Note: Descriptions are shown in the official language in which they were submitted.
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METHOD OF EVALUATING FORMATION RESISTIVITY
AT A SELECTED DEPTH OF INVESTIGATION
FIELD OF THE INVENTION
The present invention relates generally to the interpretation of downhole
property
measurements. More particularly, the present invention relates to an improved
method for
interpreting the measurements made by tools having multiple depths of
investigation.
BACKGROUND OF THE INVENTION
The gathering of downhole information has been done by the oil well industry
for many
years. Modern petroleum drilling and production operations demand a great
quantity of
information relating to the parameters and conditions downhole. Such
information typically
includes the location and orientation of the well bore and drilling assembly,
earth formation
properties, and drilling environment parameters downhole. The collection of
information relating
to formation properties and conditions downhole is commonly referred to as
"logging", and can
be performed by several methods.
In conventional wireline logging, a probe or "sonde" having various sensors is
lowered
into the borehole after some or all of the well has been drilled. The sonde is
typically constructed
as a hermetically sealed steel cylinder for housing the sensors, and is
typically suspended from the
end of a long cable or "wireline". The wireline mechanically suspends the
sonde and also provides
electrical conductors between the sensors (and associated instrumentation
within the sonde) and
electrical equipment located at the surface of the well. Normally, the cable
transports power and
control signals to the sonde, and transports information signals .from the
sonde to the surface. In
accordance with conventional techniques, various parameters of the earth's
formations adjacent the
CA 02346193 2001-05-02
borehole are measured and correlated with the position of the sonde in the
borehole as the sonde is
pulled uphole.
An alternative to wireline logging entails the collection of data during the
drilling process
itself. Designs for measuring conditions downhole along with the movement and
location of the
drilling assembly, contemporaneously with the drilling of the well, have come
to be known as
"measurement-while drilling" techniques, or "MWD". Similar techniques,
concentrating more on
the measurement of formation parameters, have commonly been referred to as
"logging while
drilling" techniques, or "LWD". While distinctions between MWD and LWD may
exist, the
terms MWD and LWD often are used interchangeably. For the purposes of this
disclosure, the
term LWD will be used with the understanding that this term encompasses both
the collection of
formation parameters and the collection of information relating to the
movement and position of
the drilling assembly.
The sensors used in a wireline sonde or a bottom hole assembly may include a
source
device for transmitting energy into the formation, and one or more receivers
for detecting the
energy reflected from the formation. Various sensors have been used to
determine particular
characteristics of the formation, including nuclear sensors, acoustic sensors,
and electrical
sensors.
For an underground formation to contain petroleum, and for the formation to
permit the
petroleum to flow through it, the rock comprising the formation must have
certain well known
physical characteristics. For example, one characteristic is that the rock in
the formation have space
to store petroleum. If the rock in a formation has openings, voids, and spaces
in which oil and gas
may be stored, it is characterized as "porous". Thus, by determining if the
rock is porous, one skilled
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in the art can determine whether or not the formation has the requisite
physical properties to store
and yield petroleum. Various well known sensors may be used to measure
formation porosity.
One type of logging tool used to measure porosity is a nuclear magnetic
resonance tool.
These tools generally function by pulsing the formation with a strong magnetic
field and measuring
the electromagnetic signatures of hydrogen nuclei falling into and out of
alignment with the
magnetic field. The electromagnetic signatures are used to determine
relaxation time distributions
for the hydrogen nuclei, which can be used to infer several secondary
attributes such as porosity.
For accurate interpretation of the measurements, it is helpful to have other
sensors measuring other
properties of the formation.
To identify the fluids held by porous rock formations, other sensors are used.
One property
that may be used to distinguish between liquid petroleum and brine in a
formation is the formation
resistivity. Porous formations having a low resistivity are likely to contain
brine, whereas
formations that contain petroleum are likely to have a high resistivity. In a
type of formation called
"shaley-sand," for example, the shale bed can have a resistivity of about 1
ohm-meter. A bed of oil-
saturated sandstone, on the other hand, is likely to have a higher resistivity
of about 10 ohm-meters
or more. The sudden change in resistivity at the boundary between beds of
shale and sandstone can
be used to locate these boundaries. Various tools well known to those of skill
in the art may be used
to acquire the resistivity measurements. Examples of suitable tools include
galvanic tools, induction
tools, and resistivity tools.
