IPTC-18090-MS

Evaluation of Superparamagnetic Nanoparticle-Based Heating for FlowAssurance in Subsea Flowlines

Prachi Mehta and Chun Huh, Center for Petroleum and Geosystems Engineering, The University of Texas atAustin; Steven L Bryant, Center for Petroleum and Geosystems Engineering, The University of Texas at Austin,Current address: Department of Chemical and Petroleum Engineering, University of Calgary

Copyright 2014, International Petroleum Technology Conference

This paper was prepared for presentation at the International Petroleum Technology Conference held in Kuala Lumpur, Malaysia, 10–12 December 2014.

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Abstract

Flow assurance is a critical problem in the oil and gas industry, as an increasing number of wells aredrilled in deep water and ultra-deep water environments. High pressures and temperatures as low as 2° Cin these environments hinder flow of hydrocarbon-based fluids by formation of methane hydrate and wax.Commonly used methods for flow assurance in flowlines are chemical injection and direct electric heatingwhich face several limitations. In this paper, an application to use superparamagnetic nanoparticle-basedheating for flow assurance, in the form of a magnetic nanopaint is presented. Superparamagneticnanoparticle-based heating has been extensively researched in the biomedical industry for cancer treat-ment by hyperthermia. Superparamagnetic nanoparticles in dispersions generate heat by application of anoscillating magnetic field as explained by Neel’s relaxation theory. In our application, superparamagneticFe3O4 nanoparticles are embedded in a thin layer of cured epoxy termed ‘nanopaint’. This nanopaintcoating on the internal surface of subsea flowlines could generate heat and thus prevent formation ofmethane hydrates and wax.

In this paper, parameters affecting heating performance of superparamagnetic nanoparticles such asparticle size, and magnetic field and frequency are discussed. Rigorous characterization of nanoparticlesand nanopaint performed using VSM, TEM etc., is used to quantify heating performance and optimize it.Heating performance of two samples of Fe3O4 nanoparticles varying in size distribution is evaluated inbatch experiments and compared to Neel’s relaxation theory. Performance of nanopaint to heat static/batch fluids and flowing fluids is evaluated. Heating performance of superparamagnetic nanoparticles indispersions and in nanopaint is found to be similar and so it is concluded that Neel’s relaxation theory isapplicable to nanopaint. Heating performance of nanopaint is flow experiment is found to be better thanin batch experiments by a factor greater than 5.

IntroductionFlow assurance is the ability to transport hydrocarbon-based fluids economically and safely from thereservoir to production facilities, over the life of the field. With increasing oil and gas production from

deep-water and ultra-deep water wells, flow assurance has become a critical problem for the oil and gasindustry. Subsea wells are at greater risk of deposit formation due to low temperatures and high pressuresin deep water environments. Methane hydrate formation and wax deposition severely limit productionrates, pose safety concerns and may also result in the shutdown of the well. Hence various methods areemployed for remediation and prevention of flow assurance problems, primarily relying on the principlesof temperature increase, pressure reduction or mechanical removal. These methods include use of piggingsolutions, chemical additive injection, SGN (nitrogen steam generation) process, direct electric heating,heated pipe-in-pipe (Hpip) solutions and have been previously summarized in [1]. Commonly usedmethods in the industry are chemical injection and direct electric heating. In chemical injection, a glycolusually methanol is injected into the pipeline to lower the hydrate formation temperature. However, highcosts and concentration limits imposed by quality control limit their usage. In direct electric heating,electricity is forced through tracer cables laid along the length of the flowline. Temperature can becontrolled by varying the power input to the system and variable heating rates can be obtained. However,there is risk of electricity leakage and component failure due to excessive heating. In this paper, we usesuperparamagnetic nanoparticle-based heating to address the issue of flow assurance.

