Subsurface storage of gases is becoming increasingly important, both for the mitigation of CO₂ emissions and for providing storage for dense energy carriers such as hydrogen as part of the ongoing energy transition (Krevor et al. 2023). However, ensuring the security of subsurface CO₂ storage, especially at early stages, is a technically challenging task. This is due mainly to the risk associated with the high mobility of CO₂, which may lead to leakage. In general, the storage security depends on a combination of evolving physical and geochemical trapping mechanisms (see Fig. 1) (IPCC 2005).

Changes in trapping mechanisms and geologic storage security over time

Since physical trapping mechanisms dominate at the early stages of storage, achieving a high displacement efficiency is crucial for efficient storage. Due to the low density and viscosity of gases, CO₂ exhibits high mobility within porous media, and its continuous injection into the subsurface can result in poor sweep efficiency (Aryana and Kovscek 2012). Injection methods, such as water-alternating-gas (WAG) and CO₂-foam help control gas mobility and improve displacement efficiency for CO₂-enhanced oil recovery (CO₂-EOR) and geologic carbon sequestration (Massarweh and Abushaikha 2021; Orujov et al. 2023; Guo and Aryana 2018). Laboratory experiments show that the use of CO₂-foams leads to increased storage capacity (Føyen et al. 2020; Guo et al. 2019). Foams consist of a discontinuous gas phase separated by a continuous liquid film, known as lamellae (Hirasaki and Lawson 1985). The use of foaming agents, such as surfactants, in conjunction with CO₂ can increase the apparent viscosity of foams by one or two orders of magnitude (Worthen et al. 2013). However, foams are often thermodynamically unstable. One approach to increasing their stability is to use nanoparticles along with surfactants (Guo et al. 2017; Emrani and Nasr-El-Din 2017). Silica, fly ash and iron-oxide (IO) nanoparticles have been shown to improve volumetric sweep efficiency when injected together with surfactants and CO₂ (Guo et al. 2017; Emrani and Nasr-El-Din 2017; Guo and Aryana 2016; Huh and Cho 2018). Nanoparticle-stabilized CO₂-foams are more stable than conventional or surfactant-stabilized foams, especially under high salinity, high-temperature subsurface conditions (Huh and Cho 2018). Therefore, applying nanoparticles for foam stabilization not only enhances the thermodynamic stability of foams, but also helps to control gas mobility, improves sweep efficiency, and enhance gas storage capacity (Rognmo et al. 2018). Some nanoparticles, such as IO, possess magnetic properties due to the atomic structure of iron (Teja and Koh 2009). These properties make IO nanoparticles extremely useful in various fields, including medicine for cancer therapy, drug delivery, and obtaining high contrast tomographic images of the human body, among others. (Chandrasekharan et al. 2018; Hergt et al. 2006). Recognizing these distinct properties, some researchers have investigated the potential use of paramagnetic IO nanoparticles as nano-sensors and for acoustic imaging of the subsurface, particularly during EOR applications (Zhang et al. 2011). For instance, Prodanovic et al. (2010) and Ryo et al. (2012) have theoretically and experimentally shown that paramagnetic nanoparticles used for formation evaluation can also be used for reservoir monitoring due to their unique magnetic properties. Reservoir monitoring is a critical yet underdeveloped aspect of geological CO₂ storage that is essential for ensuring safety and security. Additionally, in the U.S., testing and monitoring the CO₂ plume through direct and indirect methods is a federal requirement for class VI wells, which are designated for geological CO₂ storage (Epa 2022). At present, the most effective method for subsurface monitoring is time-lapse seismic imaging, which is costly and has limited application for monitoring gases (Huang 2022). Therefore, there is a knowledge gap and a research need to develop new monitoring technologies for subsurface gas storage. One of the most challenging issues with nanoparticles in complex environments, including subsurface and biological environments, is their transportability. Additionally, applied magnetic forces weaken quickly over distance, and the presence of fluids in the medium can significantly affect the transport rate (Wirthl et al. 2024). Computational techniques have been developed to study the transportability and transport phenomena of nanofluids in various, but mostly for simple geometries (Basha et al. 2024). However, in experimental environments, assessing the transportability of these particles relies on the ability to detect their presence over distances.

In this paper we developed two methods to detect the presence of IO nanoparticles in subsurface fluid chemistry. The presence of these nanoparticles, particularly in the context of nanoparticle-stabilized CO₂-foam injection serves as an indicator for the extent of the CO₂ plume in the subsurface. Consequently, these methods hold potential for aiding in the monitoring of CO₂ plumes within the subsurface.

