U.S. patent application number 14/162687 was filed with the patent office on 2014-07-31 for constrained optimization for well placement planning.
This patent application is currently assigned to SCHLUMBERGER TECHNOLOGY CORPORATION. The applicant listed for this patent is SCHLUMBERGER TECHNOLOGY CORPORATION. Invention is credited to PETER GERHARD TILKE.
Application Number | 20140214387 14/162687 |
Document ID | / |
Family ID | 51223866 |
Filed Date | 2014-07-31 |
United States Patent
Application |
20140214387 |
Kind Code |
A1 |
TILKE; PETER GERHARD |
July 31, 2014 |
CONSTRAINED OPTIMIZATION FOR WELL PLACEMENT PLANNING
Abstract
A method, apparatus and program product utilize a constrained
optimization framework to generate a well placement plan based on a
reservoir model. Candidate well placement plans are generated from
control vectors proposed by an optimization engine to optimize
based upon an objective function that generally involves an access
to a reservoir simulator. Inexpensive constraints that are not
based on computation of the objective function are evaluated prior
to accessing the reservoir simulator to avoid unnecessary accesses
to the reservoir simulator for candidate well placement plans
determined to be infeasible in view of the inexpensive constraints.
For candidate well placement plans that are determined to be
feasible based upon the inexpensive constraints, the objective
function may be calculated and additional expensive constraints may
thereafter be evaluated to further determine the feasibility of
candidate well placement plans.
Inventors: |
TILKE; PETER GERHARD;
(BELMONT, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
SCHLUMBERGER TECHNOLOGY CORPORATION |
SUGAR LAND |
TX |
US |
|
|
Assignee: |
SCHLUMBERGER TECHNOLOGY
CORPORATION
SUGAR LAND
TX
|
Family ID: |
51223866 |
Appl. No.: |
14/162687 |
Filed: |
January 23, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61756800 |
Jan 25, 2013 |
|
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Current U.S.
Class: |
703/10 |
Current CPC
Class: |
E21B 43/305
20130101 |
Class at
Publication: |
703/10 |
International
Class: |
E21B 43/00 20060101
E21B043/00 |
Claims
1. A method for well placement planning, the method comprising:
generating a control vector comprising a plurality of control
variables over which to optimize; translating the control vector to
a candidate well placement plan; performing a first feasibility
evaluation for the candidate well placement plan against one or
more inexpensive constraints; and in response to determining a
feasibility of the candidate well placement plan from the first
feasibility evaluation: computing a result for an objective
function based upon the candidate well placement plan using a
reservoir simulator; and performing a second feasibility evaluation
for the candidate well placement plan by evaluating the computed
result for the objective function based upon the candidate well
placement plan against one or more expensive constraints.
2. The method of claim 1, further comprising performing a
feasibility evaluation for the control vector against one or more
linear constraints prior to translating the control vector, wherein
translating the control vector is only performed in response to
determining a feasibility of the control vector from the third
feasibility evaluation.
3. The method of claim 1, wherein the control vector comprises an
initial control vector, and wherein the method further comprises
generating the initial control vector by translating an initial
well placement plan to the initial control vector.
4. The method of claim 1, further comprising, in response to
determining an infeasibility of the candidate well placement plan
from the first feasibility evaluation, bypassing computing the
result for the objective function and performing the second
feasibility evaluation.
5. The method of claim 1, further comprising, in response to
determining a feasibility of the candidate well placement plan from
the second feasibility evaluation, determining that the candidate
well placement plan is a feasible well placement plan.
6. The method of claim 1, further comprising, for each of a
plurality of control vectors, performing a trial processing
operation associated therewith, wherein each trial processing
operation comprises: determining feasibility for the associated
control vector against one or more linear constraints; and in
response to determining a feasibility of the associated control
vector against the one or more linear constraints: translating the
associated control vector to an associated candidate well placement
plan; performing the first feasibility evaluation for the
associated candidate well placement plan against the one or more
inexpensive constraints; and in response to determining a
feasibility of the associated candidate well placement plan from
the first feasibility evaluation: computing a result for the
objective function based upon the associated candidate well
placement plan using the reservoir simulator; and performing the
second feasibility evaluation for the associated candidate well
placement plan by evaluating the computed result for the objective
function based upon the associated candidate well placement plan
against the one or more expensive constraints.
7. The method of claim 6, further comprising, generating at least
one of the plurality of control vectors by extrapolating from a
prior control vector based at least in part on a feasibility
evaluation performed during a trial processing operation for the
prior control vector.
8. The method of claim 7, wherein the prior control vector is
associated with an associated candidate well placement plan
determined as infeasible, and wherein extrapolating from the prior
control vector is based upon a result of at least one feasibility
evaluation performed during the trial processing operation for the
prior control vector.
9. The method of claim 7, further comprising terminating well
placement planning after performing the trial processing operation
for each of the plurality of control vectors in response to a
termination condition, wherein the termination condition is based
on a determination that a maximum number of trial processing
operations have been performed, a determination that improvement in
the objective function has stalled, or a combination thereof.
10. The method of claim 1, wherein the reservoir simulator
comprises an analytical reservoir simulator that accesses a coarse
scale reservoir simulation model.
11. The method of claim 10, further comprising generating the
coarse scale reservoir simulation model by upscaling a fine scale
reservoir geology model.
12. The method of claim 1, wherein the objective function includes
one or more of net present value, return on investment,
profitability, production index, or combinations thereof.
13. The method of claim 1, wherein computing the result of the
objective function comprises computing a plurality of results for a
plurality of realizations to account for uncertainty in the
reservoir model, the method further comprising optimizing on a
utility function based on the plurality of results computed for the
plurality of realizations.
14. The method of claim 1, wherein translating the control vector
to the candidate well placement plan comprises identifying a
plurality of target locations in a reservoir, determining a
completion geometry for each target location, and determining a
trajectory for each target location.
15. The method of claim 14, wherein determining the completion
geometry for a first target location among the plurality of target
locations comprises determining at least one completion location
based upon at least one property of a plurality of cells associated
with the first target location and retrieved from a fine scale
reservoir geology model.
