耦合双重分形蚓孔的表皮因子计算模型

Skin factor calculation model coupled with dual fractal wormhole

基质酸化是碳酸盐岩油气藏最经济有效的增产方式之一,表皮因子是此类油藏酸化设计中的关键因素。鉴于酸岩反应影响因素多,酸蚀蚓孔生长随机性强,且呈分支型体积展布,以往的表皮因子计算模型通常只将其简化为一等效半径,计算结果可靠性较低。为此,引入了以不规则几何形态为研究对象的分形几何学方法,验证了室内实验得到的单蚓孔平面分布的分形性,得到了其分形维数及单蚓孔长度扩展模型。结合Golfier模型,对多蚓孔同时扩展模拟结果进行了分析,建立了描述多蚓孔间竞争分布的双重分形数学模型。在此基础上,按照酸蚀蚓孔长度与污染半径间对比关系,将表皮因子计算模型改进为两区模型、三区模型和交叉分布模型3种模式。结合现场实际数据,对计算结果进行了参数敏感性分析。根据表皮因子随用酸量、施工排量的变化趋势可以优选施工参数,渗透率差异系数代表储层污染程度,也是影响表皮因子和增产效果的重要因素和选井选层的重要依据。对比表明,通过常规等效半径模型得到的表皮因子小于双重分形模型下的计算值,这也解释了碳酸盐岩储层在负表皮因子下,经过酸化后仍能增产的原因。

Matrix acidizing is one of the most cost-effective methods to increase the oil yield from carbonate reservoirs,and the calculation of skin factor is the most critical parameter in designing acidification process for such reservoirs.Because of multiple factors affecting acid-rock reaction,the high randomness and branching-type distribution of acid wormhole growth,wormholes were usually simplified as an equivalent radius in conventional skin factor models,thus resulting in the low reliability of calculation results.Therefore,the fractal geometry method focus on studying irregular geometry was introduced to validate the fractal property of singlewormhole planar distribution obtained by laboratory experiments,so as to obtain the fractal dimensions and single-wormhole length extension model.In combination with Golfier model,the simulation results of multi-wormhole simultaneous expansion were analyzed to establish the dual fractal model describing multi-wormhole competitive distribution.On this basis,the skin factor calculation model was improved according to the relativities between acid wormhole length and pollution radius,and evolved into two-region model,three-region model and cross-distribution model.Based on actual field data,parameter sensitivity analysis was conducted on calculation results.Operation parameters can be optimized in consideration of the changing skin factor trend with acid volume and pumping rate.Permeability difference coefficient represents formation pollution degree,taken as not only the important factor affecting skin factor and stimulation effect,but also a key foundation for well and layer selection.The comparative results show that the skin factor obtained by conventional equal-radius model is less than the calculation value of dual fractal model.This also well explains why oil yield can be increased even by acidizing the carbonate reservoirs with negative skin factor.