微纳米孔隙页岩气藏分形表观渗透率计算模型
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摘要
微纳米孔隙页岩气藏运移机制多样,孔隙结构复杂,分形理论能比较精确地描述复杂系统。基于单根直圆管质量流量公式,推导出考虑迂曲分形维数的单根分形迂曲毛细管质量流量表达式,进一步推导出单位分形集内考虑管径分形维数与迂曲分形维数的总质量流量表达式,从而获得微纳米孔隙页岩气藏分形表观渗透率计算公式。通过实验数据,完成模型验证,对比分析文中模型与传统模型的差异,进行分形参数敏感性分析。结果表明:文中分形表观渗透率计算模型计算结果略高于Javadpour模型,略低于Xiong X模型,但与实验结果最为接近;页岩气藏分形表观渗透率随有效压力增大而逐渐减小,在压力较低时,下降较快,压力较高时,趋于平稳;分形表观渗透率受管径分形维数与迂曲分形维数的影响,随管径分形维数的增大呈非线性增大,随迂曲分形维数增大呈非线性减小。
The micro/nano porous shale gas reservoirs have the characteristics of multiple migration mechanism and complex pore structure. However, fractal theory provides a method to describe the complex system. Therefore, fractal approach is introduced.According to single straight capillary mass flow formula, a fractal capillary mass flow formula that considers tortuosity fractal dimension was derived. And then, expression of total mass flow per unit area that considers tortuosity fractal dimension and diameter fractal dimension was obtained. Furthermore, a formula for calculating the apparent permeability of micro nano/pore gas reservoir was obtained. The model was verified by experimental data. The differences between the model and the traditional model were compared and analyzed. Finally, the sensitivity of fractal parameters was analyzed. The results show that fractal apparent permeability of this model is slightly higher than the Javadpour model and is slightly lower than the Xiong X model; however, it is the closest to the experimental results. Besides, the apparent permeability of shale gas reservoir decreases with the increase of effective stress. At lower pressures, the apparent permeability decreases rapidly with increasing pressure. When the pressure is high,the apparent permeability tends to be stable. Fractal apparent permeability is affected by tortuosity fractal dimension and diameter fractal dimension. The fractal apparent permeability increases nonlinearly with the increase of diameter fractal dimension, and decreases nonlinearly with the increase of tortuosity fractal dimension.
The micro/nano porous shale gas reservoirs have the characteristics of multiple migration mechanism and complex pore structure. However, fractal theory provides a method to describe the complex system. Therefore, fractal approach is introduced.According to single straight capillary mass flow formula, a fractal capillary mass flow formula that considers tortuosity fractal dimension was derived. And then, expression of total mass flow per unit area that considers tortuosity fractal dimension and diameter fractal dimension was obtained. Furthermore, a formula for calculating the apparent permeability of micro nano/pore gas reservoir was obtained. The model was verified by experimental data. The differences between the model and the traditional model were compared and analyzed. Finally, the sensitivity of fractal parameters was analyzed. The results show that fractal apparent permeability of this model is slightly higher than the Javadpour model and is slightly lower than the Xiong X model; however, it is the closest to the experimental results. Besides, the apparent permeability of shale gas reservoir decreases with the increase of effective stress. At lower pressures, the apparent permeability decreases rapidly with increasing pressure. When the pressure is high,the apparent permeability tends to be stable. Fractal apparent permeability is affected by tortuosity fractal dimension and diameter fractal dimension. The fractal apparent permeability increases nonlinearly with the increase of diameter fractal dimension, and decreases nonlinearly with the increase of tortuosity fractal dimension.
引文
[1]李亚洲,李勇明,罗攀,等.页岩气渗流机理与产能研究[J].断块油气田,2013,20(2):186-190.
[2]胡璐宇,朱炎铭,周晓刚.宁武盆地构造演化及页岩气成藏[J].断块油气田,2016,23(3):290-293.
[3]王敬,罗海山,刘慧卿,等.页岩气吸附解吸效应对基质物性影响特征[J].石油勘探与开发,2016,43(1):145-152.
[4]封钦亚,许艺博,张欣,等.页岩气藏三重介质模型压力动态分析及其应用[J].断块油气田,2015,22(5):600-605.
[5]樊冬艳,姚军,孙海,等.考虑多重运移机制耦合页岩气藏压裂水平井数值模拟[J].力学学报,2015,47(6):906-915.
[6]姚军,孙海,樊冬艳,等.页岩气藏运移机制及数值模拟[J].中国石油大学学报(自然科学版),2013,37(1):91-98.
[7]刘化普.微纳米孔隙页岩气藏表观渗透率计算模型研究进展[J].中外能源,2017,22(2):33-40.
[8]JAVADPOUR F.Nanopores and apparent permeability of gas flow in Mudrocks(Shales and Siltstone)[J].Journal of Canadian Petroleum Technology,2009,48(8):16-21.
[9]CIVAN F.Effective correlation of apparent gas permeability in tight porous media[J].Transport in Porous Media,2010,82(2):375-384.
[10]CLIFFORD K H,WEBB S W.Gas transport in porous media[J].Encyclopedia of Ecology,2006,14(8/9):3576-3582.
[11]XIONG X,DEVEGOWDA D,VILLAZON G G M,et al.A fullycoupled free and adsorptive phase transport model for shale gas reservoirs including non-darcy flow effects[R].SPE 159758,2012.
