U.S. patent application number 10/872116 was filed with the patent office on 2005-01-27 for evaluation of fracture geometries in rock formations.
This patent application is currently assigned to SCHLUMBERGER TECHNOLOGY CORPORATION, Incorporated in the State of Texas. Invention is credited to Entov, Vladimir Mordukhovich, Evgeny Mikhailovich, Chekhonin, Gordeev, Yury Nikolaevich, Thiercelin, Marc Jean.
Application Number | 20050017723 10/872116 |
Document ID | / |
Family ID | 32768747 |
Filed Date | 2005-01-27 |
United States Patent
Application |
20050017723 |
Kind Code |
A1 |
Entov, Vladimir Mordukhovich ;
et al. |
January 27, 2005 |
Evaluation of fracture geometries in rock formations
Abstract
A method of evaluating the geometry of a hydraulic fracture in a
rock formation comprises the steps of: obtaining measured values of
electric and/or magnetic fields induced by the forward or back
propagation of a fracturing fluid between the fracture and the rock
formation; and determining the geometry of the fracture from the
measured values.
Inventors: |
Entov, Vladimir Mordukhovich;
(Moscow, RU) ; Gordeev, Yury Nikolaevich; (Moscow,
RU) ; Evgeny Mikhailovich, Chekhonin; (Orenburg,
RU) ; Thiercelin, Marc Jean; (Ville D'Avray,
FR) |
Correspondence
Address: |
SCHLUMBERGER-DOLL RESEARCH
36 OLD QUARRY ROAD
RIDGEFIELD
CT
06877-4108
US
|
Assignee: |
SCHLUMBERGER TECHNOLOGY
CORPORATION, Incorporated in the State of Texas
Ridgefield
CT
|
Family ID: |
32768747 |
Appl. No.: |
10/872116 |
Filed: |
June 18, 2004 |
Current U.S.
Class: |
324/346 ;
166/250.1; 166/308.1 |
Current CPC
Class: |
E21B 43/26 20130101;
G01V 3/26 20130101 |
Class at
Publication: |
324/346 ;
166/250.1; 166/308.1 |
International
Class: |
E21B 047/00 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 25, 2003 |
RU |
2003123596 |
Claims
What is claimed is:
1. A method of evaluating the geometry of a hydraulic fracture in a
rock formation, comprising the steps of: obtaining measured values
of electric and/or magnetic fields induced by the forward or back
propagation of a fracturing fluid between the fracture and the rock
formation; and determining the geometry of the fracture from the
measured values.
2. A method of evaluating the geometry of a hydraulic fracture in a
rock formation, comprising the steps of: injecting into a borehole
a fracturing fluid at a pressure allowing the fluid to create a
fracture in a formation surrounding the borehole and to propagate
into the fracture and further into the formation through the
fracture faces; measuring downhole the values of electric and/or
magnetic fields induced by the propagation of the fluid into the
fracture and further into the formation; and determining the
geometry of the fracture from the measured values.
3. A method of evaluating the geometry of a hydraulic fracture in a
rock formation, comprising the steps of: injecting into a borehole
a fracturing fluid at a pressure allowing the fluid to create a
fracture in a formation surrounding the borehole and to propagate
into the fractures and further into the formation through the
fracture faces; lowering the pressure in the borehole such that the
fluid propagates back from the formation into the fracture;
measuring downhole the values of electric and/or magnetism fields
induced by the back propagation of the fluid from the formation
into the fracture; and determining the geometry of the fracture
from the measured values.
4. The method according to claim 2, wherein the step of measuring
the values of the electric and/or magnetic fields is performed
inside a further borehole or boreholes.
5. The method according to claim 3, wherein the step of measuring
the values of the electric and/or magnetic fields is performed
inside a further borehole or boreholes.
6. A method according to claim 1, further comprising the step of:
providing a model from which expected values of the electric and/or
magnetic field at the positions and/or times of the measured values
can be calculated for adjustable fracture geometries and injection
pressures; wherein the geometry of the fracture is determined by
adjusting the model to minimize the differences between the
expected and measured values.
