Influence of Microwave Energy on Fractal Dimension of Coal Cores

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Influence of Microwave Energy on Fractal Dimension of Coal Cores: Implications from Nuclear Magnetic Resonance Yi-du Hong, Bai-quan Lin,* Chuan-jie Zhu, and He Li School of Safety Engineering, State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China ABSTRACT: The effect of microwave heating on the fractal dimension of coal cores is evaluated by an experimental work, which is carried out by nuclear magnetic resonance. This paper verifies that the membrane-bound water model is appropriate for explaining the state of bound-water in pores of coal samples. The paper also verifies fractal dimension as an intrinsic property of a surface that does not depend on porosity. The pore size, pore number, connectivity, and porosity increased after microwave irradiation. Furthermore, a theoretical equation was proposed to calculate fractal dimensions based on the transverse relaxation time (T2). The fractal dimensions of coal cores decreased after microwave treatment along with the permeability increase. These results suggest that microwave irradiation is a potential method for degassing coal seams in the future.

1. INTRODUCTION Methane in coal seams (CBM), which is generated during the coalification process, is both hazardous and potentially beneficial to human kind.1−3 On the one hand, it may induce dangerous rock outbursts,4−6 gas explosions,7 and increment the energy requirements of mine ventilation systems.8 As a greenhouse gas, CH4 is approximately 21 times more effective at trapping heat from the atmosphere than that of CO2.9,10 On the other hand, CBM is an important natural clean energy source that can be utilized to meet increasing global commercial energy requirements.8,11−13 Unfortunately, most of the target coal seams for CBM production have extremely low reservoir permeability values, especially in China.14−16 Therefore, numerous methods (widely used in the industry) have been proposed to enhance CBM recovery, such as hydraulic slotting,17 hydraulic fracturing,18−21 N2 injection,22,23 and CO2 injection.22−28 However, these methods may not work very well in some situations. For instance, hydraulic fracturing is not an effective method when the treatment zone includes a natural fracture or cleat because fracturing fluid would leak out along the cleat and not generate enough pressure to fracture the coal seam.29 Therefore, finding some new methods suitable for this special situation are required. Thermal recovery methods are effective techniques for enhancing oil recovery and have been employed commercially in the oil industry for many years.30−34 This method introduces heat into the reservoir to reduce oil viscosity for enhancing oil productivity. Thermal methods include the steam injection process (CSS),35 steam flooding (SF),36 and steam-assisted gravity drainage (SAGD).37 However, these methods (CSS, SF, and SAGD) may not work very well in some situations, such as if the treatment zone is too deep or too shallow.38−40 In these cases, radiofrequency or microwave irradiation methods introduce energy into the reservoir by a downhole radiating antenna, which can be a sound alternative for in situ heating.40−45 Interestingly, coalbeds and oil reservoirs share some characteristics in geological conditions. Increasing the temperature of coalbeds can decrease methane adsorption46 and increase the permeability47 of the coalbed, thus facilitating © XXXX American Chemical Society

CBM extraction. Therefore, microwave irradiation may have feasibly be used for CBM recovery. However, little work has been carried out to examine the feasibility of this method.1,38,48,49 Therefore, it is necessary to better understand the influence of microwave irradiation on the petrophysical characteristics of coal. As a complex geological material, coal has discontinuous, multiphase composite structures.50 Numerous parameters, such as the strength, elastic modulus, permeability, conductivity, wave velocity, and fractal dimension can be used to describe the petrophysical characteristics of coal. In this paper, the fractal features of coal will be applied to analysis of the influence of microwave heating on coal cores. Fractal theory, a nonlinear mathematic method initially proposed by Mandelbrot,51 has become increasingly popular in social and natural sciences as a means of characterizing intricate phenomena.52 Numerous scholars have developed fractal theory to study the fractal characteristics of the inner pore network and particle surface of coals.52,53 These studies have demonstrated that the pore space of coals is statistically selfsimilar. Therefore, fractal dimension has been extensively employed for quantifying the complexity of structure and physical properties of coal.54−56 Determination of fractal dimensions may be accomplished by analysis of microstructural images (such as the box-counting method, the fractional Brownian motion method, and the area measurement method).50,57 Measurements of adsorption capacity (such as CH4 adsorption)55,58 or capillary pressure (such as the mercury injection method)52,56 have also been proposed to estimate fractal dimensions, but these measurements are generally destructive and time-consuming. Nuclear magnetic resonance (NMR), by contrast, is a rapid and nondestructive method of fractal dimension analysis and provides information on pore size and surface area. Moreover, NMR measurements have been previously validated for the characterization of Received: August 23, 2016 Revised: October 25, 2016 Published: October 31, 2016 A

