U.S. patent application number 15/548763 was filed with the patent office on 2018-01-25 for multi-phase polymer shear viscosity calculation in polymer coreflood simulation study workflow.
The applicant listed for this patent is Schlumberger Technology Corporation. Invention is credited to Andrew Clarke, Edmund J. Fordham, Marie Ann Giddins, Paul Naccache, Shi Su.
Application Number | 20180023374 15/548763 |
Document ID | / |
Family ID | 56564623 |
Filed Date | 2018-01-25 |
United States Patent
Application |
20180023374 |
Kind Code |
A1 |
Su; Shi ; et al. |
January 25, 2018 |
Multi-Phase Polymer Shear Viscosity Calculation in Polymer
Coreflood Simulation Study Workflow
Abstract
An apparent viscosity of an aqueous polymer composition used in
a polymer flood may be determined by generating a relative
permeability interpolation computer simulation model that is
associated with a capillary desaturation function and that
interpolates relative permeability curves for a coreflood
experiment, validating the relative permeability interpolation
computer simulation model using experimental data generated from
the coreflood experiment using a water flood performed at a
plurality of incremental flow rates on a core plug, determining an
interpolated relative permeability to water for the aqueous polymer
composition using experimental data generated from the coreflood
experiment using a multi-phase flood with the aqueous polymer
composition, and determining an apparent viscosity of the aqueous
polymer composition from the interpolated relative permeability to
water. The determined apparent viscosity may then be used to run a
simulation to model the flow of the aqueous polymer
composition.
Inventors: |
Su; Shi; (Maisons-Alfort,
FR) ; Giddins; Marie Ann; (Abingdon, GB) ;
Naccache; Paul; (Abingdon, GB) ; Clarke; Andrew;
(Cambridge, GB) ; Fordham; Edmund J.; (Cambridge,
GB) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Schlumberger Technology Corporation |
Sugar Land |
TX |
US |
|
|
Family ID: |
56564623 |
Appl. No.: |
15/548763 |
Filed: |
February 3, 2016 |
PCT Filed: |
February 3, 2016 |
PCT NO: |
PCT/US2016/016273 |
371 Date: |
August 3, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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62111162 |
Feb 3, 2015 |
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62111158 |
Feb 3, 2015 |
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62111166 |
Feb 3, 2015 |
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Current U.S.
Class: |
703/10 |
Current CPC
Class: |
E21B 43/20 20130101;
G06F 9/455 20130101; E21B 49/00 20130101; E21B 49/02 20130101; G06F
30/20 20200101; E21B 47/12 20130101; E21B 49/005 20130101; C09K
8/588 20130101; E21B 41/0092 20130101; E21B 43/16 20130101; C09K
8/584 20130101 |
International
Class: |
E21B 43/16 20060101
E21B043/16; G06F 17/50 20060101 G06F017/50; E21B 41/00 20060101
E21B041/00 |
Claims
1. A method of determining an apparent viscosity of an aqueous
polymer composition used in a polymer flood, the method comprising:
generating a relative permeability interpolation computer
simulation model that is associated with a capillary desaturation
function and that interpolates relative permeability curves for a
coreflood experiment; validating the relative permeability
interpolation computer simulation model using experimental data
generated from the coreflood experiment using a water flood
performed at a plurality of incremental flow rates on a core plug;
determining an interpolated relative permeability to water for the
aqueous polymer composition using experimental data generated from
the coreflood experiment using a multi-phase flood with the aqueous
polymer composition; and determining an apparent viscosity of the
aqueous polymer composition from the interpolated relative
permeability to water.
2. The method of claim 1, further comprising performing history
matching to validate the relative permeability interpolation
computer simulation model.
3. The method of claim 1, wherein validating the relative
permeability interpolation computer simulation model includes
running a simulation using the relative permeability interpolation
computer simulation model in a computer-implemented reservoir
simulator.
4. The method of claim 1, further comprising running a simulation
using the relative permeability interpolation computer simulation
model and the determined apparent viscosity in a
computer-implemented reservoir simulator to model flow of the
aqueous polymer composition.
5. The method of claim 4, wherein running the simulation includes
running a coreflood simulation.
6. The method of claim 4, wherein running the simulation includes
running a reservoir simulation.
7. The method of claim 1, further comprising validating the
determined apparent viscosity using experimental data.
8. The method of claim 1, further comprising generating a table
that maps a plurality of values of the apparent viscosity against a
plurality of flow conditions, wherein determining the apparent
viscosity includes determining the apparent viscosity from the
table.
9. A method of simulating an aqueous polymer composition injection,
the method comprising: determining an apparent viscosity of the
aqueous polymer composition from a relative permeability
interpolation computer simulation model that is associated with a
capillary desaturation function and that is generated using
experimental data generated from a coreflood experiment using a
multi-phase flood with the aqueous polymer composition; and running
a simulation in a computer-implemented reservoir simulator using
the determined apparent viscosity to model flow of the aqueous
polymer composition.
10. The method of claim 9, wherein the relative permeability
interpolation computer simulation model further interpolates
relative permeability curves for the coreflood experiment and is
validated in part using experimental data generated from the
coreflood experiment using a water flood performed at a plurality
of incremental flow rates on a core plug.
11. The method of claim 9, wherein running the simulation includes
running a coreflood simulation.
12. The method of claim 9, wherein running the simulation includes
running a reservoir simulation.
13. An apparatus, comprising: a memory, the memory storing a
relative permeability interpolation computer simulation model that
is associated with a capillary desaturation function and that is
generated using experimental data generated from a coreflood
experiment using a multi-phase flood with the aqueous polymer
composition; at least one processing unit; and program code
configured upon execution by the at least one processing unit to
simulate an aqueous polymer composition injection to determine an
apparent viscosity of the aqueous polymer composition from the
relative permeability interpolation computer simulation model and
run a simulation in a computer-implemented reservoir simulator
using the determined apparent viscosity.
14. The apparatus of claim 13, wherein the relative permeability
interpolation computer simulation model further interpolates
relative permeability curves for the coreflood experiment and is
validated in part using experimental data generated from the
coreflood experiment using a water flood performed at a plurality
of incremental flow rates on a core plug.
15. The apparatus of claim 13, wherein the simulation includes a
coreflood simulation.
16. The apparatus of claim 13, wherein the simulation includes a
reservoir simulation.
17. The apparatus of claim 13, wherein the program code is further
configured to validate the relative permeability interpolation
computer simulation model using experimental data generated from
the coreflood experiment using a water flood performed at a
plurality of incremental flow rates on a core plug.
18. The apparatus of claim 17, wherein the program code is further
configured to determine an interpolated relative permeability to
water for the aqueous polymer composition using the experimental
data generated from the coreflood experiment using the multi-phase
flood with the aqueous polymer composition.
19. The apparatus of claim 13, wherein the program code is further
configured to perform history matching to validate the relative
permeability interpolation computer simulation model.
20. A program product, comprising: a non-transitory computer
readable medium; and program code stored on the computer readable
medium and configured upon execution by at least one processing
unit to run a simulation in a computer-implemented reservoir
simulator using an apparent viscosity of the aqueous polymer
composition determined from a relative permeability interpolation
computer simulation model that is associated with a capillary
desaturation function and that is generated using experimental data
generated from a coreflood experiment using a multi-phase flood
with the aqueous polymer composition.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the filing benefit of U.S.
Provisional Patent Application Ser. No. 62/111,158, U.S.
Provisional Patent Application Ser. No. 62/111,162, and U.S.
Provisional Patent Application Ser. No. 62/111,166, each of which
filed on Feb. 3, 2015, and each of which incorporated by reference
herein in its entirety.