16. The method of claim 15, wherein the one or more inexpensive
constraints includes a feasibility of the first target location
based on a geometric relation to the fine scale reservoir geology
model, wherein the geometric relation includes a minimum completion
length, a minimum standoff relative to a fluid contact, a minimum
distance to a fault, or a combination thereof.
17. The method of claim 15, wherein the one or more inexpensive
constraints includes a feasibility of the first target location
based on a property of the fine scale reservoir geology model,
wherein the property includes minimum porosity, minimum
permeability, maximum water saturation, or a combination
thereof.
18. The method of claim 1, wherein performing the first feasibility
evaluation for the candidate well placement plan against the one or
more inexpensive constraints comprises performing anti-collision
analysis on the candidate well placement plan.
19. The method of claim 1, wherein the one or more inexpensive
constraints includes one or more of dogleg severity, maximum
inclination, maximum reach, number of platforms, number of wells,
flowing producers, slot number, platform location, minimum tie
point separation, minimum completion spacing, or combinations
thereof.
20. The method of claim 1, wherein the one or more expensive
constraints includes one or more of sub-economic wells, flowing
producers or a combination thereof.
21. The method of claim 1, wherein the control vector comprises one
or more of target location coordinates, tie point coordinates,
azimuth of a pattern, pattern spacing, or combinations thereof.
22. An apparatus, comprising: at least one processing unit; and
program code configured upon execution by the at least one
processing unit to perform well placement planning by: generating a
control vector comprising a plurality of control variables over
which to optimize; translating the control vector to a candidate
well placement plan; performing a first feasibility evaluation for
the candidate well placement plan against one or more inexpensive
constraints; and in response to determining a feasibility of the
candidate well placement plan from the first feasibility
evaluation: computing a result for an objective function based upon
the candidate well placement plan using a reservoir simulator; and
performing a second feasibility evaluation for the candidate well
placement plan by evaluating the computed result for the objective
function based upon the candidate well placement plan against one
or more expensive constraints.
23. A program product, comprising: a computer readable medium; and
program code stored on the computer readable medium and configured
upon execution by at least one processing unit to perform well
placement planning by: generating a control vector comprising a
plurality of control variables over which to optimize; translating
the control vector to a candidate well placement plan; performing a
first feasibility evaluation for the candidate well placement plan
against one or more inexpensive constraints; and in response to
determining a feasibility of the candidate well placement plan from
the first feasibility evaluation: computing a result for an
objective function based upon the candidate well placement plan
using a reservoir simulator; and performing a second feasibility
evaluation for the candidate well placement plan by evaluating the
computed result for the objective function based upon the candidate
well placement plan against one or more expensive constraints.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit of U.S. Provisional
Patent Application Ser. No. 61/756,800 filed Jan. 25, 2013, which
is incorporated herein by reference in its entirety.
BACKGROUND
[0002] Well placement planning is used in a number of industries to
plan out the placement of prospective wells. In the oil & gas
industry, for example, well placement planning is used to select
placements and trajectories for proposed wells into a subsurface
reservoir to reach specific locations in the reservoir that are
believed to contain recoverable hydrocarbons. Well placement
planning may be used to produce a well placement plan (WPP) that
includes one or more wells, as well as additional information such
as well trajectories, well completions, drilling schedules, etc.
Generally, a reservoir simulator is used in connection with well
placement planning so that reservoir simulation may be performed to
determine the potential value of any well placement plan.
[0003] Well placement planning may generally be considered to be an
optimization problem. Generally, well placement planning has been
performed in a predominantly manual process in which a user selects
target and well locations, performs a reservoir simulation
forecast, and then calculates a value based on the forecast oil or
gas recovered and the cost of the wells. The user generally may
repeat the process a number of times, but modify the number and
location of the wells and completions. The modifications may
include, for example, different water flooding strategies, well
spacing, well types, platform locations, etc.
[0004] Well placement planning, however, has been found to be a
very time-consuming process from both the user's perspective and a
computational perspective. Well placement planning has also been
found to be a relatively inefficient process because it may be
difficult for a user to objectively explore the complete solution
space.
[0005] A need therefore exists in the art for a more effective and
computationally efficient approach to well placement planning
SUMMARY
[0006] The embodiments disclosed herein provide a method,
apparatus, and program product that utilize constrained
optimization framework to generate a well placement plan based on a
reservoir model. Candidate well placement plans are generated from
control vectors proposed by an optimization engine to optimize
based upon an objective function that generally involves an access
to a reservoir simulator. Constraints that are not based on
computation of the objective function, referred to herein as
inexpensive constraints, are evaluated prior to computation of the
objective function (e.g., by accessing the reservoir simulator) to
avoid unnecessary computationally expensive operations for
candidate well placement plans determined to be infeasible in view
of the inexpensive constraints. For candidate well placement plans
that are determined to be feasible based upon the inexpensive
constraints, the objective function may be calculated and
additional constraints, referred to herein as expensive
constraints, may thereafter be evaluated to further determine the
feasibility of candidate well placement plans.
[0007] Therefore, in accordance with some embodiments, a method for
well placement planning is performed that includes generating a
control vector comprising a plurality of control variables over
which to optimize, translating the control vector to a candidate
well placement plan, performing a first feasibility evaluation for
the candidate well placement plan against one or more inexpensive
constraints, and in response to determining a feasibility of the
candidate well placement plan from the first feasibility
evaluation, computing a result for an objective function based upon
the candidate well placement plan using a reservoir simulator and
performing a second feasibility evaluation for the candidate well
placement plan by evaluating the computed result for the objective
function based upon the candidate well placement plan against one
or more expensive constraints.
[0008] In accordance with some embodiments, an apparatus is
provided that includes at least one processing unit and program
code configured upon execution by the at least one processing unit
to perform well placement planning by generating a control vector
comprising a plurality of control variables over which to optimize,
translating the control vector to a candidate well placement plan,
performing a first feasibility evaluation for the candidate well
placement plan against one or more inexpensive constraints, and in
response to determining a feasibility of the candidate well
placement plan from the first feasibility evaluation, computing a
result for an objective function based upon the candidate well
placement plan using a reservoir simulator and performing a second
feasibility evaluation for the candidate well placement plan by
evaluating the computed result for the objective function based
upon the candidate well placement plan against one or more
expensive constraints.
