Absorption of electromagnetic waves in sandstone saturated with brine and nanofluids for application in enhanced oil recovery

In this study, scattering parameters of sandstone saturated with brine and nanofluids are evaluated experimentally and numerically for the application in enhanced oil recovery (EOR). Zinc Oxide (ZnO) and Bismuth ferrite BiFeO3 (BFO) nanoparticles were synthesized via facile sol–gel method followed by nanofluid preparation. Sandstone samples were saturated with brine and nanofluids for 48 h. Electromagnetic properties of the saturated sandstones were measured experimentally using the vector network analyzer, and the scattering parameters of the samples were studied numerically by finite element method. BFO displayed higher permeability value of 1.52 and 1.30, as well as superior dielectric permittivity value 11.55 and 6.59 for real and imaginary parts, respectively. In addition, the sandstone saturated with BFO showed an impressive reflection loss (RL) value of −9.77 dB at high frequency. Conclusively, BiFeO3 nanofluids showed the best potential to enhance oil recovery which can be accredited to the superior electromagnetic properties of BFO.

Real part calculated permeability μ Imaginary part calculated permeability ε Real part calculated Dielectric permittivity ε Imaginary part calculated dielectric permittivity tanδ μ Magnetic loss factor tanδ ε Dielectric loss factor S11 EM wave transmitted and received at port 1 S12 EM wave transmitted at port 1 and received at port 2 Abbreviations S 0 Dry sandstone S B Sandstone soaked in Brine S Zn Sandstone soaked in ZnO nanofluid S Bi Sandstone soaked in BiFeO 3 nanofluid ε s Dielectric permittivity with sandstone ε B Dielectric permittivity with Brine ε Zn Dielectric permittivity with ZnO ε Bi Dielectric permittivity with BiFeO3

Introduction
The global demand for energy is increasing and it is predicted to rise by 50% in 2030 [1]. Although renewable energy sources are being adopted to fulfil these energy needs, the oil will remain as the primary energy source for the next few decades [2]. So, along with the exploration of new oil fields, it is also necessary to maximize the production of oil from the existing oil fields [3,4]. Use of nanotechnology for enhanced oil recovery (EOR) has been gaining more attention of researchers as the nanoparticles can improve the rock-fluid properties such as wettability alteration, interfacial tension reduction, thermal conductivity, specific heat improvement, and viscosity enhancement. Nanoparticles and nanofluids can accelerate the transfer rate of oil due to the migration of nanoparticles from the aqueous phase to the oleic phase affecting both the oil properties and rock oil properties to change [5][6][7]. For example, oil mobility may increase owing to the change in viscosity which may enhance the ultimate recovery of oil in fractured reservoirs.
Many researchers have used different categories of nanoparticles for EOR, such as the metal oxide nanoparticles [8,9], carbon-based nanoparticles [10][11][12], polymeric nanoparticles [13], and ferrite nanoparticles [14,15]. Kothari et al. for the first time flipped the term of "smart-nanofluids" when the ferrofluid was used as a surfactant for EOR, but the only the rheological properties of ferrofluids were studied [16]. Zinc Oxide (ZnO) has also been considered as a potential material for EOR because of its excellent dielectric properties and high dielectric loss in the presence of EM field [17]. To increase the activity of nanoparticles, electromagnetic waves of a specific frequency creates resonance in the nanoparticles changes the oil viscosity and compels to move inside the porous medium [18,19]. Various theoretical models were also proposed by researchers to describe the mechanisms involved in the chain-like formation, such as water-bridge model, electric double layer model and polarization model [20,21]. Later, among these models, has been considered as the most reliable model, which involves the dielectric loss to influence the electrorheological effect [22].
Ferrite nanocomposites have been of great interest in modern science and technology, which show substantial dielectric and magnetic properties [23,24]. They are not only known for their perspective of solid-state physics, but they have demonstrated a higher potential a variety of applications in electronic devices, wireless communications, medicine and industry [25][26][27][28][29]. Ferroic materials exhibit a unique property of spontaneously switching internal order of materials because of magneto-electric coupling, which results in the swapping of the magnetic field with electric polarization and vice versa [30]. This unique behaviour makes the ferrite nanocomposites favourable agent for EM-assisted EOR, which uses a novel class of smart nanofluids under the influence of electromagnetic field to stimulate them and create a disturbance at the oil-water interface [31][32][33][34]. The smart-nanofluids can drastically alter the viscosity, wettability and interfacial tension of oil-water; hence increasing the mobility of oil [35,36].
When the EM wave travels across an inhomogeneous material, it could change the material characteristics such as permittivity, permeability, conductivity, is, interference and phase-shift [37,38]. The absorption properties of such "smart-nanofluids" attribute to the reflection and transmission coefficients (S-Parameters) [19,39]. The dielectric materials can absorb the EM waves incident on them in synchronized frequencies which results in the polarization and the magnetoelectric coupling and later dissipate the energy [40]. However, some of the disadvantages which restrict their broad applications are narrow EM frequency bandwidth, poor mechanical properties and low environmental adaptability [41,42]. The factors which affect the absorbing properties of materials are the materials complex permittivity ε , complex permeability μ and dielectric losses δ [43]. In case of homogenous materials, the behaviour of wave can be measured analytically by using Fresnel equations and Snell's law, but for complex structures like sandstone numerical techniques are used for the calculation process, and a lot of programs have been used for realization of numerical modelling such as, MATLAB, ANSYS, COMSOL, etc [44].
In this work, synthesis of ZnO and BiFeO 3 nanoparticles was carried out using the sol-gel combustion technique. Then, nanofluids were prepared by dispersing the as-prepared nanoparticles in brine. Different samples of sandstone were saturated in nanofluids as well as brine. Subsequently, the magnetic and dielectric properties of the samples were measured with vector network analyzer (VNA). A numerical model based on the finite element method (FEM) was proposed to simulate the propagation of EM waves in multiphase porous media for the comparative analysis of experimental and simulation results.

