求取压裂后气井产能的椭圆流方法

ELLIPTICAL FLOW METHOD TO CALCULATE PRODUCTIVITY OF GAS WELLS AFTER FRACTURING

气井的绝对无阻流量是确定气井产量的主要指标。通常在确定压裂后气井的产能从而求取无阻流量时,采用近似的流动模式来表征压裂后流体渗流规律的变化,而没有考虑其真实流动形态。文章根据气藏的渗流机理,对于有对称双翼人工裂缝的均质等厚气藏,地层中的真实渗流情形是拟径向非达西渗流,流动等势线为以井眼为中心的椭圆族,流线为垂直椭圆族的放射线。根据椭圆族的特征与渗流规律,从广义的达西定律出发,可推导出裂缝区域外椭圆族内的流动公式。而对于c椭圆内区域的渗流,由于存在两种渗流介质,认为压裂裂缝内和垂直裂缝附近区域的流动为非达西单向渗流,从而推导出裂缝区域附近的流动公式。综合裂缝区域内外的渗流,可以推导出稳态情况下的气藏产能公式,根据该公式便可求取无阻流量,其中c可根据协调条件求出,给出的计算实例结果与试井数据相吻合。

The absolute open flow of gas wells is the key index to determine the production of gas wells. Usually, when the productivity of gas wells after fracturing is determined to calculate the open flow, the approximate flow pattern is used to characterize the variation of the fluid percolation law after fracturing without considering its real flow state. Based on the percolation mechanism of gas reservoirs, for homogenous isopachous gas reservoirs with symmetric dual-wing artificial fractures, the real percolation state in reservoirs is pseudo-radial non-Darcy flowi the flow isopotential lines are a group of ellipses taking the well-bore as the center; and the flow lines are radiometric lines vertical to the group of ellipses. According to the characteristics of the group of ellipses and the percolation law, based on the generalized Darcy law, the flow formula can be derived within the group of ellipses outside the fractured zone. As for the percolation with in the 'c' ellipse, regarding the flow as non-Darcy uniflux inside the fractured fractures and near the vertical fractures since there are 2 kinds of mediums, the flow formula is derived for near the fractured region. Integrating the percolations in and out the fractured region, the productivity formula of the gas reservoir can be derived under steady state. According to the formula, the open flow can be obtained while 'c' can be derived by corresponding conditions. With real case calculation, the results match the well test data well.