含水变化规律广义数学新模型的建立与应用

根据已有含水变化规律在半对数坐标系中呈直线关系的基础上，归纳出一种新的含水变化规律广义数学模型，并推导了该数学模型的油水渗流特征方程和对应的水驱特征曲线。新的数学模型在特征参数n、m取不同值时，不仅能转化为经典的凸形、S-凸形、S形、S-凹形、凹形含水变化曲线，而且也能描述近S形或近直线形含水变化曲线，克服了以往依靠原油黏度去选择某个特定含水变化规律的经验性方法的不足。利用新型含水变化规律广义数学模型，对国内外14个不同油藏稳定水驱阶段数据进行拟合的结果显示，特征参数n、m与原油的流度存在一定的关系，据此可以为不同油藏横向之间含水上升因素的对比分析提供新的研究方向。雁木西油田古近系—新近系油藏和Kumkol North油田Ⅲ油藏的应用结果表明，无论是采用新型广义数学模型进行直接拟合，还是采用其对应的水驱特征曲线进行间接拟合，其拟合效果均较好，表明新型广义数学模型具有较强的自适应性和稳定性。

Establishment and application of a new generalized mathematical model of water cut change law

Based on the linear relationship of the existing water cut change law in the semi logarithmic coordinate system, a new generalized mathematical model of water cut change law is summarized, and the oil-water flow characteristic equation and the corresponding water drive characteristic curve of the mathematical model are derived. When the characteristic parameters n and m are taken as different values, the new mathematical model can not only be transformed into the classic water cut curves of Convex, S-Convex, S, S-Concave and Concave types, but also can describe the water cut curves of nearly S-shape or nearly linear type, which overcomes the previous empirical practice of selecting a specific water cut change law by relying on the viscosity of crude oil. By using the new generalized mathematical model of water cut change law, the data of 14 different reservoirs at home and abroad in stable water drive stage are fitted. The preliminary results show that there is a certain relationship between the characteristic parameters n and m and the mobility ratio of crude oil, which provides a new research direction for the comparative analysis of water cut rise factors between different reservoirs. Through the application of Paleogene-Neogene reservoir in Yanmuxi oilfield and the third reservoir in Kumkol North oilfield, whether the new generalized mathematical model is used for direct fitting or the corresponding water drive characteristic curve is used for indirect fitting, the fitting effect is good. This shows that the new generalized mathematical model has strong adaptability and stability, which is worth learning from other oilfields.