Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Subsurface Fluid Flow and Imaging
  • Cited by 25
Publisher:
Cambridge University Press
Online publication date:
July 2016
Print publication year:
2016
Online ISBN:
9781139018876
DOI:
https://doi.org/10.1017/CBO9781139018876
Subjects:
Earth and Environmental Sciences, Solid Earth Geophysics, Hydrology, Hydrogeology and Water Resources
Information

Book description

This book introduces methodologies for subsurface imaging based upon asymptotic and trajectory-based methods for modeling fluid flow, transport and deformation. It describes trajectory-based imaging from its mathematical formulation, through the construction and solution of the imaging equations, to the assessment of the accuracy and resolution associated with the image. Unique in its approach, it provides a unified framework for the complete spectrum of physical phenomena from wave-like hyperbolic problems to diffusive parabolic problems and non-linear problems of mixed character. The practical aspects of imaging, particularly efficient and robust methods for updating high resolution geologic models using fluid flow, transport and geophysical data, are emphasized throughout the book. Complete with online software applications and examples that enable readers to gain hands-on experience, this volume is an invaluable resource for graduate-level courses, as well as for academic researchers and industry practitioners in the fields of geoscience, hydrology, and petroleum and environmental engineering.

Reviews

'The presentation is really innovative and allows [readers] to get a unified view on the modelling of different physical processes from wave-like hyperbolic problems, to diffusive parabolic problems and non-linear coupled problems of mixed character. The exposed imaging techniques present the advantage of being well adapted for further determining accuracy and spatial resolution of the simulated results. The book is well written, many clear figures are used … The references and index lists are very useful for the interested reader.'

A. Dassargues Source: Mathematical Geosciences

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References
References
Abbaszadeh, D. M., and Brigham, W. E. 1984. Analysis of well-to-well tracer flow to determine reservoir layering. Journal of Petroleum Technology, 36, 1753–1762.
Abramowitz, M., and Stegun, I. A. 1972. Handbook of Mathematical Functions. NewYork: Dover Publications Inc.
Ajo-Franklin, J., Daley, T., Butler-Veytia, B., Peterson, J., Wu, Y., Kelly, B., and Hubbard, S. 2011. SEG-2011-3727. Multi-level continuous active source seismic monitoring (ML-CASSM): Mapping shallow hydrofracture evolution at a TCE contaminated site. Society of Exploration Geophysics Annual Meeting. San Antonio, Texas.
Aki, K., and Richards, P. G. 1980a. Quantitative Seismology. San Francisco:W. H. Freeman and Sons.
Aki, K., and Richards, P. G. 1980b. Quantitative Seismology. San Francisco:W. H. Freeman and Company.
Anile, A. M., Hunter, J. K., Pantano, P., and Russo, G. 1993. Ray Methods for Nonlinear Waves in Fluids and Plasmas. Essex: Longman Scientific and Technical.
Annable, M., Rao, P., Hatfield, K., Graham, W., Wood, A., and Enfield, C. 1998. Partitioning tracers for measuring residual NAPL: Field-scale test results. Journal of Environmental Engineering, 124, 498–503.
Aster, R. C., Borchers, B., and Thurber, C. 2013. Parameter Estimation and Inverse Problems. San Diego: Academic Press.
Auriault, J. L. 1980. Dynamic behavior of a porous medium saturated by a Newtonian fluid. International Journal of Engineering Science, 18, 775–785.
Auriault, J. L., Moyne, C., and Amaral Souto, H. P. 2010. On the asymmetry of the dispersion tensor in porous media. Transport in Porous Media, 85, 771–783.
Aziz, K., and Settari, A. 1979. Petroleum Reservoir Simulation. Amsterdam: Elsevier.
Backus, G. E., and Mulcahy, M. 1976. Moment tensors and other phenomenological descriptions of seismic sources I- Continuous displacements. Geophysical Journal of the Royal Astronomical Society, 46, 341–371.
Barenblatt, G. I. 1979. Similarity, Self-Similarity, and Intermediate Asymptotics. NewYork: Consultants Bureau.
Bear, J. 1961. On the tensor form of dispersion in porous media. Journal of Geophysical Research, 66, 1185–1197.
Bear, J. 1972. Dynamics of Fluids in Porous Media. New York: Dover Publications.
Bear, J., Corapcioglu, M. Y., and Balakrishna, J. 1984. Modeling of centrifugal filtration in unsaturated deformable porous media. Advances in Water Resources, 7, 150–167.
Behrens, R., Condon, P., Haworth, W., Bergeron, M., Wang, Z., and Ecker, C. 2002. 4D seismic monitoring of water influx at bay marchand: The practical use of 4D in an imperfect world. SPE Reservoir Evaluation and Engineering, 5, 410–420.
Bell, J. B., Trangenstein, J. A., and Shubin, G. R. 1986. Conservation laws of mixed type describing three-phase flow in porous media. SIAM Journal on Applied Mathematics, 46, 1000–1017.
Belytschko, T., Liu, W. K., Moran, B., and Elkhodary, K. I. 2014. Nonlinear Finite Elements for Continua and Structures. West Sussex: Wiley and Sons.
Benamou, J. D. 1996. Big ray tracing: Multivalued travel time field computation using viscosity solutions of the eikonal equation. Journal of Computational Physics, 128, 463–474.
Bender, C.M., and Orszag, S. A. 1978. Advanced Mathematical Methods for Scientists and Engineers. New York: McGraw-Hill Book Company.
Berryman, J. G. 1986. Effective medium approximation for elastic constants of porous solids with microscopic heterogeneity. Journal of Applied Physics, 59, 1136–1140.
Berryman, J. G. 1995. Mixture theory for rock properties. In: Ahrens, T. J. (ed), Rock Physics and Phase Relations. Washington, D. C.: American Geophysical Union.
