在页岩气试井分析中Bessel函数溢出问题的解决方法

发布时间：2018-03-05 02:34

本文选题：试井　切入点：页岩气　出处：《天然气工业》2017年06期 　论文类型：期刊论文

【摘要】：Bessel函数在页岩气藏多段压裂水平井的试井解释理论中发挥着非常重要的作用,但变形Bessel函数I_n(x)和K_n(x)在自变量趋于无限小或无限大时,使用多项式逼近的方法求解往往会溢出,难以得到典型曲线致使试井解释困难。为此,从理论上剖析了当储集层渗透率非常低时在无因次时间低于10~(-6)时变形Bessel函数都会溢出的原因。结果表明:对于第一类Bessel函数I_n(x),当x650,I_0(x)与I_1(x)部分计算机出现浮点数溢出,高于10~(215)。页岩气试井理论中根据无因次时间的定义,渗透率越小,压裂裂缝半长越大,测试时间越短,根据Laplace反演I_0与I_1的值非常容易溢出,难以绘制出早期典型曲线。在理论研究的基础上,通过对第一、二类变形Bessel函数的重新组合计算,将I_0与I_1计算过程中都乘以,保证了变形Bessel函数在计算过程中不会溢出。结论认为,大长度水平井或大型压裂井模型中,由于水平段长度或裂缝长度越大,无因次时间相应的就越短、Laplace变量就越大,必须用该方法处理Bessel函数的I_0与I_1,才能获得完整的典型曲线,否则计算就会溢出。
[Abstract]:The Bessel function plays a very important role in the well test interpretation theory of multistage fracturing horizontal wells in shale gas reservoirs, but the deformation Bessel function I _ NX) and Knn _ x) often overflow when the independent variables tend to be infinitely small or infinite. The difficulty of obtaining typical curves makes well test interpretation difficult. This paper theoretically analyzes the reason why the Bessel function of deformation will overflow when the permeability of reservoir is very low, when the dimensionless time is less than 10 ~ (-6). The result shows that for the first kind of Bessel function I _ Bessel _ X, when x _ 650 / I _ T _ 0) and I _ S _ 1x) appear floating-point overflow. In shale gas testing theory, according to the definition of dimensionless time, the smaller the permeability, the larger the fracture half length, the shorter the test time, and the easier it is to overflow the values of I _ S _ 0 and I _ 1 from the inversion of I _ 0 and I _ 1 based on Laplace. It is difficult to draw an early typical curve. On the basis of theoretical research, by recombining the Bessel functions of the first and second kinds of deformation, we multiply the I _ S _ 0 and I _ s _ 1 by, It is concluded that in large length horizontal wells or large fracturing wells, the larger the horizontal section length or fracture length, the shorter the dimensionless Bessel variable is. This method must be used to deal with the Bessel function I _ s _ 0 and I _ s _ 1 in order to obtain a complete typical curve, otherwise the calculation will overflow.
【作者单位】：中国石油川庆钻探工程公司地质勘探开发研究院;中国石油西南油气田公司川东北气矿;西南石油大学;
【基金】：国家科技重大专项“低丰度致密低渗油气藏开发关键技术”(编号:2016ZX05048-004)
【分类号】：TE373

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