Abstract

Modification of Pride’s equations, describing the interrelated process of acoustic and electromagnetic waves’ propagation in saturated porous medium, arising due to the electrokinetic effect, is proposed. This modification allows taking into account Joule heating during the propagation of acoustic oscillations, generated by electromagnetic source, and is implemented by adding “thermoelastic terms” into the state equations for porous fluid and formation. Temperature change is determined by heat conduction equation. Method of constructing of corresponding finite-difference scheme in axially symmetric case is described. The results of numerical simulations are presented, which show that at low frequencies the Stoneley wave can be used to estimate formation permeability, and the fast acoustic wave can be used for this purpose at high frequencies, when the influence of Joule heating can be neglected. However, if the conductivity of porous or especially borehole fluid is high enough, then the thermoelastic wave arises due to Joule heating, whose contribution is hard to account for due to the nonlinearity of such an effect.

中文翻译：

---

焦耳加热等电声测井的数值模拟

摘要

提出了对Pride方程的修正，该方程描述了由于电动效应引起的声波和电磁波在饱和多孔介质中传播的相互关系过程。此修改允许在电磁波传播的声波传播过程中考虑焦耳加热，并通过在多孔流体和地层的状态方程中添加“热弹性项”来实现。温度变化由导热方程确定。描述了在轴对称情况下构造相应的有限差分方案的方法。给出了数值模拟的结果，结果表明，在低频情况下，斯通利波可用于估算地层渗透率，而在高频情况下，可将快速声波用于此目的，可以忽略焦耳加热的影响。然而，如果多孔或特别是井眼流体的电导率足够高，则由于焦耳热而产生热弹性波，由于这种效应的非线性，其贡献难以解释。