Evaluation of the cavitation generator efficiency in the hydro impulsive loosening of a coal-bed

. The paper presents the results of mining and experimental work, bench tests and theoretical studies of the energy characteristics of the stationary and pulsating fluid flow, which allow to estimate the efficiency of the cavitation generator in the hydro impulsive loosening of an outburst-prone coal-bed. The active stage of the hydro impulsive loosening and the effective range of the amplitude-frequency (AF) spectrum of the generator operation acoustic signal have been established by the AF spectrum of the sound accompaniment of the hydro impulse impact and the backup pressure of the liquid in the well. By calculation for this range the energy characteristics of the static and dynamic components of the pulsating fluid flow were determined. This made it possible to determine that the efficiency of the cavitation generator, all other conditions of the coal-bed hydro loosening being equal, is 4.8–1.2 times higher than the efficiency of the static impact.


Introduction
It is known that the imposition of dynamic loads on the block-layered structure of a coalbed increases the speed and quality of its hydro loosening. In the Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine it was developed promising device for hydro impulsive impact on the coal-bed [1]. The device is created based on the standard sealer of the well "Taurus".
The generator of cavitational self-oscillations (hereinafter the generator) is installed in the tip of the sealer. This made it possible to eliminate energy losses and transfer the dynamic load to the coal-bed directly in the filtration section of the well.
The generator is the Venturi tube of special geometry in the flow part of which highfrequency self-oscillations of fluid pressure occur [2,3]. In the filtration section of the well, the energy of the cavitational oscillations of liquid medium is transformed into the energy of a hydro-impulse vibration. High-frequency impact of power pulses on the block-layered structure of the coal-bed leads to its fatigue state. Therefore, even at medium stresses that do not reach the strength of coal [4], a multidirectional network of microcracks develops and it is occurred the discontinuity in the coal-bed.
The indisputable advantage of this device, in contrast to the known mechanisms and methods [5][6][7], is the absence of additional energy sources and moving mechanical parts. The generator is located in the well and all the energy of cavitation self-oscillations is spent on the hydro impulsive loosening of the bed. When it is conducted the mining operations at threatened and dangerous beds by sudden coal and gas emissions, the "Rules ..." [8] defines the requirements for forecasting and controlling the danger of coal-bed for gas-dynamic phenomena (GDP). In order to control the dynamic parameters and evaluate the effectiveness of the new method of hydroimpulsive loosening [9], based on standard methods [8], new methods were developed to monitor the state of the coal bed and control the hydroimpulsive effect. The developed methods make it possible to control the process of hydro-loosening, but do not allow to estimate the effectiveness of the device operation. Therefore, the purpose of this work is to determine the efficiency of the device and evaluate its effectiveness. To achieve this goal, it was used the results of mining and experimental works, the results of bench tests of the device for hydro impulsive impact on the coal bed, theoretical studies of the energy characteristics of stationary and pulsating fluid flow.

Validation of the range for research
The basis of our research will take the results of mining and experimental works at the pressure of the fluid at the generators inlet Р n = 11 МPa.
In Figure 1 it is shown the amplitude-frequency (AF) spectrum of the sound of a hydroimpulsive loosening of a coal bed, recorded by the ZUA-98 equipment [10,11]. The seismogram reflects the intensity of acoustic emission (AE) of the signal in the frequency range from zero to 3.0 kHz. The soundtrack spectrum of AE characterizes its energy at different intensity of the process. In our example, the range of low-frequency vibrations of 100-150 Hz is associated with electrical noise. Part of the energy of highfrequency oscillations of 200-800 Hz is associated with the process of fluid filtration and the development of cracks around the well, and some with ultrasonic vibrations of the coal bed.
The high-frequency region of the spectrum is associated with pressure pulses, which are realized by the device generator. If there are no high-frequency components in the AF spectrum with a high level of energy of the sound impulse of a hydro-impulse effect, then the generator operates without load, i.e. hydro impulsive loosening of bed does not occur. By the results of the control it was found that at Р n = 11 MPa, the active process of hydro impulsive loosening starts at a backup pressure in the well is about 1.5 MPa. The most intense cracking in the bed occurs at the backup pressure from 3.0 MPa to 6.0 MPa within 5-6 minutes, while its maximum was 7.5 MPa. After that, the backup pressure sharply decreased to 2.0 MPa, and then, after 20-30 seconds, to about 0.8 MPa.
The analysis of the results of the monitoring of the backup pressure of the liquid in the well and the sound accompaniment spectrum of the hydro-impulsive loosening (see Fig. 1) are allowed to establish the following: 1. The active stage of hydro impulsive loosening of the bed occurs within 6-7 minutes at the backup pressure of the liquid in the well from 1.2 MPa to 7.5 MPa. The frequency response of the generator in this range is from 1.5 kHz to 6.3 kHz; 2. The range of the AF spectrum of the signal generator operation AE is from 1.4 kHz to 2.8 kHz. The most effective stage corresponds to the frequency of 1.6-2.4 kHz, and the maximum values of the energy level f≈2.0 kHz.

