Abstract
Simulating and predicting wave propagation in porous media saturated with two fluids is an important issue in geophysical exploration studies. In this work, wave propagation in porous media with specified structures saturated with two immiscible fluids was studied, and the main objective was to establish a wave equation system with a relatively simple structure. The wave equations derived by Tuncay and Corapcioglu were analyzed first. It was found that the coefficient matrix of the equations tends to be singular due to the inclusion of a small parameter that characterizes the effect of capillary stiffening. Therefore, the previously established model consisting of three governing equations may be unstable under natural conditions. An improved model based on Tuncay and Corapcioglu’s work was proposed to ensure the nonsingularity of the coefficient matrix. By introducing an assumption in which one fluid was completely wrapped by the other, the governing equation of the wrapped fluid was degenerated. In this way, the coefficient matrix of wave equations became nonsingular. The dispersion and attenuation prediction resulting from the new model was compared with that of the original model. Numerical examples show that although the improved model consists of only two governing equations, it can obtain a result similar to that of the original model for the case of a porous medium containing gas and water, which simplifies the complexity of the calculations. However, in a porous medium with oil and water, the predictions of dispersion and attenuation produced by the original model obviously deviate from the normal trend. In contrast, the results of the improved model exhibit the correct trend with a smooth curve. This phenomenon shows the stability of the improved model and it could be used to describe wave propagation dispersions and attenuations of porous media containing two immiscible fluids in practical cases.
Highlights
Wave propagation in partially saturated porous media is of interest in the research areas of geophysics, petroleum engineering and underground science
Theoretical analysis showed that the model developed by Tuncay and Corapcioglu based on the volume averaging method may be unstable since the structure of the wave equations may be problematic
An effective fluid model of wave propagation is proposed based on their study
Summary
Wave propagation in partially saturated porous media is of interest in the research areas of geophysics, petroleum engineering and underground science. White (1975) established the first bulk modulus expression that considered dissipation mechanisms on a mesoscopic scale, which is known as the patch saturation model. A model of concentric spheres with periodic distribution was formulated to simulate the heterogeneity of fluids in porous media. Based on the quasistatic Biot theory (Biot, 1956; Biot, 1962), Johnson (2001) proposed a dynamic frequency-dependent bulk modulus to calculate the dispersion and attenuation relations of patches with arbitrary geometries. Tserkovnyak and Johnson (2003) improved this model by considering the effect of membrane surface tensions between two fluids in pore space. Thereafter, a patch saturation model with a random distribution was proposed by Müller and Gurevich (2015)
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