Superparamagnetic nanoparticles (SPM-NPs) have been used for selectively heating tumor cells, asdiscussed in [2], [3]. Heating by SPM-NPs is induced by application of an oscillating magnetic field, asexplained by Neel’s relaxation theory. Applications involving SPM-NPs have several merits: a) controlover surface area of heating; b) localized heating; c) control of heating rates by varying concentration ofnanoparticles and magnetic field; d) moderate requirement of infrastructure or chemicals; and hence, useof these for prevention and remediation of problems associated with cooling-induced deposition of solidsis an interesting application. Earlier work in this field [4] has described heating of superparamagneticnanoparticles in liquid and embedded in a solid by freeze-drying. However, it does not discuss the abilityof nanoparticle embedded solid medium to transfer heat to a fluid. The novel application of nanoparticle-based paint for flow assurance is first described in [5]. The ability of nanopaint to heat fluids in static andin flow system has been discussed [5]. This nanopaint has the potential to efficiently heat up a thin layerof hydrocarbon at the immediate vicinity of pipe’s inner surface, by converting the energy of appliedmagnetic field to heat. However, the characterization of nanopaint; and limits and parameters that affectnanopaint-based heating has not been discussed. Heating by SPM-NPs is mainly dependent on particlesize distribution, magnetic field, and frequency, among other parameters. It is important to understandthese limits and parameters to optimize heating performance of superparamagnetic nanoparticles. Thefocus of the current paper is to perform rigorous quantification of the nanopaint; and the identification andquantification of the governing parameters to optimize nanopaint-based heating in batch and flowexperiments.

In the present work, two commercially available superparamagnetic Fe3O4 nanoparticles are evaluatedin terms of their heating performance and physical properties that affect heating. Rigorous characterizationof nanopaint is presented. Heating performance of nanopaint is evaluated for two different scenarios,heating batch fluid (static) in a nanopainted container, and heating fluid flowing through a nanopaintedpipe. The comparison of physical properties of the two nanoparticle samples; heating performance ofnanoparticles in two different medium, liquid and solid paint; and heating performance in batch and flowexperiments, are discussed in detail.

Magnetic nanoparticle-based heatingTheoryThe principle of superparamagnetism is briefly discussed here. Ferromagnetic nanoparticles (�100 nm forFe3O4) are multi-domain structures whose direction of magnetic moment varies across domains, thusresulting in zero net magnetic moment. As the particle size is decreased, domain walls collapse in favorof the more energetically stable single domain state. For nanoparticles with a single magnetic domain,

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magnetic moment lies on a preferred easy axis,determined by magnetic anisotropy (dependent oncrystal structure and shape). There exists an energybarrier that needs to be overcome for the particlemoment to change direction called the activationenergy. As the particle size is further decreased, thisactivation energy becomes small and can be sup-plied by thermal fluctuations under normal condi-tions. At this limit, the particles transition into thesuperparamagnetic state. Superparamagnetic nanoparticles (SPM-NPs) have zero coercivity and zeroremanence, i.e., no hysteresis.

Heat generation by SPM-NPs is by relaxation of magnetic moment as it crosses an energy barrier inthe presence of oscillating magnetic field. At a sufficiently high frequency of the applied magnetic field,the magnetic moment relaxation is almost entirely internal, i.e., with negligible rigid body movement ofthe particles. This process is called Neel’s relaxation. Heating also occurs due to rigid body rotation ofparticle called Brown’s relaxation. However, for frequencies of interest, Neel’s relaxation is the primarymechanism of heating. Detailed discussion of the theory of SPM-NP based heating can be found in [6],[7]. The heating performance is described in [8], [9] in terms of specific absorption rate (SAR) as the heatenergy produced under certain conditions of magnetic field and particle properties. Theoretically, SAR isgiven by,

(1)

(2)

where SAR � specific absorption rate (W/g), m � �oMdV is the magnetic moment (Jm/A), Md is thedomain magnetization of nanoparticle (A/m), �o is the permeability of free space (N/A2), H is themagnetic field amplitude (A/m), f is the frequency (Hz), T is the temperature (°K), V is particle volume(m3), KB is Boltzmann constant (J/K), K is volumetric magnetic anisotropy of nanoparticle (J/m3), �o isa constant and �N is the Neel relaxation time (s). SAR shows quadratic dependence on magnetic fieldstrength and is inversely proportional to temperature. Superparamagnetic nanoparticles undergoing Neel’srelaxation are known to follow this dependence. Empirically, SAR for batch experiments can becalculated from the measurement of temperature increase for a SPM-NP sample subjected to a prescribedmagnetic field oscillation by,