[0009] In accordance with some embodiments, a program product is
provided that includes a computer readable medium and program code
stored on the computer readable medium and configured upon
execution by at least one processing unit to perform well placement
planning by generating a control vector comprising a plurality of
control variables over which to optimize, translating the control
vector to a candidate well placement plan, performing a first
feasibility evaluation for the candidate well placement plan
against one or more inexpensive constraints, and in response to
determining a feasibility of the candidate well placement plan from
the first feasibility evaluation, computing a result for an
objective function based upon the candidate well placement plan
using a reservoir simulator and performing a second feasibility
evaluation for the candidate well placement plan by evaluating the
computed result for the objective function based upon the candidate
well placement plan against one or more expensive constraints.
[0010] In accordance with some embodiments, an apparatus is
provided that includes at least one processing unit, program code
and means for performing well placement planning by generating a
control vector comprising a plurality of control variables over
which to optimize, translating the control vector to a candidate
well placement plan, performing a first feasibility evaluation for
the candidate well placement plan against one or more inexpensive
constraints, and in response to determining a feasibility of the
candidate well placement plan from the first feasibility
evaluation, computing a result for an objective function based upon
the candidate well placement plan using a reservoir simulator and
performing a second feasibility evaluation for the candidate well
placement plan by evaluating the computed result for the objective
function based upon the candidate well placement plan against one
or more expensive constraints.
[0011] In accordance with some embodiments, an information
processing apparatus for use in a computing system is provided, and
includes means for performing well placement planning by generating
a control vector comprising a plurality of control variables over
which to optimize, translating the control vector to a candidate
well placement plan, performing a first feasibility evaluation for
the candidate well placement plan against one or more inexpensive
constraints, and in response to determining a feasibility of the
candidate well placement plan from the first feasibility
evaluation, computing a result for an objective function based upon
the candidate well placement plan using a reservoir simulator and
performing a second feasibility evaluation for the candidate well
placement plan by evaluating the computed result for the objective
function based upon the candidate well placement plan against one
or more expensive constraints.
[0012] In some embodiments, an aspect of the invention involves
performing a feasibility evaluation for the control vector against
one or more linear constraints prior to translating the control
vector, where translating the control vector is only performed in
response to determining a feasibility of the control vector from
the third feasibility evaluation.
[0013] In some embodiments, an aspect of the invention includes
that the control vector comprises an initial control vector, and
involves generating the initial control vector by translating an
initial well placement plan to the initial control vector.
[0014] In some embodiments, an aspect of the invention involves, in
response to determining an infeasibility of the candidate well
placement plan from the first feasibility evaluation, bypassing
computing the result for the objective function and performing the
second feasibility evaluation.
[0015] In some embodiments, an aspect of the invention involves, in
response to determining a feasibility of the candidate well
placement plan from the second feasibility evaluation, determining
that the candidate well placement plan is a feasible well placement
plan.
[0016] In some embodiments, an aspect of the invention involves,
for each of a plurality of control vectors, performing a trial
processing operation associated therewith, where each trial
processing operation comprises determining feasibility for the
associated control vector against one or more linear constraints
and, in response to determining a feasibility of the associated
control vector against the one or more linear constraints,
translating the associated control vector to an associated
candidate well placement plan, performing the first feasibility
evaluation for the associated candidate well placement plan against
the one or more inexpensive constraints, and in response to
determining a feasibility of the associated candidate well
placement plan from the first feasibility evaluation, computing a
result for the objective function based upon the associated
candidate well placement plan using the reservoir simulator, and
performing the second feasibility evaluation for the associated
candidate well placement plan by evaluating the computed result for
the objective function based upon the associated candidate well
placement plan against the one or more expensive constraints.
[0017] In some embodiments, an aspect of the invention involves
generating at least one of the plurality of control vectors by
extrapolating from a prior control vector based at least in part on
a feasibility evaluation performed during a trial processing
operation for the prior control vector.
[0018] In some embodiments, an aspect of the invention includes
that the prior control vector is associated with an associated
candidate well placement plan determined as infeasible, and
extrapolating from the prior control vector is based upon a result
of at least one feasibility evaluation performed during the trial
processing operation for the prior control vector.
[0019] In some embodiments, an aspect of the invention involves
terminating well placement planning after performing the trial
processing operation for each of the plurality of control vectors
in response to a termination condition, where the termination
condition is based on a determination that a maximum number of
trial processing operations have been performed, a determination
that improvement in the objective function has stalled, or a
combination thereof.
[0020] In some embodiments, an aspect of the invention includes
that the reservoir simulator comprises an analytical reservoir
simulator that accesses a coarse scale reservoir simulation
model.
[0021] In some embodiments, an aspect of the invention involves
generating the coarse scale reservoir simulation model by upscaling
a fine scale reservoir geology model.
[0022] In some embodiments, an aspect of the invention includes
that the objective function includes one or more of net present
value, return on investment, profitability, production index, or
combinations thereof.
[0023] In some embodiments, an aspect of the invention includes
that computing the result of the objective function comprises
computing a plurality of results for a plurality of realizations to
account for uncertainty in the reservoir model, the method further
comprising optimizing on a utility function based on the plurality
of results computed for the plurality of realizations.
[0024] In some embodiments, an aspect of the invention includes
that translating the control vector to the candidate well placement
plan comprises identifying a plurality of target locations in a
reservoir, determining a completion geometry for each target
location, and determining a trajectory for each target
location.
[0025] In some embodiments, an aspect of the invention includes
that determining the completion geometry for a first target
location among the plurality of target locations comprises
determining at least one completion location based upon at least
one property of a plurality of cells associated with the first
target location and retrieved from a fine scale reservoir geology
model.
[0026] In some embodiments, an aspect of the invention includes
that the one or more inexpensive constraints includes a feasibility
of the first target location based on a geometric relation to the
fine scale reservoir geology model, where the geometric relation
includes a minimum completion length, a minimum standoff relative
to a fluid contact, a minimum distance to a fault, or a combination
thereof.
