改进的斜井和水平井IPR方程

Modified IPR equation for vertical and inclined wells.

油井的流入动态（ＩＰＲ） 曲线是描述油井产量和井底流压关系的曲线。目前常用的斜井和水平井的流入动态（ＩＰＲ） 方程是由Ｃｈｅｎｇ 在数值模拟研究的基础上按照Ｖｏｇｅｌ 型ＩＰＲ方程的形式回归而得到的。但是Ｃｈｅｎｇ型ＩＰＲ方程第一项系数ａ 只有在垂直井情况下才为１ ，导致其ＩＰＲ曲线两端不合理：当井底流压为零时，计算的产量并不等于油井的最大产量；当生产压差为零时，计算的采油指数不为零，这些显然与油井的实际情况不符。而Ｆｅｔｏｋｏｖｉｃｈ 型ＩＰＲ 方程则可避免这些错误。针对Ｃｈｅｎｇ 型ＩＰＲ方程的存在问题，给出了Ｆｅｔｋｏｖｉｃｈ 型斜井和水平井的ＩＰＲ方程，此类ＩＰＲ 方程在端点处更合理，应用更可靠。另外，还给出了井斜角与Ｆｅｔｋｏｖｉｃｈ型ＩＰＲ方程的指数ｎ 的关系。

An IPR equation of a production well describes the relationship between production rate and the bottom hole pressure. Most popularly used inflow IPR equation for an inclined or a horizontal well is that one based on a numerical simulation and regressed from the form of Vogel IPR equation by Mr. Cheng. However in Cheng type equation the first item “ a ” is 1.0 only when the well is a vertical one, thus the end points of the curve described this equation are irrational: the production rate calculated by this equation does not equal to its maximum production rate when the bottom hole inflow pressure is “0”, and the productivity index well not be “0”, when inflow bottom hole pressure differential is 0; these does not conform with the actual case. However Fetokovich type IPR equation can avoid these errors with the problems in Cheng type equation, Fetokovich type IPR equation for horizontal and inclined well are given. This type of IPR equation has a more reasonable result in the treatment of end points and is more reliable in application. Furthermore, the relation between the angle of inclination and the exponent “ n ” of Fetokovich IPR equation is given also.