The method of calculating the generator efficiency
The useful energy that realized under hydro-impulsive action consists of static and dynamic components. Following the works [12], the total energy flow E is determined by the expression where Р p Q n = E S is the energy flow corresponding to a steady flow, not associated with oscillations. It is determined by the backup pressure Р p and flow rate through the pump Q n . The second term in equation (1) is determined by the oscillatory components of pressure -∆Р and flow rate ∆Q and called the flow of vibrational energy.
Oscillatory component ∆Q is determined from the condition of the balance of its equality of the detached part of the settled cavitation cavity ∆V c multiplied by oscillation frequency f The frequency of self-oscillations f is determined by the formula [13] , cr cr e where Sh e -Strouhal number, whose approximation equation is determined on the basis of experimental data Sh e =0.0066 r cr +0.0749 with certainty R 2 =0.99; , r cr и v cr -the cavitation parameter, the radius of the generator's critical section, and the fluid velocity were determined by known formulas.
The amplitudes of the self-oscillations of the volume ∆V к were determined from the condition of the maximum volume of the settled cavitation cavity at the moment of its separation at  c   d (where  c and  d -axial lengths of the cavern and generator diffuser) where  -expansion angle of the generator diffuser,  -the angle of expansion of the fluid jet, µ -generator flow rate coefficient equal to 0.95.
The axial length of the cavity depending on the degree of development of cavitation is determined in accordance with [14] by the formula Thus, the calculation of the total energy flow E (1) is made taking into account the oscillatory components of the flow rate ∆Q according to the formula (2) taking into account (3)-(5), and the pressure Р -according to the refined linear mathematical model of the cavitation generator [15].

Analysis of the results
Calculated dependencies of oscillatory components of pressure Р, flow rate Q and frequency f from backup pressure Р n in the range of its change from 0.5 to 9 MPa are presented on Figure 2. From the above results it can be seen that the range of the AF spectrum of the AE signal of the most effective stage of the generator operation (1.6-2.4 kHz) corresponds to the backup pressure in the well from 1.2 to 3 MPa.
The analysis of the established dependencies ΔР=f(Р p ) and ∆Q=f(Р p ) shows that with growth of Р p values of oscillatory components Р, ∆Q increases dramatically and, at certain values of Р p ≈1.8 and Р p ≈1.3 MPa respectively, reach their maximum. The maximum value of ΔР approximately 1.9 times exceeds the pressure at the inlet to the generator Р n . Further, with an increase in the backup pressure of the liquid in the well, it is observed decreasing of their values to almost zero.
The calculations allowed us to determine the energy flux, which corresponds to oscillatory components E o =∆Р·∆Q, and the total energy flux E (Fig. 3). 3. With an increasing of the backup pressure value Р p from zero to ≈1.7 MPa, the total energy flux E increases under hydrodynamic action, reaching a maximum value of E max ≈ 6.5 kJ/s, with its subsequent decreasing. When Р p ≈ 5.5 MPa, the total flux E reaches the minimum value Consideration of the calculated dependencies of efficiency under pulsed and static effects on the bed on the backup pressure Р p (see Fig. 3) shows that with increasing of backup pressure Р p from 0.5 MPa the efficiency η o first increases sharply, reaching a maximum value of 0.87 at Р p ≈1.9 MPa, and, further, decreases to 0.6 at Р p ≈ 5.5 MPa.
This behavior of η o =f (Р p ) is caused by the nature of the dependence of E on Р p (Fig. 3). A further increasing of efficiency η o at Р p >5.5 MPa is explained by the significant domination of the energy flux corresponding to the steady-state flow over the oscillatory component, which practically acquires a zero value at Р p ≈8.5 MPa.
Comparison of dependencies η o =f (Р p ) and η s = f(Р p ) shows that in the range of backup pressure Р p variation from 0.5 MPa to 6 MPa, the impulse effect on the coal bed is much more effective than the static injection.

Conclusions
Analysis of the results of mining and experimental studies made it possible to establish the working frequencies range of the device for the hydro impulsive effect on the coal bed. By calculation for the established frequency range the energy fluxes are determined corresponding to the static and hydro impulsive injection of the liquid into the coal bed. It made it possible to establish that: -ceteris paribus (in pressure of injection and in the range of backup pressure from 1 to 6 MPa ) the efficiency of hydro impulsive action exceeds the efficiency of static action by about 4.8-1.2 times, which leads to decreasing in energy consumption by about 50 %; -the proposed method for evaluating the effectiveness of the device for hydroimpulsive action on a coal bed is of practical importance. At the design stage of new or improved existing equipment it allows to evaluate the effectiveness of the operation of cavitation generators in the process of hydro impulsive action without additional experimental studies.