(3)

where Cp,system is the specific heat capacity (Jg-1K-1) of the system (nanoparticle dispersion/nanopaint-water system), �T is the temperature rise in the system during an increment of time �t, WNP is mass ofnanoparticles in the sample, Wsample is the total mass of the sample (nanoparticle dispersion or nanopaint-water system). According to (1), SAR is independent of nanoparticle concentration (WNP/Wsample),thermal properties of the medium/system containing nanoparticles, and time of measurement. Hence, SARshould essentially be the same for the same nanoparticles at different concentrations, except whenmagnetic interaction between individual nanoparticles sets in. In literature, SAR values as high as 400W/g have been reported [10]. The physical limit of hyperthermia by superparamagnetic nanoparticle isdescribed by Neel’s relaxation theory [11]. Heating performance of magnetic nanoparticle can becontrolled by variation of particle size, applied field frequency and amplitude [4], [12]. It is important to

Table 1—Values of parameters used for prediction

Symbol Value

Md (KA/m) 447

�o(s) 10-9

KB (J/m3) 1.38 E-23

K (J/m3) 8000

T (°K) 298

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understand these limits and parameters to optimize heating performance of superparamagnetic nanopar-ticles.

Theoretical prediction of parameters that affect heating performanceThe importance of nanoparticle size, magnetic field and temperature on heating efficiency optimizationis demonstrated employing the theoretical SAR equation (1) and (2). The values of the parameters [9] usedfor these predictions are shown in Table 1.

Particle size Prediction of SAR as a function of nanoparticle diameter at two frequencies of interest, 450kHz and 630 kHz, is shown in Figure 1a. It shows a sharp increase in SAR across a narrow size range.There is a shift in the peak as the frequency changes. SAR is highest for a certain nanoparticle size range.So, SAR optimization is dependent on nanoparticle size distribution for a given magnetic field amplitudeand frequency.

Magnetic field strength/amplitude Prediction of SAR at 450 kHz as a function of magnetic fieldstrength is shown in Figure 1b. It shows that SAR dependence on particle diameter does not shift andsimply scales up with the square of the magnetic field.

Temperature Prediction of SAR as a function of temperature is shown in Figure 2. It is seen that heatingrate decreases at higher temperatures. Thus the ability to transfer heat generated in nanopaint to the fluidflowing past the nanopaint will be an important factor for overall performance. Localized heat accumu-lation due to poor thermal conductivity can thus result in significant decrease in SAR with time.

Application to nanoparticle/epoxy compositeThe application of nanopaint exploits the fact that superparamagnetic nanoparticles can generate heatwhile fixed in a solid medium. The paint is simply a method of fixing a thin layer of nanoparticles to asurface. Here we use the approach of Davidson et al. [5] in which magnetite nanoparticles are embeddedin epoxy to create nanopaint. The nanopaint is then applied to the surface of the object to be heated, andafter drying the nanopaint is capable of generating and dissipating heat to its surroundings. The focus ofthe current paper is the identification and quantification of the governing parameters for the optimizationof nanopaint-based heating in batch and flow experiments. This necessitates the description of SAR in aflow system, and is calculated by,

Figure 1a—Prediction of SAR dependence on nanoparticle diameter and frequency at H�600 A/m and K�8000 J/m3

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(4)

where is the mass flow rate (g/s) of the fluid flowing through the pipe, Cp,system is the specific heatcapacity (Jg-1K-1) of the flowing fluid plus the nanopaint on the pipe wall, �T is the temperature rise ofthe fluid between outlet and inlet, and WNP is total mass of nanoparticles in the nanopaint.

Materials and MethodsMaterials

All investigations presented in this paper are based on iron oxide (Fe3O4) nanoparticles (EMG 1400and EMG 605) procured from Ferrotec, Germany. EMG 1400 with hydrophobic surface treatment wasprovided as Fe3O4 solid and EMG 605 with a hydrophilic surface treatment was provided as an aqueousdispersion at a concentration of 15 – 18 wt. % Fe3O4. In our experiments, EMG 1400 was dispersed in

Figure 1b—Prediction of SAR dependence on nanoparticle diameter and magnetic field at f�450 kHz, K�8000 J/m3

Figure 2—Prediction of SAR dependence on temperature of surroundings at f�450 kHz, H�600 A/m

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toluene/hexane and EMG 605 was diluted by DI water. Paint was prepared using Sherwin WilliamsMacropoxy 646 in the ratio 1:1 by weight.

