THE SIMILAR STRUCTURE OF SOLUTIONS IN FRACTAL MUlTILAYER RESERVOIR INCLUDING A QUADRATIC GRADIENT TERM  

作　　者：LI Wei LI Xiao-ping LI Shun-chu LI Quan-yong 

机构地区：[1]State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University,Chengdu 610500, China [2]Institute of Applied Mathematics, Xihua University, Chengdu 610039, China

出　　处：《Journal of Hydrodynamics》2012年第3期332-338,共7页水动力学研究与进展B辑（英文版）

基　　金：supported by the National Science and Technology Major Project of China(Grant No.2008ZX50443-14);the National Basic Research Program of China(973Program,Grant No.2011CB201005)

摘　　要：When the classical nonlinear partial differential equations are used to model the fractal reservoir, based on the assumption of low compressibility fluids, the effects of the quadratic gradient term are ignored, which would be questionable for mixed gas reservoirs and low permeability reservoirs. To consider the influence of the wellbore storage, the nonlinear mathematical flow model of the fractal multilayer reservoir is built in this paper, with three kinds of outer boundaries （infinite boundaries, constant pressure boundaries and closed boundaries）. Using the Laplace transform method, the solutions for the dimensionless reservoir pressure and the bottom hole pressure in the Laplace space are obtained. An analysis shows that the solutions involve similar structures even for three different kinds of outer boundaries, and can be unified as a continuous fraction. The unified expression would make it more convenient to analyze the formation parameters, which greatly facilitates the development of the well test analysis software.When the classical nonlinear partial differential equations are used to model the fractal reservoir, based on the assumption of low compressibility fluids, the effects of the quadratic gradient term are ignored, which would be questionable for mixed gas reservoirs and low permeability reservoirs. To consider the influence of the wellbore storage, the nonlinear mathematical flow model of the fractal multilayer reservoir is built in this paper, with three kinds of outer boundaries （infinite boundaries, constant pressure boundaries and closed boundaries）. Using the Laplace transform method, the solutions for the dimensionless reservoir pressure and the bottom hole pressure in the Laplace space are obtained. An analysis shows that the solutions involve similar structures even for three different kinds of outer boundaries, and can be unified as a continuous fraction. The unified expression would make it more convenient to analyze the formation parameters, which greatly facilitates the development of the well test analysis software.

关 键 词：fractal multilayer reservoir quadratic gradient wellbore storage similar structure 

分 类 号：TE312[石油与天然气工程—油气田开发工程] TP13[自动化与计算机技术—控制理论与控制工程]