Study On Nonlinear Flow Law Of Fluids In Near-well Reservoir Of Horizontal Well

In this paper,based on the fracture characteristics in near-wellbore reservoirs of horizontal wells,we studied the nonlinear flow law of fluids in hydraulic fracturing fractures and rock matrix porous media.Specifically,we explored the equation which completely describes the law of nonlinear flow and the reasons for the nonlinear flow in a single rough fracture.On this basis,we established a modified porous media model for fluid flow in a single rough fracture and a two-way fluid-solid coupling model for fractured shale rock,then studied the hydraulic fracturing process of fractured shale rock.Three representative types of flow in microchannels were experimentally observed,including the first type of nonlinear flow,Darcy linear flow,and the second type of nonlinear flow.Using regression analysis of the experimental data,the cubic Forchheimer equation was sufficient to describe the full nonlinear water flow caused by viscosity,inertia,boundary layer,and surface tension.The coefficients of the Forchheimer equation have been explicitly evaluated.Notably,when the fracture aperture((7)increases,the coefficient,which is related to the viscous force between fluid layers,is dropping.Meanwhile,the coefficient,which is related to the ratio of boundary layer thickness to fracture aperture,will become 0.However,the surface tension,which is only related to the natural properties of fluids and solids,remains unchanged.Finally,the coefficient,which reflects the inertial force of fluid convection,is negative,suggesting that the inertial force helps the water to escape from the boundary layer.Based on the critical Reynolds numbers Re_Ⅰand Re_Ⅱin the experimental results,zones for the three types of flow were divided.The first type of nonlinear flow of air and water in porous media of coal rock was experimentally observed,and the relationship between the cubic Forchheimer equation coefficients and permeability was parametrically evaluated.The coefficientrelated to viscous flow and the coefficientrelated to the boundary layer flow are positive.The coefficientrelated to the inertial flow is negative,indicating that the inertial force helps fluids escape the boundary layer flow and viscous flow.And the surface tensionremains unchanged.When the permeability of coal porous media decreases,the coefficientin the cubic Forchheimer equation increases,coefficientdecreases,and coefficientdecreases,indicating that the resistance of flow viscous and boundary layer flow increases,the flow velocity decreases,then the inertial force decreases.When the permeability of coal porous media increases,the coefficientin the cubic Forchheimer equation decreases proportionally,the square root of the absolute value of coefficientdecreases proportionally,and the cubic root of coefficientdecreases proportionally.A 3D lattice Boltzmann method is applied to simulate the flow in a 3D stochastically generated rough fracture with complex geometry by solving the Navier-Stokes equation.The results show that the flow in a rough fracture is always nonlinear whether high or low Reynolds number.The reasons for nonlinear fracture flow are the eddy flow and effective aperture reduction,which are simultaneously caused by both walls roughness and fluids viscosity.The inertial loss is 7.17 times of Poiseuille flow,caused by both walls roughness and fluids viscosity.The velocity distributions in a 3D rough fracture were further examined to illustrate that it is no more a parabola whether high or low Reynolds number.The fracture flow far away from rough walls is the Poiseuille flow,but flow near rough walls is boundary-layer flow.Then,the boundary-layer flows near rough walls include the effective boundary-layer flow and eddy flow.As the Reynolds number increases,the height of boundary-layer flow increases,and the height of the Poiseuille flow decreases.Then,the height of eddy flow increases in boundary-layer flow,and the height of effective boundary-layer flow decreases.The water in a single rough rock fracture is deemed to flow through porous media,and then a modified porous media model in a single rough fracture is established.The results indicate that the water pressure distribution in a single rough rock fracture is parabolic during hydraulic fracturing,which gradually changes in the form of a parabolic distribution.The asperity on walls has a weak impact on water flow into a single rough rock fracture with an aperture of more than 3mm.The pressure drop increases proportionally with the length of water intrusion.A fluid-solid coupling model of fractured shale rock during hydraulic fracturing was established by solving the Navier-Stokes equations and evaluated the changing process of hydraulic fracturing.Our results show that in the hydraulic fracturing process,the changing process of water pressure in a single shale fracture with or without fluid-solid coupling is similar,and both have a water hammer effect.Single shale rock fracture opened instantly in an elliptical shape.The maximum instantaneous water pressure at the fracture tip considering fluid-solid coupling was 3.01 times the initial water pressure.The Mises stress at the fracture tip caused by the maximum instantaneous water pressure was 2.97 times the Mises stress at the fracture tip caused by the water pressure in the fracture after stable water pressure change.ModeⅠfracture occurred in the fractured shale rock when high-pressure water rapidly invaded2/3 of the length of the fracture.