Abstract
We present theoretical models and laboratory experiments for guided wave propagation within fluid-filled, open and partially open, and proppant-filled fractures. The laboratory experiments are conducted using an analogue fracture (a "trilayer" model) consisting of a pair of slender glass plates with a water and proppant-filled gap between them. Velocity and attenuation of the waves are predicted by dispersion (frequency) equations, which are derived by plane-wave analysis that employs seismic-linear-slip interface (displacement-discontinuity-boundary) conditions for modeling the low-frequency behavior of a fluid-filled fracture. The theory and the experiment are in good agreement, showing highly dispersive (i.e., the velocity changes with frequency) and attenuating wave behavior. Additionally, we present co-seismically induced electrical fields via the electokinetic effect within a proppant layer, and discuss their possible application for fracture characterization..
1. INTRODUCTION
Open and partially open fractures can trap and guide seismic (pressure) waves within fluid contained in the aperture. Krauklis [1] first predicted the behavior of these waves—we will call them "Krauklis waves" in this paper—which are (1) highly dispersive (the velocity depends on the frequency), (2) strongly attenuating, and (3) their propagation velocity can be far below the acoustic velocity of the fluid at low frequencies (tens of m/s to a few hundred m/s, over frequencies of a few hertz up to several kilohertz). These are essentially the characteristics of Biot’s slow compressional waves in porous, fluid-saturated rock. However, for highly permeable fractures, Krauklis waves should propagate for a substantial distance away from the source, which may allow us to use them for subsurface fracture detection and characterization (e.g., [2]).
Although the theoretical models for Krauklis wave propagation in an open, fluid-filled fracture have been developed by many (e.g., [3][4][5]), experimental confirmations in the laboratory and in the field are still scarce. Recently, Hassan and Nagy [6], conducting laboratory ultrasonic wave propagation tests on a fluid-filled fracture, demonstrated strong velocity dispersion of the waves guided by the fracture. Nakagawa et al. [7] also conducted similar experiments at low frequencies below 1 kHz, on fractures with varied mechanical compliance and permeability. (Part of the results from this experiment will be reviewed in this paper.)
