The alteration of shales, caused by adsorption of water while drilling, is one of many contributors to the wellbore stability problem that costs the industry in the order of $ 400–500 million annually (Bol et.al., 1992). This alteration of shale problem has acquired a logging perspective due to the increasing use of measurements while drilling. The capability of taking real time and time-lapse measurements while still drilling introduces the possibility of detecting a swelling problem while something can still be done about it.
The objective of this study (Adisoemarta, 1999) is to observe the changes of complex electrical characteristic of shale as a function of water content. The word "complex" in the electrical characteristic term means this study will not only observe the "in-phase" electrical response but also the "out-of-phase""response.
By taking the ratio of the in-phase to the out-of-phase electrical response, this study found that this ratio, the dissipation factor, changes linearly as a function of shale water content. This method can be easily applied to both the drilling / wellbore stability or formation evaluation areas.
Maxwell's equations and certain constitutive relationships describe the macroscopic electrical behavior of conducting dielectrics subjected to a harmonic sinusoidal field.
All electromagnetic fields are created from distributions of charges and currents in which the electric field (resulting from the charge distributions), and the current densities (from the current distributions) are related through the complex transfer functions that result from Maxwell's equations:
and with the conservation of charge defined as:
are the components of the electromagnetic field, where:
- E =
electric field intensity (volt/meter)
- B =
magnetic flux density (webers/meter2)
- H =
magnetic field intensity (ampere-turn/meter)
- D =
electric displacement (coulomb/meter2)
- J =
electric current density (ampere/meter2)
- q =
charge density (coulomb/meter3).
For the case of homogeneous, isotropic, and a non-zero electrical conductivity medium, the electric field becomes
For the case of materials that exhibit electromagnetically linear behavior, the following relationships are valid:
e= dielectric permittivity (farad/m)
s= electric conductivity (mho/m or siemens/m)
µ= magnetic permeability (henry/m).
The equation for total current density, JT, is the result of solving equations (2), (5), and (6):
where sE is the conduction current component (in phase with applied voltage), and edE/dt is the displacement current component (the out of phase response).