基于最小應變能密度因子斷裂準則的巖石裂紋水力壓裂研究

董卓; 唐世斌; 郎穎嫻

doi:10.13374/j.issn2095-9389.2019.04.003

基于最小應變能密度因子斷裂準則的巖石裂紋水力壓裂研究

doi: 10.13374/j.issn2095-9389.2019.04.003

董卓^{1, 2},
唐世斌^{1, 2, ,},
郎穎嫻^{1, 2}

1.
大連理工大學海岸和近海工程國家重點實驗室, 大連 116024
2.
大連理工大學土木工程學院, 大連 116024

基金項目:

國家自然科學基金面上項目 51874065

國家自然科學基金資助項目 U1562103

國家自然科學基金資助項目 51474046

詳細信息

通訊作者:
唐世斌, E-mail: tang_shibin@dlut.edu.cn

中圖分類號: TG142.71
計量
- 文章訪問數: 1219
- HTML全文瀏覽量: 666
- PDF下載量: 29
- 被引次數: 0
出版歷程
- 收稿日期: 2018-03-08
- 刊出日期: 2019-04-15

Hydraulic fracture prediction theory based on the minimumstrain energy density criterion

DONG Zhuo^{1, 2},
TANG Shi-bin^{1, 2
, ,},
LANG Ying-xian^{1, 2}

1.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
2.
School of Civil Engineering, Dalian University of Technology, Dalian 116024, China

More Information

Corresponding author: TANG Shi-bin, E-mail: tang_shibin@dlut.edu.cn

摘要

摘要: 建立了考慮裂紋尖端非奇異項T應力的最小應變能密度因子斷裂準則, 研究了不同裂紋類型條件下T應力和泊松比對起裂角的影響, 結果表明裂紋起裂角不僅與奇異項應力強度因子有關, 而且還需要考慮非奇異項T應力和泊松比的影響作用.同時計算了含井筒對稱雙裂紋水力壓裂模型的起裂角和臨界水壓, 表明依據本文斷裂準則計算得到理論解與實驗結果吻合良好.在此基礎上, 利用該準則從理論上分析了臨界裂紋區尺寸、T應力、比奧系數、側壓系數、泊松比等因素對水力壓裂裂紋起裂特性的影響.參數分析表明: 臨界裂紋區尺寸、T應力和側壓系數對臨界水壓和臨界起裂角有顯著影響.臨界水壓隨著泊松比增大而減小, 而臨界起裂角呈現相反變化趨勢.比奧系數對臨界起裂角沒有影響, 但是在高水壓條件下對起裂角具有顯著影響.
- 應變能密度因子 /
- T應力 /
- 水力壓裂 /
- 泊松比 /
- 比奧系數 /
- 起裂角 /
- 臨界水壓
Abstract: Hydraulic fracturing is a promising technique used in oil and gas reservoirs, enhanced geothermal systems, and coal gas production.Although its use is widespread, many aspects of hydraulic fracturing are still not well understood and need to be further investigated to achieve increases in oil and gas production while mitigating the adverse aspects of hydraulic fracturing.Understanding how hydraulic pressure extends preexisting fractures and forms a complex fracture network is essential for the design and treatment of hydraulic fracturing.Critical water pressure and fracture initiation angle are two important parameters involved in the hydraulic fracture propagation process and production from a well.In the present study, a minimum strain energy density criterion, which considers the effects of T-stress and Poisson's ratio, was proposed to analyze fracture initiation during hydraulic fracturing.The fracture initiation angle for different crack types was investigated using the proposed theoretical method, and the results indicate that the fracture initiation angle is not only related to the stress intensity factor but also affected by the T-stress and Poisson's ratio.The critical water pressure and critical initiation angle for two symmetric radial cracks emanating from a pressurized borehole were investigated, and the theoretical results were consistent with the experimental results.Through the proposed theoretical method, the influence of T-stress, radius of the fracture process zone, Biot's coefficient, lateral pressure coefficient and Poisson's ratio on the hydraulic fracturing behavior was analyzed.Parameter analysis indicates that the radius of the fracture process zone, T-stress, and lateral pressure coefficient play an important role in the critical initiation angle and critical water pressure.The critical water pressure increases with the decrement of Poisson's ratio, whereas the critical initiation angle shows the opposite trend.Biot's coefficient has no effect on the critical initiation angle but has a significant influence on the fracture initiation angle under high water pressure.The theoretical model enables a comprehensive understanding of the characteristics of hydraulic fracturing under complex loading conditions.The results also provided a basis for quantitative investigations of the engineering design of hydraulic fracturing treatments.
- strain energy density /
- T-stress /
- hydraulic fracturing /
- Poisson's ratio /
- Biot's coefficient /
- fracture initiation angle /
- critical water pressure

