Model of Isothermal Internal Erosion in Deformable Soil
Abstract
In this paper, a mathematical model of isothermal internal erosion in a poroelastic medium is considered. Removal of moving solid particles from a flow region happens after achieving a certain value of a filtration rate. The equations of mass conservation and Darcy law for water, air and moving solids are taken as constitutive equations of the mathematical model. The motion of the solid skeleton is modeled by the equation of mass conservation with "solid skeleton-moving particles"phase transition, the law of momentum conservation for the entire system, and an equation for effective pressure and porosity in the form of Maxwell’s rheological law. In section 1, a statement of the problem is given and a brief review of internal suffusion models is presented. In section 2, the hypotheses determining intensity of the phase transition are described. In section 3, development of the composite type system is discussed. A degenerate parabolic equation for the saturation of water phase, an elliptic equation for a so-called "reduced pressure and a first-order equation for the porosity and velocity of soil are the development results. It is shown that there is a similarity with the classical Musket-Leverett model of two-phase filtration.
DOI 10.14258/izvasu(2017)4-24
Downloads
Metrics
References
Vardoulakis I. Sand-production and sand internal erosion: Continuum modeling // Alert School: Geomechanical and Structural Issues in Energy Production. — 2006.
Vardoulakis I., Stavropoulou M., Papanastasiou R. Hydro-Mechanical Aspects of the Sand Production Problem // Transport in Porous Media 22, 1996.
Нигматулин Р.И. Динамика многофазных сред. — М., 1987. — Ч. 1.
Варченко А.Н., Зазовский А.Ф. Трехфазная фильтрация несмешивающихся жидкостей // Итоги науки и техники. Серия: Комплексные и специальные разделы механики. — М., 1991. — Т. 4.
Vardoulakis I., Stavropoulou M., Papanastasiou R. Sand Erosion in Axial Flow Conditions // Transport in Porous Media 45, 2001.
Gard S.K., Pritchett J.W. Dynamics of gasfluidized beds. Journal of Applied Phisics // Journal of Applied Phisics, Vol. 46, № 10. — 1975.
Бэр Я., Заславски Д., Ирмей С. Физико-математические основы фильтрации воды. — М., 1971.
Антонцев С.Н., Кажихов А.В., Монахов В.Н. Краевые задачи механики неоднородных жидкостей. — Новосибирск, 1983.
Антонцев С.Н., Папин А.А. Приближенные методы решения задач двухфазной фильтрации // Докл. АН СССР. — 1979. — Т. 247. — № 3.
Папин А.А., Вайгант В.А., Сибин А.Н. Математическая модель неизотермической внутренней эрозии // Известия Алтайского гос. ун-та, — 2015. — № 1/1. DOI: 10.14258/izvasu(2015)1.1-16.
Папин А.А., Сибин А.Н. О разрешимости первой краевой задачи для одномерных уравнений внутренней эрозии // Известия Алтайского гос. ун-та. — 2015. — № 1/2. DOI: 10.14258/izvasu(2015)1.2-25.
Papin A.A., Sibin A.N. Model isothermal internal erosion of soil // Journal of physics: Conference Series 722 (2016) 012034.
Connolly J.A.D., Podladchikov Y.Y. Compaction-driven fluid flow in viscoelastic rock // Geodin. Acta. — 1998. — Vol. 11.
Connolly J.A.D., Podladchikov Y.Y. Temperature-dependent viscoelastic compaction and compartmentalization in sedimentary basins // Tectonophysics. — 2000. — Vol. 324.
Tantserev E., Cristophe Y. Galerne, Podladchikov Y. Multiphase flow in multicomponent porous visco-elastic media // The Fourth Biot Conference on Poromechanics. — 2009.
Wang J., Walters D. A., Settari A., Wan R. G. Simulation of cold heavy oil production using an integrated modular approach with emphasis on foamy oil flow and sand production effects // 1st Heavy Oil Conference. — 2006.
Рекомендации по методике лабораторных испытаний грунтов на водопроницаемость и суффозионную устойчивость. — Л., 1983.
Bonelli S. Erosion of Geomaterials. UK, 2012.
Папин А.А., Подладчиков Ю.Ю. Изотермическое движение двух несмешивающихся жидкостей в пороупругой среде // Известия Алтайского гос. ун-та. — 2015. — № 1/2. DOI: 10.14258/izvasu(2015)1.2-24.
Солонников В. А. О разрешимости начально-краевой задачи для уравнений движения вязкой сжимаемой жидкости // Зап. науч. семинаров ЛОМИ АН СССР. — 1976. — Т. 56.
Copyright (c) 2017 А.А. Папин, А.Н. Сибин, К.А. Шишмарев
This work is licensed under a Creative Commons Attribution 4.0 International License.
Izvestiya of Altai State University is a golden publisher, as we allow self-archiving, but most importantly we are fully transparent about your rights.
Authors may present and discuss their findings ahead of publication: at biological or scientific conferences, on preprint servers, in public databases, and in blogs, wikis, tweets, and other informal communication channels.
Izvestiya of Altai State University allows authors to deposit manuscripts (currently under review or those for intended submission to Izvestiya of Altai State University) in non-commercial, pre-print servers such as ArXiv.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).