7. A method according to claim 2, further comprising the step of:
providing a model from which expected values of the electric and/or
magnetic field at the positions and/or times of the measured values
can be calculated for adjustable fracture geometries and injection
pressures; wherein the geometry of the fracture is determined by
adjusting the model to minimize the differences between the
expected and measured values.
8. A method according to claim 3, further comprising the step of:
providing a model from which expected values of the electric and/or
magnetic field at the positions and/or times of the measured values
can be calculated for adjustable fracture geometries and injection
pressures; wherein the geometry of the fracture is determined by
adjusting the model to minimize the differences between the
expected and measured values.
9. A computer system which is operatively configured to determine
the geometry of a hydraulic fracture in a subterranean rock
formation from measured values of electric and/or magnetic fields
induced by the forward or back propagation of a fracturing fluid
between the fracture and the rock formation.
10. An apparatus for evaluating a shape of a hydraulic fracture in
a rock formation, the apparatus comprising: a rig for injecting a
fracturing fluid into a borehole at a pressure allowing the
injected fluid to create a fracture and propagate into the created
fracture around the borehole; at least one downhole tool for
measuring electric and/or magnetic fields induced by the
propagation of said fluid into the fracture through the fracture
faces and by the propagation of this fluid back into the formation
from the fracture; and a computer system according to claim 9, for
determining the geometry of the fracture from the measured values
of the electric and/or magnetic fields.
Description
FIELD OF THE INVENTION
[0001] The present invention relates to a method for evaluating the
shape or geometry of hydraulic fractures in rock formations. It can
be advantageously applied to determine the shapes of fractures
surrounding oil well boreholes.
BACKGROUND OF THE INVENTION
[0002] Hydraulic fracturing is generally used to stimulate
production of hydrocarbons from hydrocarbon wells. Hydraulic
fractures are created in subterranean formations by injecting high
viscosity fluid (also referred to as fracturing fluid) at a high
flow rate into well boreholes. The tensile fractures thus-created
can be about 100 m long. The fracturing procedure generally takes
from about 30 minutes to 4 hours.
[0003] In order to create a high conductivity drain in the
formation, the fracturing fluid usually contains proppants, small
particles which are added to the fluid to keep the fracture open
once the injection is stopped and pressure is released. These
particles can be sand grain or ceramic grains. The width of the
fracture during propagation is about 1 cm, and 4 mm once closed on
proppant
[0004] To be efficient, the fracture should be contained within the
reservoir formation and not propagate in the adjacent layers. It
should also be of sufficient length and width. Evaluation of the
geometry of the fracture is therefore an important step to ensure
treatment optimization.
[0005] Fracture geometries can be evaluated utilizing various
techniques and methodologies. The mostly widely used is a method of
indirect evaluation based on analysis of a pressure response during
the fracture treatment and subsequent production. The method is
described, for example, in Reservoir Stimulation, Third Edition, M.
J. Economides and K. G. Nolte (Ed.), Chichester, UK, Wiley, (2000).
This approach provides, however, only very general information
about fracture length and fracture width and does not provide any
information about the exact fracture geometry. More reliable
acoustic fracture imaging technology for field applications can be
based on event location using passive acoustic emission. Such
technology is described, for example, in A practical guide to
hydraulic fracture diagnostic technologies, by D. Barree, M. K.
Fisher and R. A. Woodroof, paper SPE 77442, presented at the SPE
Annual Technical Conference and Exhibition held in San Antonio,
Tex., USA, 28 September to Oct. 2, 2002. Acoustic emission events
generated by micro-earthquakes around the fracture during hydraulic
fracturing are recorded by an array of geophones or accelerators
placed in adjacent boreholes. The micro-earthquakes may be caused
by the high stress concentration ahead of the fracture or by the
decrease of stress around the fracture following fracturing fluid
leak-off into the formation. In the best cases, the events can be
analyzed to provide some information about the source mechanism
(energy, displacement field, stress drop, source size, etc.).
However, they do not provide direct quantitative information on the
main fracture. The approach is commonly used in the field and is
particularly suited for the estimation of fracture azimuth and dip,
but not for an accurate determination of the position of the
fracture tip. Another disadvantage of the approach is that the
micro-earthquakes are spread around the fracture and produce a
cloud of events, which do not allow a precise determination of
fracture geometry.
