The Application of the Radiotracer Techniques in Hydrometallurgy: A Method for Online Monitoring of Solvent Extraction Processes Using ¹⁸¹Hf

Abstract

The increasing demand for critical metals essential for renewable energy technologies necessitates efficient and environmentally sustainable extraction methods. Ilmenite (FeTiO₃) and similar ore deposits serve as abundant sources of primary elements while also incorporating a suite of strategically significant trace elements, including REEs and Hf, among others. Mixer–settler units are extensively utilized in metal purification processes. It is important to develop approaches for tracking the metal’s extraction process online and optimizing flow dynamics. One widely adopted technique for evaluating the flow dynamics of the various components is the residence time distribution (RTD) measurement, which provides insights into the hydrodynamic behavior of process reactors. This study explored the application of radiotracer techniques for online monitoring of solvent extraction processes in hydrometallurgy, focusing on Hf recovery. A mixer–settler system was employed using di(2-ethylhexyl) phosphoric acid (D2EHPA) as the extractant and the 1M HNO₃ aqueous phase of Ti ore. The radiotracer ¹⁸¹Hf was synthesized via neutron activation and introduced into the system to track phase distribution and RTD. Real-time monitoring revealed over 95% extraction efficiency within 133 min (8000 s). The RTD studies validated system performance using perfect mixers in series and axial dispersion models. The calculated mean residence time of 100 min (6000 s) closely aligned with the theoretical 104 min (6240 s), confirming the model accuracy. The findings demonstrate the viability of radiotracers in monitoring solvent extraction, offering real-time insights into flow dynamics and extraction efficiency.

1. Introduction

Worldwide energy resource consumption, mostly from fossil fuels, has skyrocketed since the Industrial Revolution [1]. It is anticipated that the global energy sector will continuously move towards renewable energy options in the next decades [2]. However, the shift from a civilization based on fossil fuels to one that is not may be hampered by the depletion of the critical metals required for advances based on renewable energy [3]. Critical metals are those that are costly, have no close substitutes, are scarce in the Earth’s crust, can be vulnerable to supply risks, and are necessary for an economically significant push. The U.S. and Europe are seriously challenged by the prospective scarcity of critical resources, which might have significant economic implications [4,5]. The European Union revised the list of key raw materials in 2023 to incorporate the following metals: Sb, Bi, Co, Ga, Be, In, HREEs, LREEs, Sc, PGMs, Si, V, Hf, W, Mg, Nb, and Ta [6]. Deposits such as Ti ore are rich in valuable metals, and their exploitation of major and trace metals might improve resource efficiency by minimizing waste and encouraging sustainable mining techniques [7]. Such a complete approach can also improve mining companies’ profitability, as the sale of byproducts generates additional revenue. Critical metals such as Hf are very useful in various applications such as nuclear reactors for structural fuel materials and cladding [8]. As a control rod material in high-flux research reactors, its resistance to corrosion and mechanical strength allow for extended reactor residence time without cladding. Additionally, Hf is used in nickel superalloys, plasma arc nozzles, high-temperature ceramics, and energy-efficient silicon-based chips [8].

Hydrometallurgical techniques are crucial for extracting metals from ores [9]. One of the main arguments in favor of the ongoing advancement and contemporary architecture of hydrometallurgical processes is the significantly reduced environmental impact. Trace amounts of metals can also be recovered using such a method, which begins with leaching followed by other approaches such as solvent extraction [10]. The solvent extraction of Hf using ligands such as D2EHPA involves a cation exchange mechanism. In nitric acid solutions, Hf⁴⁺ ions react with the dimeric form of D2EHPA (H₂A₂) to form an organic-phase complex, releasing H⁺ ions into the aqueous phase. The extraction efficiency is influenced by factors such as the nitric acid concentration, D2EHPA concentration, and temperature [11]. Increasing the acidity of the aqueous phase can decrease the distribution coefficient, as the chemical equilibrium shifts. The extracted species are suggested to be HfOA₂·2HA.

In different stages of the solvent extraction process, mixer–settler units are commonly used due to their high efficiency, operational flexibility, and ease of scaling up [12]. The mixer section within these units plays a crucial role in pumping and dispersing two immiscible liquids through impeller motion, enabling effective mass transfer between the contacting phases. Following this, the settler section allows the dispersed droplets to coalesce, leading to the separation of the two immiscible phases. The number of mixer–settler units required in an operation depends on their efficiency. Several factors influence the effectiveness of metal purification, including the flow rates of the aqueous and organic phases, the extent of their mixing in the mixer and settler sections, and the performance across different stages of the system.

