Application of Image Processing in Evaluation of Hydraulic Fracturing with Liquid Nitrogen: A Case Study of Coal Samples from Karaganda Basin

Abstract

Research of microstructure and permeability evolution of coal following LN₂ treatment elucidate the process of cryogenic fracturing due to environmentally friendly behavior in comparison with conventional hydraulic fracturing. The evolution of the 2D microstructure of bituminous coal before and after LN₂ treatment was examined using a high-resolution camera. The image processing was implemented using functions from the OpenCV Python library that are sequentially applied to digital images of original coal samples. The images were converted into binary pixel matrices to identify cracks and to evaluate the number of cracks, crack density, total crack area, and average crack length. Results were visualized using Seaborn and Matplotlib Python libraries. There were calculations of total crack area (TCA), total number of cracks (TNC), crack density (CD), the average length of cracks (Q2), first (Q1) and third (Q3) quartiles in fracture length statistics. Our findings demonstrate a progressive increase in the Total Crack Area (δTCA) with longer freezing times and an increased number of freezing–thawing cycles. In contrast, the change in crack density (δCD) was generally unaffected by freezing time alone but exhibited a significant increase after several freezing–thawing cycles. Among the freezing times investigated, the highest crack density (CD) value of 300 m⁻¹ was achieved in FT60, while the lowest CD value of 31.25 m⁻¹ was observed in FT90 after liquid nitrogen (LN2) treatment. Additionally, the FTC4 process resulted in a 50% augmentation in the number of cracks, whereas the FTC5 process tripled the number of small cracks.

1. Introduction

In 2020, the world’s entire energy consumption was 556.63 exajoules (556.63 × 10¹⁸ joules), 83.1% of which was provided by hydrocarbons [1,2,3,4], and the condition will not change dramatically in the forthcoming years [5,6,7]. To meet the growing energy demands of society, there is a need for continuous advancement in upstream industry technologies. These technological advancements are crucial for increasing production rates and improving the recovery factor of energy resources. By enhancing these factors, we can effectively address the increasing energy requirements of humanity. According to Muggeridge et al. (2006), the average recovery factor in the world ranges from 20% to 40%, which means that approximately ⅔ of total oil and gas reserves cannot be recovered [8]. Usually, the gas production rate in low permeable reservoirs decreases quickly. Stimulation processes are needed in coal beds, tight sandstones, and shale to accelerate recovery since permeability and porosity of the reservoir formation are some of the main factors that affect the rate of oil and gas recovery [9]. Thus, developing technologies in the oil and gas industry is needed to increase the production and recovery factor to cover human energy needs [10,11,12,13]. Hydraulic fracturing is widely recognized as the primary technique for enhancing gas production rates, particularly in regions where water resources are abundant. This method entails the injection of water, sand, and chemicals into the reservoir to create and extend fractures, thereby facilitating the more efficient flow of fluids from the reservoir [14,15,16,17]. In addition, proppants, e.g., treated sand, are used in hydraulic fracturing, as they lodge inside the fracture and prevent these fractures from closing [18]. Stimulation is often required for the economic viability of a hydrocarbon extraction project [19,20,21]. Most coalbed methane (CBM) reservoirs have low permeability, below 10 mD, impeding gas flow from coal to the wellbore [22].

In hydraulic fracturing, various types of power fluids can be used, e.g., water, oil, foam, acid, or cryogenic fluid. The most common is slick water [23] with friction-reducing additives. With low-viscosity slick water, the fracture expands more in length than width, and chemical additives avoid corrosion and bacterial growth. Moreover, water is often the most economical, and furthermore, this water can be recycled [24,25], reducing makeup volume in further stimulation jobs or stages. However, total water consumption is still very high, and low-viscosity water does not transport proppant agents easily. Oil-based fluid was the first implemented in hydraulic fracturing with high viscosity [23]. This type of fluid can be applied in colder regions, where water freezing is a concern [26]; however, oil-based fluid is more expensive and involves higher safety and ecological damage risks [23]. Cryogenic fracturing technology overcomes many of these problems with minimal ecologic damage [27,28,29,30].