[0006] Yet another technique for evaluating hydraulic fracture
shapes is tiltmeter mapping, also discussed in the paper by D.
Barree, et al. referenced above. This technique involves monitoring
the deformation pattern in the rock surrounding the fracture. An
array of tiltmeters measures the gradient of the displacement
(tilt) field versus time. The induced deformation field is
primarily a function of fracture azimuth, dip, depth to fracture
middle point and total fracture volume. The shape of the induced
deformation field is almost completely independent of reservoir
mechanical properties, if the rock is homogeneous, and in-situ
stress state.
[0007] Disadvantages of this technique are first of all in that
surface tiltmeters cannot accurately resolve fracture length and
height due to the depth of the fracture below the surface. Also the
measurement distance is large compared to the fracture dimensions,
so there is a blurring of the fracture source edges. Although
downhole tiltmeters placed in the treatment borehole can provide
better information on fracture height they still cannot resolve
fracture length.
[0008] The electrokinetic effect is based on the generation of
electric current by fluid flow through porous media. Its primary
cause is the difference in mobility of ions, some of which are
fixed at the surface of the solid skeleton (matrix) of the porous
medium, while dissolved counter ions can move with the pore fluid,
or force it to move, if an electric field is applied.
[0009] In U.S. Pat. No. 5,519,322 the effect is used to measure the
permeability of a formation surrounding a borehole by measuring the
magnetic field generated by the flow of fluid injected into the
formation. The permeability measured in this way provides
information on the capacity of the reservoir to produce oils.
[0010] A need exists to provide approaches for evaluating shapes of
hydraulic fractures in rock formations, which approaches mitigate
or even exclude disadvantages and deficiencies explained above.
SUMMARY OF THE INVENTION
[0011] It is an object of the present invention to provide a method
for evaluating fracture geometries in rock formations surrounding
oil boreholes. An insight of the inventors was that the
electrokinetic effect could be used to make such evaluations.
[0012] Thus, in general terms, the present invention provides a
method of evaluating the geometry of a hydraulic fracture in a rock
formation, comprising the steps of:
[0013] obtaining measured values of electric and/or magnetic fields
induced by the forward or back propagation of a fracturing fluid
between the fracture and the rock formation; and
[0014] determining the geometry of the fracture from the measured
values, e.g. as a function of the positions and/or times of the
measurements.
[0015] The term "fracture" as used herein covers a single fracture
or a plurality of related fractures all caused by the same
fracturing event.
[0016] In a first aspect, the present invention provides a method
of evaluating the geometry of a hydraulic fracture in a rock
formation, comprising the steps of:
[0017] injecting into a borehole a fracturing fluid at a pressure
allowing the fluid to create a fracture in a formation surrounding
the borehole and to propagate into the fracture and further into
the formation through the fracture faces;
[0018] measuring downhole the values of electric and/or magnetic
fields induced by the propagation of the fluid into the fracture
and further into the formation; and
[0019] determining the geometry of the fracture from the measured
values, e.g. as a function of the positions and/or times of the
measurements.
[0020] Particular embodiments of this aspect of the present
invention provide a method of evaluating a shape of hydraulic
fractures in a rock formation, in which method: at least one
borehole is provided; given fluid is injected into at least one of
the provided boreholes at a pressure allowing the fluid to create
fractures around the borehole and to propagate into the created
fractures and further into the formation through fracture faces;
electric and/or magnetic fields induced by the propagation of the
fluid into the fractures and further into the formation through
fracture faces are measured downhole; and the shape of the
fractures is determined using values of either or both of the
measured fields as a function of either or both of the position and
time of the measurements.
[0021] In a second related aspect, the present invention provides a
method of evaluating the geometry of a hydraulic fracture in a rock
formation, comprising the steps of:
[0022] injecting into a borehole a fracturing fluid at a pressure
allowing the fluid to create a fracture in a formation surrounding
the borehole and to propagate into the fractures and further into
the formation through the fracture faces;
[0023] lowering the pressure in the borehole such that the fluid
propagates back from the formation into the fracture;
[0024] measuring downhole the values of electric and/or magnetic
fields induced by the back propagation of the fluid from the
formation into the fracture; and
[0025] determining the geometry of the fracture from the measured
values, e.g. as a function of the positions and/or times of the
measurements.