DOI: 10.1021/acs.energyfuels.6b02133 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels Table 1. Power and Heating Time of Coal Samples sample

P (kW)

Th (s)

sample

P (kW)

Th (s)

sample

P (kW)

Th (s)

SM-01 SM-02 SM-03 SM-04 SM-05 SM-06 SM-07

6 4 6 4 6 6 4

48 36 24 48 36 20 30

SM-08 SM-09 SM-10 SM-11 SM-12 SM-13 SM-14

2 6 4 2 6 4 2

60 16 24 48 12 18 36

SM-15 SM-16 SM-17 SM-18 SM-19 SM-20

6 4 2 6 4 2

8 12 24 4 6 12

Figure 1. Experimental procedure.

coal.38,48,59−65 This work is designed to assess the effect of microwave irradiation on fractal features of coals by NMR measurements.

generators, and waveguides. Its frequency is 2.45 GHz, and three microwave powers (2, 4, and 6 kW) can be selected. In addition, the heating times can be set to any value.

2. EXPERIMENTAL SECTION

3. RESULTS AND DISCUSSION 3.1. Theoretical Relation between T2 Distribution and Fractal Dimension. NMR can measure the longitudinal (T1) and transverse (T2) relaxation times to characterize the pore structure of rocks. However, the measurement of T2 has an advantage in testing time and usually provides similar results with respect to T1. Therefore, T2 is the preferred measurement method.68 Therefore, T2 distribution was measured in this paper for analyzing fractal dimension. Three possible relaxation mechanisms contribute to T2 spectra. They are the bulk fluid process (TB), surface interactions at the pore−solid interface (TS), and diffusion in internal field gradients (TD).67

2.1. Coal Cores. Twenty bituminous coal cores 50 mm in diameter and 60 mm in height from ShenMu Coal Field (northwest in China) were obtained. Proximate analysis of coal was accomplished according to the Chinese Coal Proximate Analysis Standard GB/T 212-2008. Maximum vitrinite reflectance (Ro,m) of the three selected samples in oil (room temperature, 23 °C) was in the narrow range of 0.65− 0.75%. Coal samples have similar maceral compositions and moisture contents. Coal cores were heated by microwave irradiation with various microwave powers (P) and heating times (Th), as shown in Table 1. The experiment was carried out according to the procedure shown in Figure 1. “Drying” signifies that coal cores were vacuum dried for 24 h (6 h each at 40 and 60 °C and 12 h at 80 °C) and then cooled to ambient temperature in a vacuum drying oven. “Saturation” is coal cores saturated with 100% distilled water for a minimum of 24 h. “Airdrying” is drying of coal cores for at least 2 weeks under ambient conditions. “Microwave heating” indicates that samples were processed with microwave irradiation at ambient conditions. The NMR measurements carried out after the coal sample include drying (Sir), saturation (Sw), and air-drying (Sad). 2.2. NMR Measurements. In general, any nucleus with an odd number of protons or neutrons or both (such as the nuclei of hydrogen (1H), carbon (13C), and sodium (23Na)) can be measured by NMR.66 However, except hydrogen, the others element of earth formations cannot be detected by a borehole NMR logging tool.67 To date, almost all NMR logging and NMR rock studies are based on responses of the nucleus of the hydrogen atom.67 In this paper, NMR measurements were conducted using a MINI MR instrument manufactured by the Shanghai Niumag Corporation (China). The instrument has a constant magnetic field strength of 0.53 T and resonance frequency of 23 MHz. Under this magnetic field strength, only hydrogen atoms can be measured. Furthermore, relaxation time of hydrogen bound to solid materials is always attenuated too quickly to collect. Therefore, hydrogen bound to matrix materials do not contribute to NMR measurements, and the results do not need to be calibrated. The constant temperature of the permanent magnet is 32 °C. The Carr−Purcell−Meiboom−Gill (CPMG) method was used to measure the transverse relaxation time (T2) distribution. In this experiment, interecho spacing is 0.232 ms, number of scans 32, sampling frequency 333.333 kHz, and number of iteration 1 × 105 using the simultaneous iterative reconstruction technique. 2.3. Microwave Heating System. The microwave heating system consists of a control system, a resonant cavity, six microwave

