对FETKOVICH(费特科维奇)典型曲线的质疑与评论

Question and comment for FETKOVICH’s typical curve

FETKOVICH(费特科维奇,以下简称为费氏)于1971年和1980年,分别提出的有限水域水侵量方程和定压典型曲线,受到国内外专家的重视和引用。由于费氏典型曲线可以通过实际数据的拟合,确定井的驱动半径和驱动面积,因此,受到业内专家的青睐。通过推导表明,费氏有限水域水侵量方程,是一个指数递减方程。费氏将该方程直接应用于定容封闭边界油井的产量递减分析,并基于初始递减率的关系式,得到了费氏典型曲线的无因次时间。费氏利用无因次压力的倒数作为无因次产量,得到了典型曲线的无因次产量。然而,由于费氏典型曲线的无因次时间和无因次产量之间没有直接的函数关系,无法建立费氏的无因次典型曲线,因此,对费氏的有限水域水侵量方程和典型曲线的无因次时间和无因次产量进行了推导,并对存在的问题提出了质疑和评论。

FETKOVICH proposed the water influx rate equation in finite aquifer and the type curve with constant pressure in 1971 and 1980 respectively,which have been widely recognized and cited by experts both domestically and internationally.His methodology allows for the determination of a well's drainage radius and area by fitting actual production data to his type curve,a technique that has gained popularity among field experts.The derivation of this paper shows that the equation for water influx rate equation in finite aquifer of FETKOVICH is an is characterized by an exponential decline,a model he directly applied to analyze production declines in wells with volumetrically closed boundaries.He derived a dimensionless time for the type curve based on the relationship with the initial decline rate and used the inverse of dimensionless pressure as a proxy for dimensionless production to develop the type curve's dimensionless production profile.However,it's important to note that FETKOVICH's model does not establish a direct functional relationship between dimensionless time and dimensionless production in the type curve model,which means that a comprehensive dimensionless type curve cannot be formulated directly from his equations.This article deduces the water influx rate equation in finite aquifer and the dimensionless time and dimensionless production of the type curve,and questioned and commented on the existing problems.