Nanoparticle and Nanopaint Characterization MethodsParticle size was determined using FEI Tecnai transmission electron microscope (TEM). Magnetization

and magnetic susceptibility were determined in a vibrating sample magnetometer (VSM). Here, themagnetization of sample was recorded as a function of the applied magnetic field to obtain the Langevincurve. A Langevin curve showing no hysteresis is a characteristic of SPM-NPs. Thermal conductivity ofpaint was measured using hot disk TPS 2200. Nanoparticles embedded in nanopaint were imaged usinga scanning electron microscope (SEM). Thickness of the paint was measured under a Keyence digitaloptical microscope.

Magnetic induction heating setupA magnetic induction heater SI-100-KWHF from Superior Induction, shown in Figure 3a, was used to

generate an oscillating magnetic field. The power unit of the heater supplied an alternating current to acoil, which generated an oscillating magnetic field inside the coil. Different coils were attached to theheater to achieve different oscillation frequencies. A three-turn coil (radius � 5 cm, height � 3 cm) wasused to produce a 450 kHz field and five-turn spiral ribbon-shaped coil (radius � 1.6 cm, height � 30 cm)was used to produce a 630 kHz field. The magnetic field strength was varied by controlling current inputto the coil from 5 to 25 A. The magnetic field is maximum at the center of the coil and decreases awayfrom this point. Hence, all samples were placed at the center. The schematic is shown in Figure 3b.Magnetic field of a long solenoid is given by Ampere’s law,

(5)

where H is the magnetic field (A/m), N is the number of turns of the solenoid or coil, I is the currentflowing through the solenoid (A), and L is the length of the solenoid (m). This equation holds true onlyfor a long solenoid whose radius is very small compared to its length which is not true for our system.Hence, the magnetic field formula used in our calculation was derived from Biot-Savart law. Here,

Figure 3—(a) Magnetic field oscillation generator and (b) schematic of magnetic nanoparticle-based heating, (inset) hollow nanopainted polycar-bonate tube used for the batch experiments

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magnetic field is calculated for each turn and the calculated cumulative value reflects the actual magneticfield. The magnetic field of each turn for the three-turn coil is calculated by,

(6)

The magnetic field formula of the three-turn coil was modified to account for the spiral ribbon shapeof the five-turn coil and is calculated by,

(7)

where Hz is magnetic field at the center axis of the coil (A/m), I is the current (A), a is the radius ofthe coil (m), h is the height of each ribbon (m), and z is the height of the coil or distance from origin(m).Temperature measurement is done using a fiber optic temperature probe, NOMAD from Neoptix,Canada.

Batch experiment setupBatch experiments of nanoparticle dispersions and nanopaint were performed at 450 kHz in the

three-turn coil (vertical configuration) by varying magnetic field between 200 to 600 A/m. The magneticfield was calculated using equation (6).

Nanoparticle dispersions Identical hollow tubes (closed on one end) made of PVC or polycarbonatewere used to hold the static nanoparticle dispersions. The experiments were performed for concentrationsranging from 0.5 to ~6 wt. % of Fe3O4 in dispersion. All samples were sonicated to maintain homogeneity.

Nanopaint Two types of nanopaint were prepared by dispersing EMG 1400 and EMG 605 in epoxy. Thedispersions were mixed well to ensure uniform distribution of nanoparticles in paint. Identical hollowtubes (closed on one end) made of PVC were coated with nanopaint and left to cure for 24 hours at roomtemperature. These were termed EMG 1400 paint and EMG 605 paint respectively. The experiments wereperformed for concentrations ranging from 0.5 to ~ 15 wt. % of Fe3O4 in the paint.

The tubes were insulated with urethane foam and placed at the center of the coil, where magnetic fieldis highest. All experiments were performed with a constant mass of sample, completely contained insidethe coil/magnetic field, and for the same time of measurement, 300 s. This ensures that comparison ofresults is made for similar experimental conditions. Temperature was measured at the center of the tubeand plotted as a function of time. The heating rate is linear initially and tends to saturate after a certaintime. The slope of the plot �T/�t in the linear region was calculated and substituted in equation (3) alongwith specific heat capacity and concentration of sample to give SAR.