BACKGROUND
[0002] Enhanced oil recovery (EOR) is aimed at increasing the
recovery factor of oilfields by injecting agents such as chemicals,
including viscoelastic polymers. The design of agent floods for
field implementation can impact the success of such operations,
both in terms of incremental oil recovery, and in net present
value. Reservoir simulation may be used to assist in the design of
such floods, and it has been found that the accuracy of the
reservoir simulation can likewise impact both the design and the
ultimate field implementation.
[0003] In addition, reservoir simulation models may be calibrated
by using experimental data collected during coreflood experiments,
during which core samples taken from an oilfield are flooded with
various fluids to measure various flow parameters for the core.
Doing so generally increases confidence in the experimental data
and in simulation results.
SUMMARY
[0004] The embodiments disclosed herein provide in one aspect a
method of determining an apparent viscosity of an aqueous polymer
composition used in a polymer flood, which includes generating a
relative permeability interpolation computer simulation model that
is associated with a capillary desaturation function and that
interpolates relative permeability curves for a coreflood
experiment, validating the relative permeability interpolation
computer simulation model using experimental data generated from
the coreflood experiment using a water flood performed at a
plurality of incremental flow rates on a core plug, determining an
interpolated relative permeability to water for the aqueous polymer
composition using experimental data generated from the coreflood
experiment using a multi-phase flood with the aqueous polymer
composition, and determining an apparent viscosity of the aqueous
polymer composition from the interpolated relative permeability to
water.
[0005] Some embodiments also include performing history matching to
validate the relative permeability interpolation computer
simulation model, and in some embodiments, validating the relative
permeability interpolation computer simulation model includes
running a simulation using the relative permeability interpolation
computer simulation model in a computer-implemented reservoir
simulator. Some embodiments further include running a simulation
using the relative permeability interpolation computer simulation
model and the determined apparent viscosity in a
computer-implemented reservoir simulator to model flow of the
aqueous polymer composition, and in some embodiments, running the
simulation includes running a coreflood simulation or a reservoir
simulation, while some embodiments also include validating the
determined apparent viscosity using experimental data. Moreover,
some embodiments further include generating a table that maps a
plurality of values of the apparent viscosity against a plurality
of flow conditions, where determining the apparent viscosity
includes determining the apparent viscosity from the table.
[0006] The embodiments disclosed herein may also provide in another
aspect a method of simulating an aqueous polymer composition
injection, which includes determining an apparent viscosity of the
aqueous polymer composition from a relative permeability
interpolation computer simulation model that is associated with a
capillary desaturation function and that is generated using
experimental data generated from a coreflood experiment using a
multi-phase flood with the aqueous polymer composition, and running
a simulation in a computer-implemented reservoir simulator using
the determined apparent viscosity to model flow of the aqueous
polymer composition.
[0007] In some embodiments, the relative permeability interpolation
computer simulation model further interpolates relative
permeability curves for the coreflood experiment and is validated
in part using experimental data generated from the coreflood
experiment using a water flood performed at a plurality of
incremental flow rates on a core plug. In addition, in some
embodiments, running the simulation includes running a coreflood
simulation or a reservoir simulation.
[0008] Other embodiments may include an apparatus including a
memory, at least one processing unit, and program code configured
upon execution by the at least one processing unit to perform any
of the above-described operations. Still other embodiments may
include a program product including a non-transitory computer
readable medium and program code stored on the computer readable
medium and configured upon execution by at least one processing
unit to perform any of the above-described operations.
[0009] These and other advantages and features, which characterize
the invention, are set forth in the claims annexed hereto and
forming a further part hereof. However, for a better understanding
of the invention, and of the advantages and objectives attained
through its use, reference should be made to the Drawings, and to
the accompanying descriptive matter, in which there is described
example embodiments of the invention. This summary is merely
provided to introduce a selection of concepts that are further
described below in the detailed description, and is not intended to
identify key or essential features of the claimed subject matter,
nor is it intended to be used as an aid in limiting the scope of
the claimed subject matter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 is a block diagram of an example hardware and
software environment for a data processing system in accordance
with implementation of various technologies and techniques
described herein.
[0011] FIGS. 2A-2D illustrate simplified, schematic views of an
oilfield having subterranean formations containing reservoirs
therein in accordance with implementations of various technologies
and techniques described herein.
[0012] FIG. 3 illustrates a schematic view, partially in cross
section of an oilfield having a plurality of data acquisition tools
positioned at various locations along the oilfield for collecting
data from the subterranean formations in accordance with
implementations of various technologies and techniques described
herein.
[0013] FIG. 4 illustrates a production system for performing one or
more oilfield operations in accordance with implementations of
various technologies and techniques described herein.
[0014] FIG. 5 illustrates an example workflow in accordance with
implementations of various technologies and techniques described
herein.
[0015] FIG. 6 is a functional diagram of an example core holder for
a coreflood experiment.
[0016] FIG. 7 is a perspective view of an example core holder
platen.
[0017] FIG. 8 is an engineering diagram of an example core holder
platen geometry.
[0018] FIG. 9 illustrates an example three dimensional simulation
model of a core plug, and including platens in accordance with
implementations of various technologies and techniques described
herein.
[0019] FIG. 10 illustrates end effects of platens in an example
reservoir simulation performed with the simulation model of FIG.
10.
[0020] FIG. 11 is an example graph of a relative permeability
model.
[0021] FIG. 12 is an example graph of a capillary desaturation
function.
[0022] FIG. 13 is an example graph of a relative permeability
interpretation model.
[0023] FIG. 14 is an example graph of a comparison of apparent
viscosity derived from single-phase corefloods and multi-phase
corefloods.
[0024] FIG. 15 is an example graph of a comparison of simulation
results against experimental data for an example oil
saturation.
[0025] FIG. 16 is an example graph of a comparison of simulation
results against experimental data for the pressure drop across an
example core.
[0026] FIG. 17 illustrates an example sequence of operations for
determining an apparent viscosity for an aqueous polymer
composition and modeling a flow of the aqueous polymer composition
using the determined apparent viscosity in accordance with
implementations of various technologies and techniques described
herein.
DETAILED DESCRIPTION
[0027] Turning now to the drawings, wherein like numbers denote
like parts throughout the several views, FIG. 1 illustrates an
example data processing system 10 in which the various technologies
and techniques described herein may be implemented. System 10 is
illustrated as including one or more computers 12, e.g., client
computers, each including a central processing unit (CPU) 14
including at least one hardware-based processor or processing core
16. CPU 14 is coupled to a memory 18, which may represent the
random access memory (RAM) devices comprising the main storage of a
computer 12, as well as any supplemental levels of memory, e.g.,
cache memories, non-volatile or backup memories (e.g., programmable
or flash memories), read-only memories, etc. In addition, memory 18
may be considered to include memory storage physically located
elsewhere in a computer 12, e.g., any cache memory in a
microprocessor or processing core, as well as any storage capacity
used as a virtual memory, e.g., as stored on a mass storage device
20 or on another computer coupled to a computer 12.
[0028] Each computer 12 also generally receives a number of inputs
and outputs for communicating information externally. For interface
with a user or operator, a computer 12 generally includes a user
interface 22 incorporating one or more user input/output devices,
e.g., a keyboard, a pointing device, a display, a printer, etc.
Otherwise, user input may be received, e.g., over a network
interface 24 coupled to a network 26, from one or more external
computers, e.g., one or more servers 28 or other computers 12. A
computer 12 also may be in communication with one or more mass
storage devices 20, which may be, for example, internal hard disk
storage devices, external hard disk storage devices, storage area
network devices, etc.
[0029] A computer 12 generally operates under the control of an
operating system 30 and executes or otherwise relies upon various
computer software applications, components, programs, objects,
modules, data structures, etc. For example, one or more
petro-technical modules or components 32 executing within an
exploration and production (E&P) platform 34 may be used to
access, process, generate, modify or otherwise utilize
petro-technical data, e.g., as stored locally in a database 36
and/or accessible remotely from a collaboration platform 38.
