Keywords

1 Introduction

Solid materials are subjected to external conditions such as mechanical and temperature loads, which generate local stress concentrations within them [1]. In this process, the strain energy is rapidly released in the form of waves, and this release process is known as acoustic emission [2]. Kaiser found in tests of the acoustic emission properties of metals that the acoustic emission of metal specimens subjected to unidirectional stretching began to be noticeable when the internal stress reached the maximum prior stress to which the material was subjected [3]. Goodman found in compression tests of rocks that the Kaiser effect still applied to rocks. Mogi [4] and Boyce experimentally derived the relationship be-tween the magnitude of rock acoustic emission activity and loading. Since then, more scientific research and technical applications have contributed to the development of AE techniques, which have been applied to various engineering problems [5].

Shales have ultra-low permeability properties and store significant hydrocarbon resources beneath them [6]. Laboratory-based hydraulic fracturing experiments have advantages over onsite microseismical monitoring experiments. Firstly, the laboratory can control the stress loading and injection pressure; secondly, the laboratory hydraulic fracturing experiments can accurately simulate the hydraulic process and obtain data with high signal-to-noise ratio [7,8,9]. The experimental shale itself has a large fracture, and the natural fracture has a strong influence on the growth direction of the newly formed fracture [10].

2 Experimental Details

2.1 Experimental Parameters

Sample size: 710 × 710 × 914 mm. A 530 mm deep borehole was drilled in the vertical laminar surface of the specimen, a high strength steel pipe with 25 mm outer diameter and 19 mm inner diameter was fixed, and a 100 mm wide slit was symmetrically cut at 405 ~ 505 mm depth to serve as a water pressure channel. In view of the complexity of shale fracture morphology, the method of 6-side average layout is adopted. As shown in Fig. 1.

Fig. 1
Left, a diagram displays the top view of the sample with inner and outer lengths and widths of 710 and 762. At the center is the pipe with R 19 millimeters. Middle, side view displays the pipe has a total height of 530 and the wall is 530 high. Right, a 3-dimensional graph in X, Y, and Z axes.

Rock sample size and sensor coordinate space

Full size image

2.2 Experimental Procedure

The Hydraulic fracturing experiment is divided into two stages. In the first stage, the active acoustic emission signal scheme is adopted. By tapping each sensor to transmit the signal, other sensors are used to capture the event and locate the active tapping position. The second stage of work is to hydraulically pressurize, crack the hole wall, capture the event with the sensor, and apply the code analysis results validated in the first stage.

3 Methodology

3.1 Event Detection

AIC method uses the concepts of entropy and variance. The calculation is based on Eq. 1, and the result is shown in Fig. 2.

$$AIC\left( {t_{w} } \right) = t_{w} *\log \left( {{\text{var}} \left( {R_{w} \left( {t_{w} ,1} \right)} \right)} \right) + \left( {T{}_{w} - t{}_{w} - 1} \right)*\log \left( {{\text{var}} \left( {R_{w} \left( {1 + t_{w} ,T_{w} } \right)} \right)} \right)$$
(1)
Fig. 2
A line graph of A U versus time. The line starts at (0, 6700), passes through (0.11, 6400), (0.125, 6700), (0.2, 6550), (0.3, 6450), to (0.4, 6700). All values are approximate.

AIC method capture event start time diagram

Full size image

3.2 Signal Location

The method of cell meshing is used to locate the active excitation signal of the test rock sample. The assumption of uniformity is made inside the rock, and the theoretical calculation time is obtained by the path/velocity integral. Then the theoretical time and t_obs output in the event detection are fitted to locate the actual unit position of the sound source. (\({t}_{obs}=tpick\_all\left[:,i\right] .-tpick\_all\left[i,i\right]\)).

The theoretical time needs to be calculated by path/velocity integral and further fitted with t_obs. The theoretical formulas needed are as follows:

$$f\left( x \right) = \frac{{\left| {\left| {g_{\left( x \right)} - d} \right|} \right|}}{2},\;d_{i} = t_{obs}^{i}$$
(2)
$${g}_{i}=\frac{1}{v}*\sqrt{{({x}_{r}^{i}-{x}_{s})}^{2}+{\left({y}_{r}^{i}-{y}_{s}\right)}^{2}+{({z}_{r}^{i}-{z}_{s})}^{2}}$$
(3)
$$t_{nobs}^{i} = g_{i} \left( {x_{r}^{i} } \right) + e,\;e\sim {\text{N}}\left( {0,\sum e } \right)$$
(4)

Formula (2) is the fitting of theoretical time and actual time, Formula (3) is the theoretical method to calculate theoretical time, and the path integral is done on the known linear path, and formula (4) is the noise e added considering the instrument error, which is determined in the fitting of the calculation time and observation time.

3.3 Spectrum Analysis

The Fourier transform, which can represent complex functions as trigonometric functions or linear combinations of their integrals, is widely used in digital signal processing [11].

$$F\left( \omega \right) = F\left( {f\left( t \right)} \right) = \int {f\left( t \right) \cdot e^{ - i\omega t} } dt$$
(5)

[ω is the frequency, t is the time, \({e}^{-i\omega t}\) is the complex function].

3.4 Tomography

Tomography is widely used in seismic waveform analysis. After the focal location is completed, the change of seismic wave transmission is analysed with the given distribution of seismic receiving stations and focal points. If the seismic wave travels through an abnormally low velocity region, the time of its arrival at the seismic station and the theoretical velocity calculation model will have a large error.

