Note: Descriptions are shown in the official language in which they were submitted.
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METHODS AND APPARATUS FOR MEASURING STREAMING POTENTIALS AND
DETERMINING EARTH FORMATION CHARACTERISTICS
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates broadly to the hydrocarbon
industry. More particularly, this invention relates to
apparatus and methods for measuring streaming potentials
resulting from pressure transients in an earth formation
traversed by a borehole. This invention also relates to
manners of making determinations regarding earth formation
characteristics as a result of streaming potential
measurements. One such characteristic is the permeability
of the formation at different depths thereof, although the
invention is not limited thereto.
2. State of the Art
The history with respect to the possibility of making
streaming potential measurements in a downhole formation is
a long one. In U.S. Patent #2,433,746, (1947) Doll
suggested that vigorous vibration of a downhole apparatus in
a borehole could generate pressure oscillations and fluid
movement relative to the formation which in turn could give
rise to measureable streaming potentials due to an
electrokinetic potential phenomenon. In U.S. Patent
#2,814,017, (1957) Doll suggested methods for investigating
the permeabilities of earth formations by observing the
differences in phase between periodic pressure waves passed
through the formations and potentials generated by the
oscillatory motion of the formation fluid caused by these
pressure waves. Conversely, a periodically varying electric
current was suggested to be used to generate oscillatory
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motion. of the formation fluid, which in turn generated
periodic pressure waves in the formation. Measurements were
to be made of the phase displacement between the generating
and the generated quantities and a direct indication of the
relative permeability of the formation thereby obtained.
In U.S. Patent #3,599,085, to A. Semmelink, entitled,
"Apparatus For Well Logging By Measuring And Comparing
Potentials Caused By Sonic Excitation", (1971) the
application of low-frequency sonic energy to a formation
surface was proposed so as to create large electrokinetic,
or streaming, pulses in the immediate area of the sonic
generator. In accordance with the disclosure of that patent,
the electrokinetic pulses result from the squeezing (i.e.
the competition of viscosity and inertia) of the formation,
and the streaming potential pulses generate periodic
movements of the formation fluid relative to the formation
rock. The fluid movement produces detectable electrokinetic
potentials of the same frequency as the applied sonic energy
and having magnitudes at any given location directly
proportional to the velocity of the fluid motion at that
location and inversely proportional to the square of the
distance from the locus of the streaming potential pulse.
Since the'fluid velocity was found to fall off from its
initial value with increasing length of travel through the
formation at a rate dependent in part upon the permeability
of the formation rock, it was suggested that the magnitude
of the electrokinetic potential at any given distance from
the pulse provided a relative indication of formation
permeability. By providing a ratio of the electrokinetic
potential magnitudes (sinusoidal amplitudes) at spaced
locations from the sonic generator, from which
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electrokinetic skin depth may be derived, actual
permeability can in turn be determined.
In U.S. Patent #4,427,944, (1984) Chandler suggested a
stationary-type borehole tool and method for determining
formation permeability. The borehole tool includes a pad
device which is forced into engagement with the surface of
the formation at a desired location, and which includes
means for injecting fluid into the formation and electrodes
for measuring electrokinetic streaming potential transients
and response times resulting from the injection of the
fluid. The fluid injection is effectively a pressure pulse
excitation of the formation which causes a transient flow to
occur in the formation. Chandler suggests a measurement of
the characteristic response time of the transient streaming
potentials generated in the formation by such flow in order
to derive accurate information relating to formation
permeability.
In U.S. Patent #5,503,001 (1996), Wong proposed a
process and apparatus for measuring at finite frequency the
streaming potential and electro-osmotic induced voltage due
to applied finite frequency pressure oscillations and
alternating current. The suggested apparatus includes an
electromechanical transducer which generates differential
pressure oscillations between two points at a finite
frequency and a plurality of electrodes which detect the
pressure differential and streaming potential signal between
the same two points near the source of the pressure
application and at the same frequency using a lock-in
amplifier or a digital frequency response analyzer.
According to Wong, because the apparatus of the invention
measures the differential pressure in the porous media
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between two points at finite frequencies close to the source
of applied pressure (or current), it greatly reduces the
effect of background caused by the hydrostatic pressure due
to the depth of the formation being measured.
Despite the long history and multiple teachings of the
prior art, it is believed that in fact, prior to field
measurements made in support of instant invention, no
downhole measurements of streaming potential transients in
actual oil fields have ever been made. The reasons for the
lack of actual implementation of the proposed prior art
embodiments are several. According to Wong, neither the
streaming potential nor the electro-osmotic measurement
alone is a reliable indication of formation permeability,
especially in formations of low permeability. Wong states
that attempts to measure the streaming potential signal with
electrodes at distances greater than one wavelength from
each other are flawed since pressure oscillation propagates
as a sound wave and the pressure difference would depend on
both the magnitude and the phase of the wave, and the
streaming potential signal would be very much lower since
considerable energy is lost to viscous dissipation over such
a distance. In addition, Wong states that application of a
DC flow to a formation and measurement of the response
voltage in the time domain will not work in low permeability
formations since the longer response time and very low
streaming potential signal is dominated by drifts of the
electrodes' interfacial voltage over time. Thus, despite
the theoretical possibilities posed by the prior art, the
conventional wisdom of those skilled in the art (of which
Wong's comments are indicative) is that useful streaming
potential measurements are not available due to low signal
levels, high noise levels, poor spatial resolution, and poor
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long-term stability. Indeed, it is difficult to obtain
pressure transient data with high spatial resolution as the
borehole is essentially an isobaric region. The pressure
sensor placed inside the borehole cannot give detailed
information on the pressure transients inside the formation
if the formation is heterogeneous. To do so, it is
necessary to segment the borehole into hydraulically
isolated zones, a difficult and expensive task to perform.
Further, it will be appreciated that some of the proposed
tools of the prior art, even if they were to function as
proposed, are extremely limited in application. For
example, the Chandler device will work only in drilled
boreholes prior to casing and requires that the tool be
stationed for a period of time at each location where
measurements are to be made. Thus, the Chandler device
cannot be used as an MWD/LWD (measurement or logging while
drilling) device, is not applicable to finished wells for
making measurements during production, and cannot even be
used on a moving string of logging devices.
SUMMARY OF THE INVENTION
It is therefore an object of the invention to provide
methods and apparatus for measuring streaming potential in
an earth formation.
It is another object of the invention to provide
methods and apparatus for measuring streaming potentials in
a formation while drilling a borehole.