Collaboration platform 38 may be implemented using multiple servers
28 in some implementations, and it will be appreciated that each
server 28 may incorporate a CPU, memory, and other hardware
components similar to a computer 12. In some embodiments, portions
of data processing system 10 may be implemented within a cloud
computing environment.
[0030] In one non-limiting embodiment, for example, the one or more
petro-technical modules 32 may include a graphical
pre/post-processor 40 such as the PETREL graphical
pre/post-processor and a general purpose reservoir simulator 42
such as the ECLIPSE reservoir simulator, E&P platform 34 may
implemented as the PETREL Exploration & Production (E&P)
software platform, while collaboration platform 38 may be
implemented as the STUDIO E&P KNOWLEDGE ENVIRONMENT platform,
all of which are available from Schlumberger Ltd. and its
affiliates. It will be appreciated, however, that the techniques
discussed herein may be utilized in connection with other platforms
and environments, so the invention is not limited to the particular
software platforms and environments discussed herein. For example,
any of the aforementioned components may be run on a server, on a
desktop device, on a mobile device, in a cloud computing
environment, as a remote desktop or in a virtual machine, etc.
[0031] In general, the routines executed to implement the
embodiments disclosed herein, whether implemented as part of an
operating system or a specific application, component, program,
object, module or sequence of instructions, or even a subset
thereof, will be referred to herein as "computer program code," or
simply "program code." Program code generally comprises one or more
instructions that are resident at various times in various memory
and storage devices in a computer, and that, when read and executed
by one or more hardware-based processing units in a computer (e.g.,
microprocessors, processing cores, or other hardware-based circuit
logic), cause that computer to perform the steps embodying desired
functionality. Moreover, while embodiments have and hereinafter
will be described in the context of fully functioning computers and
computer systems, those skilled in the art will appreciate that the
various embodiments are capable of being distributed as a program
product in a variety of forms, and that the invention applies
equally regardless of the particular type of computer readable
media used to actually carry out the distribution.
[0032] Such computer readable media may include computer readable
storage media and communication media. Computer readable storage
media is non-transitory in nature, and may include volatile and
non-volatile, and removable and non-removable media implemented in
any method or technology for storage of information, such as
computer-readable instructions, data structures, program modules or
other data. Computer readable storage media may further include
RAM, ROM, erasable programmable read-only memory (EPROM),
electrically erasable programmable read-only memory (EEPROM), flash
memory or other solid state memory technology, CD-ROM, DVD, or
other optical storage, magnetic cassettes, magnetic tape, magnetic
disk storage or other magnetic storage devices, or any other medium
that can be used to store the desired information and which can be
accessed by computer 10. Communication media may embody computer
readable instructions, data structures or other program modules. By
way of example, and not limitation, communication media may include
wired media such as a wired network or direct-wired connection, and
wireless media such as acoustic, RF, infrared and other wireless
media. Combinations of any of the above may also be included within
the scope of computer readable media.
[0033] Various program code described hereinafter may be identified
based upon the application within which it is implemented in a
specific embodiment of the invention. However, it should be
appreciated that any particular program nomenclature that follows
is used merely for convenience, and thus the invention should not
be limited to use solely in any specific application identified
and/or implied by such nomenclature. Furthermore, given the endless
number of manners in which computer programs may be organized into
routines, procedures, methods, modules, objects, and the like, as
well as the various manners in which program functionality may be
allocated among various software layers that are resident within a
typical computer (e.g., operating systems, libraries, API's,
applications, applets, etc.), it should be appreciated that the
invention is not limited to the specific organization and
allocation of program functionality described herein.
[0034] Furthermore, it will be appreciated by those of ordinary
skill in the art having the benefit of the instant disclosure that
the various operations described herein that may be performed by
any program code, or performed in any routines, workflows, or the
like, may be combined, split, reordered, omitted, and/or
supplemented with other techniques known in the art, and therefore,
the invention is not limited to the particular sequences of
operations described herein.
[0035] Those skilled in the art will recognize that the example
environment illustrated in FIG. 1 is not intended to limit the
invention. Indeed, those skilled in the art will recognize that
other alternative hardware and/or software environments may be used
without departing from the scope of the invention.
Oilfield Operations
[0036] FIGS. 2A-2D illustrate simplified, schematic views of an
oilfield 100 having subterranean formation 102 containing reservoir
104 therein in accordance with implementations of various
technologies and techniques described herein. FIG. 2A illustrates a
survey operation being performed by a survey tool, such as seismic
truck 106.1, to measure properties of the subterranean formation.
The survey operation is a seismic survey operation for producing
sound vibrations. In FIG. 2A, one such sound vibration, sound
vibration 112 generated by source 110, reflects off horizons 114 in
earth formation 116. A set of sound vibrations is received by
sensors, such as geophone-receivers 118, situated on the earth's
surface. The data received 120 is provided as input data to a
computer 122.1 of a seismic truck 106.1, and responsive to the
input data, computer 122.1 generates seismic data output 124. This
seismic data output may be stored, transmitted or further processed
as desired, for example, by data reduction.
[0037] FIG. 2B illustrates a drilling operation being performed by
drilling tools 106.2 suspended by rig 128 and advanced into
subterranean formations 102 to form wellbore 136. Mud pit 130 is
used to draw drilling mud into the drilling tools via flow line 132
for circulating drilling mud down through the drilling tools, then
up wellbore 136 and back to the surface. The drilling mud may be
filtered and returned to the mud pit. A circulating system may be
used for storing, controlling, or filtering the flowing drilling
muds. The drilling tools are advanced into subterranean formations
102 to reach reservoir 104. Each well may target one or more
reservoirs. The drilling tools are adapted for measuring downhole
properties using logging while drilling tools. The logging while
drilling tools may also be adapted for taking core sample 133 as
shown.
[0038] Computer facilities may be positioned at various locations
about the oilfield 100 (e.g., the surface unit 134) and/or at
remote locations. Surface unit 134 may be used to communicate with
the drilling tools and/or offsite operations, as well as with other
surface or downhole sensors. Surface unit 134 is capable of
communicating with the drilling tools to send commands to the
drilling tools, and to receive data therefrom. Surface unit 134 may
also collect data generated during the drilling operation and
produces data output 135, which may then be stored or
transmitted.
[0039] Sensors (S), such as gauges, may be positioned about
oilfield 100 to collect data relating to various oilfield
operations as described previously. As shown, sensor (S) is
positioned in one or more locations in the drilling tools and/or at
rig 128 to measure drilling parameters, such as weight on bit,
torque on bit, pressures, temperatures, flow rates, compositions,
rotary speed, and/or other parameters of the field operation.
Sensors (S) may also be positioned in one or more locations in the
circulating system.
[0040] Drilling tools 106.2 may include a bottom hole assembly
(BHA) (not shown), generally referenced, near the drill bit (e.g.,
within several drill collar lengths from the drill bit). The bottom
hole assembly includes capabilities for measuring, processing, and
storing information, as well as communicating with surface unit
134. The bottom hole assembly further includes drill collars for
performing various other measurement functions.
[0041] The bottom hole assembly may include a communication
subassembly that communicates with surface unit 134. The
communication subassembly is adapted to send signals to and receive
signals from the surface using a communications channel such as mud
pulse telemetry, electro-magnetic telemetry, or wired drill pipe
communications. The communication subassembly may include, for
example, a transmitter that generates a signal, such as an acoustic
or electromagnetic signal, which is representative of the measured
drilling parameters. It will be appreciated by one of skill in the
art that a variety of telemetry systems may be employed, such as
wired drill pipe, electromagnetic or other known telemetry
systems.