[0027] In some embodiments, an aspect of the invention includes
that the one or more inexpensive constraints includes a feasibility
of the first target location based on a property of the fine scale
reservoir geology model, where the property includes minimum
porosity, minimum permeability, maximum water saturation, or a
combination thereof.
[0028] In some embodiments, an aspect of the invention includes
that performing the first feasibility evaluation for the candidate
well placement plan against the one or more inexpensive constraints
comprises performing anti-collision analysis on the candidate well
placement plan.
[0029] In some embodiments, an aspect of the invention includes
that the one or more inexpensive constraints includes one or more
of dogleg severity, maximum inclination, maximum reach, number of
platforms, number of wells, flowing producers, slot number,
platform location, minimum tie point separation, minimum completion
spacing, or combinations thereof.
[0030] In some embodiments, an aspect of the invention includes
that the one or more expensive constraints includes one or more of
sub-economic wells, flowing producers or a combination thereof.
[0031] In some embodiments, an aspect of the invention includes
that the control vector comprises one or more of target location
coordinates, tie point coordinates, azimuth of a pattern, pattern
spacing, or combinations thereof.
[0032] 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
[0033] 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.
[0034] 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.
[0035] 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.
[0036] FIG. 4 illustrates a production system for performing one or
more oilfield operations in accordance with implementations of
various technologies and techniques described herein.
[0037] FIG. 5 is a flowchart illustrating an example sequence of
operations for a well placement planning workflow in accordance
with implementations of various technologies and techniques
described herein.
[0038] FIG. 6 is a cross section of an automatically generated
vertical well through a reservoir, with three completions
corresponding to three feasible (porous) intervals.
[0039] FIG. 7 is a three dimensional model view of a single
platform with S well trajectories connected to targets.
[0040] FIG. 8 is a plot of an objective function for a plurality of
trials, illustrating the progress of an optimization workflow.
[0041] FIG. 9 is an illustration of a feasible region and bounding
box used in a target driven vertical wells case study.
[0042] FIG. 10 is a three dimensional model view of eight optimized
vertical wells in feasible regions above oil water contact in the
target driven vertical wells case study referenced in FIG. 9.
[0043] FIG. 11 is a pattern control vector for a five spot pattern
in a pattern driven vertical wells case study.
[0044] FIG. 12 is a three dimensional model view of an optimized
five spot pattern in the pattern driven vertical wells case study
referenced in FIG. 11.
DETAILED DESCRIPTION
[0045] The herein-described embodiments provide a method,
apparatus, and program product that implement a constrained
optimization framework to generate a well placement plan based on a
reservoir model. Candidate well placement plans are generated from
control vectors proposed by an optimization engine to optimize
based upon an objective function that generally involves an access
to a reservoir simulator. Constraints that are not based on
computation of the objective function, referred to herein as
inexpensive constraints, are evaluated prior to accessing the
reservoir simulator to avoid unnecessary accesses to the reservoir
simulator for candidate well placement plans determined to be
infeasible in view of the inexpensive constraints. For candidate
well placement plans that are determined to be feasible based upon
the inexpensive constraints, the objective function may be
calculated and additional constraints, referred to herein as
expensive constraints, may thereafter be evaluated to further
determine the feasibility of candidate well placement plans.
[0046] In this regard, a well placement plan, also referred to as a
field development plan, may be considered to include one or more
wells proposed for a geographic region such as an oilfield, as well
as additional planning information associated with drilling and
completing the wells, including, for example, location and/or
trajectory information, completion information, drilling schedule
information, projected production information, or any other
information suitable for use in drilling the proposed wells.
[0047] A constrained optimization framework, in turn, may be
considered to include a framework through which a constrained
optimization approach may be applied to the generation of a well
placement plan (WPP) in the presence of uncertainty and risk, based
upon one or more reservoir models, and based upon a set of
constraints that drive the feasibility of candidate well placement
plans developed by the framework. Constraints may be geometric,
operational, contractual and/or legal in nature, and as discussed
in greater detail below, may vary in terms of their computational
expense. Inexpensive constraints, for example, may generally be
considered to include constraints that may be evaluated without
accessing a reservoir simulator, while expensive constraints may
generally be considered to include constraints that do involve an
access to a reservoir simulator prior to evaluation. Generally, one
or more reservoir simulators are used in the illustrated
embodiments in the computation of an objective function that drives
the optimization to a desired end result, e.g., to maximize net
present value, return on investment, profitability, production,
etc., and well placement plans are associated with control vectors
that are used to calculate the objective function for different
well placement plans.
[0048] Other variations and modifications will be apparent to one
of ordinary skill in the art.
Hardware and Software Environment
[0049] 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.
[0050] 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.
[0051] 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, a petro-technical
module or component 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.
[0052] In one non-limiting embodiment, for example, 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, both 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.
[0053] 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.
[0054] 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.
[0055] 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.
[0056] 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.
[0057] 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
[0058] 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.
[0059] 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.
[0060] 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.
[0061] 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.
[0062] 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.
[0063] 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.
[0064] 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
[0065] 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.
[0066] 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.
[0067] 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.
[0068] 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.
[0069] 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.
[0070] 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.
[0071] 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.
[0072] 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).
[0073] 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.
[0074] 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.
[0075] 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.
[0076] 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.
[0077] 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.
[0078] 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.
[0079] 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.
[0080] 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.
[0081] 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.
[0082] 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.
[0083] 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.
[0084] 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.
Constrained Optimization for Well Placement Planning
[0085] Embodiments consistent with the invention may be used to
facilitate well placement planning through the use of an
optimization framework that applies a constrained optimization
approach to generate an optimal well placement plan based upon an
objective function representing a desired end goal, e.g., net
present value, profitability, return on investment, production,
etc.
[0086] In general, well placement planning is an optimization
problem. It involves discovering the optimal wells and completions
to attempt to maximize the value of an asset. As such well
placement planning may be framed as a general nonlinear constrained
optimization problem, e.g., by minimizing an objective function
f(x) subject to:
l.sub.i.ltoreq.x.sub.i.ltoreq.u.sub.i for i=1, . . . , n (1)
g.sub.j(x).ltoreq.0 for j=1, . . . , q (2)
h.sub.j(x).ltoreq.0 for j=1, . . . , m (3)
where [0087] x={x.sub.1, . . . , x.sub.n}.OR right..sub.n is a set
of n control variables over which to optimize, [0088] f:
.sub.n.fwdarw. is the objective function, [0089] l, u the lower and
upper bounds respectively, [0090] g: .sup.n.fwdarw..sup.q the
inequality constraints, and [0091] h: .sup.n.fwdarw..sup.m the
inequality constraints.