Flow experiment setupFlow experiments were performed at 630 kHz in a five-turn coil (horizontal configuration) by varying

magnetic field between 300 to 1000 A/m. The magnetic field was calculated using equation (7). A longtube of ID � 1.6 cm, L � 24 cm was coated with EMG 605 paint. The tube was insulated with urethanefoam and placed inside the coil. It was connected to the HPLC pump in an open loop setting and flow rateswere varied between 0.5 to 5 mL/s. Temperature was measured at different points on the pipe, with probecentered at the axis of pipe. The temperature rise at any given time was expressed in terms of SARflow

using equation (4).

Results and DiscussionCharacterization of nanoparticlesTEM images of EMG 1400 and EMG 605 are shown in Figure 4. EMG 1400 shows a mean size of 10.6� 2 nm and EMG 605 shows a mean size of 11.3 � 3 nm. Though the mean size of the samples are very

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close to each other, Figure 1 shows that different particle size distribution can contribute quite differentlyto the overall SAR. To quantify this for the nanoparticles we employed, a representative sample of 100particles from the TEM image was analyzed using an image processing software, ImageJ to obtain the sizedistribution, shown in Figure 5. Each particle size provides a particular theoretical SAR value; the overalltheoretical SAR value is calculated by summing the contributions from individual particle sizes. Substi-tuting this data in equation (1) for magnetic field and frequencies used in the experiment, it is predictedthat SAR of EMG 605 should be higher than EMG 1400, at least by a factor of ~6.6. These values andparticle characterization are summarized in Table 2.

Characterization of nanopaintThe absence of hysteresis in the Langevin curves for nanoparticles and nanopaint shown in Figure 6confirm that the particles are superparamagnetic. The slope of these curves, measured at the limit of 3 Oe

Figure 4—TEM images (scale: 50nm) of (a) EMG 1400 and (b) EMG 605 Fe3O4 nanoparticles

Figure 5—Particle size distribution of EMG 1400 (red) and EMG 605 (blue) obtained from analysis of TEM images

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by VSM, provide the value of magnetic susceptibility. Magnetic susceptibility measured for variousconcentrations of Fe3O4 as a dispersion of EMG 605 in water, as a liquid/solid mixture of EMG 605 insand and as EMG 605 nanoparticles embedded in nanopaint, is shown in Figure 7. Magnetic susceptibilityof Fe3O4 is the same for EMG 605 nanoparticles in dispersion and in sand, respectively. However, the datafor paint shows lower susceptibility value. It is believed that non-uniform distribution of nanoparticle inpaint and also possibly, the slightly diamagnetic nature of paint may have yielded this result.

A SEM image of nanopaint is shown in Figure 8. There appears to be particle clusters greater than 100nm that are coated with paint. However, VSM data (Figure 6) showing that the sample is superparamag-netic confirms that the individual integrity of nanoparticles is intact. This suggests that the nanoparticlesare still the same size as they retain their superparamagnetic behavior but are trapped in a shell of paint.The cross-section of the dried paint sample shown in Figure 9 indicates that the thickness varied between100 and 300 �m. This suggests that water (fluid) is in contact with varying amount of nanoparticles atdifferent sections of pipe. So, heat transfer is not constant across various cross-sections of the tube, butcan be compared when normalized over the entire volume.

Batch Experiments

Heating performance of magnetic nanoparticles The ability of nanoparticles to heat dispersions isexpressed in terms of SAR using equation (3). It is shown as a quadratic function of magnetic fieldstrength in Figure 10. We compare our experimental SAR values to those obtained by Hergt et al., 2004

Table 2—Characterization of nanoparticles

Property Symbol/Unit EMG 1400 EMG 605

Surface coating - Hydrophobic Hydrophilic

Mean particle diameter (TEM) Dp (nm) 10.6 �/- 2.4 11.3 �/-3.1

Volume % % 70 3.9

Saturation magnetization of nanoparticle Ms (103 A/m) 450.5 451.5

Figure 6—VSM results normalized per unit mass of different samples (EMG 1400, EMG 605) and in different forms (aqueous dispersion, nanopaint,and solid powder)

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[10] for Fe3O4 nanoparticles having comparable size distribution to EMG 605. They report a SAR valueof ~90 W/g corresponding to a field of ~ 6000 to 8000 A/m, and 410 kHz. Our experiment with EMG 605shows the same result of ~90 W/g for a much lower field of ~600 A/m, and 450 kHz. We expect theperformance of EMG 605 to be similar to that reported by Hergt et al. considering the similarity in particlesize distributions and in experimental conditions. However the disparity in the magnetic field strength inthe two cases with other parameters kept constant, leads us to believe that the theoretically calculatedvalues from the current measurements may not be accurate. Real-time measurement of magnetic field byhall sensors is planned in the future for effective comparison of predicted values with experiments.