The nature of homogenization has been extensively studied and analyzed utilizing colorimetry, thermometry, pH metric, and conductivity methodologies in conjunction with the conventional impulse-response paradigm [13]. These methods need the probe to be inserted into the reactor, which disrupts the flow of liquid. Additionally, conventional techniques for monitoring the recovery of metals online often entail invasive sampling and time delays, resulting in errors in extraction efficiency estimation [14]. Such issues can be addressed using a radioisotope(s)/radiotracer(s). These are atoms with unstable nuclei making them decay by emitting radiation in the form of alpha gamma rays, beta particles, or alpha particles. The released gamma radiation provides the basis for the identification and quantification of the activated metal(s) [15]. Equation (1) depicts the nuclear reactions that occur during the interaction of the neutrons with the nucleus of an element.

$${}_0{}^{1}n+{}_Z{}^{A}X\to {}_Z{}^{A+1}X^{*}\stackrel{IT}{\to }{}_Z{}^{A+1}X+\mathsf{\gamma }\stackrel{\mathsf{\beta },\mathsf{\gamma }}{\to }{}_{Z+1}{}^{A+1}Y+{\mathsf{\beta }}^{-}+{\overline{\nu }}_e+\mathsf{\gamma }$$

(1)

where X is the target nuclide, Z represents the atomic number, n is the neutron, X* is the nucleus is in the excited state, IT is the isomeric transition, β represents beta particle, A is the atomic mass, γ is gamma radiation, ${\overline{\nu }}_e$ is the electron anti-neutrino and Y is the product nucleus. To analyze the induced radioactivity, various types of gamma-ray detectors can be employed, such as NaI (Tl) scintillation detectors or high-purity germanium (HPGe) semiconductor detectors [15,16]. The primary requirement for a radiotracer is its identical behavior to the nuclides it represents, coupled with an appropriate half-life and gamma-emission characteristics to facilitate detection [16].

The estimation of the extraction efficiency of metals in technological processes using conventional probing techniques is widely accepted. Nonetheless, the use of radiotracers aims to improve this process by making it faster, more efficient, and easier. Through analysis of the tracer concentration, the radiotracer technique allows for continuous monitoring online of the mixing and metal extraction process. The technique is effective for analysis in both transparent and opaque systems. The use of radiotracers is favored for evaluating cation concentrations during solvent extraction. This is because the metal concentrations can be determined individually in both phases devoid of the need for additional separation techniques [17]. The level of sensitivity can be adjusted across a wide range based on the requirements of the particular task. It is feasible to get information about the distribution patterns of extractants and diluents using reagents that have been labelled using radiotracers. The quantification of extraction processes requires this kind of information. This approach is statistically reliable, yielding reproducible and repeatable outputs within a short timeframe. The method allows for automation of the system, minimizing human intervention in data collection which reduces the risk of human error [18]. The setup is mostly cost-effective coupled with the feasibility of having a portable system for different applications. Unlike radiotracer methods, no conventional technique meets all these criteria.

A crucial factor in the use of radiolabel procedures in flow profiling is residence time distribution (RTD) [19]. RTD serves as a probability distribution model designed to project the duration that a fluid element remains within a reactor. It aids in identifying flaws within the reactor and offers an understanding of the flow patterns and mixing properties within such systems [20,21]. The approach plays a pivotal role in determining the RTD of process materials in both large-scale and pilot industrial systems [22]. The method helps determine the flow characteristics, including the mixing degree, dead volume extent, bypassing, and mean residence time (MRT) [23]. They have an outstanding detection potential and the capacity to provide real-time measurements, among their numerous advantages [20,21]. Measuring the MRT of a flowing fluid and characterizing flow in chemical reactors are common applications of the RTD concept [24,25].

The utilization of ¹⁸¹Hf radiotracers has not been employed in the exploration processes for the solvent extraction of several metals. This underscores the existence of an untapped potential that can be explored by applying radiotracer methods in hydrometallurgy since the method is sensitive and dependable. Therefore, the goal of this study was to demonstrate the application of ¹⁸¹Hf for online monitoring of the Hf extraction process by D2EHPA from titanium ore using a mixer–settler system. Additionally, the research aimed to use the same radioisotope for RTD studies in the mixer–settler system. The half-life of ¹⁸¹Hf is 42.39 days, which is long enough for hydrometallurgical analysis. Such a relatively short half-life reduces the discharge of radioactive waste during the measurements, guaranteeing safety and reducing environmental impact [26]. The benefits of real-time, non-invasive analysis and precise measurements offered by ¹⁸¹Hf outweigh the demerits associated with its half-life. ¹⁸¹Hf is also readily available from different suppliers specializing in the production of radioisotopes for industrial and scientific operations.