1 1 1 1 = + + T2 TB TS TD

(1)

⎛S⎞ 1 = ρ2 ⎜ ⎟ ⎝V ⎠ T2S

(2)

where ρ2 [μm/ms] is the transverse surface relativity and S/V is the surface to volume ratio that relates to the pore size. TB can often be neglected, but it is important for some situations, such as when the pore fluid is very viscous, the pore fluid has a high concentration of paramagnetic ions, or the pore fluid has fine suspended particulates.68,69 As previously mentioned (in section 2.1), the coal core is saturated with 100% distilled water during measurements; distilled water does not have a high concentration of paramagnetic ions or fine particulates in suspension. Additionally, the viscosity of water is 1.002 mpa·s,70 and water is not considered a viscous fluid. Therefore, the influence of TB on T2 can be neglected in this work. TD is the molecular diffusion in the magnetic field gradient. Diffusion in internal field gradients exhibits a complicated pore size dependence that may affect the overall T2 distribution.71 The magnetic susceptibility contrast between grain materials and pore fluid is an essential contribution to the magnetic field gradient. Water is weakly diamagnetic with a susceptibility of −0.72 × 10−6 cgs/cm3,68 whereas the susceptibility of coal is B

DOI: 10.1021/acs.energyfuels.6b02133 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels −7.7 × 10−6∼−4.2 × 10−6 cgs/cm3.72 Therefore, the magnetic susceptibilities of coal and water do not contrast with each other. The CPMG method is the best pulse sequence known for mitigating the effect of diffusion in a magnetic field gradient68 and has been used to measure the T2 spectrum in this paper. Therefore, the influence of TD on the T2 distribution can also be neglected in this paper, and eq 1 can be simplified to ⎛S⎞ 1 = ρ2 ⎜ ⎟ ⎝V ⎠ T2

(3)

Generally, the T2 spectrum is directly proportional to pore size r, which is given by the equation

T2 ∝ r

Figure 2. NMR bound-water model.67

(4)

in all of the pore apertures. In the SPBW model, whether the sample is saturated or not, the T2 distribution is related to pore size. However, in the MBW model, the T2 distribution is related not only to pore size but also to water saturation of samples. Researchers have generally found that the MBW model is more reasonable than the SPBW model.74,75 In NMR measurements, the pore system is always treated as a single pore, and the water in the pore system can freely diffuse; the water in the small pore is thus always treated as a part of the large pore.67 In other words, the small pore would not show in the T2 distribution at Sw. However, if there is some space in a pore system because of air or other gas, the membrane-bound water has still been reserved; the small pores would show in the T2 distribution,75 and the degree of water saturation would influence the T2 distribution. Therefore, the T2 distributions at Sw, Sad, and Sir differ from one other, which is shown in Figure 3.

