Pressure and frequency dependence of elastic moduli of fluid‐saturated dual‐porosity rocks

Abstract

AbstractThe elastic moduli of subsurface rocks saturated with geofluid often depend on the wave frequency and confining pressure due to the wave‐induced fluid flow and their significant intrinsic compressibility. Therefore, the knowledge of the pressure‐dependent dispersion of elastic moduli is usually used in broad practical scenarios such as geofluid discrimination and in situ abnormal pressure detection. We propose a simple dual‐porosity model to describe the pressure and frequency dependence of elastic moduli of fluid‐saturated rocks. First, we follow the idea of the Shapiro dual‐porosity model to yield more accurate formulas for pressure‐dependent stiff porosity and crack porosity. Then the new formulas for stiff and crack porosities are utilized to express the bulk and shear moduli of dry rocks as a function of pressure. Further, the bulk and shear moduli of a modified frame (i.e. a rock skeleton with the dry stiff pores and fluid‐saturated cracks) are formulated with the pressure‐dependent elastic moduli of dry rock. In order to consider the wave energy attenuation induced by fluid in cracks, the frequency‐independent fluid modulus imbedded in the formulas for bulk and shear moduli of a modified frame is replaced with a frequency‐dependent one incorporating the effect of viscoelastic relaxation. The effective bulk and shear moduli of entire fluid‐saturated body can be computed by inserting the pressure‐dependent stiff porosity and elastic moduli of a modified frame into the Gassmann equation. Moreover, appropriate simplification is performed on the central equations in the case of low porosity and weak deformation of stiff pores to yield an approximate model. Modelling results show that the proposed model can reasonably account for the nonlinear variation of bulk and shear moduli with the elevating effective pressure and cautiously predict the wave dispersion and attenuation. We validate our model by comparing the predicted elastic moduli with the corresponding results given by Shapiro model–based equations and with the laboratory measurements of five different fluid‐saturated rock samples.