<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">proneft</journal-id><journal-title-group><journal-title xml:lang="ru">PROНЕФТЬ. Профессионально о нефти</journal-title><trans-title-group xml:lang="en"><trans-title>PROneft. Professionally about Oil</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2587-7399</issn><issn pub-type="epub">2588-0055</issn><publisher><publisher-name>«Газпром нефть»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.24887/2587-7399-2020-1-18-25</article-id><article-id custom-type="elpub" pub-id-type="custom">proneft-186</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>РАЗРАБОТКА И ЭКСПЛУАТАЦИЯ НЕФТЯНЫХ МЕСТОРОЖДЕНИЙ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>DEVELOPMENT AND OPERATION OF OIL FIELDS</subject></subj-group></article-categories><title-group><article-title>Моделирование возникновения микросейсмических событий при распространении трещины гидроразрыва пласта</article-title><trans-title-group xml:lang="en"><trans-title>Modelling of the occurrence of microseismic events during hydraulic fracture propagation</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Шварёв</surname><given-names>Н. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Shvarev</surname><given-names>N. G.</given-names></name></name-alternatives><bio xml:lang="en"><p>Saint-Petersburg</p></bio><email xlink:type="simple">shvarev_ng@spbstu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Марков</surname><given-names>Н. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Markov</surname><given-names>N. S.</given-names></name></name-alternatives><bio xml:lang="en"><p>Saint-Petersburg</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>НОЦ «Газпромнефть-Политех»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Gazpromneft-Polytech REC</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2020</year></pub-date><pub-date pub-type="epub"><day>08</day><month>06</month><year>2022</year></pub-date><volume>0</volume><issue>1</issue><fpage>18</fpage><lpage>25</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Шварёв Н.Г., Марков Н.С., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Шварёв Н.Г., Марков Н.С.</copyright-holder><copyright-holder xml:lang="en">Shvarev N.G., Markov N.S.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://proneft.elpub.ru/jour/article/view/186">https://proneft.elpub.ru/jour/article/view/186</self-uri><abstract><p>В работе представлены физико-математическая модель и алгоритм генерации микросейсмической активности при распространении трещины гидроразрыва пласта (ГРП). Дефекты (неоднородности) породы описываются с помощью ESC-модели. Получены формулы скачков перемещений и характеристик сейсмических и асейсмических событий. Рассмотренный алгоритм реализован и протестирован в программе. Проведены расчеты для псевдотрехмерной и планарной моделей распространения трещины ГРП. Установлено, что по полю микросейсмических событий можно приближенно восстановить эволюцию трещины ГРП во времени, что согласуется с данными наблюдений.</p></abstract><trans-abstract xml:lang="en"><p>This paper presents a physico-mathematical model and an algorithm for generating microseismic activity during hydraulic fracture propagation. Defects (inhomogeneities) of the rock are described using the ESC-model. Formulas for displacements discontinuities and characteristics of seismic and aseismic events are obtained. The algorithm was implemented and tested in the program. Calculations for pseudo3D and planar3D models of fracture propagations are carried out. It was found that the field of microseismic events can approximately restore the evolution of a hydraulic fracture in time, what is consistent with observations.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>сейсморазведка</kwd><kwd>сейсмичность</kwd><kwd>микросейсмические события</kwd><kwd>гидравлический разрыв пласта (ГРП)</kwd><kwd>ESC-модель</kwd><kwd>псевдотрехмерная и планарная модели</kwd></kwd-group><kwd-group xml:lang="en"><kwd>seismic</kwd><kwd>seismicity</kwd><kwd>microseismic events</kwd><kwd>hydraulic fracturing</kwd><kwd>ESC-model</kwd><kwd>pseudo3D and planar3D models</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при финансовой поддержке Министерства науки и высшего образования в рамках ФЦП «Исследования и разработки по приоритетным направлениям развития научно-технологического комплекса России на 2014-2020 годы», Мероприятие 1.2., Соглашение о предоставлении субсидии №14.575.21.0146 от 26.09.2017, уникальный идентификатор ПНИ: RFMEFI57517X0146</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Linkov A.M. Key-note lecture: numerical modeling of seismicity: theory and applications // Rockbursts and Seismicity in Mines, Proceedings for 8th International Symposium RaSiM, Geophysical Survey of RAS, Mining Institute of Ural Branch of RAS, Obninsk-Perm. – 2013. – Р. 197-218.</mixed-citation><mixed-citation xml:lang="en">Linkov A.M., Key-note lecture: numerical modeling of seismicity: theory and applications, In: Rockbursts and Seismicity in Mines, Proceedings for 8th International Symposium RaSiM, Geophysical Survey of RAS, Mining Institute of Ural Branch of RAS, Obninsk-Perm, 2013, pp. 197-218.