A typical formation does not have a uniform (or "homogeneous") resistivity
throughout, so
it is usually desirable to measure the resistivity in various regions around
the borehole to fully
characterize the formation. Tools commonly measure the resistivity along a
concentric volume
around the borehole, at an average radius which is called the "depth of
investigation" or "radius of
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investigation." To thoroughly characterize the formation, measurements are
taken with a variety of
depths of investigation and at a variety of vertical positions within the
borehole. The depth of
investigation generally is determined by the distance between the transmitter
and receiver, with a
longer spacing resulting in a deeper depth of investigation and a shorter
spacing providing a
shallower depth of investigation. Other factors also influence the depth of
investigation, such as the
signal frequency and whether phase resistivity or attenuation resistivity is
used.
The tools of interest to the present application make several measurements
that have
corresponding different depths of investigation. The need for multiple depths
of investigation is in
part motivated by a phenomenon known as "formation invasion". As the
formations near the
borehole are exposed to fluids contained in the borehole (such as drilling
mud), the borehole fluids
diffuse a short distance into the formation, significantly altering the
formation resistivity in the
immediate proximity of the borehole. To determine the true resistivity of the
undisturbed formation,
it is necessary to account for the effects of invasion. Existing methods for
doing this treat the
invaded region as a cylinder of uniformly altered resistivity but variable
diameter.
While effective for determining undisturbed formation resistivity, this
approach provides
only a crude support for identifying the present resistivity of a formation at
a particular radius.
Consequently it is inadequate for use in conjunction with Nuclear Magnetic
Resonance logging
tools that benefit from accurate estimates of the resistivity in their
specific volumes of investigation.
2o SLJwIMARY OF THE INVENTION
Accordingly, there is disclosed herein a method for radially profiling a
property of a
formation around a borehole that is suitable for combining measurements from
multiple tools. In
one embodiment, the method includes: (i) using a first downhole tool to obtain
property
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measurements associated with multiple investigation depths; and (ii)
determining from the
property measurements estimated property values in predetermined radial zones.
The
predetermined radial zones preferably include one zone that is the region of
investigation by a
second tool. This allows the estimated property value to be used in
conjunction with any
S measurements by the second tool, or alternatively, provides a reference for
calibrating the second
tool. The estimated property values for the various predetermined radial zones
are preferably
those that minimize a distance metric value (e.g. the Euclidean distance)
between the actual
property measurements and the measurements expected to result from a formation
profile having
the estimated property values. The first downhole tool could illustratively be
a resistivity tool,
and the second downhole tool could illustratively be a nuclear magnetic
resonance tool.
BRIEF DESCRIPTION OF THE DRAWINGS
A better understanding of the present invention can be obtained when the
following
detailed description of preferred embodiments is considered in conjunction
with the following
drawings, in which:
Figure 1 shows a computer system that will support execution of a resistivity
profile
determination method;
Figure 2 shows a first resistivity profile model;
Figure 3 shows a second, preferred resistivity profile model;
Figure 4 shows an environmental view of a well in which a resistivity tool
according to
the present invention may be used; and
Figure 5 shows a LWD resistivity tool having multiple volumes of
investigation.
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DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Given a set of property measurements at multiple depths of investigation, it
is desired to
interpret the measurements so as to determine the formation property in a
given region. Recall
that the measurements for the deeper depths of investigation correspond to
regions that include
the regions having the shallower depths of investigation, and that all
measurements are
influenced by the properties of the borehole fluid. Accordingly, to estimate
the actual formation
property values in selected regions, it is necessary to perform compensation
on the measurements
provided by the tool.
