基于孔喉腔模型研究孔隙结构对于多孔介质孔隙度指数的影响
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摘要
多孔介质的导电特性取决于多孔介质的孔隙空间结构,孔隙空间结构通常使用孔隙尺寸和孔隙迂曲度描述,而已有模型仅仅研究了孔隙尺寸对于孔隙度指数的影响.为了全面研究孔隙空间孔隙尺寸和孔隙迂曲度对于孔隙度指数的影响,基于孔隙网络基本单元孔喉腔,以及孔喉腔等效电路中喉道并联导电而后与孔隙体串联的假设,推导出孔喉腔电阻率.使用阿尔奇公式建立孔喉腔孔隙度指数计算模型,研究孔隙结构对于孔隙度指数影响.对于毛管模型,孔隙度指数随着孔隙迂曲度或孔隙横截面积的增大而增大,当孔隙迂曲度为1时,孔隙度指数不受孔隙横截面积的影响恒为1.0.当孔喉腔只有一个喉道时,该模型等价于溶孔发育的双孔隙度模型.在该孔喉腔中,随着孔隙与喉道迂曲度的增大,孔隙度指数增大;随着孔隙横截面积的增大,孔喉比增大,孔隙度指数增大;而随着喉道面积的增大,孔喉比降低,孔隙度指数首先降低而后增大.孔隙度指数与孔喉比有关.对于具有两个喉道的孔喉腔,该模型等价于溶孔、裂缝发育的三孔隙度模型,能够研究孔隙类型,孔隙几何特性对于孔隙度指数的影响.当孔隙固定,两个喉道的迂曲度增大时,孔隙度指数增大;两个喉道横截面积增大时,孔喉比降低,然而孔隙度指数增大,最大孔隙度指数对应的孔喉比并非最大值.当一个喉道固定,孔隙的横截面积增大时,孔隙度指数增加;喉道的横截面积增大时,孔隙度指数首先降低而后增大.孔喉比与孔隙度指数具有一定相关性,而孔隙度指数最大情况下的孔喉比与模型最大孔喉比并不完全对应.孔隙度指数是孔隙空间几何与拓扑特性共同作用的结果.岩心图像分析获取迂曲度与孔喉比后建立孔喉腔孔隙度指数模型的结果符合岩电实验数据,岩心分析饱和度和测井解释结论,表明孔喉腔孔隙度指数模型在地层评价中具有实际测井解释能力.
The electrical resistivity of porous media depends on the pore structure of the porous media, and the pore structure is traditionally characterized by the pore size and pore tortuosity. While the existing porosity exponent models just investigate the effect of the pore size on the porosity exponent. In order to thoroughly study the pore size and pore tortuosity impact on the porosity exponent, based on the basic unit of the pore network, pore throat conjunction, in the pore space, and the assumption that the throats are parallel and then connect to the pore body in series in their equivalent electrical circuit, a calculation model of porosity exponent relating to the pore morphology was derived with the porosity exponent calculated by Archie law. For capillary tube model, that is, pore throat conjunction with just a pore body and no throat bond, the porosity exponent increased with the increase of the tortuosity and the pore size respectively. When the tortuosity was equal to 1, the porosity exponent was always equal to 1 independent of the pore size. For the pore throat conjunction with one throat bond, this model enabled represent the vuggy dual porosity model investigating the effect of the pore geometry on the porosity exponent. The increase of the pore tortuosity and throat tortuosity both resulted in the increase of the porosity exponent; the cross sectional area of the pore body caused the increase of the cross sectional Area Ratio of Pore to Throat(PTAR), and then the increase of the porosity exponent, while the increase of the cross sectional area of the throat reduced the PTAR, the porosity exponent firstly reduced and then went up, the porosity exponent was related to the PTAR. For the pore throat conjunction with two throats, this model was equivalent to the triple porosity model with vug and fracture in the matrix pore system, this model enabled investigate the effects of the pore types, pore size and tortuosity on the porosity exponent. When the pore body was fixed, the increase of the throat tortuosity increased the porosity exponent, and the increase of the cross sectional area of the throat increased the porosity exponent with PTAR decreased, the distribution of the maximal porosity exponent did not match the distribution of the maximal PTAR; when a throat was fixed, the increase of the cross sectional area of pore caused the increase of the PTAR and then the porosity exponent, while the increase of the cross sectional area of throat firstly decreased and then slowly increased the porosity exponent, the porosity exponent correlated to the PTAR while the distribution of the maximal PTAR did not totally agree well with the distribution of the maximal porosity exponent. The porosity exponent of the porous media was the comprehensive effects of the pore size and pore tortuosity. The data from pore throat conjunction model with tortuosity and PTAR calculated from two dimensional image analysis matched the experimental formation factor,porosity,water saturation and well logging interpretation well. This validated the accuracy of the pore throat conjunction model and proved the feasibility of the model for well logging interpretation in formation evaluation.