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Aki K., Richards P.G. Quantitative seismology. 2 publication. – University Science Books, Sausalito, CA, 2002. – 700 р.</mixed-citation><mixed-citation xml:lang="en">Aki K., Richards P.G., Quantitative seismology, 2nd ed., University Science Books, Sausalito, CA, 2002, 700 p.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Gibowicz S.J., Kijko A. An introduction to mining seismology // Academic Press, San Diego, 2013. – 399 р.</mixed-citation><mixed-citation xml:lang="en">Gibowicz S.J., Kijko A., An introduction to mining seismology, Academic Press, San Diego, 2013, 399 p.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Mendecki A.J. Seismic monitoring in mines. – London: Chapman and Hall, 1997. – 261 р.</mixed-citation><mixed-citation xml:lang="en">Mendecki A.J., Seismic monitoring in mines, Chapman and Hall, London, 1997, 261 p.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Rice J.R. The mechanics of earthquake rupture // Physics of the Earth’s Interior. – 1980. – Р. 555-649.</mixed-citation><mixed-citation xml:lang="en">Rice J.R., The mechanics of earthquake rupture, Physics of the Earth’s Interior, North-Holland, Amsterdam, 1980, pp. 555-649.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Доброскок А.А., Линьков А.М. Моделирование течения, напряженного состояния и сейсмических событий в породах при сбросе давления в трещине гидроразрыва // Физико-технические проблемы разработки полезных ископаемых. – 2011. – № 1. – C. 12-22.</mixed-citation><mixed-citation xml:lang="en">Dobroskok A.A., Lin'kov A.M., Modeling of fluid flow, stress state and seismicity induced in rock by an instant pressure drop in a hydrofracture (In Russ.), Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh = Journal of Mining Science, 2011, no. 1, pp. 12-22.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Яскевич С.В., Гречка В.Ю., Дучков А.А. Обработка данных микросейсмического мониторинга геодинамических событий с учетом сейсмической анизотропии массива горных пород // Физико-технические проблемы разработки полезных ископаемых. – 2014. – №6. – С. 41-52.</mixed-citation><mixed-citation xml:lang="en">Yaskevich S.V., Grechka V.Yu., Duchkov A.A., Processing microseismic monitoring data considering seismic anisotropy of rocks (In Russ.), Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh = Journal of Mining Science, 2014, no. 6, pp. 41-52.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Dobroskok A.A., Linkov A.M. Modeling of fluid flow, stress state and seismicity induced in rock by an instant pressure drop in a hydrofracture // Journal of Mining Science. – 2011. – Т. 47. – №. 1. – Р. 10-19.</mixed-citation><mixed-citation xml:lang="en">Dobroskok A.A., Linkov A.M., Modeling of fluid flow, stress state and seismicity induced in rock by an instant pressure drop in a hydrofracture, Journal of Mining Science, 2011, V. 47, no. 1, pp. 10-19.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Integrating microseismic mapping and complex fracture modeling to characterize fracture complexity / C. Cipolla, X. Weng, M. Mack [et al.] // SPE 140185. – 2011.</mixed-citation><mixed-citation xml:lang="en">Cipolla C., Weng X., Mack M., Ganguly U., Gu H., Kresse O., Cohen C., Integrating microseismic mapping and complex fracture modeling to characterize fracture complexity, SPE140185-MS, 2011.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Kresse O., Cohen C., Weng X. Numerical modeling of hydraulic fracturing in naturally fractured formations // 45th US Rock Mechanics/Geomechanics Symposium. – American Rock Mechanics Association. – 2011. – 11 р.</mixed-citation><mixed-citation xml:lang="en">Kresse O., Cohen C., Weng X., Numerical modeling of hydraulic fracturing in naturally fractured formations, Proceedings of 45th US Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association, 2011, p. 11.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Malovichko D., Basson G. Simulation of mining induced seismicity using Salamon-Linkov method // Proceedings of the Seventh International Conference on Deep and High Stress Mining, Australian Centre for Geomechanics, Perth. – 2014. – Р. 667-680.</mixed-citation><mixed-citation xml:lang="en">Malovichko D., Basson G., Simulation of mining induced seismicity using Salamon-Linkov method, Proceedings of the Seventh International Conference on Deep and High Stress Mining, Australian Centre for Geomechanics, Perth, 2014, pp. 667-680.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Linkov A.M. Key-note address: New geomechanical approaches to develop quantitative seismicity // Proceedings of the 4th International Symposium on Rockbursts and Seismicity in Mines, Balkema, Rotterdam. – 1997. – Р. 151-166.</mixed-citation><mixed-citation xml:lang="en">Linkov A.M., Key-note address: New geomechanical approaches to develop quantitative seismicity, Proceedings of the 4th International Symposium on Rockbursts and Seismicity in Mines, Balkema, Rotterdam, 1997, pp. 151-166.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Linkov A.M. Integration of numerical modeling and seismic monitoring: general theory and first steps // Proceedings of the International Conference on New Developments in Rock Mechanics. – 2002. – Р. 259-264.