Velocity and attenuation of elastic wave in a developed layer with the initial inner percolation in the pores

Xiaodong Han,Hongfu Shi,Liming Zheng,Cunliang Chen

doi:10.1007/s13202-018-0468-x

Abstract

An improved model based on Biot poroelastic theory is presented incorporating the initial seepage flow in the matrix. The proposed model quantifies wave propagation in the oil field development process as VSP, transient well tests, and seismic production technology. Porosity variation, fluid–solid compressibility, and pseudo-threshold pressure gradient in low permeability reservoir are simultaneously considered, resulting in a modified form of continuity and motion equations. Integrating the equations and decomposition for the fluid–solid displacements helps to derive the analytical wave vectors of the fast P, slow P, and S waves in porous media. The sensitivity of affecting factors, such as petrophysical parameter, fluid property, and vibration frequency, on the wave velocity and attenuation is subsequently evaluated. Furthermore, the Biot model can be considered a special situation when the initial flow rate in this model tends to zero. The increase in initial percolating rate, expressed by the ratio of initial flow rate and solid scalar potential, causes an obvious decrease in the fast P wave velocity and an increase in its quality factor. Propagation of the slow P wave and the S wave is scarcely influenced. Low vibration frequency and low permeability also contribute to a large difference between the wave propagation parameters of the improved and Biot models. Cognition of the proportion in the inertia and viscosity effects is helpful in analyzing the complicated multiple mechanisms in wave propagation in the actual developed layer.

Highlights

In the development process of low permeability reservoir, acoustic wave or artificial seismic wave inside the wellbore is applied to stimulate fluid percolation and enhance oil recovery in the media saturated with the initial percolating fluid
This method is called seismic production technology or lowfrequency vibration oil extraction technology (Cidoncha 2007; Kurawle et al 2009), which has been tested in many oil fields with certain effects, including increase in injection rate, production rate improvement, and plugging removal
1 Qc dPf where e is the bulk strain of rock; Kf is the bulk modulus of fluid; Qc is a coefficient representing the coupling relationship between volume changes of fluid and solid; is the ratio of the porosity change of porous media caused by low-frequency vibration to the porosity change due to only matrix deformation by the traditional solid–fluid coupling effect

Summary

Introduction

In the development process of low permeability reservoir, acoustic wave or artificial seismic wave inside the wellbore is applied to stimulate fluid percolation and enhance oil recovery in the media saturated with the initial percolating fluid (simplified as seepage media hereafter). The general Darcy law is shown, the way which Darcy equation is incorporated in the models above is substantially different from that in seismic production technology The former flow or filtration is induced by changes in the stress field and pore pressure caused by the seismic loading. The latter is applied in seismic recovery or field tests (Fig. 1a) assisted with fluctuations in the bottom pressure or wellbore stress, assuming that the initial fluid displacement is not zero Another difference is that the percolation in former models follows Darcy’s law with a fluid acceleration term, whereas the latter may be non-Darcy flow accompanied with a pseudo-pressure gradient (Wang et al 2016a, b, 2018). Fluid density is expressed as a function of pressure difference and fluid compressibility or modulus in the mechanics of the seepage flow:

Qc dPf

Conclusions