多孔介質細觀流動理論研究進展

朱維耀; 李華; 鄧慶軍; 馬啟鵬; 劉雅靜

doi:10.13374/j.issn2095-9389.2020.11.30.005

多孔介質細觀流動理論研究進展

doi: 10.13374/j.issn2095-9389.2020.11.30.005

1.
北京科技大學土木與資源工程學院，北京 100083
2.
大慶油田第一采油廠，大慶163000

基金項目: 國家自然科學基金資助項目（51974013）

詳細信息

通訊作者:
E-mail: weiyaook@sina.com

中圖分類號: TE31
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- 被引次數: 0
出版歷程
- 收稿日期: 2020-11-30
- 網絡出版日期: 2021-01-20
- 刊出日期: 2022-05-25

Review on mesoscopic flow theory in porous media

1.
School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
2.
First Oil Production Plant, Daqing Oilfield, Daqing 163000, China

More Information

Corresponding author: E-mail: weiyaook@sina.com

摘要

摘要: 首先，從理論分析、實驗研究和數值模型三個方面概述了當前多孔介質細觀流動的研究現狀，重點圍繞納微孔隙中流體流動界面作用與細觀力學特性關系及表征、細觀?宏觀網絡仿真模擬、細觀尺度流體（油/水、氣/水）流動細觀動力學機制及數學模型等關鍵問題展開論述。在此基礎上介紹了當前細觀流動界面作用與細觀力學特性研究情況，明確了細觀尺度流體非線性流動機理，構建了反映微觀力作用下細觀尺度流動的數學模型，形成了網絡仿真模擬方法。將為非常規油氣開發過程中揭示影響流動細觀成因，進一步闡明不同條件下的動用機理，確定高效開發方法提供指導，同時促進滲流力學學科的發展，具有重要的理論和現實意義。
- 多孔介質 /
- 細觀流動 /
- 界面效應 /
- 微觀力 /
- 孔隙網絡模型
Abstract: Porous media are widely found in underground rocks, biomimetic, and engineering materials. However, the current flow theory of fluids (liquid and gas, etc.) is incomplete to study flows in small and complex pores, thus a new theory is urgently needed for studying a large number of fluid flows in porous media. The theory of meso-scale flow in porous media is a “mysterious key” to unlock the flow of nano-micron porous media. At present, a large number of fluid flow problems need an immediate solution in porous media such as shale oil and gas development, soil seepage, human capillary network, and carbon nanotube (CNT). With the advancement of world petroleum engineering technology, unconventional oil and gas reservoirs have become the main areas of development in the petroleum industry. There are a large number of nano-scale pores in unconventional oil and gas reservoirs, and the existing macro-statistical methods of Darcy and non-Darcy percolation cannot reveal the nonlinear flow mechanism and effective production mechanism of fluid in mesopores. Thus, it is urgent to carry out theoretical research on meso-flow in porous media to provide a theoretical basis for unconventional oil and gas development. This paper summarizes the research results in this area, including those of the authors. The current research status of fine and meso flow in porous media is summarized from three aspects: (1) theoretical analysis, (2) experimental research, and (3) numerical model, focusing on key issues such as the relationship and characterization of meso-scale fluid flow interface and micro-mechanical properties, meso–macro network simulation, meso-scale fluid (oil/water, gas/water) flow, meso-dynamic mechanism, and mathematical models. On this basis, the importance of the research on the interface effect and meso-mechanical characteristics of fine and micro-scale fluid flow, the nonlinear flow mechanism of the fine and meso-scale fluids, the construction of a mathematical model reflecting the meso-scale flow under the action of micro-forces, and the formation of a network simulation method are introduced. The study provides certain guiding significance for unconventional oil and gas development processes, revealing the meso-causes affecting flow, clarifying the production mechanism under different conditions, and promoting further development of the discipline of seepage mechanics.
- porous media /
- mesoscopic flow /
- interface effect /
- micro force /
- pore network model

HTML全文

圖 1 不同“努森數”下的氣體流動方程^[29]

Figure 1. Gas flow equations at different “Knudsen numbers”^[29]

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圖 2 不同“微測量儀器”的尺度范圍

Figure 2. Scale range of different “micro-measuring apparatus”

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圖 3 孔隙網絡模型及應用軟件分類^{[27, 46]}

Figure 3. Pore network model and application software classification^{[27, 46]}

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圖 4 “三大區，五小區”多尺度模型^[8]

