The Fluid-Solid Coupling Seepage Mathematical Model of Shale Gas

2013 ◽  
Vol 275-277 ◽  
pp. 598-602
Author(s):  
Wei Jun Shen ◽  
Xi Zhe Li ◽  
Jia Liang Lu ◽  
Xiao Hua Liu
Keyword(s):  
Mathematical Model ◽  
Shale Gas ◽  
Continuity Equation ◽  
Fluid Pressure ◽  
Seepage Flow ◽  
Stress Equation ◽  
Pore Fluid Pressure ◽  
Seepage Field ◽  
Fluid Coupling ◽  
Realistic Significance

In this paper, the stress equation is available by introducing the principle of effective stress in porous media into fluid-solid coupling seepage and considering the conditions of equilibrium. According to the continuity equation of fluid mechanics, considering the interactions between shale gas and rock-soil body, the differential equation of seepage flow is obtained. Through introducing the velocity component of rock particles into the seepage field, the pore fluid pressure in seepage field is introduced into the deformation field, so as to realize the interaction between the fluid-solid coupling seepage. Based on auxiliary boundary conditions in the above equations, the paper establishes the integrated fluid-coupling seepage mathematical model of shale gas, and it will provide the corresponding theoretical and realistic significance in the development of shale gas.

scholarly journals Correction to: Stress and pore fluid pressure control of seismicity rate changes following the 2016 Kumamoto earthquake, Japan

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Kodai Nakagomi ◽  
Toshiko Terakawa ◽  
Satoshi Matsumoto ◽  
Shinichiro Horikawa
Keyword(s):  
Fluid Pressure ◽  
Pressure Control ◽  
Pore Fluid ◽  
2016 Kumamoto Earthquake ◽  
Pore Fluid Pressure ◽  
Seismicity Rate ◽  
Kumamoto Earthquake ◽  
The 2016 Kumamoto Earthquake ◽  
Seismicity Rate Changes

An amendment to this paper has been published and can be accessed via the original article.

scholarly journals Analytical Solution of Seepage Field in Karst Tunnel

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chong Jiang ◽  
Han-song Xie ◽  
Jia-li He ◽  
Wen-yan Wu ◽  
Zhi-chao Zhang
Keyword(s):  
Analytical Solution ◽  
Permeability Coefficient ◽  
Complex Function ◽  
Great Influence ◽  
Pressure Head ◽  
Seepage Flow ◽  
Seepage Field ◽  
Karst Tunnel ◽  
Lining Structure ◽  
Initial Support

An analytical solution for the seepage field in water-filled karst tunnel is derived based on the inversion of complex function and groundwater hydraulics theory. The solution considers the distance between the tunnel and the cavern, the size of the cavern, and the properties of the lining structure, such as the permeability coefficient as well as the radius of the grouting ring. This paper also performed numerical simulations for two cases: the application of gravity and the absence of gravity. The numerical solution was obtained to verify the analytical solution, and a good agreement was found. Then, the effect of parameters is discussed in detail, including the distance between the tunnel and the cavern, the radius of the cavern, the grouting ring, and the initial support. The results show that when the radius of the cavern is constant, the pressure head and seepage flow decrease as the distance between the tunnel and the cavern increases. When the distance is constant, the pressure head and seepage flow increase with the increase of the radius of the cavern. In addition, the pressure head and the seepage flow decrease with the increase of the thickness of the grouting ring and decrease with the decrease of the permeability coefficient. As the thickness of the initial support increases, the pressure head gradually increases and the percolation decreases. Furthermore, due to the great influence of the grouting ring and initial support on the pressure head and seepage flow, the thickness and permeability coefficient of the grouting ring and initial support should be taken into account carefully during construction.

