US 4,361,808 A · Dielectric constant well logging with current and voltage electrodes

Abstract

This invention provides for methods and systems for measuring the dielectric constant of an earth formation. In a preferred embodiment, an alternating current is passed through a portion of the formation and a reference resistor in series with the portion. The capacitance and the dielectric constant of the portion may be determined from the phase difference between the voltage across the reference resistor and the voltage across the portion. This phase difference may be obtained by generating a voltage which is in phase with the voltage across the reference resistor, but which has the magnitude of the voltage across the portion. To obtain the phase difference by an alternate digital method, the voltage across the referenced resistor and the voltage across the portion are each transformed into a square wave signal. The two square wave signals are then compared to obtain the sign and the magnitude of the phase difference between the two square waves. In an alternate preferred embodiment, an alternating current is passed through the portion of the earth formation and through a capacitor and a resistor connected in series with the portion. The first DC signal is generated by filtering out the high frequency components from the product of the voltages across the capacitor and across the portion. A second DC signal is generated by filtering out the high frequency components from the product of the voltages across the referenced resistor and across the portion. The phase difference between the voltage across the portion and the current through the portion may be determined, from which the capacitance and the dielectric constant of the portion may then be calculated.

Claims11

Dependent claims

An apparatus for determining the dielectric constant of a portion of an earth formation traversed by a bore hole, comprising:

a current source capable of supplying alternating current of a substantially constant magnitude to said portion of the earth formation;
a reference resistor connected in series with the current source and said portion;
a first differential isolation amplifier for measuring the voltage across said portion of the earth formation;
a second differential isolation amplifier for measuring the voltage across the reference resistor;
means for generating a positive first voltage with substantially the magnitude of the voltage across said portion;
a four-quadrant multiplier having as inputs the voltage across the reference resistor and the positive first voltage generated;
a first amplifier with a predetermined gain connected to the multiplier for amplifying the multiplier output so that the output voltage of the first amplifier is substantially in phase with the voltage across the reference resistor but has substantially the magnitude of the voltage across said portion;
and
a second amplifier for taking the voltage difference E.phi. between the voltage across said portion and the output voltage of the first amplifier so that the capacitance C.sub.s of said portion may be determined from the relationship:
##EQU26## wherein E.sub.s =the voltage across aid portion;
E.sub.R =the voltage across the reference resistor;
R=the resistance of the reference resistor;
.omega.=the angular frequency of the alternating current;
and
.alpha.=the bore hole correction factor.

12 more elements

An apparatus for determining the dielectric constant of a portion of an earth formation traversed by a bore hole comprising:

a current source capable of supplying alternating current to said portion of the earth formation;
a reference resistor connected in series with the current source and with said portion of the earth formation;
means for measuring the voltage across the reference resistor;
means for measuring the voltage across said portion of the earth formation;
means for generating a positive voltage with substantially the magnitude of the voltage across said portion;
means for generating a positive voltage with substantially the magnitude of the voltage across the reference resistor;
a first four-quadrant multiplier for multiplying the voltage across the reference resistor and the positive voltage generated with the magnitude of the voltage across said portion;
a first operational amplifier with the negative input at virtual ground;
a first resistor connecting the output of said first multiplier to the negative input of the first operational amplifier;
a second four-quadrant multiplier for multiplying the positive voltage generated having substantially the magnitude of the voltage across the reference resistor and the output voltage of the first operational amplifier;
and
a second resistor connecting the output of said second multiplier to the negative input of the first operational amplifier so that the output voltage of the first operational amplifier has substantially the magnitude of the voltage across said portion and is substantially in phase with the voltage across the reference resistor;
and
a second operational amplifier for taking the voltage difference E.phi. between the voltage across said portion and the output voltage of the first operational amplifier so that the capacitance C.sub.s of said portion may be determined from the relationship:
##EQU27## wherein E.sub.s =the voltage across said portion;
E.sub.R =the voltage across the reference resistor;
R=the resistance of the reference resistor;
.omega.=the angular frequency of the alternating current;
and
.alpha.=the bore hole correction factor.

17 more elements

An apparatus for determining the dielectric constant of a portion of an earth formation traversed by a bore hole, comprising:

a reference resistor;
a capacitor;
an alternating current source connected in series with the reference resistor, the capacitor and said portion of the earth formation;
means for measuring the voltage across said portion of the earth formation;
means for measuring the voltage across the capacitor;
means for measuring the voltage across the reference resistor;
a first four-quadrant multiplier to provide a first voltage signal substantially proportional to the product of the voltage across the capacitor with the voltage across said portion;
a first low pass filter connected to said first four-quadrant multiplier for filtering out substantially the high frequency components of the output voltage of said first multiplier to obtain a second voltage signal substantially proportional to the product of (a) the magnitude of the signal voltage across said portion, (b) the magnitude of the signal voltage across the capacitor, and (c) the phase angle .phi. between the voltage across said portion and the voltage across the reference resistor;
a second four-quadrant multiplier to provide a third voltage signal substantially proportional to the product of the voltage across said portion with the voltage across the reference resistor;
and
a second low pass filter connected to said second four-quadrant multiplier for filtering out substantially the high frequency components of the output voltage of said second multiplier to obtain a fourth voltage signal substantially proportional to the product of the magnitudes of the signal voltages across said portion and across the reference resistor;
and
a filtered rectifier for obtaining a positive voltage having substantially the magnitude of the voltage across the reference resistor, so that the capacitance C.sub.s of said portion of the earth formation may be determined by the relationship:
##EQU29## wherein .alpha.=a bore hole correction factor;
.vertline.E.sub.R .vertline.=the magnitude of the voltage signal across the reference resistor;
E.sub.1 =the second voltage signal;
C=the capacitance of the capacitor;
A=a predetermined constant;
and
E.sub.2 =the fourth voltage signal.

17 more elements

Dependencies are inferred from the claim text.

Dielectric constant well logging with current and voltage electrodes

Life of this patent

Dielectric constant well logging with current and voltage electrodes

Life of this patent

Abstract

Claims11