It is a further object of the invention to provide
methods and apparatus for measuring streaming potentials in
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a formation around a device permanently installed in a
wellbore.
It is also an object of the invention to provide
methods and apparatus for measuring streaming potentials in
a formation with a moving borehole tool.
It is an additional object of the invention to provide
methods of determining formation characteristics using
streaming potentials measurements.
Another object of the invention is to provide methods
of characterizing fractures in a formation using streaming
potential measurements.
A further object of the invention is to provide methods
of determining one or more of formation permeability, skin
permeability, effective fracture permeability, and
horizontal and vertical permeabilities of a formation using
streaming potential measurements.
In accord with these objects, which will be discussed
in detail below, different methods and apparatus for
measuring streaming potential in an earth formation are
provided. A first embodiment of the invention relates to
measuring streaming potential while drilling a borehole.
For purposes herein, measurement-while-drilling (MWD) and
logging-while-drilling (LWD) applications will be considered
interchangeable. A second embodiment of the invention
relates to measuring streaming potential with a borehole
tool which is adapted to make measurements while moving
through the borehole. A third embodiment of the invention
relates to measuring streaming potential with apparatus
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which is permanently installed (e.g., cemented) about the
wellbore. All embodiments of the invention can be utilized
to find characteristics of the formation. In particular,
since the streaming potential measurement relates directly
to fluid flow, the streaming potential measurements can be
used to track flow of fluids in the formation. In turn,
this information may be used to find the permeability of the
formation in different strata about the borehole and/or to
find and characterize fractures in the formation.
Additional objects and advantages of the invention will
become apparent to those skilled in the art upon reference
to the detailed description taken in conjunction with the
provided figures.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 is a schematic diagram of a completed horizontal
well having electrodes deployed thereabout for purposes of
measuring streaming potentials.
Fig. 2 is a schematic diagram of electrodes mounted on
insulated joint sections of the sand-screen completion of
Fig. 1.
Fig. 3 is a plot of pressure transients measured for
two of the zones shown in Fig. 1.
Fig. 4 is a plot showing pressure transients and
streaming potentials over time for the well of Fig. 1.
Fig. 5 is a plot showing the streaming potentials
measured by electrodes in zone 2 of Fig. 1.
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Fig. 6 is a plot showing the streaming potentials
measured by electrodes in zone 3 of Fig. 1.
Fig. 7 is a plot showing voltage drifts of the
electrodes in zone 1 of Fig. 1.
Fig. 8 is a plot showing streaming potentials measured
by electrodes in zone 1 of Fig. 1.
Fig. 9 is a schematic diagram of the well of Fig. 1
showing qualitative determinations made from information
obtained by the electrodes disposed about the well.
Fig. 9a is a schematic representing a forward model of
a heterogeneous formation.
Fig. 9b is a plot of streaming potentials generated by
the forward model of Fig. 9a.
Fig. 9c is a schematic representing a forward model of
a fractured f ormat ion .
Fig. 9d is a plot of streaming potentials generated by
the forward model of Fig. 9c.
Fig. 10 is a schematic diagram of a completed vertical
well having electrodes deployed thereabout for purposes of
measuring streaming potentials.
Fig. 11 is a schematic diagram of the manner in which
electrodes were mounted in the completed well of Fig. 10.
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Fig. 12 is a plot of the uphole pressure applied to the
well of Fig. 10 over a period of days.
Fig. 13 is a plot showing the uphole pressure of Fig.
12 and the streaming potentials measured by a series of
electrodes in a reservoir location shown in Fig. 10.
Fig. 14 is an enlarged version of a portion of Fig. 13.
Fig. 15 is a plot showing the uphole pressure of Fig.
12 and the streaming potentials measured by a group of
electrodes above the reservoir location.
Fig. 16 is an enlarged version of a portion of Fig. 15.
Fig. 17 is a plot showing the uphole pressure of Fig.
12 and the streaming potentials measured by a group of
electrodes below the reservoir location.
Fig. 18 is a schematic diagram of the well of Fig. 10
showing qualitative determinations made from information
obtained by the electrodes disposed about the well.
Fig. 18a is a schematic representing a forward model of
a vertical producing well having a fracture.
Fig. 18b is a plot of streaming potentials generated by
the forward model of Fig. 18a.
Fig. 19 is an enlarged ve'rsion of a portion of Fig. 17
which is used to show the stability of the electrodes.
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Fig. 20 is a schematic diagram of an open hole
completion with electrodes located about an insulated zone
surrounding a tubing.
Fig. 21 is a schematic diagram of a cased-hole
completion with electrodes incorporated into the casing.
Fig. 22 is a schematic diagram of an LWD tool with
streaming potential electrodes disposed thereon.
Fig. 23 is a schematic diagram of a wireline tool
having streaming potential electrodes disposed thereon.
Fig. 23a is a schematic representing a forward model of
a wireline tool which is adapted to slit borehole mudcake.
Fig. 23b is a plot of streaming potentials generated by
the forward model of Fig: 23a with respect to an uninvaded
zone.
Fig. 23c is a plot of streaming potentials generated by
the forward model of Fig. 23a with respect to an invaded
zone.
Fig. 23d is a plot generated by the forward model of
Fig. 23a of the sensitivity of the streaming potential with
respect to depth of invasion.
Fig. 23e is a plot which shows an inversion for
permeability of synthetic data and a best fit for a five
parameter model.
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DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Prior to turning to the Figures, some theoretical
considerations governing the physics of the invention are
useful. In reservoir rocks there exists a thin charged
double layer at the interface between the rock matrix and
the water in the pore. The matrix surface is negatively
charged, and the water is positively charged. When water
moves under a pressure gradient Vp,an electrical currentie
is created with the water current. The electrical current
is proportional to the water current, which is proportional
to the pressure gradient:
le= LVp. (1)
where L is a coupling constant which is a property of the
rock.
Pressure transients are created in the formation by
many different operations that occur over the lifetime of a
well such as drilling, mud invasion, cementing, water and
acid injection, fracturing, and oil and gas production.
Pressure transient testing is an established technique to
determine reservoir properties such as permeability,
reservoir size, and communication between different zones
and between different wells. As is set forth below,
streaming potential transients associated with the pressure
transients can also be used to determine these properties.
The modeling of the reservoir pressure p can be carried
out with multiphase flow models. For the modeling of the
streaming potential, it is useful to start with the
diffusion equation of a single-phase flow:
k P=0 c atp' (2)
p
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where k is the permeability, ,u is the viscosity, 0 is the
porosity, and C is the fluid compressibility. From the
modeled pressure field p, the streaming potential V can be
calculated by solving the Poisson Equation:
-0=o7OV = 0=LVp, (3)
where 6is the electrical conductivity.
