Multi-frequency band rock physics model for saturated rock based on pore aspect ratio spectral inversion
HAN Xu, WANG Shangxu, LIU Haojie, LIU Tao, TANG Genyang
1 School of Geophysics, China University of Petroleum-Beijing, Beijing 102249, China 2 Sinopec Shengli Oilfield Geophysical Research Institute, Shandong 257000, China 3 Sinopec Exploration and Development Research Institute, Beijing 100728, China
In conventional sandstone, the velocity is primarily controlled by porosity, mineral composition and pore fluids.However, experimental measurements show that the pore structure of the rock is also one of the main controlling factors of the elastic parameters of rocks. The microscopic pore structure characteristics of rocks not only affect the elastic parameters of rocks, but also determine the dispersion and attenuation effects caused by fluid flow in fluid-saturated rocks. The Gassmann theoretical model ignores the influence of microscopic pore structure and often cannot explain the pressure and frequency dependence of rock elastic properties. In this paper, the Kuster–Toks?z (K-T) model is extended to characterize the influence of pressure on the elastic modulus of fluid-saturated rocks. On this basis, the frequency-dependent fluid bulk modulus calculated by the squirt flow model is brought into the K-T model to establish the frequency dependence of the rock. First, based on the functional relationship between the velocity-pressure curve and the pore structure parameters, the measured ultrasonic velocity data is used to invert the pore aspect ratio distribution and its porosity (i.e., the pore aspect ratio spectrum); secondly, dry stiff pores are added to the rock matrix, Based on the K-T effect medium model, the elastic modulus of the dry skeleton of the rock is calculated, and the fluid frequency-dependent bulk modulus is introduced to calculate the elastic modulus of the rock "dry skeleton" after adding saturated soft pores. Finally, the elastic modulus of saturated fluid in stiff pores is calculated by using Gassmann fluid replacement theory. In order to verify the accuracy of the model, ultrasonic velocity measurement was carried out on an oil-saturated tight sandstone sample and compared with the prediction results of the model. The results show that compared with the Gassmann model, the new model can better explain the measurement results and predict the pressure and frequency dependence of the velocity of saturated rocks. Actual measurements and modeling results show that the effects of pressure and frequency are coupled because they are interconnected by the microstructure of the pores. The model does not require redundant fitting parameters, and all parameters are measured and calculated in the laboratory, which improves the accuracy of theoretical modeling. The new model can be used to describe the elastic dispersion and attenuation of saturated rocks in a wide frequency band. If the elastic moduli of dry and saturated states can be obtained through seismic data inversion, the model can be used to extract rock pore microstructure and fluid properties.
Key words：
pore structure; velocity dispersion; acoustic properties; rock physical model
