Introduction

I.1. Context

Hydraulic fracturing is used not only for the production of hydrocarbons, but also for geothermal energy production or fresh water production. It was implemented for the first time in 1947 in Kansas. Two years later, the first commercial fracturing treatments were conducted in oil wells in Oklahoma; but, it was only with the massive exploitation of shale gas, during the last decade, that the process became popular in the media outside the circle of experts. In 2008, over 50,000 well fractures were carried out around the world and it is estimated that over one in every two wells drilled today undergoes a fracturing treatment.

Hydraulic fracturing involves the high pressure injection of a fluid in a wellbore, at a specified depth. When the pressure applied by the fluid is greater than the lithostatic gradient (weight of the rock above the place where the pressure is applied) and the local resistance of the rock, a fracture is created that can extend over several hundred meters, provided that enough fluid is injected to maintain a sufficient pressure. During the process, a proppant (generally grains of sand or ceramic) is injected to prevent the crack from closing. Drilling water contains additives suited to the type of rock encountered, to facilitate the fracturing operation and to prevent the closure of the cracks created. These cracks act as drains, granting access to volumes of rock located a long way from the wellbore, but close enough to the created drain.

Hydraulic fracturing was first applied to conventional geological reservoirs. However, its use in low-permeability formations called tight gas reservoirs (TGRs), which are a thousand times less permeable than conventional reservoirs, has meant overcoming severe problems. Tight gas reservoirs and shale gas reservoirs contain gas mainly, stored in low-permeability rocks (0.1 mD). Hydraulic fracturing generates a few large cracks and gas may migrate toward these cracks and bubbles be produced. The extracted gas originates from a volume of rock near the surface of the fracture, through which the gas migrates due to the difference in pressure. Gas production consists of draining this zone where permeability is low. The gas trapped between the drained areas remains inaccessible. Once drainage is carried out, the production undergoes a very rapid decline.

The questions raised by hydraulic fracturing in the context of unconventional resources concern several issues. First, the rise of methane to the ground surface or to water tables has fueled public debate, although the extent of the phenomenon is still being discussed. The second issue concerns the water used during the fracturing process. It contains chemical elements that have been used for the fracturing process or dissolved from the underground host rock. This water ought to be stored safely on the surface and subsequently treated. Third, hydraulic fracturing may induce seismicity. The injection of water has reactivated existing faults in some cases in Switzerland and Great Britain. Finally, and probably more importantly, extracting gas with a sufficiently attractive economical benefit calls for a large number of wells that are closely spaced, and thus for a concentration of infrastructures within a dense logistic network is required to provide water and drilling equipment. Therefore, the environmental impact may be severe, particularly in protected or densely inhabited areas.

Under these circumstances and while waiting for the necessary feedback from experience, some European countries have banned hydraulic fracturing, opening the path to research on potential alternatives.

A first option is to change the fracturing fluid. The penetration of the fracturing fluid in the porous host rock depends directly on its viscosity. By reducing this parameter, the fluids more easily penetrate the porous rock and then if we apply enough pressure, induce a dense crack system. This principle being set, the problem resolves around finding the "right" fluid. There are many candidates such as propane, nitrogen, carbon dioxide, etc. In its liquid state, carbon dioxide has a viscosity 10 times lower than water; in the supercritical state (normal conditions of deposit), its viscosity is even lower. Each solution has benefits, beyond the simple fact that the fracturing fluid is no longer water and that, strictly speaking, we can no longer call it "hydraulic fracturing". Nitrogen is not harmful for the environment, and using carbon dioxide can help store it at the same time. There are also disadvantages: replacement fluids are more compressible than water, which makes the process less efficient; carbon dioxide can recombine with water and form a corrosive acid that may corrode the surrounding carbonate rocks.

The second approach is dynamic loading. In statics, the surface of a crack created in a material is proportional to the energy transferred to the volume of material that will break. Dynamic loading, however, forces, a large amount of energy into a small volume of material. In this volume, and because there is such a large amount of energy, a large area of cracks will be created, inducing a dense fracture network. As the loading wave spreads inside the material, it will therefore cause fragmentation, thereby connecting the initial and newly-created network of cracks. In quasi-brittle materials such as rocks, damage generated by dynamic loads results in distributed microcracking compared to damage generated by static loads, which is localized and consists of large cracks. On the basis of this observation, the objective is to use dynamic loads to generate distributed damage around a borehole, i.e. dense microcracking which should subsequently increase the rock permeability [CAO 01a, CAO 01b, DEN 02].

Dynamic loading can be induced, for example, by explosives placed in the wells. There is another possibility, on which we will focus in this book: dynamic loads generated by pulsed arc electrohydraulic discharges (PAEDs).

I.2. Principle of the technique and illustrative experiments

There is considerable interest in the use of PAEDs in engineering practice. They can be used for several purposes, for instance treating water to remove organic chemical impurities, as acoustic sources in medical or sonar applications, selective separation of solids or plasma blasting in the mining industry. In plasma blasting, there are two different technologies: the first one consists of placing the electrodes directly on the rock. The electrical arc is generated inside the rock. It produces a spall and drilling consists of generating successive spalls. The second technology involves generating the electrical arc in a liquid. The electrical discharge induces a shock wave, which is subsequently transmitted to the rock.

As we will see in the following chapters, the load applied to the rock in the proximity of the drilling site is a pressure wave generated by an electrical discharge between two electrodes placed in a wellbore filled with water. The amplitude of this pressure wave can reach up to 200 MPa, while its duration is about 100 microseconds. This pressure wave is transmitted to the rock by the fluid inside the wellbore, and creates microcracks of decreasing density with increasing the distance from the well.

In order to study the feasibility of PAEDs for fracturing rocks, preliminary experiments have been carried out [MAU 10]. The objective was to investigate the experimental correlation between cracking and damage due to a compression shock wave with the intrinsic permeability of the material and with its microstructure characteristics. The wave was generated under water and then transmitted to a cylindrical specimen 100 mm diameter and 125 mm in height (see Figure I.1). The amplitude of the compressive shock wave was prescribed by the amount of energy that is involved in the PAED. Microcracking and compression damage were due to local extensions induced by the Poisson's effect developed in the course of loading. Single and repeated shocks were considered.

Figure I.1. Experimental set-up for PAED on mortar samples

Then, the cylindrical specimens tested in the above apparatus were cut into disks that were 50 mm thick and their permeability to nitrogen was measured (flow in the axial direction). The intrinsic permeability of the specimen was obtained according to Klinkenberg's model which relates the apparent gas permeability of the material to its intrinsic permeability and to the inverse of the gas pressure [KLI 41]:

where (K, Ka) are the intrinsic and the apparent permeability, respectively.

Two sequences of tests have been carried out. In the first one, the specimens were subjected to a single shock wave under variable pressure levels. The peak pressure ranged from 0 to 250 MPa (0, 15, 30, 45; 60 90, 180 and 250 MPa). The variation of the intrinsic permeability with the peak pressure is shown in Figure I.2. Two distinct zones were observed. If the peak pressure was below 90 MPa, no significant change in permeability was observed. The experimental data in this range spaned from 2.10-17 to 6. 10-17 m2, which was a rather usual scattered for the intrinsic permeability of mortar measured on various samples of the same mix. Then, permeability increased almost linearly in a semi-log plot when the peak pressure increased from 90 to 250 MPa.

Figure I.2. Evolution of the permeability with applied pressure

In the second sequence, the specimens were subjected to...