The distribution of pore sizes in rock may be described by a mass fractal model in which the distribution of pore sizes follows a fractal scaling as54,71,73

N ( > r ) ∝ r −D

(5)

where N is the number of pores and D is the fractal dimension. The volume fraction VP of the total pore volume composed of pores of size r and smaller is given by71

VP =

3−D

( ) r

rmax

3−D

( ) 1−( ) −

rmin rmax

rmin rmax

3−D

(6)

where rmax and rmin are the largest and smallest pore sizes present. respectively. By combined eqs 4 and 6, eq 6 can be rewritten as 3−D

( ) V = P

3−D

( ) 1−( )

T2 T2max

−

T2min T2max

T2min rmax

3−D

(7)

where T2min and T2max are the shortest and longest values of the T2 spectrum, respectively. Considering that the value of T2min is sufficiently small compared with the value of T2max, eq 7 can be simplified as ⎛ T2 ⎞3 − D VP = ⎜ ⎟ ⎝ T2max ⎠

(8)

which can then be rewritten as D=3−

ln VP ln T2 − ln T2max

Figure 3. NMR T2 distribution of the coal sample. (9)

Water is assumed to be in the wetting phase and remains at the fast-diffusion limit as the water saturation degree (Sd) varies. The volume of water in a pore at any Sd is SdV, and the interfacial contact area for water S is independent of Sd; therefore, eq 3 can be rewritten as75 ρ ⎛S⎞ 1 = 2⎜ ⎟ T2 Sd ⎝ V ⎠ (10)

However, when T2 = T2max, VP is equal to 1, and eq 8 can be rewritten as 1 = 13−D, and the fractal dimension D cannot be calculated at this point. Therefore, eq 9 is used to calculate the fractal dimensions of the coal samples in section 3.3, except the data point at T2max. 3.2. NMR Relaxation Time Distributions of Coals. In general, the pore water can falls into two classes: bound and movable water. The state of bound-water in pores can always be explained by two models: the small pore bound-water model (SPBW) and the membrane bound-water model (MBW) (as shown in Figure 2).67 The main difference in these two models is that SPBW hypothesizes that the bound water only exists in the small-aperture pore and MBW believes bound water exists

When the T2 relaxation time is at Sw, the value of Sd is equal to 1. Therefore, the NMR T2 distribution of the coal sample at Sw is proportional to the pore size. The T2 distribution at Sw after microwave irradiation (red line in Figure 3) is shifted to the right compared to that before microwave irradiation (green line in Figure 3). This suggests that the pore diameter of coal C

