Numerical Simulation of Non-Darcy Flow Caused by Cross-Fracture Water Inrush, Considering Particle Loss

Numerische Simulation der Nicht-Darcy Fluidströmung verursacht durch Wassereinbruch bei Querbrüchen unter Berücksichtigung des Partikelverlusts

Simulación numérica del flujo no dársico causado por la irrupción de agua en las fracturas considerando la pérdida de partículas

考虑颗粒流失条件下交叉裂隙突水的非达西流数值模拟

Abstract

A flow erosion model of water inrush was developed that couples the Darcy, Forchheimer, and Navier–Stokes fields under the theory of continuum mechanics. Water flow and fluidized particles were regarded as single-phase mixed fluids based on the fundamentals of flow transition (aquifer laminar flow to turbulent flow) being the main cause of mine water inrush; the effects of rock disintegration and the coupled effects of flow and erosion were incorporated. The water source of the aquifer, water-inrush channel of the fracture network, and flow path of the slope roadway export were organically connected in a unified flow field. The weak integral forms of the Darcy, Forchheimer, and Navier–Stokes equations were constructed according to the principle of virtual displacement. The convective terms were discretized by the finite volume method and the other terms were discretized by the finite element method; the calculation source program was developed based on the finite element language and its compiler (FELAC). The source program system was used to numerically simulate water inrush in a fractured zone in the Jiangjiawan Mine. It reproduced the entire dynamic process of a water inrush and revealed the distribution and variation characteristics of the pressure field, velocity field, porosity, and concentration, as well as the mechanisms underlying the sudden change in water flow.

Zusammenfassung

Es wurde ein Fließerosionsmodell des Wassereinbruchs entwickelt, das die Darcy-, Forchheimer- und Navier–Stokes-Felder gestützt auf die Theorie der Kontinuumsmechanik miteinander verbindet. Wasserströmung und fluidisierte Partikel wurden als einphasige Mischfluide betrachtet, basierend auf den Grundlagen des Strömungsübergangs (Aquifer-Laminarströmung zu turbulenter Strömung), der die Hauptursache für Wassereinbruch in Bergwerken ist. Die Auswirkungen des Gesteinszerfalls und die gekoppelten Effekte von Strömung und Erosion wurden einbezogen. Die Wasserquelle des Aquifers, der Wassereinbruchskanal des Bruchnetzes und der Fließweg des Hangstreckenaustrags waren in einem einheitlichen Strömungsfeld auf natürliche Weise miteinander verbunden. Die schwachen Integralformen der Darcy-, Forchheimer- und Navier–Stokes-Gleichungen wurden nach dem Prinzip der virtuellen Verschiebung konstruiert. Die konvektiven Terme wurden mit der Finite-Volumen-Methode und die anderen Terme mit der Finite-Elemente-Methode diskretisiert; das Quellprogramm zur Berechnung wurde auf der Grundlage der Finite-Elemente-Programmiersprache und deren Compiler (FELAC) entwickelt. Das Quellprogrammsystem wurde verwendet, um den Wassereinbruch in einer Bruchzone in der Jiangjiawan-Mine numerisch zu simulieren. Es reproduzierte den gesamten dynamischen Prozess eines Wassereinbruchs und enthüllte die Verteilungs- und Schwankungscharakteristika des Druckfeldes, des Geschwindigkeitsfeldes, der Porosität und der Konzentration sowie die Mechanismen, die der plötzlichen Änderung des Wasserflusses zugrunde liegen.

Resumen

Se desarrolló un modelo de erosión del flujo de entrada de agua que acopla los campos de Darcy, Forchheimer y Navier–Stokes bajo la teoría de la mecánica del continuo. El flujo de agua y las partículas fluidizadas se consideraron como fluidos mixtos monofásicos basándose en los fundamentos de la transición de flujo (flujo laminar a flujo turbulento) como la principal causa de irrupción de agua en la mina; se incorporaron los efectos de la desintegración de la roca y los efectos acoplados del flujo y la erosión. La fuente de agua del acuífero, el canal de irrupción de agua de la red de fracturas y la ruta de flujo de la exportación del talud se conectaron orgánicamente en un campo de flujo unificado. Las formas integrales débiles de las ecuaciones de Darcy, Forchheimer y Navier–Stokes fueron construidas de acuerdo con el principio de desplazamiento virtual. Los términos convectivos se discretizaron por el método de volúmenes finitos y los demás términos se discretizaron por el método de elementos finitos; el programa fuente de cálculo se desarrolló basándose en el lenguaje de elementos finitos y su compilador (FELAC). El sistema del programa fuente se utilizó para simular numéricamente la entrada de agua en una zona fracturada en la mina de Jiangjiawan. Se reprodujo todo el proceso dinámico de una irrupción de agua y se revelaron las características de distribución y variación del campo de presión, el campo de velocidad, la porosidad y la concentración, así como los mecanismos subyacentes al cambio repentino del flujo de agua.

概要

基于连续介质力学理论, 建立了耦合Darcy, Forchheimer和Navier–Stokes场的突水水流侵蚀模型。依据流态转换(含水层的层流转变为紊流)是矿井突水主要原因的基础认识, 视水流与液化颗粒为单相混合流, 综合考虑岩石破裂和水流与侵蚀耦合的作用。含水层水源, 裂隙网络突水通道和斜巷出口水流路径在均匀流场中有机相连。根据虚位移原理, 构造了达西, Forchheimer和Navier–Stokes方程的弱积分形式。有限体积法离散对流项, 有限元法离散其它项, 计算源程序基于有限元语言及编译器(FELAC)开发。利用源程序系统数值模拟了江家湾矿裂隙带突水; 再现了突水的完整动力学过程, 揭示了压力场, 速度场, 孔隙度和浓度的分布与变化, 揭示了水流突变的机理。

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Acknowledgements

The current thesis was supported by the State Key Program of National Natural Science of China (U1710253) and the National Natural Science Foundation of China (51574059, 51274053).

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Correspondence to Tianhong Yang.

Supplementary Information

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Supplementary file1. Supplemental Figure S-1 Space-time evolution process of the pressure (Unit: Pa): t = 1 s; b t = 25 s; c t = 50 s; d t = 100 s; e t = 150 s; f t = 200 s. (EPS 26293 KB)

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Supplementary file8. Supplemental Figure S-2 Space-time evolution process of the velocity (Unit: m/s): t = 1 s; b t = 25 s; c t = 50 s; d t = 100 s; e t = 200 s; f t = 1000 s. (EPS 26060 KB)

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Supplementary file15. Supplemental Figure S-3 Space-time porosity evolution: t = 1 s; b t = 25 s; c t = 50 s; d t = 100 s; e t = 200 s; f t = 1000 s. (EPS 23807 KB)

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Supplementary file22. Supplemental Figure S-4 Space-time evolution of the concentration: t = 1 s; b t = 25 s; c t = 50 s; d t = 100 s; e t = 200 s; f t = 1000 s. (EPS 26286 KB)

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Yang, B., Yang, T. & Hu, J. Numerical Simulation of Non-Darcy Flow Caused by Cross-Fracture Water Inrush, Considering Particle Loss. Mine Water Environ (2021). https://doi.org/10.1007/s10230-021-00762-6

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Keywords

  • Fracture network
  • Disintegration
  • Flow erosion
  • Numerical simulation
  • Turbulent fracture flow