Adsorption/Desorption of Tungsten from Ammonium Tungstate Pentahydrate using Anion Exchange Resins

doi:10.12972/ksmer.2014.51.3.448

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2014 Vol.51, Issue 3 Preview Page Next Page

Technical Report

Adsorption/Desorption of Tungsten from Ammonium Tungstate Pentahydrate using Anion Exchange Resins 저류층 유체 치환에 따른 Gassmann 방정식 기초 탄성파 탐사 암석 물리 모델 구성법 고찰: 박찬호·남명진
Jonghyuk Jeon, Younghun Kim, Jinyoung Lee, Choon Han

30 June 2014. pp. 448-467

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Abstract

Rock physics model (RPM) in recent time-lapse seismic survey has been widely used. RPM can be called optimal seismic attribute analysis method about the change in fluid saturation and movement. The most representative Gassmann’s equation among RPMs is commonly used until now. It is method for calculating the bulk modulus of the fluid saturated porous media and has the physically clear and simple advantage. Also, It can easily understood change in elastic wave velocity by dealing with a change in bulk modulus. In this paper, we introduce induction process of the Gassmann’s equation and the features as well as the method of calculating the basic parameters that make up the Gassmann’s equation. Further, this paper show the flow chart of construction method about actual RPM construction example and change in the elastic wave velocity as well as change in the elastic modulus in accordance with CO₂ saturation changes during CO₂ geological storage.

Keywords

Gassmann’s equation

Rock physics model

bulk modulus

elastic wave velocity

최근 시간-경과 탄성파 탐사자료 해석에 많이 적용되고 있는 암석 물리 모델(rock physics model; RPM)은 저류층 내 유체 포화도의 변화와 더불어 유체 이동이 탄성파 속성에 미치는 변화에 관한 최적의 분석 방법이라고 할 수 있다. 암석 물리 모델 중 가장 대표적인 Gassmann 방정식은 현재까지도 가장 널리 이용되고 있는 모델로써 탄성파 속도를 구성하는 매개변수인 유체 포화 다공질 매질의 부피 탄성률을 계산하는 방법이며, 물리적 의미가 간단 명료하다는 장점이 있다. 또한, 유체 치환 시 유체의 부피 탄성률이 가장 많이 변한다는 전제조건 하에 부피 탄성률의 변화를 다룸으로써 탄성파 속도의 변화를 손쉽고 파악할 수 있다. 이 논문에서는 Gassmann 방정식의 유도 과정 및 Gassmann 방정식을 구성하는 기초 매개변수의 계산법과 특징들을 소개한다. 이와 더불어Gassmann 방정식에 기초한 암석 물리 모델 구성법에 대한 모델 구성 흐름도와 실제 RPM 구성 예시를 들고 CO₂ 지중 저장 시 CO₂ 포화도 변화에 따른 탄성 계수의 변화와 탄성파 속도의 변화 양상을 보여주고자 한다.

