4种水驱特征曲线与Arps递减曲线的关系

Relationships among 4 Types of Water-Drive Characteristic Curves and Arps Decline Curve

水驱特征曲线和Arps递减曲线作为动态评价方法,在已开发油田评价可采储量和预测开发指标中发挥了重要的作用。由于两种方法的理论基础不同,导致它们无法直接建立联系。从Arps递减理论公式出发,通过推导产油量—时间的表达式认识到:如果某种水驱特征曲线的表达式能够通过变形得到关于瞬时递减率与产油量的表达式,那么这种水驱特征曲线和Arps递减曲线存在着联系。选择了常用的4种水驱特征曲线,假设油藏产液量不随时间变化,通过两次对时间求导,得到了这4种水驱特征曲线的关于瞬时递减率与产油量的表达式。乙型水驱特征曲线和调和递减的递减趋势一致,丙型水驱特征曲线和n=0.5双曲递减的递减趋势一致,甲型水驱特征曲线、丁型水驱特征曲线只有在油藏含水较高时才能与Arps递减曲线有相似的递减趋势。根据这4种水驱特征曲线的瞬时递减率与产油量的表达式,建立了相关开发指标的预测方法,经过实例验证,达到了较高的预测精度。

Water-drive characteristic curves and decline curve as the methods of production performance evaluation play significant roles in recoverable reserves evaluation and development index prediction in developed oilfields. But direct relationship between the two methods cann＇ t be established due to different theoretical bases of them. Oil production vs time expression is derived from Arps decline formula in this paper and it is considered that if an expression related to transient decline rate and oil production could be obtained from the deformation of a water-drive characteristic curve expression, there must be a kind of relationship between the water-drive type curve and Arps decline curve. 4 commonly used water-drive characteristic curves are selected. Assume that liquid production doesn＇t change with time, take the derivative of time twice, expressions of the relationships among the 4 type curves in regard to transient decline rate and oil production are obtained. The decline trend of Type B water-drive type curve is in accordance with that of harmonic decline, the decline trend of Type C is matched with that of hyperbolic decline when n=0.5. Type A and D curves are similar to Arps decline curve only when the reservoir water cut is relatively high. Based on the expressions of transient decline rate and oil production of the 4 water-drive characteristic curves, a method is established for development index prediction, whose high accuracy has been proved by some cases.