The Inverse Problem Of The Horizontal Well Percolation Mathematical Model

Horizontal well technology has become the main focus of world oil industry development,has broad developmentprospects,and it’s also an important technology in the market competition. Horizontal well technology plays an important role in obtaining economic benefits and improving recovery rate. The current percolation models of horizontal well is regared as the known conditions to calculate the pressure, but if the flow is not uniformly distributed, then each point current source intensity is different. Constant pressure production of horizontal well productivity formula is discussed less by people, and most well test analysis are discussed under the set production. In order to study the phenomenon of production under constant pressure in head of the well, in this paper, I establish the inverse problem of horizontal well of seepage model.This paper mainly studies the infinite reservoir bottom closed horizontal unstead-y flow model. Firstly,we use orthogonal transformation method to derive the analytic solution for percolation model, and extend this to the analytic solution of line source in horizontal well. Secondly, we assume pressure is constant.and we establish the inverse problem of a line source of horizontal well unsteady seepage model. Using Laplace transform to time variables and assume a current source intensity can be separated into the product of the function of t and x.Then the inverse problem of nonlinear simplifies a mathematical physics equation of t and a linear inverse problem of x.Thirdly, we use steepest descent method to solve the flow source intensity.At last. we get the productivity formula of horizontal wells.In Chapter Ⅰ,the paper describes the horizontal well production and development of significance, as well as the research background at home and abroad.In Chapter Ⅱ,it contains the basic situation of horizontal well technology and percolation models of horizontal well testing analysis theory, including the basic principles, orthogonal transform, FFT theory, percolation mechanics etc.In ChapterⅢ,according to horizontal well reservoir seepage characteristics and seepage mechanism,I establish of horizontal well percolation mathemmathematical model, and use orthogonal transformation method to deduce the precise point source solution of unsteady seepage problem. And promote the line source of horizontal well.At last,I establish the inverse problem of a line source of horizontal well unsteady seepage model. In Chapter Ⅳ, I use Laplace transform to time variables and assume a current source intensity can be separated into the product of the function of t and x.Then the inverse problem of nonlinear simplifies a mathematical physics equation of t and a linear inverse problem of x,I use steepest descent method to do the numerical calculation of inverse problem of a line source of horizontal well unsteady seepage model,and work out current source strength. At last,we get the productivity formula of horizontal wells.In Chapter Ⅴ, I have a summary and outlook, pointing out the advantages and disadvantages of areas which needs improvement in this paper.