Cryogenic fracturing can replace traditional hydraulic fracturing processes [31], with the principal mode of rock breakage being thermal shock [32,33]. As cold liquid nitrogen is injected into the hot formation, heat, due to the laws of thermodynamics, will move from the formation to nitrogen; consequently, sudden cooling occurs in the formation. During this heat transfer and rock cooling, enormous thermal stresses develop over very short distances, often exceeding rock strength, resulting in fracturing. The greater the temperature difference, it is anticipated that cryogenic fracturing performance will also increase [34,35]. The emulsification issue of injected fluid with reservoir fluid is also avoided with cryogenic fracturing, as liquid nitrogen is more compatible [36]. While solids contract with reduced temperature, water inside the formation converts to ice and expands in volume, thereby expanding the cracks [37,38,39,40]. Besides creating new fractures, the positive effects of cryogenic fracturing on the petrophysical properties of the rock include cumulative porosity increase and residual porosity decrease, as during fracturing, closed pores open and interconnect with each other. In addition, it was found that added cycles of freezing and thawing, as compared to only adjusting freezing time, improve the permeability dramatically. After multiple cycles of freezing–thawing, particles from the rock surface operate further as proppants [41,42,43]. In terms of injected proppants, liquid nitrogen is a suitable transport medium compared to other types of fluid [44]. The freezing of water during cryogenic fracturing improves the relative permeability of nitrogen [45,46]. Various experiments demonstrated that cryogenic fracturing is very efficient in tight and low permeability shale reservoirs, as it improves gas recovery and minimized formation damage, water consumption, and contamination, compared to water-based fluid [47,48].

Karaganda basin is one of the greatest-producing regions in central Asia, with proven reserves of 41.3 billion tons of coal, of which 11 million tons are produced every year. The coal basin is a latitudinal and asymmetrical syncline partitioned into three main troughs by two transverse uplift zones: the Alabayskaya I anticline and the Maykudukskoe uplift enclosing the central Karagandinskaya syncline where the city of Karaganda is located as shown in Figure 1 [49]. This paper examines alterations in pore structure characteristics from coal specimens taken from the Karaganda region after exposure to LN₂ as a waterless fracturing method for CBM reservoirs. The recommended parameter for the present study of LN₂ fracturing is the time in the LN₂ treatment with two different methods. This research investigates the impact of the recommended parameter on the physical properties of the samples.

2. Experimental Process

Our specimens were initially cored with a diamond bit to 16 mm in length and 32 mm in diameter from a large coal mass recovered from mining operations in the Karaganda basin in Kazakhstan. The coal samples were first cut using a rock saw and then carefully abraded to achieve appropriate dimensions while minimizing the presence of external fissures. The coal samples were drilled in a way that the axial direction of each coal rock was vertical to its bedding plane. The permeability of original coal specimens is very small (~1 mD), which shows that Karaganda coal cannot supply satisfactory gas production without stimulation. Given the limited water resources in Kazakhstan, conventional water stimulation methods are not feasible. Moreover, the use of water for hydraulic fracturing would prolong the dewatering period, worsen water-blocking issues, and hinder methane production.

After preparing the coal samples, they were placed in a drying oven for 24 h and immediately immersed in LN₂. Implementing LN₂ use was divided into freezing time (FT) and freezing–thawing cycles (FTC). The freezing times were set as 30, 60, 90, 120, and 150 min, whereas as many as five freezing–thawing cycles were included in FTC experiments, labeled as C1–C5 cycles. Each freezing–thawing cycle included 30 min of freezing and 30 min of thawing at room temperature. Figure 2 shows the region and the coal mine from which samples were taken, and Figure 3 presents the experimental process.

3. Methodology of Image Post-Processing for Crack Evaluation

Python code was developed to evaluate the fracture of coal samples using functions implemented in the Python OpenvCV library [50]. First, the color image of a crack sample is resized and transformed to a grayscale image using OpenvCV commands resize() and cvtColor(), respectively. Then, the bilateral filter bilateralFilter() is employed. This filter is highly effective in noise removal while keeping edges sharp. Next, the image brightness and its contrast are accordingly adjusted. To compute the binary pixel matrix, adaptive Gaussian thresholding adaptive threshold () is used where entries with ones corresponding to dark regions. Pixels representing the disc with the sample are selected using the user-defined function crop_center(). The cropped disc region’s connected components are analyzed using the function connectedComponentWithStats(), which computes a Boolean image’s connected components and produces statistical output for each label. The OpenCV implementation of this function is based on the Spaghetti Labeling algorithm of Bolelli et al. [51]. The components with an area less than the prescribed threshold are considered negligible. This step is necessary to remove those pixels that constitute noise and do not represent the real cracks. Those pixels of the processed image which do not represent the fracture are removed manually. Finally, pixel groups disconnected by only a few white pixels are reconnected using two morphological operations erode() and dilate(). Statistical sample characteristics are computed using OpenCV, numpy, pandas libraries, while the visualization is realized using matplotlib and seaborn libraries. The user-defined function get_params() returns the statistical parameters listed in

Table 1. Statistical parameters for crack evaluation.

