The Similar Structure Of Solution Of Fractal Homogeneous Reservoir Seepage Model With The Elastic Outer Boundary

In previous,researchers have always established seepage models based on three outer boundaries(i.e.constant pressure,closed,and infinite),however,they rarely exist in real strata,resulting in large experimental errors.Based on this,this paper improves this shortcoming by introducing the elastic outer boundary.The study shows that when considering the elastic outer boundary,the characteristic curve of dimensionless bottom hole pressure and its derivative lie between the closed and constant pressure outer boundary,which indicates that this boundary condition regards the above outer boundary as special cases and expands the range of well test analysis,so it is helpful for us to explore the change laws of reservoir much better.In order to simplify the process of solving those models,this paper uses the similar construction method to solve them,and it obtains their solution with the similar structure,for the expression is very simple,thus it is convenient for compiling the well test program.The structure of this paper isThe introduction mainly introduces the research progress under three kinds of ideal outer boundaries,including solution,experimental results and so on.Chapter 2 mainly explores the properties of a class of extended modified Bessel functions,and extracts a similar construction method to solve a class of extended modified Bessel equation boundary value problems.Chapter 3 deduces the elastic outer boundary's representation by the knowledge of the elastic theories and seepage mechanics.Chapter 4 establishes a fractal homogeneous reservoir seepage model with the elastic outer boundary,and its Laplace solution is obtained by using the similar construction method.Then its numerical solution is gotten by using the Stehfest numerical inversion method,also the dimensionless characteristic curves are drawn.Comparing with seepage models established with those special outer boundary conditions,this paper further expounds the advantages of introducing the elastic outer boundary.Chapter 5 establishes a fractal homogeneous reservoir seepage model considering the effective well radius with the elastic outer boundary,its Laplace solution is obtained by means of the similar construction method,then the Stehfest numerical inversion method is used to get its numerical solution,finally,the advantages of introducing the elastic outer boundary are explained by parameter analysis and models' comparison.Chapter 6 establishes a fractal homogeneous reservoir seepage model considering the quadratic pressure gradient with the elastic outer boundary,its Laplace solution is obtained according to the similar construction method and its numerical solution by using the Stehfest numerical inversion method,and the parameter analysis are carried out.Comparing this model's results with the model in Chapter 4,so the necessity of considering the quadratic pressure gradient with the elastic outer boundary is expounded.Chapter 7 establishes a effective well radius fractal homogeneous reservoir seepage model considering the quadratic pressure gradient with the elastic outer boundary.First,its Laplace solution is obtained by using the similar construction method and its numerical solution is gotten by using the Stehfest numerical inversion method,and the dimensionless characteristic curves are drawn.Then this chapter's results are compared with Chapter 5,so the importance of considering the quadratic pressure gradient in the effective well radius model with the elastic outer boundary condition is expounded.