Berryman, J. G., and Milton, G. W. 1991. Exact results for generalized Gassmann's equations in composite porous media with two constituents. Geophysics, 56, 1950–1960.
Berryman, J. G., Thigpen, L., and Chin, R. C. Y. 1988. Bulk elastic wave propagation in partially saturated porous solids. Journal of the Acoustical Society of America, 84, 360–373.
Bertrand, A., Folstad, P. G., Lyngnes, B., Buizard, S., Hoeber, H., Pham, N., PS, De, and Grandiierrepont, . 2014. Ekofisk life-of-field seismic: Operations and 4D processing. The Leading Edge, 33, 142–148.
Biot, M. A. 1941. General theory of three-dimensional consolidation. Journal of Applied Physics, 12, 155–164.
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, 168–178.
Biot, M. A. 1956b. Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher-frequency range. Journal of the Acoustical Society of America, 28, 179–1191.
Biot, M. A. 1962a. Generalized theory of acoustic propagation in porous dissipative media. Journal of the Acoustical Society of America, 34, 1254–1264.
Biot, M. A. 1962b. Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 33, 1482–1498.
Bishop, A. W., and Blight, G. E. 1963. Some aspects of effective stress in saturated and partially saturated soils. Geotechnique, 13, 177–197.
Bracewell, R. N. 2000. The Fourier Transform and Its Applications. Boston: McGraw-Hill Book Company.
Bratvedt, F., Gimse, T., and Tegnander, C. 1996. Streamline computations for porous media flow including gravity. Transport in Porous Media, 25, 63–78.
Brauchler, R., Hu, R., Vogt, T., Al-Halbouni, D., Heinrichs, T., Ptak, T., and Sauter, M. 2010. Cross-well slug interference tests: An effective characterization method for resolving aquifer heterogeneity. Journal of Hydrology, 384, 33–45.
Bruining, H., Darwish, M., and Rijnks, A. 2012. Computation of the longitudinal and transverse dispersion coefficients in an adsorbing porous medium using homogenization. Transport in Porous Media, 91, 833–859.
Buckley, S. E., and Leverett, M. C. 1942. Mechanism of fluid displacement in sands. Transactions of the American Society of Mechanical Engineers, 146, 107–116.
Burridge, R., and Keller, J. B. 1981. Poroelasticity equations derived from microstructure. Journal of the Acoustical Society of America, 70, 1140–1146.
Butler, J. J., Garnett, E., and Healey, J. M. 2003. Analysis of slug test in formations of high hydraulic conductivity. Groundwater, 41, 620–630.
Calvert, R. 2005. Insights and methods for 4D reservoir monitoring and characterization. Distinguished Instructor Short Course 8: EAGE/SEG.
Carbonell, H. B. G., and Whitaker, S. 1983. Dispersion in pulsed systems - II Theoretical developments for passive dispersion in porous media. Chemical Engineering Science, 38, 1795–1802.
Carcione, J. M., Morency, C., and Santos, J. E. 2010. Computational poroelasticity – A review. Geophysics, 75, A229–A243.
Chapman, C. H. 2004. Fundamentals of Seismic Wave Propagation. Cambridge: Cambridge University Press.
Charlaix, E., Kushnick, A. P., and Stokes, J. P. 1988. Experimental study of dynamic permeability in porous media. Physical Review Letters, 61, 1595–1598.
Chen, Z. X. 1988. Some invariant solutions to two-phase fluid displacement problems including capillary effects. SPE Reservoir Engineering, 30, 691–700.
Cheng, H., Datta-Gupta, A., and He, Z. 2005. A comparison of travel-time and amplitude inversion for scale production data integration into geologic models: Sensitivity, nonlinearity, and practical implications. SPE Journal, 10, 75–90.
Chorin, A. J., and Marsden, J. E. 1993. A Mathematical Introduction to Fluid Mechanics. Berlin: Springer-Verlag.
Cleary, R. W., and Ungs, M. J. 1978. Groundwater pollution and hydrology, mathematical models, and computer programs. Water Resources Program Report, 78, 1–34.
Cole, J. D. 1951. On a quasilinear parabolic equation occurring in aerodynamics. Quarterly of Applied Mathematics, 9, 225–236.
Cole, J. D., and Kevorkian, J. 1963. Uniformly valid asymptotic approximations for certain nonlinear differential equations. Pages 113–120 of: Nonlinear Differential Equations and Nonlinear Mechanics. New York: Academic Press.
Courant, R., and Friedrichs, K. O. 1948. Supersonic Flow and Shock Waves. New York: Interscience Publishers.
Courant, R., and Hilbert, D. 1962a. Methods of Mathematical Physics. New York: John Wiley and Sons.
Courant, R., and Hilbert, D. 1962b. Methods of Mathematical Physics. New York: Interscience.
Coussy, O. 2010. Mechanics and Physics of Porous Solids. Chichester: John Wiley and Sons.
Crandall, M. G., and Lions, P. 1983. Viscosity solutions of Hamilton-Jacobi equations. Transactions of the American Mathematical Society, 277, 1–43.
Crandall, M. G., and Majda, A. 1980. Monotone difference approximations for scalar conservation laws. Mathematics of Computation, 34, 1–21.
Crandall, M. G., Evans, L. C., and Lions, P. 1984. Some properties of viscosity solutions of Hamilton-Jacobi equations. Transactions of the American Mathematical Society, 282, 487–502.
Crane, M. J., and Blunt, M. J. 1999. Streamline-based simulation of solute transport. Water Resources Research, 35, 3061–3078.
Crank, J. 1975. The Mathematics of Diffusion. London: Oxford University Press.
Dafermos, C. M. 1972. Polygonal approximation of solutions of the initial value problem for a conservation law. Journal of Mathematical Analysis and Applications, 38, 33–41.
Dafermos, C. M. 2000. Hyperbolic Conservation Laws in Continuum Physics. New York: Springer.
