王利,胡文恒,曹运兴,等.水力压裂流量-压裂效果的理论模型[J].河南理工大学学报（自然科学版）,2024,43(3):23-33.

WANG L , HU W H , CAO Y X, et al.Theoretical model of injection flow rate influencing hydraulic fracturing effects[J].Journal of Henan Polytechnic University(Natural Science) ,2024,43(3):23-33.

水力压裂流量-压裂效果的理论模型

王利1, 胡文恒1, 曹运兴2, 石玢2, 南亚坤1

1.河南理工大学 土木工程学院，河南 焦作  454000 2.河南理工大学 资源环境学院，河南 焦作  454000

摘要:  目的 为了评价流量对水力压裂效果的影响， 方法 提出流量-压裂效果理论模型。该模型定义在储层RVE尺度，压裂效果由体积张开度、孔隙流体压力和骨架有效应力表征，其中体积张开度分为裂缝体积张开度和孔隙体积张开度，二者分别代表RVE中主裂缝及其周围分布性分支裂隙网络的体积张开。流量对压裂效果的影响通过裂缝体积张开度与其解析解的匹配拟合，获得基质骨架断裂损伤演化的最佳参数组合，从而获得一定流量下的压裂效果演化规律。  结果 实例计算表明，该模型可以反映水力压裂过程中的压裂效果演化、脆-韧性断裂机理等诸多特征。流量对压裂效果的影响主要取决于断裂传播机制。黏性-储存M下，流量较小时，孔隙体积张开度处于较高水平，表明网络裂缝形态发育；大流量域中，孔隙体积张开度随流量增大而减小，表明大流量对网络裂缝有抑制作用；裂缝体积张开度随流量增大按指数小于1的幂律增大。黏性-滤失机制M下，孔隙体积张开度基本不随流量变化；主裂缝体积张开度随流量增大呈线性增大。 结论 这些结果对于水力压裂实验和现场应用具有一定的指导意义。

关键词:水力压裂;注入流量;体积张开度;损伤;裂隙网络

doi:10.16186/j.cnki.1673-9787.2023020074

基金项目:国家自然科学基金资助项目（12272126，42230814）；河南省研究生精品教材项目（YJ2023JC05）

收稿日期:2023/02/27

修回日期:2023/10/10

出版日期:2024/05/15

Theoretical model of injection flow rate influencing hydraulic fracturing effects

WANG Li1, HU Wenheng1, CAO Yunxing2, SHI Bin2, NAN Yakun1

1.School of Civil Engineering，Henan Polytechnic University，Jiaozuo  454000，Henan，China 2.School of Resources and Environment，Henan Polytechnic University，Jiaozuo  454000，Henan，China

Abstract:Hydraulic volumetric openings（HVO），which are referred to as the total volume increment over the original pore volume in the reservoir formation in the process of hydraulic fracturing，are direct measures of hydraulic fracturing effects.  Objectives In order to evaluate the HVO quantitatively，in this paper， Methods a new Finite Element Method （FEM） based on the HVO model defined on the RVE scale is established within the framework of the seepage-damage coupling Finite Element Method. This method involves establishing the controlling equations and parameter representations based on the RVE HVO model， and recognizing the damage evolution state based on the principle of energy conservation.  Results The novelties of the new method lie in that the results can output both the increments of pore volume and fracture volume and their temporal evolutions；and that the damage evolution parameters are determined not by the anhydrous tests，but by the coupling between the fluid load and the characters of rock breakdown damage evolution，which indicates the difference between the hydraulic fracturing and anhydrous fracture.The example is to perform a numeric simulation of hydraulic fracturing of a horizontal well for CBM.The calculation program is developed on the ANSYS platform.Firstly，the finished hydraulic fracturing project is simulated，which is used to verify the proposed method.The verification shows that the change of computed horizontal well pressure is basically conformed to the monitored casing pressure curve，and the computed fracturing zone is basically conformed to the spatial distribution of micro tremors，which shows the validity of the proposed method.Then，a series of simulations are performed at varied cluster spaces on the same numeric models.The results show that the fracturing area，HVO，and fracturing efficiency decrease following negative power laws with cluster space increasing，and the small cluster space is inclined to produce stress disturbances thereby improve the fracturing efficiency.  Conclusions The proposed method opens up a new prospect for damage FEM in hydraulic fracturing and supplies more exact theoretical guidance for hydraulic fracturing design.

Key words:hydraulic fracture;injection flow rate;volumetric opening;damage;fracture network