Statistical Parameter	Description
TCA	Total crack area
Q2	Median of the crack lengths
Q1	The 25th percentile score of crack lengths
Q3	The 75th percentile score of crack lengths
TNC	Total number of cracks
CD	Crack density

.

The total crack area (TCA) is defined as a ratio between the area occupied by cracks (A_C) and the total area of the analyzed area (A_I), and it directly determines the degree of surface cracking. The total crack area is evaluated as follows:

$$TCA=\frac{A_C}{A_I}\cdot 1000 \left[\frac{{\mathrm{cm}}^2}{{\mathrm{m}}^2}\right],$$

(1)

while the crack density was calculated according to

$$CD=\frac{{\sum }_{i=1}^n{N}_{C,i}}{n\cdot L_s} \left[\frac{1}{m}\right],$$

(2)

where L_S is the length of the test line, i.e., the diameter of the analyzed area in the longitudinal direction, N_C,i is the number of cracks intersecting the i-th test line, and n = 4 stands for the number of test lines in a single sample [52]. The area occupied by cracks (A_C) and the total area of the analyzed region (A_I) is measured in pixels. A_C stands for the number of black pixels corresponding to zero entries in the Boolean image, while A_I = 480² is its total number of pixels. In the formula for computing TCA, the multiplier 10,000 is to show the result in $\left[\frac{{\mathrm{cm}}^2}{{\mathrm{m}}^2}\right]$.

The length of each crack was calculated using outputs of the OpenCV function connectedComponentsWithStats. To calculate the crack lengths, the list of thicknesses of each fracture is created as follows. The thickness is evaluated as the area of the fracture divided by the length of the diagonal of the bounding box surrounding it. After that, we take the average thickness of all cracks as the median of the list of thicknesses. Then, the list of lengths is created by dividing the area of each crack by the average thickness.

For each parameter p listed in Table 1, its relative change ${\delta }_p$ is defined as

$${\delta }_p=\frac{p_a-p_b}{p_b},$$

(3)

where $p_a, p_b$ correspond to the values of parameter $p$ after and before LN₂ treatment. For instance, ${\delta }_{TCA}$ denotes the relative change in TCA.

The results of the aforementioned program sections are illustrated in Figure 4, providing a visual representation of the digital image processing performed on the coal sample. The Python code for image processing is presented in Appendix A. The complete code with scripts for statistics evaluation is available at https://github.com/armanbolatov/coal_image_processing (accessed on 29 April 2023).

4. Experimental Results and Discussions

The coal samples were investigated under different LN₂ treatment conditions, comparing freezing time and freezing–thawing processes. Figure 5 presents the high-resolution photos of coal samples before and after different LN₂ treatment processes. The red dots were located on the samples as regions of interest to conduct SEM analysis. The digital images of coal samples were post-processed using our Python program, see Appendix A.

It can be observed that the number of black pixels corresponding to cracks increased after the LN₂ treatment. In particular cases, the parameters for the image processing function process_image were adjusted manually to reduce noise due to non-constant light conditions.

The total crack area (TCA) by Equation (1) and its relative change (δ_TCA) by Equation (3) are presented for each process in Figure 6a,b, respectively. In the following, we investigate δ_TCA for FT and FTC processes of different durations. The highest δ_TCA is achieved for the processes FTC4 and FTC5, while the maximal TCA is observed in FT150. The δ_TCA for FT30–FT150 and FTC1–FTC5 processes show an increasing tendency. Additionally, it can be noted that δ_TCA for FT30 and FT60 remains the same, but it increases by 430% and 390% from FT60 to FT90 and from FT90 to FT150, respectively. For the FTC process, we can see a similar trend, namely δ_TCA for FTC1 and FTC2 is almost identical; however, there is an increase of 600% and 690% from FTC2 to FTC3 and from FTC3 to FTC5. The relative changes for FT30 and FTC1 are the same, as shown in Figure 4b. The relative change of TCA for FTC2 is more by 66% compared to FT60, while for the FTC3 process, it is more by 130% compared to FT90. The trend remains for FT120 compared to FTC4 and FT150 compared to FTC5: δ_TCA of FTC4 is six times larger than for FT120, and δ_TCA of FTC5 is four times larger than for FT150.