2. Materials and Methods

2.1. Materials

A titanium ore sample sourced from Norway was selected for this study. Due to confidentiality agreements aimed at protecting the supplier’s reputation, their identity remains undisclosed. Each sample was carefully labeled with a unique code, date, and sampling location for proper identification. To enhance the reaction between the material and leaching agents, the selected sample was ground using a pestle and mortar, increasing its surface area. Following this, the quartering method was employed to achieve homogeneity in the finely ground material for further analysis. Different fractions of the bulk sample were manually separated using a 75 µm sieve. Additionally, the required sample masses for analytical procedures were accurately measured using a calibrated Pioneer™ PX224/1 (OHAUS Europe GmbH, Göttingen, Germany) analytical balance.

2.2. Reagents

Di(2-ethylhexyl) phosphoric acid (D2EHPA), with 97% purity (Sigma-Aldrich, Poznań, Poland) was chosen as the ligand due to its high efficiency in Hf recovery. Kerosene, a commercially available diluent with a density of 0.85 g/dm³, was incorporated as a diluent into the mixture (Sigma-Aldrich, Poznań, Poland). HfOCl₂ standard solution (Sigma-Aldrich, Poznań, Poland) was used to prepare the radiotracer. A total of 65% of the HNO₃ solution was used as a leaching agent (Sigma-Aldrich, Poznań, Poland).

2.3. The Experimental Setup Based on a Mixer–Settler System

The detection of peaks was performed using a Na(Tl) scintillation detector (with TDR v.2.8.0.0 data acquisition software, both manufactured by TD Electronics from Warszawa, Poland). The glass mixer–settler system (SX Kinetics Inc., Cobourg, ON, Canada) was used in the extraction process of Hf. Peristaltic pumps (Masterflex^® L/S^®, Iwaki, Japan) were used to pump the organic and aqueous phases into the mixer–settler system.

The mixer–settler system for pilot scale studies comprises several key components designed for efficient solvent extraction processes (Figure 1). Its features include glass construction for visibility, precise mixing and settling capacities, and reliable peristaltic pumps. Below is a detailed breakdown:

• It consists of a mixing chamber (mixer) with a capacity of 270 mL, allowing for precise control and manipulation of the solvent and feed phases during mixing.
• Decanter (settler): The system includes a decanter with a larger capacity of 1050 mL. The decanter is used for the settling phase of the solvent extraction process, where the phases separate based on their densities. This larger capacity allows for adequate settling time and separation of the phases.
• Peristaltic pumps: The system was equipped with two peristaltic pumps.
• Extraction and re-extraction system: The mixer–settler system is integrated with an extraction and re-extraction system, which involves the use of solvent phases to extract and separate desired components from the feed solution. This system is essential for carrying out solvent extraction processes effectively and efficiently in a maximum of six stages.
• Four scintillation probes with wound- and Pb-shielded tubes.

2.4. The Procedure for Sample Preparation and Analysis

(a)

Leaching

The leaching tests were performed using a 5M HNO₃ solution as the lixiviant alongside 10% ascorbic acid as the reductant. A 3L double-jacketed glass batch reactor was utilized in the process under a steady temperature of 70 °C for 24 h. Thermal regulation was controlled using a thermostat connected to a peristaltic pump, which continuously circulated hot silicon oil in a closed-loop system to the reactor. The reactants were prepared and transferred into the reactor based on a predefined solid-to-liquid (S/L) ratio of 1:7. Constant mixing of the solutions within the reactor was performed using a mechanical stirrer to ensure uniform dispersion of the mixture. The resulting metal-rich solution was passed through 0.45 µm pore-size nylon membrane filters (AlfaChem, Lublin, Poland) and collected in labeled containers for subsequent procedures. A 1M aqueous medium was then prepared for further analysis.

(b)

Solvent extraction process

Ti ore samples were selected for the studies on tracking the recovery of ¹⁸¹Hf using the mixer–settler extraction system. Hf is a very important metal in the nuclear industry because of its high-neutron-absorption cross-section which is used to moderate nuclear reactions in reactors [27]. The radioisotope was prepared by irradiating 1 mg of HfOCl₂ standard solution at the MARIA research reactor in Świerk, Poland. The average cost of irradiation of a sample in such a reactor for 1 h at a neutron flux of 1 × 10¹⁴ [n/cm²s] in a given channel is approximately USD 300. The neutron activation of ¹⁸¹Hf was initiated using the stable isotope ¹⁸⁰Hf (thermal neutron cross-section is 12.87 barns), which captures a neutron to form radioactive ¹⁸¹Hf, shown in Equation (2). ¹⁸¹Hf is a beta-minus emitter and decays by emitting a beta particle, transforming into stable ¹⁸¹Ta with the release of gamma rays. ¹⁸¹Hf has a gamma peak at 482.2 keV with an intensity of 80.6% and a half-life of 42.39 days [28]. Its other gamma-emitting energies are at 56, 57, 65, 136, 345, 476, and 615 keV.