DOI: 10.1021/acs.energyfuels.6b02133 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels samples enlarges after microwave irradiation. In addition, the T2 distribution at Sw is always shown as three peaks. However, when the T2 distribution is at Sir and Sad, the value of Sd is less than 1. At this time, the annular layer of irreducible water would remain in the pores. Therefore, the T2 distribution at Sir and Sad provides information on the small pores that was not visible at the Sw condition. Conversely, the drying process removes the mobile water in large pores and the long T2 components in the spectra at Sw. Consequently, the T2 distribution at Sir and Sad are all located to the left-hand side of the T2 distribution at Sw, and the T2 distribution at Sir and Sad is unimodal whereas Sw is trimodal, as shown in Figure 3. This verifies that the membrane-bound water model is more reasonable in this work. Interestingly, the effect of microwave irradiation on the amplitude of the T2 distribution is different at Sir and Sad. The amplitude of the T2 distribution at Sir before microwave irradiation is larger than that after, suggesting that the pore size of coal cores would increase after microwave irradiation. Therefore, the larger the pore size is, the more easily the water migrates when coal cores are drying. The changing amplitude also indicates that the connectedness of pore space in coal samples increases after microwave irradiation. However, the amplitude of T2 distribution at Sad before microwave irradiation is smaller than that after microwave irradiation, suggesting that the number of small pores increases after microwave irradiation. Interestingly, the amplitude of T2 distribution at Sad is always larger than that at Sw, implying that some water remains in the larger pores. This is strong evidence supporting the reasonableness of the membrane-bound water model, i.e., each pore size group has a nonzero irreducible water saturation associated with it. In general, the bound water associated with each pore size group is a decreasing function of pore size,74 and the membrane-bound water model is more reasonable for coal cores in this paper. The T2 spectrum, which normally ranges from 0.01 to 10,000 ms, provides the pore size distribution. As mentioned previously, the small pores would not be evident in the T2 distribution at Sw but would be evident in the T2 distribution at Sir and Sad. The T2 spectrum at less than 1 ms corresponds to micropores; the T2 spectrum between 1 and 10 ms corresponds to mesopores, and the T2 spectrum at longer than 10 ms corresponds to micropores/microfractures, which is also shown in Figure 3. 3.3. Fractal Dimensions and Porosity of Coals. The curve of ln(Vp) versus ln(T2/T2max) of the coal core is shown in Figure 4. Theoretically, the fractal dimension is an intrinsic property of a surface and does not depend on its size,76 and thus, the linear regression equation was used to calculate the fractal dimension. The slopes of curves in Figure 4 were determined to obtain the fractal dimensions of coal cores pre(Dpre) and postmicrowave (Dpost) heating. Fractal dimensions Dpre and Dpost of all cores are compiled in Table 2. The resulting values of fractal dimensions for all investigated coal cores vary between two (the topological dimension of a surface) and three (the topological dimension of a volume). The values of Dpre range from 2.156 to 2.228 with an average value of 2.196 (red line in Figure 5), and Dpost range from 2.001 to 2.184 with an average of 2.111 (blue line in Figure 5). Both the ranges and average values of Dpost are smaller than those of Dpre, indicating that microwave heating decreases fractal dimensions of the coal core. In general, permeability of a coal core increases with decreasing fractal dimensions.56,77 Therefore, microwave heating of coals increases the permeability. It is interesting to

Figure 4. Curve of ln(Vp) versus ln(T2/T2max) of the coal sample.

note that Dpost increases initially but then decreases with increasing microwave energy (red arrow line in Figure 5). In this paper, the coal sample was heated under an air environment, which causes oxidation of the surface of the coal sample with increasing temperature. The oxidation of the pore surface tends to decrease the fractal dimension.78 However, decreased fractal dimensions give water access to previously inaccessible regions that tends to increase this dimension. The changes in the fractal dimension of coals with microwave heating are determined by a balance between these two main mechanisms of pore development. The relationship between fractal dimension and microwave energy is illustrated in Figure 5. Interestingly, when microwave energy is larger than 150 kJ, the difference between Dpre and Dpost increases, and the value of Dpost is closer to two. This suggests that surface of the pore space would be more flat after heating with a certain amount of microwave energy. It should be noted that the microwave energy can be determined by multiplying microwave power by heating time. Unfortunately, raw coal was used to carry out the experiments described in this paper, so the inside temperature of the cores could not be determined. According to the work of Feng and Zhao, this critical temperature may be 300 °C.79 In this paper, the gravimetric method was used to measure the porosity of coal samples. The porosities of coal samples pre(φpre) and postmicrowave (φpost) of all samples are compiled in Table 3. It can be clearly seen that the value of φpost is always larger than that of φpre, suggesting that microwave irradiation can increase cleats or induce fractures in coal samples. The relationship between porosity and surface integral area of T2 distribution at Sw is shown in Figure 6 and can be fit using an exponential function. However, there is no remarkable functional relationship between porosity and fractal dimension, as shown in Figure 7. This indicates that the fractal dimension is an intrinsic property of a surface and does not depend on its porosity.

