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

To account for large-volume low-permeability storage porosity and low-volum e high-permeability fracture/crack porosity in oil and gas reservoirs, phen omenological equations for the poroelastic behavior of a double porosity me dium have been formulated and the coefficients in these linear equations id entified. This generalization from a single porosity model increases the nu mber of independent inertial coefficients from three to six, the number of independent drag coefficients from three to six, and the number of independ ent stress-strain coefficients from three to six for an isotropic applied s tress and assumed isotropy of the medium. The analysis leading to physical interpretations of the inertial and drag coefficients is relatively straigh tforward, whereas that for the stress-strain coefficients is more tedious. In a quasistatic analysis, the physical interpretations are based upon cons iderations of extremes in both spatial and temporal scales. The limit of ve ry short times is the one most pertinent for wave propagation, and in this case both matrix porosity and fractures are expected to behave in an undrai ned fashion, although our analysis makes no assumptions in this regard. For the very long times more relevant to reservoir drawdown, the double porosi ty medium behaves as an equivalent single porosity medium. At the macroscop ic spatial level, the pertinent parameters (such as the total compressibili ty) may be determined by appropriate field tests. At the mesoscopic scale, pertinent parameters of the rock matrix can be determined directly through laboratory measurements on core, and the compressibility can be measured fo r a single fracture. We show explicitly how to generalize the quasistatic r esults to incorporate wave propagation effects and how effects that are usu ally attributed to squirt now under partially saturated conditions can be e xplained alternatively in terms of the double-porosity model. The result is therefore a theory that generalizes, but is completely consistent with, Bl ot's theory of poroelasticity and is valid for analysis of elastic wave dat a from highly fractured reservoirs. Published by Elsevier Science Ltd.