基于分形理论的导电模型及应用
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摘要
理论与实验研究证明,岩石的组成成分以及孔隙的几何形状对其电导率的影响很大,然而实际岩石的微观结构和传导机制十分复杂,影响其电性特征的因素复杂多样,很难对其准确表征。储层岩石孔隙具有分形特征,其分形维数与孔隙度有着较好的一致性,一定程度上能够反映岩石的内部孔隙结构特征,这是定量描述复杂孔隙结构特征的基础。本文基于分形理论,建立了适用于多孔介质的导电模型,并以岩心数据和测井数据为基础,开展了实际应用。实际资料处理结果表明,基于分形导电模型计算得到的饱和度与岩心分析数据一致性很高,说明了该方法的可行性与有效性。
A lot of research works both on theory and experiments have proved that the rock conductivity mainly depends on rock mineral composition and the pore geometry.However,the microstructure and conduction mechanism of real rock are fairly complicated.Factors affecting the changes of electrical characteristics are complex and diverse.As a consequence,it is difficult to characterize them accurately.There is a fractal property in pore space of reservoir rocks,and the variation trend of fractal dimension and porosity are in good agreement.To a certain extent,the fractal dimension can reflect the internal pore structure characteristics,providing an effective mean for quantitatively describing this complex feature.Based on the fractal theory,a conductive model is established for porous media.Practical applications are carried out with core and well logging data.The real data processing shows that the saturation results calculated by the fractal electrical conductivity model are in good agreement with the core analysis data,indicating the feasibility and effectiveness of the proposed method.
A lot of research works both on theory and experiments have proved that the rock conductivity mainly depends on rock mineral composition and the pore geometry.However,the microstructure and conduction mechanism of real rock are fairly complicated.Factors affecting the changes of electrical characteristics are complex and diverse.As a consequence,it is difficult to characterize them accurately.There is a fractal property in pore space of reservoir rocks,and the variation trend of fractal dimension and porosity are in good agreement.To a certain extent,the fractal dimension can reflect the internal pore structure characteristics,providing an effective mean for quantitatively describing this complex feature.Based on the fractal theory,a conductive model is established for porous media.Practical applications are carried out with core and well logging data.The real data processing shows that the saturation results calculated by the fractal electrical conductivity model are in good agreement with the core analysis data,indicating the feasibility and effectiveness of the proposed method.
引文
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[21] Pitchumani R,Ramakrishnan B.A fractal geometry model for evaluating permeabilities of porous performs used in liquid composite molding[J].International Journal of Heat and Mass Transfer,1999,42(12):2219-2232.
[22] Rieu M,Sposito G.Fractal fragmentation,soil porosity,and soil water properties Ⅰ:Theory[J].Soil Science Society of America Journal,1991,55(5):1231-1238.
[23] Yu B,Cheng P.A fractal permeability model for bi-dispersed porous media[J].International Journal of Heat and Mass Transfer,2002,45(14):2983-2993.
[24] Wyllie M R J,Gardner G H F.Permeability and the size distribution of pores[J].Nature,1958,181(4607):477.
[25] Cornell D,Katz D L.Flow of gases through consolidated porous media[J].Industrial & Engineering Chemistry,1953,45(10):2145-2152.
[26] Abdassah D,Permadi P,Sumantri Y,et al.Saturation exponent at various wetting condition:fractal modeling of thin-sections[J].Journal of Petroleum Science and Engineering,1998,20(3-4):147-154.
[27] Waxman M H,Smits L J M.Electrical conductivities in oil-bearing shaly sands[J].Society of Petroleum Engineers Journal,1968,8(2):107-122.
[28] Clavier C,Coates G,Dumanoir J.Theoretical and ex-perimental bases for the dual-water model for inter-pretation of shaly sands[J].Society of Petroleum Engineers Journal,1984,24(2):153-168.
[29] Budebes S,Hamdy T,Al-Farisi O,et al.Carbonate archie exponants correction model and variable determination[C].SPE Reservoir Characterization and Simulation Conference and Exhibition,Society of Petro-leum Engineers,2011.
[2] Archie G E.The electrical resistivity log as an aid in determining some reservoir characteristics[J].Tran-sactions of the AIME,1942,146(1):54-62.
[3] Wyllie M R J,Rose W D.Some theoretical considerations related to the quantitative evaluation of the physical characteristics of reservoir rock from electrical log data[J].Journal of Petroleum Technology,1950,2(4):105-118.
[4] Winsauer W O.Resistivity of brine-saturated sands in relation to pore geometry[J].AAPG Bulletin,1952,36(2):230-252.
[5] Perkins Jr F M,Osoba J S,Ribe K H.Resistivity of sandstones as related to the geometry of their interstitial water[J].Geophysics,1956,21(4):1071-1084.
[6] Mandelbrot B B.The fractal geometry of nature[M].W H Freeman,New York,1982.
[7] Hutchinson J E.Fractals and self similarity[J].Indiana University Mathematics Journal,1981,30(5):713-747.
