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

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.