Elastic wave propagation and attenuation in a double-porosity dual-permeability211 medium

摘要

To account for large-volume low-permeability storage porosity and low-volume high-211u001epermeability fracture/crack porosity in oil and gas reservoirs, phenomenological 211u001eequations for the poroelastic behavior of a double porosity medium have been 211u001eformulated and the coefficients in these linear equations identified. The 211u001egeneralization from a single porosity model increases the number of independent 211u001einertial coefficients from three to six, the number of independent drag 211u001ecoefficients from three to six, and the number of independent stress-strain 211u001ecoefficients from three to six for an isotropic applied stress and assumed 211u001eisotropy of the medium. The analysis leading to physical interpretations of the 211u001einertial and drag coefficients is relatively straightforward, whereas that for 211u001ethe stress-strain coefficients is more tedious. In a quasistatic analysis, the 211u001ephysical interpretations are based upon considerations of extremes in both 211u001espatial and temporal scales. The limit of very short times is the one most 211u001erelevant for wave propagation, and in this case both matrix porosity and 211u001efractures are expected to behave in an undrained fashion, although our analysis 211u001emakes no assumptions in this regard. For the very long times more relevant for 211u001ereservoir drawdown, the double porosity medium behaves as an equivalent single 211u001eporosity medium. At the macroscopic spatial level, the pertinent parameters (such 211u001eas the total compressibility) may be determined by appropriate field tests. At 211u001ethe mesoscopic scale pertinent parameters of the rock matrix can be determined 211u001edirectly through laboratory measurements on core, and the compressibility can be 211u001emeasured for a single fracture. We show explicitly how to generalize the 211u001equasistatic results to incorporate wave propagation effects and how effects that 211u001eare usually attributed to squirt flow under partially saturated conditions can be 211u001eexplained alternatively in terms of the double-porosity model.