Two different nanoparticles, referred to as NP#1 and NP#2, were used during the experiments employing the two approaches. Transmission Electron Microscopy (TEM) results show that NP#1 consisted of Fe₃O₄ nanoparticles with an average size of 15 ± 5 nm, synthesized by Guo et al.(2017) and shown to improve CO₂-foam stability and displacement efficiency. NP#2 comprised commercially available nanoparticles from U.S. research Nanoparticles, Inc., with an average particle size of 100 nm per TEM results. Aqueous nanoparticle solutions were prepared under constant ultrasonication by a probe sonicator (QSonica Q700) to prevent agglomeration prior to experiments. To determine the aqueous stability of the nanoparticles, a Brookhaven Zeta PALS instrument was used to obtain the average hydrodynamic diameter, zeta potential, and particle size distribution data. Zeta potential measurements were performed using 0.01 M KCl nanoparticle solutions in DI water for preventing polarization and maintain a constant ionic strength. Figure 2 shows the intensity (%) versus particle size distribution of the particles, and the mean hydrodynamic diameter, polydispersity index, and zeta potentials for NP#1 and NP#2 as tabulated in Table 1.

Hydrodynamic size and size distribution of nanoparticles in DI water

DI water was used as the solvent during the experiments unless specified. Additionally, lab grade salts—NaCl, KCl, CaCl₂·2H₂O and MgCl₂·6H₂O—and surfactants Alpha-olefin sulfonate (AOS) and 35% active Lauramidopropyl betaine (LAPB) were used to replicate foams in subsurface settings. Table 2 shows the details of salts and surfactants used for the experiments.

The magnetic properties of the nanoparticles were measured using vibrating-sample magnetometry (VSM) in a Physical Property Measurement System (PPMS) from Quantum Design. Figure 3 shows the magnetization curves for NP#1 and NP#2.

Magnetization curve for a NP#1 and b NP#2

The reported saturation magnetization values are obtained using the asymptotes of the magnetization curves in Fig. 3. The magnetometry results indicate that NP#1 has a saturation magnetization of 70.1 emu/g, whereas NP#2 has a saturation magnetization of 65.7 emu/g, with coercivities (H_c) of approximately 1 mT (107.5 for NP#1 and 104.34 Oe for NP#2). These findings suggest that both nanoparticles are ferromagnetic and the obtained values are in agreement with the literature (Guo et al. 2017; Bharath et al. 2023).

2.1 Methods

2.1.1 Induction Heating Method

The first approach for detecting the presence of nanoparticles in complex fluids involves recording the temperature rise of nanoparticle carrier fluid when exposed to a magnetic field. This rise in temperature is due to the losses that occur during the magnetization reversal process of magnetic nanoparticles subjected to an alternating magnetic field (Hergt et al. 2006). Magnetic nanoparticles, including IO, are used for similar approaches in diverse applications such as intercellular hyperthermia in medicine (Kobayashi 2011). The colloidal suspension of nanoparticles in a carrier fluid, known as nanofluids, generates heat. This heat in magnetic nanofluids is the sum of the relative contributions of hysteresis loss, Neel, and Brownian relaxations, which depend on multiple factors including particle size and composition (Ahmed et al. 2020; Tiwari et al. 2022). The Rosensweig equation (Eq. 1.) is an analytical formula that demonstrates the relationship between the dissipated power, P, the magnetic field, and the fluid’s magnetic properties. This equation is expressed as (Rosensweig 2002)

where, \({\mu }_{0}\) is the permeability of free space, \({\chi }_{0}\) is the equilibrium magnetic susceptibility of the particles, H denotes the magnetic field intensity, f is the frequency of the magnetic field, and \(\tau\) is the effective relaxation time, a combination of Néel and Brownian relaxation times. These relaxation times are a function of several key parameters related to the magnetic properties of the nanoparticles including nanoparticle size, magnetic anisotropy, core properties, surface characteristics, surrounding environment, and the frequency of the applied magnetic field (Rosensweig 2002). According to Eq. 1, the heating power loss increases as a function of both the frequency (f) and the field intensity (H) (Hergt et al. 2006). Therefore, to achieve high heating power, selecting a source with maximum field amplitude and frequency is crucial. However, obtaining a large field amplitude at high frequency presents a technical challenge (Hergt et al. 2006) and it also increases the cost of the power supply (Mei et al. 2018).

