Numerical Well Test Of Multiple Wells With Finite Element Method

Finite element method is a numerical method used to solve partial differential equation, the base of which is the functional variation principle or weight function orthogonalization. While studying percolation problem, finite element method has special advantages: the treatment of well and boundary condition is simple and flexible, there is no limitation of reservoir shape and well number, and the complex problems can be solved which can't be solved by conventional methods. At present, along with the continuous deepening of adjusting and potential trapping measures for water flooding oilfield, the testing data of oil wells are influenced by adjacent wells basically under the condition of thick well pattern, so the conventional welltest analysis method and formation pressure calculation method can't meet the requirements of oilfield development gradually. It is necessary to study the pressure buildup process of transient welltet in multi-well system according to dynamic and static data such as geological characteristics, well pattern types and injection-production condition, etc.Therefore, finite element numerical welltest analysis method of multi-well system is studied based on the existing research results. The major works are as follows:First, mathematical model of stable flow in multi-well system is developed and solved by finite element method, the pressure profiles of multi-well system are drawn, the characteristics of pressure distribution are analyzed, and the influences of boundry condition, well spacing, threshold pressure gradient and fracture conductivity are also researched.Secondly, transient welltest mathematical model with threshold pressure gradient in multi-well system is developed and solved by finite element method, then the wellbore storage coefficient and skin factor are introduced by Laplace Transformation and Stethfest Inversion, the type curves are drawn and the basic shapes and influence factors are analyzed, such as the production time, injection-production ratio and threshold pressure gradient, et al.Finally, a part of practical welltest datas are matched and analyzed, and the basic parameters, such as permeability, skin factor, wellbore storage factor and the average pressure of reservoir, are obtained through welltest interpretation. It is shown in the results: the welltest theory is developed and completed through the study in this paper, at the same time which provides a new favorable method for interpreting welltest data in multi-well system and also provides necessary scientific basis for solving a series of problems in the oilfield development with small well spacing and thick well pattern.