[0092] The constraint functions (g, h) may be linear or non-linear
with respect to the control variables.
[0093] A number of approaches exist for discovering the optimal set
of control variables x, also referred to herein as a control vector
that optimizes the objective function. For example, well placement
may be treated as an integer or a mixed integer problem in which
all or some of the control variables assume integer values, e.g.,
if all drilling targets are known. However, if the target and well
tie point locations are continuous functions of the surface,
overburden and reservoir properties, then the control variables
generally assume continuous real values that cannot be treated as
an integer or mixed integer problem.
[0094] In addition to the control variables being continuous, well
placement optimization problems generally have computationally
complex objective and constraint functions for which simple
functional forms are generally not available. As such, this problem
generally will also not have derivatives of the objective and
constraint functions available, because the analytical form
generally cannot be obtained and the numerical form may be too
noisy to be useful.
[0095] In embodiments consistent with the invention, on the other
hand, a derivative free optimization approach, e.g., a nonlinear
downhill simplex pattern search algorithm or a stochastic
optimization algorithm, may be used. Other optimization techniques
that may be used in the embodiments discussed herein include
Genetic Algorithms (GA), Simulated Annealing (SA), Branch and Bound
(B&B), Covariance Matrix Adaptation-Evolution Strategy
(CMA-ES), Particle Swarm Optimization (PSO), Spontaneous
Perturbation Stochastic Approximation (SPSA), Retrospective
Optimization using Hooke Jeeves search (ROHJ), Nelder-Mead downhill
Simplex (N-M), or Generalized Reduced Gradient (GRG) Genetic, among
others. The embodiments discussed hereinafter will focus on a
nonlinear downhill simplex algorithm because of its simplicity and
robustness across a wide spectrum of domains; however, it will be
appreciated by those of ordinary skill in the art having the
benefit of the instant disclosure that other optimization
algorithms or techniques may be used in other embodiments without
departing from the spirit and scope of the invention.
[0096] With any of the aforementioned optimization algorithms, an
optimization engine generally proposes a control vector, and the
objective function is evaluated. The algorithm then proposes a new
"trial" of the control vector using information from the results of
previous trials, with the goal of selecting a control vector that
improves the value of the objective function. The optimization
generally terminates when the maximum number of trials has been
evaluated or a desired accuracy of the objective function and
control vector values has been reached.
[0097] In optimization problems of this nature, the question of the
global versus local optimum may arise. In global optimization, the
true global solution to the optimization problem is found. However,
global optimization is only suitable for problems with a small
number of variables. When optimizing a problem such as that
described herein, it may be difficult to ascertain whether a global
optimum has been found. However, it has been found that there are a
number of safeguards available to ensure an answer, if not provably
optimal, is not an unreasonable local optimum. The safeguards may
include, for example, generating a good initial guess so that the
downhill simplex engine has a good starting point, and when an
optimum solution has been found, the optimal control vector can be
used as an initial guess for a repeat optimization, with such
nested optimizations optionally repeated until no substantial
improvement in the optimum is found.
[0098] The general downhill simplex method is an unconstrained
optimization technique in which the elements of the control vector
x are unbounded. However, well placement optimization has been
found to be a highly constrained problem in which the control
vector elements are not only bounded as shown in equation (1) but
also subjected to linear and non-linear constraints as shown in
equations (2) and (3).
[0099] To extend the nonlinear downhill simplex method to support
constrained optimization a sequential lexicographic approach may be
used, where the original problem is reformulated into another
minimization problem in which the original objective function f(x)
is minimized subject to .PHI.(x).ltoreq.0, where the constraint
violation function .PHI.(x) is strictly positive for infeasible
control vectors and less than or equal to zero for feasible ones,
that is:
.PHI.(x)>0 if x
.PHI.(x).ltoreq.0 if x.di-elect cons.
where [0100] is the feasible region.
[0101] In this transformed problem, control vectors may be compared
using the lexicographic order comparison operator (<.sub.CL)
rather than simple comparison of the objective function values,
that is:
( f 1 , .PHI. 1 ) < CL ( f 2 , .PHI. 2 ) .revreaction. { if ( x
1 x 2 ) : .PHI. 1 < .PHI. 2 else f 1 < f 2 ##EQU00001##
[0102] This approach may be further refined in the
hereinafter-described embodiments to distinguish between
inexpensive and expensive constraints, particularly where an
objective function evaluation is computationally expensive.
Inexpensive constraints may be considered to be constraints for
which the feasibility can be determined before the objective
function is evaluated or otherwise without using results of the
objective function in the determinations, while expensive
constraints may be considered to be constraints determined after
the objective function is evaluated or otherwise using results of
the objective function in the determinations. Reformulating the
problem in this manner allows for a reduction in the number of
evaluations of a relatively expensive objective function, and a new
lexicographic sequential order comparison operator (<.sub.SL)
may be defined as follows:
( f 1 , .PHI. l 1 , .PHI. nI 1 , .PHI. nE 1 ) < SL ( f 2 , .PHI.
l 2 , .PHI. nI 2 , .PHI. nE 2 ) .revreaction. { if ( x 1 l x 2 l )
: .PHI. l 1 < .PHI. l 2 else if ( x 1 nI x 2 nI ) : .PHI. nI 1
< .PHI. nI 2 else if ( x 1 nE x 2 nE ) : .PHI. nE 1 < .PHI.
nE 2 else f 1 < f 2 ##EQU00002##
[0103] Put another way, when an optimization engine compares two
control vectors x.sub.1 and x.sub.2, feasibility with respect to
the linear constraints .sub.l may first be determined. If either
vector is infeasible then the vector with the lower constraint
violation function (.PHI.) is determined to be better, and no
further comparisons may be made. This comparison may then be
repeated, but with respect to non-linear inexpensive constraints
.sub.nI, and thereafter if necessary with respect to non-linear
expensive constraints .sub.nE. If both vectors are determined to be
feasible with respect to all of these constraints then the
objective function values may be compared directly.