Figure 7—Volume susceptibility as a function of volume % of Fe3O4 measured as a dispersion of EMG 605 in water, as a liquid/solid mixture of EMG605 in sand, and as EMG 605 nanoparticles embedded in nanopaint respectively

Figure 8—SEM image (scale: 1 �m) of nanopaint shows particle size of 100 nm

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It is seen that SAR for EMG 605 and EMG 1400 is independent of concentration. With the aim ofcomparing heating performance of EMG 605 and EMG 1400, SAR values at different concentrations wereaveraged at each value of magnetic field and are shown in Table 3. It is seen by experimental results thatSAREMG 605/SAREMG 1400 is ~ 4 to 8, depending on magnetic field amplitude. This is in line with theprediction that EMG 605 is better based on particle size distribution. However, the predicted factor ofSAR

EMG 605/ SAREMG 1400 ~ 6.5 is not followed by experimental results. SAR of EMG 605 shows quadratic

dependence on magnetic field amplitude as predicted by equation (1) whereas EMG 1400 does not showthe same correlation. It is believed that some aggregation of EMG 1400 particles may have occurred,making them no longer superparamagnetic. Similar observations have been made by Davidson et al. [4]

Figure 9—Optical microscope image (scale: 500 �m) of nanopaint shows thickness at 3 locations as 99.1, 297.8, and 113.2 �m

Figure 10—SAR results for EMG 605 and EMG 1400 dispersions in water and toluene respectively as a quadratic function of magnetic field fordifferent concentrations of Fe3O4 at 450 kHz

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but the reasons for the departure of EMG 1400 from equation (1) are not clear at present. This deviationmay have resulted in the variation between theoretical and experimental performance ratio, SAREMG 605/SAREMG 1400. Accurate quantitative comparison will require experiments with Fe3O4 nanoparticlesamples of a known size distribution, and accurate measurement of the spatial distribution of magneticfield strength among other parameters.

Heating performance of nanopaint The ability of nanopaint on the inner wall of a container to raise thetemperature of static water is expressed in terms of SAR using equation (3). SAR of nanopaint is plottedas a quadratic function of magnetic field in Figure 11. It is seen that SAR for nanopaint is similar todispersions at a given magnetic field and frequency. Thus nanoparticles fixed in a solid medium showsame heating performance as nanoparticles in dispersions. Similar to dispersion results, experimental SARvalues are much higher than predicted for a given magnetic field. Accurate measurement of magnetic fieldcan lead to an effective comparison to theoretical values. The averaged SAR values of EMG 605 andEMG 1400 dispersion and nanopaint are plotted as a function of magnetic field strength/amplitude inFigure 12.

It is seen that magnetic nanopaint shows a slight deviation in SAR compared to magnetic nanoparticlesamples for a given magnetic field and frequency but this may be due to experimental error. It is generallyconcluded that nanoparticles in liquid, and in paint follow the same heating trend. Neel’s relaxation theoryhas been used to explain heating performance of SPM-NPs in dispersion. We show that nanoparticles in

Table 3—Experimental average SAR of nanoparticle dispersions at 450 kHz

Magnetic field (A/m) SAREMG 605 (W/g) SAREMG 1400 (W/g) SAREMG 605/SAREMG 1400

236 19.3 4.5 4.3

354 36.6 7.1 5.1

472 62.1 9.6 6.4

590 94.7 11.6 8.1

Figure 11—SAR results for EMG 605 nanopaint and EMG 1400 nanopaint at different concentrations of Fe3O4 as a quadratic function of magneticfield at 450 kHz

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solid (nanopaint) show same heating performance as dispersion. Hence, it is concluded that Neel’srelaxation theory is applicable to nanopaint.

