1. MMC
  2. All Volumes and Issues
  3. Volume 3, Number 2, 2016
  4. Mathematical modeling of elastic disturbance propagation in a structure containing a porous layer saturated with gas and water

Mathematical modeling of elastic disturbance propagation in a structure containing a porous layer saturated with gas and water

MMC.
2016;
Volume 3, Number 2
: pp. 120-134
https://doi.org/10.23939/mmc2016.02.120
Received: October 01, 2016

Math. Model. Comput. Vol. 3, No. 2, pp. 120-134 (2016)

Authors:
  1. V. Chekurin
  2. A. Yu. Pavlova
1
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine; Kuyawy and Pomorze University in Bydgoszcz
2
Carpathian Branch of Subbotin Institute of Geophysics of NAS of Ukraine

A horizontally layered elastic structure containing a homogeneous porous layer saturated partly with gas and partly with water is considered. The paper is aimed at studying of interaction of elastic waves, caused by local pulse source, with the structure. The boundary-value problem describing the wave dynamics of the structure is formulated. A mathematical model describing distributions of the gas and water in a pore space of the porous layer depending of the amount of the gas accumulated in the layer is developed. The problem is solved with the use of Fourier transform. It was established that wavefield pattern on the free surface of the structure is dependent on amount of gas accumulated in the porous layer. Quantitative measures relating the wavefield parameters on the structure's free surface and the amount of gas accumulated in the porous layer are introduced. The obtained results can be used to develop distance methods for accounting of amount of natural gas accumulated in underground gas storage facilities built in aquifers.

layered structure
porous media
elastic disturbance
  1. Underground Storage of Natural Gas, in Encyclopeadia of Hydrocarbons, vol. 1/ Exploration, Production and Transport. Rome: Eni. Istituto della Enciclopedia italiana (2005).
  2. Gassmann F. Elastic waves through a packing of sferes. Geophysics. 16 (4), 673–685 (1951).
  3. Sun W., Ba J., Carcione J. M. Theory of wave propagation in partially saturated double-porosity rocks: a triple-layer patchy model. Geophys. J. Int. 205 (1), 22–37 (2016).
  4. Carcione J. M. Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media. 3rd edn. Elsevier Science (2015), 690 p.
  5. Rubino J. G., Holliger K. Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks. Geophys. J. Int. 188, 1088–1102 (2012).
  6. Aki K., Richards P. G. Quantitative Seismology. 2-nd Edition W. H. Freeman and Company (2002), 700 p.
  7. Fryer G. J., Frazer L. N. Seismic waves in stratified anisotropic media. Geophys. J. Roy. and Soc. 78 (4), 691–710 (1984).
  8. Fryer G. J., Frazer L. N. Seismic waves in stratified anisotropic media. II. Elastodynamic eigensolutions for some anisotropic systems. Geophys. J. Roy. and Soc. 91 (4), 73–101 (1987).
  9. Ba J., Carcione J. M., Sun W. T. Seismic attenuation due to heterogeneities of rock fabric and fluid distribution. Geophys. J. Int. 202 (3), 1843–1847 (2015).
  10. Ba J., Carcione J. M., Nie J. X. Biot-Rayleigh theory of wave propagation in double-porosity media. J. geophys. Res. 116, 1–12 (2011).
  11. Sona M. S., Kangb Y. J. Propagation of shear waves in a poroelastic layer constrained between two elastic layers. Applied Mathematical Modelling. 36 (8), 3685–3695 (2012).
  12. Hirsh M. W., Smale S., Devaney R. L. Differential equations, dynamical systems & Chaos. Academic press (2004), 418 p.
  13. Quintal B., Steeb H., Frehner M., Schmalholz S. M. Quasi-static finite element modeling of seismic attenuation and dispersion due to wave-induced fluid flow in poroelastic media. J. geophys. Res.: Solid Earth. 116, 1–17 (2011).
  14. Boruah N., Chatterjee R. Rock physics template (RPT) analysis of well logs and seismic data for lithology and fluid classifications. Petroview. 3, 1–8 (2010).