基于分形理论的多因素耦合酸蚀裂缝导流能力预测模型研究

Research on the Prediction Model of Multi Factor Coupled Acid Fracture Conductivity Based on Fractal Theory

摘要: 导流能力是衡量碳酸盐岩酸压效果的关键参数，其稳定性和持久性直接影响深层、高温高压碳酸盐岩储层的改造效果。然而，由于岩石力学性质、矿物组成及储集空间特征等多因素的耦合作用，酸蚀裂缝的导流能力难以精准预测。为此，本文基于分形理论，结合实验测定与数学建模，构建了多因素耦合酸蚀裂缝导流能力预测模型。研究结果表明，渗透率是主控因素，其增加可显著提升导流能力(40%~136%)，远超其他参数。矿物组成亦起关键作用，方解石和白云石含量的增加可分别提升导流能力(5.30%~23.90%)，而非碳酸盐岩矿物含量增加则导致导流能力下降(8.5%~15.2%)。此外，杨氏模量与导流能力呈正相关，每增加10 GPa可提升1%~52%，而泊松比呈负相关，每增加0.02使导流能力降低1%~5%。相比之下，孔隙度的影响相对较小，每增加1%仅提升约1%。本研究为酸蚀裂缝导流能力的精确预测提供了理论支持，可为酸压施工优化提供重要参考。

Abstract: Conductivity is a key parameter to measure the effect of acid fracturing in carbonate rocks, and its stability and durability directly affect the transformation effect of deep, high-temperature and high-pressure carbonate reservoirs. However, it is difficult to accurately predict the flow-conducting capacity of acid fracture due to the coupling of multiple factors, such as rock mechanical properties, mineral composition and reservoir space characteristics. For this reason, this paper constructs a multifactor coupled acid-etched fracture flow capacity prediction model based on fractal theory, combining experimental measurement and mathematical modelling. The results show that permeability is the main controlling factor, and an increase in permeability can significantly increase the flow capacity (40%~136%), which is much higher than other parameters. Mineral composition also plays a key role, as the increase of calcite and dolomite content can enhance the flow conductivity (5.30%~23.90%), while the increase of non-carbonate rock mineral content leads to the decrease of flow conductivity (8.5%~15.2%). In addition, Young’s modulus was positively correlated with the hydraulic conductivity, with each increase of 10 GPa enhancing it by 1%~52%, while Poisson’s ratio was negatively correlated, with each increase of 0.02 decreasing hydraulic conductivity by 1%~5%. In contrast, the effect of porosity is relatively small, with only about 1% enhancement per 1% increase. This study provides theoretical support for the accurate prediction of the flow conductivity of acid-etched fractures, which can provide an important reference for the optimization of acid pressure construction.