[8] 毛宁波,戴塔根,常德双,等.沉积旋回的地震时频特征、地震分形特征和地震灰色特征研究[J].石油地球物理勘探,2003,38(增刊1):134-137.MAO Ningbo,DAI Tagen,CHANG Deshuang,et al.Seismic time-frequency characteristics of sedimentary cycles,seismic fractal features and seismic grey features[J].Oil Geophysical Prospecting,2003,38(S1):134-137.
[9] 吴国铭,李熙喆,高树生,等.基于分形理论探究碳酸盐岩CT图像二值化最佳阈值[J].石油地球物理勘探,2017,52(5):1025-1032.WU Guoming,LI Xizhe,GAO Shusheng,et al.Optimal thresholding in carbonate reservoir CT image binarization based on fractal theory[J].Oil Geophysical Prospecting,2017,52(5):1025-1032.
[10] Li K.More general capillary pressure and relative permeability models from fractal geometry[J].Journal of Contaminant Hydrology,2010,111(1-4):13-24.
[11] Cámara J,Gómez-Miguel V,Martín M á.Identification of bedrock lithology using fractal dimensions of drainage networks extracted from medium resolution LiDAR digital terrain models[J].Pure & Applied Geophysics,2015,173(3):1-17.
[12] Boadu F K.Use of multifractal seismic waveform parameters to characterize the hydraulic properties of fractured media:numerical experiments[J].Geophysical Journal International,2003,155(2):557-566.
[13] 饶华,李建民,孙夕平.利用分形理论预测潜山储层裂缝的分布[J].石油地球物理勘探,2009,44(1):98-103.RAO Hua,LI Jianmin,SUN Xiping.Using fractal theory to predict distribution of fracture in buried-hill reservoir[J].Oil Geophysical Prospecting,2009,44(1):98-103.
[14] Sarkheil H,Hassani H,Alinia F.Fractures distribution modeling using fractal and multi-fractal-neural network analysis in Tabnak hydrocarbon field,Fars,Iran[J].Arabian Journal of Geosciences,2013,6(3):945-956.
[15] 董少群,曾联波,Xu Chaoshui,等.储层裂缝随机建模方法研究进展[J].石油地球物理勘探,2018(3):625-641.DONG Shaoqun,ZENG Lianbo,XU Chaoshui,et al.Some progress in reservoir fracture stochastic modeling research[J].Oil Geophysical Prospecting,2018,53(3):625-641.
[16] Katz A J,Thompson A H.Fractal sandstone pores:implications for conductivity and pore formation[J].Physical Review Letters,1985,54(12):1325.
[17] Krohn C E,Thompson A H.Fractal sandstone pores:Automated measurements using scanning-electron-microscope images[J].Physical Review B,1986,33(9):6366-6374.
[18] Roy S,Tarafdar S.Archie’s law from a fractal model for porous rocks[J].Physical Review B,1997,55(13):8038-8041.
[19] Nigmatullin R R.The generalized fractals and statistical properties of the pore space of the sedimentary rocks[J].Physica Status Solidi (b),1989,153(1):49-57.
[20] Wei W,Cai J,Hu X,et al.An electrical conductivity model for fractal porous media[J].Geophysical Research Letters,2015,42(12):4833-4840.
[21] Pitchumani R,Ramakrishnan B.A fractal geometry model for evaluating permeabilities of porous performs used in liquid composite molding[J].International Journal of Heat and Mass Transfer,1999,42(12):2219-2232.
[22] Rieu M,Sposito G.Fractal fragmentation,soil porosity,and soil water properties Ⅰ:Theory[J].Soil Science Society of America Journal,1991,55(5):1231-1238.
[23] Yu B,Cheng P.A fractal permeability model for bi-dispersed porous media[J].International Journal of Heat and Mass Transfer,2002,45(14):2983-2993.
[24] Wyllie M R J,Gardner G H F.Permeability and the size distribution of pores[J].Nature,1958,181(4607):477.
[25] Cornell D,Katz D L.Flow of gases through consolidated porous media[J].Industrial & Engineering Chemistry,1953,45(10):2145-2152.
[26] Abdassah D,Permadi P,Sumantri Y,et al.Saturation exponent at various wetting condition:fractal modeling of thin-sections[J].Journal of Petroleum Science and Engineering,1998,20(3-4):147-154.
[27] Waxman M H,Smits L J M.Electrical conductivities in oil-bearing shaly sands[J].Society of Petroleum Engineers Journal,1968,8(2):107-122.
[28] Clavier C,Coates G,Dumanoir J.Theoretical and ex-perimental bases for the dual-water model for inter-pretation of shaly sands[J].Society of Petroleum Engineers Journal,1984,24(2):153-168.
[29] Budebes S,Hamdy T,Al-Farisi O,et al.Carbonate archie exponants correction model and variable determination[C].SPE Reservoir Characterization and Simulation Conference and Exhibition,Society of Petro-leum Engineers,2011.