[0026] Particular embodiments of this aspect of the present
invention provide a method of evaluating a shape of hydraulic
fractures in a rock formation, in which method: at least one
borehole is provided, given fluid is injected into at least one of
the provided boreholes at a pressure allowing the fluid to create
fractures around the borehole and propagate into the created
fractures and further into the formation through fracture faces;
pressure in the borehole used for the injection is lowered to a
value allowing the fluid to propagate back from the formation into
the fractures through the fracture faces; electric and/or magnetic
fields induced by the back propagation of the fluid from the
formation is measured downhole; and the shape of the fractures is
determined using values of either or both of the measured fields as
a function of either or both of the position and time of the
measurements.
[0027] The following optional features relate to both of these
aspects.
[0028] The step of measuring downhole the values of the electric
and/or magnetic fields may be performed inside a further borehole
or boreholes. In relation to the particular embodiments mentioned
above, for at least two provided boreholes the method allows the
measurement of electric or magnetic fields to be performed inside
one of the provided boreholes while the fluid which induces these
fields is injected into another of the provided boreholes and
propagates into the fractures and further into the formation from
the fracture faces around this another of the provided
boreholes.
[0029] The method may further comprise the step of:
[0030] providing a model from which expected values of the electric
and/or magnetic field at the positions and/or times of the measured
values can be calculated for adjustable fracture geometries and
injection pressures;
[0031] wherein the geometry of the fracture is determined by
adjusting the model to minimize the differences between the
expected and measured values. In relation to the particular
embodiments mentioned above, the method may further comprise:
providing a forward model of electric and/or magnetic field
distributions for a given fracture shape and injection pressure by
calculating such distributions as a function of a measurement
position and/or time; measuring downhole the electric and/or
magnetic fields at the same positions and/or times as used for
providing the forward model to provide observed electric and/or
magnetic field distributions; and evaluating the shape of fractures
in the rock formations by minimizing errors between the forward
model distribution(s) and the observed distribution(s).
[0032] A further aspect of the invention provides a computer system
which is operatively configured to determine the geometry of a
hydraulic fracture in a subterranean rock formation from measured
values of electric and/or magnetic fields induced by the forward or
back propagation of a fracturing fluid between the fracture and the
rock formation.
[0033] Thus, in certain embodiments, the invention also provides an
apparatus for evaluating a shape of a hydraulic fracture in a rock
formation, the apparatus comprising:
[0034] a rig for injecting a fracturing fluid into a borehole at a
pressure allowing the injected fluid to create a fracture and
propagate into the created fracture around the borehole;
[0035] at least one downhole tool for measuring electric and/or
magnetic fields induced by the propagation of said fluid into the
fracture through the fracture faces and by the propagation of this
fluid back into the formation from the fracture; and
[0036] a computer system according to this aspect of the invention,
for determining the geometry of the fracture from the measured
values of the electric and/or magnetic fields.
[0037] In certain other embodiments, the invention also provides an
apparatus for evaluating a shape of a hydraulic fracture in a rock
formation, the apparatus comprising means for injecting a given
fluid into at least one borehole at a pressure allowing the
injected fluid to create fractures and propagate into the created
fractures around the borehole; at least one downhole tool for
measuring electric and/or magnetic fields induced by the
propagation of said fluid into the fractures and by the leaking-off
of this fluid into the formation from the fracture face; and means,
such as a computer system, for determining a shape of the fractures
using values of either or both of the measured fields as a function
of measurement position and time.
[0038] In relation to the apparatus embodiments, the or each
downhole tool may be movable along the borehole. The means for
injecting the given fluid may be a surface pump. The apparatus
itself may further comprise: at least one memory unit for storing
expected values of the electric and/or magnetic fields for a given
fracture shape and injection pressure according to a measurement
position and/or time; means for evaluating the location of the
downhole tool in the borehole; at least one processing unit for
selecting electric and/or magnetic field values measured by the
downhole tool at the positions and/or times for which the values
are stored in the memory unit, and for minimizing errors between
the stored and selected values; and means for outputting data on
the evaluated shape of the fractures in the rock formation.
