砂岩射孔井基质酸化数学模型的建立及应用

MATHEMATICAL MODEL OF MATRIX ACIDIZING FOR PERFORATED WELL IN SANDSTONE AND ITS APPLICATIONS

在射孔井中，井筒仅通过炮眼与周围地层相互作用。炮眼周围液体的流动形态、压力分布以及酸液的运动前缘等与裸眼井中的平面径向流截然不同。但目前我国的酸化设计全都按照裸眼井进行。为使射孔井的酸化设计更为准确、合理，在椭圆坐标系中建立了射孔井砂岩基质酸化的压力微分方程和酸平衡方程。同时将砂岩中的矿物划分为两种以不同速度溶解的拟化学矿物，以硅酸盐和石英为代表。通过求解椭圆坐标系中的基本方程组，获得目标区域内的压力分布、氢氟酸浓度分布、硅酸盐及石英矿物的浓度分布、孔隙度和渗透率分布，求得酸液有效作用距离和增产倍比，从而预测酸化效果。

Wellbore is linked to formation by perforation tunnels in perforated well. The flowing pattern, pressure distribution and the flowing front of acid fluid in perforated well are different that in openhole well. But the acidizing is always designed on the basls of openhole well in China at the moment. In order to obtain more reasonable acidizing design, the pressure differential equation and acid equilibrium equation for matrix acidizing of perforated well in sandstone are esiablished in elliptic coordinate system. Moreover, the minerals in sandstone are dIvlded into two kinds of pseudo-mineral with different dissolution velocity taking si1icate and quartz as representative respectively. The pressure distribution, aciJ concentratlon distribution, sillcate or quartz concentration distribution, porosity and permeabllity distributlon, effective operating radius and production increment multiple can be calculated and predicted by solving the basic equation group in elliptic coordinate system.