基于分形理论的页岩基质表观渗透率研究
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摘要
为了表征页岩基质表观渗透率,研究其动态变化规律,基于迂曲毛细管束分形理论及气体微观渗流机理,分别建立考虑吸附、滑脱、扩散及渗流的无机质和有机质表观渗透率模型,并通过面积系数加权得到页岩基质表观渗透率模型。结合实验数据及已有模型验证了新建模型的可靠性,定量分析了页岩基质微观孔隙结构(孔径、孔隙度、分形维数),外界环境(压力、含水饱和度、有效直径修正因子)及气体性质对页岩基质表观渗透率的影响。研究结果表明:随着储层压力的降低,无机质孔隙水膜厚度增大,有效直径减小,迂曲度分形维数增大,孔隙分形维数减小,气体滑脱效应增强,但仍以吸附影响为主,无机质表观渗透率总体呈下降趋势;有机质孔隙吸附气解吸使有效直径修正因子逐渐增大,迂曲度分形维数减小,孔隙分形维数增大,滑脱效应及努森扩散在低压小孔中增强,有机质表观渗透率总体呈上升趋势;有机质与无机质表观物性参数随压力、吸附层变化规律不同,渗透率差值较大,因此在页岩基质表观渗透率研究时应予以区分计算,避免其差异性所带来的误差。
In order to characterize the apparent permeability of shale matrix and research its dynamic variation,apparent permeability model of organic and inorganic matter has been derived theoretically by considering absorption,slip,diffusion and seepage based on the fractal theory of tortuous capillary bundles and microscopic gas percolation mechanism. Thereby a fractal apparent permeability model of shale matrix is built by weighting the area factor. Reliability of this model was verified through experimental results and existing permeability calculation models,and then the effect of pore structure(pore size,porosity,fractal dimension),external environment(pressure,water saturation,effective diameter correction factors)and gas property on the apparent permeability of the shale matrix was quantitatively analyzed. The research results show that for the inorganic pore,with the decrease of formation pressure,the apparent permeability presents overall downward trend,which is influenced by the increase of water film thickness and the decrease of effective pore size,along with the increase of fractal dimension of tortuosity and the decrease of pore fractal dimension,and the gas slippage effect increases but the adsorption is still the main influential factor;for the organic pore,the permeability presents overall upward trend when the correction factor of effective diameter increases gradually with the desorption of shale gas,and the fractal dimension of tortuosity decreases while that of pore increases,and thus the slippage effect and Knudsen diffusion are enhanced in the small pore with low pressure;the variation of the apparent physical properties with the pressure and the adsorbed layer isdifferent for the organic and inorganic matter,and the difference of permeability between the organic and inorganic matter is large. Therefore,the apparent permeability of the organic and inorganic matter in shale matrix should be calculated respectively to avoid errors brought by this difference.
In order to characterize the apparent permeability of shale matrix and research its dynamic variation,apparent permeability model of organic and inorganic matter has been derived theoretically by considering absorption,slip,diffusion and seepage based on the fractal theory of tortuous capillary bundles and microscopic gas percolation mechanism. Thereby a fractal apparent permeability model of shale matrix is built by weighting the area factor. Reliability of this model was verified through experimental results and existing permeability calculation models,and then the effect of pore structure(pore size,porosity,fractal dimension),external environment(pressure,water saturation,effective diameter correction factors)and gas property on the apparent permeability of the shale matrix was quantitatively analyzed. The research results show that for the inorganic pore,with the decrease of formation pressure,the apparent permeability presents overall downward trend,which is influenced by the increase of water film thickness and the decrease of effective pore size,along with the increase of fractal dimension of tortuosity and the decrease of pore fractal dimension,and the gas slippage effect increases but the adsorption is still the main influential factor;for the organic pore,the permeability presents overall upward trend when the correction factor of effective diameter increases gradually with the desorption of shale gas,and the fractal dimension of tortuosity decreases while that of pore increases,and thus the slippage effect and Knudsen diffusion are enhanced in the small pore with low pressure;the variation of the apparent physical properties with the pressure and the adsorbed layer isdifferent for the organic and inorganic matter,and the difference of permeability between the organic and inorganic matter is large. Therefore,the apparent permeability of the organic and inorganic matter in shale matrix should be calculated respectively to avoid errors brought by this difference.