From Eq. (2) it follows that the time At for a
pressure transient and the associated streaming potential
transient created at the borehole surface to diffuse through
a distance dx into the formation is given by
At - O~'~ (dx)2 (4)
The early time pressure and streaming potential transients
are sensitive mainly to reservoir properties near the
borehole, and the late time transients are sensitive to
reservoir properties both near the borehole and farther away
from the borehole. By interpreting the measured transients
in a time ordered fashion, reservoir properties at different
distances to the borehole can be determined. The
interpretation of pressure transients in this time ordered
fashion is an established art. For example, early time
pressure transients are used to determine damage to
permeabilities or "skin", and late time pressure transients
are used to determine reservoir boundaries.
The applications are much more limited if the steady
state values of the streaming potentials are the only
measurements available. At a steady state, equation (2)
becomes
V k p=0 . (5)
p
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The pressure drop Op across a depth interval Ax is then
proportional to
OpOekAx. (6)
The drop in the streaming potential 0 V is related to Ap by
AV =-LAp (7)
a
which is proportional to
AV oc Lp dx. (8)
a-k
The steady state streaming potential can only give
information on the average value of a reservoir property and
as a result is dominated by intervals with high values of
(L,u)/(6k). It is believed that in the presence of a
mudcake, the,steady state streaming potential is dominated
by the mudcake and is insensitive to reservoir properties.
The permeability of the mudcake is extremely low, and the
steady state pressure drop mainly exists across the mudcake.
While in principle it is possible to determine
reservoir properties at all distances to the borehole (i.e.,
radially from the borehole) by interpreting the transients
in a time ordered fashion, the critical question in practice
is whether the measurements can be made with sufficient
quality: accuracy, spatial resolution, and stability over
long time. It is difficult to get pressure transient data
with high spatial resolution as the borehole is essentially
an isobaric region. A pressure sensor placed inside the
borehole cannot give detailed information on the pressure
transients inside the formation if the formation is
heterogeneous. To do so, it would be necessary to segment
the borehole into hydraulically isolated zones, a difficult
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and expensive task to perform. On the other hand, the
borehole is not an equipotential surface for electric
current flow. Thus, streaming potential transients may be
measured by an array of electrodes placed inside the
borehole and electrically isolated (i.e., insulated) one
from the other and can provide equivalent information to
that of hydraulically isolated zone pressure transient
testing because the streaming potential is determined by the
pressure gradient. In fact, by utilizing an array of
isolated streaming potential electrodes, the streaming
potential can be measured with a higher spatial resolution
than hydraulically isolated zone pressure transient testing.
Given the theoretical understandings above, according
to one aspect of the invention, insulated electrodes are
deployed in or about a borehole or a well in order to
measure streaming potential transients. According to
different embodiments of the invention, and as will be
discussed in more detail below, the electrodes may be
deployed on insulated sections of a drill pipe in while-
drilling (MWD or LWD) applications, or on the body of a tool
which is moved through the borehole in wireline logging
applications. In post-completion applications, the
electrodes may be deployed on an insulating sonde placed in
an open hole for an open-hole completion, or on (or as part
of) centralizers in sand-screen completions, or in
insulation surrounding a casing in a cemented completion.
In a cased-hole completion with electrically isolated casing
sections, the metal casings can serve as electrodes.
Regardless of how the electrodes are deployed, DC voltage
differences indicative of streaming potentials are measured
between a reference electrode and other electrodes of an
array. Initial voltage difference values between the
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reference electrode and other electrodes typically due to
surface chemistry differences of the electrodes are
subtracted from all data subsequent to the creation of
pressure transients.
According to another aspect of the invention, the
streaming potential transients are generated in any of
various manners. According to one embodiment of the
invention associated with drilling a borehole, the pressure
difference between the formation and the borehole creates
mud invasion, pressure transients and streaming potential
transients. In another embodiment of the invention
associated with wireline logging of the borehole, streaming
potential transients are generated by providing the wireline
tool with one or more cutting edges mounted on one or more
retractable arms which cut slits across the mudcake while
logging. Because of a large overbalancing pressure
difference between the formation and the borehole, when the
mudcake is slit, fluid will flow through the slit and the
resulting pressure transient can be measured. According to
another embodiment of the invention associated with
completion and post-completion applications, streaming
potential transients are generated by injection of
completion fluid, cement, gravel, acids, fracturing
propellant, water injection testing, production testing,
etc. In fact, any change in the rate of production will
also create streaming potential transients. As long as
there is a flow of conducting fluids associated with
pressure transients, a streaming potential transient will be
created and will be measurable with high precision using the
deployed electrodes.
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According to another aspect of the invention, data
related to streaming potential transients obtained by the
electrodes is interpreted to provide useful information.
Those skilled in the art will appreciate that the
interpretation of pressure transient data (as opposed to
streaming potential transient data) to obtain reservoir
properties such as permeability is a well-established art.
In formations with high permeability, the pressure
transients change with time rapidly, while in formations
with low permeability, the pressure transients change
slowly. The streaming potential transients produced by the
pressure transients depend on the formation permeability in
the same way as the pressure transients.
As will be appreciated by those skilled in the art,
there exist analytical and numerical tools to model the
pressure transients. The reservoir parameters of interest
can be determined by varying the parameters in the model
until the calculated pressure matches with the measured
data. Formally, let Rdenote the set of reservoir
parameters to be determined, and let fp(R)denote the
modeled pressure transient. A mismatch between the modeled
and the measured pressure transient is defined:
Ep(R) =11 .fp(R)-p11. (9)
The mismatch is minimized at R= RO to get the inverted
values of the reservoir parameters.
The quantitative interpretation of streaming potential
data to determine reservoir parameters such as formation
permeability can be carried out in the same way as the
interpretation of the pressure transient data. Let S
denote a set of measured transients. The set may contain
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only the streaming potential transients V , or it may
contain both the streaming potential transients and the
pressure transients. Let fs(R,L)denote the modeled
transients, which depend on an additional set of parameters:
the coupling constants L in equation (3). (The
conductivity (7in equation (3) is usually known from
resistivity logging data.) A mismatch between the modeled
and the measured pressure transients is defined according
to:
Es(R,L) =jj.fs(R,L)-Sjj= (10)
The mismatch is minimized at R= Ro and L= 4 to get the
inverted values of the reservoir parameters.
