This paper investigates the spatial behavior of the solutions of the Forchheimer equations in a semi-infinite cylinder.Using the energy estimation method and the differential inequality technology,the differential ine...This paper investigates the spatial behavior of the solutions of the Forchheimer equations in a semi-infinite cylinder.Using the energy estimation method and the differential inequality technology,the differential inequality about the solution is derived.By solving this differential inequality,it is proved that the solutions grow polynomially or decay exponentially with spatial variables.展开更多
Understanding the complex flow behavior along a rough rock fracture under high-temperature,high-stress,and high-seepage pressure(HTHM)coupling conditions is of great significance for optimizing deep resource extractio...Understanding the complex flow behavior along a rough rock fracture under high-temperature,high-stress,and high-seepage pressure(HTHM)coupling conditions is of great significance for optimizing deep resource extraction.This study investigates the complex flow behavior of a single rock fracture under coupled HTHM conditions using a self-developed multi-field coupling experimental system,considering real-time high temperatures(20–90℃),confining pressures(30–120 MPa),and seepage pressures(5–60 MPa).Experimental results show that as confining pressure increases,two typical nonlinear flow behaviors are observed,which are Forchheimer flow and low-velocity nonlinear flow.The increase in temperature and decrease in roughness significantly promote the fluid flow and enhance the nonlinear relationship between the volumetric flow rate and the hydraulic gradient at lower confining pressures(30 MPa).However,the change in temperature and fracture surface roughness does not affect the nonlinear type of fluid flow.Under a given hydraulic gradient,the influence of temperature and fracture roughness on the volumetric flow rate varies with changes in confining pressure.Additionally,this study considers both the viscous and inertial terms,and a modified Forchheimer equation is proposed using two parameters:the contact area ratio and the thermal expansion coefficient of the rock.The proposed model can effectively predict the nonlinear flow behavior of fluid along rough fractured rocks under varying temperatures and surface roughness.The experimental results and the proposed model provide valuable data and theoretical guidance for deep oil and gas exploration as well as hydraulic fracturing design.展开更多
Compared to single layer porous media,fluid flow through layered porous media(LPMs)with contrasting pore space structures is more complex.This study constructed three-dimensional(3-D)pore-scale LPMs with different gra...Compared to single layer porous media,fluid flow through layered porous media(LPMs)with contrasting pore space structures is more complex.This study constructed three-dimensional(3-D)pore-scale LPMs with different grain size ratios of 1.20,1.47,and 1.76.The flow behavior in the constructed LPMs and single layer porous media was numerically investigated.A total of 178 numerical experimental data were collected in LPMs and single layer porous media.In all cases,two different flow regimes(i.e.,Darcy and Non-Darcy)were observed.The influence of the interface of layers on Non-Darcy flow behavior in LPMs was analyzed based pore-scale flow data.It was found that the available correlations based on single layer porous media fail to predict the flow behavior in LPMs,especially for LPM with large grain size ratio.The effective permeability,which incorporated the influence of the interface is more accurate than the Kozeny-Carman equation for estimating the Darcy permeability of LPMs.The inertial pressure loss in LPMs,which determines the onset of the Non-Darcy flow,was underestimated when using a power law expression of mean grain size.The constant B,an empirical value in the classical Ergun equation,typically equals 1.75.The inertial pressure loss in LPMs can be significantly different from it in single lager porous media.For Non-Darcy flow in LPMs,it is necessary to consider a modified larger constant B to improve the accuracy of the Ergun empirical equation.展开更多
基金Supported by Innovation Team Project of Humanities and Social Sciences in Colleges and Universities of Guangdong Province(Grant No.2020WCXTd008)Research Team Project of Guangzhou Huashang College(Grant No.2021HSKT01).
文摘This paper investigates the spatial behavior of the solutions of the Forchheimer equations in a semi-infinite cylinder.Using the energy estimation method and the differential inequality technology,the differential inequality about the solution is derived.By solving this differential inequality,it is proved that the solutions grow polynomially or decay exponentially with spatial variables.
基金supported by the National Natural Science Foundation of China(Nos.52034010 and 52479113)the Natural Science Foundation of Shandong Province,China(No.ZR2024ME165)the Postgraduate Education and Teaching Reform Project of China University of Petroleum(East China)(No.YJG2024005).
文摘Understanding the complex flow behavior along a rough rock fracture under high-temperature,high-stress,and high-seepage pressure(HTHM)coupling conditions is of great significance for optimizing deep resource extraction.This study investigates the complex flow behavior of a single rock fracture under coupled HTHM conditions using a self-developed multi-field coupling experimental system,considering real-time high temperatures(20–90℃),confining pressures(30–120 MPa),and seepage pressures(5–60 MPa).Experimental results show that as confining pressure increases,two typical nonlinear flow behaviors are observed,which are Forchheimer flow and low-velocity nonlinear flow.The increase in temperature and decrease in roughness significantly promote the fluid flow and enhance the nonlinear relationship between the volumetric flow rate and the hydraulic gradient at lower confining pressures(30 MPa).However,the change in temperature and fracture surface roughness does not affect the nonlinear type of fluid flow.Under a given hydraulic gradient,the influence of temperature and fracture roughness on the volumetric flow rate varies with changes in confining pressure.Additionally,this study considers both the viscous and inertial terms,and a modified Forchheimer equation is proposed using two parameters:the contact area ratio and the thermal expansion coefficient of the rock.The proposed model can effectively predict the nonlinear flow behavior of fluid along rough fractured rocks under varying temperatures and surface roughness.The experimental results and the proposed model provide valuable data and theoretical guidance for deep oil and gas exploration as well as hydraulic fracturing design.
基金financially supported by the National Key Research and Development Program of China(No.2019YFC1804303)the National Natural Science Foundation of China(Grant Nos.41877171 and 41831289)。
文摘Compared to single layer porous media,fluid flow through layered porous media(LPMs)with contrasting pore space structures is more complex.This study constructed three-dimensional(3-D)pore-scale LPMs with different grain size ratios of 1.20,1.47,and 1.76.The flow behavior in the constructed LPMs and single layer porous media was numerically investigated.A total of 178 numerical experimental data were collected in LPMs and single layer porous media.In all cases,two different flow regimes(i.e.,Darcy and Non-Darcy)were observed.The influence of the interface of layers on Non-Darcy flow behavior in LPMs was analyzed based pore-scale flow data.It was found that the available correlations based on single layer porous media fail to predict the flow behavior in LPMs,especially for LPM with large grain size ratio.The effective permeability,which incorporated the influence of the interface is more accurate than the Kozeny-Carman equation for estimating the Darcy permeability of LPMs.The inertial pressure loss in LPMs,which determines the onset of the Non-Darcy flow,was underestimated when using a power law expression of mean grain size.The constant B,an empirical value in the classical Ergun equation,typically equals 1.75.The inertial pressure loss in LPMs can be significantly different from it in single lager porous media.For Non-Darcy flow in LPMs,it is necessary to consider a modified larger constant B to improve the accuracy of the Ergun empirical equation.
