Conductivity model for pyrite-bearing laminated and dispersed shaly sands based on a differential equation and the generalized Archie equation
Guo Zhi-Hua1,2, Song Yan-Jie1,2, Tang Xiao-Min1,2, and Wang Chao1,3
1. College of Geo-science, Northeast Petroleum University, Heilongjiang Daqing 163318, China.
2. Accumulation and Development of Unconventional Oil and Gas, State Key Laboratory Cultivation Base jointly constructed by Heilongjiang Province and the Ministry of Science and Technology, Heilongjiang Daqing 163318, China.
3. No. 9 Oil Production Company Geological Team of Daqing Oilfield Company Ltd, Heilongjiang Daqing 163000, China.
Abstract：
The conductance of pyrite-bearing laminated and dispersed shaly sands is not well understood and resistivity models for pyrite-bearing shaly sands are nonexistent. Thus, we first synthesize clean pyrite-matrix samples, and quartz-matrix samples with variable laminated shale, dispersed shale, and pyrite content and then perform petrophysics experiments to assess the effect of pyrite content on the conductivity of pyrite-bearing shaly sands. Second, based on the differences in conductivity and conduction pathways and geometries because of the variable composition of the pyrite-bearing laminated and dispersed shaly sands, we divide the shaly sands into their components, i.e., laminated shale, quartz grains, pyrite grains, hydrocarbon, dispersed shale, microscopic capillary water, and mobile water. A generalized resistivity model is proposed to describe the conductivity of pyrite-bearing laminated and dispersed shaly sands, based on the combined conductivity differential equation and generalized Archie equation. In the generalized resistivity model, the conductivity differential equation is used to describe the conductivity of dispersed inclusions in a host, whereas the generalized Archie equation is used to describe the conductivity of two conducting phases. Moreover, parallel conductance theory is used to describe the conductivity of dispersed shaly sands and laminated shale. Theoretical analysis suggests that the proposed model satisfies the physical constraints and the model and experimental results agree. The resistivity and resistivity index of shaly sands decrease with increasing conductivity and pyrite. Finally, the accuracy of the resistivity model is assessed based on experimental data from 46 synthetic core samples with different oil saturation. The model can describe the conductivity of clean pyrite-matrix samples, and quartz-matrix samples with different volumes of laminated shale, dispersed shale, and pyrite. An accurate saturation model of pyrite-bearing laminated and dispersed shaly sands is thus obtained and the log data interpretation in complex shaly sands can improve with the proposed model.
. Conductivity model for pyrite-bearing laminated and dispersed shaly sands based on a differential equation and the generalized Archie equation[J]. APPLIED GEOPHYSICS, 2018, 15(2): 208-221.
[1]
Berg, C. R., 1998, A comparison of SATORI and HB effective-medium conductivity models: The Log Analyst, 39(5), 34-39.
[2]
Bian, H. L., Guan, J., Mao, Z. Q., et al., 2014, Pore structure effect on reservoir electrical properties and well logging evaluation: Applied Geophysics, 11(4), 374-383.
[3]
Bootle, R., 2016, Graphical solutions for laminated and dispersed shaly sands: Petrophysics, 57(1), 51−59.
[4]
Bussian, A. E., 1982, A generalized Archie equation: SPWLA 23th Annual Logging Symposium, society of Petrophysicists and Well-Log Analysts, Corpus Christi, Texas.
[5]
Bussian, A. E., 1983, Electrical conductance in a porous medium: Geophysics, 60(9), 1258-1268.
[6]
Chen, D. X., 2011, On interpretation method of complex oil zone and water zone in southern Gulong area: MSc. Thesis, Northeast Petroleum University.
[7]
Chen, J. Q., 2010, Study on the effective medium pore combination resistivity model for low porosity and permeability shaly sand reservoir in the East China Sea: MSc. Thesis, Daqing petroleum institute.
[8]
Clavier, C., Coates, G., and Dumanoir, J., 1984, The theoretical and experimental bases for the dual-water model for interpretation of shaly sands: Society of Petroleum Engineers Journal, 24(2), 153-168.
[9]
De Kuijper, A., Sandor, R. K. J., Hofman, J. P., et al., 1996, Electrical conductivities in oil-bearing shaly sand accurately described with the satori saturation model: The Log Analyst, 37(5), 22-31.
[10]
Garcia, A. P., Jagadisan, A., Rostami, A., and Heidari, Z., 2017, A new resistivity-based model for improved hydrocarbon saturation assessment in clay-rich formations using quantitative clay network geometry and rock fabric: SPWLA 58th Annual Logging Symposium, Society of Petrophysicists and Well-log Analysts, Oklahoma City, Oklahoma, USA.
[11]
Glover, P. W. J., 2009, What is the cementation exponent? A new interpretation: The leading Edge, 28(1), 82-85.
[12]
Glover, P. W. J., 2010, A generalized Archie’s law for n phases: Geophysics, 75(6), E247-E265.
