Evolution of pore structure and fractal characteristics of marine shale during electromagnetic radiation

Electromagnetic radiation has been proposed to non-aqueously stimulate shale formations, which can generate fractures and enhance the porosity of the matrix. The proposed method consumes electricity and thereby possesses significant advantages for sustainable and environmental hydrocarbon production. In this study, we investigate the pore structure variations of marine shale during electromagnetic radiation. First, the prepared marine shale samples are exposed to electromagnetic radiation for different times; an infrared thermometer monitors the temperatures. Then, the nitrogen adsorption/desorption technique is applied to examine the evolutions of the pore structure. Next, a scanning electron microscope is adopted to reveal the morphology and identify newly developed pores. Lastly, fractal analyses are performed to quantify pore structure variations. The sample exhibits quick temperature rises, whose temperature reaches about 300 °C after 5 min of electromagnetic radiation. The elevated temperature causes clay dehydration, thermal expansion, and organic matter decomposition, leading to significant changes in pore structures. The nitrogen adsorption/desorption characteristics demonstrate enhancements in pore spaces, including volume, size, and surface area. Fractal analyses show that the pores become rougher and exhibit less heterogeneity after electromagnetic radiation. The obtained results demonstrate a great potential of using electromagnetic radiation to enhance the porosity of shale rocks.


Introduction
Shale gas, shale oil, and oil shale possessing considerable reserves have been crucial sequential energy resources for the increasing energy demand [1,2]. Because of the low permeability of shale formations, stimulations, such as hydraulic fracturing, gas (CO 2 /N 2 ) fracturing, and foam fracturing, are required to create high permeable fractures to enhance the hydrocarbon production [3,4]. These stimulation techniques rely on injecting a substantial amount of fluids to fracture the shale rocks, which consume a massive amount of water and cause ecology problems [5]. Meanwhile, the injected fluid and the residual chemicals can block the pores, causing formation damages and reducing the permeability of the matrix [6]. Also, hydraulic fracturing requires extensive surface facilities and injects a massive amount of proppant and fracturing fluid. Electromagnetic radiation can be achieved by installing a downhole antenna to fracture the formation rock, which eliminates the injecting process and saves space for the surface facilities. Formation heat treatment (FHT) has been proposed to stimulate formation rocks; previous investigations summarized the mechanisms as dehydration to enhance the porosity and thermal stress to create fractures [7][8][9][10][11]. Electromagnetic radiation has been proposed as a nonaqueous method to stimulate shale formations [12]. Unlike the conventional methods, electromagnetic radiation fractures the formation rocks by the internal thermal stresses generated by the heterogeneous expansions of minerals [13]. Electromagnetic radiation can generate fractures in the rock and enlarge the pores in the matrix, possessing significant advantages compared with the stimulating techniques that fracture the shales but damage the rock matrix. Hu et al. [14] investigated the petrophysical property changes of continental shale rocks under electromagnetic heating; results show that many fractures are generated by electromagnetic heating. Zhu et al. [15] showed that a higher power could significantly raise the heating rate and alter the pore structure of the shale sample. Li et al. [16] evaluated the fractal characteristics of pore structure of coal during microwave radiation and found a positive relationship between fractal dimension and thermal heterogeneity. Previous studies demonstrated great potentials of using electromagnetic radiation to fracture the shale rocks, and extensive fractures can be thermally induced. However, the pore structure changes of the matrix for marine shale under electromagnetic radiation are not fully understood.
In this study, we conduct experiments to understand the evolution of the pore structure of marine shale formation under electromagnetic radiation. The electromagnetic radiation experiments are performed by using a commercial microwave oven, while the temperature responses of the sample are monitored by the infrared thermometer. First, marine shale rocks are subjected to electromagnetic radiation at different times. Then, the isothermals of each sample are determined by the nitrogen adsorption/desorption technique. Also, the evolution of the pore structure and porosity of the samples is evaluated. Lastly, the fractal analysis is performed to reveal the geometric and morphology features of the samples.

Materials
A downhole full diameter marine shale core, retrieved from Longmaxi Formation of Sichuan Basin, is utilized to investigate the pore structure evolution under electromagnetic radiation. Fig 1 summarizes the experimental workflow. We first drill multiple standard cores with a diameter of 2.54 cm and varying lengths from 3cm to 5 cm. Then, the geochemical properties of the core samples are characterized by the X-ray diffraction technique; the ones with similar composition are used to reduce the effect of heterogeneity on the experiments. Lastly, we conduct the low-pressure nitrogen gas adsorption and FE-SEM analysis to reveal the pore structure changes by electromagnetic radiation. Table 1 lists the compositions of the selected samples as well as calculated average values and standard deviations. Results show that samples (S0-S7) consist of quartz, feldspar, calcite, dolomite, clay mineral, and organic matters. The mineral compositions of the selected samples are within a narrow range, with standard deviations smaller than 3.62.   to electromagnetic radiation for 1min, 2min, 3min, 4min, 5min, respectively; an infrared thermometer measures the surface temperature of shale samples. Lastly, samples #6-7 are used to check the reproducibility of the experiments. After the electromagnetic radiation experiments, these samples are crushed and then sieved between 60 and 80 meshes for the nitrogen adsorption/desorption characterization. A Quadrasorb SI apparatus (USA) is adopted to reveal the pore structure characteristics, including the shape, size distribution, specific surface area, and volume of pores. Also, the effect of electromagnetic radiation on the pore morphology is examined by field emission scanning electron microscope (FE-SEM) (Quanta 250 FEG, USA). Fig 3 shows the images of the adopted characterization setups.