$${}^{180}\mathrm{Hf}+n\to {}^{181}\mathrm{Hf} \stackrel{\mathsf{\beta }-}{\overbrace{\to }} {}^{181}\mathrm{Ta}+{\mathsf{\beta }}^{-}+{\overline{\nu }}_e+\mathsf{\gamma }$$

(2)

Its relatively short half-life has made it a suitable candidate for solvent extraction studies since the short half-life enables online monitoring of the extraction processes and gives accurate information on the behavior of Hf in various extraction systems.

In a clean and dry plastic container, 15% D2EHPA ligand was prepared by using kerosene, which functioned as the diluent. To meet the experimental conditions, aqueous phase (Ti ore leached with 5M HNO₃ + 10% ascorbic acid) and the required concentration of Hf⁴⁺ ions were prepared simultaneously. All components, comprising mixers, settlers, pipes, and pumps, were connected and aligned correctly into the mixer–settler system following the manufacturer’s specifications (Figure 2). Before starting the extraction procedure, the sensitivity and baseline readings of the Na(Tl) scintillation detector were established through calibration. The energy calibration was performed before each experiment using the ¹⁵²Eu standard, with calibration set on five gamma peaks: 344.3, 778.9, 964.1, 1112.1, and 1408 keV.

A total of 400 µL of 1.66 MBq of ¹⁸¹Hf⁴⁺ radiotracer in 1M HNO₃ was quickly injected to the aqueous phase using a syringe to act as a real-time marker for monitoring the effectiveness of recovering Hf. The TDSP spectrometer used to acquire the data was a 512-channel analyzer connected to a computer through an RS-232 cable; it supplied high voltage of 500 to 1200 V to a photomultiplier probe. The SSTD3 probe had an 86 mm diameter NaI (Tl) scintillator and was operated using TDR v.2.8.0.0 software to control operating parameters and to store measured data. The analysis was conducted for around three hours. To aid in the mass transfer of ¹⁸¹Hf⁴⁺ ions into the organic phase, the phases were extensively agitated in the mixer. During the experiment, the devices such as the pumps and stirrers were adjusted to the right pumping and mixing rate. The system was covered on the operators’ side by the flexible lead foil meant to minimize radiation exposure.

The hose pipes linked to the mixer–settler apparatus were wound three times around the probes to increase the volume of the solution enough for count detection. The probes were placed in a lead shield and measured in different phases (inlet organic phase, outlet organic phase, inlet aqueous phase, and raffinate). Calibrated peristaltic pumps were used to pump the organic and aqueous phases into the mixer–settler system. The mixer–settler system was used to run the solvent extraction process at ambient temperature in a 2-stage unit (the total volume of the solutions in the mixers, settlers, and pipes was 2.8 L). The extraction process was initiated by sequentially pumping the aqueous and organic phases into the mixer–settler system. To optimize extraction efficiency, the system was set up to run in a counter-current flow mode, with the organic and aqueous phase flow rates controlled to maintain a 1:1 ratio. The average flow rate for the aqueous phase was 29 mL/min while the organic phase was 24 mL/min.

Readings were taken at regular intervals of 20 s to follow the extraction efficiency of ¹⁸¹Hf⁴⁺ in real time. Radioactivity data were analyzed after the extraction procedure to determine the extraction efficiency of the element of interest. Data collected from the detectors were corrected for background and normalized [29]. Radioactive decay was not corrected because the half-life of the tracer was long considering the duration of the experiment. The obtained corrected data allowed for the calculation of RTD curves, providing insights into the system’s performance and guiding potential improvements. The objective of the RTD analysis was to optimize the system by assessing mean residence time and mixing rate.

