To account for large-volume low-permeability storage porosity and low-volume high-permeability fracture/crack porosity in oil and gasreservoirs, phenomenological equations for theporoelastic behavior of a double porosity medium havebeen formulated and the coefficients in these linearequations identified. This generalization from asingle porosity model increases the number ofindependent inertial coefficients from three to six,the number of independent drag coefficients from threeto six, and the number of independent stress-straincoefficients from three to six for an isotropicapplied stress and assumed isotropy of the medium. Theanalysis leading to physical interpretations of theinertial and drag coefficients is relativelystraightforward, whereas that for the stress-straincoefficients is more tedious. In a quasistaticanalysis, the physical interpretations are based uponconsiderations of extremes in both spatial andtemporal scales. The limit of very short times is theone most pertinent for wave propagation, and in thiscase both matrix porosity and fractures are expectedto behave in an undrained fashion, although ouranalysis makes no assumptions in this regard. For thevery long times more relevant to reservoir drawdown,the double porosity medium behaves as an equivalentsingle porosity medium. At the macroscopic spatiallevel, the pertinent parameters (such as the totalcompressibility) may be determined by appropriatefield tests. At the mesoscopic scale, pertinentparameters of the rock matrix can be determineddirectly through laboratory measurements on core, andthe compressibility can be measured for a singlefracture. We show explicitly how to generalize thequasistatic results to incorporate wave propagationeffects and how effects that are usually attributedto squirt flow under partially saturated conditionscan be explained alternatively in terms of thedouble-porosity model. The result is therefore atheory that generalizes, but is completely consistentwith, Biot's theory of poroelasticity and is valid foranalysis of elastic wave data from highly fractured reservoirs.
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