[0042] Generally, the wellbore is drilled according to a drilling
plan that is established prior to drilling. The drilling plan sets
forth equipment, pressures, trajectories and/or other parameters
that define the drilling process for the wellsite. The drilling
operation may then be performed according to the drilling plan.
However, as information is gathered, the drilling operation may
need to deviate from the drilling plan. Additionally, as drilling
or other operations are performed, the subsurface conditions may
change. The earth model may also need adjustment as new information
is collected
[0043] The data gathered by sensors (S) may be collected by surface
unit 134 and/or other data collection sources for analysis or other
processing. The data collected by sensors (S) may be used alone or
in combination with other data. The data may be collected in one or
more databases and/or transmitted on or offsite. The data may be
historical data, real time data, or combinations thereof. The real
time data may be used in real time, or stored for later use. The
data may also be combined with historical data or other inputs for
further analysis. The data may be stored in separate databases, or
combined into a single database.
[0044] Surface unit 134 may include transceiver 137 to allow
communications between surface unit 134 and various portions of the
oilfield 100 or other locations. Surface unit 134 may also be
provided with or functionally connected to one or more controllers
(not shown) for actuating mechanisms at oilfield 100. Surface unit
134 may then send command signals to oilfield 100 in response to
data received. Surface unit 134 may receive commands via
transceiver 137 or may itself execute commands to the controller. A
processor may be provided to analyze the data (locally or
remotely), make the decisions and/or actuate the controller. In
this manner, oilfield 100 may be selectively adjusted based on the
data collected. This technique may be used to optimize portions of
the field operation, such as controlling drilling, weight on bit,
pump rates, or other parameters. These adjustments may be made
automatically based on computer protocol, and/or manually by an
operator. In some cases, well plans may be adjusted to select
optimum operating conditions, or to avoid problems.
[0045] FIG. 2C illustrates a wireline operation being performed by
wireline tool 106.3 suspended by rig 128 and into wellbore 136 of
FIG. 2B. Wireline tool 106.3 is adapted for deployment into
wellbore 136 for generating well logs, performing downhole tests
and/or collecting samples. Wireline tool 106.3 may be used to
provide another method and apparatus for performing a seismic
survey operation. Wireline tool 106.3 may, for example, have an
explosive, radioactive, electrical, or acoustic energy source 144
that sends and/or receives electrical signals to surrounding
subterranean formations 102 and fluids therein.
[0046] Wireline tool 106.3 may be operatively connected to, for
example, geophones 118 and a computer 122.1 of a seismic truck
106.1 of FIG. 2A. Wireline tool 106.3 may also provide data to
surface unit 134. Surface unit 134 may collect data generated
during the wireline operation and may produce data output 135 that
may be stored or transmitted. Wireline tool 106.3 may be positioned
at various depths in the wellbore 136 to provide a survey or other
information relating to the subterranean formation 102.
[0047] Sensors (S), such as gauges, may be positioned about
oilfield 100 to collect data relating to various field operations
as described previously. As shown, sensor S is positioned in
wireline tool 106.3 to measure downhole parameters which relate to,
for example porosity, permeability, fluid composition and/or other
parameters of the field operation.
[0048] FIG. 2D illustrates a production operation being performed
by production tool 106.4 deployed from a production unit or
Christmas tree 129 and into completed wellbore 136 for drawing
fluid from the downhole reservoirs into surface facilities 142. The
fluid flows from reservoir 104 through perforations in the casing
(not shown) and into production tool 106.4 in wellbore 136 and to
surface facilities 142 via gathering network 146.
[0049] Sensors (S), such as gauges, may be positioned about
oilfield 100 to collect data relating to various field operations
as described previously. As shown, the sensor (S) may be positioned
in production tool 106.4 or associated equipment, such as christmas
tree 129, gathering network 146, surface facility 142, and/or the
production facility, to measure fluid parameters, such as fluid
composition, flow rates, pressures, temperatures, and/or other
parameters of the production operation.
[0050] Production may also include injection wells for added
recovery. One or more gathering facilities may be operatively
connected to one or more of the wellsites for selectively
collecting downhole fluids from the wellsite(s).
[0051] While FIGS. 2B-2D illustrate tools used to measure
properties of an oilfield, it will be appreciated that the tools
may be used in connection with non-oilfield operations, such as gas
fields, mines, aquifers, storage, or other subterranean facilities.
Also, while certain data acquisition tools are depicted, it will be
appreciated that various measurement tools capable of sensing
parameters, such as seismic two-way travel time, density,
resistivity, production rate, etc., of the subterranean formation
and/or its geological formations may be used. Various sensors (S)
may be located at various positions along the wellbore and/or the
monitoring tools to collect and/or monitor the desired data. Other
sources of data may also be provided from offsite locations.
[0052] The field configurations of FIGS. 2A-2D are intended to
provide a brief description of an example of a field usable with
oilfield application frameworks. Part, or all, of oilfield 100 may
be on land, water, and/or sea. Also, while a single field measured
at a single location is depicted, oilfield applications may be
utilized with any combination of one or more oilfields, one or more
processing facilities and one or more wellsites.
[0053] FIG. 3 illustrates a schematic view, partially in cross
section of oilfield 200 having data acquisition tools 202.1, 202.2,
202.3 and 202.4 positioned at various locations along oilfield 200
for collecting data of subterranean formation 204 in accordance
with implementations of various technologies and techniques
described herein. Data acquisition tools 202.1-202.4 may be the
same as data acquisition tools 106.1-106.4 of FIGS. 2A-2D,
respectively, or others not depicted. As shown, data acquisition
tools 202.1-202.4 generate data plots or measurements 208.1-208.4,
respectively. These data plots are depicted along oilfield 200 to
demonstrate the data generated by the various operations.
[0054] Data plots 208.1-208.3 are examples of static data plots
that may be generated by data acquisition tools 202.1-202.3,
respectively, however, it should be understood that data plots
208.1-208.3 may also be data plots that are updated in real time.
These measurements may be analyzed to better define the properties
of the formation(s) and/or determine the accuracy of the
measurements and/or for checking for errors. The plots of each of
the respective measurements may be aligned and scaled for
comparison and verification of the properties.
[0055] Static data plot 208.1 is a seismic two-way response over a
period of time. Static plot 208.2 is core sample data measured from
a core sample of the formation 204. The core sample may be used to
provide data, such as a graph of the density, porosity,
permeability, or some other physical property of the core sample
over the length of the core. Tests for density and viscosity may be
performed on the fluids in the core at varying pressures and
temperatures. Static data plot 208.3 is a logging trace that
generally provides a resistivity or other measurement of the
formation at various depths.
[0056] A production decline curve or graph 208.4 is a dynamic data
plot of the fluid flow rate over time. The production decline curve
generally provides the production rate as a function of time. As
the fluid flows through the wellbore, measurements are taken of
fluid properties, such as flow rates, pressures, composition,
etc.
[0057] Other data may also be collected, such as historical data,
user inputs, economic information, and/or other measurement data
and other parameters of interest. As described below, the static
and dynamic measurements may be analyzed and used to generate
models of the subterranean formation to determine characteristics
thereof. Similar measurements may also be used to measure changes
in formation aspects over time.
[0058] The subterranean structure 204 has a plurality of geological
formations 206.1-206.4. As shown, this structure has several
formations or layers, including a shale layer 206.1, a carbonate
layer 206.2, a shale layer 206.3 and a sand layer 206.4. A fault
207 extends through the shale layer 206.1 and the carbonate layer
206.2. The static data acquisition tools are adapted to take
measurements and detect characteristics of the formations.