(c)

Simulation of the flow dynamics

The software from the International Atomic and Energy Agency, RTD Version 1.0.0.1 (Vienna, Austria), is a special application allowing users to predict the behavior of substances in flow systems utilizing a radiotracer. Using the software, researchers can identify how long material remains in a given system which is important in optimizing processes like mixing, reaction, and separation. The primary functions of the RTD software are to:

• Compute the response: This allows estimation of the response E∗H(t) of a model with respect to the specified inlet signal E(t). Here, H(t) stands for impulse response for the model while E∗H(t) refers to convolution of the inlet signal with the model’s impulse response.
• Optimize model parameters: If the actual system response S(t) has been acquired, the software can use that information to optimize the parameters of the model in such a manner that the calculated response E∗H(t) matches the actual S(t). This optimization is useful in making sure that the model reliably describes the behavior of the system. Some of the common parameters include mean residence time (τ) which denotes the average time a particle stays in the system, helping in understanding flow dynamics and the performance of the mixers in the extraction processes. The exchange coefficient (N) measures the degree of particle exchange between system phases, with high values signifying more efficient mass transfer. The time constant (t) assesses the response of the system to changes, where a short Tm indicates a quick and stable reaction. Péclet number (Pe) offers insight into the relative significance of diffusion and advection (convection) in a fluid system.

The RTD software offers several classical models intended for the simulation and analysis of fluid flow behavior through different system configurations. Each model has certain parameters that are useful for predicting the RTD in radiotracer studies, especially in the liquid phase. For modeling the mixers, the perfect mixers in series with exchange model was selected, depicted by Equation (3). That is because the extraction was performed in two stages, and the model is in the best position to describe such a system. The model assumes a number of perfectly mixed reactors where the fluid is fully mixed before passing to the next stage. This model is particularly applicable for determining RTD in systems that can be modeled as a series of mixed vessels (Figure 3). Ideal stirred vessels connected in a series model are frequently used to describe the systems where it is assumed that the injected tracer is immediately mixed with the entire volume of the system as a result of either mechanical mixing or some circulation. As indicated by its name, the “perfect mixers in series” model is composed of N perfect mixers with the same volume connected in series. In such a case, the concentrations of the tracer at the inlet and the outlet are equal. For an instantaneous injection, the theoretical RTD is given by Equation (3);

$$E\left(t\right)={\left({\displaystyle \frac{N}{\mathsf{\tau }}}\right)}^N{\displaystyle \frac{t^{N-1}\mathit{exp}\left(-\frac{Nt}{\mathsf{\tau }}\right)}{\left(N-1\right)!}}$$

(3)

where N is the number of perfect mixers and τ is the mean residence time.

To compare E(t) curves for different flow conditions and mixing efficiencies, the normalization to dimensionless time θ is performed: θ = t/τ. Then, the normalized RTD function can be expressed in the form of Equation (4):

$$E\left(t\right)=\left[{\displaystyle \frac{N^N}{N-1!}}\right]\times {\mathsf{\theta }}^{N-1}\mathit{exp}\left(-N\times \mathsf{\theta }\right)$$

(4)

For plug flow, N = infinite, and for completely mixed flow, N = 1. For one perfect mixer (N = 1), the theoretical RTD is a simple exponential function. This expression behaves in much the same way as the one for the axial dispersed plug flow model, with N playing the same role as the Péclet number. As N gets larger, impulse response gets closer and closer to that of the axial dispersed flow model. Differences are insignificant beyond N = 25 (for N > 25 the model is almost plug flow and better fits with normal Gauss distribution function) (Figure 3).

The settler part of the system was simulated using the axial dispersed plug flow model [12]. It depicts a system in which the fluid in a reactor or a channel flow in an axial direction, and there is a dispersion of the fluid particles along this direction as they do not flow in a straight line, as is assumed in the plug flow model (Figure 4). This model employs the Péclet number to determine the relative levels of convective transport to dispersive transport, with higher Pe values denoting low dispersion and flow that is closer to plug flow. The mean residence time is also used, and it represents the average time taken by a tracer to stay within the system. For an instantaneous injection, the theoretical RTD is given by Equation (5):

$$C\left(t,x\right)={\displaystyle \frac{M}{\sqrt{4\pi Dt}}}\mathit{exp}\left(-{\displaystyle \frac{{\left(x-Ut\right)}^2}{4Dt}}\right)$$

(5)

where C is concentration at a distance x at time t, D denotes the axial dispersion coefficient, M represents the mass of tracer (moles) injected into the cross-section at the inlet, while U is the mean velocity of advective transport. The model parameter normally used as the index of mixing is the non-dimensional Péclet number, Pe = U/D (Pe = infinite, for plug flow, whereas Pe = 0 for completely mixed flow). In this case, the above formulation is written as shown in Equation (6):

$$E\left(t\right)={\displaystyle \frac{1}{2}}{\left\{{\displaystyle \frac{Pe}{\pi \mathsf{\tau }t }}\right\}}^{{\displaystyle \frac{1}{2}}}exp\left\{-{{\displaystyle \frac{Pe(\mathsf{\tau }-t)}{4\mathsf{\tau }t}}}^2\right\}$$

(6)

The axial dispersed plug flow model has two parameters: τ and Pe. The former sets the time scale of E(t). The curves get sharper and sharper when Pe is increased. They always have one single peak, and the peak height and tail length are correlated (the tail is short when the peak is sharp and vice versa). For Pe > 50 the model is almost plug flow and better fits with normal Gauss distribution function.

