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摘要: 頁巖氣儲層中存在大量的納微米孔隙，且孔隙裂縫結構復雜，氣體滲流阻力大，存在多尺度滲流的問題；頁巖氣儲層壓力擾動隨時間向外傳播并非瞬時到達無窮遠，其滲流規律就是一個壓力擾動邊緣動邊界的問題。基于對以上問題的研究，本文建立了滲透率分形分布和高斯分布的滲透率表征模型，對不同形態縫網壓裂特征就滲流規律進行了描述，并利用穩態依次替換法，考慮頁巖儲層中擴散、滑移及解吸作用，進一步研究了多級壓裂水平井不穩定滲流壓力擾動的傳播模型，得到不同壓裂條件下壓力擾動邊界隨時間變化的關系，并結合我國南方海相龍馬溪組頁巖氣藏儲層參數，應用MATLAB編程。研究表明：壓力傳播動邊界隨時間增加逐漸向外擴展，滲透率越小，壓力傳播越慢；未壓裂儲層壓力傳播速度<滲透率分形分布壓裂儲層傳播速度<滲透率高斯分布壓裂儲層傳播速度。對于滲透率極低的頁巖氣儲層，壓力傳播慢，氣井自然產能低，必須對頁巖氣儲層進行大規模的儲層壓裂改造，并控制壓裂程度，以提高頁巖氣開發效果；基于壓力傳播動邊界的擴展優化頁巖儲層壓裂井段間距90 m，優化滲透率分形分布壓裂井井間距318 m，滲透率高斯分布壓裂井井間距252 m。因此應合理控制頁巖儲層壓裂改造規模，實現優產高產。模型模擬結果與實際生產數據擬合較好，驗證了本研究理論模型的適用性。Abstract: Shale gas reservoirs are extremely tight, their pores are mainly nano-micron size, and their gas flow resistance is greater than that of conventional gases. Thus, the flow with low-velocity non-Darcy seepage characteristics of diffusion, slippage, and desorption needs to be solved. Moreover, the fractured reservoir has a complicated structure of pores and fractures, which causes the problem of multi-scale flow. The pressure disturbance propagates over time and does not instantaneously reach infinity. Another problem is that the moving boundary pressure disturbance of unstable seepage propagates slowly with time. Based on the above issues, in this paper, the permeability model of fractal distribution and Gaussian distribution was obtained to describe the different fracturing characteristics. Using the method of successive replacements of steady states and considering desorption, diffusion, and slippage, the mathematical model of unstable flowing pressure disturbance in a multistage fractured horizontal well was established. The moving characteristics of the different fractured conditions were compared and analyzed. The research shows that the pressure moving boundary increases with time, and the lower the permeability, the slower the pressure boundary moves. In general, the shale gas reservoir pressure propagates slowly, the natural productivity of the gas well is low, and the velocity of the pressure moving boundary of the matrix reservoir is less than the fractal distribution of the fractured reservoir and less than the Gaussian distribution of the fractured reservoir. Thus, it is necessary to carry out the large-scale fracturing treatment and reasonable control of the fracturing degree to improve the permeability as well as the development effect. When the production time is 6000 days, based on the moving boundary of the fractured horizontal well, the horizontal section length was optimized to 90 m. The optimum well distance of the well with fractal distribution permeability was 318 m, while the well with Gaussian distribution permeability was 252 m. Thus, the fracture treatment scale should be reasonably controlled to achieve optimal production and high yield.
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Key words:
- shale gas /
- moving boundary /
- slip and diffusion /
- fracture /
- pressure characteristics
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圖 2 不同分形因數α對壓裂縫網區滲透率分布的影響（rm=200 m）
Figure 2. Effect of different α on the permeability distribution（rm=200 m）
圖 3 不同尺度參數對壓裂縫網區滲透率分布的影響
Figure 3. Effect of different scales on the permeability distribution
圖 5 生產數據擬合曲線. （a）CH1井；（b）CH2井；（c）CH3井；（d）CH4井
Figure 5. Fitting curve of the production data: (a) CH1 well; (b) CH2 well; (c) CH3 well; (d) CH4 well
圖 6 不同滲透率條件下未壓裂井動邊界隨時間變化關系
Figure 6. Pressure disturbance propagation boundary change over time under different permeabilities
圖 8 不同滲透率條件下（滲透率分形）動邊界隨時間變化
Figure 8. Pressure disturbance propagation boundary change over time under fractional permeability
圖 10 不同滲透率條件下（滲透率高斯分布）動邊界隨時間變化
Figure 10. Pressure disturbance propagation boundary change over time under contaminated permeability
圖 7 動邊界對地層壓力分布的影響（未壓裂）
Figure 7. Effect of moving boundary on formation pressure（constant permeability）
圖 9 動邊界對地層壓力分布的影響（滲透率分形分布）
Figure 9. Effect of moving boundary on formation pressure（fractional permeability）
圖 11 動邊界對地層壓力分布的影響（滲透率高斯分布）
Figure 11. Effect of moving boundary on formation pressure（contaminated permeability）
圖 12 不同條件井動邊界隨時間變化對比圖
Figure 12. Pressure disturbance propagation boundary change over time under different conditions
圖 13 壓裂井橢圓滲流區域動邊界隨時間變化. （a）滲透率分形分布；（b）滲透率高斯分布
Figure 13. Pressure disturbance propagation boundary change over time: (a) fractional permeability; (b) contaminated permeability
圖 14 不同條件井動邊界對地層壓力分布的影響對比圖
Figure 14. Effect of moving boundary on formation pressure under different conditions
表 1 壓裂水平井壓裂生產參數
Table 1. Production parameters of the fractured well
井名 井類別 壓裂段數 平均壓裂段間距/m 實際生產時間/d 20年累計產氣量，EUR/（108 m3） CH1 I類 21 69.40 562 3.10 CH2 I類 19 71.68 670 1.76 CH3 II類 17 76.47 837 1.05 CH4 III類 22 72.50 681 0.76 
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表 2 頁巖氣儲層基礎模擬參數
Table 2. Simulation parameters of shale gas reservoir
基本參數 數值 基本參數 數值 儲層厚度，h/m 30 孔隙度，φ 0.05 井底流壓，pw/MPa 6 絕對滲透率，K0/（10?15 m2） 0.0005 邊界壓力，pe/MPa 24 標準狀態下氣體密度，ρgsc/（kg·m?3） 0.7 擴散系數，DK/（cm2·s?1） 8.4067×10?7 標準狀態下氣體壓縮因子，Zsc 1 井筒半徑，rw/m 0.1 標準狀態下溫度，Tsc/K 293 泄壓半徑，re/m 400 標準狀態下氣井產量，qsc/（m3·d?1） 200 壓縮因子，Z 0.89 標準狀態下壓力，psc/MPa 0.1 地層溫度，T/K 366.15 分形因數，α ?1.0 黏度，μ/（mPa·s） 0.027 尺度參數，σ 20
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