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P.S. Adisoemarta

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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Permian Basin Oil and Gas Recovery Conference, March 21–23, 2000

Paper Number: SPE-59532-MS

Abstract

Abstract 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. Electromagnetic Theory 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: Equation (1) Equation (2) and with the conservation of charge defined as: Equation (3) are the components of the electromagnetic field, where: E = electric field intensity (volt/meter) B = magnetic flux density (webers/meter 2 ) H = magnetic field intensity (ampere-turn/meter) D = electric displacement (coulomb/meter 2 ) J = electric current density (ampere/meter 2 ) q = charge density (coulomb/meter 3 ). For the case of homogeneous, isotropic, and a non-zero electrical conductivity medium, the electric field becomes Equation (4) For the case of materials that exhibit electromagnetically linear behavior, the following relationships are valid: Equation (5) Equation (6) Equation (7) where e= dielectric permittivity (farad/m) s= electric conductivity (mho/m or siemens/m) µ= magnetic permeability (henry/m). The equation for total current density, J T , is the result of solving equations (2), (5), and (6): Equation (8) where s E is the conduction current component (in phase with applied voltage), and e dE/dt is the displacement current component (the out of phase response).

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Permian Basin Oil and Gas Recovery Conference, March 21–23, 2000

Paper Number: SPE-59699-MS

Abstract

Abstract Archie's laboratory experiments established a relationship between theformation resistivity factor and porosity, which set forth the use of twoconstants: m and a . From Archie's work these constants wereregression constants representing the slope and intercept, respectively.Subsequent researchers used the general form of Archie's relation, but theyfound differing values for m and a . The terms cementation factorand tortuosity factor have been used to describe each of these terms.Conventional wisdom believes that a higher m relates to vuggy porosity and alower m suggests fracture porosity. This is generally true if thetortuosity factor is assumed (typically 0.81 or 1.0) and the cementation factoris calculated. However, if m and a are found simultaneously, theory and manylaboratory observations suggest the opposite may be more likely. This studyshows that the tortuosity factor, a , is a function of the average angleof electrical movement with respect to the bulk fluid flow, and cementationfactor m is related to the flow area contrast between pore throat and porebody. Historical Background In 1942, Archie published the results of his investigations on therelationship of true formation resistivity and certain characteristic physicalproperties of a reservoir rock. The impetus for his work was the challenge todevelop methods and relationships that could be used in the quantitativeapplication of electrical resistivity log information in the detection andevaluation of a subsurface hydrocarbon accumulation. He reasoned that in orderto be able to recognize a reservoir formation containing hydrocarbons andconnate water, it is first necessary to be able to recognize the resistivity ofa formation when all its pores are filled with connate water (S w =100%). Without this understanding, it would not be possible toappreciate the resistivity added to a formation when some connate water in thepore system of a reservoir rock is replaced by hydrocarbons. Archie's work established the following simple relationship: F = R o /R w where: F = Formation resistivity factor R o = Resistivity of rock/formation with pores filled withbrine R w = Resistivity of the brine The concept of the formation resistivity factor was straightforward. If theresistivity of a brine is measured, then the resistivity of a reservoir rockwhose pores are 100% saturated with that brine is also measured, therock-saturated measurement will be larger than the first. The difference inthese resistivity values is the result of the effects of the formation on thepath of the electrical current travelling through the electrolytic brine in therock pore system.