The percentage error (δ) difference between the theoretical (υ_t) and experimental mean residence time (υ) was tested using Equation (7).

$$\mathsf{\delta }(\%)=\left|{\displaystyle \frac{\upsilon -{\upsilon }_t}{\upsilon }}\right|\times 100$$

(7)

3. Results and Discussion

3.1. Online Monitoring of the Solvent Extraction Process of Hf

The characterization of Ti ore has been carried out and published quite extensively in our previous studies [15,30]. In these studies, the ore contained different elements at varying concentrations. The ICP-MS showed that the amount of Hf was 67.14 ± 3 μg/L in the 1M HNO₃ aqueous phase. Other metals included Sc, Ti, V, Mn, Fe, Co, Ni, Cu, Zn, Hf, La, Ce, Nd, Y, Pr, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu [30]. The use of neutron activation analysis allows for the activation of specific isotopes of the elements that emit only gamma radiation, enabling precise tracking and analysis. The figures obtained from the experiment show the distribution and mobility of ¹⁸¹Hf⁴⁺ between the organic and aqueous phases in the course of the extraction process (Figure 5).

In Figure 5A, the count rate was very low throughout the experiment (≈0 counts). It shows that there was no ¹⁸¹Hf⁴⁺ in the fresh organic-phase feed (not contaminated with the radioisotope), as expected at the beginning of the experiment. Figure 5B represents the count rate of the inlet aqueous phase. There was a high count rate (around 89,000 counts) at the initial stage of the experiment. This peak represents the point at which the ¹⁸¹Hf⁴⁺ radiotracer was quickly introduced into the aqueous phase. Such impulses were significantly higher than the ones recorded in the outlet organic phase and raffinate demonstrated in Figure 5C,D. The recorded data in these phases ranged from 815 (maximum counts in raffinate phase) to 20,060 (maximum counts in outlet organic phase). This large variation in intensity is linked to the undiluted state of ¹⁸¹Hf⁴⁺ at the time of injection, contrasted to its relatively low concentration in the mixer–settler system, where it became diluted and distributed across the phases.

The counts of the outlet organic phase are shown in Figure 5C, which were comparatively low at the beginning and then increased and reached the maximum at around 50 min. This rise suggests the ability to complex ¹⁸¹Hf⁴⁺ from the aqueous phase to the organic phase as the extraction process continues. The peak indicates the highest level of ¹⁸¹Hf⁴⁺ in the organic phase at that particular time before it reduced as the system approached equilibrium where the extraction efficiency stabilized. Moreover, the reduction in the counts over time could be attributed to the continuous flow of the fresh organic phase into the system which recovered the remaining ¹⁸¹Hf⁴⁺ as the process continued. Figure 5D depicts the raffinate data which were below 815 throughout the experiment. That implies that the extraction of Hf⁴⁺ by the ligand into the organic phase was successful. A cationic exchange process is typically used by acidic extractants (D2EHPA) to remove metal ions (Equation (8)) [31]. The anionic ligand and metal cation interact to create a neutral complex, which dissolves predominantly in the organic phase. Acid extractant extraction depends on pH, so maintaining a stable pH is essential to both the extraction and stripping processes.

$${Hf}_{\left(aq\right)}^{4+}+{4D2EHPA}_{\left(org\right)}\rightleftharpoons {Hf\left(D2EHPA\right)}_{4\left(org\right)}+{4H}_{\left(aq\right)}^{+}$$

(8)

The overall analysis of solvent extraction processes indicated that real-time monitoring using radiotracers is essential in determining the efficiency and the dynamic behavior of the extraction process. The smooth running of the mixer–settler system and the proper working of the peristaltic pumps and stirrers helped in the successful completion of the experiment. Therefore, the minor variations in the time of measurements may not have affected the result significantly.