It will be appreciated by those skilled in the art that
the Poisson equation (3) is linear in the coupling constants
L, since the coupling of the streaming potential back into
the governing equations for the pressure by electro-osmosis
is completely negligible. Therefore, the inversion for the
coupling constants is a straightforward linear inversion.
Indeed, the minimization of equation (10) is carried out in
two steps. The first step is to fix Rand vary L, and find
the sub-optimal minimum of the mismatch by solving a linear
problem for L. The solution gives L as a function of R.
The sub-optimal minimum is then a function of R only:
Es1(R) = E's(R,L(R)) = (11)
The second step is a nonlinear search for the minimum of
equation (11), containing the same number of unknowns as
equation (9). Therefore, the additional task of estimating
the coupling constants does not add to the computational
complexity or mathematical uncertainly to the inversion
problem.
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According to another aspect of the invention, the
measured streaming potential transients associated with the
fluid movement in the formation can be used inter alia to:
track movement of cement slurries during cementing thereby
detecting possible cementing problems; track slurries
carrying gravel thereby monitoring gravel packing; track
acid movement during injection of acid into the formation as
acid injection will create streaming potential transients;
monitor fracturing of formations in real time; evaluate
fracture jobs quantitatively; track water movement resulting
from water injection; improve the effectiveness of pressure
transient testing; and monitor reservoir parameter changes
over long periods of time, including water saturation,
relative permeability and water cut.
Using the various aspects of the invention previously
described, field tests were run on a horizontal production
well, part of which is shown schematically in Fig. 1. The
horizontal production well 100 of Fig. 1 was completed in
formation 105 with sand screens 114 (see Fig. 2) and
segmented into three zones with external casing packers
111a, lllb, lllc. The zone closest to the heel of the
horizontal well is labeled as Zone 1, the middle zone as
Zone 2, and the zone closest to the toe as Zone 3. Each
zone was provided with a valve unit 113a, 113b, 113c
respectively, extending through the screen 114, with two
pressure sensors 115-1 and 115-2 associated with each valve
unit 113 (see Fig. 2). Electrodes 118 were deployed as
discussed below.
Turning now to Fig. 2, deployment of the electrodes 118
according to the invention is seen. As seen in Fig. 2, the
well 100 is completed with sand-screen sections 114 which
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are coupled together by insulated joint sections 116 to form
the completion string. It will be appreciated that the
screen sections cannot be electrically insulated from the
formation 105 or from the annulus fluid (not shown). The
joint sections 116 are electrically insulated. Mounted in
the middle of each joint section is a centralizer 118.
Because of the weight of the completion string 114,116, the
centralizers 118 are always in good contact with the
formation 105. Therefore, in accord with the invention, the
centralizers 118 are equipped as electrodes with preferably
high impedance voltage measurement circuits and are coupled
to surface electronics by cable wires (not shown).
Appropriate centralizer hardware is described in PCT
Application WO 02/053871.
It will be appreciated by those skilled in the art that
the completion string, being made of metal, forms a short
circuit for electrical currents. The screen sections 114
used to complete well 100 were fifteen feet long, and the
joint sections 116 were five feet long. Since the insulated
joint sections 116 of the completion string covered only a
small area near the electrodes 118, much of the electrical
currents were able to leak through the exposed screen
sections 114, resulting in the reduction of signal level.
However, as shown hereinafter, there still existed
significant levels of signal to be measured. It should be
noted that for quantitative interpretation, it is sufficient
to include the current leakage in the forward modeling.
As shown in Fig. 1, seven electrodes were provided per
zone for a total of twenty-one electrodes (labeled 118-1,
118-2..., 118-21. With a fifteen foot screen section and a
five foot joint section, the distance between neighboring
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electrodes in the same zone was approximately twenty feet.
The distance between the nearest two electrodes in different
zones was just over one hundred feet.
Pressure testing data gathered by the pressure gauges
on both sides of the completion string showed that Zone 1 is
hydraulically isolated from Zone 2 and Zone 3. This is seen
in Fig. 3, since Zone 1 pressure 125a is significantly
higher than Zone 2 and Zone 3 pressures 125b, 125c thereby
indicating isolation. Therefore, for the voltages of the
electrodes in Zone 1 (118-1 through 118-7), the reference
electrode was chosen to be in Zone 2 or Zone 3, and for the
voltages of the electrodes in Zone 2 and Zone 3, the
reference electrode was chosen to be in Zone 1.
In order to create a streaming potential transient, the
three electrical valves 113a, 113b, 113c, and a rod pump
(not shown) at the formation surface were utilized to
control the fluid flow. The fluid in the annulus of each
zone flowed into the tubing through the valve opening. The
pressure gauge 115-1 on the tubing side of the opening
measured the tubing pressure, and the pressure gauge 115-2
on the annulus side measured the pressure in the annulus
region between the formation and the screen. By turning the
pump on and off and by opening and closing the valves 113,
pressure transients were created in the formation 105 and
measured by the pressure gauges 115-2 on the annulus side.
For each of the three zones, the annulus pressure was
equal to the formation pressure. As seen in Fig. 3, the
Zone 2 and Zone 3 annulus pressures 125b, 125c were
approximately equal, indicating that the two zones are in
hydraulic communication. The Zone 1 annulus pressure 125a
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was higher, indicating that Zone 1 is hydraulically
isolated. By pumping the fluid out of the borehole, the
tubing pressure was kept at a value -150 psi lower than the
annulus pressures in Zone 2 and Zone 3. The Zone 2 valve
and the Zone 3 valve were opened for three hours and then
shut. The Zone 2 annulus pressure, shown as curve 125a in
Figure 3, dropped 150 psi (from approximately 840 psi to
approximately 690 psi) to the level of the tubing pressure
immediately after the valve opening, and then started to
build up back to the formation pressure. The Zone 3 annulus
pressure is shown as curve 125b in Figure 3. The Zone 3
pressure buildup curve rose faster than the Zone 2 pressure
buildup curve, indicating that Zone 3 is more permeable than
Zone 2.
It will be appreciated by those skilled in the art,
that immediately after the opening of valves, the pressure
gradient existed mainly in the damaged zone near the well.
The permeability of the damaged zone, or skin, is known to
be lower than that of the undamaged formation. If the
coupling constant between the pressure gradient and the
electric current is also lower in the skin than in the
formation, then the streaming potential should increase with
time initially when the pressure gradient diffuses from the
skin to the undamaged formation. At later times, the
pressure builds back to the formation pressure, the pressure
gradient diminishes and diffuses deep into the formation
farther away from the electrodes, and the streaming
potential decreases. The rates of the initial increase and
the subsequent decrease of the streaming potential are
determined by the permeability of the skin, the thickness of
the skin, and the permeability of the undamaged formation.