[12]YANG F,NING Z,LIU H.Fractal characteristics of shales from a shale gas reservoir in the Sichuan Basin,China[J].Fuel,2014,115(1):378-384.
[13]TURCIO M,REYES J M,CAMACHO R,et al.Calculation of effective permeability for the BMP model in fractal porous media[J].Journal of Petroleum Science&Engineering,2013,103(3):51-60.
[14]CHANG J,YORTSOS Y C.Pressure-transient analysis of fractal reservoirs[J].SPE Reservoir Evaluation&Engineering,1990,5(1):31-38.
[15]LIU X,XIONG J,LIANG L.Investigation of pore structure and fractal characteristics of organic-rich Yanchang formation shale in central China by nitrogen adsorption/desorption analysis[J].Journal of Natural Gas Science&Engineering,2015,22(7):62-72.
[16]MANDELBROT B B,AIZENMAN M.Fractals:form,chance,and dimension[J].Encyclopedia of Physical Science&Technology,1979,1(5):185-207.
[17]刘化普,刘慧卿,王敬.缝洞型三重介质油藏分形渗流规律[J].新疆石油地质,2017,38(2):204-208.
[18]陶军.页岩气分形渗流模型研究[D].成都:西南石油大学,2014.
[19]FLORENCE F A,RUSHING J,NEWSHAM K E,et al.Improved permeability prediction relations for low permeability sands[J].Rocky Mountain Oil&Gas Technology Symposium,2007.
[20]YU B,CHENG P.A fractal permeability model for bi-dispersed porous media[J].International Journal of Heat&Mass Transfer,2002,45(14):2983-2993.
[21]YU B.Analysis of flow in fractal porous media[J].Applied Mechanics Reviews,2008,61(5):1239-1249.
[22]陈志明,汪伟英,蔡雨桐,等.致密砂岩和页岩渗透率实验研究[J].断块油气田,2013,20(1):80-84.
[2]胡璐宇,朱炎铭,周晓刚.宁武盆地构造演化及页岩气成藏[J].断块油气田,2016,23(3):290-293.
[3]王敬,罗海山,刘慧卿,等.页岩气吸附解吸效应对基质物性影响特征[J].石油勘探与开发,2016,43(1):145-152.
[4]封钦亚,许艺博,张欣,等.页岩气藏三重介质模型压力动态分析及其应用[J].断块油气田,2015,22(5):600-605.
[5]樊冬艳,姚军,孙海,等.考虑多重运移机制耦合页岩气藏压裂水平井数值模拟[J].力学学报,2015,47(6):906-915.
[6]姚军,孙海,樊冬艳,等.页岩气藏运移机制及数值模拟[J].中国石油大学学报(自然科学版),2013,37(1):91-98.
[7]刘化普.微纳米孔隙页岩气藏表观渗透率计算模型研究进展[J].中外能源,2017,22(2):33-40.
[8]JAVADPOUR F.Nanopores and apparent permeability of gas flow in Mudrocks(Shales and Siltstone)[J].Journal of Canadian Petroleum Technology,2009,48(8):16-21.
[9]CIVAN F.Effective correlation of apparent gas permeability in tight porous media[J].Transport in Porous Media,2010,82(2):375-384.
[10]CLIFFORD K H,WEBB S W.Gas transport in porous media[J].Encyclopedia of Ecology,2006,14(8/9):3576-3582.
[11]XIONG X,DEVEGOWDA D,VILLAZON G G M,et al.A fullycoupled free and adsorptive phase transport model for shale gas reservoirs including non-darcy flow effects[R].SPE 159758,2012.
[12]YANG F,NING Z,LIU H.Fractal characteristics of shales from a shale gas reservoir in the Sichuan Basin,China[J].Fuel,2014,115(1):378-384.
[13]TURCIO M,REYES J M,CAMACHO R,et al.Calculation of effective permeability for the BMP model in fractal porous media[J].Journal of Petroleum Science&Engineering,2013,103(3):51-60.
[14]CHANG J,YORTSOS Y C.Pressure-transient analysis of fractal reservoirs[J].SPE Reservoir Evaluation&Engineering,1990,5(1):31-38.
[15]LIU X,XIONG J,LIANG L.Investigation of pore structure and fractal characteristics of organic-rich Yanchang formation shale in central China by nitrogen adsorption/desorption analysis[J].Journal of Natural Gas Science&Engineering,2015,22(7):62-72.
[16]MANDELBROT B B,AIZENMAN M.Fractals:form,chance,and dimension[J].Encyclopedia of Physical Science&Technology,1979,1(5):185-207.
[17]刘化普,刘慧卿,王敬.缝洞型三重介质油藏分形渗流规律[J].新疆石油地质,2017,38(2):204-208.
[18]陶军.页岩气分形渗流模型研究[D].成都:西南石油大学,2014.
[19]FLORENCE F A,RUSHING J,NEWSHAM K E,et al.Improved permeability prediction relations for low permeability sands[J].Rocky Mountain Oil&Gas Technology Symposium,2007.
[20]YU B,CHENG P.A fractal permeability model for bi-dispersed porous media[J].International Journal of Heat&Mass Transfer,2002,45(14):2983-2993.
[21]YU B.Analysis of flow in fractal porous media[J].Applied Mechanics Reviews,2008,61(5):1239-1249.
[22]陈志明,汪伟英,蔡雨桐,等.致密砂岩和页岩渗透率实验研究[J].断块油气田,2013,20(1):80-84.