We constructed an experimental setup using an IHG-10 induction heating (IH) unit by Across International®. The power supply unit can resonate within a 100–500 kHz frequency range with a maximum input power of 10 kW. Through experimentation, we discovered that a custom C-shaped coil (see Fig. 4) produces a larger temperature change (ΔT) and offers a larger inner space for the sample holder compared to a cylindrical coil of similar overall dimensions. The heater is coupled with a chiller (WAC-4 by Across International®) to prevent overheating the heater’s electronics and the induction coil. A schematic of the experimental setup is shown in Fig. 4.

Experimental setup for induction heating of magnetic nanoparticles

Thermal measurements in an induced high-frequency magnetic field are challenging. Therefore, an IR pyrometer (Optris®, Csmicro LT15) with an 8 -14 µm spectral range and adjustable emissivity and transmissivity function was used to measure and record the temperature changes from a distance on the solution’s surface. A special sample holder was designed to insulate the samples as much as possible to prevent heat exchange between the samples and their surroundings.

The dimensions of the sample holder were determined based on the distance to spot (D:S) ratio of the pyrometer, the distance from the induction coil, and the inner diameter of the coil. The magnetic field and field distribution of the C-shaped induction coil were simulated using the AC/DC Magnetics toolbar in COMSOL Multiphysics®. A 1:1 scale 3D geometry of the coil, due to its complex geometry, was modelled in SolidWorks® and imported into COMSOL. The calculation of the electromagnetic field around an inductor depends on the ability to solve Maxwell’s equations in the frequency domain, given the initial and boundary input conditions (Rudnev et al. 2017). Figure 5 shows the magnetic flux density norm from the simulations.

Magnetic flux density norm (T) for a C-shaped induction coil. Simulations were performed in the frequency domain (180 kHz) with a coil current of 45.1 Amps

Simulations indicate that the magnetic flux density is mostly uniform in the middle of the coil.

2.1.2 Oscillator frequency shift method

The second approach for the detection of magnetic nanoparticles involved monitoring the frequency shift of a transistor oscillator circuit. This type of electronic oscillator generates a sinusoidal voltage waveform at its output, where the oscillation frequency depends on the inductance and capacitance in the feedback loop of the oscillator. The presence of magnetic nanoparticles creates a slight change in the magnetic permeability inside a coil, thereby altering the coil’s inductance and resulting in a shift in the oscillator’s frequency. To maximize the frequency shift, we chose a Colpitts oscillator configuration, which utilizes a single inductor and two capacitors, for this application. The key to this detection scheme is the frequency stability of the oscillator itself, as the anticipated shift in frequency due to the magnetic nanoparticles is expected to be very small. There is an inherent limit to the frequency stability related to the load/losses in the oscillator. Consequently, we chose a JFET common drain (CD) configuration. The high input impedance of this amplifier configuration results in minimal loading of the oscillator. While capacitors typically exhibit low loss, inductors can be quite lossy due to their construction, essentially a wire wrapped in a cylindrical fashion. This can significantly reduce the frequency stability of the oscillator by lowering the Q of the resonant LC circuit. To minimize the inductor losses, we wound our custom coil using Litz wire, consisting of 175 strands of 46 AWG wire, around a plastic tube with an outside diameter just under 16mm. The 50 turns resulted in a coil length of approximately 37.5 mm and a free air inductance of approximately 14.5 µH.

The final circuit is depicted in Fig. 6. The J309 represents the low noise JFET used in the CD amplifier, and the OP27A is serves as a buffer amplifier to prevent any connected devices from loading the oscillator. Resistor R1 sets the bias of the CD amplifier stage to just under 3 mA and also provides bias stability. The 6V source is two 2032 Li batteries in series, chosen for their low noise and drift, which are essential to the frequency stability of the circuit. The values of the feedback capacitor divider, C1 and C2, were chosen to produce an oscillation frequency of around 500kHz, in accordance with the Colpitts oscillator, Eq. (2). Additionally, it is generally observed (Hajimiri and Lee 1998) that a C1/C2 ratio of around 0.25 yields optimal frequency stability. Readily available capacitors from the stockroom were used, but more temperature-stable COG capacitors would likely have produced better results.

JFET Colpitts oscillator circuit with buffer amplifier

It was also found that external forces on the circuit impacted frequency stability. Consequently, the entire circuit was housed in a metal box to shield it from surrounding electromagnetic fields and temperature fluctuations in the lab. A hole was drilled in the top of the box, directly above the coil, to allow for the placement of the sample inside the coil. The output of the oscillator circuit was then connected to a BK Precision 1823A frequency counter, which can accurately measure the oscillation frequency with sample times of up to 10 s. The longer the sample time, the more precision can be achieved in the frequency measurement. We choose a 1-s sample time as a reasonable compromise between displayed precision and thermal drift.

