低频振动对低渗油藏径向渗流影响的变参量Biot固结分析

Biot's consolidation with variables for influence of low-frequency vibration stimulation on radial flow in low-permeability developed reservoir

基于波动采油对低渗储层物性改善的动态过程,利用变参量的岩土固结模型分析弹性波对饱和渗流流体径向模型流固位移、孔隙压力等的影响规律。通过Laplace变换与迭代消去,得到拉氏变换下低渗开发油藏波动控制方程为变系数高阶微分方程;利用变系数向量拆分与矩阵求法,推导了波动采油作用下饱和单相流体径向(定流量或定压)开发储层的流固位移近似解。通过Matlab编程,算例分析了饱和水相介质和不同振动频率下饱和油相介质的渗流、物性变化。结果表明,低频波动采油技术可增加低渗开发储层孔压和渗流速度,文中基础参数下,存在最佳振动频率5~30 Hz使得增幅最大,作用范围可达60 m,径向模型Laplace变换–Durbin离散近似求解适用于波传播时间较小的情况。

The low-frequency vibration stimulation technology can improve the seepage of fluid in low-permeability reservoir, which is rather deeper than that of the regular geotechnical formation. Few researches on the mechanisms of low-frequency vibration on seepage in developing reservoir are available through Biot＇s consolidation analysis. Changes in the seepage rate, pore pressure and porosity in radial model under low-frequency vibration are thereby investigated. Through the Laplace transformation and iterative elimination, a four-order differential equation with non-linear coefficients is obtained. Then, vector splitting and matrix solution for the non-linear coefficients are done successively. Utilizing the boundary and initial conditions in actual developed reservoirs, the approximate displacements of fluid are derived. The displacements in two cases, constant boundary pressure or constant flow, are given. Based on the formula for rock properties in Yanchang oilfield, numerical analysis is carried out with Durbin inverse transform and Matlab programming. Two examples, as in the medium saturated with oil phase under different vibration frequencies and in the medium saturated with water phase, are given. The results show that the physical properties are improved obviously by the low-frequency vibration stimulation technology. There is an optimal frequency, 5~30 Hz under basic parameters, making the largest increase in porosity, permeability, pore pressure and seepage velocity. The action radius is up to sixty meters, which far exceeds that of high-frequency vibration treatment. The approximate calculation of Laplace-transform and Durbin-discrete in two-dimensional model is applicable to the wave propagation with short duration.