[13]
Glover, P. W. J., Hole, M. J., and Pous, J., 2000, A modified Archie’s law for two conducting phases: Earth and Planetary Science Letters, 180(3), 369-383.
[14]
Giao, P. H., 2016, Geoelectric modeling-based estimation of shale resistivity to enhance water saturation calculation for a low-resistivity shaly sand formation in the Cuu Long basin, Vietnam: 2016 SEG International Exposition and Annual Meeting, Society of Exploration Geophysicists, Dallas, Texas.
[15]
Givens, W. W., and Schmidt, E. J., 1988, A generic electrical conduction model for low-contrast resistivity sandstones: SPWLA 29th Annual Logging Symposium, Society of Petrophysicists and Well-Log Analysts, San Antonio, Texas.
[16]
Koelman, J. M. V. A., and De Kuijper, A., 1997, An effective medium model for the electric conductivity of an n-component anisotropic percolating mixture phases: PHYSICA (Section A), 247(1), 10-22.
[17]
Li, Z. B., and Mo, X. W., 1999, Study on the electric property of shaly sand and its interpretation method: Journal of Geoscientific Research in Northeast Asia, 2(1), 110-114.
[18]
Luo, M., Wood, J. R., and Cathles, L. M., 1994, Prediction of thermal conductivity in reservoir rocks using fabric theory: Journal of Applied Geophysics, 32(4), 321-334.
[19]
Myers, M. T., 1989, Pore Modeling: Extending The Hanai-Bruggeman Equation: SPWLA 30th Annual Logging Symposium, Society of Petrophysicists and Well-Log Analysts, Denver, Colorado.
[20]
Poupon, A., Loy, M. E., and Tixier, M. P., 1954, A contribution to electrical log interpretation in shaly sands: Journal of petroleum Technology, 6(6), 27-34.
[21]
Sarihi, A., and Vargas-Murillo, B., 2015, A method to compute water saturation in tight rocks accounting for conductivity of clay minerals: Abu Dhabi International Petroleum Exhibition and Conference, Society of Petroleum Engineers, Abu Dhabi, UAE.
[22]
Silva, L. P., and Bassioni, Z., 1985, A shaly sand conductivity mode1 based on variable equivalent counter-ion conductivity and dual water concepts: SPWLA 26th Annual Logging Symposium, Society of Petroleum Engineers, Dallas, Texas.
[23]
Silva, L. P., and Bassioni, Z., 1986, Statistical evaluation of the S-B conductivity model for water-bearing shaly formations: The Log Analyst, 27(3), 9-19.
[24]
Silva, L. P., and Bassioni, Z., 1988, Hydrocarbon saturation equation in shaly sands according to the S-B conductivity model: SPE Formation Evaluation, 3(3), 503-509.
[25]
Song, Y. J., Li, X. J., Tang, X. M., and Fu, J., 2014, Matrix-conducting resistivity model for clean sands based on connectivity conductance theory and HB equation: Journal of China University of Petroleum (edition of natural science), 38(5), 66-74.
[26]
Song, Y. J., and Tang, X. M., 2008, Generalized effective medium resistivity model for low resistivity reservoir: Science in China (Series D: Earth Sciences), 38(7), 896-909.
[27]
Song, Y. J., Tang, X. M., and Yu, B., 2009, experimental study of conductance mechahanism in laminated and dispersed shaly sands: Progress in geophysics (in Chinese), 24(6), 2186-2193.
[28]
Song. Y. J., Wang, X. M., and Lu, S. F., 2005, Generalized matrix-conducting pore combination resistivity model in laminated and dispersed shaly sands: Progress in geophysics (in Chinese), 20(3), 747-756.
[29]
Tang, X. M., Song, Y. J., Liu, Y., et al., 2016, Basic research on application of symmetrical effective medium conduction theory in complex shaly sands: Progress in geophysics (in Chinese), 31(4), 1670-1677.
[30]
Waxman, M. H., and Smits, L. J. M., 1968, Electrical conductivities in oil-bearing shaly sands: Society of petroleum Engineers, 8(2), 107-122.
[31]
Waxman, M. H., and Thomas, E. C., 1974, Electrical Conductivities in Shaly Sands-I. The Relation between Hydrocarbon Saturation and Resistivity Index; II. The Temperature Coefficient of Electrical Conductivity: SPE Journal, 12(3), 213-225.
[32]
Yue, W. Z., Tao, G., Chai, X. Y., et al., 2011, Digital core approach to the effects of clay on the electrical properties of saturated rocks using lattice gas automation: applied Geophysics, 8(1), 11-17.
[33]
Zhao, J., Dai, X. Y., Lu, Y. Fan., et al., 2017, Shale reservoir conductive mechanism based on percolation network: Chinese Journal of Geophysics, 60(5), 2020-2028.
2018, Vol. 15 
