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УДК 530.1+519.6
ИЗМЕРЕНИЕ ПОРИСТОСТИ И ПРОНИЦАЕМОСТИ ФОРМАЦИИ. РАДИАЛЬНЫЕ СКВАЖИННЫЕ ВОЛНЫ
Виталий Николаевич Доровский
Baker Hughes, Новосибирский технологический центр, 630128, Россия, г. Новосибирск,
ул. Кутателадзе, 4а, доктор физико-математических наук, технический советник, тел. (383)332-94-43, e-mail: [email protected]
Юрий Вадимович Перепечко
Baker Hughes, Новосибирский технологический центр, 630128, Россия, г. Новосибирск, ул. Кутателадзе, 4а, кандидат физико-математических наук, научный сотрудник, тел. (383)332-94-43, e-mail: [email protected]
Предлагается скважинный метод измерения пористости формации. Акустические колебания возбуждаются в скважине. Максимальное значение спектрального давления на резонансной частоте зависит от пористости. Коэффициент затухания давления также зависит от пористости. Имея две функциональные зависимости от пористости и проницаемости, полученные теоретически, и измеряя максимальное значение давления и коэффициент затухания, математически из системы двух уравнений определяется проницаемость и пористость.
Ключевые слова: скважинное измерение, пористость, проницаемость, радиальные волны, резонанс, формация.
MEASUREMENT OF POROSITY AND PERMEABILITY. RADIAL BOREHOLE WAVES
Vitaly N. Dorovsky
Baker Hughes, Novosibirsk Technology Center, 630128, Russia, Novosibirsk, Kutateladze Str. 4a, Doctor of Sciences, Technical Advisor, tel. (383)332-94-43, e-mail: [email protected]
Yury V. Perepechko
Baker Hughes, Novosibirsk Technology Center, 630128, Russia, Novosibirsk, Kutateladze Str. 4a, Ph. D., Scientist, tel. (383)332-94-43, e-mail: [email protected]
The paper proposes a method for measuring formation porosity. Acoustic waves are generated in a borehole. The maximal value of the spectral pressure at the first resonant frequency depends on the porosity and permeability of the formation, as well as the attenuation parameter. Having two computed functional dependences together with measured maximal value of pressure and attenuation factor, we can find formation porosity and permeability from a system of two equations.
Key words: borehole measurement, porosity, permeability, radial waves, resonance, formation.
It will not be exaggeration to say that the variety of modern logging methods used for simultaneous porosity and permeability measuring of a formation beyond a borehole has been rather limited. This paper outlines the physical foundations of a
fairly simple and effective resonance method for measuring porosity and permeability in a saturated porous medium beyond a borehole. In the method, the borehole is considered to contain a cylindrical source placed along its axis. The source generates acoustic signals at a resonant frequency of borehole's radial eigenwaves and a frequency close to the resonant one. The parameters of the physical model: borehole fluid density is 1.0 g/cm , sound velocity in borehole fluid is 1.45 km/s, porosity is
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0.05-0.40, solid matrix density is 2.57 g/cm , saturating fluid density is 1.0 g/cm , first compressional sound velocity in formation is 2.2 km/s, second compressional sound velocity of sound in formation is 0.9 km/s, shear sound velocity in formation is 1.6 km/s, saturating fluid viscosity is 0.0105 P, formation permeability is 0.020.22 D.
In the method proposed, a source with an arbitrary shape of the pulse may be used. The main requirement to the source is that pulse duration should ensure the maximum of its spectrum to be close to the resonant frequency of the borehole. In the system under consideration (source radius 1 cm, borehole radius 10.46 cm), the resonant frequency is about 2 kHz, which is close to the maximum of the pulse spectrum. In the case of attenuating radial waves (after the source stops operating at the resonant frequency) the characteristic pressure change in time follows the pattern presented in Fig.1.
the first resonant frequency
In Fig. 2, you can see the spectrum of borehole eigenwaves. The blue curve corresponds to the spectrum of the signal obtained via 2D modeling and the red curve corresponds to the spectrum of the borehole eigenwaves computed analytically. The first resonant peak is similar in the both cases.
saturated formation
As the next step, the way the pressure behaves at the lower resonant frequency is analyzed. The pressure value at the first maximum (pressure at the frequency of the first resonant peak) is determined by the formation permeability k and the porosity ^ : A™« =v( k, . The graph of this dependence as a function of porosity is presented in Fig. 3.
0,008 0,007 p* f max
0,006
0,005 0,004 0,003
-k=10 mD
-k=50 mD
0,002 -k=100 mD
-k=200 mD
0,001 0,000 k=300 mD
0, p.U.
0,00 0,10 0,20 0,30 0,40 0,50
Fig. 3. The spectral pressure at the first resonant frequency as a function of porosity
at different values of permeability
The pressure attenuation in time at the resonant frequency is plotted in Fig. 4, where the blue curve denotes the signal; the red curve is the signal filtered by the
Butterworth high pass filter of 7th order (at 5 kHz cutoff frequency); and the green curve denotes the exponential envelope of the filtered signal.
The envelope of maximal pressure values
The attenuation factor of the pressure waves (the envelope of the maximal values of pressure) is determined by permeability k and porosity ^ : P = ^(k,. The graph of this dependence is presented in Fig. 5.
ß, 103 S"1
k=50mD
- k=100mD
k=300mD
0, p.U
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45
Fig. 5. The attenuation factor as a function of porosity at different values of
permeability
The expressions P = ^( k, and pmax = y( k, at given sound velocities in the fluid and the formation constitute a set of equations for finding permeability and porosity.
Measuring pmax , p and solving the system of two equations k,^) = P, k,^) = pmax, one finds k and ^ . To perform the procedure described above, one needs to know or find independently such parameters as the sound velocity and the physical medium densities. Unlike the first compressional and shear sound velocities, the second compressional sound velocity in a saturated formation usually is not measured using borehole logging and remains unknown. In order to establish this value in the method proposed, you can select the characteristic velocity of the second compressional mode for the porous medium under consideration, because the changes in the second compressional velocity cp 2 do not affect, within the error bars, the measured values of
porosity and permeability. The functions k, , k, are determined theoretically
for a two-velocity physical model [1].
The present article describes the principles of a new borehole method for finding formation porosity and permeability based on measuring and analyzing parameters of the radial waves in the borehole at frequencies close to the resonance of borehole eigenwaves. The maximum value of pressure and its attenuation factor at the boundary between the borehole and the porous formation beyond the borehole wall depend on formation porosity and permeability, so these two parameters can be found mathematically. Variations of the second compressional velocity of sound in the porous formation beyond the borehole bring corrections to the porosity value found that remain within the measurement error bars.
REFERENCES
1. Blokhin A.M., Dorovsky V.N. Mathematical modelling in the theory of: Multivelocity Continuum. - New York: Nova Science Publishers Inc., 1995. - 183 p.
© B. H. ffopoecKUU, №. B. nepeneHKO, 2016
