Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2000-12-15
2002-05-21
Lefkowitz, Edward (Department: 2862)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C324S323000
Reexamination Certificate
active
06393363
ABSTRACT:
This invention claims priority to International Application No. PCT/US00/17695 filed on Jun. 28, 2000.
BACKGROUND OF THE INVENTION
Geologic formations defining a reservoir for the accumulation of hydrocarbons in the subsurface of the earth contain a network of interconnected paths in which fluids are disposed that ingress or egress from the reservoir. To determine the nature and behavior of the fluids in the aforementioned network, knowledge of both the nature of the pore fluids and the porosity of the geologic formations is desired. From this information, efficient development and management of hydrocarbon reservoirs may be achieved. For example, the resistivity of geologic formations is a function of both porosity of the formations and resistivity of the fluids. Considering that hydrocarbons are electrically insulative and most formation water contains salts, resistivity measurements are a valuable tool to determine the presence of hydrocarbon reservoirs in geologic formations and to monitor the changes in hydrocarbon content as production of the hydrocarbon proceeds.
To that end, there have been many prior art attempts to determine the electrical resistivity of geologic formations surrounding and between boreholes drilled into the geologic formations of interest. In two articles,
Crosshole electromagnetic tomography: A new technology for oil field characterization
, The Leading Edge, March 1995, by Wilt et al. and
Crosshole electromagnetic tomography: System design considerations and field results
, Society of Exploration Geophysics, Vol. 60, No. 3, 1995 by Wilt et al., measurement of geologic formation resistivity is described employing a low frequency electromagnetic (em) systems.
FIG. 1
shows the configuration of equipment used in the measurement of geologic formation resistivity between two boreholes. A transmitter, T, is located in one borehole and consists of a coil C
T
having multi-turn horizontal loop (vertical solenoid) of N
T
turns, having an effective cross section A
T
. The multi-turn horizontal loop carries an alternating current, I
T
, at a frequency of f
0
Hz. In free space this multi-turn horizontal loop produces a time varying magnetic field, B
0
. The magnetic field, B
0
, is proportional to the magnetic moment of the transmitter, M
T
, and to a geometric factor, k
1
. The magnetic moment of the transmitter M
T
is defined as follows:
M
T
=N
T
I
T
A
T
(1)
The geometric factor, k
1
, is a function of a spatial location and orientation of a field component of the magnetic field, B
0
, measured by a receiver, R, with respect to the magnetic moment of the transmitter, M
T
. The receiver is located spaced-apart from the transmitter, T, and typically disposed in a borehole in the earth. In free space, therefore, the magnetic field, B
0
, is defined as follows:
B
0
=k
1
M
T.
(2)
The receiver, R, typically includes a multi-turn loop of wire, i.e., a coil, C
R
, having N
R
turns of wire, wound about a core of high permeability metal or ferrite. The changing magnetic field B
R
, sensed by the receiver, R, with frequency f
0
, creates an induced voltage V
R
in the coil which is proportional to, B
R
; the frequency, f
0
; the number of turns of wire, N
R
; the effective cross-sectional area of the coil, A
R
; and the effective permeability, &mgr;
R
, of the core of coil C
R
. From the foregoing, it is shown that V
R
is defined as follows:
V
R
=f
0
B
R
N
R
A
&mgr;R
(3)
Simplifying equation (3) above, V
R
may be written as follows:
V
R
=k
R
B
R
(4)
where k
R
=f
0
N
R
A
R
&mgr;
R
. The product of A
R
&mgr;
R
is difficult to calculate. To accurately determine A
R
&mgr;
R
, C
R
is calibrated in a known field, at a known frequency to find an exact value for k
R
. Thereafter, the magnetic field, B
R
sensed by the receiver, R, is related directly to the measured voltage V
R
by the following:
B
R
=V
R
/k
R
(5)
Such sensors measure the magnetic field in the direction of the axis of the solenoid.
When this system is placed in a conducting geologic formation the time varying magnetic field, B
0
, produces an electromotive force in the geologic formation, which in turn drives currents therein, shown schematically as L
1
. The currents, L
1
, are proportional to the conductivity of the geologic formation and are concentric about the longitudinal axis of the borehole. The magnetic field proximate to the borehole is a result of the free space field, B
0
, called the primary magnetic field, and the field from the current L
1
, called the secondary magnetic field. The sum of these fields is a vector and the described sensors thus measure a component of the vector field in the direction of the solenoidal axis. In the examples used in the description of this invention the components of the magnetic field along the axis of the bore hole are used. In the convention used here this is defined as the z axis. Other components may be used and indeed the referenced studies indicate that other components may be used to improve the resulting determination of the distribution of resistivity in the formation.
The current L
1
is typically out of phase with respect to the transmitter current I
t
. At very low frequencies, where the inductive reactance of the surrounding formation is small, the induced current L
1
, is proportional to dB/dt and is consequently 90° out of phase with respect to I
t
. As the frequency increases, the inductive reactance increases and the phase increases to be greater than 90°.
The secondary magnetic field at the receiver, R, is caused by the induced current and consequently also has a phase shift and so the total field is complex. The total measured field has a component, B
R
, in-phase with the transmitter current I
T
, (called the real component) and a component, B
I
, phase shifted by 90° (called the imaginary or quadrature component). The values of the real, B
R
, and quadrature components, B
I
, of the magnetic field at a given frequency and geometrical configuration uniquely specify the electrical resistivity of a homogenous formation pierced by the drill holes. In an inhomogeneous geologic formation, the complex field is measured at a succession of points along the longitudinal axis of the receiver borehole for each of a succession of transmitter locations. The multiplicity of T-R locations suffices to determine the inhomogeneous resistivity between the holes as described in the papers above.
In general, the inhomogeneous distribution of electrical resistivity is determined through a process called inversion which is well described by
Audio-frequency electromagnetic tomography in
2-
D
, Geophysics, Vol. 58, No. 4, 1993 by Zhou et al.,
Electromagnetic conductivity imaging with an iterative born inversion
, IEEE Transactions on Geoscience and Remote Sensing, Vol. 31, No. 4, 1993 by Alumbaugh et al.,
An approach to nonlinear inversion with applications to cross-well EM tomography
63
rd
Annual International Meeting, Society of Exploration Geophysics, Expanded Abstracts, 1993 by Torres-Verdin et al., and
Crosswell electromagnetic inversion using integral and differential equations
, Geophysics, Vol. 60, No. 3, 1995 by Newman. This process has been well demonstrated for the determination of resistivity in the vicinity of a single borehole or between spaced-apart boreholes wells and is described in detail by
Crosswell electromagnetic tomography: System design considerations and field results
, Geophysics, Vol. 60, No. 3, 1995 by Wilt et al.,
Theoretical and practical considerations for crosswell electromagnetic tomography assuming a cylindrical geometry
, Geophysics, Vol. 60, No. 3, by Alumbaugh and Wilt, and 3
D EM imaging from a single borehole; a numerical feasibility study
, 1998 by Alumbaugh and Wilt.
In brief one embodiment of the inversion process consists in assigning resistivities to a multitude of cells or elements of the volume surrounding, or between, boreholes. The resistivities are systematically varied until, in a least squares sense
Nichols Edward
Wilt Michael
Ryberg John J.
Segura Victor H.
Taylor Victor J.
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