear rate | s^{-1} |

λ | Kolmogorov length scale | m |

φ | Signal phase | - |

φ_{i} |
Prediction of property value on grid i | - |

Acronyms | Transcript |
---|---|

CCD | Charged-Couple Device |

CFD | Computational Fluid Dynamics |

CISTR | Continuous Ideally Stirred-Tank Reactor |

CMC | Carboxy Methyl Cellulose |

FEM | Finite Element Method |

HWA | Hot Wire Anemometry |

LDA | Laser Doppler Anemometry |

MCR | Modular Compact Rheometer |

Nd:Yag | Neodymium-doped yttrium aluminum garnet |

PIV | Particle Image Velocimetry |

UDV | Ultrasonic Doppler Anemometry |

vvm | Volume of gas per volume of mixed solution per minute |

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