[0039] Further aspects of the invention provide: (i) a computer
program for determining the geometry of a hydraulic fracture in a
subterranean rock formation from measured values of electric and/or
magnetic fields induced by the forward or back propagation of a
fracturing fluid between the fracture and the rock formation; and
(ii) a computer program product carrying such a program.
BRIEF DESCRIPTION OF THE DRAWINGS
[0040] Specific embodiments of the present invention will now be
described with reference to the following drawings in which:
[0041] FIG. 1a is a schematic diagrams respectively showing a
borehole with a movable sensor arrangement, and FIG. 1b is a
schematic diagram showing a borehole with a fixed sensor
arrangement;
[0042] FIG. 2 is a schematic diagram showing an embodiment
according to the invention;
[0043] FIG. 3 is a schematic diagram showing a borehole with
perforated casing and cemented sensors;
[0044] FIG. 4 is a schematic diagram showing an embodiment for two
boreholes according to the invention;
[0045] FIG. 5 is a schematic diagram showing another embodiment
according to the invention;
[0046] FIG. 6 is a schematic diagram showing yet another embodiment
according to the invention;
[0047] FIG. 7 is a block diagram of an apparatus according to one
embodiment of the invention;
[0048] FIG. 8 is a schematic diagram showing a formation comprising
three layers;
[0049] FIGS. 9a and b are three-dimensional plots showing
distributions of electric potential as a function of horizontal
position coordinates and depth.
DETAILED DESCRIPTION OF THE INVENTION
[0050] FIG. 1a is a schematic view of a borehole 1 with a sensor
arrangement (associated with a downhole tool) 21 which comprises
electric field sensors 2 and magnetic field sensors 3. The electric
field sensors 2 are voltage electrodes which contact the borehole
and the magnetic field sensor 3 is a magnetometer, such as a
high-precision nuclear magnetic resonance device of the type
provided, for example, by Schlumberger. Examples of suitable
electrodes and magnetometers are described in: U.S. Pat. No.
5,642,051 and U.S. Pat. No. 6,441,618 for electrodes behind casing;
EP0544583 and EP0715187 for electrodes on a wireline tool in
openhole; and U.S. Pat. No. 6,597,178B1 and Etchecopar et al.
(1993), Harnessing Paleomagnetics for Logging, Oilfield Review,
October 1993, Volume 5, Number 3 for magnetometers. The sensor
arrangement 21 is movable along the borehole by means of a drive 5,
thus providing measurement of electric and magnetic fields in
different parts of the borehole. In this example, measurement
processing means 4 is outside the borehole. The sensor arrangement
comprises two voltage electrodes and one magnetic field sensor 3,
but the number of sensors may be selected depending on the
particular implementation requirements.
[0051] FIG. 1b shows a fixed sensor arrangement 22 which comprises
a plurality of electric field sensors 2 and magnetic field sensors
3. The number and spacing of the sensors along the borehole may be
such as to provide measurements above and below the predicted
positions of formation 23 boundaries. It will be apparent to those
skilled in art that the locations of sensors 2 and 3 in the fixed
arrangement may be adjusted as required.
[0052] An example of the invention is shown in the schematic
diagram of FIG. 2. In addition to the sensor arrangement which is
placed in the borehole 1, the apparatus comprises pump 6 connected
by channel 11 to the borehole 1. The pump 6 is also connected to a
reservoir 12 which is filled with fracturing fluid 7. Fracturing
fluid 7 may be water based or oil based, and is generally either a
high viscosity (crossed-linked or uncrossed-linked) polymer fluid,
or a surfactant-based fracturing fluid. The sensor arrangement may
be either movable or fixed as described above. The surface pump 6
may be also be provided with a pressure controlling unit (not
shown) to continuously increase or decrease the pressure in the
borehole.
[0053] The pump 6 injects fluid 7 into the borehole 1 through
channel 11. Fluid 7 is injected at a pressure which is high enough
to fracture the formation, whereby movement of the fluid into the
borehole occurs. Fractures are create around the borehole and the
fluid propagate through the faces of these fractures into formation
23 around the oil borehole. Propagation of fluid 7 into the
formation is indicated schematically by arrows 24.