Synthesis of nanoparticles
ZnO nanoparticles were synthesized using zinc nitrate hexahydrate (Zn(NO 3 ) 2 ·6H 2 O) and NaOH solution, and the citric acid was used as a catalyst. The reaction was carried out using sol-gel combustion method by mixing 12 g of zinc nitrate hexahydrate in 100 ml of water in a beaker and 3.2 g of NaOH was dissolved in 30 ml of water in a separate beaker. Then the solution of NaOH added dropwise in the beaker and stirred for two hours at 70°C. The solution was then filtered with Whatman filter papers and dried in an oven for 3 h at 160°C, and later calcinated at 400°C for 3 h.
For bismuth ferrite (BFO) nanocomposite, bismuth nitrate pentahydrate (Bi(NO 3 ) 2 ·5H 2 O) and iron nitrate Fe(NO 3 ) 2 were used with nitric acid as an oxidizing agent. All the chemicals were purchased from Sigma Aldrich with analytical grade. BFO was synthesized by using solvent evaporation technique. Equal amounts of 0.1 M solutions of iron nitrate nonahydrate Fe(NO 3 ) 3 · 9H 2 O and bismuth nitrate pentahydrate Bi(NO 3 ) 3 ·5H 2 O were mixed, and dilute nitric acid was added as an oxidizing agent. The transparent solution was obtained by heating the mixture at 150-160°C under constant stirring until all the liquid evaporated from the solution. A green colour residual is obtained, which was grinned to make it a fine powder. The sample was annealed at 500°C for 2 h to remove the impurities to get singlephase BFO nanoparticles.