</mixed-citation><mixed-citation xml:lang="en">Linkov A.M., Integration of numerical modeling and seismic monitoring: general theory and first steps, Proceedings of the International Conference on New Developments in Rock Mechanics, New York, 2002, pp. 259-264.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Линьков А.М. Численное моделирование сейсмических и асейсмических событий в трехмерных задачах кинетики горных пород // Физико-технические проблемы разработки полезных ископаемых. – 2006. – №. 1. – Р. 3-17.</mixed-citation><mixed-citation xml:lang="en">Lin'kov A.M., Numerical modeling of seismic and aseismic events in three-dimensional problems of rock mechanics (In Russ.), Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh = Journal of Mining Science, 2006. – №. 1. – S. 3-17.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Linkov A. M. Numerical modeling of seismic and aseismic events in three-dimensional problems of rock mechanics //Journal of Mining Science. – 2006. – Т. 42. – №. 1. – Р. 1-14.</mixed-citation><mixed-citation xml:lang="en">Linkov A.M., Numerical modeling of seismic and aseismic events in three-dimensional problems of rock mechanics, Journal of Mining Science, 2006, V. 42, no. 1, pp. 1-14.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Линьков А.М. Комплексный метод граничных интегральных уравнений теории упругости. – СПб: Наука, 1999. – 382 с.</mixed-citation><mixed-citation xml:lang="en">Lin'kov A.M., Kompleksnyy metod granichnykh integral'nykh uravneniy teorii uprugosti (The complex method of boundary integral equations of elasticity theory), ST. Petersburg: Nauka Publ., 1999, 382 p.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Linkov A.M. Stability of inelastic, geometrically nonlinear, discrete systems // Soviet Physics Doklady. – 1987. – Т. 32. – Р. 376-378.</mixed-citation><mixed-citation xml:lang="en">Linkov A.M., Stability of inelastic, geometrically nonlinear, discrete systems, Soviet Physics Doklady, 1987, V. 32, pp. 376-378.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Grechka V.I.U., Heigl W.M. Microseismic monitoring // Society of Exploration Geophysicists. – 2017. – 449 р.</mixed-citation><mixed-citation xml:lang="en">Grechka V.I.U., Heigl W.M., Microseismic monitoring, Society of Exploration Geophysicists, 2017, 449 p.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Salamon M.D.G. Keynote address: Some applications of geomechanical modelling in rockburst and related research // Proceedings of the 3rd International Symposium on Rockbursts and Seismicity in Mines, Balkema, Rotterdam, 1993. – Р. 297-309.</mixed-citation><mixed-citation xml:lang="en">Salamon M.D.G., Keynote address: Some applications of geomechanical modelling in rockburst and related research, Proceedings of the 3rd International Symposium on Rockbursts and Seismicity in Mines, Balkema, Rotterdam, 1993, pp. 297-309.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Maxwell S. Microseismic imaging of hydraulic fracturing: Improved engineering of unconventional shale reservoirs // Society of Exploration Geophysicists. – 2014. – 197 р.</mixed-citation><mixed-citation xml:lang="en">Maxwell S., Microseismic imaging of hydraulic fracturing: Improved engineering of unconventional shale reservoirs, Society of Exploration Geophysicists, 2014, 197 p.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Guglielmi A.V. Interpretation of the Omori law // Izvestiya, Physics of the Solid Earth. – 2016. – Т. 52. – №. 5. – Р. 785-786.</mixed-citation><mixed-citation xml:lang="en">Guglielmi A.V., Interpretation of the Omori law, Izvestiya, Physics of the Solid Earth, 2016, V. 52, no. 5, pp. 785-786.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Markov N.S., Linkov A.M. Correspondence principle for simulation hydraulic fractures by using pseudo 3D model // Materials Physics and Mechanics. – 2018. – №40. – Р. 181-186.</mixed-citation><mixed-citation xml:lang="en">Markov N.S., Linkov A.M., Correspondence principle for simulation hydraulic fractures by using pseudo 3D model, Materials Physics and Mechanics, 2018, V. 40, pp. 181-186.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Старобинский Е.Б., Степанов А.Д. Использование явной схемы интегрирования по времени при моделировании гидроразрыва пласта с применением модели Planar3D // PROНЕФТЬ. – 2019. – № 2. – С. 16-20.</mixed-citation><mixed-citation xml:lang="en">Starobinskiy E.B., Stepanov A.D., Use of the explicit time integration scheme within the planar3d approach for simulating hydraulic fracturing (In Russ.), PRONEFT'', 2019, no. 2, pp. 16-20.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Подходы к моделированию гидроразрыва пласта и направления их развития / М.М. Хасанов, Г.В. Падерин, Е.В. Шель [и др.] // Нефтяное хозяйство. – 2017. – №. 12. – С. 37-41.</mixed-citation><mixed-citation xml:lang="en">Khasanov M.M., Paderin G.V., Shel' E.V., Yakovlev A.A., Pustovskikh A.A., Approaches to modeling hydraulic fracturing and their development (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2017, no. 12, pp. 37-41.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
