Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2001-04-03
2003-06-03
Lefkowitz, Edward (Department: 2862)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C702S006000
Reexamination Certificate
active
06574562
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention is related generally to the field of interpretation of measurements made by well logging instruments for the purpose of determining the properties of earth formations. More specifically, the invention is related to a method for determination of anisotropic formation resistivity using multifrequency, multicomponent resistivity data.
2. Background of the Art
Electromagnetic induction and wave propagation logging tools are commonly used for determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that when properly interpreted are diagnostic of the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in, H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud, Journal of Petroleum Technology, vol. 1, p.148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517; U.S. Pat. No. 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al.
A limitation to the electromagnetic induction resistivity well logging instruments known in the art is that they typically include transmitter coils and receiver coils wound so that the magnetic moments of these coils are substantially parallel only to the axis of the instrument. Eddy currents are induced in the earth formations from the magnetic field generated by the transmitter coil, and in the induction instruments known in the art these eddy currents tend to flow in ground loops which are substantially perpendicular to the axis of the instrument. Voltages are then induced in the receiver coils related to the magnitude of the eddy currents. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. The response of the typical electromagnetic induction resistivity well logging instrument will be largely dependent on the conductivity of the conductive layers when the layers are substantially parallel to the flow path of the eddy currents. The substantially non-conductive layers will contribute only a small amount to the overall response of the instrument and therefore their presence will typically be masked by the presence of the conductive layers. The non-conductive layers, however, are the ones which are typically hydrocarbon-bearing and are of the most interest to the instrument user. Some earth formations which might be of commercial interest therefore may be overlooked by interpreting a well log made using the electromagnetic induction resistivity well logging instruments known in the art.
The effect of formation anisotropy on resistivity logging measurements have long been recognized. Kunz and Moran studied the anisotropic effect on the response of a conventional logging device in a borehole perpendicular to the bedding plane of t thick anisotropic bed. Moran and Gianzero extended this work to accommodate an arbitrary orientation of the borehole to the bedding planes.
Rosthal (U.S. Pat. No. 5,329,448) discloses a method for determining the horizontal and vertical conductivities from a propagation or induction well logging device. The method assumes that &thgr;, the angle between the borehole axis and the normal to the bedding plane, is known. Conductivity estimates are obtained by two methods. The first method measures the attenuation of the amplitude of the received signal between two receivers and derives a first estimate of conductivity from this attenuation. The second method measures the phase difference between the received signals at two receivers and derives a second estimate of conductivity from this phase shift. Two estimates are used to give the starting estimate of a conductivity model and based on this model, an attenuation and a phase shift for the two receivers are calculated. An iterative scheme is then used to update the initial conductivity model until a good match is obtained between the model output and the actual measured attenuation and phase shift.
Hagiwara shows that the log response of an induction-type logging tool can be described by an equation of the form
V
∝
ⅈ
L
3
(
-
2
ⅇ
ⅈ
kL
(
1
-
ⅈ
kL
)
+
ⅈ
kl
(
ⅇ
ⅈ
k
β
-
ⅇ
ⅈ
kL
)
)
(
1
)
where
&bgr;
2
=cos
2
&thgr;+sin
2
&thgr; (2)
and
k
2
=&ohgr;
2
&mgr;(∈
h
+i&sgr;
h
/&ohgr;) (3)
where, L is the spacing between the transmitter and receiver, k is the wavenumber of the electromagnetic wave, &mgr; is the magnetic permeability of the medium, &thgr; is the deviation of the borehole angle from the normal to the formation, &lgr; is the anisotropy factor for the formation, &ohgr; is the angular frequency of the electromagnetic wave, &sgr;
h
is the horizontal conductivity of the medium and ∈
h
is the horizontal dielectric constant of the medium.
Eq. (3) is actually a pair of equations, one corresponding to the real part and one corresponding to the imaginary part of the measured signal, and has two unknowns. By making two measurements of the measured signal, the parameters k and &bgr; can be determined. The two needed measurements can be obtained from (1) R and X signals from induction logs, (2) phase and attenuation measurements from induction tools, (3) phase or attenuation measurements from induction tools with two different spacings, or (4) resistivity measurements at two different frequencies. In the low frequency limit, ∈ can be neglected in Eq. (3) and from known values of &ohgr; and &mgr;, the conductivity &sgr; can be determined from k, assuming a value of &mgr; equal to the permittivity of free space
Wu (U.S. Pat. No. 6,092,024) recognized that the solution to eqs. (1)-(3) may be nonunique and showed how this ambiguity in the solution may be resolved using a plurality of measurements obtained from multiple, spacings and/or multiple frequencies.
One solution to the limitation of the induction instruments known in the art is to include a transverse transmitter coil and a transverse receiver coil on the induction instrument, whereby the magnetic moments of these transverse coils is substantially perpendicular to the axis of the instrument. Such as solution was suggested in Tabarovsky and Epov, “Geometric and Frequency Focusing in Exploration of Anisotropic Seams”, Nauka, USSR Academy of Science, Siberian Division, Novosibirsk, pp. 67-129 (1972). Tabarovsky and Epov suggest various arrangements of transverse transmitter coils and transverse receiver coils, and present simulations of the responses of these transverse coil systems configured as shown therein. Tabarovsky and Epov also describe a method of substantially reducing the effect on the voltage induced in transverse receiver coils which would be caused by eddy currents flowing in the wellbore and invaded zone. The wellbore is typically filled with a conductive fluid known as drilling mud. Eddy currents which flow in the drilling mud can substantially affect the magnitude of voltages induced in the transverse receiver coils. The wellbore signal reduction method described by Tabarovsky and Epov can be described as “frequency focusing”, whereby induction voltage measurements are made at more than one frequency, and the signals induced in the transverse receiver coils are combined in a manner so that the effects of eddy currents flowing within certain geometries, such as the wellbore and invasion zone, can be substantially eliminated from the final result. Tabar
Rabinovich Michael B.
Tabarovsky Leonty A.
Baker Hughes Incorporated
Gutierrez Anthony
Lefkowitz Edward
Madan Mossman & Sriram P.C.
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