[0059] While a specific subterranean formation with specific
geological structures is depicted, it will be appreciated that
oilfield 200 may contain a variety of geological structures and/or
formations, sometimes having extreme complexity. In some locations,
generally below the water line, fluid may occupy pore spaces of the
formations. Each of the measurement devices may be used to measure
properties of the formations and/or its geological features. While
each acquisition tool is shown as being in specific locations in
oilfield 200, it will be appreciated that one or more types of
measurement may be taken at one or more locations across one or
more fields or other locations for comparison and/or analysis.
[0060] The data collected from various sources, such as the data
acquisition tools of FIG. 3, may then be processed and/or
evaluated. Generally, seismic data displayed in static data plot
208.1 from data acquisition tool 202.1 is used by a geophysicist to
determine characteristics of the subterranean formations and
features. The core data shown in static plot 208.2 and/or log data
from well log 208.3 are generally used by a geologist to determine
various characteristics of the subterranean formation. The
production data from graph 208.4 is generally used by the reservoir
engineer to determine fluid flow reservoir characteristics. The
data analyzed by the geologist, geophysicist and the reservoir
engineer may be analyzed using modeling techniques.
[0061] FIG. 4 illustrates an oilfield 300 for performing production
operations in accordance with implementations of various
technologies and techniques described herein. As shown, the
oilfield has a plurality of wellsites 302 operatively connected to
central processing facility 354. The oilfield configuration of FIG.
4 is not intended to limit the scope of the oilfield application
system. Part or all of the oilfield may be on land and/or sea.
Also, while a single oilfield with a single processing facility and
a plurality of wellsites is depicted, any combination of one or
more oilfields, one or more processing facilities and one or more
wellsites may be present.
[0062] Each wellsite 302 has equipment that forms wellbore 336 into
the earth. The wellbores extend through subterranean formations 306
including reservoirs 304. These reservoirs 304 contain fluids, such
as hydrocarbons. The wellsites draw fluid from the reservoirs and
pass them to the processing facilities via surface networks 344.
The surface networks 344 have tubing and control mechanisms for
controlling the flow of fluids from the wellsite to processing
facility 354.
EOR Chemical Coreflood Simulation Study Workflow
[0063] Chemical EOR processes, such as surfactant or polymer
flooding (among others), are used in the oil and gas industry to
improve the recovery of hydrocarbons. In order to design these
processes, laboratory experiments such as coreflood experiments,
may be used. Coreflood experiments, however, generally look at very
small scales, e.g., using cores (also referred to herein as core
plugs) that are at most several centimeters in diameter and length,
and experiments on cores are generally time-consuming. Pilot
studies may also be used to design these processes; however
implementing such pilot studies can be very expensive and
collecting results can take a substantial amount of time. Reservoir
simulation offers the potential for being cheaper and faster,
thereby potentially facilitating the EOR design process.
[0064] In this regard, EOR chemical flooding, or coreflooding,
generally refers to the injection of a chemical composition
including one or more chemical agents suitable for use in
connection with enhanced oil recovery. Such compositions may
include, in some embodiments, one of more chemical structures each
with one or more molecular weights that together with zero, one or
more subsidiary components such as salts, pH adjusters or
surfactants form an aqueous solution. In the embodiments discussed
below, for example, the focus is on polymer flooding using aqueous
polymer solutions incorporating one or more polymers along with any
of the aforementioned subsidiary components. Any references herein
to polymers therefore may be considered to refer to various aqueous
polymer compositions. It will appreciated, however, that other EOR
chemical floods, using other EOR chemicals (including, for example,
formation water, low salinity water, surfactant, alkali, polymer
gel, foam, nanoparticles, other chemical additives, some
combination of two or more of the aforementioned EOR agents, etc.)
may be used in other embodiments, so the invention is not limited
specifically to polymer flooding.
[0065] Embodiments consistent with the invention may be used to
model in a reservoir simulator the results of an EOR chemical
coreflood experiment and thereby generate a coreflood simulation
model. As such, a general purpose reservoir simulator
conventionally used for modeling an oilfield, e.g., the ECLIPSE
reservoir simulator available from Schlumberger Ltd. and its
affiliates, among others, may be used to model an EOR chemical
coreflood experiment. In this regard, the term "general purpose
reservoir simulator" is used to refer to a reservoir simulator that
is used for modeling an oilfield, as opposed to a special purpose
simulator built specifically to model a core or a coreflood
experiment.
[0066] Moreover, in the embodiments discussed hereinafter, the term
"core" or "core plug" may be used to refer to rock core samples
extracted from a wellbore, as well as other bodies upon which a
coreflood experiment may be performed, including, for example,
reconstituted cores, sandpacks, bead packs, etc. Further, while the
embodiments discussed hereinafter may refer to water floods, it
will be appreciated that the term "water" may be used to refer to
other types of aqueous solutions including different brine
formulations.
[0067] An example workflow is disclosed herein, in particular, to
demonstrate the feasibility of an EOR chemical coreflood simulation
study using the ECLIPSE reservoir simulator. The invention,
however, may be utilized in connection with other reservoir
simulators, so the invention is not limited to use solely with the
ECLIPSE reservoir simulator as used herein. It will be appreciated
that the workflow may be implemented solely within a computer
environment and with the use of one or more processors in some
embodiments, whereas in other embodiments, some acts or operations
in the work flow may be performed by a user outside of the computer
environment, with other acts or operations performed with the use
of one or more processors.
[0068] FIG. 5 illustrates an example workflow 400, which may be
performed to process the results of an EOR chemical coreflood
experiment, and in particular, a polymer coreflood experiment, and
thereby conduct a polymer coreflood simulation study for enhanced
oil recovery through reservoir simulation for a viscoelastic
polymer. As will be appreciated, viscoelastic polymers may be
injected into a reservoir along with water or another fluid to form
an aqueous polymer composition and thereby increase the overall
viscosity of the injected composition, among other reasons, and one
goal of an EOR chemical coreflood simulation study is to attempt to
predict an increase in production as a result of a field
implementation of an EOR operation.
[0069] Workflow 400 may begin as illustrated in block 402 by
performing analysis of the lab experiments. For example, the
experimental apparatus and experimental protocol used for the
experiments may be analyzed, as may how the data was measured and
the precision to which the data was measured in the experiments.
Doing so enables suitable reservoir simulator parameters to be
determined prior to building a simulation model.
[0070] In some embodiments, for example, an experiment may be
performed on a core sample of substantially homogeneous material
within a core holder that includes fluid introduction and
extraction elements referred to as platens that allow fluids to
circulate through the core, and that are designed to distribute the
entry and exit of fluids in the core across a large area of the
faces of the core.
[0071] In one non-limiting example experiment, the core may be
filled with oil, e.g., at a rate of about 10 cm.sup.3/min during 20
PV, until the core is substantially saturated with oil (e.g., about
96%). An initial water (brine) flood may then be performed at a
constant rate, e.g., at about 0.2 cm.sup.3/min during 20 PV, during
which a relatively large initial residual oil saturation (e.g.,
about 64%) may be reached. Then, another water (brine) flood may be
performed at incremental or stepwise increasing flow rates, e.g.,
ranging from about 0.01 cm.sup.3/min to about 100 cm.sup.3/min.
Subsequently, a polymer flood (e.g., with an aqueous polymer
composition comprising an anionic polysaccharide such as Xanthan
and a partially hydrolyzed polyacrylamide (HPAM) synthetic
polyanion), may also be performed at incremental or stepwise
increasing flow rates, e.g., ranging from about 0.01 cm.sup.3/min
to about 100 cm.sup.3/min. Thereafter, the core may be flushed with
water or brine at about 0.01 cm.sup.3/min during 30 PV to flush out
any polymer remaining within the core and enable the experiment to
be repeated for other aqueous polymer compositions. During each
flood, measurements may be made of both pressure (e.g., at the
entrance and outlet to derive a pressure drop across the core) and
oil saturation (e.g., using nuclear magnetic resonance (NMR)
measurements in the middle-third of the core to minimize
end-effects introduced by the platens).