HTML全文

圖 1 純I型裂紋起裂角與泊松比υ和T應力的關系

Figure 1. Relationship between Poisson's ratio, T-stress, and fracture initiation angle under pure Mode I

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圖 2 純II型裂紋起裂角θ₀與泊松比υ和T應力的關系

Figure 2. Relationship between Poisson's ratio, T-stress, and fracture initiation angle under pure Mode II

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圖 3 計算模型. (a) 實驗模型^[16]; (b) 雙軸壓縮中心裂紋模型

Figure 3. Calculating model: (a) experimental model^[16]; (b) center preexisting crack under biaxial compression

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圖 4 數值模型及裂紋尖端網格

Figure 4. Numerical model and crack tip mesh pattern

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圖 5 起裂角θ₀實驗數據與理論計算(有無T應力) 的對比. (a) σ_H /σ_h = 4; (b) σ_H /σ_h = 6

Figure 5. Experimental and theoretical results (with or without T-stress) of the fracture initiation angle: (a) σ_H /σ_h = 4; (b) σ_H /σ_h = 6

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圖 6 臨界水壓P_c和臨界起裂角θ₀實驗數據與理論計算對比. (a) σ_H /σ_h = 4; (b) σ_H /σ_h = 6; (c) σ_H /σ_h = 4; (d) σ_H /σ_h = 6

Figure 6. Experimental and theoretical results of the critical water pressure and fracture initiation angle: (a) σ_H /σ_h = 4; (b) σ_H /σ_h = 6; (c) σ_H /σ_h = 4; (d) σ_H /σ_h = 6

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圖 7 T應力的影響.(a) 臨界水壓P_c; (b)臨界起裂角θ₀

Figure 7. Effect of T-stress: (a) critical water pressure P_c; (b) critical initiation angle θ₀

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圖 8 比奧系數的影響. (a) 臨界水壓P_c; (b) 臨界起裂角θ₀

Figure 8. Effect of Biot's coefficient: (a) critical water pressure P_c; (b) critical initiation angle θ₀

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圖 9 側壓系數k的影響. (a) 臨界水壓P_c; (b) 臨界起裂角θ₀

Figure 9. Effect of lateral pressure coefficient : (a) critical water pressure P_c; (b) critical initiation angle θ₀

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圖 10 泊松比υ的影響. (a) 臨界水壓P_c; (b) 臨界起裂角θ₀

Figure 10. Effect of Poisson's ratio: (a) critical water pressure P_c; (b) critical initiation angle θ₀

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圖 11 不同泊松比υ條件下裂紋尖端最大主應力

Figure 11. Maximum principal stresses of the crack tip under different Poisson's ratios

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圖 12 高注水壓力對起裂角θ₀的影響

Figure 12. Effect of high injected water pressure on the fracture initiation angle

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圖 13 不同因素對起裂角θ₀的影響. (a) 側壓系數; (b) 比奧系數; (c) 泊松比

Figure 13. Effect of different factors on the fracture initiation angle: (a) lateral pressure coefficient; (b) Biot's coefficient; (c) Poisson's ratio

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