**5. Conclusions**

from the sample boundary dependence on time of AE event occurrences is shown in figure

which is a solution of one-dimensional porous elasticity equation, is shown in Figure 14 by red curve. It should be noted that the sample length was 83 mm, which is shown in the diagram by dotted line. The number of registered AE events was not high, it restricts an accuracy of the

t, sec

The number of registered AE events was not high, it restricts an accuracy of the method.

which is a solution of one-dimensional porous elasticity equation, is shown in Figure 14 by red curve. It should be noted that the sample length was 83 mm, which is shown in the diagram by dotted line.

If we compare Table 1, Table 2 and Table 3 we will see, that the permeability based on AE variation in time estimation gives values which are close to that obtained using data on pore pressure drop; nevertheless, r-t method gives values which are not contradict other results but differ from them

Events

Sample boundary

Figure 14. Dependence of distance from the sample boundary on time of AE event occurrences.

t, sec

**Figure 14.** Dependence of distance from the sample boundary on time of AE event occurrences.

14. An envelope curve.

1008 Effective and Sustainable Hydraulic Fracturing

significantly.

exp.6

exp.22

r, mm

r, mm

*r* = 4*πD*(*t* −*ts*),

method.

In the paper, the results of experimental study of saturated porous sample fracturing due to pore pressure rapid drop are discussed. It was found, that acoustic emission AE (corresponded to microfracturing) was spreading from the end of the pressure drop to the closed end of the sample, and that maximal number of AE events was registered at some distance from the opened end.

The number of AE pulses increased with every next pressure drop, meanwhile the number of pulses with high amplitudes diminished. The prolongation of the pressure gradient maximal values is in agreement with AE maximal rate.

It was found that multiple microfracturing occurred during the pore pressure drop; the microfractiring is governed by pore pressure gradient.

The model of AE relation with the pore pressure gradient was considered based on the following assumptions: AE event occurred when the pore pressure gradient reaches some critical value; the critical value varies and can be described by Weibull distribution, which is often used to describe fragment size distributions in fractured rocks.

Permeability variation during the fluid pressure drop was estimated by means of fluid pressure data and pore-elastic equation solution for small time intervals (0.01 sec). It was found that the sample permeability is high in initial stage of the pressure discharge and decrease during pore pressure drop.

It is shown that if the change in microseismic activity in time is measured, the distribution of the critical pressure gradient is known for the considered material and the boundary conditions are given (for example, the change in pressure in the well), it is possible to calculate the pressure gradient, and on this basis, the permeability of the porous medium.

The study showed possibility to solve an inverse problem of defining permeability by registering microseismic activity variation in particular volume of porous medium alongside with pore pressure measurements at some point.

#### **Acknowledgements**

The idea of the study was suggested by Dimitry Chuprakov. The authors wish to acknowledge the generous support of Russian Foundation for Basic Research (RFBR project # 10-05-00638) and of the Russian Academy of Sciences Presidium Program #4.

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