[0104] Now turning to FIG. 5, an example well placement planning
workflow 400 in accordance with implementations of various
technologies and techniques described herein is illustrated, to
perform well placement planning the presence of a geological model
of a reservoir. Workflow 400 may utilize a framework that
automatically generates an optimal Well Placement Plan (WPP) based
on a reservoir model, and in the illustrated embodiment a suite of
high-speed computational components generally allows a WPP to be
generated quickly (e.g., in minutes).
[0105] Workflow 400 may be used to automate the process of placing
new wells in a reservoir and/or sidetracking or recompleting
existing wells, and does so using constraint-based optimization
techniques. As will become more apparent below, optimization of a
WPP using one embodiment of workflow 400 may utilize a constrained
downhill simplex approach. During a trial, WPP's proposed by an
optimization engine in earlier trials may be extrapolated to
propose a new WPP. A proposed WPP may be evaluated for satisfying a
range of geometric, operational, contractual and legal constraints
on the surface, and in the overburden and reservoir. Collision and
hazard avoidance computation may also use a geocomputation topology
approach. When a feasible WPP is discovered a production forecast
may be computed using high-speed (e.g., in seconds) reservoir
simulator that analytically computes pressure and explicitly
computes saturation. In addition to recovery, a variety of
additional objective functions, e.g., Net Present Value, Return on
Investment, Profitability Index, Maintain Production Rate, etc. may
also be used. Optimization in the presence of subsurface
uncertainty may also be considered by using an ensemble of
reservoir models.
[0106] Specifically, as will be discussed in greater detail below,
workflow 400 is dominated by a loop that generally involves the
creation of a control vector by an optimization engine, the
translation of this control vector into a WPP, the feasibility
constraints analysis of that WPP, and the evaluation of the
objective function for the WPP. A single pass through the loop is
termed a "trial," and this sequence of steps is termed a trial
processing operation or element. The optimization engine, in this
case, the constrained downhill simplex discussed previously, then
proposes a new control vector with the intention of discovering an
optimal control vector. The optimization loop is then complete when
one or more termination conditions is satisfied.
[0107] Workflow 400 may be implemented, for example, at least in
part within petro-technical module 32 of FIG. 1, which may be
implemented as, or otherwise access an optimization engine. Module
32 may also access one or more reservoir simulators (e.g., resident
in E&P platform 34) for use in accessing one or more reservoir
models. It will be appreciated by those of ordinary skill in the
art having the benefit of the instant disclosure that some
operations in workflow 400 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
workflow illustrated in FIG. 5.
[0108] Referring again to FIG. 5, workflow 400 may incorporate some
initialization operations, including, as illustrated in block 402,
a reservoir upscaling operation. The reservoir upscaling operation
may be performed, for example, to upscale one or more fine scale or
high resolution geology models 404 to generate a coarse scale or
low resolution simulation model suitable for use by an analytical
reservoir simulator when computing an objective function, such that
computation of the objective function may be performed using a
high-speed (e.g., in seconds) reservoir simulation. Additional
initialization operations, e.g., parsing existing wells and
geologic hazards in the overburden for collision avoidance, may
also be performed.
[0109] Thereafter, block 402 passes control to block 408 to
generate an initial guess control vector 410, which is then
processed by a trial processing element 412, which upon completion
of a trial, passes control to block 414 to generate another control
vector 410. Control vectors and their associated trial results,
including feasibility or infeasibility with respect to various
constraints and the magnitudes of such feasibility/infeasibility,
may also be maintained in a database or other data storage as
illustrated at 416.
[0110] With respect to creation of a control vector in blocks 408
and 414, a control vector may be implemented as a vector of control
variables, that is:
x={x.sub.1, . . . , x.sub.n}.OR right..sup.n
where each control variable assumes a value in the range:
0.ltoreq.x.sub.i.ltoreq.1.
[0111] The optimization engine in general may be unaware of the
domain and physical meaning of each control variable. It is,
however, one role of the trial processing element 412 of the
workflow to analyze the control vector, generate a WPP and inform
the optimization engine of the feasibility and objective function
values.
[0112] To generate an "initial guess" control vector in block 408,
random numbers may be assigned in some embodiments, although in
some instances, doing so may be inefficient as generally some
knowledge of feasible and favorable values for at least some of the
control variables will be known at the outset. In other
embodiments, however, an initial guess control vector may be
generated from an initial WPP from candidate target and platform
tie point locations, in an operation that is effectively the
inverse of generating a WPP from a control vector (which is
performed in block 420, discussed below).
[0113] Targets for the initial control vector may be selected with
criteria under a user's control. For example, it may be favorable
to use targets near the crest of anticlines, or focus on regions
with the maximum productivity index, or minimum water saturation.
Other manners of generating an initial control vector will be
appreciated by one of ordinary skill in the art having the benefit
of the instant disclosure.
[0114] Next, turning to trial processing element 412, a trial is
initiated for a control vector by performing a feasibility
evaluation for the control vector against one or more linear
constraints in block 418. For some workflows, control variables may
map directly to tie point or target locations, so in these cases,
the control variables' values may be transformed directly into
project coordinates and evaluated for inclusion or exclusion in the
project's region of interest. If a control vector is determined to
be infeasible as a result of this evaluation, trial processing ends
for the control vector and control passes to block 414 to generate
a new control vector.
[0115] If feasible, however, the control vector advances to the
next stage of creating a candidate WPP, as illustrated by block
420, which may also be referred to as translating the control
vector into a candidate WPP. In this operation, target
identification, trajectory creation and completion creation are
performed for one or more wells based upon the control variables in
the control vector to generate a WPP 422.
[0116] Target identification generally refers to identification of
target locations in a reservoir. For some workflows, some of the
control variables in a control vector may correspond directly to
targeted locations (X, Y). In such embodiments, the
high-resolution, or fine scale, geological model 404 may be
analyzed to extract the cells corresponding to each targeted
location (e.g., as illustrated by effective porosity and water
saturation columns 450, 452 in FIG. 6). For a vertical well, this
generally corresponds to the cells including the X, Y coordinate.