The electrical resistivity of porous media depends on the pore structure of the porous media, and the pore structure is traditionally characterized by the pore size and pore tortuosity. While the existing porosity exponent models just investigate the effect of the pore size on the porosity exponent. In order to thoroughly study the pore size and pore tortuosity impact on the porosity exponent, based on the basic unit of the pore network, pore throat conjunction, in the pore space, and the assumption that the throats are parallel and then connect to the pore body in series in their equivalent electrical circuit, a calculation model of porosity exponent relating to the pore morphology was derived with the porosity exponent calculated by Archie law. For capillary tube model, that is, pore throat conjunction with just a pore body and no throat bond, the porosity exponent increased with the increase of the tortuosity and the pore size respectively. When the tortuosity was equal to 1, the porosity exponent was always equal to 1 independent of the pore size. For the pore throat conjunction with one throat bond, this model enabled represent the vuggy dual porosity model investigating the effect of the pore geometry on the porosity exponent. The increase of the pore tortuosity and throat tortuosity both resulted in the increase of the porosity exponent; the cross sectional area of the pore body caused the increase of the cross sectional Area Ratio of Pore to Throat(PTAR), and then the increase of the porosity exponent, while the increase of the cross sectional area of the throat reduced the PTAR, the porosity exponent firstly reduced and then went up, the porosity exponent was related to the PTAR. For the pore throat conjunction with two throats, this model was equivalent to the triple porosity model with vug and fracture in the matrix pore system, this model enabled investigate the effects of the pore types, pore size and tortuosity on the porosity exponent. When the pore body was fixed, the increase of the throat tortuosity increased the porosity exponent, and the increase of the cross sectional area of the throat increased the porosity exponent with PTAR decreased, the distribution of the maximal porosity exponent did not match the distribution of the maximal PTAR; when a throat was fixed, the increase of the cross sectional area of pore caused the increase of the PTAR and then the porosity exponent, while the increase of the cross sectional area of throat firstly decreased and then slowly increased the porosity exponent, the porosity exponent correlated to the PTAR while the distribution of the maximal PTAR did not totally agree well with the distribution of the maximal porosity exponent. The porosity exponent of the porous media was the comprehensive effects of the pore size and pore tortuosity. The data from pore throat conjunction model with tortuosity and PTAR calculated from two dimensional image analysis matched the experimental formation factor,porosity,water saturation and well logging interpretation well. This validated the accuracy of the pore throat conjunction model and proved the feasibility of the model for well logging interpretation in formation evaluation.
引文
Abousrafa E M, Somerville J M, Hamilton SA, et al. 2009. Pore geometrical model for the resistivity of brine saturated rocks [J]. Journal of Petroleum Science and Engineering, 65(3- 4): 113-122, doi: 10.1016/j.petrol.2008.12.009.
Aguilera M S, Aguilera R. 2003. Improved models for petrophysical analysis of dual porosity reservoirs [J]. Petrophysics, 44(1): 21-35.
Aguilera R. 1976. Analysis of Naturally Fractured Reservoirs From Conventional Well Logs (includes associated papers 6420 and 6421) [J]. Journal of Petroleum Technology, 28(07): 764-772.
Aguilera R F, Aguilera R P. 2004. A triple porosity model for petrophysical analysis of naturally fractured reservoirs [J]. Petrophysics, 45(2): 157-166.
Archie G E. 1942. The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics [J]. Transactions of the AIME, 146(1): 54- 62, doi: 10.2118/942054-G.
Ballay R E. 2012. The “m” Exponent in Carbonate Petrophysics. http://www.geoneurale.com/. Accessed 15 April 2012.
Blunt M J, Bijeljic B, Dong H, et al. 2013. Pore-scale imaging and modelling [J]. Advances in Water Resources, 51: 197-216, doi: 10.1016/j.advwatres.2012.03.003.
Bultreys T, de Boever W, Cnudde V. 2016. Imaging and image-based fluid transport modeling at the pore scale in geological materials: A practical introduction to the current state-of-the-art [J]. Earth-Science Reviews, 155: 93-128, doi: 10.1016/j.earscirev.2016.02.001.
Chen F X. 1987. Pore throat-cavity junction theory and its application to physical properties of rock [J]. Journal of Southwestern Petroleum Institute (in Chinese), 9(1): 1-24.