Temperature responses
Due to the heterogeneity of mineral distribution of the sample, temperature responses under electromagnetic radiation vary at different measuring points. Hence, we measure surface temperatures of shale samples for three times to obtain average values as the radiation temperature responses. Fig 4 shows the average temperature profiles and temperature-changing rates of shale samples under electromagnetic radiation. The temperatures increase as the electromagnetic radiation continues. The roaring temperature at the beginning of the experiment is caused by the clay-bound water that is an excellent electromagnetic wave absorber. Once the clay-bound water vaporizes, the temperature steadily increases and reaches about 300˚C after 5 min of electromagnetic radiation.

Nitrogen adsorption/desorption isotherms
The nitrogen adsorption/desorption technique is adopted to investigate the evolution of pore structures under electromagnetic radiation. Fig 5 summarizes the obtained isotherms of shale samples at different radiation times. The adsorption isotherms steadily increase when the relative pressures (P/P 0 ) are lower than 0.9, while the adsorption isotherms sharply rise once the P/P 0 is over 0.9 due to the effect of capillary condensation. Also, the adsorption and desorption curves only exhibit insignificant differences when the P/P 0 is smaller than 0.45, suggesting that small pores are connected by one pore throat [17].  The adsorption/desorption volumes continuously increase as the electromagnetic radiation goes on; the maximum absorption volumes increase from 4 to 14 cm 3 /g after 5 min of electromagnetic heating, indicating many new pores are generated. Also, the shape of the isothermal curves changes after electromagnetic radiation. Based on the classification of the International Union of Pure and Applied Chemistry (IUPAC) [18], the patterns of the isothermals can be used to detect the shape of the pore. The patterns of adsorption and desorption curves remain the same for the first 3 min of electromagnetic radiation; the obtained isotherms belong to type H 4 that indicates a slit-like shape of pores. However, the pattern of adsorption and desorption isotherms change after 4 min of electromagnetic radiation. The developed new pores after electromagnetic radiation turn the pattern to H 2 type that suggests an ink-bottle shape or flat-shape pore.

Validation
To validate the experiments, we conduct another two runs (samples #6-7) to repeat the case of 5min of electromagnetic radiation (sample #5). Fig 6 shows the obtained isothermals and the pore-size distributions of samples #5-7. Results show that the temperature responses, isothermals, and pore-size distributions of three cases vary within a small range. To quantify the differences, we calculate the average absolute relative deviations (AARD ¼ 1 Table 2 lists the AARDs of temperature responses, absorption/desorption volumes, pore-size distributions, and porosities. The detailed procedures of calculating the pore-size distribution and porosity will be introduced in the next section. Given the slight differences in the compositions of the samples, the results of the additional two cases (samples #6-7) echo relatively well with the base one (sample #5).

Evolution of pore structure under electromagnetic radiation
By using the obtained isothermal data, we use the Brunauer-Emmett-Teller (BET) method to calculate the total pore volume and specific surface area of the shale sample at different radiation times, as shown in Table 3. Results show that electromagnetic radiation significantly enhances the total pore volume and surface area because of the newly generated pores. The pore volume increases about four times after 5 min of electromagnetic radiation, and the specific area enhances about five times. Such a significant enhancement in pores changes the pattern of isotherms from H4 type to H1 type; similar observations have also been found in Wang et al. [19]. The increment in pore at early radiation times (before 1 min) is contributed by the evaporation of bound water [20]. Then, the organic matter is converted and decomposed to volatile contents, which promotes a significant number of new organic pores in the marine shale [21]. Also, micro-fractures in the matrix have been generated due to the induced thermal stress by electromagnetic radiation [22]. The mechanisms mentioned above contributed to the enhancement of total pore volume and specific surface area, which increase from 5.712×10 −3 to 22.054×10 −3 cm 3 /g, and 0.979 to and 5.123 m 2 /g, respectively.
Moreover, we calculate the pore-size distributions of the marine shale sample by the Barrett-Joyner-Halenda method, which assumes the capillary condensation phenomenon in a cylindrical pore. Fig 7 shows the calculated pore-size distributions at different radiation times. Results show that the micropores and mesopores significantly enhance after electromagnetic radiation, suggesting that electromagnetic radiation can enlarge and generate organic pore. Similar phenomena have been observed in the research of Bai et al. [23].