The interpretation methods are systematic algorithms that may be carried out
by a
processor of microcontroller of any kind, including that found in a general
purpose computer
system such as that shown in Fig. 1. The system of Fig. 1 includes a computer
"tower" 102, a
display device 106, and a user input device 108. The computer tower 102 houses
a power supply,
a processor, short and long term data storage, and input/output cannectors for
peripheral devices.
Typically, the computer tower 102 also includes one or more types of readers
for portable data
storage media. A user initiates via user input device 108 retrieval and
execution of the
compensation method. The processor in computer tower 102 retrieves the
compensation method
from the internal or portable data storage media, converts it to executable
form if necessary, and
executes it. The interpretation method is normally embedded in a larger
software module that
specifies where the resistivity data is found, and specifies where the
compensation results are to
be stored. Most such software modules will also provide feedback to the user
via display device
106. It is noted that the compensation method can also be performed in
hardware or firmware as
an application-specific integrated circuit (ASIC).
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For any set of resistivity measurements a finite number of investigation
depths, there are
an infinite number of resistivity profiles that could produce those
measurement values.
Consequently, the best interpretation approach is to use a model of the
resistivity profile. The
number of "degrees of freedom" (i.e. independent parameters) in the model is
less than or equal
to the number of measurements. An example of a resistivity profile model is
shown in Fig. 2.
In the model of Fig. 2, it is assumed that the radius of the borehole (rb,,)
and the resistivity
of the borehole fluid (R",) are known. Indeed, these can be directly measured
by other
instruments. The model has three parameters: the near-borehole resistivity
(RXO), the invasion
depth (D;), and the undisturbed formation resistivity (R,). These parameters
can be determined by
processing measurements from a tool that has three or more depths of
investigation. The
parameter values are preferably those that minimize the measurement error E:
N 2
E= ~ LRk °g - Rk °ae~ (R~ ~ Rx° ~ Dr ~~ ~ (Eqn 1 )
k=1
where Rk°g, i=1,2,...N, are the log measurements at different
investigation depths, and
Rk odel (~, ~°, D~ ) are the expected log measurements for the model
profile. If the expected log
measurements are in the form of analytic expressions, this minimization can be
done by
evaluating the derivative of Eqnl and setting it equal to zero. If not, or
even if they are, this
minimization can be done using standard numerical computation techniques, such
as those taught
in William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P.
Flannery,
Numerical Recipes in C: The Art of Scientific Computing., 2°d edition
published January 1993 by
Cambridge University Press; ISBN: 0521431085. If repeated evaluation of the Rk
odel (~, ~°, Dt )
function is unduly burdensome, a look-up table for each Rk °de' (IZ~,
Rx°, D; ) as a function of the
CA 02346193 2001-05-02
parameters may be created and iteratively accessed by a processor that
identifies the parameters
corresponding to the minimum error.
In an alternative embodiment, a look-up table for the parameter set as a
function of the
log measurements Rk°g can be created. In this table, the solutions for
a range or probable log
measurements are precalculated and stored. The solution parameter set can then
be easily
retrieved (by interpolation if necessary) without iterative processing.
Because the delineation between resistivity regions is mobile, this model is
not suitable
for determining the resistivity of the formation at a specific radius, unless
that radius happens to
be very close to the borehole or very far away from the borehole. The ability
to estimate the
resistivity at a specific radius is desirable for combining the measurements
of the resistivity tool
with other downhole measurements, such as, e.g., those obtained using a
nuclear magnetic
resonance tool.
Accordingly, a preferred resistivity profile model is that shown in Fig. 3,
where the
resistivity zones are predetermined. In other words, a number of zones is
selected and the limits
of the zones defined before resistivity values are calculated. One of the
zones is preferably
selected to correspond to the region of interest for other instrument
measurements (e.g. rl-r2),
while another zone is preferably selected to correspond to the invaded region
(e.g. rbh-rl), and yet
another zone is selected to correspond to the undisturbed formation region
(e.g. >r4). In the
model of Fig. 3, the values for Rm, rb,,, rl, r2, and r3 are fixed, and the
resistivity values Rl, R2, R3,
and R4 are determined from the log measurements. The procedure is similar to
that previously
described. Namely, the measurement error E:
N 2
E-~~Rk~g -~°aBr~R~~~~R3~R4~ ~ (Eqn2)
k=1
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is minimized using analytic or numerical computation techniques. Since four
parameters are
being determined, resistivity measurements for at least four investigation
depths are needed.