Figure 4. Multi-scale model of the “three large zones, five small zones”^[8]

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圖 5 水驅和聚驅后剩余油飽和度(S_o)二維分布情況。（a）水驅后；（b）聚驅后^[74]

Figure 5. Two-dimensional distribution of remaining oil saturation: (a) after water flooding; (b) after polymer flooding^[74]

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表 1 不同尺度油氣滲流數學模型

Table 1. Mathematical models of oil and gas seepage in different scales

Scale	Reservoir type	Mathematical model of seepage		Expression	Literature Source
Meso-Scale (l=10 nm–1 mm)	Ultra-low permeability reservoirs, Shale reservoirs, Tight reservoirs	Ultra-low permeabiliy shallow sandstone	$ v = - \dfrac{k}{\mu }\left[ {\dfrac{{{\text{d}}p}}{{{\text{d}}x}} - \lambda } \right] $			[54]
		Tight oil reservoir	$ v = \left( {2am{k^r} + b} \right)\dfrac{{{\text{d}}p}}{{{\text{d}}x}}\left( {1 - \dfrac{{{\lambda _{\text{c}}}}}{{\dfrac{{{\text{d}}p}}{{{\text{d}}x}} + {\lambda _{\text{c}}} - \lambda }}} \right) $			[55]
		Shale gas reservoir	$ v = - \dfrac{{{k_{\text{o}}}}}{\mu }\left( {1 + \dfrac{{3{\text{π }}a}}{{16{k_{\text{o}}}}}\dfrac{{\mu {D_{\text{k}}}}}{p}} \right)\left( {\dfrac{{{\text{d}}p}}{{{\text{d}}x}}} \right) $			[56]
	Low permeability reservoir	Power function fitting nonlinear segment (Piecewise function)	$\left\{ \begin{gathered} v = \dfrac{k}{\mu }\nabla p{\text{ }}\|\nabla p\| \leqslant b \hfill \\ v = \dfrac{k}{\mu }\nabla p\left( {1 - \dfrac{\lambda }{{\|\nabla p\|}}} \right){ ^n} a < \|\nabla p\| < b \hfill \\ v = 0 \|\nabla p\| \leqslant a \hfill \\ \end{gathered} \right.$			[57]
		Piecewise function	$ \left\{\begin{array}{l}\text{Ultra-low speed zone}：\dfrac{\Delta p}{L}=0\\ \text{Low speed transition zone}：v=c{\left(\dfrac{\Delta p}{L}\right)}^{\frac{1}{2-n}}\\ \text{Darcy flow zone}：v=-\dfrac{k}{\mu }\Delta p\end{array} \right.$			[58]
		Two-parameter model (Continuous model)	$ v = \dfrac{k}{\mu }\left( {1 - \dfrac{1}{{a + b\|\nabla p\|}}} \right)\nabla p $			[59]
		Three-parameter model (Continuous model)	$ v\left( {{a_{\text{1}}} + \dfrac{{{a_{\text{2}}}}}{{1 + bv}}} \right) = - \nabla p $			[60]
		Three-parameter model (Continuous model)	$ v = {\left( {\dfrac{k}{\mu }} \right)_{\text{o}}}\dfrac{{{\text{d}}p}}{{{\text{d}}x}}\left( {1 - \dfrac{{{\lambda _{\text{c}}}}}{{\dfrac{{{\text{d}}p}}{{{\text{d}}x}} + {\lambda _{\text{c}}} - \lambda }}} \right) $			[61]
	Medium permeability reservoir	Darcy’s Law	$ v = - \dfrac{k}{\mu }\Delta p $			[25]
Macro-Scale (l>1 mm)	High permeability reservoir	Darcy’s Law	$v = - \dfrac{k}{\mu }\Delta p$			[25]
Macro-Scale (l>1 mm)	Fractured reservoir	Darcy’s Law	$v = - \dfrac{k}{\mu }\Delta p$			[25]
Note: v—fluid velocity, m·s^?1; k—permeability, 10^?3 μm; k_o—oil permeability, 10^?3 μm; μ—formation crude oil viscosity, mPa·s; p—formation pressure, MPa; λ—starting pressure gradient, MPa·m^?1; λ_c—proposed start pressure gradient, MPa·m^?1; a, b, c—constant coefficient, dimensionless; m=0.0186; r=?0.579; D_k—diffusion coefficient, cm²·s^?1; a₁, a₂, n—constant coefficient, dimensionless; L—model length, cm.

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