[0054] Propagation of fluid 7 into the fractures and the formation
induces both electric and magnetic fields which are detected by
electric field sensors 2 and magnetic field sensor 3. Measurement
processing means 4 then processes the signals received from the
sensors 2 and 3 to provide their output in a suitable form, i.e. as
intermediate information for further processing or as final
information. Output received from the processing means 4 allows
evaluation of the fracture shape or geometry.
[0055] Many boreholes used for oil production are cased inside, the
casing being perforated to allow produced oil to enter the
borehole. Such situation is shown in FIG. 3 where borehole 1 has
casing 25 with perforations 8. The casing can be made of different
materials, but the most commonly used casing material is steel.
However, to provide reliable and accurate measurements by magnetic
field sensors, the magnetic field measurement should be made in an
open (uncased) section of the borehole or in a cased section if the
casing does not strongly disturb the magnetic field (a composite
casing, for example).
[0056] It is preferable, but not essential, that the electric field
is also measured in an open or non-metallic cased section of the
borehole. However, if necessary the electric field can be
successfully measured by sensors embedded in the cemented outer
annulus 26 with which the casing is insulated, as shown in FIG.
3.
[0057] In situations when the casing 25 does not allow the sensor
arrangement to be successfully used within the borehole, the method
according to the invention can be implemented using a different
borehole located near the first borehole 1. The implementation of
such a method is shown schematically in FIG. 4. Fracturing fluid 7
is injected by pump 6 into the borehole 1 which has casing 25 with
perforations 8. Another borehole 9, in which is placed the sensor
arrangement 21, is located near the first borehole 1. As described
above, the sensor arrangement 21 comprises voltage electrodes 2 in
contact with the borehole and a high precision magnetometer 3. Such
devices can measure the induced electric and magnetic fields up to
about 100 to 500 meters from the borehole in which the fluid is
injected. If necessary, a number of boreholes located around the
borehole 1 within a range of about 500 meters can each be used for
receiving a movable sensor arrangement 21 or a fixed arrangement 22
and obtaining corresponding measurements.
[0058] Measurable electric and magnetic fields are induced not only
by the flow of pressurized injected fluid into rock formations
surrounding the borehole, but also by backflow of the fracturing
fluid, i.e. when it retreats into the borehole from the created
fractures. This situation takes place when the pressure inside the
borehole 1 is reduced, for example by means of valve 10, to a value
equal or below the pressure of the fracturing fluid 7 in the
formations and fractures. This backflow is schematically shown in
FIG. 5 by the reversal of arrows 24. Such back propagation of fluid
7 induces measurable electric and magnetic fields which can be
detected by electric field sensors 2 and magnetic field sensors 3.
The signals from the sensors are supplied to measurement processing
means 4 as described above with reference to FIG. 2.
[0059] FIG. 6 shows schematically an example of the invention, in
which the borehole 1 is cased and the casing 25 has perforations 8.
Cemented annulus 26 is provided around the casing 25 and a number
of electric field sensors 2 are embedded in the annulus 26.
Magnetic field sensors 3 are attached to a sensor arrangement 27
which is either movably or fixedly located in another borehole 9
situated from the borehole 1 at a distance allowing the sensors 3
to detect the magnetic field induced by fracturing liquid flowing
back from fractures into the borehole 1 when valve 10 reduces the
pressure inside the borehole 1. The signals from the sensors are
supplied to measurement processing means 4 as described above with
reference to FIG. 2.
[0060] The above examples described with references to FIG. 1 to 6
may be implemented in various combinations, for example, a number
of sensor arrangements 21 or 27 may be movably or fixedly located
in boreholes surrounding the borehole 1 in which fracturing fluid 7
is injected or flowing back from the created fractures. Such
combinations may allow measurements to be taken simultaneously in a
ring around the borehole 1. As an alternative, a sensor arrangement
21 or 27 can be placed sequentially in the boreholes encircling
borehole 1. In further embodiments fixed and movable sensor
arrangements 21 or 27 may be located in one and the same
borehole.
