That is why various submersible resonance devices are used, in which a set frequency vibration source is rigidly tied with acoustic reflecting filters [17]. These devices include a generator and a resonator enclosed in the body. At that, the fluid column filling the cavity of a resonator chamber forms a vibration contour in which a standing wave is generated. The resonance excitation of vibrations is achieved if the reflector length L and generator operating frequency νo are tied as follows:
where c is the wave propagation phase velocity.
Using of similar devices with fixed parameters in practice is not sufficiently efficient because the elastic wave phase velocity in a well fluid depends on the reservoir elastic properties and immersion depth and besides may change from one well to the next [4]. If the wave running in a productive interval of a well with perforation holes in the casing, then its phase velocity also depends on the reservoir porosity, permeability, compressibility, and well fluid viscosity [23]. All this results in a substantial instability of the existing devices resonance regime because these devices have been designed according to simplified rules without considering the aforementioned factors. Besides, these devices cannot be too long, and this in restricting the frequency regime of vibration excitation. As a result, resonance lengthwise vibrations of the fluid within the device are created, and at irradiation into the well, the vibration energy is passed along the column of the well fluid beyond the productive interval limits and is irradiated into overlying and underlying unproductive rocks. A possibility of achieving a well fluid effective lengthwise resonance was studied using “sliding” reflecting filters installed within the productive interval.
For instance, a well’s resonance excitation regime may be achieved using hollow downhole reflector-filters filled with gas and fit on the production tubing. Such design does not require a hermetic contact with casing walls. Before running into a well, positions of the reflecting filters along the well length and relative the vibration generator may be changed. Distances between the reflectors are selected so that most energy from the generator was concentrated in the productive interval. The field excited in the enclosing rocks is close in its character to a finite length pulsating cylinder.
At the operation of the downhole vibration source within the limits of productive interval, a vibrating energy may be additionally irradiated which creates the emergence of pulsating fluid flows in the well’s perforation holes. As the perforation channels are narrow, the fluid motion velocity in then is high compared with the fluid flows within the well proper. Within some volume small compared with the wave length is alternatively created the excess or shortage of a given medium’s matter; its surface is permeable for a given medium and is a sovereign type radiator. That is why every perforation channel of radius rk and length lk at low frequency may be considered a point monopole exciting a spherically symmetric wave in the enclosing rocks. This wave is mostly defined not by geometric size of the perforation channel but by the size of generator’s created outflowing fluid flow.
The vibration energy irradiated by an individual perforation channel, in considering of its geometrical parameters, may be presented as follows:
(2.34)
where V is the velocity amplitude of fluid motion in a perforation channel,
The irradiation efficiency of each individual perforation channel is low mostly due to a low resistance to the irradiation at low frequency. However, if a system is available of closely spaced monopole irradiators and a condition
At synphase operation of a group of similar irradiators, the total irradiation power is equal to the power of every one of them multiplied by squared number of the irradiators [16]. If for a perforation interval Hp th condition
(2.35)
here, n is the perforation density (number of holes per unit length of the perforation interval).
For studying additional energy of individual channel, it is necessary to provide a sufficiently efficient transition mechanism of pulsating pressure in wells into vibration velocity fluid motion in channels. This process is accompanied by a high extent of tube wave fading in the well fluid caused by a low absorption on the casing walls and in the fluid as well as by the elevated acoustic irradiation of the perforation channels. Most of the casing wave energy is absorbed through acoustic irradiation in channels in the reservoir perforation interval.
A similar mechanism is operating in a well with a fluid and perforation channels as an oscillator with lumped parameters. A low basic frequency of vibration in such as oscillator is reached either by the participation in vibration of two media with drastically different properties (for instance, gas bubbles, and liquid) or by the realization of mechanism present in a Helmholtz resonator (where at a small actual mass of the vibrating medium it is possible to create a large amount of effective mass).
When a vibration source is operating in a well, fluid flows are generated in perforation holes. Due to a narrow channels’ diameter, the motion flow in them is high compared with the fluid’s velocity in the well. The kinetic energy
is concentrated in perforation channels despite that the actual fluid mass in the well is much greater than the fluid mass in the channels. Whereas the elastic energy is concentrated within the well. Therefore, as the potential and kinetic energy are localized in different media (channel medium and in the well medium), the well may be considered an analog of Helmholtz resonator. On coordinating the generator operating frequency with eigen frequency of such resonator effective transmission of the generator energy in to kinetic energy of a fluid in the perforation channels occurs. The perforation channels represent monopole sources having purely active resistance at resonance frequency. The resonance vibration frequency of such an oscillator is [8]:
where Sk and lk are, respectively, the area and length of a channel, respectively; ρ and β are the density and compressibility of a vibrating fluid, respectively; and Ω is the volume of fluid amount possessing potential elastic energy.
One can now estimate the amount of fluid volume possessing a store of the potential elastic energy.
For this case,