Corbett P WM, Wang H, Camara R N,et al. 2017. Using the porosity exponent (m) and pore-scale resistivity modelling to understand pore fabric types in coquinas (Barremian-Aptian) of the Morro do Chaves Formation, NE Brazil [J]. Marine and Petroleum Geology, 88: 628- 647, doi: 10.1016/j.marpetgeo.2017.08.032.
Li W, Zou C C, Wang H, et al. 2017. A model for calculating the formation resistivity factor in low and middle porosity sandstone formations considering the effect of pore geometry [J]. Journal of Petroleum Science and Engineering, 152: 193-203, doi: 10.1016/j.petrol.2017.03.006.
Li X, Qin R, Liu C, et al. 2013. The effect of rock electrical parameters on the calculation of reservoir saturation [J]. Journal of Geophysics and Engineering, 10(5): (055007) 055001- 055008, doi: 10.1088/1742-2132/10/5/055007.
Lucia F J. 1983. Petrophysical parameters estimated from visual descriptions of carbonate rocks, a field classification of carbonate pore space [J]. Journal of Petroleum Technology, 35(3): 629- 637, doi: 10.2118/10073-PA.
Müller-Huber E, Sch?n J, B?rner F. 2015. The effect of a variable pore radius on formation resistivity factor [J]. Journal of Applied Geophysics, 116: 173-179, doi: 10.1016/j.jappgeo.2015.03.011.
Piedrahita J, Aguilera R. 2016. A petrophysical dual-porosity model for evaluation of secondary mineralization and tortuosity in naturally fractured reservoirs [C]. Paper presented at the SPE Low Perm Symposium, Denver, Colorado, U.S.A., 5- 6 May.
Tian H, Li C, Jia P. 2017. Research of water saturation interpretation models for carbonate reservoir [J]. Progress in Geophysics (in Chinese), 32(1): 0279- 0286, doi: 10.6038/pg20170319.
Verwer K, Eberli GP, Weger RJ. 2011. Effect of pore structure on electrical resistivity in carbonates [J]. AAPG Bulletin, 95(2): 175-190, doi: 10.1306/06301010047.
Wang H. 2015. Numerical Simulation of Resistivity and Investigation of Porosity Exponent in Carbonates [D]. Institute of Petroleum Engineering,School of Energy, Geoscience, Infracture and Society, Heriot-Watt University.
Wang M. 2013. Improvement and Analysis of Carbonate Reservoir Saturation Model [J]. Journal of Southwestern Petroleum University (Science & Technology Edition) (in Chinese), 35(5): 31- 40, doi: 10.3863/j. issn.1674-5086. 2013.05.005.
Weger RJ, Eberli GP, Baechle GT, et al. 2009. Quantification of pore structure and its effect on sonic velocity and permeability in carbonates [J]. AAPG Bulletin, 93(10): 1297-1317, doi: 10.1306/05270909001.
Zeng W C, Liu X F. 2013. Interpretation of Non-Archie phenomenon for carbonate reservoir [J]. Well Logging Technology (in Chinese), 37(4): 341-351.
陈福煊. 1987. 孔隙喉腔结理论及其在岩石物性中的应用[J]. 西南石油大学学报, 9(1): 1-24.
田瀚, 李昌, 贾鹏. 2017. 碳酸盐岩储层含水饱和度解释模型研究[J]. 地球物理学进展, 32(1) 0279- 0286, doi: 10.6038/pg20170319.
王敏. 2013. 碳酸盐岩储层含水饱和度模型发展及分析[J]. 西南石油大学学报:自然科学版 35(5): 31- 40, doi: 10.3863/j.issn.1674-5086.2013.05.005.
曾文冲, 刘学峰. 2013. 碳酸盐岩非阿尔奇特性的诠释[J]. 测井技术, 37(4): 341-351.
Aguilera M S, Aguilera R. 2003. Improved models for petrophysical analysis of dual porosity reservoirs [J]. Petrophysics, 44(1): 21-35.
Aguilera R. 1976. Analysis of Naturally Fractured Reservoirs From Conventional Well Logs (includes associated papers 6420 and 6421) [J]. Journal of Petroleum Technology, 28(07): 764-772.
Aguilera R F, Aguilera R P. 2004. A triple porosity model for petrophysical analysis of naturally fractured reservoirs [J]. Petrophysics, 45(2): 157-166.
Archie G E. 1942. The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics [J]. Transactions of the AIME, 146(1): 54- 62, doi: 10.2118/942054-G.
