Inverting Crack Parameters Based On Tang’s Cracked Porous Medium Elastic Wave Theory

Rocks in the earth’s crust usually contain pores and cracks. With the development of “an elastic wave theory for the cracked porous rock” recently, we can use the theory to analyze and interpret acoustic/seismic data measured in such rocks. And in this paper, we firstly modified the squirt flow model in the cracked porous medium elastic wave theory; and then based on the theory, we study the effect of the crack density, the aspect ratio, the fluid viscosity, permeability and gas saturation on the dispersion and attenuation of the fast- and slow- compressional wave and shear wave in the infinite formations.In this paper, we apply the theory mentioned above to multi-pole borehole acoustic field in porous rocks with cracks, firstly, we provide the detailed formulation for calculating acoustic waveforms along a borehole with a cracked porous formation. We then study the effect of the parameters-crack density, aspect ratio, permeability and gas saturation on the dispersion and attenuation of the mode waves(the monopole and the dipole mode waves are included), and the effect on the monopole and dipole waveforms.We then present modeling examples and analyze the effect of cracks on the acoustic responses. Emphasis will be given on tight formations having low permeability and porosity but with abundant cracks. The modeling results showed that the multi-pole acoustic waveforms were significantly affected by the presence of cracks even when the formation had low permeability and porosity, and so it can help explain acoustic wave phenomena observed in tight formations. Particularly, cracks can cause the monopole P- and Stoneley waves and the dipole flexural wave to have significant sensitivity to hydrocarbon saturation, suggesting use of the waveform characteristics for hydrocarbon detection in tight formations. The modeling results can help explainThe recent development of the elastic wave theory for a cracked porous medium significantly enhances our ability to model and predict acoustic response of real rocks. As an important application and verification of the theory, we apply it to model and interpret laboratory ultrasonic velocity data of rock samples measured under pressure loading conditions. The important model parameters, such as crack density and aspect ratio, are obtained by inverting the velocity versus pressure data. The results show that the theory can well describe the elastic velocity variation with pressure under dry and saturated conditions. The theory is applicable for both porous sandstone and very tight granite. The cause of the velocity variation with pressure is the closure of microcracks and the decreasing of crack density within the rock under pressure loading. This paper also suggests using crack density as an important rock property parameter and provides a method for determining the crack parameter.And then we use this method to obtain the crack density versus the depth profile and the gas saturation versus depth profile, and this provides support for studying the crack development and fluid property.