The streaming potential transient recorded by electrode 118-
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8 in Zone 2, shown alongside with the pressure transient in
Figure 4, first rises then falls. The time scale of the
fall of the streaming potential is comparable to the time
scale of the buildup of the pressure, as expected.
The Zone 2 streaming potential data recorded by all
seven electrodes 118-8 through 118-14 in Zone 2 are shown
alongside the pressure data in Figure 5. The Zone 3
streaming potential data are shown in Figure 6. The
reservoir is clearly heterogeneous within each zone;
individual streaming potential curves in Figure 5 and Figure
6 all have very different rise and decline rates, indicating
large variations in permeability. Thus, it is seen that
measuring streaming potential with an array of electrodes
yields significantly increased information relative to the
information that can be gleaned from a single pressure
buildup curve for each zone which would yield only the
average permeability for that zone.
Careful review of the curve from electrode 118-12 in
Figure 5 reveals a double peak. The double peak is
consistent with the superimposition of a fast rising and
fast fallirig element and a slow rising and slow falling
element. The fast element arises from flow in a fracture
having a high permeability, and the slow element arises from
a flow in a formation matrix with low permeability. This
interpretation is consistent with borehole images which were
obtained from a borehole imaging tool and with modeling
results discussed hereinafter.
According to the invention, the magnitude of the
streaming potential is an indicator of the water fraction of
flow, and it varies from electrode to electrode. As seen in
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Figure 5, there is little water production near electrode
118-13 (i.e., the streaming potential remains near 0 mV),
and in Figure 6, there is no or little water production near
electrodes 118-16 and 118-17.
The voltages of the Zone 1 electrodes are shown in
Figure 7. Since Zone 1 is hydraulically isolated from Zone
2 and Zone 3 and the Zone 1 valve remained closed, the
observed voltages were drifts in the electrodes. The drifts
are of the order of less than one millivolt per day. Since
the electrodes are steel centralizers exposed to the annulus
fluid, drifts of such magnitude are expected.
In a later production test, Zone 2 and Zone 3 valves
were shut and Zone 1 valve was opened and remained open.
The pressure transient and the streaming potentials
resulting from that test are shown in Figure 8. The large
streaming potential measurement and double peak associated
with electrode 118-1 revealed a fracture. In addition to
the fracture, the significant variations in streaming
potential rise times (e.g., compare electrode 118-6 with
electrode 118-5, indicated large variations in formation
permeability along Zone 1.
Turning now to Fig. 9, qualitative interpretations of
the streaming potential transient data in Figures 5, 6 and 8
is summarized. As seen in Fig. 9, electrode 118-1 revealed
a fracture in the formation with high permeability, while
electrodes 118-2 through 118-5 and electrode 118-7 indicated
formation locations having medium permeability and electrode
118-6 indicated a formation location of high permeability.
In Zone 2, electrodes 118-8 through 118-10 and 118-14
indicated formation locations of medium permeability, while
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electrodes 118-11 and 118-12 indicated a formation location
or mini-zone of low permeability. In addition, electrode
118-12 revealed a fracture in the formation. Electrode 118-
13 indicated a formation location with no water flow. In
Zone 3, electrodes 118-15 and 118-18 through 118-20
indicated formation locations of high permeability, while
electrode 118-21 indicated a formation location of medium
permeability, and electrodes 118-16 and 118-17 indicated
formation locations or mini-zone of no water flow. It will
be appreciated by those skilled in the art that the
streaming potential transient data of Figures 5, 6, and 8
summarized in Fig. 9 provides significantly more detailed
information than what was previously obtainable by pressure
transient information.
The qualitative interpretations summarized in Fig. 9
are supported by forward modeling. In particular, using
equation (2) for single-phase flow, the streaming potential
transients are computed from a forward model of a
heterogeneous formation shown graphically in Figure 9a. The
modeled response is shown in Figure 9b. As seen in Fig. 9b,
the streaming potential recorded by an electrode placed in
the high permeability region rises faster and decays faster
than that the streaming potential recorded by an electrode
placed in the low permeability region. Qualitatively this
modeled response agrees with the data presented in Figures 5
and 6. Similarly, in supporting the analysis related to
fractures, the streaming potential transients are computed
from a forward model of another heterogeneous formation
shown in Fig. 9c. As seen in Fig. 9d, the streaming
potential transient computed from a forward model shown
graphically in Figure 9c supports the interpretation of the
streaming potential recorded by electrode 18-12 (Figure 5);
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i.e., that a fracture will produce a double peaked streaming
potential transient response.
In light of the above, with the streaming potential
information, it is clear that an appropriate forward
modeling and inversion can be carried out with a Laplace
equation solver and a two-phase flow model (i.e., oil/water)
as discussed above with reference to equations (9) - (11) or
with a multi-phase flow model. As a result, the streaming
potential transient data obtained can be used to quantify
formation permeability, skin permeability, effective
fracture permeability, horizontal and vertical
permeabilities, communication between zones and wells, and
reservoir boundaries in much greater detail than pressure
transient testing alone can. As a result, a better
understanding of the well and the reservoir may be obtained,
leading to better management of the well and reservoir.
Turning now to Figs. 10 - 19, the use of streaming
potential transient information is shown with respect to a
vertical injection well 200 located in formation 205. As
seen in Fig. 10, the formation 205 includes a hydrocarbon
reservoir with a location identified at between 1026 ft and
1047 ft. In addition, there is a thin layer of sand at
1020.55 ft, which is hydraulically isolated from the
hydrocarbon reservoir.
As seen in Figs. 10 and 11, the well 200 includes a
casing 209 around which electrical insulation 211 is
provided. An electrode array 218, including electrodes 218-
1 through 218-16 with associated preferably high impedance
voltage measurement circuitry, is mounted in or outside the
insulation. The casing, insulation and array are cemented
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in place by cement layer 217. Thus, the electrodes 218-1
through 218-16 are in contact with the cement 217 but not
with the metal casing 209. As shown schematically in Fig.
11, in order to produce hydrocarbons, the casing must be
perforated with oriented perforations 219 so as not to
damage the electrodes and the connecting cables (not shown).
In this case, no perforations were made above the top of the
reservoir (i.e., above 1026 ft.) After perforation,
electrical current can leak through the perforation holes
219 to the metal casing 209. The electrical insulation of
the casing is imperfect but functional, as is shown by field
test results. The bottom electrode 218-16 in Figure 10 was
used as a reference electrode.
