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Ɋɚɫɫɦɨɬɪɟɧɚɫɬɚɰɢɨɧɚɪɧɚɹɧɚɩɨɪɧɚɹɮɢɥɶɬɪɚɰɢɹɧɟɫɠɢɦɚɟɦɵɯɝɪɭɧɬɨɜɵɯɜɨɞɜɧɟɨɞ -ɧɨɪɨɞɧɨɦɩɥɚɫɬɟ, ɞɥɹɤɨɬɨɪɨɝɨɩɪɨɢɡɜɟɞɟɧɢɟɤɨɷɮɮɢɰɢɟɧɬɚɩɪɨɧɢɰɚɟɦɨɫɬɢɧɚɬɨɥɳɢɧɭɩɥɚ -ɫɬɚɩɪɟɞɫɬɚɜɥɹɟɬɫɹɤɜɚɞɪɚɬɨɦɩɪɨɢɡɜɨɥɶɧɨɣɝɚɪɦɨɧɢɱɟɫɤɨɣɮɭɧɤɰɢɢɤɨɨɪɞɢɧɚɬɬɨɱɟɤɩɥɚ -ɫɬɚ. ɂɫɫɥɟɞɨɜɚɧɢɟɮɢɥɶɬɪɚɰɢɢɝɪɭɧɬɨɜɵɯɜɨɞɜɧɟɨɞɧɨɪɨɞɧɨɦɩɥɚɫɬɟ «ɦɟɬɨɞɨɦɩɟɪɟɯɨɞɚ» ɫɜɟɞɟɧɨɤɩɨɢɫɤɭɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯɩɥɨɫɤɨɩɚɪɚɥɥɟɥɶɧɵɯɩɨɬɟɧɰɢɚɥɶɧɵɯɬɟɱɟɧɢɣɢɞɟɚɥɶɧɨɣ ɧɟɫɠɢɦɚɟɦɨɣɠɢɞɤɨɫɬɢɫɩɨɦɨɳɶɸɫɭɩɟɪɩɨɡɢɰɢɢɬɨɱɟɱɧɵɯɢɫɬɨɱɧɢɤɨɜ ɢɦɭɥɶɬɢɩɨɥɟɣɪɚɡ -ɥɢɱɧɨɝɨɩɨɪɹɞɤɚ. ɉɪɢɦɟɧɟɧɢɟ «ɦɟɬɨɞɚɩɟɪɟɯɨɞɚ» ɜɦɟɫɬɨɨɛɵɱɧɨɝɨɢɧɬɟɝɪɢɪɨɜɚɧɢɹɞɢɮɮɟ -ɪɟɧɰɢɚɥɶɧɨɝɨɭɪɚɜɧɟɧɢɹɜɪɹɞɚɯɩɨɡɜɨɥɹɟɬɧɚɢɛɨɥɟɟɩɪɨɫɬɨɢɧɚɝɥɹɞɧɨɨɛɨɛɳɢɬɶɢɡɜɟɫɬɧɭɸ ɮɨɪɦɭɥɭȾɸɩɸɢɞɥɹɞɟɛɢɬɚɫɤɜɚɠɢɧɵɜɨɞɧɨɪɨɞɧɨɦɩɥɚɫɬɟ, ɪɚɫɲɢɪɢɜɟɟɩɪɢɦɟɧɟɧɢɟɧɚɜɫɟ ɦɧɨɠɟɫɬɜɨɧɟɨɞɧɨɪɨɞɧɵɯɩɥɚɫɬɨɜ, ɞɥɹɤɨɬɨɪɵɯɩɪɨɢɡɜɟɞɟɧɢɟɤɨɷɮɮɢɰɢɟɧɬɚɩɪɨɧɢɰɚɟɦɨɫɬɢ ɝɪɭɧɬɚɧɚɬɨɥɳɢɧɭɩɥɚɫɬɚɩɪɟɞɫɬɚɜɢɦɨɤɜɚɞɪɚɬɨɦɝɚɪɦɨɧɢɱɟɫɤɨɣɮɭɧɤɰɢɢ. ɉɪɢɷɬɨɦɩɨɥɭ -ɱɚɟɬɫɹɤɨɦɩɚɤɬɧɚɹɮɨɪɦɭɥɚɞɥɹɪɚɫɩɪɟɞɟɥɟɧɢɹɞɚɜɥɟɧɢɹɜɧɚɩɨɪɧɨɦɩɥɚɫɬɟɩɪɢɤɪɭɝɨɜɨɦ ɤɨɧɬɭɪɟɩɢɬɚɧɢɹɝɪɭɧɬɨɜɵɯɜɨɞ.
