Research On The Well Test Model Of Horizontal Wells In Shale Gas Reservoirs Based On Elliptical Seepage

As a special kind of gas reservoir,shale gas has attracted more and more attention.At present,the research of seepage law of shale gas reservoirs are generally carried out in rectangular or Cartesian coordinates by mathematical modeling to describe the flow characteristics.It can be seen from the shale gas accumulation mechanism that shale gas have a flow direction of the opposite sex,and through multi-stage fracturing and horizontal well perforating technology,the flow direction is more the opposite sex.So a mathematical model of anisotropic shale gas reservoirs should be established.This paper aims to establish an anisotropic shale gas reservoir mathematical model based on elliptic flow,the establishment of elliptical flow of partial differential equations can't be solved directly by numerical calculation method,so it is necessary to study its function by using Mathieu solution method and elliptic differential equations of the flow in order to determine the mathematical expression of vertical well testing model,horizontal well testing model and fracturing horizontal well testing model.By using the numerical methods and numerical inversion Stehfest preparation corresponding computer program is programmed so the curve of well test model can be drawn and well test model factors can be analyzed.It can be concluded that:(1)By introducing Warren-Root Dual Porosity model the equations of shale gas quasi steady state seepage-diffusion and seepage-Seepage/percolation diffusion mathematical expression of two kinds can be established under Cartesian,two mathematical expressions of percolation model can be determined.By Laplace transform,the mathematical expression of shale gas reservoirs of gas seepage elliptic differential equations can be expressed as Mathieu equation form,so the problem can be solved by the Mathieu function.(2)Combining the use of Mathieu function and the solve of oval seepage differential equation,the mathematical expression of shale gas reservoirs of vertical wells,horizontal wells and horizontal well fracturing well test model can be proposed.The use of numerical methods and conduct Stehfest numerical inversion,and by programming shale gas well test curve of two typical mathematical model can be drawn.(3)The typical curve can be plotted by programming and shale gas well testing mathematical model,typically affecting factors of shale gas curve include adsorption and desorption curve constant,crossflow coefficient,storage capacity ratio,transport mechanisms,length and location of horizontal wells,crack spacing and crack article of fractured horizontal well.By analyzing the influence of typical curve respectively,conclusions are summarized.