Dagan, G. 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resources Research, 18, 835–848.
Daley, T. M., Ajo-Franklin, J. B., and Doughty, C. 2011. Constraining the reservoir model of an injected CO2 plume with crosswell CASSM at the Frio-II brine pilot. International Journal of Greenhouse Gas Control, 5, 1022–1030.
Datta-Gupta, A., and King, M. J. 1995. A semianalytic approach to tracer flow modeling in heterogeneous permeable media. Advances in Water Resources, 18, 9–24.
Datta-Gupta, A., and King, M. J. 2007. Streamline Simulation: Theory and Practice. Richardson, Texas: Society of Petroleum Engineers.
Datta-Gupta, A., Yoon, S., Vasco, D. W., and Pope, G. A. 2002. Inverse modeling of partitioning interwell tracer tests: A streamline approach. Water Resources Research, 38(6), 1–15.
Davis, H. F. 1967. Introduction to Vector Analysis. Boston, Massachuetts: Allyn and Bacon.
de Boer, R. 2000. Theory of Porous Media. Berlin: Springer.
de Josselin de Jong, G. 1958. Longitudinal and transverse diffusion in granular deposits. Transactions of the American Geophysical Union, 39, 67–74.
de Marsily, G. 1986. Quantitative Hydrogeology. San Diego: Academic Press.
Debnath, L. 2005. Nonlinear Partial Differential Equations for Scientists and Engineers. Boston: Birkhauser.
Deschamps, T., and Chen, L. D. 2001. Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Medical Image Analysis, 5, 281–299.
Dingle, R. B. 1973. Asymptotic Expansions: Their Derivation and Interpretation. London: Academic Press.
Dorny, C. N. 1983. A Vector Space Approach toModels and Optimization. Malabar, Florida: Robert E. Krieger Publishing Company.
Drumheller, D. S. 1978. Theoretical treatment of a porous solid using mixture theory. International Journal of Solids and Structures, 14, 441–456.
Drumheller, D. S. 1998. Introduction to Wave Propagation in Nonlinear Fluids and Solids. Cambridge: Cambridge University Press.
Dutta, N. C., and Ode, H. 1979a. Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model) – Part I: Biot theory. Geophysics, 44, 1777–1788.
Dutta, N. C., and Ode, H. 1979b. Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model) – Part II: Results. Geophysics, 44, 789–805.
Dvorkin, J., Mavko, G., and Nur, A. 1995. Squirt flow in fully saturated rocks. Geophysics, 60, 97–107.
Erdélyi, A. 1956. Asymptotic Expansions. New York: Dover Publications Inc.
Euler, L. 1754. De seriebus divergentibus. Novi Commentarii Acad. Sci. Petropolitanae, 5, 205–237.
Falls, A. H., and Schulte, W. M. 1992. Features of three component, three phase displacement in porous media. SPE Reservoir Engineering, 7, 426–432.
Faucette, W. J. 1996. A geometric interpretation of the solution of the general quartic polynomial:. The American Mathematical Monthly, 103, 51–57.
Ferretti, A. 2014. Satellite InSAR Data: Reservoir Monitoring from Space. Netherlands: European Association of Geoscientists and Engineers.
Fick, A. 1855. Ueber Diffusion. Annalen der Physik und Chemie von J. C. Pogendorff, 94, 59–86.
Fletcher, R. 2000. Practical Methods of Optimization. Cornwall: John Wiley and Sons.
Fokas, A. S., and Yortsos, Y. C. 1982. On the exactly solvable equation occurring in two-phase flow in porous media. SIAM J. Appl. Math, 42, 318–332.
Formal, S., and Sethian, J. A. 2002. Fast-phase space computation of multiple arrivals. Proceedings of the National Academy of Sciences, 99, 7329–7334.
Fourier, J. B. 1822. Theorie Analytique de la Chaleur. New York: Dover Publications, English translation by A., Freeman (1955).
Frenkel, J. 1944. On the theory of seismic and seismoelectric phenomena in a moist soil. Journal of Physics, 8(September), 879–887.
Fujita, Y., Datta-Gupta, A., and King, M. J. 2015. A comprehensive reservoir simulator for unconventional reservoirs based on the Fast Marching Method and diffusive time of flight. SPE 173269 In: Proceedings of Society of Petroleum Engineers Reservoir Simulation Symposium. Society of Petroleum Engineers, Houston, Texas. SPE Journal 2016. http://dx.doi.org/10.2118/173269-PA.
Fung, Y. C. 1969. A First Course in Continuum Mechanics. New Jersy: Prentice-Hall.
Gardner, C. S., and Morikawa, G. K. 1960. Similarity in the asymptotic behavior of collision-free hydromagnetic waves and water waves. Courant Institute of Mathematical Sciences, 9082, 1–30.
Garg, S. K. 1971. Wave propagation effects in a fluid-saturated porous solid. Journal of Geophysical Research, 76, 7947–7962.
Garg, S. K., and Nayfeh, A. H. 1986. Compressional wave propagation in liquid and/or gas saturated elastic porous media. Journal of Applied Physics, 60, 3045–3055.
Gassmann, F. 1951a. Elastic waves through a packing of spheres. Geophysics, 16, 673–685.
Gassmann, F. 1951b. Ueber die elastizitat poroser medien. Viertel. Naturforsch. Ges. Zurich, 96, 1–23.
Gelhar, L. W., and Axness, C. L. 1983. Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resources Research, 19, 161–180.
Gelhar, L. W., Gutjahr, A. L., and Naff, R. L. 1979. Stochastic analysis of macrodispersion in a stratified aquifer. Water Resources Research, 15, 1387–1397.
Gautier, Y., Noetinger, B., and Roggero, F. 2001. History matching using a streamline-based approach and exact sensitivity coefficients. SPE 716626 In: Proceedings of the Society of Petroleum Engineers Annual Technical Conference and Exhibition, New Orleans, Louisiana.