With well 200, streaming potential transients were
created by injectin,g water into the well. The injection of
water was controlled by a surface pump 221 and a surface
valve 223 (both shown schematically in Fig. 10), and
monitored by a pressure sensor 225 placed between the valve
223 and the wellhead. Initially, the injectivity of the
well was too low, so the well was acidized and fractured. A
cement evaluation job showed the possible existence of a
poor cement bond. Therefore, the formation outside the
reservoir interval of interest could be fractured, and
injected water could flow into such fractures.
The uphole injection pressure is shown in Figure 12.
Before the start of the data shown in Fig. 12, the valve had
been shut for a long time. The injection pressure increased
suddenly at the opening of the valve, and then periodically
dropped and recovered as the pump was shut down for brief
periods of time.
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The streaming potential transients sensed by the
electrodes of primary interest inside the reservoir interval
of interest are shown in Figure 13 and in an expanded time
scale in Figure 14 (it being noted that electrode 218-12
failed and thus no data is shown for it). The streaming
potential transients clearly have two components: one
component changes very quickly in response to pressure
changes, and the other component changes slowly over a
period of days. The fast component relates to water flowing
into fractures with high permeability. The changes in the
fast component in Figs. 13 and 14 are such that the
streaming potentials decrease with increasing injection
pressure and increase with decreasing injection pressure.
This is expected since injection water carrying positive
charges moves away from the borehole and away from the
electrodes. The signs of the streaming potential of well
200 are opposite to those of the streaming potential
transients shown with respect to well 100, as the data for
well 100 was collected with water carrying positive charges
moving into the borehole toward the electrodes during
production. The slow component of the transient curve comes
from water injection from the borehole directly into the
rock matrix with low permeability, or from the cross-flow
from the fractures into the rock matrix. The direct flow of
injection water into the rock matrix is always away from the
electrodes. The cross-flow from fractures into matrix is
also away from the electrode if the electrode is situated
directly at the fracture. The streaming potential recorded
by such electrodes will decrease slowly as water moves into
the matrix. If the electrode is at some distance away from
the fracture, the cross-flow passes across the electrode.
As a result, the streaming potential will either decrease
slowly or increase slowly as water moves into the matrix,
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depending on the exact location of the electrode relative to
the fracture. The data in Figures 13 and 14 can be
interpreted as showing that electrode 218-5 is situated
directly at a strong fracture, while electrode 218-9 is
situated a little distance away from a fracture.
The streaming potential transients sensed by the
electrodes above the reservoir interval of interest are
shown in Figure 15 and in an expanded time scale in Figure
16. Electrode 218-2 is located very close to the thin
permeable sand adjacent a non-perforated portion of the
casing. Yet, the streaming potential of electrode 218-2
reached a value of 150 mV, which is five times higher than
the streaming potentials recorded by any electrode in the
reservoir interval. This may be explained by understanding
that the interval above the perforated interval had been
fractured, presumably from a cement annulus (which was
confirmed by the cement evaluation job). Thus, the shapes
of the streaming potential transients in this interval are
different from those in the reservoir interval. In this
interval, the streaming potential appears to be comprised of
three components: fast, medium, and slow. This is seen more
clearly with respect to electrode 218-2 in Figure 16. A
shale layer located between the reservoir and the thin sand
layer is probably fractured. Flow through the fractures in
the shale layer has a time scale in between the flow time
scales of the sand and matrix.
Turning now to Fig. 17, the streaming potentials sensed
by the electrodes 218-13 through 218-15 below the reservoir
are seen. The voltages sensed by these electrodes are less
than 1 millivolt. Thus, it can be concluded that there is
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very little injection water flowing below the reservoir
interval.
Given the measurements made by the electrodes as shown
in Figs. 13-17, a qualitative interpretation of the
streaming potential transient data may be made and
summarized as shown in Figure 18. In particular, as seen in
Fig. 18, a fracture with cross-flow exists through a shale
layer atop the reservoir; a fracture with cross-flow exists
at 1028.55 feet (electrode #4); a fracture with cross-flow
exists near 1037.55 feet (electrode #9); and a fracture with
cross-flow exists at 1042.05 feet (electrode #11) (see Fig.
.13) .
The qualitative interpretation of Fig. 18 is supported
by the forward model shown graphically in Figure 18a and the
modeled response shown in Fig. 18b which show that the
streaming potential from cross flows can either have the
same sign or the opposite sign to that of the fracture flow.
Thus, qualitatively the modeled response successfully
reproduced the observed data of electrode 218-9 of Figure 13
and electrode 218-2 of Fig. 15.
The streaming potential data of electrodes 218-13
through 218-15 shown in Figure 17 are shown in expanded time
and voltage scales in Figure 19. Before the surface valve
223 was turn on at day/time 116.43, the voltages of
electrodes 218-14 and 218-15 were stable to one digitization
level (i.e., to 10 microvolts). Electrode 218-13 voltage
had some noise spikes up to 100 microvolts. The noise
spikes happened at a very short time scale, were unrelated
to the surface stabilities of the electrodes, and were
likely due to noise picked up on the wire 235 connecting the
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electrode and the surface electronics 233 (Fig. 10). These
noise spikes can be lessened or eliminated by better wiring
and electronics, or by downhole electronics.
As seen in Fig. 19, the voltages of electrodes 218-13
through 218-15 correlated very well with the uphole pressure
data. At the opening of the valve 223 at 116.43, all three
voltages decreased, and when the pump 221 stopped
momentarily near day/time 116.8, all three voltages showed a
small but visible peak. The correlation is very similar to
those observed in the much larger voltages measured by
electrodes located in the reservoir and in the interval atop
the reservoir. Based on this information, it can be
concluded that the electrode stability for the cemented
electrodes is of the orderof 10 micro-volts and signal
levels of 100 micro-volts are adequate to determine
reservoir properties of interest. The stability of the
cemented electrode array 218 is at least one hundred times
better than the exposed centralizer electrodes 118 shown
with reference to well 100.
According to another aspect of the invention, the
electrodes of the electrode array utilized to sense and
measure streaming potential transients are preferably
covered or coated with a semi-porous covering material (such
as cement), whether utilized as centralizers as shown with
reference to a sand-screen completion or in other permanent
installations, or when used in MWD or wireline applications
as discussed hereinafter. The semi-porous covering material
should have a significant electrical conductivity but a very
low permeability so that ions can reach the electrode to
enable voltage measurements, but no new fluid reaches the
electrode surface during the time period of measurement.
