George V. Chilingar - Acoustic and Vibrational Enhanced Oil Recovery

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 r kand length l kat 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, is the channel’s cross-sectioned area, and ρ is the fluid density.

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 is satisfied where L is the distance between irradiators and λ is the wave length in the medium, then these irradiators interact between themselves. At that, every individual irradiator is working in the pressure field of all other irradiators, which is equivalent to increased resistance to irradiation. As a result, active power increases and passive power, decreases.

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 H pth condition is satisfied, then accrual of the estimated irradiation power in the well should be expected to be as follows:

(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

(2.36)

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]:

(2.37)

where S kand l kare, 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, The total area of channel openings in the well length H pis equal to Using Equation (2.37), the resonance frequency for a well with perforation channels is equal to

(2.38)

At the resonance frequency, irradiated on average the reservoir power is

(2.39)

and this is the reason why the effective absorption of the generator energy which is expended for irradiation through the perforation channels is determined by the density of perforation holes. As Equation (2.38)indicates, this value also defines the generator’s resonance frequency. Considering Equations (2.36)and (2.39), we will evaluate fading factor of the casing wave (caused by the acoustic irradiation through perforation channels) as