Figure 6 depicts the data in terms of cumulative counts for the radiotracer analysis of ¹⁸¹Hf⁴⁺ aimed to measure the extraction efficiency of 15% D2EHPA. The count increases steeply in the beginning because the radiotracer was selectively bound and extracted from the aqueous phase by the ligand. The sharp increase in the curve up to 2000 s indicates that most of the ¹⁸¹Hf⁴⁺ was separated in the initial phase of the process. With time, the curve becomes less steep, meaning that the extraction of ¹⁸¹Hf⁴⁺ became less efficient, probably because the D2EHPA was saturated or there were no more ¹⁸¹Hf⁴⁺ ions in the solution. It was evident that near complete recovery of ¹⁸¹Hf⁴⁺ above 95% happened at around 8000 s (133 min) with no significant changes thereafter (Figure 6). From these data, it can be inferred that although the extraction process was efficient in the first stages, the final stages of extraction to nearly 100% require a longer contact time, probably to allow the establishment of equilibrium conditions. The employment of cumulative counts in radiotracer studies is important in the determination of extraction efficiency over time [18]. That is because it combines the rate of extraction and the equilibrium point in the assessment of the efficiency of the extraction system. The results prove the effectiveness of 15% D2EHPA in the extraction of ¹⁸¹Hf⁴⁺ ions from nitric acid solutions.

3.2. ¹⁸¹Hf⁴⁺ for the RTD Studies on the Mixer–Settler System

(a)

The mixer

The data gathered during the extraction process were employed for the RTD studies based on perfect mixers in series with exchange (Figure 7). The simulation of this model yielded the following optimal parameters: a mean residence time (τ) of about 1811 s (≈30.18 min), the exchange coefficient (N) of 5.55, and the time constant (t) of 140 s (≈2.33 min) (

Table 1. The optimization of the parameters in the mixer for the perfect mixers in series with exchange (the unit of τ is seconds, N is dimensionless, while t is also seconds).

Model Parameters	Before Optimization	Optimized Parameters
τ	200	1811
N	10	5.55
t	300	140

). The mean residence time shows that ¹⁸¹Hf⁴⁺ remained in the mixer for half an hour, which was quite sufficient for phase contact and extraction. The exchange coefficient implies that there was little back-mixing within the system. That was beneficial when it came to phase separation during extraction, hence improving extraction rates. The short time constant means that the system was able to give a quick response to any variation in flow or concentration. That was important during the continuous operation of the process at a steady state. The sum of the square of errors (SSE) value given by the model was 0.11195 × 10⁻⁹ (Figure 7). Such a low SSE value indicates that the simulation provided a good fit for the experimental data. That is because the variation between the observed values (from the experiment) and the predicted values (from the model) was relatively small. All these factors point to the fact that the mixer–settler system was effective with the simulated parameters being in good agreement with the required operating condition.

(b)

The settler

The experiment aimed at the RTD investigation of the settler part of the mixer–settler system modeled with the help of the axial dispersion flow model. The values of the optimum parameters derived from this simulation were a mean residence time (τ) of 4165 s (69.42 min) and a Péclet number of 6.67 s (Figure 8 and

Table 2. The optimization of the settler’s parameters using the axial dispersion flow model (the unit of τ is seconds while Pe is dimensionless).

Model Parameters	Before Optimization	Optimized Parameters
τ	70	4165
Pe	10	6.67

). The sum of the square of errors value given by the model was 0.34151 × 10⁻⁹, suggesting that the simulation was reliable. The mean residence time suggests that ¹⁸¹Hf⁴⁺ remained in the settler for more than an hour. This time was enough for the phases to settle out and for ¹⁸¹Hf⁴⁺ to move from the aqueous to the organic phase. The Péclet number, which is a measure of the relative importance of advection to dispersion, indicates moderate dispersion within the settler. The value of 6.67 means that back-mixing existed but was not dominant, and hence, the system can be approximated to behave more like an ideal plug flow reactor while taking into account the effects of axial dispersion. This balance was very important so that the phases had enough contact time for extraction while at the same time reducing remixing. In general, the simulation reveals that the settler works effectively with the right contact time and proper dispersion to enhance the extraction of ¹⁸¹Hf⁴⁺ in the system.

The RTD of the system depended on the contribution from the mixer and the settler where the mixer and settler worked differently. The mixer provided enough contact between phases and primary extraction while the settler helped to separate the phases and improve the extraction efficiency. When the mean residence time from the mixer was added to that of the settler, the overall residence time gained gave the time distribution of the fluid elements within the system. That offered a complete picture of the extraction process, as it occurred in the two stages. Therefore, the overall mean residence of the mixer system was found to be the summation of τ (1811s or 30.18 min) from perfect mixers in series plus the τ (4165 s or 69.42 min) from the axial dispersion model. That total RTD was found to be around 5976 s or 100 min. This approach made it possible to capture all the mixing and settling dynamics, thus providing a more accurate measure of the system performance.

