油气藏产量旋回泛函数学模型的建立及应用

Establishment and Application of Functional Mathematical Model for Production Cycle of Oil and Gas Reservoirs

在系统梳理油气藏产量旋回数学模型的基础上,引入泛函产量递减通式,替换广义产量全过程数学模型中的递减函数,不需要根据油气藏驱动类型和渗流特征确定递减函数;考虑到广义产量全过程数学模型可积分,对其递增函数项表达式进行归纳,形成了3类递增函数表达式。新的广义产量全过程数学模型在复合时间和待定参数取不同值时,不仅可以转化为各类产量旋回基础数学模型,而且还能形成其他新的产量旋回数学模型,具备了产量全过程数学模型的通式及拓展性。为了降低待定参数求解难度,给出了5种最简单、最常见的复合时间关系式和产量旋回泛函数学模型求解方法。实例应用效果好,值得在其他油气藏进一步推广应用。

The mathematical models for production cycle of oil and gas reservoirs were reviewed systematically.On this basis,the general⁃ized functional production decline formula was introduced to replace the decline function in the generalized whole⁃process mathematical model for production cycle,and it is no longer necessary to determine the decline function according to the driving type and flow character⁃istics of the oil and gas reservoirs.Meanwhile,considering that the generalized whole⁃process mathematical model for production cycle can be integrated,the expressions of its increasing function items were summarized to form three types of increasing function expressions.When the composite time and undetermined parameters take different values,the new generalized whole⁃process mathematical model for production cycle can not only be converted into the basic mathematical models for various production cycles,but also form other new mathe⁃matical models for production cycle,possessing the general formula and extensibility in the whole⁃process mathematical model for produc⁃tion cycle.In order to reduce the difficulty in solving the undetermined parameters,five simplest and most common methods for solving the composite time formula and functional mathematical model for production cycle are given.The satisfactory application results verify that the new model is worthy of promotion in other oil and gas reservoirs.