Reflection and transmission of inhomogeneous waves in a composite porous solid saturated by two immiscible fluids |
| |
| Authors: | Abhishek Painuly Ashish Arora |
| |
| Affiliation: | Department of Mathematics, I. K. Gujral Punjab Technical University, India |
| |
| Abstract: | This paper is concerned with reflection and transmission of a plane, elastic, and inhomogeneous wave striking obliquely at some discontinuity inside a porous medium composed of two distinct solids and saturated by two immiscible fluids. It is found that four P‐ and two SV‐waves are reflected, whereas four P‐ and two SV‐waves are transmitted at the interface. All reflected and transmitted waves are inhomogeneous in nature and specified with different directions of propagation and attenuation vectors. An expression for the Umov–Poynting energy flux vector is derived for the system. Continuity of energy flux along normal to the interface gives 12 required boundary conditions. Expressions of amplitude and energy ratios of various reflected and transmitted waves are derived. Variations in amplitude and energy coefficients of reflected and transmitted waves with angle of incidence are numerically studied for a porous matrix composed of shaley sandstone and clay, saturated with water and oil. The effects of change in oil saturation and volume fraction of clay are also observed on amplitude ratios. Numerical simulation reveals that the change in sign in the difference of capillary pressure across the interface causes jump in the values of amplitude ratios of all waves. |
| |
| Keywords: | Composite medium Inhomogeneous wave Umov– Poynting vector Amplitude ratios Energy ratios Attenuation |
|