LN₂ treatment weakens coal at the pore level with dependency on grain sorting, pressure, and temperature, but it is ambiguous if one or more mechanisms dominate over others. Pore water can induce damage to coal specimens through three distinct mechanisms: frost force, formation of ice lenses or wedges, and hydraulic pressure. Among these, frost force emerges as the primary factor responsible for pore structure damage, ultimately leading to increased permeability.

The total number of cracks (TNC) and its relative change (δ_TNC) are presented for each process in Figure 7a,b, respectively. FT processes achieved the highest TNC after LN₂ treatment for FT60 (173 cracks), while the lowest was for FT90 (7 cracks). In the case of FTC processes, the highest TNC was achieved for FTC2 (61 cracks), while the lowest was for FTC4 (17 cracks). Hence, the highest TNC is 25 or 3.5 times more significant than the lowest TNC for FT or FTC processes, respectively. The δ_TNC increases for FTC1-FTC5 processes, whereas there is no similar trend for FT30-FT150 processes. In the case of FT90, the TNC slightly decreases. Comparing FT and FTC processes with the exact duration of treatment, we observe that δ_TNC of FT30, FT60, and FT120 are more significant than for corresponding FTC processes, namely FTC1, FTC2, and FTC4. This can be explained by the fact that some cracks get connected as their size increases during the LN₂ treatment, consequently reducing TNC. In freezing time experiments, ice behaves as a consolidating factor of the coal sample, which prevails over the frost forces that decrease the sample strength and create more cracks than in freezing–thawing cycle experiments. On the other hand, the last experiment for both processes is an exception where FTC5 relative change is higher than FT150 due to insufficient time for force frost to act and create small fissures inside the coal seams. These observations agree with the work of previous researchers [53,54,55]. For example, compression stress is minor when there are sufficient cycles, but in initial cycles, compression stress is higher than in freezing time experiments with the same time in LN₂ treatment.

The crack density (CD) calculated by Equation (2) and its relative change (δ_CD) are shown for various processes in Figure 8. The highest crack density is achieved for FT60 and FT150 before and after the LN₂ treatment. The highest values of CD were achieved for the FT60 (300 m⁻¹) and FT150 (275 m⁻¹), while the lowest value of CD was for FT90 (31.25 m⁻¹) after LN₂ treatment. In the case of FTC processes, the highest CD was achieved for the FTC5 (131.25 m⁻¹), while the lowest was for FTC3 (43.75 m⁻¹) after LN₂ treatment. The highest CD is 9.6 or 3 times bigger than the lowest for FT or FTC processes. For all processes, δ_CD stays positive from 0.5 to 1.0 for FT processes, whereas the range of δ_CD is higher from 0.13 to 3.0. The relative changes in crack densities increase significantly for FTC2-FTC4 processes. The positive values of δ_CD indicate that CD increases during the LN₂ treatment. The highest δ_CD is achieved for FTC4 and FTC5, while the lowest for FTC2 and FTC3.

It can be noted that the average crack length and the quartiles decrease during the LN₂ treatment, as shown in Figure 9. There is no visible trend in results regarding crack length. The first and third quartiles for relative changes are the highest for the FTC4 process. For FT processes, the highest values of Q1, Q2, and Q3 after LN₂ treatment were achieved for FT150, while the lowest ones were for FT60. In the case of FTC, the highest values of Q1, Q2, and Q3 after LN₂ treatment were achieved for the FTC1, FTC1, and FTC5, while the lowest ones were for FTC2, FTC3, and FTC3, respectively. The negative trend of relative changes in the average crack length can be explained by the appearance of new cracks with small fracture lengths during the LN₂ treatment, as shown in Figure 5c and Figure 10c for the FT60 process.