키워드

Gassmann 방정식

암석 물리 모델

부피 탄성률

탄성파 속도

References

Batzle, M.L. and Wang, Z., 1992, “Seismic properties of pore fluids,” Geophysics, Vol. 57, No. 11, pp. 1396-1408.
Berryman, J.G., 1998, “Transversely isotropic poroelasticity arising from thin isotropic layers,” Mathematics of Multiscale Materials, K. M. Golden, G. R. Grimmett, R. D. James, G. W. Milton, and P. N. Sen (eds.), Springer, New York, pp. 37-50.
Berryman, J.G., 1999, “Origin of Gassmann’s equation,” Stanford Exploration Project, Report 102, October 25, pp. 187-192.
Biot, M.A. and Willis, D.G., 1957, “The elastic coefficients of the theory of consolidation,” J. of Applied Mechanics, Vol. 24, pp. 594-601.
Brie, A., Schlumberger, K.K., Pampuri, F., Marsala, A.F. and Meazza, O., 1995, “Shear sonic interpretation in gas-bearing sands,” Society of Petroleum Engineers, October 22-25, pp. 701-710.
Brown, R. and Korringa, J., 1975, “On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid,” Geophysics., Vol. 40, pp. 608-616.
Duffy, J. and Mindlin, R.D., 1957, “Stress-strain relations and vibrations of a granular medium,” J. of Applied Mechanics, Vol. 24, pp. 585-593.
Gassmann, F., 1951, “Über die elastizität poroser medien,” Veirteljahrsschrift der Naturforschenden Gesellschaft in Zürich, No. 96, pp. 1-23.
Geertsma, J. and Smit, D.C., 1961, “Some aspects of elastic wave propagation in fluid-saturated porous solids,” Geophysics, Vol. 26, No. 2, pp. 169-181.
Hashin, Z. and Shtrikman, S., 1963, “A variational approach to the theory of the elastic behavior of multiphase materials,” J. of the Mechanics and Physics of Solids, Vol. 11, No. 2, pp. 127-140.
Hill, R., 1952, “The elastic behavior of a crystalline aggregate,” Proceedings of the Physical Society, Vol. 65, pp. 349-354.
Kim, J.W., Nam, M.J. and Matsuoka, T., 2013, “Estimation of CO₂ saturation during both CO₂ drainage and imbibition processes based on both seismic velocity and electrical resistivity measurement,” Geophysical Journal International, Vol. 195, pp. 292-300.
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, Vol. 31, pp. 355-369.
Kumar, D., 2006, “A Tutorial on Gassmann Fluid Substitution: Formulation, Algorithm and Matlab Code,” Geohorizons, Vol. 11, pp. 4-12.
Mavko, G., 1980, “Velocity and attenuation in partially molten rocks,” J. of Geophysical Research, Vol. 85, pp. 5173-5189.
Mavko, G., Mukerji, T. and Dvorkin, J., 2009, The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media, 2^rd ED., Cambridge University Press, USA, pp. 1-503.
Mindlin, R.D., 1949, “Compliance of elastic bodies in contact,” J. of Applied Mechanics, Vol. 16, pp. 259-268.
Nur, A., Mavko, G., Dvorkin, J. and Gal, D., 1998, “Critical porosity: A Key to Relating Physical Properties to Porosity in Rocks,” The Leading Edge, Vol. 17, pp. 357-362.
Raymer, L.L., Hunt, E.R. and Gardner, J.S., 1980, “An improved sonic transit time-to-porosity transform,” Trans. Soc. Prof. Well Log Analysts, 21st Annual Logging Symposium, pp. 1-12.
Russell, B.H. and Smith, T., 2007, “The relationship between dry rock bulk modulus and porosity – An empirical study,” CREWES Research Report, Vol. 19, pp. 1-14.
Skempton, A.W., 1954, “The pore-pressure coefficients A and B,” Geotechnique, Vol. 4, No. 4, pp. 143-147.
Pickett, G.R., 1963, “Acoustic character logs and their applications in formation evaluation,” J. Petrol. Technol., Vol. 15, pp. 650-667.
Walpole, L.J., 1966, “On bounds for the overall elastic moduil of inhomogeneous systems,” J. Mech. Phys. Solids, Vol. 14, pp. 151-162.
Walton, K., 1987, “The effective elastic moduli of a random packing of spheres,” J. of the Mechanics and Physics of Solids, Vol. 35, No. 2, pp. 213-226.
Wood, A.B., 1955, A Textbook of Sound, McMillan Co., New York, USA.
Wyllie, M.R.J., Gregory, A.R. and Gardner, L.W., 1956, “Elastic Wave Velocities in Heterogeneous and Porous Media,” Geophysics, Vol. 21, No. 1, pp. 41-70.
Zhu, X. and McMechan, G.A., 1990, “Direct estimation of the bulk modulus of the frame in fluid saturated elastic medium by Biot theory,” 60^th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstract, pp. 787-790.

Information

Publisher :The Korean Society of Mineral and Energy Resources Engineers
Publisher(Ko) :한국자원공학회
Journal Title :Journal of the Korean Society of Mineral and Energy Resources Engineers
Journal Title(Ko) :한국자원공학회지
Volume : 51
No :3
Pages :448-467
DOI :https://doi.org/10.12972/ksmer.2014.51.3.448

[1] Batzle, M.L. and Wang, Z., 1992, “Seismic properties of pore fluids,” Geophysics, Vol. 57, No. 11, pp. 1396-1408.

[2] Berryman, J.G., 1998, “Transversely isotropic poroelasticity arising from thin isotropic layers,” Mathematics of Multiscale Materials, K. M. Golden, G. R. Grimmett, R. D. James, G. W. Milton, and P. N. Sen (eds.), Springer, New York, pp. 37-50.

[3] Berryman, J.G., 1999, “Origin of Gassmann’s equation,” Stanford Exploration Project, Report 102, October 25, pp. 187-192.