引文
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[27]Cussler E L.Diffusion-mass transfer in fluid systems[M].Cambridge:Cambridge University Press,2000.
[28]高树生,于兴河,刘华勋.滑脱效应对页岩气井产能影响的分析[J].天然气工业,2011,31(4):55-58.Gao Shusheng,Yu Xinghe,Liu Huaxun.Impact of slippage effect on shale gas well productivity[J].Natural Gas Industry,2011,31(4):55-58.
[29]齐银,张宁生,任晓娟,等.裂缝性储层岩石自吸水性实验研究[J].西安石油大学学报:自然科学版,2005,20(1):34-36.Qi Yin,Zhang Ningsheng,Ren Xiaojuan,et al.Experimental study on the hydroscopicity of fracture reservoir[J].Journal of Xi’an Shiyou University:Natural Science Edition,2005,20(1):34-36.
[2]张东晓,杨婷云,吴天昊,等.页岩气开发机理和关键问题[J].科学通报,2016,61(1):62-71.Zhang Dongxiao,Yang Tingyun,Wu Tianhao,et al.Recovery mechanisms and key issues in shale gas development[J].Chinese Science Bulletin,2016,61(1):62-71.
[3]张爽,隋微波.页岩储层有机质分布定量分析及重构模型[J].油气地质与采收率,2016,23(2):22-28.Zhang Shuang,Sui Weibo.Reconstruction and quantitative analysis methods for organic matter distribution in shale reservoirs[J].Petroleum Geology and Recovery Efficiency,2016,23(2):22-28.
[4]赵建华,金振奎,耿一凯,等.四川盆地龙马溪组富有机质页岩形成主控因素[J].大庆石油地质与开发,2016,35(2):140-147.Zhao Jianhua,Jin Zhenkui,Geng Yikai,et al.Main diagenesis controlling factors for Longmaxi Formation organic matter rich shale in Sichuan Basin[J].Petroleum Geology&Oilfield Development in Daqing,2016,35(2):140-147.
[5]胡明毅,邱小松,胡忠贵,等.页岩气储层研究现状及存在问题探讨[J].特种油气藏,2015,22(2):1-7.Hu Mingyi,Qiu Xiaosong,Hu Zhonggui,et al.Current researches on shale gas reservoirs and existing problems[J].Special Oil&Gas Reservoirs,2015,22(2):1-7.
[6]Beskok A,Karniadakis G E.A model for flows in channels,pipes and ducts at micro and nano scales[J].Microscale Thermophysical Engineering,1999,3(1):43-77.
[7]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.
[8]Civan F.Effective correlation of apparent gas permeability in tight porous media[J].Transport in Porous Media,2010,82(2):375-384.
[9]Shi J T,Zhang L,Li Y S,et al.Diffusion and flow mechanisms of shale gas through matrix pores and gas production forecasting[R].SPE 167226,2013.
[10]Wu K L,Li X F,Guo C C,et al.Adsorbed gas surface diffusion and bulk gas transport in nanopores of shale reservoirs with real gas effect-adsorption-mechanical coupling[C].Houston:SPE Reservoir Simulation Symposium,2015.
[11]曹成,李天太,刘刚,等.考虑吸附、滑脱和自由分子流动效应的页岩基质渗透率计算模型[J].西安石油大学学报:自然科学版,2015,30(5):48-53.Cao Cheng,Li Tiantai,Liu Gang,et al.Permeability calculation model of shale matrix with adsorption,slippage and free molecule flow effects[J].Journal of Xi’an Shiyou University:Natural Science Edition,2015,30(5):48-53.
[12]Kang S M,Fathi E.Carbon dioxide storage capacity of organicrich shales[J].SPEJ,2013,16(4):842-855.
[13]李菊花,郑斌.微观孔隙分形表征新方法及其在页岩储层中的应用[J].天然气工业,2015,35(5):52-59.Li Juhua,Zheng Bin.A new method for fractal characterization of microscopic pores and its application in shale reservoirs[J].Natural Gas Industry,2015,35(5):52-59.
