Abstract:

On basis of the theory of mechanics of fluid flow through porous media，by applying the instantaneous source,continuous source,convolution formula and Laplace transformation method,a productivity calculation model of finite-conductivity vertical fracture is set up.The derived integral equation is soluted with the boundary element method (BEM) in Laplace space.By using of Stehfest numerical inversion,the solution of real space is obtained and thus an accurate method is given for calculating the productivity of finite-conductivity vertical fracture.In addition,by quantitative calculation,how various parameters affect the productivity is analyzed.By analyzing,it can be seen that the productivity increases when the fracture length,fracture permeability and fracture width increase,but the increase rate gradually slows down.So in the design of hydraulic fracturing for actual reservoir,reasonable parameters should be designed by considering fracturing cost and benefit.The results in this paper have certain value for predicting productivity of fracturing well and designing the reasonable parameters on the process of hydraulic fracturing.

Key words: vertical fracture, fractured well, productivity, source, Laplace transform, numerical inversion