[0061] A general block diagram of an exemplary apparatus for
implementing the method is shown in FIG. 7. In the exemplary
apparatus, signals from sensors 2 and 3 and from drive 13 are
supplied to converting unit 14. Converting unit 14 outputs the
signals in a form suitable for their further processing and storing
in digital form in random-access memory (RAM) 16 and in
data/program memory (DPM) 19. DPM 19 stores programs for
implementing modelling calculations. Processing unit 15 receives
data from RAM 16 and performs calculations to produce output
information and signals to control pump 6, valve 10 and drive 13 by
means of controlling unit 18. Output information from processing
unit 15 is stored in RAM 16 and DPM 19. Output data may also be
monitored at display unit 20. Synchronization and internal timing
for the described units is provided by a clocking unit 17.
[0062] The method of the invention may be implemented by providing
a forward model of an electric or magnetic field distribution for a
given fracture shape and downhole pressure and evaluating the shape
of fractures in the rock formations by minimizing errors between
the forward model of electric and magnetic field distributions and
the corresponding downhole measured distributions.
[0063] The forward model provides field distributions based on the
following equations. The electrokinetic effect involves the
generation of an electric current by fluid flow through porous
media (the reverse effect involves inducing flow through the
application of an electric field). Its primary cause is the
difference in mobility of ions, some of which are fixed at the
surface of the solid skeleton (matrix) of the porous medium, while
dissolved counter ions move with the pore fluid (or force it to
move, if an electric field is applied).
[0064] Macroscopically, the flow and electric current are described
by the equations: 1 u = - k f p + ( 1 ) j = - S ( - C p ) , C = S (
2 )
[0065] in which k is the reservoir permeability, .eta..sub.f is the
reservoir fluid conductivity, p is the fluid pressure, .psi. is the
electrokinetic potential, S is the rock electric conductivity, and
C is the electro-kinetic coupling coefficient.
[0066] The Onsager relation holds between the coupling coefficients
C and .beta.:
.beta.=.alpha..ident.Cs (3)
[0067] The magnetic field generated by the flow-induced current can
be evaluated generally using Biot-Savart's law. However, for the
specific case considered, it is more convenient to use an
expression for the magnetic induction vector B in terms of the
vector potential A:
B=[.gradient..times.A] (4)
[0068] where the vector potential satisfies the equation (in SI
units):
.DELTA.A=-.mu.j (5)
[0069] The forward model of electric field and magnetic field
distributions is calculated by solving the equations above taking
account of conservation laws, boundary conditions, symmetry
consideration and Fourier transform used. The model cam also take
into account the influence of several formation layers.
[0070] An example application is illustrated below during
production from a reservoir. The formation is composed of three
layers S.sub.1, S.sub.2 and S.sub.3, as shown in FIG. 8, and the
electric conductivities of the layers, which have been previously
measured with conventional resistivity wireline logs, are
respectively about 0.001, 0.1 and 0.001 in Siemens/m. The fracture
is entirely in the reservoir (i.e. layer S.sub.2) and is of height
H and length 2L as shown in FIG. 8. The following dimensionless
parameters are used:
H*=H/L
X*=x/L
Y*=y/L
Z*=z/L (6)
[0071] FIGS. 9a and 9b show the expected electric potential
predicted by the forward model as a function of X* and Y* at two
different measurement depths (Z*). The distributions shown in these
figures have characteristic lengths related to the fracture length
and fracture height, and an anisotropy related to fracture
direction.
[0072] The real distributions of electric and magnetic fields
induced by fracturing fluid flow in the borehole and fractures are
revealed by downhole measuring these fields at the same positions
and times of measuring as used for calculating the forward model of
the electric or magnetic field distributions. The measured
distributions are also referred to as "observed electric or
magnetic field distributions". The orientation, length and height
of the fracture are adjusted in the forward model until
minimization of the difference between the forward model values and
the measured values is achieved. In this way, the orientation,
length and height of the fracture can be determined.
[0073] While the invention has been described in conjunction with
the exemplary embodiments described above, many equivalent
modifications and variations will be apparent to those skilled in
the art when given this disclosure. Accordingly, the exemplary
embodiments of the invention set forth above are considered to be
illustrative and not limiting. Various changes to the described
embodiments may be made without departing from the spirit and scope
of the invention.
[0074] All the references mentioned herein are hereby incorporated
by reference.
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