[14]曹涛涛,宋之光,刘光祥,等.氮气吸附法—压汞法分析页岩孔隙、分形特征及其影响因素[J].油气地质与采收率,2016,23(2):1-8.Cao Taotao,Song Zhiguang,Liu Guangxiang,et al.Characteristics of shale pores,fractal dimension and their controlling factors determined by nitrogen adsorption and mercury injection methods[J].Petroleum Geology and Recovery Efficiency,2016,23(2):1-8.
[15]张雪芬,陆现彩,张林晔,等.页岩气的赋存形式研究及其石油地质意义[J].地球科学进展,2010,25(6):597-604.Zhang Xuefen,Lu Xiancai,Zhang Linye,et al.Occurrences of shale gas and their petroleum geological significance[J].Advances in Earth Science,2010,25(6):597-604.
[16]Yu B M,Li J H,Li Z H,et al.Permeabilities of unsaturated fractal porous media[J].International Journal of Multiphase Flow,2003,29(6):1 625-1 642.
[17]黄延章.低渗透油层渗流机理[M].北京:石油工业出版社,1998:59-99.Huang Yanzhang.Flow mechanics in low-permeability reservoir[M].Beijing:Petroleum Industry Press,1998:59-99.
[18]Yu B M,Cheng P.A fractal model for permeability of bi-dispersed porous media[J].International Journal of Heat&Mass Transfer,2002,45(14):2 983-2 993.
[19]Costa A.Permeability-porosity relationship:A reexamination of the Kozeny-Carman equation based on a fractal pore space geometry assumption[J].Geophysical Research Letters,2006,33(2):L02318.
[20]郑仟.分形多孔介质中气体流动与扩散的输运特性研究[D].武汉:华中科技大学,2012.Zheng Qian.Study of some transport properties for gas flow and diffusion through fractal porous media[D].Wuhan:Huazhong University of Science and Technology,2012.
[21]Passey Q R,Bohacs K,Esch W L.From oil-prone source rock to gas-producing shale reservoir-geologic and petrophysical characterization of unconventional shale gas reservoirs[R].SPE 131350,2010.
[22]Bird R B,Stewart W E,Lightfoot E N.Transport phenomena[M].Rev.2nd ed.New York:John Wiley&Sons Inc,2002.
[23]Ziarani A S,Aguilera R.Knudsen’s permeability correction for tight porous media[J].Transport in Porous Media,2012,91(1):239-260.
[24]Klinkenberg L J.The permeability of porous media to liquids and gases[J].Drilling and Production Practice,1941,2(2):200-213.
[25]何更生.油层物理学[M].北京:石油工业出版社,1994:43,297.He Gengsheng.Petrophysics[M].Beijing:Petroleum Industry Press,1994:43,297.
[26]王瑞,张宁生,刘晓娟,等.页岩气扩散系数和视渗透率的计算与分析[J].西北大学学报:自然科学版,2013,43(1):75-80.Wang Rui,Zhang Ningsheng,Liu Xiaojuan,et al.The calculation and analysis of diffusion coefficient and apparent permeability of shale gas[J].Journal of Northwest University:Natural Science Edition,2013,43(1):75-80.
[27]Cussler E L.Diffusion-mass transfer in fluid systems[M].Cambridge:Cambridge University Press,2000.
[28]高树生,于兴河,刘华勋.滑脱效应对页岩气井产能影响的分析[J].天然气工业,2011,31(4):55-58.Gao Shusheng,Yu Xinghe,Liu Huaxun.Impact of slippage effect on shale gas well productivity[J].Natural Gas Industry,2011,31(4):55-58.
[29]齐银,张宁生,任晓娟,等.裂缝性储层岩石自吸水性实验研究[J].西安石油大学学报:自然科学版,2005,20(1):34-36.Qi Yin,Zhang Ningsheng,Ren Xiaojuan,et al.Experimental study on the hydroscopicity of fracture reservoir[J].Journal of Xi’an Shiyou University:Natural Science Edition,2005,20(1):34-36.