APPLIED GEOPHYSICS
 
        Home  |  Copyright  |  About Journal  |  Editorial Board  |  Indexed-in  |  Subscriptions  |  Download  |  Contacts Us  |  中文
APPLIED GEOPHYSICS  2019, Vol. 16 Issue (1): 15-26    DOI: 10.1007/s11770-019-0756-3
article Current Issue | Next Issue | Archive | Adv Search Previous Articles  |  Next Articles  
Simultaneous prediction of rock matrix modulus and critical porosity*
Li Nuo, Chen Hao, Zhang Xiu-Mei, Han Jian-Qiang, Wang Jian, Wang Xiu-Ming
1. State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China.
2. University of Chinese Academy of Sciences, Beijing 100049, China.
3. Beijing Engineering Research Center of sea deep drilling and exploration, Beijing 100190, China.
 Download: PDF (883 KB)   HTML ( KB)   Export: BibTeX | EndNote (RIS)      Supporting Info
Abstract The matrix modulus and critical porosity in rocks are two critical parameters to seismic rock physics models; however, the critical porosity is difficult to obtain. Based on the linear relation between the effective bulk modulus and porosity, we propose a fast method for calculating the matrix modulus and critical porosity by least square fitting of effective bulk modulus and porosity data measured in laboratory or field. The proposed method is well suited for samples with wide porosity range. The calculation results accurately reflect the differences in clay content, pressure, and saturation state. Samples with high clay content have low matrix modulus and critical porosity. The matrix modulus is independent of pressure, whereas the critical porosity increases with increasing pressure. The calculated matrix modulus for watersaturated samples is higher than that for dry rock samples.
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Key wordsmodulus   porosity   clay content   pressure   saturation     
Fund:

This study was supported by the National Nature Science Foundation of China (Nos. 11574347, 11774373, 11734017, 91630309 and 41604123) and the PetroChina Innovation Foundation (No. 2016D-5007-0304)

Corresponding Authors: Chen Hao (Email: chh@mail.ioa.ac.cn)   
 E-mail: chh@mail.ioa.ac.cn
About author: Li Nuo is a Ph.D. student in Acoustics at the Institute of Acoustics, Chinese Academy of Sciences, Beijing, China. He received a B.E. (2013) in Exploration Technology and Engineering and an M.S. (2016) in Geological Resources and Geological Engineering from China University of Petroleum, Qingdao, China. His research interests are rock physics and acoustic logging methods. E-mail: linuo91@163.com
Cite this article:   
. Simultaneous prediction of rock matrix modulus and critical porosity*[J]. APPLIED GEOPHYSICS, 2019, 16(1): 15-26.
 
[1] Avseth, P., Mukerji, T., and Mavko, G., 2010,Quantitative seismic interpretation: Applying rock physics tools to reduce interpretation risk: Cambridge university press.
[2] Ba, J., Nie, J. X., Cao, H., et al., 2008, Mesoscopic fluid flow simulation in double−porosity rocks: Geophysical Research Letters, 35(4), 228?236.
[3] Ba, J., Zhao, J., Carcione, J. M., et al., 2016, Compressional wave dispersion due to rock matrix stiffening by clay squirt flow:Geophysical Research Letters, 43(12), 6186?6195.
[4] Batzle, M. L., Han, D. H., and Hofmann, R., 2006, Fluid mobility and frequency dependent seismic velocity−Direct measurements: Geophysics, 71(10), N1?N9.
[5] Biot, M. A., 1956a, Theory of propagation of elastic waves in a fluid saturated porous solid. I. Low−frequency range: Journal of the Acoustical Society of America, 28(2), 168?178.
[6] mdash;—, M. A., 1956b, Theory of propagation of elastic waves in a fluid saturated porous solid. II. Highfrequency range: Journal of the Acoustical Society of America, 28(2), 179?191.
[7] Brown, R. J., and Korringa, J., 1975, On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid: Geophysics, 40(4), 608?616.
[8] Dvorkin, J., and Nur, A., 1993, Dynamic poroelasticity: A unified model with the squirt and the Biot mechanisms: Geophysics, 58(4), 524?533.
[9] Feng, Q., Jiang L., Liu M., et al., 2014, Fluid substitution in carbonate rocks based on the Gassmann equation and Eshelby−Walsh theory: Journal of Applied Geophysics, 106(7), 60?66.
[10] Gassmann, F., 1951, Elastic waves through a packing of spheres: Geophysics, 16, 673?685.
[11] Gor, G. Y. and Gurevich, B., 2018, Gassmann theory applies to nanoporous media: Geophysical Research Letters, 45(1), 146?155.