It is noted that while the example uses four parameters, the preferred
resistivity profile
model is not so limited. The actual number of parameters will vary as needed
up to the number
of resistivity measurements available.
This profile model can be used for calculating the resistivity in preselected
zones from
measurements made by any multi-depth-of investigation resistivity tool.
Advantageously, the
resistivity from one of the zones can then be used for comparison,
calibration, or adjustment of
the measurements made by other tools specific to that zone. This approach may
also be
applicable to other formation property measurements, such as porosity and
density.
The following description is now provided to describe an illustrative
environment where
this technique may be used. Fig. 4 shows a well during drilling operations. A
drilling platform 2
is equipped with a derrick 4 that supports a hoist 6. Drilling of oil and gas
wells is carried out by
a string of drill pipes connected together by "tool" joints 7 so as to form a
drill string 8. The hoist
6 suspends a kelly 10 that is used to lower the drill string 8 through rotary
table 12. Connected to
the lower end of the drill string 8 is a drill bit 14. The bit 14 is rotated
and drilling accomplished
by rotating the drill string 8, by use of a downhole motor near the drill bit,
or by both methods.
Drilling fluid, termed mud, is pumped by mud recirculation equipment 16
through supply pipe
18, through drilling kelly 10, and down through the drill string 8 at high
pressures and volumes
to emerge through nozzles or jets in the drill bit 14. The mud then travels
back up the hole via
the annulus formed between the exterior of the drill string 8 and the borehole
wall 20, through a
blowout preventer (not specifically shown), and into a mud pit 24 on the
surface. On the surface,
the drilling mud is cleaned and then recirculated by recirculation equipment
16. The drilling mud
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is used to cool the drill bit 14, to carry cuttings from the base of the bore
to the surface, and to
balance the hydrostatic pressure in the rock formations.
In a preferred embodiment, downhole sensors 26 are coupled to a telemetry
transmitter
28 that transmits telemetry signals by modulating the mud flow in drill string
8. A telemetry
receiver 30 is coupled to the kelly 10 to receive transmitted telemetry
signals. Other telemetry
transmission techniques are well known and may be used.
One of the sensors 26 is a resistivity tool having multiple depths of
investigation. An
example of one such resistivity tool is shown in Fig. 5. Resistivity tool 40
has a series of
transmitters 42 and a pair of receivers 44. When one of the transmitters 42 is
excited by an
oscillatory signal, it generates an electromagnetic wave that propagates into
the formation. The
receiver pair 44 detects the electromagnetic wave as modified by the
formation. The attenuation
and phase difference between the receivers may be used to identify the average
resistivity in a
volume around the borehole 20 having an average depth of investigation 46
determined by the
transmitter/receiver-pair spacing.
1 S Since resistivity tool 40 has six transmitter/receiver-pair spacings, the
resistivity for at
least six depths of investigation may be measured. It is important to note
that because the larger
volumes of investigation include the smaller volumes of investigation, the
resistivity
measurements for the deeper depths of investigation are influenced by the
resistivities nearer the
borehole. Conceptually, the shallower depth resistivity measurements are used
to compensate the
deeper depth resistivity measurements, so that a more accurate estimate of the
undisturbed
formation resistivity may be obtained.
It is noted that the use of the term resistivity tool is intended to include
both induction
tools, galvanic tools, and any other tools that produce resistivity or
conductivity measurements at
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multiple depths of investigation. The selected resistivity profile model may
have two, but
preferably has three or more, fixed zones for which the resistivity is
calculated.
Numerous variations and modifications will become apparent to those skilled in
the art
once the above disclosure is fully appreciated. For example, the present
invention is not limited
to resistivity, but may alternatively be applied to the interpretation of
other downhole property
measurements. It is intended that the following claims be interpreted to
embrace all such
variations and modifications.
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