WAVES IN A POROUS MEDIUM WITH A GAS HYDRATE CONTAINING LAYER
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WAVES IN A POROUS MEDIUM WITH A GAS HYDRATE CONTAINING LAYER A. A. Gubaidullina,b,∗ and O. Yu. Boldyrevaa
UDC 532.546:534.1
Abstract: This study describes the propagation of harmonic and pulsed waves in a layered porous medium, with one of its layers containing gas hydrate. It is shown that the resulting wave pattern makes it possible to predict the presence of a hydrate in a layer and its thickness provided that thermobaric conditions for the existence of the gas hydrate are fulfilled. Keywords: porous medium, gas hydrate, waves, reflection. DOI: 10.1134/S0021894420040045 INTRODUCTION The study of the properties of acoustic waves in porous media is important in terms of their numerous applications, such as determination of the elastic properties of the environment [1–3]. Particularly in geophysics, acoustic waves are used to characterize water-saturated and hydrocarbon reservoirs. In this case, it becomes necessary to interpret seismograms describing wave reflection from layers in rocks. Recently, a number of works have been published, devoted to investigating the reflection, refraction, and propagation of acoustic waves in layered media [4–7]. There are studies on the evolution of a wave pulse as it passes through a porous obstacle located in a gas and saturated with the this gas [4], and the reflection and refraction of an acoustic pulse on a porous layer, located in a liquid, as a function of the angle of incidence [5]. A pulse of finite duration passing through a pure gas–porous medium interface and its reflection from a rigid wall behind a porous layer [6] have been investigated. The problem of the refraction of elastic waves at the boundary of two half-spaces (rocks) filled with immiscible fluids has been solved [7]. The most interesting is the study of gas hydrate containing layers. As shown in [1–3], a signal passing and being reflected as it intersects boundaries can be considered in a linear one-dimensional approximation.
STATEMENT AND SOLUTION OF THE PROBLEM Let us consider the problem of plane wave propagation in a porous medium with a hydrate-containing layer (Fig. 1). An intermediate layer 2 contains a gas hydrate, while the properties of layers 1 and 3 may differ). The propagation and decay of waves in a porous medium is investigated using a two-velocity model of a saturated porous medium [8, 9]. It is assumed that, in the gas hydrate containing layer of a porous medium, a skeleton consists of a basic rock cemented by a gas hydrate and is modeled by a homogeneous solid phase with effective parameters.
a
Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Tyumen, 625026 Russia. b Tyumen State University, Tyumen, 625003 Russia; ∗ [email protected]; [email protected]. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 4, pp. 31–38, July–August, 2020. Original article submitted April 20, 2020; revision submitted April 20, 2020; accepted for publication April 27, 2020. ∗ Corresponding author. c 2020
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