[12] Gurevich, B., Brajanovski, M., Galvin, R. J., et al., 2009, P−wave dispersion and attenuation in fractured and porous reservoirs−poroelasticity
[13] approach: Geophysical Prospecting, 57(2), 225?237.
[14] Han, D. H., Nur, A., and Morgan, D., 1986, Effects of porosity and clay content on wave velocities in sandstones: Geophysics, 51(11), 2093?2107.
[15] He, X. L., He Z. H., Wang R. L., et al., 2011, Calculations of rock matrix modulus based on a linear regression relation: Applied Geophysics, 8(3), 155.
[16] He, T., Zou, C.C., Pei, F. G., Ren, K.Y., Kong F.D., and Shi G., 2010, Laboratory study of fluid viscosity induced ultrasonic velocity dispersion in reservoir sandstones: Applied Geophysics, 7(2), 114−126.
[17] Jiang, L., Wen, X. T., He, Z. H., et al., 2011, Pore Structure Model Simulation and Porosity Prediction in Reef ‐ Flat Reservoirs: Chinese Journal of Geophysics, 54(3), 403?414.
[18] Krief, M., Garat, J., Stellingwerff, J., and Ventre, J., 1990, A petrophysical interpretation using the velocities of P−and S−waves (full waveform sonic): The Log Analyst, 31(6), 355?369.
[19] Ma, X. Y., Wang, S. X., Zhao, J. G., et al., 2018, Velocity dispersion and fluid substitution in sandstone under partially saturated conditions: Applied Geophysics, 15(2), 188?196.
[20] Mavko, G., and Mukerji, T., 1995, Seismic pore space compressibility and Gassmann’s relation: Geophysics, 60(6), 1743?1749.
[21] Mavko, G., Mukerji, T., and Dvorkin, J., 2003, The rock physics handbook: tools for seismic analysis of porous media, Cambridge University Press.
[22] Nur, A., 1992, Critical porosity and the seismic velocities in rocks: EOS, Transactions American Geophysical Union, 73, 43−66.
[23] O’Connell, R. J., and Budiansky, B., 1974, Seismic velocities in dry and saturated cracked solids: Journal of Geophysical Research, 79(35), 5412?5426.
[24] Passos de Figueiredo, L., Grana, D., Luis Bordignon, F., et al., 2018, Joint Bayesian inversion based on rock−physics prior modeling for the estimation of spatially correlated reservoir properties: Geophysics, 83(5), 1?53.
[25] Pride, S. R., Berryman, J. G., and Harris, J. M., 2004, Seismic attenuation due to wave−induced flow: Journal of Geophysical Research Solid Earth, 109(B1).
[26] Reuss, A., 1929, Berechnung der fliessgrenze von mischkristallen auf grund der plastizitätsbedingungen für einkristalle: Zeitschrift für Angewandte Mathematic und Mechanik, 9, 49?58.
[27] Russell, B. H. and Smith, T., 2007, The relationship between dry rock bulk modulus and porosity−An empirical study: CREWES Research Report, 19, 1?14.
[28] Saul, M. J. and Lumley, D. E., 2013, A new velocity−pressure−compaction model for uncemented sediments: Geophysical Journal International, 193(2), 905?913.
[29] Tang X. M., 2011, A unified theory for elastic wave propagation through porous media containing cracks—An extension of Biot’s poroelastic wave theory: Science China Earth Sciences, 54(9), 1441?1452.
[30] Vernik, L., 2016, Seismic petrophysics in quantitative interpretation, Society of Exploration Geophysicists.
[31] Walsh, J. B., 1965, The effect of cracks on the compressibility of rock: Journal of Geophysical Research, 70(2), 381?389.
[32] Wang, D. X., 2016, Study on the rock physics model of gas reservoirs in tight sandstone: Chinese Journal of Geophysics, 60(1), 64?83.
[33] Winkler, K. W., 1983, Frequency dependent ultrasonic properties of high−porosity sandstones: Journal of Geophysical Research, 88(B11), 9493?9499.
[34] mdash;—, K. W., 1986, Estimates of velocity dispersion between seismic and ultrasonic frequencies: Geophysics, 51(1), 183 - 189
[35] Yin, X. Y., Zong, Z. Y., and Wu, G. C., 2015, Research on seismic fluid identification driven by rock physics: Science China Earth Sciences, 58(2), 159?171.
[36] Zhang, J. J., Li, H. B., and Yao, F. C., 2012, Rock critical porosity inversion and S−wave velocity prediction: Applied Geophysics, 9(1), 57?64.