Ʉɥɸɱɟɜɵɟɫɥɨɜɚ: ɧɚɩɨɪɧɚɹɮɢɥɶɬɪɚɰɢɹ, ɜɨɞɨɩɪɢɬɨɤ, ɪɚɫɩɪɟɞɟɥɟɧɢɟɞɚɜɥɟɧɢɣ, ɞɟɛɢɬ ɫɤɜɚɠɢɧɵ, ɦɟɬɨɞɩɟɪɟɯɨɞɚ, ɤɪɭɝɨɜɨɣɤɨɧɬɭɪɩɢɬɚɧɢɹ.
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Ȼɢɛɥɢɨɝɪɚɮɢɱɟɫɤɢɣɫɩɢɫɨɤ
1. Ȼɟɪɟɫɥɚɜɫɤɢɣɗ.ɇ. //
. 2006. . 33. № 4. . 455—458.
2. ɗɦɢɯȼ.ɇ. //
. 2008. . 35. № 2. . 216—222.
3. ɒɭɩɥɢɧɆ.ɇ., Ȼɨɪɢɫɟɧɤɨȼ.ɇ.
// -
-. 2006-. № 8. . 381—384.
4. Ȼɚɬɭɪɢɧɘ.ȿ., Ɇɚɣɟɪȼ.ɉ.
, // . 2009. № 3. . 60—70.
5. Ȼɟɪɟɫɥɚɜɫɤɢɣɗ.ɇ. //
. 2003. . 67. № 5. . 78—84.
6. Bachman R.C., Harding T.G., Settari A. and Walters D.A. Coupled Simulation of Reservoir Flow, Geomechanics and Formation Plugging With Application to High-Rate Produced Water Reinjection, paper SPE 79695, SPE Reservoir Simulation Symposium, Houston, TX. Feb. 3-5, 2007.
7. Settari A. Reservoir Geomechanics and Subsidence, Proc. 8th Int. Forum on Reservoir Simulation, Iles Borromees, Stresa, Italy, June 20-24, 2005.
9. Tang Y., Yildiz T., Ozkan E., Kelkar M. Effects of Formation Damage and High-Velocity Flow on the Productivity of Perforated Horizontal Wells, SPE Reservoir Evaluation and Engineering Journal, V.8, N 4, P. 315—324, Aug. 2005.
10. ȽɨɥɭɛɟɜɚɈ.ȼ. . . : . ., 1972. 368 .
ɉɨɫɬɭɩɢɥɚɜɪɟɞɚɤɰɢɸɜɫɟɧɬɹɛɪɟ 2012 ɝ.
: Ⱥɧɬɨɧɨɜȼɢɤɬɨɪɂɜɚɧɨɜɢɱ — ,
, ɎȽȻɈɍȼɉɈ «Ɇɨɫɤɨɜɫɤɢɣɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣɫɬɪɨɢ -ɬɟɥɶɧɵɣɭɧɢɜɟɪɫɢɬɟɬ» (ɎȽȻɈɍȼɉɈ «ɆȽɋɍ»), 129337, . , , . 26, (499) 183-24-01, theormech@mgsu.ru;
ȻɟɥɨɜȼɢɤɬɨɪȺɧɚɬɨɥɶɟɜɢɱ — - ,
, ɎȽȻɈɍȼɉɈ «Ɇɨɫɤɨɜɫɤɢɣɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣɫɬɪɨɢ -ɬɟɥɶɧɵɣɭɧɢɜɟɪɫɢɬɟɬ» (ɎȽȻɈɍȼɉɈ «ɆȽɋɍ»), 129337, . , , . 26, (499) 183-24-01, theormech@mgsu.ru.
: Ȼɟɥɨɜȼ.Ⱥ., Ⱥɧɬɨɧɨɜȼ.ɂ.
// . 2012. № 11. . 191—197.
