Geodesic
Numerical modelling of electroacoustic logging including Joule heating
Matematičeskoe modelirovanie, Tome 32 (2020) no. 2, pp. 58-76.

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Modification of Pride 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 medium. 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 showed that at low frequencies the Stoneley wave can be used to estimate formation permeability, and the fast acoustic wave can be used 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, taking into account the contribution of which is difficult task due to the nonlinearity of such effect.
Keywords: electrokinetic effect, Joule heating, numerical modelling, electro-acoustic logging. 
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B. D. Plyushchenkov; A. A. Nikitin. Numerical modelling of electroacoustic logging including Joule heating. Matematičeskoe modelirovanie, Tome 32 (2020) no. 2, pp. 58-76. http://geodesic.mathdoc.fr/item/MM_2020_32_2_a3/

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