The theoretical mean residence time was found to be 6240 s or 104 min obtained by $\mathsf{\tau }={\displaystyle \frac{V}{Q}}$; where Q denotes the overall flow rate of the system (0.027 L/min) while V was 2.8 L, representing the total volume of the mixers, settlers, and pipes around the probes. There was no significant difference between the experimental (104 min) and modeled RTD (100 min). That is because the computed percentage error was 4%. This small deviation signifies the fact that the actual behavior of the system was as expected from the theoretical model (p > 0.05). The RTDs are close to each other due to the nature of the experimental conditions; therefore, it could be ascertained that the system had good performance.

3.3. Recommendations and Possibilities for the Potential Application of the Radiotracer Studies Based on ¹⁸¹Hf⁴⁺ in the Hydrometallurgical Processes

The developed approach of using radiotracer studies and RTD modeling in the mixer–settler system has a great prospect in hydrometallurgical processes. Thus, the application of radiotracers like ¹⁸¹Hf⁴⁺ enables the direct observation of the extraction process. It provided a comprehensive picture of the distribution and migration of the metal ions between the organic and aqueous phases [32]. This capability could be essential in the separation and recovery of Hf⁴⁺ from complex nuclear waste solutions. For such cases, the extraction environment has to be controlled to achieve high efficiency and high purity of the desired product. The fact that the recovery process can be monitored online means that improvements can be made when necessary to increase extraction efficiency. That makes the approach so beneficial for laboratory experiments and for large-scale industrial use.

Furthermore, the use of this method in the extraction processes of any gamma-emitting radioisotope will result in efficient ways of handling the radioactive materials. The online monitoring technique as exemplified by the extraction of ¹⁸¹Hf⁴⁺ using 15% of D2EHPA allows for the tracking of the extraction process without the need for interruption or for compromising on the safety of the process. The information that is collected from such real-time monitoring could in turn be used to fine-tune the flow rates, residence times, and phase ratios in the recovery process. This will in turn improve the efficiency of the whole process. Furthermore, the signals of radiotracers are detected with great accuracy; any lack of efficiency or departure from the normal extraction process is easily detected, and appropriate corrective measures can be taken. Moreover, during the extraction process, the radiotracer is taken out of the system (and gathered to the canister of the loaded organic) after the extraction process is complete. This rich organic phase after extraction consists of only selected metal ions, which can be stripped (re-extracted) using mixer–settler units. The regenerated organic phase after stripping can be used again in the next extraction process working in a closed-loop system, which, from a hydrometallurgical point of view, has high economical value. The whole system can work for a number of hours without any interruption. This approach is not only a valuable instrument in improving extraction processes in hydrometallurgy but is also an indispensable factor in the management of hazardous radioactive waste.

4. Conclusions

The mining and extraction of strategic and critical metals have been acknowledged as crucial for technology and development. The integration of various methods of analysis could improve the effectiveness of metal extraction procedures. This study successfully demonstrated the application of radiotracer techniques for the real-time monitoring of solvent extraction processes in hydrometallurgy. By employing ¹⁸¹Hf as a radiotracer in a mixer–settler system using D2EHPA as the extractant, the process achieved an extraction efficiency of over 95% within approximately 133 min. The residence time distribution (RTD) analysis, modeled using the perfect mixers in series and axial dispersion approaches, confirmed the accuracy of the system simulations and provided valuable insights into the hydrodynamic behavior of the process. The calculated mean residence time of 100 min closely aligned with the theoretical value of 104 min, further validating the robustness of the modeling approach.

This study highlights the advantages of radiotracer techniques over conventional monitoring methods which require invasive sampling and cause time delays and potential human errors. In contrast, radiotracer monitoring enables precise, non-invasive tracking of metal distribution through different phases, ensuring real-time data acquisition with high sensitivity. This kind of approach is crucial for optimizing process conditions, reducing operational interruptions, and minimizing reagent consumption.

The selection of ¹⁸¹Hf as the radiotracer proved advantageous due to its suitable half-life of around 42 days, which is long enough to facilitate extended process analysis while minimizing radioactive waste generation. The ability to conduct radiotracer experiments with minimal environmental impact and operator exposure makes this approach both practical and sustainable for industrial applications. Moreover, the method’s adaptability allows for potential applications in various solvent extraction systems using a proper radiotracer, extending to other critical and rare metals essential for industries.

The results of this study highlight the great potential of radiotracer methodologies in the field of hydrometallurgy, particularly in enhancing process control, increasing metal recovery rates, and reducing resource wastage. Future research should focus on expanding the application of radiotracers to different extraction systems, optimizing modeling techniques for complex flow dynamic studies, and even integrating artificial intelligence (AI)-driven data analysis to further improve process efficiency. Additionally, scaling up these methodologies for industrial implementation will be essential to fully realize the benefits of real-time monitoring in large-scale solvent extraction operations.