The Similar Structure Of Solution Of Homogeneous Spherical Flow Reservoir Problem Under Elastic Outer Boundary

In the mathematical model of oil and gas seepage,because the boundary conditions are complex and difficult to determine,the outer boundary conditions are always regarded as three special cases:closed,constant pressure and infinite.Under these three boundary conditions,many outstanding achievements have been achieved.But in many cases,only based on the above three premises,it is difficult to fully meet the needs of the actual reservoir research.In order to study the influence of reservoir parameters on reservoir pressure distribution effectively,this paper introduced the concept of the elasticity of pressure difference on the boundary,confirmed that the outer boundary has the characteristics of elasticity,and established a spherical flow seepage model in homogeneous reservoir based on the elastic outer boundary conditions.In the process of solving the similar structure of the solution of semi-order modified Bessel equation boundary value problem,we get the Similar Construction Method for solving this kind of boundary value problems,and find that the solution of this kind of equations can be obtained by assembling the similar kernel function and the internal boundary condition coefficient in a specific form,in which the similar kernel function is determined by the outer boundary condition coefficient and the two solutions of the definite solution equation.Then,the Laplace space solution of dimensionless bottom hole pressure in the seepage model of homogeneous reservoir with spherical flow based on elastic outer boundary condition is obtained by using the Similar Construction Method.Finally,we can use Stehfest inversion to inverte the solution from Laplace space to real one,and draw the characteristic curves,then the influence of reservoir parameters on the solution is analyzed.The elastic outer boundary is the third kind of boundary condition,and three kinds of ideal boundary conditions are taken as its special cases.The introduction of elastic outer boundary conditions in the seepage model of homogeneous reservoir with spherical flow makes the study of the pressure distribution of this kind of reservoir expand from special to general,greatly increasing the matching degree between the results of the mathematical model of oil and gas seepage and the dynamic data of measured reservoir pressure.In addition,through the Similar Construction Method,the solution of the spherical flow seepage model seepage model in the homogeneous reservoir can be expressed clearly and concisely with the similar structure,and it can also simplify the procedure of well test programming,so as to improve the programming and analysis efficiency of well test analysis software.