[1] Wang Da-Xing, Wang Hao-Fan, Ma Jin-Feng, Wang Yong-Gang, Zhang Na, Li Lin, Jia Ling-Yun, and Yang Yang. Fluids discrimination by ray-path elastic impedance inversion: A successful case from Sulige tight gas field[J]. APPLIED GEOPHYSICS, 2019, 16(2): 231-245.
[2] Hu Jun, Cao Jun-Xing, He Xiao-Yan, Wang Quan-Feng, and Xu Bin. Numerical simulation of fault activity owing to hydraulic fracturing[J]. APPLIED GEOPHYSICS, 2018, 15(3-4): 367-381.
[3] Ma Qi-Qi and Sun Zan-Dong. Elastic modulus extraction based on generalized pre-stack PP–PS joint linear inversion[J]. APPLIED GEOPHYSICS, 2018, 15(3-4): 466-480.
[4] Tan Wen-Hui, Ba Jing, Guo Meng-Qiu, Li Hui, Zhang Lin, Yu Ting, and Chen Hao. Brittleness characteristics of tight oil siltstones[J]. APPLIED GEOPHYSICS, 2018, 15(2): 175-187.
[5] Ma Xiao-Yi, Wang Shang-Xu, Zhao Jian-Guo, Yin Han-Jun, and Zhao Li-Ming. Velocity dispersion and fluid substitution in sandstone under partially saturated conditions[J]. APPLIED GEOPHYSICS, 2018, 15(2): 188-196.
[6] Duan Xi and Liu Xiang-Jun. Two-phase pore-fluid distribution in fractured media: acoustic wave velocity vs saturation[J]. APPLIED GEOPHYSICS, 2018, 15(2): 311-317.
[7] Li Lin, Ma Jin-Feng, Wang Hao-Fan, Tan Ming-You, Cui Shi-Ling, Zhang Yun-Yin, Qu Zhi-Peng. Shear wave velocity prediction during CO2-EOR and sequestration in the Gao89 well block of the Shengli Oilfield[J]. APPLIED GEOPHYSICS, 2017, 14(3): 372-380.
[8] Liu Jie, Liu Jiang-Ping, Cheng Fei, Wang Jing, Liu Xiao-Xiao. Rock-physics models of hydrate-bearing sediments in permafrost, Qilian Mountains, China[J]. APPLIED GEOPHYSICS, 2017, 14(1): 31-39.
[9] Ma Jin-Feng, Li Lin, Wang Hao-Fan, Tan Ming-You, Cui Shi-Ling, Zhang Yun-Yin, Qu Zhi-Peng, Jia Ling-Yun, Zhang Shu-Hai. Geophysical monitoring technology for CO2 sequestration[J]. APPLIED GEOPHYSICS, 2016, 13(2): 288-306.
[10] Li Sheng-Jie, Shao Yu, Chen Xu-Qiang. Anisotropic rock physics models for interpreting pore structures in carbonate reservoirs[J]. APPLIED GEOPHYSICS, 2016, 13(1): 166-178.
[11] Cao Cheng-Hao, Zhang Hong-Bing, Pan Yi-Xin, and Teng Xin-Bao. Relationship between the transition frequency of local fluid flow and the peak frequency of attenuation[J]. APPLIED GEOPHYSICS, 2016, 13(1): 156-165.
[12] Zhang Ru-Wei, Li Hong-Qi, Zhang Bao-Jin, Huang Han-Dong, Wen Peng-Fei. Detection of gas hydrate sediments using prestack seismic AVA inversion[J]. APPLIED GEOPHYSICS, 2015, 12(3): 453-464.
[13] Cui Li-Qin, Long Xin, Qin Jian-Min. A bellow pressure fiber optic sensor for static ice pressure measurements[J]. APPLIED GEOPHYSICS, 2015, 12(2): 255-262.
[14] LIN Kai, HE Zhen-Hua, XIONG Xiao-Jun, HE Xi-Lei, CAO Jun-Xing, XUE Ya-Juan. AVO forwarding modeling in two-phase media: multiconstrained matrix mineral modulus inversion[J]. APPLIED GEOPHYSICS, 2014, 11(4): 395-404.
[15] SUN Wen-Jie, LI Ning, WU Hong-Liang, WANG Ke-Wen, ZHANG Gong. Establishment and application of logging saturation interpretation equation in vuggy reservoirs[J]. APPLIED GEOPHYSICS, 2014, 11(3): 257-268.
Copyright © 2011 APPLIED GEOPHYSICS
Support by Beijing Magtech Co.ltd support@magtech.com.cn