Research on the influence of the discharge breakdown process on the crater formation during EDM

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wenchao Zhang
Keyword(s):  
Mathematical Model ◽  
Discharge Channel ◽  
Electrical Discharge Machining ◽  
Pulse Discharge ◽  
Single Pulse ◽  
Crater Formation ◽  
Content Type ◽  
Breakdown Process ◽  
Positive Ions ◽  
Fluid Coupling

PurposeThis paper aims to study the breakdown, oscillation and vanishing of the discharge channel and its influence on crater formation with simulation and experimental methods. The experiment results verified the effect of the oscillating characteristics of the discharge channel on the shape of the crater.Design/methodology/approachA mathematical model that considers the magnetohydrodynamics (MHD) and the discharge channel oscillation was established. The micro process of discharging based on magnetic-fluid coupling during electrical discharge machining (EDM) was simulated. The breakdown, oscillation and vanishing stage of the discharge channel were analyzed, and the crater after machining was obtained. Finally, a single-pulse discharge experiment during EDM was conducted to verify the simulation model.FindingsDuring the breakdown of the discharge channel, the electrons move towards the center of the discharge channel. The electrons at the end diverge due to the action of water resistance, making the discharge channel appear wide at both ends and narrow in the middle, showing the pinch effect. Due to the mutual attraction of electrons and positive ions in the channel, the transverse oscillation of the discharge channel is shown on the micro level. Therefore, the position of the discharge point on the workpiece changes. The longitudinal oscillation in the discharge channel causes the molten pool on the workpiece to be ejected due to the changing pressure. The experimental results show that the shape of the crater is similar to that in the simulation, which verifies the correctness of the simulation results and also proves that the crater generated by the single pulse discharge is essentially the result of the interaction between transverse wave and longitudinal wave.Originality/valueIn this paper, the simulation of the discharge breakdown process in EDM was carried out, and a new mathematical model that considers the MHD and the discharge channel oscillation was established. Based on the MHD module, the discharge breakdown, oscillation and vanishing stages were simulated, and the velocity field and pressure field in the discharge area were obtained.

Nonlinear Dynamics of the Bombardier Beetle

1999 ◽  
Author(s):  
Richard H. Rand ◽  
Erika T. Wirkus ◽  
J. Robert Cooke
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Defense Mechanism ◽  
Fluid Pressure ◽  
Pulsed Jet ◽  
Dependent Variables

Abstract This work investigates the dynamics by which the bombardier beetle releases a pulsed jet of fluid as a defense mechanism. A mathematical model is proposed which takes the form of a pair of piece wise continuous differential equations with dependent variables as fluid pressure and quantity of reactant. The model is shown to exhibit an effective equilibrium point (EEP). Conditions for the existence, classification and stability of an EEP are derived and these are applied to the model of the bombardier beetle.

scholarly journals NUMERICAL MODEL OF BREAKWATER WAVE FLOWS

1988 ◽  
Vol 1 (21) ◽  
pp. 149 ◽  
Author(s):  
Alex C. Thompson
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Reflection Coefficient ◽  
Water Wave ◽  
Wave Equations ◽  
Seepage Flow ◽  
Experimental Results ◽  
Simplified Model ◽  
Flow Equations ◽  
Shallow Water Wave Equations

A mathematical model of flow on a sloping breakwater face is described and results of calculations compared with some experimental results to show how the model can be calibrated. Flow above the surface of the slope is represented by the shallow water wave equations solved by a finite difference method. Flow within the breakwater is calculated by one of two methods. A solution of the linear seepage flow equations, again using finite differences or a simplified model of inflow can be used. Experimental results for runup and reflection coefficient are from tests performed at HRL Wallingford.

scholarly journals Fracture-induced pore fluid pressure weakening and dehydration of serpentinite

2019 ◽  
Vol 767 ◽  
pp. 228168 ◽  
Author(s):  
Melodie E French ◽  
Greg Hirth ◽  
Keishi Okazaki
Keyword(s):  
Fluid Pressure ◽  
Pore Fluid ◽  
Pore Fluid Pressure
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