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Pore structure and fractal characteristics changes of shale during electromagnetic radiation

Variation in porosity at different electromagnetic radiation time
Porosity is a critical petrophysical property for the exploitation of shale resources. The electromagnetic radiation can significantly enhance the porosity of shale by dehydration of claybound water, decomposition of organic matter, and enlargement of pores by thermal expansion [14,22]. By using the obtained pore-size distribution, we calculate the variations of porosity under electromagnetic radiation and specify the contribution of micropores and mesopores, as shown in Fig 8. After 5 min of electromagnetic radiation, the porosity sufficiently increases by about 5.84%; the micropores add about 4.3%, while the mesopores boost about 1.54%. The micropores continue to enhance in the first four minutes, which corresponding to the generation and enlargement of organic pores. However, the temperature

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Pore structure and fractal characteristics changes of shale during electromagnetic radiation gradually rises to high temperature as the radiation lasts to five minutes; consequently, the kerogen is decomposed to bitumen that is blocked the part of the pores, leading to reduced micropores. The mesopores steadily increase, which is caused by the vaporization of clay-bound water at the early stages and thermal expansion at the late stage.

Changes of pore morphology
In this section, the FE-SEM imaging analysis is performed to investigate the changes in the microstructure of shale samples under electromagnetic radiation experiments. By comparing the FE-SEM images of the raw sample and the ones that are exposed to electromagnetic radiation, we identified intensive newly developed organic pores and micro-fractures. Fig 9 summarizes the FE-SEM images of shale samples before and after 5min of electromagnetic radiation, which focuses on the organic pores/fractures. Before the electromagnetic radiation, the morphology of pores is smooth and flat. However, after 5 min of electromagnetic radiation, the organic matter becomes rough and uneven. Also, new pores are generated within the organic matter, which tends to exhibit in a circular shape. Fig 10 compares the morphology of clay minerals before and after electromagnetic radiation. The additional micro-fractures are observed in the clay-rich area of the sample. The clays are excellent electromagnetic energy absorber, whose thermal expansion induces stress and generates fractures [14].

Fractal dimension characterization
The evolution of pore structures of marine shale under electromagnetic radiation is a complex process, which involves multiphysics and several processes. To quantitively determine the pore structure changes, we performed fractal analyses to characterize the geometric and surface irregularity of marine shales in this process [24]. Fractal dimension is generally in the range of two to three; the minimum value represents smooth and homogeneous pores, while the maximum value indicates rough pore surface or heterogeneous pore structure [25]. For the fractal analyses of tight formation rocks, fractal dimension D 1 (P 0 /P: 0~0.5) and D 2 (P 0 /P: 0.5~1.0) are used to evaluate the degree of roughness and heterogeneity of pores [26]. The fractal dimension D 1 can indicate the pore roughness, while D 2 can represent the complexity of the pore structure [27,28].
In this study, we use the Frenkel-Halsey-Hill (FHH) method and obtained nitrogen adsorption/desorption isotherm data to calculate the fractal dimension of shale samples [21,29]. The FHH model is defined as follows [21]: where P is equilibrium pressure, P 0 is the vapor saturation pressure, V is the adsorption volume at equilibrium pressure, C is constant, and D is the fractal dimension. (D-3) can be obtained by the slope of the curve of LnV versus Ln[Ln(P 0 /P)]. Fig 11 shows the relationships between LnV and Ln [Ln (P 0 /P)] for the shale sample under different electromagnetic radiation times. The analyses are performed twice for the relative pressures smaller and larger than 0.5 to calculate D 1 and D 2 , respectively. The obtained determination coefficients are higher than 0.98, showing a good fitting performance. Fig 12 shows the variations of D 1 and D 2 at different radiation times. Results show that D 1 steadily increases by electromagnetic radiation, while D 2 slightly decreases under electromagnetic radiation. The increasing fractal dimension D 1 indicates that the pores become rough after electromagnetic radiation, which echoes well the CT characterization by Tiwari et al. [30]. Meanwhile, the slightly decreased fractal dimension D 2 suggests that the pore complexity of the shale sample is slightly reduced. Both experimental observations and fractal analyses reveal that electromagnetic radiation can significantly boost the pore space, demonstrating a great potential for enhancing shale oil and gas recovery.

Conclusions
In this study, a systematic study has been conducted to elucidate the pore structure changes of marine shale by electromagnetic radiation. The following conclusion can be drawn: 1. The shale samples exhibit a quick temperature rise under electromagnetic radiation; the surface temperature increases to about 300˚C after about 5 min of radiation. The temperature elevation provided by electromagnetic radiation causes dehydration of clay-bound water, thermal expansion, and decomposition of organic contents, which significantly enhances the pore spaces of marine shale samples.
2. The evolution of isothermal under electromagnetic radiation has been determined. Results show that the pore volume increases about four times after electromagnetic radiation, and the porosity enhances about 5.84%. The SEM characterization shows that organic pores are substantially generated by electromagnetic radiation, which significantly increases the micropores. However, part of the mesopores is blocked by the kerogen converted bitumen.
3. The fractal analyses have been performed to quantify the changes in the pore structure. Fractal dimensions D 1 and D 2 are calculated. The increasing D 1 shows that the pores become rough after electromagnetic radiation.
4. The obtained experimental results and fractal analyses show a great potential of using electromagnetic radiation to enhance the pore spaces of marine shale, providing a non-aqueous stimulating technique for shale resource recovery.