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The surfaces of the electrodes are in a stable chemical
environment, which gives rise to measurement stability. A
presently preferred semi-porous material is cement, although
a semi-porous ceramic, clay, or other material could be
utilized. As an alternative, liquid junction electrodes can
be utilized, as the semi-porous plug of a liquid junction
electrode stops fluid movement but allows ionic diffusion.
A stable electrode allows the measurement of a transient
over a longer period of time, thereby permitting an analysis
deeper into the formation, and also permitting measurements
at weaker signal levels.
With the streaming potential measurements described
with reference to Figs. 10-19, it will be appreciated that
determinations can be made of the formation (matrix)
permeabilities and the effective fracture permeabilities
along the well utilizing equations (9) through (11) as
discussed above and by considering fractures as a thin
medium with given permeability. In addition, the streaming
potential measurements can be utilized to obtain real time
monitoring of fracturing jobs. For example, when well 200
was fractured, the target was the middle reservoir interval
of interest, and the fracturing of the upper interval was
not desired. However, the injected water did not go where
it was desired. Had the streaming potential data been
acquired during the fracturing procedure, it would have been
observed at a very early time that the fracturing fluid was
moving mainly toward the upper interval (above the
reservoir). The fracture job could then have been stopped,
a cement squeeze job applied, and the fracture plan properly
executed.
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Turning now to Fig. 20, a formation 305 is seen
traversed by an open hole completed well 300 having a tubing
306 extending therein. An insulated sonde 311 is shown
around the tubing with electrodes 318-1, 318-2... disposed
on the insulated sonde 311. Thus, the tubing 306 is
essentially just a conveyance means for moving the sonde 311
to desired locations. Other conveyance means, which are
preferably relatively solid, but somewhat flexible, could be
utilized. Those skilled in the art will appreciate that
wires connecting the electrodes, measuring electronics, and
telemetry or data storage, which are standard in the art,
are provided in, on, or with the sonde 311 and electrodes
318 but are not shown in Figure 20.
A cased hole completion is shown in Fig. 21, with a
formation 405 traversed by a well 400. The well includes an
insulated tubing 406, and a casing having conductive
electrode portions 418-1; 418-2, 418-3,... separated by
electrically insulated portions 416 which are cemented into
the well by cement 417. Thus, the metal casing serves as an
electrode array with individual sections of the casing
electrically isolated from one another. The casing sections
may be regular casing sections connected by isolation
joints, or specially designed casing sections made of two or
more electrically isolated subsections. As seen in Fig. 21,
the electrodes 418 are in contact with the cement 417 and
with the fluid inside the casing. If the tubing 406 inside
the well is metallic, the tubing is preferably electrically
insulated or partially insulated.
According to another embodiment of the invention, a
tool and method.for measuring streaming potentials while
drilling a borehole is provided. In particular, during
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drilling, a pressure difference between the formation and
the borehole creates mud invasion and pressure transients,
and thus, streaming potential transients. In wells drilled
with an oil-based mud, a streaming potential will exist if
the mud contains a water fraction.
Turning now to Fig. 22, a schematic design of an while-
drilling streaming potential tool 510 is shown in borehole
500 surrounded by formation 505. Drilling tool 510 includes
a drill bit 507 and electrodes 518-1, 518-2, 518-3..., 518-R
(all preferably coated with a semi-porous covering such as
cement) mounted on electrically insulated sections 511-1,
511-2, 511-3 of the drill pipe 515. The electrodes 518 move
with the tool 510. Thus, different electrodes in the array
will sense at different points in time the streaming
potential transient at a fixed spatial point. The spacing
between the electrodes 518 in the array and the drilling
speed determines the temporal sampling rate of the streaming
potential transient. In other words, the time at which
electrode 518-2 is located at a particular previously
measured by electrode 518-1 is dependent upon both the
drilling speed and the distance between the electrodes. In
the embodiment of Fig. 22, the top electrode 518-R is used
as the voltage reference electrode, as it is farthest from
the drill bit and will often arrive at locations in the
formation when the streaming potential transient has already
reached steady state values. Those skilled in the art will
appreciate that wires connecting the electrodes, measuring
electronics, and telemetry, which are standard in the art,
are provided in, on, or with the LWD tool 510 but are not
shown in Figure 22. A processor 550 and associated data
storage 560 are shown which are used to obtain answer
products are shown in Fig. 22. It will be appreciated that
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the processor 550 and data storage 560 are applicable to the
other embodiments as well, although the processor may
utilize different forward and inverse models.
With the while-drilling tool 510, the streaming
potential measurements made are passive voltage
measurements, which can be made in a highly resistive
borehole by using high impedance electronics. In wells
drilled with oil-based mud, the electrodes need to be as
large as possible and placed as close as possible to the
formation to reduce electrode impedance.
It will be appreciated by those skilled in the art that
in order to properly analyze the data obtained by the LWD
tool 510, a model of mudcake built up during drilling should
be included in the forward model. Accurate models such as
disclosed in E. J. Fordham and H. K. J. Ladva, "Crossflow
Filtration of Bentonite Suspensions", Physico-Chemical
Hydrodynamics, 11(4), 411-439 (1989) can be utilized.
Given the while-drilling tool 510 and an appropriate
model, the streaming potential information obtained by the
tool and processed can yield various answer products. Since
the streaming potential transients created by drilling will
change rapidly with time for a formation with high
permeability and slowly for formation with low permeability,
with an inversion model that contains the mudcake built-up
model, formation permeability of the invaded zone and the
uninvaded zone can be obtained.
With the LWD tool 510 and an appropriate model, a
system for early detection of drilling fluid loss may be
implemented. In particular, there may be sudden fluid loss
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from natural or induced fractures during drilling. In that
case, streaming potential will rise instantaneously as
fluids rush into the formation. The changes in borehole
pressure will be somewhat slower, since the borehole has a
storage capacity. Noticeable fluid loss at the surface will
happen much later. For drilling induced fractures, large
changes in the streaming potential will be detectable long
before the fractures becomes serious. Therefore, monitoring
of the streaming potential measurements can be used for
early detection of fluid loss.
Likewise, the streaming potential information can be
utilized for the early detection of abnormal formation
pressures. For example, if the formation pressure becomes
higher than the borehole pressure, the signs of the
streaming potential will reverse. This reversal of sign
will be observable before sufficient amount of fluid has
flowed into the borehole for the pressure kick to be
observable. The build-up of the flow reversal may happen
over a short but finite period of time as the abnormal
pressure zone is being drilled. Any reversal of flow will
be immediately observable in the streaming potential
measurements. Therefore, streaming potential measurements
have value in the early detection of abnormal formation
pressure.