Nanofluid preparation
In a typical experiment, 0.1wt% of as-synthesized nanopartilces were dispersed in brine (3 wt% Nacl) as the basefluid, shown in Table 1. The solution was stirred for 1hour to achieve homogenous dispersion. The concentration and weight percent of NaCl and nanoparticles used in this work was adopted to avoid the agglomeration and favour better suspension [45]. The sandstone was cut perfectly with a size of 3 × 4 × 10 mm so that it could be placed in the sample holder of the VNA. These sandstone samples were then dipped in the prepared solutions of brine, ZnO and BFO separately for 48 h so that it gets entirely saturated with nanofluids and brine, as shown in Figure 1.

Characterization of synthesized particles
X-ray diffraction (XRD) patterns obtained for the nanoparticles were carried out using powder X-ray diffractometer with Cu-Ka radiation operated at 45 kV and 40 ma [19]. The particle morphology and elemental analysis were carried out by Zeiss supra 55 VP FESEM [46].
Electromagnetic properties and microwave absorption were studied using a Keysight VNA at X-band frequencies. Dielectric and magnetic properties of lossless and lossy materials influence the electromagnetic field distribution. Relative permittivity (ε = ε − jε ) and relative permeability (μ = μ − jμ) defines the dielectric and magnetic properties of the materials, respectively, and influence the reflection of EM waves at the interfaces and the attenuation of the wave within the materials [43,47,48]. Here ε and μ are the real parts and express the energy stored in the material when the  electromagnetic field is passed through it. Whereas, the complex quantities ε and μ defines the loss factor and influences the energy absorption and attenuation. Another critical parameter for dielectric properties of the material is the tangent of loss angle (tanδ ε = ε /ε ) and (tanδ μ = μ /μ ), it contributes to the electromagnetic loss in heterogeneous media [49,50]. The measurement of frequency dependences of the real and complex relative permittivity of porous rocks saturated with brine and nanofluid is helpful for the petrophysical analysis of rocks for EOR. The rock samples were obtained from the Angsi-E2 and were soaked with brine, ZnO and BFO nanofluids, to saturate the rock. For simplicity, the samples were named as S 0 , S B , S Zn and S Bi for dry sandstone, and the sandstone saturated with brine, ZnO and BFO nanofluids, respectively. The measurements were carried out at X-Band frequency range of 8-12.5 GHz using the VNA. A VNA is a precision measuring tool that measures the dielectric properties of the materials as well as the reflection and transmission responses or S-Parameters. The rock samples were cut in the specific dimensions so that they can be placed in the sample holder without any gap. The network analyzer was calibrated using twoport transmission reflection line, and then after putting the frequency values the measurements were carried out.

Numerical simulation
A numerical model based on the FEM has been adopted to solve the system of equations to describe the scattering parameters and propagation of EM waves across the sandstone just like in VNA system [51]. Two-port rectangular waveguide system was used in which Port 1 was for the incident wave, and Port 2 behaves as a receiver to study the reflection, transmission and losses of EM waves in the porous medium as shown in Figure 2.
In this model, the electromagnetic waves frequency domain interface with the rectangular waveguide Transverse electric (TE10) mode was used, and the twoport boundary conditions were selected for wave excitation. The other boundaries were specified with zero electric field conditions which are expressed as (n × E = 0), wheren is the normal to the boundary [52]. The mesh dependence study was performed with respect to several computational meshes of various resolutions. A typical mesh consisting of 4932 total mesh vertices and 25748 tetrahedra elements in the entire domain.was selected for numerial investigations. The wave equation for the propagation of electric field "E" by solving the Maxwell equations is given as [53], The wavenumber k 0 for free space is defined as [54],  The electric displacement field model was selected for the refractive index, which was calculated using the permittivity and permeability values of the materials. The average values of relative permittivity for S 0 , S B , S Zn, and S Bi presented in Table 2 have been calculated using the measured values from VNA. By making the assumptions as σ = 0 and μ r = 1, we get Equation (1) in terms of refractive index as ε r = n 2 , Scattering parameters (or S-parameters) describe the input and output parameters between two ports of an electrical system [55]. If we have a two-port system and each port is provided with some voltage and current, then S21 is defined as the power transferred from port 1-2, and S11 is the power transmitted and reflected at port 1 [56]. The simulations were carried separately for dry rock, the rock saturated with brine and nanofluids to study the reflection and transmission coefficients. The equations used for S-parameters at port 1 and port 2 are given in Equations (4) and (5), respectively [57].
Here the subscript 1 and 2 are for the port-1 and port-2, E is the electric field and A is the surface area.
By using these equations, the reflection and transmission coefficients of the electromagnetic field have been calculated.