Gibson-Poole, C. M., and Raikes, S. 2010. Enhanced understanding of CO2 storage at Krechba from 3D seismic. Pages 10–13 of: Proceedings of the 9th Annual Conference on Carbon Capture and Sequestration. Pittsburgh, May, 2010: Pennsylvania.
Gill, P. E., Murray, W., and Wright, M. H. 1982. Practical Optimization. New York: Academic Press.
Godunov, S. K. 1959. Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Matematicheskii Sbornik, 47, 271–306.
Goldstein, H. 1950. Classical Mechanics. Reading, MA: Addison-Wesley.
Golub, G. H., and Van Loan, C. F. 1989. Matrix Computations. Baltimore: The John Hopkins University Press.
Gradshteyn, I. S., and Ryzhik, I. M. 1965. Tables of Integrals, Series, and Products. New York: Academic Press.
Green, A. E., and Naghdi, P. M. 1965. A dynamical theory of interacting continua. International Journal of Engineering Science, 3, 231–341.
Guzman, R. E., and Fayers, F. J. 1997. Solutions to the three-phase Buckley-Leverett problem. SPE Journal, 2, 301–311.
Hanyga, A., and Seredynska, M. 1999. Some effects of the memory kernel singularity on wave propagation and inversion in poroelastic media Forward problems – I. Geophysical Journal International, 137, 319–335.
Hart, R. D. and St. John, C. M. 1986. Formulation of a fully coupled thermal-mechanicalfluid flow model for nonlinear geologic systems. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 23(3), 213–224.
Harten, A. 1983. High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics, 49, 357–393.
Harten, A., and Osher, S. 1987. Uniformly high-order accurate nonoscillatory schemes I. SIAM Journal on Numerical Analysis, 24, 279–309.
He, Z., Yoon, S., Datta-Gupta, A. 2002. Streamline-based production data integration under changing field conditions. SPE Journal, 7(4), 423–436.
Helfferich, F. G. 1981. Theory of multicomponent, multiphase displacement in porous media. SPE Journal, 21, 51–62.
Hohl, D., Jimenez, E., and Datta-Gupta, A. 2006. Field experiences with history matching an offshore turbidite reservoir using inverse modeling. SPE 101983 In: Proceedings of the SPE Annual Technical Conference and Exhibition. San Antonio, Texas.
Holden, H., and Risebro, N. H. 2002. Front Tracking for Hyperbolic Conservation Laws. New York: Springer-Verlag.
Holden, H., Holden, L., and Hoegh-Krohn, R. 1988. A numerical method for first order nonlinear scalar conservation laws in one-dimension. Computers and Mathematics with Applications, 15, 595–602.
Hopf, E. 1950. The partial differential equatio. Communications on Pure and Applied Mathematics, 3, 201–230.
Huang, X., Meister, L., and Workman, R. 1998. Improving production history matching using time-lapse seismic data. The Leading Edge, 17, 1430–1433.
Hubbert, M. K. 1940. The theory of ground-water motion. The Journal of Geology, 48(8), 785–944.
Jaeger, J. C., Cook, N. G. W., and Zimmerman, R. W. 2007. Fundamentals of Rock Mechanics. Oxford: Blackwell Publishing.
Javandel, I., Doughty, C., and Tsang, C. F. 1984. Groundwater Transport: Handbook of Models. Washington, D. C.: American Geophysical Union Monograph.
Jeffrey, A., and Kawahara, T. 1982. Asymptotic Methods in Nonlinear Wave Theory. Boston: Pitman Advanced Publishing Program.
Jin, M., Delshad, M., Varadrajan, D., McKinney, D., Pope, G. A., Sepehrnoori, K., Tilburg, C. E., and Jackson, R. E. 1995. Estimation and remediation performance assessment of subsurface nonaqueous phase liquids. Water Resources Research, 31, 1201–1211.
Johnson, D. L. 2001. Theory of frequency dependent acoustics in patchy-saturated porous media. Journal of the Acoustical Society of America, 110, 682–694.
Johnson, D. L., Koplik, J., and Dashen, R. 1987. Theory of dynamic permeability and tortuosity in fluid-saturated porous media. Journal of Fluid Mechanics, 176, 379–402.
Juanes, R., and Patzek, T. W. 2004. Analytical solution to the Riemann problem of threephase flow in porous media. Transport in Porous Media, 55, 47–70.
Kam, D., and Datta-Gupta, A. 2016. Streamline-based Transport Tomography With Distributed Water Arrival Times, SPE Reservoir Evaluation and Engineering, http://dx.doi.org/10.2118/169105-PA.
Karasaki, K., Long, J., and Witherspoon, P. 1988. Analytical models of slug tests. Water Resources Research, 24, 115–126.
Karpman, V. I. 1975. Non-Linear Waves in Dispersive Media. Oxford: Pergamon Press.
Keller, J. B. 1954. Geometrical acoustics I. The theory of weak shock waves. Journal of Applied Physics, 25, 938–947.
Keller, J. B. 1977. Effective behavior of heterogeneous media. Pages 213–224 of: Landman, U. (ed), Statistical Mechanics and Statistical Methods in Theory and Applications. New York. 23: Plenum.
Kevorkian, J., and Cole, J. D. 1996. Multiple Scale and Singular Perturbation Methods. New York: Springer-Verlag.
Kim, J. U., Datta-Gupta, A., Jimenez, E., and Hohl, D. 2010. A dual scale approach to production data integration into high resolution geologic models. Journal of Petroleum Science and Engineering, 71, 147–159.
King, M. J., and Datta-Gupta, A. 1998. Streamline simulation: A current perspective. In Situ, 22, 91–140.
Kline, M., and Kay, I. W. 1965. Electromagnetics Theory and Geometrical Optics. New York: Interscience Publishers.
