摘要：

致密碳酸盐岩储层常采用多级交替注入酸压技术来增加裂缝面差异刻蚀和提高酸蚀裂缝导流能力。通过数值模拟可优化多级交替注入施工参数，从而提高酸压改造效果，对压后增产及稳产具有重要作用。但目前关于多级交替注入酸压的数值模拟常忽略酸岩反应或采用等效粘度方法开展研究，模拟结果与实际情况仍存在较大偏差。针对该问题，本文基于流体体积法(VOF)建立了考虑流体界面追踪和酸岩反应的多级交替注入酸压数学模型。采用有限差分法对数学模型进行离散，得到数值模型,并通过编程求解。通过将本模型模拟结果与实验结果以及解析解进行对比，验证了模型在模拟粘性指进及酸液刻蚀方面的准确性。在此基础上，利用该模型开展了多级交替注入酸压模拟，分析了不同交替注入级数下的酸液流动反应规律、粘性指进特征及刻蚀缝宽变化规律。同时，综合考虑酸液作用距离、指进数量及其覆盖面积，提出粘性指进系数，评价了多级交替注入酸压的差异刻蚀效果。研究结果表明，在典型缝宽及交替注入条件下，低粘酸液在粘度差作用下在裂缝中逐渐形成优势通道，即指进现象。随着注入级数增加，相邻的指进分支之间竞争发育，指进合并。酸液有效作用距离随着交替注入级数增加而增加。存在某一临界注入级数，当注入级数大于该级数后，酸液作用距离增加速度变缓。此时，增加级数只能使指进区域内刻蚀增加。因此，对于给定的裂缝条件和酸液体系，存在一个较优的注入级数范围，使得裂缝差异刻蚀和酸液作用距离同时达到较佳效果。本文模型可为多级交替注入酸压提供优化模拟工具，模拟结果可为现场施工方案设计提供理论依据。

关键词: 多级交替注入, 酸压, VOF, 界面追踪, 粘性指进, 酸液作用距离, 数值模拟

Abstract:

Multi-stage alternating injection acid fracturing is commonly employed in the stimulation of tight carbonate reservoirs to enhance differential etching along the fracture surfaces and improve the conductivity of acid-etched fractures. The numerical simulation technique serves as an effective tool for optimizing the operational parameters of such treatments, significantly contributing to the enhancement of post-fracturing productivity and long-term production stability. However, existing numerical simulation approaches for multi-stage alternating injection acid fracturing often neglect acid-rock reactions or adopt simplified equivalent viscosity methods, which result in considerable deviations between simulation results and actual field observations. To address this issue, this study developed a mathematical model for multi-stage alternating injection acid fracturing based on the Volume of Fluid (VOF) method. This model incorporated both the interface tracking between reactive and non-reactive fluids, and also the acid-rock reaction. The governing equations of the mathematical model were discretized using the finite difference method, and the resulting numerical model was solved through computer programming. The accuracy of the model in capturing viscous fingering behavior and acid-etching profiles was verified by comparing the simulation results with the experimental data and analytical solutions. Based on this validated model, simulations were conducted to investigate the flow and reaction behavior of acid under different numbers of alternating injection stages, as well as the evolution of viscous fingering patterns and changes in etched fracture width. To comprehensively evaluate the effectiveness of differential etching, a viscous fingering index was introduced, which was accounted for acid penetration distance, the number of fingering branches, and the area covered by the viscous fingering. Simulation results demonstrate that under typical fracture widths and alternating injection conditions, low-viscosity acid gradually forms preferential flow channels in the fracture due to the viscosity contrast, which is the manifestation of the fingering phenomenon. As the number of alternating stages increases, the competitive development and mergence between the adjacent fingers happens. The effective acid penetration distance continues to increase with the number of alternating injection stages. However, when it is beyond a certain critical stage number, the growth rate of acid penetration distance slows, and further increasing of the alternating injection stages primarily only enhances the acid-etched width within the existing viscous fingering regions. Therefore, for a given fracture geometry and acid system, there is an optimal range of alternating stages, which simultaneously maximizes differential etching and the acid penetration distance. This model provides an effective simulation tool for the optimization of multi-stage alternating injection acid fracturing and offers theoretical guidance for the design of field treatment.

Key words: multi-stage alternating injection, acid fracturing, VOF, interface tracking, viscous fingering, acid penetration distance, numerical simulation

中图分类号: 

• TE357.2

• TE344