Ballay R E. 2012. The “m” Exponent in Carbonate Petrophysics. http://www.geoneurale.com/. Accessed 15 April 2012.
Blunt M J, Bijeljic B, Dong H, et al. 2013. Pore-scale imaging and modelling [J]. Advances in Water Resources, 51: 197-216, doi: 10.1016/j.advwatres.2012.03.003.
Bultreys T, de Boever W, Cnudde V. 2016. Imaging and image-based fluid transport modeling at the pore scale in geological materials: A practical introduction to the current state-of-the-art [J]. Earth-Science Reviews, 155: 93-128, doi: 10.1016/j.earscirev.2016.02.001.
Chen F X. 1987. Pore throat-cavity junction theory and its application to physical properties of rock [J]. Journal of Southwestern Petroleum Institute (in Chinese), 9(1): 1-24.
Corbett P WM, Wang H, Camara R N,et al. 2017. Using the porosity exponent (m) and pore-scale resistivity modelling to understand pore fabric types in coquinas (Barremian-Aptian) of the Morro do Chaves Formation, NE Brazil [J]. Marine and Petroleum Geology, 88: 628- 647, doi: 10.1016/j.marpetgeo.2017.08.032.
Li W, Zou C C, Wang H, et al. 2017. A model for calculating the formation resistivity factor in low and middle porosity sandstone formations considering the effect of pore geometry [J]. Journal of Petroleum Science and Engineering, 152: 193-203, doi: 10.1016/j.petrol.2017.03.006.
Li X, Qin R, Liu C, et al. 2013. The effect of rock electrical parameters on the calculation of reservoir saturation [J]. Journal of Geophysics and Engineering, 10(5): (055007) 055001- 055008, doi: 10.1088/1742-2132/10/5/055007.
Lucia F J. 1983. Petrophysical parameters estimated from visual descriptions of carbonate rocks, a field classification of carbonate pore space [J]. Journal of Petroleum Technology, 35(3): 629- 637, doi: 10.2118/10073-PA.
Müller-Huber E, Sch?n J, B?rner F. 2015. The effect of a variable pore radius on formation resistivity factor [J]. Journal of Applied Geophysics, 116: 173-179, doi: 10.1016/j.jappgeo.2015.03.011.
Piedrahita J, Aguilera R. 2016. A petrophysical dual-porosity model for evaluation of secondary mineralization and tortuosity in naturally fractured reservoirs [C]. Paper presented at the SPE Low Perm Symposium, Denver, Colorado, U.S.A., 5- 6 May.
Tian H, Li C, Jia P. 2017. Research of water saturation interpretation models for carbonate reservoir [J]. Progress in Geophysics (in Chinese), 32(1): 0279- 0286, doi: 10.6038/pg20170319.
Verwer K, Eberli GP, Weger RJ. 2011. Effect of pore structure on electrical resistivity in carbonates [J]. AAPG Bulletin, 95(2): 175-190, doi: 10.1306/06301010047.
Wang H. 2015. Numerical Simulation of Resistivity and Investigation of Porosity Exponent in Carbonates [D]. Institute of Petroleum Engineering,School of Energy, Geoscience, Infracture and Society, Heriot-Watt University.
Wang M. 2013. Improvement and Analysis of Carbonate Reservoir Saturation Model [J]. Journal of Southwestern Petroleum University (Science & Technology Edition) (in Chinese), 35(5): 31- 40, doi: 10.3863/j. issn.1674-5086. 2013.05.005.
Weger RJ, Eberli GP, Baechle GT, et al. 2009. Quantification of pore structure and its effect on sonic velocity and permeability in carbonates [J]. AAPG Bulletin, 93(10): 1297-1317, doi: 10.1306/05270909001.
Zeng W C, Liu X F. 2013. Interpretation of Non-Archie phenomenon for carbonate reservoir [J]. Well Logging Technology (in Chinese), 37(4): 341-351.
陈福煊. 1987. 孔隙喉腔结理论及其在岩石物性中的应用[J]. 西南石油大学学报, 9(1): 1-24.
田瀚, 李昌, 贾鹏. 2017. 碳酸盐岩储层含水饱和度解释模型研究[J]. 地球物理学进展, 32(1) 0279- 0286, doi: 10.6038/pg20170319.
王敏. 2013. 碳酸盐岩储层含水饱和度模型发展及分析[J]. 西南石油大学学报:自然科学版 35(5): 31- 40, doi: 10.3863/j.issn.1674-5086.2013.05.005.
曾文冲, 刘学峰. 2013. 碳酸盐岩非阿尔奇特性的诠释[J]. 测井技术, 37(4): 341-351.
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