﻿ 煤层气直井水力压裂裂缝起裂模型研究

Hydraulic Fracturing Fracture Initiation Model for a Vertical CBM Well
Li Yuwei, Ai Chi
College of Petroleum Engineering, Northeast Petroleum University, Daqing, Heilongjiang, 163318, China
Abstract:There are many cleats, fractures and other structural weak planes in coal seams. Fractures may origin from coal body or cleat cracks during hydraulic fracturing. Consequently, mechanisms related to fracture initiation may be significantly different from those observed in conventional reservoir formations. In this regard, a new calculation model of fracture initiation pressure suitable for gas wells in coal-bed methane formations should be established. Considering the delivery network distribution characteristics of the coal seam cleat system and change of cleats in their spatial positions, the stress distribution around the perforated holes and cleats walls was determined based on the rock mechanics and fracture mechanics theory. According to conditions related to tensile and shear failures, the calculation model for fracture initiation pressure of coal was established under different well completion methods. The calculation model was used for two fractured wells and the fracture initiation pressure difference between the calculated value and the measured value in the conditions of open hole completion and perforated completion were 3.96% and 4.72%, respectively. It could be seen that the calculated results coincided well with measured values. The results showed that a seam fracture could be generated from cleats, and the fracture initiation pressures were closely related to coal bed cleat angle, coefficient of internal friction of cleat walls, coal bed horizontal principle stress differences and other factors.
Key words: coal bed methane    cleat    hydraulic fracturing    fracture initiation pressure    physical model    mathematical model

1 井壁围岩与射孔完井力学模型

 图 1 煤层割理系统简化模型 Fig.1 Simplified model of a coal bed cleat system

 图 2 煤层气井井壁围岩与射孔完井力学模型 Fig.2 Mechanical model of sidewall surrounding rock and perforated completion in a CBM well

2 井壁与射孔孔壁周围应力分布计算模型

 图 3 射孔孔眼围岩受力示意 Fig.3 Forces on rocks around perforation holes

3 裸眼完井水力压裂起裂压力计算模型

 图 4 割理与煤层裸眼井筒的相交情况示意 Fig.4 Intersection between open borehole and cleats in a coal bed

3.1 井壁煤岩本体起裂

3.2 沿与井壁相交的割理起裂

3.2.1 沿面割理张性起裂

3.2.2 沿面割理剪切破坏起裂

J.C.Jaeger等人[12]建立了裂隙岩体强度计算模型，金衍等人[5]将其应用于裂缝性地层垂直井水力裂缝起裂计算。煤岩割理相对于煤岩本体而言，也可看成是力学性质薄弱的结构弱面，当作用于面割理的剪切应力大于面割理本身的抗剪切强度时，面割理发生剪切破坏，故有：

3.2.3 沿端割理起裂

3.3 裸眼井起裂压力的确定 3.3.1 煤层裸眼完井起裂压力和起裂模式判别

3.3.2 裸眼井起裂模型应用实例及影响因素分析

 图 5 HX-L1井压裂施工井底压力变化曲线 Fig.5 Changes of bottom hole pressures during fracturing of Well HX-L1

1) 割理倾角对起裂压力的影响。面割理和端割理分别在张性破裂、剪切破裂时，其水平倾角与破裂压力的关系曲线如图6所示。

 图 6 割理倾角对割理起裂压力的影响 Fig.6 Impacts of cleat angles to fracture initiation pressures

2) 割理内煤岩粘聚力和壁面内摩擦系数对起裂压力的影响。由于割理内煤岩粘聚力和壁面内摩擦系数的变化只对压裂时割理的剪切破坏起裂压力产生影响，因此只根据计算结果绘制了面割理和端割理的剪切破坏起裂压力变化曲线，粘聚力-破裂压力曲线见图7，内摩擦系数-破裂压力曲线见图8

 图 7 割理内煤岩粘聚力对割理剪切破裂压力的影响 Fig.7 Effect of adhesive forces in coal-bed cleat to shear fracture pressures

 图 8 割理壁面内摩擦系数对割理剪切破裂压力的影响 Fig.8 Impacts of internal friction coefficients in cleat to shear fracture pressures of cleat

3) 煤层水平主应力差值对起裂压力的影响。为了分析煤层最大、最小水平主应力差值对裸眼井起裂压力的影响，保证其他参数不变，最小水平主应力分别为8.29,9.29,10.29,11.29和12.29 MPa，使对应的煤层水平主应力差分别为4，3，2，1和0 MPa，计算并绘制了破裂压力-水平主应力差曲线(见图9)。

 图 9 煤层水平主应力差值对割理起裂压力的影响 Fig.9 Impacts of differences in coal bed horizontal principle stresses to fracture initiation pressures

4 煤层射孔完井裂缝起裂压力计算模型 4.1 射孔完井压裂起裂模型的建立 4.1.1 射孔完井煤岩本体起裂分析

4.1.2 沿与射孔孔眼相交割理的起裂计算

 图 10 射孔孔眼与面割理相交时的井壁应力分布 Fig.10 Distribution of sidewall stresses around intersections between perforation holes and face cleats

4.2 射孔完井起裂压力计算 4.2.1 射孔完井起裂压力的确定

4.2.2 射孔完井起裂压力实例计算分析

 图 11 HX-3井压裂施工井口、井底压力测量结果 Fig.11 Measured surface and bottom pressures during fracturing of Well HX-3

5 结 论

1) 建立的煤层裸眼和射孔完井方式下水力压裂起裂压力计算模型,其计算结果与实测结果吻合较好，也证明了煤层水力压裂能够从割理处发生起裂，并且起裂压力低于煤岩本体起裂的压力。

2) 随着面割理和端割理水平倾角的增大，压裂时面割理和端割理发生张性破裂和剪切破裂的起裂压力减小；水平倾角等于0°时，压裂时面割理和端割理发生破坏所需的压力最大。

3) 割理内煤岩粘聚力改变对割理剪切破坏起裂压力的影响并不显著，而壁面内摩擦系数变化对割理剪切破坏起裂压力影响明显，随着割理壁面内摩擦系数的增大，面割理和端割理的剪切破坏起裂压力明显增大。

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#### 文章信息

Li Yuwei, Ai Chi

Hydraulic Fracturing Fracture Initiation Model for a Vertical CBM Well

Petroleum Drilling Techniques, 2015, 43(04): 83-90.
http://dx.doi.org/10.11911/syztjs.201504015