[0072] Next, in block 404, detailed modeling may be performed to
create a three-dimensional (3D) simulation model in the reservoir
simulator capturing the design of the experiment. In particular, a
3D simulation model of the core sample may be created, mirroring
the geometry of the core sample and partitioned into a three
dimensional grid of cells. In some embodiments, the core sample may
be treated as a homogeneous material, such that all of the grid
cells associated with the core sample are assigned the same
property values such as porosity and permeability. In addition, in
some embodiments, and as will be described in greater detail below,
additional aspects of the experimental apparatus, e.g., the core
holder platens, may also be incorporated into the simulation model
to more effectively model end effects. In other embodiments,
however, a core sample may be treated as a heterogeneous material,
with some or all of the grid cells associated with the core sample
having varying property values.
[0073] Next, in block 406, the data may be reviewed, e.g., by
performing data quality analysis and quality control to identify
uncertainty on the data, and potential errors in the data due to
calibration of measurement devices or other sources of
inaccuracy.
[0074] Next, in block 408, three simulation studies 410, 412 and
414 may be performed in consecutive stages to validate the data.
First, in study 410, the water (brine) flood at constant flow rate
is analyzed. Study 410, in particular, may ensure that data such as
the fluid model (oil, water), the rock properties (porosity,
permeability, relative permeability) and the simulation model
itself are defined accurately. As noted above, in the example
experiment, water or brine is injected into a core that is full of
oil, and the constant flow rate flood reduces the oil saturation to
a residual oil saturation as defined by relative permeability
curves. Validation may occur by comparing the result of the water
flood against calculated results based on Darcy's law.
[0075] Second, in study 412, the water (brine) flood an incremental
flow rates is analyzed. A capillary desaturation model may be used
to represent the further decrease of oil saturation beyond the
residual oil saturation. This capillary desaturation model may
include an interpolation between the relative permeability curves
defined in the previous study, and hypothetical relative
permeability curves corresponding to a state where the rock is
fully stripped from the oil (i.e., where residual oil saturation is
decreased to zero). During this study, the simulated interpolated
relative permeability may be compared to the relative permeability
derived from the experimental data using Darcy's law. This step may
be used, for example, to validate the capillary desaturation model
and the relative permeability curves that are used for simulation.
It will be appreciated that studies 410-412 effectively establish a
water base case, representing the amount of oil desaturation
obtainable through water flooding alone, and against which the
performance of the EOR chemical flood (e.g., in terms of additional
observed reduction in residual oil saturation as a result of the
EOR chemical flood) may be compared. In this regard, a water base
case may be considered in some embodiments to be a base case
established for the simulation model in which water, substantially
free of other chemical additives, is injected into the core.
[0076] Third, in study 414, the polymer flood at incremental flow
rates is analyzed. This study may use the capillary desaturation
model and the validated relative permeability curves from the
previous study. Polymer properties may be characterized and input
to the simulation. Polymer properties may include, for example,
solution viscosity as a function of the solution concentration,
polymer solution shear rheology (relating the solution's shear
viscosity with the water velocity), adsorption properties (e.g.,
tables of adsorbed polymer as a function of polymer concentration
surrounding the rock, rock density, maximum adsorption
concentration, and resulting maximum residual resistance factor,
and whether the polymer can desorb from the rock), an inaccessible
pore volume fraction (e.g., to estimate the proportion of pore
volume that will not be penetrated by the polymer solution), etc.
Additional properties, e.g., apparent viscosity (viscosity under
shear stress when the polymer is injected in the rock) may not be
known during a multi-phase flood and may be calculated.
[0077] It will be appreciated that polymer properties may more
broadly be considered to be types of EOR chemical properties.
Further, for EOR chemical floods using compositions other than
aqueous polymer solutions, other types of properties relevant to
the particular EOR chemicals utilized in such floods (e.g.,
adsorption rates, decay rates, chemical reaction rates, mobility
reduction effects, interfacial tension, capillary pressure,
temperature effects, shear rates, relative permeability hysteresis
effects, etc.) may also be studied in a corresponding manner. As
such, the invention is not limited to the particular study and
analyzed properties disclosed herein in connection with a polymer
coreflood with an aqueous polymer solution.
[0078] Upon completion of study 414, the workflow may return to
block 406 to perform additional data review, e.g., to perform
sensitivity analysis to investigate the impact of various uncertain
simulation and/or physical parameters on the match between the
simulation and experimental data. Thus, blocks 406 and 408 may be
repeated multiple iterations in some instances (e.g., using history
matching) to iteratively calibrate the reservoir simulation model
and better match the experimental results. In addition, as
illustrated by block 416, each stage or study 410-414 may also
include iterative data review and corrections performed as desired
to calibrate the reservoir simulation model.
[0079] In some embodiments of the invention, therefore, once a
simulation model is designed to reproduce the experimental setup,
an initial water or brine flood at a constant injection rate may be
simulated and compared against experimental data to validate the
simulation model. Then, the water or brine floods at incremental
injection rates may be simulated and matched to the experimental
data to validate the relative permeability curves and the modeling
of the observed reduction in residual oil saturation. Thereafter,
the EOR chemical floods may be simulated and matched to the
experimental data to establish appropriate input parameters for the
EOR chemical properties and to validate the models embedded in the
reservoir simulator. Sensitivity analysis may thereafter be
performed to investigate the impact of a number of uncertain
simulation and physical parameters on the match between the
simulation and the experimental data, and the simulation model may
be revised accordingly.
[0080] In addition, it will be appreciated that validation of a
model may be performed in various manners, as will be appreciated
by those of ordinary skill in the art having the benefit of the
instant disclosure. For example, in some embodiments, the reservoir
simulator may produce output summary data including numerical
values of pressure, flow rates, fluid saturations, etc. for each
simulated time step, and this output data may be compared directly
with the observed experimental results, or used to calculate
derived quantities for comparison with the experimental
results.
[0081] As also illustrated in block 418, once the simulation model
is generated and validated in the manner described above, the
simulation model may thereafter be used in connection with other
coreflood and/or reservoir simulations. In addition, performing
simulations with the simulation model either in connection with
generating and validating the model or using the model for other
simulations may result in the generation or modeling of various
properties, including, for example, one or more of fluid flow,
fluid distribution in a core, pressure drop across a core, or other
properties that will be appreciated by those of ordinary skill in
the art.
[0082] It will be appreciated that the manner in which workflow 400
may be implemented may vary in different embodiments. In some
embodiments, for example, a graphical pre/post-processor, e.g., the
PETREL graphical pre/post-processor, in communication with a
general purpose reservoir simulator such as the ECLIPSE reservoir
simulator, may be used in connection with the performance of a
number of steps in the workflow, including, for example, generating
the model, performing the aforementioned simulation studies on the
simulation model, validating the simulation model, inputting data
into the reservoir simulator, examining experimental data to check
validity, visualizing simulation results (including visualizing
results in one, two, three or more dimensions), and examining
simulation results for comparison with the experimental data, among
others. In addition, in some embodiments, some or all of the
workflow may be implemented using a plug-in or script, e.g., to
perform one or more of building a model, performing calculations to
define input parameters, interpreting simulation results, comparing
results with observed or experimental data, performing multiple
realizations for sensitivity analysis, history matching, etc.