XRD Analysis
The XRD patterns of ZnO nanoparticles calcinated at 400°C in Figure 3

FESEM analysis
The morphology of ZnO and BFO nanoparticles were characterized using field emission scanning electron  microscope (FESEM). Energy dispersive X-ray (EDX) was also performed for nanoparticles, which confirmed the formation of ZnO and BFO. Figure 4 shows the micrographs of ZnO nanoparticles; the average size of the particles was above 150 nm because of the low calcination temperature and possible oxidation of nanoparticles. The shape of nanoparticles formed is hexagonal which is consistent with XRD results. The EDX results of ZnO shows that the zinc and oxygen elements are present with an atomic percentage of 36.41% and 63.59%. FESEM micrographs of BFO shown in Figure 5 was carried out at magnification of 30 KX. Nanoparticles got agglomerated and formed plane surfaces, which happened because of the oxidation at high temperature. The EDX analysis shows the atomic percentage of elements present are bismuth 20.37%, iron 20.49% and oxygen 59.14%.
FESEM micrographs of BFO shown in Figure 5 was carried out at magnification of 30 KX. Nanoparticles got agglomerated and formed plane surfaces, which happened because of the oxidation at high temperature. The EDX analysis shows the atomic percentage of elements present are bismuth 20.37%, iron 20.49% and oxygen 59.14%.

Measurement of EM wave absorption
The real part of dielectric permittivity (ε ) is measured for all the samples at a range of frequencies 8.5-12.5 GHz as shown in Figure 6(a). The analysis of the dielectric permittivity dependence shows that S Bi exhibits the maximum average value for dielectric permittivity ε . This behaviour is due to the presence of additional relaxation due to the polarization of BFO nanoparticles in S Bi . The samples S 0 and S B show no variation until the frequency reached 9.5 GHz, after surpassing this frequency there is a rapid increase in dielectric permittivity, this abnormal change in behaviour occurs at that frequency range due to the effective conductivity dependence. Figure 6(b) shows the dielectric loss (ε ) with the X-band frequency for S 0 , S B , S Zn and S Bi . It is observed that the dielectric loss for S Bi and S Zn fall in the same range and is maximum for all the X-band frequencies. For S 0 and S B the value of ε goes in the negative direction, which is an abnormal behaviour, the average value for these samples is zero. The dielectric loss as a function of frequency is increasing with the increasing frequency in S Bi , which is due to the space charge polarization and reduced ionic conductivity. The variation of dielectric loss factor (tanδ ε ) with frequency for all the samples is shown in Figure 6(c). The tanδ ε is defined as the energy dissipation in dielectric media due to the domain wall resonance. As the value of (tanδ ε ) is directly proportional to ε , it shows the same pattern as dielectric loss. The maximum loss factor at higher frequency is recorded for S Zn and S Bi, which is due to the relaxation of ions. Figure 7 represents the μ , μ and tan (δ μ ) as a function of X-band frequency. The value of μ and μ are generally smaller in magnitude as compared to dielectric loss. For S B and S Bi the value of μ does not vary much with increasing frequency, S Zn shows a negative  trend and then increases slightly after 10 GHz because of the absence of magnetic properties of ZnO. S Bi shows positive values of μ as the permeability increases with increasing frequency. S 0 shows an abnormal behaviour after a frequency of 10 GHz. The imaginary part μ shows at the frequency of 8-9.5 GHz brine has the maximum magnetic loss while as the frequency increases S Bi shows a positive trend for μ . S 0 at a lower frequency, have zero magnetic loss, but with increasing frequency, it shows an abrupt increase and decrease in magnetic loss properties. Then there is magnetic loss factor tan(δ μ ) which is given by tan(δ μ ) = μ /μ . At frequency range of 8-10 GHz S Zn have the highest tan(δ μ ), while at a frequency greater than 10 GHz, S Bi shows an increment in tangent loss factor. The magnetic loss occurs because of the domain wall resonance, natural resonance and eddy current loss. Domain wall resonance mainly occurs in the MHz frequency range, so in the microwave range, the S Bi can be graded as the best material for absorbing EM waves and exhibit the natural resonance phenomenon.