Koch, D. L., and Brady, J. F. 1987. The symmetry properties of the effective diffusivity tensor in anisotropic porous media. Physics of Fluids, 30, 642–650.
Kosten, C. W., and Zwikker, C. 1941. Extended theory of the absorption of sound by compressible wall-coverings. Physica, 8, 968–978.
Kravtsov, Y. A., and Orlov, Y. I. 1990. Geometrical Optics of Inhomogeneous Media. Berlin: Springer-Verlag.
Lake, L. W. 1989. Enhanced Oil Recovery. Englewook: Prentice Hall.
Lanczos, C. 1962. The Variational Principles of Mechanics. New York: Dover Publications.
Landro, M. 2001. Discrimination between pressure and fluid saturation changes from timelapse seismic data. Geophysics, 66, 836–844.
Lawson, C. L., and Hanson, R. J. 1974. Solving Least Squares Problems. Englewood Cliffs, New Jersey: Prentice-Hall.
Le Veque, R. J. 1990. Numerical Methods for Conservation Laws. Basel: Birkhauser- Verlag.
Lee, W. J. 1982. Well Testing. Richardson, Texas: Society of Petroleum Engineers.
Levy, T. 1979. Propagation of waves in a fluid-saturated porous elastic solid. International Journal of Engineering Science, 17, 1005–1014.
Lie, K. a., and Juanes, R. 2005. A front-tracking method for the simulation of three-phase flow in porous media. Computational Geosciences, 9, 29–59.
Lighthill, M. J. 1958. The Fourier Transform and Generalized Functions. Cambridge: Cambridge Tracts on Mechanics and Applied Mathematics.
Lindstedt, A. 1883. Beitrag zur Integration der Differentialgleichungen der Storungsteorie. Mémoires de l'Académie impériale des sciences de St. Pétersbourg, 31(4).
Liu, Y., and Si, B. C. 2008. Analytic modeling of one-dimensional diffusion in layered systems with position-dependent diffusion coefficients. Advances in Water Resources, 31, 251–268.
Lo, W. C., Sposito, G., and Majer, E. 2002. Immiscible two-phase fluid flows in deformable porous media. Advances in Water Resources, 25, 1105–1117.
Logan, J. D. 2008. An Introduction to Nonlinear Partial Differential Equations. Hoboken: John Wiley and Sons.
Ludwig, J. B. 1966. Uniform asymptotic expansions at a caustic. Communications in Pure and Applied Mathematics, 19, 215–250.
Luenberger, D. G. 1973. Introduction to Linear and Nonlinear Programming. Reading Massachusetts: Addison-Wesley.
Luke, J. C. 1966. A perturbation method for nonlinear dispersive wave problems. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 292(1430), 403–412.
Luneburg, R. K. 1966. Mathematical Theory of Optics. Berkeley: University of California Press.
Ma, X., Al-Harbi, M., Datta-Gupta, A., and Efendiev, Y. 2008. An efficient two-stage sampling method for uncertainty quantification in history matching geological models. SPE Journal, 3(1), 77–87.
MacBeth, C., and Al-Maskeri, Y. 2006. Extraction of permeability from time-lapse seismic data. Geophysical Prospecting, 54, 333–349.
MacNeal, R. H. 1953. An asymmetric finite difference network. Quarterly of Applied Mathematics, 2, 295–310.
Marsden, J. E., and Tromba, A. J. 1976. Vector Calculus. San Francisco: W. H. Freeman and Company.
Maslov, V. P., and Omel'yanov, G. A. 2001. Geometric Asymptotics for Nonlinear PDE. I. Providence: American Mathematical Society.
Masson, Y. J., and Pride, S. R. 2007. Poroelastic finite difference modeling of seismic attenuation and dispersion due to mesoscopic-scale heterogeneity. Journal of Geophysical Research, 112, 1–17.
Masson, Y. J., and Pride, S. R. 2010. Finite-difference modeling of Biot's poroelastic equations across all frequencies. Geophysics, 75, N33–N41.
Masson, Y. J., and Pride, S. R. 2011. Seismic attenuation due to patchy saturation. Journal of Geophysical Research, 116, 1–17.
Masson, Y. J., Pride, S. R., and Kihei, K. T. 2006. Finite difference modeling of Biot's poroelastic equations at seismic frequencies. Journal of Geophysical Research, 111, 1–13.
Mavko, G., and Nur, A. 1975. Melt squirt in the asthenosphere. Journal of Geophysical Research, 80, 1444–1448.
Mavko, G., and Nur, A. 1979. Wave attenuation in partially saturated rocks. Geophysics, 44, 161–178.
Mavko, G., Mukerji, T., and Dvorkin, J. 1998. The Rock Physics Handbook: Tools for Seismic Analysis in Porous Media. Cambridge: Cambridge University Press.
McWhorter, D. B. 1971. Infiltration affected by flow of air. Hydrol. Paper 49. Colorado State University, Fort Collins.
McWhorter, D. B., and Sunada, D. K. 1990. Exact integral solution for two-phase flow. Water Resources Research, 26(3), 399–413.
Menke, W. 1989. Geophysical Data Analysis: Discrete Inverse Theory. San Diego: Academic Press.
Miller, W. 1977. Symmetry and Separation of Variables. Reading: Addison-Wesley.
Miura, R. M., and Kruskal, M. D. 1974. Application of a nonlinear WKB method to the Korteweg-DeVries equation. SIAM Journal on Applied Mathematics, 26(2), 376–395.
Morency, C., Yang, L., and Tromp, J. 2011. Acoustic, elastic and poroelastic simulations of CO2 sequestration crosswell monitoring based on spectral-element and adjount methods. Geophysical Journal International, 185, 955–966.
Morland, L. W. 1972. A simple constitutive theory for a fluid-saturated porous solid. Journal of Geophysical Research, 77, 890–900.