Flow ExperimentsThe temperature increase of the flowing water by nanopaint at different flow rates and magnetic fields isquantified in terms of SARflow by equation (4). SARflow is plotted as a function of residence time atdifferent magnetic fields in Figure 13. It is seen that SARflow is maximum corresponding to optimumresidence times at different magnetic fields. This indicates the time required for complete heat dissipation

Figure 12—Correlation of SAR as a function of magnetic field for EMG 605 and EMG 1400 in dispersion and nanopaint at 450 kHz

Figure 13—SAR of EMG 605 nanopaint as a function of residence time of water in pipe at different magnetic fields, and 630 kHz

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from the paint medium to water. At these peak points, SARflow is higher than SAR for batch experimentsby factor of ~ 5 to 8, depending on magnetic field. For instance, at 500 A/m, EMG 605 paint showed SARof 70 W/g compared to 500 W/g for flow experiments. Thus, it is seen that flow induced mixing facilitatesbetter heat transfer. It is hypothesized that in batch experiments slow heat dissipation from surface of paintdecreases SAR. Low thermal conductivity increases temperature locally at the surface of paint, whichdecreases heating performance of nanoparticles, as indicated by equation (1) and Figure 2. In flowexperiments, flow of fluids maintains conducive temperature at surface of paint for further heat generationand conduction.

ConclusionIn this paper, heating by superparamagnetic Fe3O4 nanoparticles is empirically evaluated for two samplesvarying in size distribution at magnetic fields ranging from 200 – 1000 A/m and frequencies of 450 kHz,and 630 kHz. Experiments are performed by varying the following parameters: medium of nanoparticles(liquid dispersions, solid paint), state of heated fluid (batch or flow), and concentration of nanoparticles,magnetic field strength and frequency. The properties of nanoparticles and nanopaint are quantitativelydetermined and related to heating performance. Based on heating performance results and theoreticalpredictions, the following conclusions are drawn –

● Heating performance of magnetic nanoparticles is independent of concentration of particles butstrongly dependent on particle size distribution, for a given magnetic field and frequency. Basedon size distribution obtained by TEM, it is predicted and experimentally verified that EMG 605shows better heating performance than EMG 1400. Experimental data shows that only SAR ofEMG 605 shows quadratic dependence on magnetic field, in line with Neel’s relaxation theory.The results are insufficient to explain deviation of EMG 1400. Several samples varying in sizedistribution need to be evaluated to understand the effect of size distribution on heating perfor-mance.

● Nanoparticle behavior in dispersions and in paints is superparamagnetic, as measured by VSM.Even though EMG 605 is hydrophilic it does not agglomerate in organic solvent-based paint, butsimply embeds in paint and shows same heating performance as dispersions. The distribution ofnanoparticles in nanopaint is found to be non-uniform based on lower susceptibility value ofnanopaint compared to dispersions, as measured by VSM. The thickness of the paint is found tobe variable between 90 to 300 �m. A methodology to coat paint of uniform thickness is neededfor future experiments.

● Experimental SAR values for batch experiments are higher than those predicted by Neel’srelaxation theory, for a given magnetic field. Comparison with literature values for similar sizenanoparticles and experimental parameters suggests that calculations of magnetic field are inac-curate. It is concluded that accurate measurement of magnetic field is needed for effectivecomparison.

● Heating performance of nanoparticles in liquid dispersions and nanopaint are comparable. Thisshows that nanoparticle-based heating by Neel’s relaxation is not constrained by the type ofmedium (liquid, solid), if thermal conductivity is maintained constant. Hence, Neel’s relaxationtheory for SPM-NPs in fluid can also be applied to nanopaint.

● Heating performance for flow experiments is better than batch experiments by a factor of ~ 5 to8. Flow-induced mixing and an increased temperature gradient between nanopaint and flowingfluid result in better heat transfer, hence higher SAR of flow experiments. In view of the strongdependence of SAR on temperature, an efficient dissipation of the generated heat from thenanoparticles is important to maintain a high SAR.

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AcknowledgementsSpecial thanks to the Nanoparticles for Subsurface Engineering (NSE) consortium for the financialsupport for this project, Dr. Mohsen Ahmadian from Advanced Energy Consortium for the VSM analysis,Mr. Devesh Agrawal from Baker Hughes for SEM and thickness analysis of paint, and Mr. Glen Baumfrom PGE, UT Austin for his technical assistance during our experiments.

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