预测油气田产量和可采储量的F模型

The F-model for predicting production rate and reserves of oil and gas fields

预测产量和可采储量是油气田编制开发规划、设计调整方案以及分析开发动态等研究工作必不可少的重要内容。用数学模型或增长曲线方法可以对油气田产量变化的全过程进行描述。根据数理统计学中的F分布,在完成模型转化的推导中首次引入时间转化常数,建立了预测油气田产量和可采储量的新数学模型———F模型。推导了F模型产量、累积产量、最高产量及其发生时间的计算公式,其中的产量和累积产量公式分别用贝塔函数和不完全贝塔函数表达。由于F模型中包含4个常数,模型曲线调节余地较大,因此既适用于油气田产量呈单峰的情形,也适用于产量为纯递减的情形;4个模型常数采用重复线性回归方法求解,便于在计算机上实现。应用F模型描述冀中坳陷的任丘雾迷山组碳酸盐岩油田和岔河集下第三系砂岩油田的产量变化,结果表明,该模型适用范围广,有较好的实用价值。图3参6(朱亚东摘)

Predicting production rate and reserves is one of the most important parts of reservoir management research. The variation of the production rates of oil and gas fields can be described by means of mathematical model or accreting curve. The papers published on this subject were more than 25 by the end of 1998. Based on the F distribution in mathematics statistics, this paper introduces the time conversion constant during the derivation of the model conversion for the first time, and establishes the F model—a new mathematical model for predicting the production rates and reserves of oil and gas fields. This paper presents the calculation formulas of F model's production rate, cumulative production, maximum production rate and its time of generation, and introduces the derivation of this formulas. Among them production rate and cumulative production are expressed by means of β function and incomplete β function, respectively. Because there are 4 parameters in the F model, the model curve can be adjusted in a wider range, it is not only suitable for predicting the situation of single peak production curve, but also for the pure decline curve. The 4 parameters are solves by means of multiple repeated linear regression. The application of the F model in the fields like Wumishan and Chaheji of Renqiu oil complex indicates that the model is very useful.