Müller, T. M., Gurevich, B., and Lebedev, M. 2010. Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks – A review. Geophysics, 75, 147–75.
Narasimhan, T. N., and Witherspoon, P. A. 1976. An integrated finite difference method for analyzing fluid flow in porous media. Water Resources Research, 12, 57–64.
Needham, T. 2000. Visual Complex Analysis. Oxford: Oxford University Press.
Nickalls, R.W. D. 2009. The quartic equation: Invariants and Euler's solution revealed. The Mathematical Gazette, 93, 66–75.
Nikolaevskii, V. N. 1959. Konvektivnaya diffusiya v poristykh sredakh. Prikladnaya Matematika i Mekhanika, 23, 1042–1050.
Noble, B., and Daniel, J. W. 1977. Applied Linear Algebra. Englewood Cliffs: Prentice- Hall.
Nocedal, J., and Wright, S. J. 2006. Numerical Optimization. New York: Springer.
Nolet, G. 1987. Seismic wave propagation and seismic tomography. Pages 1–23 of: Nolet, G. (ed), Seismic Tomography. Dordrecht: D. Reidel.
Norris, A. N. 1993. Low frequency dispersion and attenuation in partially saturated rocks. Journal of the Acoustical Society of America, 94, 359–370.
O'Connell, R. J., and Budiansky, B. 1977. Viscoelastic properties of fluid-saturated cracked solids. Journal of Geophysical Research, 82, 5719–5735.
Oleninik, O. A. 1957. On the uniqueness of the generalized solution of the Cauchy problem for a non-linear system of equations occurring in mechanics. Uspekhi Matematicheskikh Nauk, 78, 169–176.
Osher, S., and Fedkiw, R. 2003. Level Set Methods and Dynamic Implicit Surfaces. New York: Springer.
Paige, C. C., and Saunders, M. A. 1982. LSQR: An algorithm for sparse linear equations and sparse linear systems. ACM Transactions on Mathematical Software, 8, 195–209.
Panday, S., and Corapcioglu, M. Y. 1989. Reservoir transport equations by compositional approach. Transport in Porous Media, 4, 369–393.
Panton, R. L. 2005. Incompressible Flow. Hoboken, New Jersey: Wiley.
Parker, R. L. 1994. Geophysical Inverse Theory. Princeton: Princeton University Press.
Peaceman, D. W. 1977. Fundamentals of Numerical Reservoir Simulation. Amsterdam: Elsevier Scientific Publishing.
Plyushchchenkov, B. D., and Turchaninov, V. 2000. Acoustic logging modeling by refined Biot's equations. International Journal of Modern Physics C, 12, 305–396.
Poincaré, H. 1886. Acta Math, 8, 295–344.
Pollock, D. W. 1988. Semianalytical computation of path lines for finite-difference models. Groundwater, 26, 743–750.
Pope, G. A. 1980. The application of fractional flow theory to enhanced oil recovery. SPE. Journal, 20, 191–205.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. 1992. Numerical Recipes. Cambridge: Cambridge University Press.
Pride, S. R. 2005. Relationships between seismic and hydrological properties. Pages 253–291 of: Rubin, Y., and Hubbard, S. S. (eds), Hydrogeophysics. New York: Springer.
Pride, S. R., and Berryman, J. G. 1998. Connecting theory to experiment in poroelasticity. Journal of the Mechanics and Physics of Solids, 46, 719–747.
Pride, S. R., and Berryman, J. G. 2003a. Linear dynamics of double-porosity and dualpermeability materials. I. Governing equations and acoustic attenuation. Phyical Review E, 68, 036603–1–10.
Pride, S. R., and Berryman, J. G. 2003b. Linear dynamics of double-porosity and dualpermeability materials. II. Fluid transport equations. Phyical Review E, 68, 036604–1–10.
Pride, S. R., Berryman, J. G., and Harris, J. M. 2004. Seismic attenuation due to waveinduced flow. Journal of Geophysical Research, 109, 1–19.
Pride, S. R., Gangi, A. F., and Morgan, F. D. 1992. Deriving the equations of motion for isotropic motion. Journal of the Acoustical Society of America, 92, 3278–3290.
Pride, S. R., Morgan, F. D., and Gangi, A. F. 1993. Drag forces of porous-medium acoustics. Physical Review B, 47, 4964–4978.
Pruess, K., and Narasimhan, T. N. 1982. On fluid reserves and the production of superheated steam from fractured, vapor-dominated geothermal reservoirs. Journal of Geophysical Research, 87, 9329–9339.
Pruess, K., Oldenburg, C., and Moridis, G. 1999. TOUGH2 User's Guide, Version 2.0. Tech. rept. 43134. Lawrence Berkeley National Laboratory. LBNL Report.
Rey, A., Bhark, E., Gao, K., Datta-Gupta, A., and Gibson, R. 2012. Streamline-based integration of time-lapse seismic and production data into petroleum reservoir models. Geophysics, 77, M73–M87.
Rice, J. R., and Cleary, M. P. 1976. Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Reviews of Geophysics and Space Physics, 14, 227–241.
Roach, G. F. 1970. Green's Functions: Introductory Theory with Applications. New York: Van Nostrand Reinhold Company.
Rucci, A., Vasco, D. W., and Novali, F. 2010. Fluid pressure arrival time tomography: Estimation and assessment in the presence of inequality constraints, with an application to production at the Krechba field, Algeria. Geophysics, 75, O39–O55.
Rucci, A., Vasco, D. W., and Novali, F. 2013. Monitoring the geologic storage of carbon dioxide using multicomponent SAR interferometry. Geophysical Journal International, 193, 197–208.
Saad, Y. 2003. Iterative Methods for Sparse Linear Systems. Philadelphia: Society for Industrial and Applied Mathematics.
Sachdev, P. L. 2000. Self-Similarity and Beyond: Exact Solutions of Nonlinear Problems. Boca Raton: Chapman and Hall.