3.1 Induction heating method

Solutions of NP#2 were exposed to an alternating magnetic field generated by the IH. Three identical samples of 60, 120, 250, 500, 1000 mg/L concentrated Fe₃O₄ were prepared using 10 ml DI water as the solvent. All samples were sonicated before being placed in the sample holder and exposed to the magnetic field for a period of 320 s at near room temperature. ΔT values across a wide range of NP concentrations were obtained. For comparison, initial temperature values were extracted from all curves, and the resulting data is plotted in Fig. 7.

T versus time for different nanoparticle solutions and DI water. The error bars are only shown for some of the data points to help with readability

Although an overall increasing trend was observed for all samples, those with higher magnetic particle concentrations generated more heat, as predicted. The ΔT associated with DI water is assumed to be due to unwanted heat transfer from the induction coil. Water circulates inside the coil that was cooled down by the chiller, which operates in cycles. The cooling cycle rapidly cools the water for a few minutes, and the pump continuously circulates it through the coil. Therefore, this is observed as temperature fluctuations (drops and rises) for DI water and samples with lower concentrations of particles in the graph. This heat could not be completely eliminated despite all efforts but may be accounted for in each sample’s analysis. The data shown in Fig. 7 were corrected by subtracting the initial temperatures and adjusting for temperature fluctuations due to the cycles of the chiller. It is also notable that the lower error bar associated with the 60 mg/L concentration overlaps with the positive error bar of DI water. Thus, the sensitivity of this approach was determined to be between 60 and 120 mg/L. ΔT values associated with each concentration at the end of 320 s are presented in Table 3.

Analyzing ΔT versus different concentrations of nanoparticles aids in understand the relationship between these two parameters. Temperature is a directly measurable parameter that can be correlated to the concentration of nanoparticles in the solution. Although in magnetic hyperthermia applications, Specific Loss Power and Specific Absorption Rate are often calculated due to regulatory requirements associated with electromagnetic radiation and human health, temperature change (ΔT) is the appropriate measure in the context of the detection of nanoparticle is solutions. A linear fit derived from 13 datapoints yields an R² value of approximately 0.98. Figure 8 illustrates the relationship between the ΔT and the concentrations of Fe₃O₄ nanoparticles. At first glance, the data from 0 to 200 mg/L in Fig. 8 seem to have a different linear trend than the overall linear fit. We attribute this apparent trend to the contribution of measurement errors associated with the preparation of the nanoparticle in water and discrepancies due to the water chiller circulation cycles.

Temperature change versus concentration of nanoparticles (NP#2)

Some authors have examined the impact of physiological components such as ions and proteins on the heat dissipation of magnetic IO nanoparticles in suspensions (Kalidasan et al. 2018). To test the effect of major ions commonly found in subsurface water chemistry on ΔT, 15,000 mg/L of four different chloride salts were added to 1000 mg/L of NP#2 separately. Figure 9 shows the ΔT generated in each case.

ΔT and ionic strength of the solution, generated by adding various salts (15,000 mg/L) to DI water along with 1000 mg/L of NP#2

Kalidasan et al. 2018 also found that the presence of ions and proteins can significantly affect the heating efficiency of a solution under applied magnetic field. According to their study, ions contribute positively to heating efficiency due to their mobility and diffusivity. In contrast, the presence of proteins impedes the overall temperature rise. The study also noted that the same concentration of different salts might contribute differently to the temperature increase (Kalidasan et al. 2018).

Further investigation has been carried out to detect the individual and combined effects of these salts, a mixture of surfactants (AOS and LAPB) and NP#1. A two-level, 2⁶ factorial design was employed for this purpose. Factorial designs allow for the measurement of the effect of each factor (independent variable) and the interactions of their effects on a single dependent variable (response variable). These independent variables can have different “levels”, but two-level factorial designs are the most common. The high levels of these factors were chosen based on the average concentrations of those ions in saline water (Silva et al. 2015) and optimal concentrations of surfactants and nanoparticles for foam stabilization (Guo et al. 2017). Table 4 presents the factors, their nomenclature, and levels used in the factorial design.

The effects of these factors were investigated based on the results from 128 experiments performed in the lab. Statistical analysis software, Minitab®, was used for this purpose. The following chart, known as a Pareto chart, was generated by Minitab® and is a very useful tool to summarize the magnitude and relative importance of factors and their combinations (see Fig. 10) (Table 4).