[0083] Thus, in some embodiments, a coreflood simulation model may
be generated by generating a three-dimensional computer simulation
model of a core plug used in a coreflood experiment in a
computer-implemented general purpose reservoir simulator,
performing one or more simulation studies on the simulation model
to establish a water base case for the simulation model, and after
performing the one or more simulation studies on the simulation
model, performing an additional simulation study on the simulation
model to establish one or more EOR chemical properties and to
further validate the simulation model by simulating an EOR chemical
flood at a plurality of incremental flow rates.
[0084] Further, in some embodiments, a coreflood may be simulated
by loading a three dimensional computer simulation model of a core
plug used in a coreflood experiment and validated by performing one
or more simulation studies on the simulation model to establish a
water base case for the simulation model and by performing an
additional simulation study on the simulation model to establish
one or more EOR chemical properties from simulation of an EOR
chemical flood at a plurality of incremental flow rate, and running
a simulation using the three-dimensional computer simulation model
of the core plug in the computer-implemented general purpose
reservoir simulator.
Modeling of Fluid Introduction Apparatus in Reservoir
Simulation
[0085] As noted above, coreflood experiments may be performed by
placing a core plug in a core holder. The core holder generally has
fluid introduction and extraction elements referred to as platens
that allow the fluids to circulate through the core, and that are
designed to distribute the entry and exit of the fluids in the core
across a relatively large area of the faces of the core.
[0086] It has been found that when the core length is small, it is
desirable to identify the end effects that could be due to the
geometry of the platens that lead to a homogenization of the flow
further away in the core, or due to capillary effects. To do that,
and as noted above, the geometry of the platens may be included in
a three dimensional simulation model of the core plug to be more
representative of the laboratory experiment.
[0087] FIG. 6, for example, illustrates an example core holder 420
for a coreflood experiment, where a core plug 422 is retained
within a pressure confinement sleeve 424 with fluid introduction
and extraction elements or platens 426, 428 disposed on the
opposing faces of the core plug 422, with the introduction and
extraction of fluids represented in the bottom and top of the
figure.
[0088] Various platen designs may be used to distribute fluid
across each face of the core plug 422. FIG. 7 illustrates one such
platen design for fluid introduction element or platen 426, which
may be used in some embodiments of the invention. In this design, a
surface 440 that faces the core plug includes four
symmetrically-disposed inlet ports 444 in fluid communication with
a pair of concentric circular recessed channels 446, 448 through a
pair of orthogonal radial recessed channels 450, 452. In some
embodiments, an identical platen design to that illustrated in FIG.
7 may be used for a fluid extraction element or platen to extract
fluid through four symmetrically-disposed outlet ports. It will be
appreciated that an innumerable number of variations, including
different numbers and/or layouts of ports, and different numbers,
layouts and/or orientations of channels, may be used for the fluid
introduction and fluid extraction elements in other embodiments, so
the invention is not limited to the particular design illustrated
herein.
[0089] In some embodiments of the invention, it may be desirable to
model the platens in three dimensions directly as part of a
simulation grid. The dimensions of all of the flow conducting
channels that have been designed to distribute the flow across the
face of the core may be determined in order to incorporate the
design within the simulation grid, and in some embodiments,
detailed engineering diagrams, e.g., as shown at 460 in FIG. 8, may
be used to integrate the platen design, and in particular, the
channels defined by the platen, into the simulation grid. In some
embodiments, software such as available in the PETREL software
platform may be used in this process.
[0090] The resulting framework may then be used to construct a full
three dimensional model that captures the overall design of the
core plug and the platens, e.g., as illustrated at 470 in FIG. 9,
where the top of the figure represents the outlet platen, with the
inlet platen also included in the model but not shown by virtue of
the orientation of the figure. An end surface 472 represents the
mating surface between the outlet platen and the end of the core,
with channels modeled as illustrated at 474 and outlet ports
modeled as illustrated at 476. The impact of modeling such an
apparatus is observed by visualizing the distribution of fluids
either when running the simulation or when the simulation has
completed. FIG. 10, for example, is a cross-sectional view of the
model, and it can be seen by the difference in shading proximate
the platens the heterogeneous distribution of fluid flow proximate
the faces of the core plug, and thus the end effects experienced
during a coreflood experiment. As such, model 470 may be used in
some embodiments to model the distribution and fingering of fluid
flow proximate one or more faces of a core plug.
[0091] Returning to FIG. 9, it may be desirable in some embodiments
to set the platen channels 474 in the model to have a porosity of 1
(assuming the channels do not include a porous material) and a high
permeability to accurately represent the flow characteristics of
the platen channels relative to the core plug. Boundary conditions
for the resulting model may be modeled by injection wells (for the
inlet platen) and production wells (for the outlet platen)
perforated at injection points in the platen that were used in the
experiment to represent the piping connected to the core holder
system (e.g., as illustrated at 476 for the outlet platen).
Injection wells may be assigned to the same group and controlled by
a group injection rate since the flow rate controlled by the pump
is that of the main pipe that splits into the various injection
points. This group injection rate may therefore be set as the pump
rate. The production wells may be controlled by a bottom hole
pressure limit set to 1 atm, since the outlet piping connects to
atmospheric pressure.
[0092] In some embodiments, if the injection and/or production
systems are symmetric about one or more planes along an axis of
symmetry of the core plug, and the core plug may be treated as
homogeneous, an even distribution of flow in each inlet/outlet port
may be assumed, and the model may be simplified to a segment
representing only a portion of the full model, e.g., as shown by
quarter cylinder segment 480 in FIG. 10 (segmented along two
orthogonal planes P1 and P2 about the core's axis of symmetry),
which may result in faster simulations (due to the reduced number
of cells) with comparable accuracy. In other embodiments, symmetry
may exist in fewer or greater numbers of planes. In one other
embodiment, for example, the injection and production systems may
be symmetric about a single plane, such that a semi cylinder
segment may be used.
[0093] The size or resolution of the simulation grid used for a
model may vary in different embodiments. For example, in some
embodiments, it may be desirable to use a resolution that
substantially matches that of a nuclear magnetic resonance scanner
used to determine oil saturation in the core during a coreflood
experiment. Other resolutions, however, may be used in other
embodiments.
[0094] It will be appreciated that by modeling the fluid
introduction and extraction elements or platens, end effects may be
simulated to provide a more accurate simulation. In some
embodiments, this may allow shorter and/or narrower core plugs to
be used in experiments. Further, in some embodiments, the
herein-described techniques may be used in the design of fluid
introduction and extraction elements or platens, e.g., to confirm
whether a particular design provides a desired fluid flow for a
particular application.
[0095] Thus, in some embodiments, a coreflood experiment may be
modeled by generating a three dimensional computer simulation model
of a core plug used in a coreflood experiment, and modeling in the
three dimensional computer simulation model of the core plug one or
both of a fluid introduction element or a fluid extraction element
of a core holder used in the coreflood experiment. Further, in some
embodiments, fluid flow through a core plug in a coreflood
experiment may be modeled by loading a three dimensional computer
simulation model of a core plug that additionally models one or
both of a fluid introduction element or a fluid extraction element
of a core holder, and running a simulation using the three
dimensional computer simulation model in a computer-implemented
reservoir simulator to model heterogeneous distribution of fluid
flow proximate one or more faces of the core plug.
Multi-Phase Polymer Shear Viscosity Calculation
[0096] In some embodiments, simulation accuracy, particularly for
the simulation of aqueous polymer composition injection, may be
further improved by estimating one or more properties of the
aqueous polymer composition (e.g., apparent viscosity, i.e.,
viscosity under shear stress when injected in the core) during a
multi-phase coreflood.