V.A. Belov, V.I. Antonov
RESEARCH INTO THE TWO-DIMENSIONAL PRESSURE FILTRATION OF THE GROUNDWATER WITHIN A HETEROGENEOUS BED
The subject of research is the steady pressure fi ltration of the unconfi ned groundwater in the heterogeneous bed, if the product of the transparency coeffi cient and bed thickness is represented as a square of an arbitrary harmonic function of coordinates of bed points. The study of the ground-water fi ltration within a heterogeneous bed using the «transition method» is reduced to the search for potential parallel-plane fl ows of the ideal incompressible fl uid using the superposition of point sources and multipoles of different order. Application of the «transition method» instead of a regular integration of differential equations in the series is a simple and obvious method of generalizing the well-known Dupuis formula to identify the well capacity within a homogeneous bed by extending it to the whole variety of heterogeneous beds, if the product of the transparency coeffi cient and bed thickness is represented as a square of an arbitrary harmonic function of coordinates of bed points. The above sequence of operations produces a compact formula describing the pressure distribution within a pressure bed, if the external boundary of the groundwater is circular.
Key words: pressure fi ltration, infl ow, pressure distribution, well capacity, transition method, circular external boundary.
References
1. Bereslavskiy E.N. Fil’tratsiya gruntovykh vod k sisteme drenazhnykh kanalov [Filtration of the Groundwater Incorporated into the System of Drainage Channels]. Vodnye resursy [Aquatic Resources]. 2006, no. 4, vol. 33, pp. 455—458.
2. Emikh V.N. Matematicheskie modeli fi l’tratsii s gorizontal’nym drenazhem [Mathematical Mod-els of Filtration with a Horizontal Drainage]. Vodnye resursy [Aquatic Resources]. 2008, no. 2, vol. 35, pp. 216—222.
3. Shuplin M.N, Borisenko V.N. Tekhnologiya iskusstvennogo zamorazhivaniya gruntov s primen-eniem tverdykh krioagentov v podzemnom stroitel’stve [Technology of Artifi cial Freezing of Soils Using Hard Refrigerants in Underground Construction]. Gornyy informatsionno-analiticheskiy byulleten’ [Mining Bulletin of Information and Analysis]. 2006, no. 8, pp. 381—384.
4. Baturin Yu.E., Mayer V.P. Uchet preryvistogo stroeniya plasta v modelyakh fi l’tratsii nefti, gaza i vody [Consideration of the Interrupted Structure of Bed in Models of Filtration of Crude Oil, Natural Gas and Water]. Vestnik TsKR Rosnedra [Bulletin of Central Commission for Development of Deposits of the Federal Agency for Recovery of Natural Resources]. 2009, no. 3, pp. 60—70.
5. Bereslavskiy E.N. Modelirovanie fi l’tratsionnykh techeniy iz kanalov [Modeling of Filtration Chan-nel Flows]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 2003, no. 5, vol. 67, pp. 78—84.
7. Settari A. Reservoir Geomechanics and Subsidence, Proc. 8th Int. Forum on Reservoir Simula-tion. Iles Borromees, Stresa, Italy, June 20-24, 2005.
8. Salehi Mojarad R. and Settar A. Coupled Numerical Modelling of Reservoir Flow with Formation Plugging. Journal of Canadian Petroleum Technology. No. 3, vol. 46, pp. 20—27, March 2007.
9. Tang Y., Yildiz T., Ozkan E., Kelkar M.Effects of Formation Damage and High-Velocity Flow on the Productivity of Perforated Horizontal Wells. SPE Reservoir Evaluation and Engineering Journal. No. 4, vol. 8, pp. 315—324, Aug. 2005.
10. Golubeva O.V. Kurs mekhaniki sploshnykh sred [Course of Continuum Mechanics]. Moscow, Vyssh. shk. publ., 1972, 368 p.
A b o u t t h e a u t h o r s: Antonov Viktor Ivanovich — Candidate of Technical Sciences, Professor, De-partment of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; theormech@mgsu.ru; +7 (499) 183-24-01;
Belov Viktor Anatol’evich — Candidate of Physical and Mathematical Sciences, Professor, De-partment of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; theormech@mgsu.ru; +7 (499) 183-24-01.
