The Electrokinetic Cross-Coupling Coefficient: Two-Scale Homogenization Approach

Эпов

2019

Fluids

Self Cite

The study is motivated by monitoring the space orientation of a hydrolic fracture used in oil production. Streaming potential arises due to the leakage of ionic fracking fluid under the rock elastic forces which make the fracture disclosure disappear after pumping stops. The vector of electric field correlates with the fracture space orientation since the fluid leakage is directed normally to the fracture surfaces. We develop a mathematical model for the numerical evaluation of the streaming potential magnitude. To this end, we perform an asymptotic analysis taking advantage of scale separation between the fracture disclosure and its length. The contrast between the virgin rock fluid and the fluid invading from the fracture is proved to be crucial in a build up of a net charge at the invasion front. Calculations reveal that an increase of the viscosity and resistivity contrast parameters results in an increase of the streaming potential magnitude. Such a conclusion agrees with laboratory experiments.

Section: Basic Equationsmentioning

confidence: 99%

Section: Basic Equationsmentioning

confidence: 99%

Ionic Fracture Fluid Leak-Off

Эпов

2019

Fluids

Self Cite

“…It is proved in Amirat and Shelukhin [2] and Shelukhin et al [23] that interfacial charges may appear due to ion transport in a fluid dielectric medium. The nature of this charge is the Maxwell-Wagner polarization which appears due to a difference in dielectric permittivities between the composite components.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of composite electrets

Amirat

2015

Eur. J. Appl. Math

We study the two-scale homogenization of the diffraction interfacial condition for the diffusion equation relevant to a composite medium which has a periodic structure. The results are applied to the electric field potential within a dielectric composite body when there is a difference in dielectric permittivity between the composite components in the presence of interfacial static charges. The principal result is that the interfacial charge distribution is equivalent to an apparent bulk charge which can be calculated starting from the composite geometry. We perform the corrector analysis and establish that the corrector terms strongly depend on the interfacial charge.

“…Waves in layered media have been studied in a number of publications. We refer the reader to several textbooks [1,8,13,20] and recent articles [3,19].…”

Section: Introductionmentioning

confidence: 99%

Elastic waves in layered media: Two-scale homogenization approach

Isakov

2012

Eur. J. Appl. Math

Using the two-scale convergence approach, we derive equations which govern transversal time-harmonic waves through a layered medium taking the form of a poroelastic composite saturated with a viscous fluid. To improve convergence, we construct a corrector. We study how wave speed and attenuation time depend on porosity and frequency. We prove that the Darcy permeability and the acoustic permeability in the Biot equations do not coincide.