In addition, the signal received by the receiver also carries a lot of information inside the transmission material, through the full use of these information can improve the resolution of the tomography.

4 Results and Discussion

4.1 Event Detection

Figure 3 shows the Akaike information criterion method for detecting the start time of an event.

Fig. 3
Forty-eight line graphs of c h 1 to c h 24.

AIC method result output

Full size image

4.2 Signal Location

As shown in the Fig. 4, take e = 60 ms by calculation.

Fig. 4
A line graph of time versus c h 1. Both lines start at (c h 1, 0). Time of observation passes through (c h 4, 450), (c h 12, 900), (c h 20, 700), to (c h 24, 700). Time of calculation passes through (c h 4, 450), (c h 12, 900), (c h 20, 700), to (c h 24, 700). All values are approximate.

Calculated time versus observed time

Full size image

The localization results are shown in Figs. 5 and 6. Ignoring the localised areas on the surface, the localised points in the interior marked by red lines are the more concentrated areas of acoustic signal emission. It roughly shows the acoustic signal emission during the hydraulic fracturing phase within the rock, demonstrating that although there are more marginal events, it is still possible to roughly identify the area of event occurrence.

Fig. 5
Six dot plots. c h 17 c h 19 c h 18 c h 20, c h 10 c h 12 c h 9 c h 11, c h 6 c h 8, c h 5 c h 7, c h 4 c h 2 c h 3 c h 1, c h 16 c h 14, c h 15 c h 13, and c h 24 c h 22 c h 21 c h 23 are plotted at (200, 500), (500, 500), (200, 250), (500, 250), respectively. All values are approximate.

Location results (active)

Full size image
Fig. 6
1, a 3 dimensional graph of x versus y, z. Dots are scattered across the space. 2 to 4, 3 dot plots of Z to X, Z to Y, and Y to X. Dots from (0, 900) to (250, 0) and (250, 900) to (800, 0), (0, 0) to (700, 900), and (100, 0) to (600, 800), respectively, are highlighted. Values are approximate.

Location results (passive)

Full size image

4.3 Spectrum Analysis

Take the first event(active) as an example for spectral analysis, and the result is shown in Fig. 7.

Fig. 7
Twenty-four line graphs of Fourier c h 1 to 24 plotted in spec versus frequency. All the graphs initially exhibit an increase, then a decreasing trend.

High frequency missing signal propagation paths

Full size image

It can be found from the pictures that these lost band points are basically after the Y = 40 cm plane, with the absence of high frequencies in the X = 0 plane not obvious, and only in sensor 6, near Y = 20 cm, where there is an absence near X = 70 cm and a missing signal across the upper and lower bottom surfaces.

It can therefore be roughly guessed that a fracture surface exists near X = 70 cm at Y = 40 cm and runs through the upper and lower bottom surfaces. The progression from the X = 70 cm surface towards the interior of the rock progresses towards the fracture surface in a progressive negative direction on the Y axis until it extends to the vicinity of sensor 6.

4.4 Tomography

To simplify the calculation process, six sections can be cut out of the rock cube, each containing eight sensors. To perform in-plane chromatographic imaging of the intercepted plane.

Through several iterations, a 4 × 5 division was determined. As shown in Fig. 8.

Fig. 8
A diagram displays meshing. 8 dots are plotted at (250, 25), (550, 25), (720, 300), (720, 600), (500, 950), (250, 950), (25, 600), and (25, 300). Each dot is linked to other dots.

Tomography meshing

Full size image

Approximating the transfer path straight line, the path length of the signal transmission path for any two sensors is calculated for all velocity cells and the data is stored in the path matrix (28 × 20).

From [\(\frac{1}{v}\)] = [\({L}^{T}*L+\lambda *I\)]\[\({L}^{T}*T\)], The distribution of calculated speeds is shown in Table 1.

Table 1 Speed distribution data
Full size table

Reduction of the velocity distribution to the section divider.

Calculation by objective data sensor 2 with sensor 4:

\(v=l/t=713\times {10}^{-3}m/806\times {10}^{-6}s=885\mathrm{ m}/{\text{s}}.\)

As shown in Fig. 9, the data in red is below average speed (885 m/s).

Fig. 9
A Cartesian plane of Y from 0 to 800 and Z from 900 to 0 is divided into 4 columns and 5 rows. Each cell has a value, from left to right, bottom to top, as 1070, 931, 748, 896, 766, 1236, 755, 890, 951, 550, 4301, 1155, 917, 1547, 840, 714, 979, 839, 645, and 2171.

Comparison of chromatography results

Full size image

5 Conclusion

The findings of this paper are as follows.

Experimental results of hydraulic fracturing acting on shales with primary natural fractures were investigated. Under pressure, new fractures develop more along the primary fractures. When the stress on the rock reaches a prior maximum stress, close to rupture, an acoustic signal is emitted from inside the rock, which is captured by externally placed sensors.

Exploration of signal processing. By mastering the principles of analysis, constructing a code system for signal processing, completing a series of tasks such as detection, localization, spectral analysis and laminar imaging, the entire state of the rock sample before and after the test was analysed and calculated. Reference is provided to further promote the application of acoustic emission technology.

This study focuses on laboratory shale hydraulic fracturing and analyses the fracture condition of cracks through data from 24 sensors. The signal processing method in the data model is also verified. Systematic ideas are also presented for work in the field of structural health monitoring in the civil engineering industry, particularly in the area of crack acoustic emission signal localization.