It will be appreciated that the extraction of cells, and in
particular, the properties associated with such cells, is
substantially less computationally-expensive than running a
numerical simulation with a high-resolution geological model.
Consequently, high resolution reservoir data may be accessed in
connection with generating a WPP in a computationally-efficient
manner.
[0117] In addition, the completion geometry corresponding to each
location may also be identified. A user may supply constraints that
are used in the construction of the completion. For example, to be
feasible, a completion generally has a minimum length and a minimum
standoff from a fluid contact (e.g., as shown by completions 454,
456 and 458 in FIG. 6). Cells may also have valid properties such
as minimum permeability, or maximum water saturation. Generally, a
completion is created if these criteria are satisfied.
[0118] Once the target locations and completions have been created
from the control vector then the trajectories that connect the
completions to the surface may be created. The control vector
generally includes either explicit or implicit tie point location
information. For example, if an existing platform is to be used for
a trajectory, the tie point will be part of the problem definition
and not included in the control vector. A trajectory may then be
constructed which connects the tie point to the target (e.g., as
illustrated by trajectory 460 coupled to target 462 in FIG. 7).
[0119] Returning to FIG. 5, once WPP 422 is generated in block 420,
block 424 then performs an evaluation of the WPP against one or
more inexpensive constraints. As noted above, the inexpensive
constraints may be constraints on the WPP that may be evaluated
without computing the objective function.
[0120] For example, one type of inexpensive constraint is related
to anti-collision. A brownfield by definition contains existing
wells, and as these existing wells may be actively flowing,
abandoned, or a combination, when new wells are proposed it may be
desirable to perform anti-collision or hazard avoidance analysis to
evaluated whether any well trajectories collide with existing wells
or other hazards in the reservoir (e.g., natural hazards). An
anti-collision analysis may be implemented, for example, in the
manner disclosed in U.S. Provisional Application No. 61/756,789
filed on Jan. 25, 2013 by Peter Tilke, the entire disclosure of
which is incorporated by reference herein. Such analysis may
therefore be performed in connection with feasibility constraint
evaluations to ensure the wells in a WPP avoid existing wells and
other hazards.
[0121] Another type of inexpensive constraint may be related to a
trajectory. For example, dogleg severity, maximum inclination and
maximum reach may be used to limit the tie points that may feasibly
connect with a target.
[0122] Another type of inexpensive constraint may be evaluated for
a target location based on one or more geometric relations between
the target location and the high resolution reservoir geology
model. These geometric relations may include, but are not limited
to, geometric relations such as minimum completion length, minimum
standoff relative to a fluid contact, minimum distance to a fault,
or combinations thereof. Yet another type of inexpensive constraint
may be evaluated for a target location based on one or more
properties of the high resolution reservoir geology model. These
properties may include, but are not limited to, minimum porosity,
minimum permeability, maximum water saturation or combinations
thereof.
[0123] Additional inexpensive constraints may include:
Number of platforms--have the correct number of platforms been
created in this WPP? Number of wells--have the correct number of
wells been created in this WPP? Flowing producers--does the WPP
result in flowing producers existing in the field? Slot
number--each new and existing platform has user specified limits on
the desired minimum and maximum number of utilized slots. The wells
assigned to each platform should satisfy this criterion. Platform
location--is each tie point in a valid location? This includes
whether or not the platform is located in a valid area, or avoids a
surface hazard, e.g., a steep slope or a riverbed. Minimum tie
point separation--tie points meet a minimum spacing from one
another as specified by a user. Minimum completion
spacing--completions meet a minimum spacing from one another as
specified by a user.
[0124] Other inexpensive constraints that may be utilized to
evaluate the feasibility of a well placement plan without
computation of the objective function will be appreciated by one of
ordinary skill in the art having the benefit of the instant
disclosure. In addition, it will be appreciated that, in response
to a well placement plan being determined to be infeasible based
upon the inexpensive constraints, block 424 terminates the trial
for the current candidate control vector and returns control to
block 414 to generate a new control vector. As such, the
computational expense of computing the objective function for this
WPP is avoided.
[0125] If, however, the WPP is still determined to be feasible
after performing feasibility evaluation against the inexpensive
constraints, block 424 passes control to block 426 to compute the
objective function. It will be appreciated that optimization
conventionally seeks to discover the feasible control vector
yielding the minimum objective function value. In well placement
planning, generally the desire is to maximize an objective function
value. As such, in the illustrated embodiment, the computed value
is negated before returning the value to the optimization
engine.
[0126] In general, different workflows have different objectives,
and therefore different objective functions may be used in
different embodiments. For example, one objective may be to simply
maximize recovery, in which case capital and operating costs along
with oil or gas price may be ignored. This may also be the case if
the objective is to maintain a plateau production rate. A more
complete financial objective function may be used in some
embodiments to calculate net present value (NPV) in which a
forecast recovery, a commodity price, and the costs are considered
along with a discount factor. Other objective functions that may be
used include, for example, fiscal parameters such as return on
investment (ROI) and profitability index.
[0127] Costs may be separated into capital and operating expenses.
Capital expenses may include drilling, and surface facility,
drilling, well, and completion construction. Operating expenses may
include personnel, injection, production and treatment costs.
Generally, the one component that adds value to the objective
function is the oil or gas recovered from the reservoir, and
everything else is cost. While a user may provide an estimate of a
forecast commodity price, the production forecast itself generally
is computed.
[0128] As noted above, the objective function is computed in block
426 whenever the proposed WPP in a trial satisfies the inexpensive
constraints. Otherwise, computation of the objective function, and
evaluation of expensive constraints (discussed below) are bypassed.