4. CONCLUSIONS This paper aimed to study the influence of microwave heating on the fractal dimension of coal cores. There were 20 coal samples heated at 2.45 GHz with variable power (2, 4, and 6 kW). A nondestructive approach, NMR, was used to perform measurements before and after microwave heating under different situations (drying, saturation, and air-drying). The transverse relaxation time (T2) distribution was acquired to D

DOI: 10.1021/acs.energyfuels.6b02133 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels Table 2. Fractal Dimension of Coal Samples before and after Microwave Heating fractal dimension

a

fractal dimension

fractal dimension

sample

Dpre

Dpost

sample

Dpre

Dpost

sample

Dpre

Dpost

SM-01 SM-02 SM-03 SM-04 SM-05 SM-06 SM-07

2.194 2.176 2.228 2.192 2.227 2.227 2.205

a 2.024 2.145 2.001 2.001 2.184 2.169

SM-08 SM-09 SM-10 SM-11 SM-12 SM-13 SM-14

2.156 2.204 2.165 2.192 2.207 2.177 2.218

2.130 2.125 2.154 2.134 2.175 2.142 2.123

SM-15 SM-16 SM-17 SM-18 SM-19 SM-20

2.207 2.198 2.169 2.206 2.188 2.175

2.138 2.106 2.106 2.094 2.142 2.125

This coal sample broke into pieces after microwave heating.

Figure 5. Relationship between fractal dimension and microwave energy.

Figure 6. Relationship between porosity and surface integral area of the T2 distribution at Sw.

analyze the influence of microwave heating on pore structure of coal cores. It was found that the membrane-bound water model is reasonable for interpreting the effect of water saturation on T2 distribution. Therefore, small pores were not evident in the T2 distribution at Sw, opposite to the T2 distribution at Sir and Sad. The T2 spectrum at less than 1 ms corresponds to micropores; the T2 spectrum between 1 and 10 ms correspond to mesopores, and the T2 spectrum at longer than 10 ms corresponds to microspores/microfractures. Additionally, it was found that the pore size, pore number, connectivity, and porosity increase after microwave irradiation. A theoretical equation relating fractal dimension and transverse relaxation time was also proposed, and the fractal dimensions of coal cores pre- and postmicrowave heating were calculated. Microwave heating decreases the fractal dimension of coal cores, suggesting that microwave heating increasing the permeability. However, the relation between porosity and fractal dimension is not significant, suggesting that the fractal dimension is an intrinsic

Figure 7. Relationship between porosity and fractal dimension.

Table 3. Porosity of Coal Samples before and after Microwave Heating porosity

a

porosity

porosity

sample

φpre (%)

φpost (%)

sample

φpre (%)

φpost (%)

sample

φpre (%)

φpost (%)

SM-01 SM-02 SM-03 SM-04 SM-05 SM-06 SM-07

4.70 14.16 13.71 13.24 8.66 13.12 14.32

a 17.48 17.17 18.08 13.56 15.69 16.96

SM-08 SM-09 SM-10 SM-11 SM-12 SM-13 SM-14

13.89 13.94 14.77 13.54 14.09 13.60 13.09

15.94 16.09 16.71 15.69 16.02 15.78 15.58

SM-15 SM-16 SM-17 SM-18 SM-19 SM-20

13.25 13.05 13.07 13.02 13.75 13.66

16.07 15.99 16.23 16.41 17.08 16.70

The coal sample broke into pieces after microwave heating. E

DOI: 10.1021/acs.energyfuels.6b02133 Energy Fuels XXXX, XXX, XXX−XXX

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property of a surface and does not depend on its porosity. In summary, microwave irradiation was found to affect the petrophysical characteristics of coals, and this approach shows the feasibility of degassing coal beds.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 051683884401. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support for this work is provided by National Basic Research Program of China (973 Program) (2011CB201205), the National Natural Science Foundation of China (51204174), the Fundamental Research Funds for the Central Universities (2012QNB01), and the Brain Gain Program & Start-up Program of China University of Mining & Technology (2011RC07), which are gratefully acknowledged.

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DOI: 10.1021/acs.energyfuels.6b02133 Energy Fuels XXXX, XXX, XXX−XXX