Reflection loss
At the X-band frequency range based on the measurements of the scattering parameter, the reflection loss (RL) of all samples were calculated by using the absorbing wall theory, Here, RL donates the reflection loss in decibel units (dB), Z is the input impedance on the surface, ε and μ are the relative permittivity and permeability, j is the complex number, f is the frequency, c is the speed of light and t is the thickness of the sample used. RL curves outline the absorption coefficient of EM waves with a range of frequency correspond to RL value less than −10 dB correspond to 90% EM wave absorption. Figure 8 shows the variation of RL curves across the X-Band frequency range for S 0 , S B , S Zn , and S Bi . The most robust value for EM wave absorption was calculated for S 0 (−38 dB). For S B and S Bi , the RL calculated was higher than -10 dB, except for S Zn , which showed impressive absorption −25 dB at the relatively lower frequency of 8.35 GHz and the bandwidth of 0.8 4 GHz. S Bi nanofluid exhibits the maximum absorption of −9.77 dB at a frequency of 11.05 GHz. The reason for high absorption in S 0 is the factors such as shape and size of the crystal, because of the porous structure the surface increases which is an essential factor for microwave absorbing materials. For all other samples, the pores of the sandstone were filled with brine or nanofluid; hence, the surface area decreases.
Numerical simulation of RL for sandstone, brine and nanofluids were carried out; all the materials show a decline in trend with increasing frequency, and the minimum RL is calculated for S 0 which means that most of the EM wave reflects from S 0 . The RL for S Bi and S Zn recorded as almost the same as it varies between −1 and −1.4 dB, while and S B the lowest RL is at −1.7 and −2.7, respectively. Figure 9 shows the experimental and simulated results for all the samples. All the samples show similar trends of decline for the experimental and simulated results, but only brine show an increase in RL with increasing frequency. The values of RL for sandstone and brine were quite high as compared to the sandstone soaked with nanofluids. The wavy plot for experimental results is because of the attenuation of the signal, while for simulated results smooth line was drawn.

Conclusion
Simulation results based on FEM show that the RL is minimum in dry sandstone and is maximum when the sandstone was soaked with BFO and ZnO nanofluids. The experimental results from network analyzer show the regular pattern for sandstone soaked in nanofluids, but for dry sandstone, there are some irregularities observed at high frequency. BFO can be regarded as the optimal EOR agent as it shows the highest dielectric permittivity values of 11.55 and 6.59 for real and imaginary parts, respectively. In addition, BFO shows superior permeability values of 1.52 and 1.30 for real and imaginary parts, respectively as compared to ZnO which has values of 1.28 and 0.93 for real and imaginary parts, respectively. Therefore, BFO is beneficial for the sufficient activation of particles with EM waves as it can interact with both magnetic and electric components of EM waves, which can enhance oil recovery. The minimum RL value was observed for sandstone at −38 dB, which matches the simulation results where dry sandstone has minimum RL value, but sandstone saturated with BFO also show impressive RL value of −9.77 dB at higher frequency. BFO can be used as a potential material for EOR because it is the most stable material at the X-band frequency and shows maximum absorption and dielectric permittivity and magnetic permeability values. In the future, BFO can be used as an EOR agent in the presence of electromagnetic field to study the core flooding experiments.

Disclosure statement
No potential conflict of interest was reported by the authors.