Pareto chart from the experimental design, where the response is ΔT and α is set at 0.005. Only the 30 most significant effects are shown. The reference line (dashed red line) indicates which effects are statistically important

As can be observed, the importance of Factor A, representing the presence of nanoparticles, is several times higher than that of other individual factors or their combinations. Based on Fig. 10, most combined effects appear to be statistically insignificant, as they fall below the reference value. However, certain combinations, such as the presence of surfactants and various salts, demonstrate a noticeable impact on temperature change. The temperature response of nanoparticles under an applied magnetic field is influenced by a multitude of complex factors. This trend is likely attributable to phenomena such as changes in nanoparticle aggregation, variations in solution conductivity and ionic strength, and the occurrence of chemical interactions and complexations among nanoparticles, surfactants, and ions (Kalidasan et al. 2018).

3.2 Oscillator frequency shift method

The frequency versus time data were obtined by inserting the sample with different nanoparticle concentration inside the custom coil of the circuit described in Fig. 6. The process was repeated at least three times, and the average Δf (Hz) values were calculated. The frequency drop, associated with the change in magnetic permeability inside the coil, can be clearly seen by plotting the frequency values against time for each concentration. Figure 11 illustrates a frequency versus time graph and the experimental procedure for a 1000 mg/L NP#1 solution in DI water.

Frequency versus time plot for 1000 mg/L Fe₃O₄ nanoparticles in DI water

Experiments conducted with various concentrations showed an overall increasing trend in Δf corresponding to the increasing nanoparticle concentration, as depicted in Fig. 12.

Corrected values of frequency drop versus nanoparticle (NP#1) concentrations

A good linear fit with an R² value of 0.93 indicates that the relationship between Δf and nanoparticle concentration is linear. It is worth mentioning that an average of frequency shift of 17.6 Hz was also observed for the control sample (DI water). This could be explained by the combination of multiple effects, including high dielectric constant of DI water, which influences parasitic capacitance, thermal instability of circuit elements (especially capacitor), and disruption of magnetization flux during experiments. Therefore, the sensitivity of this method is estimated at approximately 150 mg/L NP#1 concentration.

Two nanoparticle detection methods, namely Induction Heating (IH) and Oscillator Frequency Shift (OFS), were introduced and experimentally tested. Each approach aims to detect small amounts of magnetic IO nanoparticles in different solutions and to establish the relationships between response and nanoparticle concentration. The IH approach applies a high-frequency AC magnetic field around a nanoparticle solution, generating heat primarily based on the amount of nanoparticles present. This heat generation is a result of a combination of multiple relaxation mechanisms (Néel and Brownian) and hysteresis losses. With the constructed experimental setup, a temperature change of 11.3 K was observed in a suspension of 1000 mg/L magnetite nanoparticles in water. These unique properties have recently led investigations into magnetic nanoparticles for cancer therapy in medicine, where biological constrains are present. However, these constraints do not apply in our case. Additionally, it was found that the presence of some ions and surfactants, which are present in subsurface fluid chemistry, also influence the generated heat. A linear relationship between the concentration of magnetic nanoparticles and temperature response was established. The IH approach successfully detected 60–120 mg/L of Fe₃O₄ nanoparticles in DI water.

The OFS method, a novel approach, detects the presence of magnetic nanoparticles based on their relative magnetic permeabilities. We constructed a transistor oscillator circuit with a stable resonance frequency for this purpose. A shift in the resonance frequency was observed when changing the medium inside the coil of the circuit, due to a change in inductance. This shift was measured for various experiments with nanoparticle solutions, and a linear relationship was established between the concentration of magnetic nanoparticles and the frequency shift. For the suspension of 1000 mg/L magnetite nanoparticles, an average drop of 25 Hz in resonance frequency was observed. The OFS method detected concentrations as low as 150 mg/L of Fe₃O₄ in DI water. However, both approaches can further be improved, and their sensitivities increased. These methods may potentially serve as a foundation for subsurface monitoring technology in geological sequestration projects.

Potential future work may include enhancing the experimental setup for both the Induction Heating (IH) and Oscillator Frequency Shift (OFS) methods. Potential improvements center around achieving better insulation of the test samples. For the IH method, unwanted heat transfer from the induction coil to the liquid sample might be minimized via a vacuum insulation to mitigate the impact of external temperature fluctuations on the recorded data. In the case of the OFS method, the entire circuit, especially the coil, is highly sensitive to environmental factors such as temperature and dielectric constant variations. Therefore, implementing an automated system with improved insulation could help minimize ambient influences.