Saffman, P. G. 1959. A theory of dispersion in porous media. Journal of Fluid Mechanics, 6, 321–349.
Santos, J. E., Corbero, J. M., and Douglas, J. 1990. Static and dynamic behavior of a porous solid saturated by a two-phase fluid. Journal of the Acoustical Society of America, 87, 1428–1438.
Scheidegger, A. E. 1954. Statistical hydrodynamics in porous media. Journal of Applied Physics, 25, 994–1001.
Scheidegger, A. E. 1957. On the theory of flow of miscible phases in porous media. Compte rendu d'Assemblée Générale Extraordinaire. Toronto, International Association of Scientific Hydrology, 2, 236–242.
Scheidegger, A. E. 1961. General theory of dispersion in porous media. Journal of Geophysical Research, 66, 3273–3278.
Schey, H. M. 1973. Div, Grad, Curl, and All That. New York: W. W. Norton and Company.
Schmid, K. S., Geiger, S., and Sorbie, K. S. 2011. Semianalytical solutions for cocurrent and countercurrent imbibition, and dispersion of solutes in immiscible two-phase flow. Water Resources Research, 47, 1–16.
Schwartz, F. W. 1977. Macroscopic dispersion in porous media: The controlling factors. Water Resources Research, 13, 743–752.
Sethian, J. A. 1996. Theory, algorithms, and applications of level set methods for propagating interfaces. Acta Numerica, 5, 309–395.
Sethian, J. A. 1999. Level Set and Fast Marching Methods. Cambridge: Cambridge University Press.
Shearer, M., and Trangenstein, J. A. 1989. Loss of real characteristics for models of threephase flow in a porous medium. Transport in Porous Media, 4, 499–525.
Silvester, J. R. 2000. Determinants of block matrices. The Mathematical Gazette, 84, 460–467.
Slattery, J. C. 1968. Multiphase viscoelastic fluids through porous media. American Institute of Chemical Engineering Journal, 14, 50–56.
Slattery, J. C. 1981. Momentum, Energy, and Mass Transfer in Continua. New York: Krieger.
Smith, R. 1981. The early stages of contaminant dispersion in shear flows. Journal of Fluid Mechanics, 111, 107–122.
Sneddon, I. N. 2006. Elements of Partial Differential Equations. New York: Dover Publications.
Sommerfeld, A. 1964. Optics. New York: Academic Press.
Stakgold, I. 1979. Green's Functions and Boundary Value Problems. NewYork: John Wiley and Sons.
Sun, N. Z. 1994. Inverse Problems in Groundwater Modeling. Norwell, Massaschuetts: Kluwer Academic Press.
Sun, N. Z., and Yeh, W. W. G. 1990. Coupled inverse problems in groundwater modeling, 1, Sensitivity analysis and parameter identification. Water Resources Research, 26, 2507–2525.
Sweby, P. K. 1984. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal on Numerical Analysis, 21, 995–1011.
Tanaka, S., Datta-Gupta, A., and King, M. J. 2013. A novel approach for incorporation of capillarity and gravity into streamline simulation using orthogonal projection. SPE 163640. In: Proceedigs of Society of Petroleum Engineering Reservoir Simulation Symposium. The Woodlands, Texas.
Taniuti, T., and Nishihara, K. 1983. Nonlinear Waves. London: Pitman Publishing.
Tarantola, A. 1987. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Amsterdam: Elseview Science Publishers.
Taylor, G. 1953. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. Royal. Society, London, Series A, 219, 186–203.
Terzaghi, K. 1943. Theoretical Soil Mechanics. New York: John Wiley.
Todd, D. K. 1959. Ground Water Hydrology. New York: John Wiley.
Trangenstein, J. A. 1988. Numerical analysis of reservoir fluid flow. In: Lecture Notes in Engineering, 34, Multiphase Flow in Porous Media, C.A., Brebbia and S.A., Orszag (eds.), Berlin–Heilderberg–New York: Springer-Verlag.
Truesdell, C. 1962. Mechanical basis of diffusion. Journal of Chemical Physics, 37, 2336–2344.
Truesdell, C. 1985. The elements of Continuum Mechanics. New York: Springer-Verlag.
Tuncay, K., and Corapcioglu, M. Y. 1997.Wave propagation in poroelastic media saturated by two fluids. Journal of Applied Mechanics, 64, 313–320.
Tura, A., and Lumley, D. E. 1998. Subsurface fluid-flow properties from time-lapse elastic wave reflection data. Pages 125–138 of: Proceedings of the 43rd Annual Meeting, SPIE. International Society of Optical Engineering.
Turcotte, D. L., and Schubert, G. 1982. Geodynamics. New York: John Wiley and Sons.
Vallis, G. K. 2006. Atmospheric and Oceanic Fluid Dynamics. Cambridge: Cambridge University Press.
van Gestel, J. P., Kimmedal, J. H., Barkved, O. I., Mundal, I., Bakke, R., and Best, K., D. 2008. Continuous seismic surveillance of Valhal field. The Leading Edge, 27, 1616–1621.
Vasco, D.W. 2004a. An asymptotic solution for two-phase flow in the presence of capillary forces. Water Resources Research, 40, 1–13.
Vasco, D.W. 2004b. Estimation of flow properties using surface deformation and head data: A trajectory-based approach. Water Resources Research, 40, 1–14.
Vasco, D.W. 2011. On the propagation of a coupled saturation and pressure front. Water Resources Research, 47, 1–21.
Vasco, D.W. 2013. On the propagation of a disturbance in a smoothly varying heterogeneous porous medium saturated with three fluid phases. Geophysics, 78, L1–L26.
Vasco, D.W., and Datta-Gupta, A. 1999. Asymptotic solutions for solute transport: A formalism for tracer tomography. Water Resources Research, 35, 1–16.