[0097] It has been found, for example, that the apparent viscosity
of an aqueous polymer composition may be straightforwardly
calculated during a single-phase flood using Darcy's law. However,
for a multi-phase flood, Darcy's law includes an additional term in
the equation for each phase: the relative permeability of that
phase. For example the water flow depends on the water relative
permeability. When the residual oil saturation is decreased beyond
its initial value (capillary desaturation), there is a change of
the water relative permeability that may be difficult to
characterize through measurements, thereby complicating the
calculation of apparent viscosity.
[0098] In some embodiments of the invention, apparent viscosity of
an aqueous polymer composition, e.g., including one or more
viscoelastic polymers, during a multi-phase coreflood experiment
may be calculated using a workflow that in part utilizes data from
the aforementioned water or brine floods performed with stepwise
incremented flow rates. These types of floods may be used to verify
that the relative permeability interpolation model associated with
capillary desaturation are appropriate. Then, these relative
permeability curves may be used to calculate the relative
permeability of an aqueous polymer composition during the
multi-phase flood, based on the state of oil saturation in the
core. The relative permeability points may then be used to
calculate the apparent viscosity of the aqueous polymer composition
using Darcy's law, and the resulting calculation may then be
validated by matching the simulation model to the coreflood
experimental results.
[0099] A capillary desaturation function may be used to account for
the reduction in residual oil saturation occurring during a
multi-phase flood of aqueous polymer composition into oil with
increasing injection flow rate. The model may interpolate relative
permeability curves between relative permeability curves associated
with the residual oil saturation of the initial brine flood, and
curves assuming that the residual oil saturation is taken down to
0, e.g., as shown in FIG. 11. A water or brine flood experiment at
varying flow rates may be performed and matched in order to
validate the relative permeability curves interpolation. The water
relative permeability obtained in the simulation may also be
compared with the curve derived from the laboratory
measurements.
[0100] To calculate the relative permeability to water, Darcy's law
may be applied:
k rw = Q .mu. L kA .DELTA. P ( Eq . 1 ) ##EQU00001##
where k.sub.rw is the relative permeability to water, Q is the
injection flow rate in m.sup.3/s, .mu. is the viscosity in Pas, L
is the length of the core, k is the absolute permeability of the
rock, A is the cross sectional area of the core and .DELTA.P is the
pressure drop across the core in Pa.
[0101] The interpolated curve from the simulation may be obtained
by outputting block summary vectors for water saturation and
k.sub.rw, and once the water relative permeability curve used for
the simulation is validated against the experimental data, the
apparent viscosity may be calculated based on Darcy's law.
[0102] The calculation of the interpolated k.sub.rw may be based on
the relative permeability curves mentioned previously and on the
capillary desaturation function. The capillary desaturation
function (an example of which is illustrated in FIG. 12) may be
defined as follows (where S.sub.or is residual oil saturation):
F c d = 1 - S or ( @ end of flow period ) S or ( @ end of initial
brine flood ) ( Eq . 2 ) ##EQU00002##
[0103] From there, the relative permeability may be calculated at
the end of each flow period from:
k.sub.rw.sub.interpolated=F.sub.cdk.sub.rw.sub.straightline+(1-F.sub.cd)-
*k.sub.rw.sub.initial (Eq. 3)
and plotted against Sw=1-S.sub.or(@end of flow period), an example
of which is illustrated in FIG. 13.
[0104] Next, the apparent viscosity may be calculated from Darcy's
law:
.mu. = kk rw interpolated A .DELTA. P QL ( Eq . 4 )
##EQU00003##
where k is the absolute permeability of the rock in m.sup.2,
k.sub.rw.sub.interpolated is the calculated interpolated relative
permeability in fraction, A is the cross sectional area of the core
in m.sup.2, .DELTA.P is the pressure drop across the core in Pa, Q
is the injection flow rate in m.sup.3/s and L is the length of the
core in m. FIG. 14, for example, compares apparent viscosity
calculations derived from multi-phase corefloods with those derived
from single-phase corefloods.
[0105] The aforementioned calculations may be validated by running
a simulation of the EOR chemical coreflood experiment. As
illustrated by FIGS. 15 and 16, an excellent match for oil
saturation in a core and pressure drop across the core has been
observed in one example embodiment.
[0106] FIG. 17, for example, illustrates an example sequence of
operations 500 for both determining an apparent viscosity for an
aqueous polymer composition used in a polymer flood and modeling a
flow of the aqueous polymer composition using the determined
apparent viscosity consistent with some embodiments of the
invention. As shown in block 502, sequence of operations 500 begins
by generating a relative permeability interpolation computer
simulation model that is associated with a capillary desaturation
function and that interpolates relative permeability curves for a
coreflood experiment. Next, in block 504, the relative permeability
interpolation computer simulation model is validated, e.g., using
experimental data generated from a coreflood experiment using a
water flood performed at a plurality of incremental flow rates on a
core plug, in the manner described above. In some embodiments, the
validation of the model may include performing history matching,
and in some embodiments, the validation may include running a
computer simulation using the model in a reservoir simulator.
[0107] Next, in block 506, an interpolated relative permeability to
water for the aqueous polymer composition using experimental data
generated from the coreflood experiment using a multi-phase flood
with the aqueous polymer composition, again in the manner described
above. Then, in block 508, the apparent viscosity of the aqueous
polymer composition may be determined from the interpolated
relative permeability to water in the manner described above. In
some embodiments, as illustrated in block 510, the determined
apparent viscosity may also be validated, e.g., using experimental
data from the coreflood experiment.
[0108] It will be appreciated that the apparent viscosity of the
aqueous polymer composition will generally depend on the flow
conditions, e.g., the apparent shear rate, in the coreflood
experiment. As such, in some embodiments, shear rate or another
parameter related to flow conditions (e.g., flow velocity) may be
calculated at different flow rates and the result of the
calculations may be used to determine apparent viscosity based on a
table, graph or other data structure or representation that maps
different values of apparent viscosity against apparent shear rate,
flow velocity or another parameter related to flow conditions. In
some embodiments, for example, the apparent viscosity may be
plotted against an apparent shear rate {dot over (.gamma.)}
calculated as follows:
.gamma. . = Q A ( Sw - Swcr ) k .PHI. ( Eq . 5 ) ##EQU00004##
where Q is the injection flow rate in m.sup.3/s, A is the cross
sectional area of the core in m.sup.2, (S.sub.w-S.sub.wcr) is the
mobile water saturation, k is the absolute permeability of the rock
in m.sup.2 and .phi. is the porosity.
[0109] Next, as illustrated in block 512, the determined apparent
viscosity, along with the relative permeability interpolation
computer simulation model (as well as the capillary desaturation
function embedded therein) may be used to model flow of the aqueous
polymer composition, e.g., by running a simulation in a reservoir
simulator. The simulation may be another coreflood simulation for
the purpose of modeling flow through a core, or may be a reservoir
simulation for more modeling flow through a reservoir, e.g., to
simulate injection of the aqueous polymer composition into a
reservoir. It will be appreciated, however, that the determined
apparent viscosity may be used in a number of other applications,
e.g., to predict the injectivity of the injection wells, to
determine the optimum injection rates and pressures for polymer
injection operations, etc.
[0110] Although the preceding description has been described herein
with reference to particular means, materials, and embodiments, it
is not intended to be limited to the particular disclosed herein.
By way of further example, embodiments may be utilized in
conjunction with a handheld system (i.e., a phone, wrist or forearm
mounted computer, tablet, or other handheld device), portable
system (i.e., a laptop or portable computing system), a fixed
computing system (i.e., a desktop, server, cluster, or high
performance computing system), or across a network (i.e., a
cloud-based system). As such, embodiments extend to all
functionally equivalent structures, methods, uses, program
products, and compositions as are within the scope of the appended
claims.
[0111] While particular embodiments 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. It will therefore be
appreciated by those skilled in the art that yet other
modifications could be made without deviating from its spirit and
scope as claimed.
* * * * *