Turning now to Fig. 23, another embodiment of the
invention is seen. In Fig. 23, a wireline streaming
potential tool 610 is provided. The wireline tool 610 is
shown suspended by a cable 611 in a borehole 600 (having mud
cake 607) traversing a formation 605. The wireline tool 610
is provided with an insulated sonde 616 on which an array of
electrodes 618-1, 618-2, 618-3... including a reference
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electrode 618-R, and associated preferably high impedance
voltage measuring circuits are provided. The electrodes are
preferably coated with a semi-porous material such as
cement. In addition, tool 610 includes one or more
preferably retractable arms 631 on which one or more cutting
edges 635 are mounted. The cutting edges 635 are designed
to cut slits across the mudcake 607 as the wireline tool is
moved through the borehole. The cutting edges may be made
with a polycrystalline diamond compound (PDC). Because
there is a large overbalancing pressure difference between
the formation and the borehole (most of the pressure
difference exists across the mudcake), after the cutting
edges 635 slit the mudcake 607, a new mudcake will quickly
build up in the slit to stop the fluid flow. In the mean
time, a pressure transient has been created in the formation
605. In wells drilled with oil-based mud, streaming
potential transients will be created if the mud has a water
fraction.
As will be appreciated by those skilled in the art, the
electrodes 618 move with the tool 610 in a continuous
logging mode. Different electrodes in the array sense the
streaming potential transient at a fixed spatial point. The
spacing between the electrodes in the array and the logging
speed determines the temporal sampling rate of the streaming
potential transient. The top electrode 618-R is used as the
voltage reference electrode, as it is farthest from the
cutting edges and no streaming potential transient has yet
been created there. Wires connecting the electrodes,
measuring electronics, and telemetry are provided but not
shown in Figure 23.
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As previously mentioned, the arms 631 are preferably
retractable. As a result, the cutting edges 635 can be
retracted where streaming potential information is not
desired, and the tool used for repeated runs to acquire
streaming potential data over long period of time, if
desired. A gamma ray detector 640 is provided in order to
help align data from repeat runs.
As was discussed above with reference to the LWD tool
510, streaming potential measurements are passive voltage
measurements which can be made in a highly resistive
borehole by using high impedance electronics. In wells
drilled with oil-based mud (without a water fraction), the
electrodes are preferably relatively large (by way of
example and not limitation, twelve inches by two inches) and
are preferably placed on articulated pads (not shown) or on
a skid sonde to insure close contact with the formation.
Using the wireline tool 610, the spurt loss from the
cutting of mudcake is likely to happen over a short time
period compared with the time needed for the pressure
transient to diffuse beyond the invaded zone. If that is
the case, then the source of the streaming potential
transient created by the cutting of mudcake can be treated
as a delta function of time. The inversion of the data for
a short period of time can be carried out without any input
from the mudcake build-up model. After the spurt loss, the
mudcake will build back up by a static process. The
thickness of the mudcake will increase with the square root
of time. The inversion of streaming potential data over a
longer period of time with a mudcake that increases with the
square root of time is still quite robust.
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The mud invasion is a continual process even with a
good mud system. The streaming potential transients created
by the mud invasion are likely to be measurable when the
logging time is not too far away from the time when the well
is drilled or reamed. Thus, the tool shown in Figure 23
with the cutting edges retracted (or without the arms and
cutting edges) can record the streaming potential created by
the previous drilling and/or reaming, and the continual mud
invasion. In such a situation, a model for a long measuring
period and a mudcake build-up will be utilized for
interpreting the streaming potential data collected. Thus,
it will be appreciated that the wireline streaming potential
tool can be used with appropriate modeling and inversion to
provide measurements of formation permeability in the
invaded zone, beyond the invaded zone, and in the far zone,
continuously along the borehole. The transients acquired
over long periods of time without the cutting blade will
help to determine the permeability in the far zone.
The ability of the wireline tool of Fig. 23 to detect
streaming potential transients and provide qualitative
determinations is supported by the forward model of Figure
23a and the results of the model shown in Figs. 23b-23e. it
is assumed in the model of Fig. 23a, that the spurt loss
from the cutting of mudcake happened over a short time
period compared with the time needed for the pressure
transient to diffuse beyond the invaded zone. The source of
the streaming potential transient created by the cutting of
mudcake was treated as a delta function of time. After the
spurt loss, it was assumed that a new mudcake stopped all
further flow.
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Figure 23b shows that the early time transients are
insensitive to the uninvaded zone. It takes a time interval
given by equation (4) for the pressure transient to diffuse
to the uninvaded zone. Figure 23c shows that both early
time streaming potential and late time streaming potential
are sensitive to the permeabilities of the invaded zone.
The fact that early time data and late time data are
sensitive to permeabilities of different zones makes the
inversion algorithm quite robust.
Figure 23d shows the dependence of the streaming
potential on the thickness of the invaded zone. Equation
(4) shows that the time it takes for the pressure transient
to diffuse through the invaded zone depends on the invaded
zone thickness Aand invaded zone permeability kthrough the
combination 02/k. Equation (8) shows that in approaching
the steady state, the streaming potential from the invaded
zone depends on Aand kthrough the combination A/k. The
difference between these two combinations suggests that the
thickness and the permeability of the invaded zone can be
individually determined by inversion.
The results of inversion with synthetic data calculated
from the forward model and 5% added noise are shown in
Figure 23e. The inverted values of the invaded zone
permeability, uninvaded zone permeability, and the thickness
of the invaded zone all agree very well with the input
values used in the forward model.
There have been described and illustrated herein
several embodiments of apparatus and methods for measuring
streaming potentials and characterizing earth formation
characteristics therefrom. While particular embodiments of
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the invention have been described, it is not intended that
the invention be limited thereto, as it is intended that the
invention be as broad in scope as the art will allow and
that the specification be read likewise. Thus, while
particular tools and electrode arrangements have been
disclosed, it will be appreciated that modifications can be
made, provided the tool or arrangement includes an electrode
array capable of measuring streaming potentials. Thus, for
example, the invention could be modified so that a two-
dimensional array of electrodes can be utilized in certain
circumstances in order to provide azimuthal streaming
potential information. It will therefore be appreciated by
those skilled in the art that yet other modifications could
be made to the provided invention without deviating from its
spirit and scope as claimed.