Vasco, D.W., and Datta-Gupta, A. 2001a. Asymptotics, saturation fronts, and high resolution reservoir characterization. Transport in Porous Media, 42, 315–350.
Vasco, D.W., and Datta-Gupta, A. 2001b. Asymptotics, streamlines, and reservoir modeling: A pathway to production tomography. The Leading Edge, 142–148.
Vasco, D.W., and Finsterle, S. 2004. Numerical trajectory calculations for the efficient inversion of transient flow and tracer observations. Water Resources Research, 40, 1–17.
Vasco, D.W., Daley, T.M., and Bakulin, A. 2014. Utilizing the onset of time-lapse changes: a robust basis for reservoir monitoring and characterization. Geophysical Journal International, 197, 542–556.
Vasco, D.W., Ferretti, A., and Novali, F. 2008a. Estimating permeability from quasistatic deformation: Temporal variations and arrival time inversion. Geophysics, 73, O37–O52.
Vasco, D.W., Karasaki, K., and Kishida, K. 2001. A coupled inversion of pressure and surface displacement. Water Resources Research, 37, 3071–3089.
Vasco, D.W., Karasaki, K., and Nakagome, O. 2002. Monitoring production using surface deformation: the Hijiori test site and the Okuaizu geothermal field, Japan. Geothermics, 31, 303–342.
Vasco, D.W., Keers, H., and Karasaki, K. 2000. Estimation of reservoir properties using transient pressure data: An asymptotic approach. Water Resources Research, 36, 3447–3465.
Vasco, D.W., Pride, S. R., and Commer, M. 2016. Trajectory-based modeling of fluid transport in a medium with smoothly-varying heterogeneity. Water Resources Research, (in press).
Vasco, D.W., Yoon, S., and Datta-Gupta, A. 1999. Integrating dynamic data into highresolution reservoir models using streamline-based analytic sensitivity coefficients. SPE. Journal, 4, 389–399.
Vasco, D.W., Bakulin, A., Baek, H., and Johnson, L. R. 2015. Reservoir characterization based upon the onset of time-lapse amplitude changes. Geophysics, 80, 1–14.
Vasco, D.W., Keers, H., Khazanehdari, J., and Cooke, A. 2008b. Seismic imaging or reservoir flow properties: Resolving water influx and reservoir permeability. Geophysics, 73, O1–O13.
Vasco, D.W., Datta-Gupta, A., Behrens, R., Condon, P., and Rickett, J. 2004. Seismic imaging of reservoir flow properties: Time-lapse amplitude changes. Geophysics, 69, 1425–1442.
Vasco, D.W., Rucci, A., Ferretti, A., Novali, F., Bissell, R., Ringrose, P., Mathieson, A., and Wright, I. 2010. Satellite-based measurements of surface deformation reveal flow associated with the geological storage of carbon dioxide. Geophysical Research Letters, 37, 1–5.
Virieux, J., Flores-Luna, C., and Gibert, D. 1994. Asymptotic theory for diffusive electromagnetic imaging. Geophysical Journal International, 119, 857–868.
Voyiadjis, G. Z., and Song, C. R. 2006. The Coupled Theory of Mixtures in Geomechanics with Applications. New York: Springer.
Wang, H. F. 2000. Theory of Linear Poroelasticity. Princeton: Princeton University Press.
Warren, J. E., and Skiba, F. F. 1964. Macroscopic dispersion. Transactions of the American Institute of Mining, Metallurgy, and Petroleum Engineering, 231, 215–230.
Watanabe, S., Han, J., Datta-Gupta, A., and King, M. J. 2014. Streamline-based time lapse seismic data integration incorporating pressure and saturation effects. Journal of Petroleum Technology, 66(4), 122–126.
Whitaker, S. 1969. Advances in the theory of fluid motion in porous media. Industrial and Engineering Chemistry, 61, 14–28.
White, J. E. 1975. Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics, 40, 224–232.
Whitham, G. B. 1974. Linear and Nonlinear Waves. New York: John Wiley and Sons.
Wilmanski, K. 2006. A few remarks on Biot's model and linear acoustics of poroelastic saturated materials. Soil Dynamics and Earthquake Engineering, 26, 509–536.
Yeh, W. W. G. 1990. Review of parameter identification procedures in groundwater hydrology: The inverse problem. Water Resources Research, 22, 95–108.
Yoon, S., Malallah, A. H., Datta-Gupta, A., Vasco, D.W., and Behrens, R. A. 2001. A multiscale approach to production data integration using streamline models. SPE . Journal, 6, 182–192.
Yortsos, Y. C., and Fokas, A. S. 1983. An analytical solution for linear waterflood including the effects of capillary pressure. SPE Journal, 23, 115–124.
Zhang, R., Vasco, D., Daley, T. M., and Harbert, W. 2015. Characterization of a fracture zone using seismic attributed at the In Salah CO2 storage project. Interpretation, 3, SM37–SM46.
Zhang, Y., Bansal, N., Fujita, Y., Datta-Gupta, A., King, M. J., and Sankaran, S. 2014. From streamlines to Fast Marching: Rapid simulation and performance assessment of shale gas reservoirs using diffusive time of flight as a spatial coordinate. SPE 168997 In: Proceedings of Society of Petroleum Engineers Unconventional Resources Conference, The Woodlands, Texas. SPE Journal, 2016. http://dx.doi.org/10.2118/168997-PA.
Zhou, C., Cai, W., Luo, Y., Schuster, G., and Hassanzadeh, S. 1995. Acoustic wave equation travel time and waveform inversion of crosshole seismic data. Geophysics, 60, 765–774.
Zhou, M., and Sheng, P. 1989. First-principles calculations of dynamic permeability in porous media. Physical Review B, 39, 12027–12039.
Zimmerman, R. W. 2000. Coupling in poroelasticity and thermoelasticity. International Journal of Rock Mechanics and Mining Science, 37, 79–87.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.