In each histogram presented in Figure 10, the kernel density estimator (KDE) that describes the randomness of the data for the sample are represented by the orange and blue lines, which stands for the data before and after the LN₂ treatment, respectively. In the case of process FT30 (Figure 10a), the number of cracks of length 0–7 mm doubled, whereas the cracks of length 9–11 mm decreased. In the process FT60 (Figure 10c), the number of cracks of length 0–2 mm significantly increased from 45 to more than 130, and those of length 2–3 mm nearly doubled, whereas the number of cracks of higher length slightly decreased. In the case of FT90 (Figure 10e), the number of tiny cracks doubled, medium cracks of length 2–7 mm strongly decreased, and a single crack of length 14 mm was formed. In the case of FT120, shown in Figure 10g, the number of cracks of length up to 9 mm increased from 20 to 40, and two more cracks of length 17 and 19 mm were formed. The trends regarding FT150 and FT90 are similar concerning the disappearance of small cracks, as confirmed by their KDEs. In the FTC1 process (Figure 10b), the number of cracks of 0–5 mm and 10–16 mm slightly increased, while the number of cracks of medium length decreased. FTC2 (Figure 10d) and FTC3 (Figure 10f) increased the number of cracks, excluding several in the 8–14 mm range and 2–3 mm, respectively. The process FTC4 (Figure 10h) increased the number of cracks by 50%, whereas FTC5 tripled the number of small cracks and formed several 12–18 mm cracks, as shown in Figure 10j. Notice that the length of a crack was determined by considering its thickness; see Section 4.

Generally, LN₂ changes the physical and mechanical properties of coal specimens, and the damage is more significant as LN₂ treatment increases. The effects of thermal stress and temperature gradients in a porous coal sample are complex. The different phases present respond to thermal stress with different magnitudes and rates. Elements with large defacement are firmly pressed, while parts with low deformation are extended by force, resulting in unequal strain. Another critical factor is moisture after the method of freezing–thawing cycle LN₂ treatment. The greater the internal water content, the more precise the effect of freezing and thawing damage on the coal sample. During the extension period, the pore wall forms the mechanical action frost heave force, which is much greater than the compressive strength of coal, and the pore walls are pressed through this period, resulting in more damage. This leads to the formation of new cracks and the evolution of pre-existing fissures (permeability increases), while the frost heaves at the tip of fractures, leading to crack extension and, finally, to the fracture network, which is the desired outcome. In the freezing time method, ice is a consolidation agent for coal samples, which prevails over the frost forces that tend to decrease specimen strength. Future research is recommended to focus on exploring various stages of freezing–thawing cycles and developing models to simulate real-world coal bed methane (CBM) reservoirs.

5. Conclusions

The LN₂ fracturing method was proposed as an alternative to conventional hydraulic fracturing, pushing for eco-acceptable solutions. This research investigated the efficacy of LN₂ in coal fracturing, focusing on two different processes: freezing time (FT) and freezing–thawing cycle (FTC), using image processing methods to characterize treatment effects. An image processing workflow was generated to identify and characterize existing, new, and augmented fractures. The findings of the study revealed the following:

• The highest change in total crack area, δ_TCA, was achieved for the freezing–thawing process with four or five cycles of treatment, FTC4, and FTC5, while the maximum total crack area was observed with a freezing time of 150 min, FT150.
• For FT processes, the highest total number of cracks, TNC, after LN₂ treatment was achieved for FT60 (173 cracks), while the lowest was for FT90 (7 cracks). The highest TNC was achieved in FTC2 (61 cracks) for FTC processes, while the lowest was for FTC4 (17 cracks).
• The highest value of crack density, CD, was achieved in FT60 (300 m⁻¹), while the lowest value of CD was found in FT90 (31.25 m⁻¹) after LN₂ treatment.
• The process FTC4 increased the number of cracks by 50%, whereas FTC5 tripled the number of small cracks and formed several cracks of length. This fact leads to the creation of a fracture network, which is the desired outcome.
• The change in Total Crack Area (δ_TCA) increased progressively with both freezing time and the number of cycles.
• While crack density was strongly affected by all treatments, the change in crack density (δ_CD), generally, was not dependent on freezing time, but it increased dramatically after several freezing–thawing cycles. Overall, cracks elongate along with an overall increase in density.
• Prolonged freezing time shows benefits over shorter freezing time cycles until a threshold number of cycles is achieved when the physical changes in samples dramatically alter. The studies in crack characteristics infer permeability enhancement, yet this must be confirmed in follow-on tests on effectiveness.