[4] Biot, M.A. and Willis, D.G., 1957, “The elastic coefficients of the theory of consolidation,” J. of Applied Mechanics, Vol. 24, pp. 594-601.

[5] Brie, A., Schlumberger, K.K., Pampuri, F., Marsala, A.F. and Meazza, O., 1995, “Shear sonic interpretation in gas-bearing sands,” Society of Petroleum Engineers, October 22-25, pp. 701-710.

[6] Brown, R. and Korringa, J., 1975, “On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid,” Geophysics., Vol. 40, pp. 608-616.

[7] Duffy, J. and Mindlin, R.D., 1957, “Stress-strain relations and vibrations of a granular medium,” J. of Applied Mechanics, Vol. 24, pp. 585-593.

[8] Gassmann, F., 1951, “Über die elastizität poroser medien,” Veirteljahrsschrift der Naturforschenden Gesellschaft in Zürich, No. 96, pp. 1-23.

[9] Geertsma, J. and Smit, D.C., 1961, “Some aspects of elastic wave propagation in fluid-saturated porous solids,” Geophysics, Vol. 26, No. 2, pp. 169-181.

[10] Hashin, Z. and Shtrikman, S., 1963, “A variational approach to the theory of the elastic behavior of multiphase materials,” J. of the Mechanics and Physics of Solids, Vol. 11, No. 2, pp. 127-140.

[11] Hill, R., 1952, “The elastic behavior of a crystalline aggregate,” Proceedings of the Physical Society, Vol. 65, pp. 349-354.

[12] Kim, J.W., Nam, M.J. and Matsuoka, T., 2013, “Estimation of CO₂ saturation during both CO₂ drainage and imbibition processes based on both seismic velocity and electrical resistivity measurement,” Geophysical Journal International, Vol. 195, pp. 292-300.

[13] 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, Vol. 31, pp. 355-369.

[14] Kumar, D., 2006, “A Tutorial on Gassmann Fluid Substitution: Formulation, Algorithm and Matlab Code,” Geohorizons, Vol. 11, pp. 4-12.

[15] Mavko, G., 1980, “Velocity and attenuation in partially molten rocks,” J. of Geophysical Research, Vol. 85, pp. 5173-5189.

[16] Mavko, G., Mukerji, T. and Dvorkin, J., 2009, The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media, 2^rd ED., Cambridge University Press, USA, pp. 1-503.

[17] Mindlin, R.D., 1949, “Compliance of elastic bodies in contact,” J. of Applied Mechanics, Vol. 16, pp. 259-268.

[18] Nur, A., Mavko, G., Dvorkin, J. and Gal, D., 1998, “Critical porosity: A Key to Relating Physical Properties to Porosity in Rocks,” The Leading Edge, Vol. 17, pp. 357-362.

[19] Raymer, L.L., Hunt, E.R. and Gardner, J.S., 1980, “An improved sonic transit time-to-porosity transform,” Trans. Soc. Prof. Well Log Analysts, 21st Annual Logging Symposium, pp. 1-12.

[20] Russell, B.H. and Smith, T., 2007, “The relationship between dry rock bulk modulus and porosity – An empirical study,” CREWES Research Report, Vol. 19, pp. 1-14.

[21] Skempton, A.W., 1954, “The pore-pressure coefficients A and B,” Geotechnique, Vol. 4, No. 4, pp. 143-147.

[22] Pickett, G.R., 1963, “Acoustic character logs and their applications in formation evaluation,” J. Petrol. Technol., Vol. 15, pp. 650-667.

[23] Walpole, L.J., 1966, “On bounds for the overall elastic moduil of inhomogeneous systems,” J. Mech. Phys. Solids, Vol. 14, pp. 151-162.

[24] Walton, K., 1987, “The effective elastic moduli of a random packing of spheres,” J. of the Mechanics and Physics of Solids, Vol. 35, No. 2, pp. 213-226.

[25] Wood, A.B., 1955, A Textbook of Sound, McMillan Co., New York, USA.

[26] Wyllie, M.R.J., Gregory, A.R. and Gardner, L.W., 1956, “Elastic Wave Velocities in Heterogeneous and Porous Media,” Geophysics, Vol. 21, No. 1, pp. 41-70.

[27] Zhu, X. and McMechan, G.A., 1990, “Direct estimation of the bulk modulus of the frame in fluid saturated elastic medium by Biot theory,” 60^th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstract, pp. 787-790.

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