Abstract: Partial differential equations for the case of an infinite homogeneous reservoir with a horizontal fracture are formulated in this paper where wellbore storage is considered.In order to solve this set of equations,Green's function of diffusivity equation not the source functions,are introduced and the horizontal fracture is taken as a uniform-source plane.The Green's function of a slab region is thus developed.The wellbore storage effect is considered indirectly by using a variable surface flow rate.With the help of Laplace transformation and Green's function,the solution of the equation is obtained in Laplace space and the relation between transient pressure and production time in this system is investigated,The conclusions reached in this paper are as follows: 1.Green's function could be used effectively to solve parabolic equations.2.The difficulty in taking wellbore storage into consideration could be solved by introduction of a variable surface flow rate.3.The dimensionless pressure could be obtained from its Laplace expression by numerical inversion of Laplace transform.4.The dimensionless Log-Log type curves commonly used in field practice are presented.5.The early-stage and long term behavior of fluid flow is analyzed An approximate analytical solution is proposed to analyze field pressure data.Furthermore,formulas describing flow coefficient,fracture radius,wellbore storage factor are presented.Gringarten's conclusions from the model of an infinite homogeneous reservoir with a horizontal fracture without wellbore storage is a special case of the solution presented in this paper.

摘要： 本文建立了单层均匀无限地层中的水平裂缝井具有续流现象时流体的流动方程式,即压力的变化与时间的关系。纵定义扩散方程的格林函数入手,不引入源函数,而是将水平裂缝视为厚度很小的均匀汇,给出石板形区域的格林函数,然后将地下流量视为变量,解决了考虑续流现象的困难。求解过程先使用拉普拉斯变换,加上内边界条件,得到井底压力的拉普拉斯变换式及各时间段的解析表达式。从而提供了求得流动系数、裂缝半径及井筒存储等参数的公式。Gringarten建立的均质无限大地层的流动模型和不考虑井筒存储效应的水平裂缝地层的流动模型均为本结论的特例。