From a computational perspective the objective function
computation, e.g., a production forecast calculation, is generally
the most computationally expensive part of a trial. For this
reason, a high-speed analytical reservoir simulator, utilizing
coarse scale model 406, may be used to compute the forecast. In one
embodiment, the analytical reservoir simulator may be founded on
the analytical solution of the diffusion equation:
.differential. p .differential. t = .eta. x .differential. 2 p
.differential. x 2 + .eta. y .differential. 2 p .differential. y 2
+ .eta. z .differential. 2 p .differential. z 2 ##EQU00003##
[0129] The simulator may be subject to initial and boundary
conditions. Iso-parametric transformation may be used to extend the
solution to irregular non-cuboid reservoirs. Regional-scale
reservoir heterogeneity may be modeled with multiple cuboids with
differing reservoir rock properties. Individual wells may refine
the modeled heterogeneity further through the skin factor (S),
which may influence the productivity index (PI) as follows:
P I = kk ro h .mu. o B o ln ( r e / r w ) + S ##EQU00004##
[0130] Also, in some embodiments, a pressure analytical saturation
explicit (PASE) method may be used to extend the solution to
waterflooding problems.
[0131] Other objective functions and manners of computing the same,
including approaches that utilize coarse scale models and/or
analytical simulators, as well as other approaches that do not
utilize such techniques, or that utilize numerical or other types
of reservoir simulators, may be used in other embodiments, and will
be apparent to one of ordinary skill in the art having the benefit
of the instant disclosure.
[0132] Once the objective function is computed for a candidate WPP,
block 426 passes control to block 428 to perform a feasibility
evaluation of the candidate WPP against a set of expensive
constraints. In particular, after the objective function has been
computed is may be possible in some embodiments that some wells in
the WPP are flowing at sub-economic rates. The WPP may therefore be
evaluated to remove sub-economic wells. The WPP may then be
evaluated to ensure that flowing producers still remain in the
solution.
[0133] Other expensive constraints that may be evaluated in other
embodiments include, for example, determining that a proposed WPP
is infeasible if no feasible producers exist but only feasible
injectors exist, as well as others that will be appreciated by
those of ordinary skill in the art having the benefit of the
instant disclosure.
[0134] If the candidate WPP is determined to be infeasible in block
428, control returns to block 414 to generate a new control vector.
Otherwise, the WPP is added to a set of feasible WPP's 430, and
control passes to block 432 to determine whether the optimization
is complete. If not, control passes to block 414 to generate
another control vector. If so, control passes to block 434 to
terminate the workflow and return results to the user.
[0135] Trial processing element 412 may therefore be repeated by
the optimization engine until an optimal solution is discovered, or
otherwise until another termination condition is met. In addition,
as illustrated by block 416, optimization engine uses information
garnered from control vectors, both infeasible and feasible, to
extrapolate new control vectors from past trials. In addition, when
the termination condition is met, feasible control vectors are
reported back as results to the user, representing the viable well
placement plans determined from the well placement planning
workflow.
[0136] FIG. 8, for example, illustrates a plot of objective
function results (here, value) computed for a plurality of trials.
In some embodiments, the plot of FIG. 8 may be progressively
generated and displayed to a user during the workflow, with updates
made for each feasible WPP added to the results. As such, a user
may view the improvement in the objective function over the course
of the workflow. FIG. 8 also illustrates at about trial 60 where
the optimization reaches a plateau and supplies the optimum as a
new initial guess for a new "restarted" optimization that
eventually yields a more-improved value, just one type of potential
optimization technique that may be used by an optimization engine
consistent with the invention.
[0137] Block 432 may terminate workflow 400 in response to
different termination conditions. For example, in one embodiment, a
termination condition may be based on a determination that a
maximum specified number of trials has been completed. In another
embodiment, a termination condition may be based on achieving an
objective function value that ceases to improve with successive
trials within a specified accuracy, or put another way, a
determination that improvement in the objective function has
stalled (e.g., insufficient improvement has occurred over a most
recent set of trials as prescribed by a tolerance). In other
embodiments, a combination of determinations may be made, e.g., to
terminate after the objective function does not improve more than X
% over the last Y trials, but in any event never exceed Z total
trials.
[0138] Embodiments consistent with the invention may also optimize
in the presence of uncertainty. During uncertain optimization, an
optimal control vector is being sought when the underlying model is
uncertain. In the case of well placement planning, the model may be
represented by the overburden and the reservoir, and during
optimization, the uncertainty in the model may be reflected in an
uncertainty in the objective function value. Under such conditions,
the overall optimization workflow may remain the same, and function
in essentially the same manner as illustrated in FIG. 5 as with
deterministic optimization. However, for uncertain optimization,
the value of the objective function being minimized may be
considered to be a function of the uncertainty distribution in the
objective function value. For example, the objective function value
may have statistical moments such as mean (.mu.) and variance
(.sigma..sup.2). The optimization engine may attempt to maximize a
single value, which is now a function of these statistical moments.
This function may be referred to as a "utility function." One
utility function that may be used for this type of problem is
defined as follows:
f.sub..lamda.=.mu.-.lamda..sigma.
where .mu. and .sigma. are respectively the mean and standard
deviation of the objective function value resulting from the
uncertain model, .lamda. is the risk aversion factor, and
f.sub..lamda. is the risk corrected objective function value.
Optimization then involves maximizing f.sub..lamda..
[0139] The risk aversion factor (.lamda.) may be a user-defined
preference, and may be roughly considered equivalent to a
confidence level. If, for a given control vector the uncertain
objective function value were to be normally distributed this would
be precisely true. For example, if .lamda.=0 there would be a 50%
probability that the objective function value f.sub.0 would be
greater than the mean .mu., so an optimum median (50% confidence
level) would be obtained by maximizing .theta..sub.0. If .lamda.=1,
there would be an 84% probability that the realized objective
function value would be greater than f.sub.1. Therefore, it can be
seen that a higher value for .lamda. generally implies a more
conservative decision.
[0140] For well placement planning problems, the underlying
overburden and reservoir models are generally complex and the
uncertainty in these models is also generally complex and
nonlinear. The uncertainty in the model may therefore be
represented as a plurality of realizations of the model in some
embodiments. For example, one may be uncertain in the orientation
of turbidite channels in a reservoir, and as such, multiple (N)
realizations of the reservoir model may be generated, each with a
likely channel orientation and geometry. The goal would be to have
the collection of models reflect the possible spectrum of channel
orientations. During optimization, a given control vector yielding
a WPP may result in a different objective function value for each
model realization. The mean and standard deviation in the objective
function value for this collection of models may be generated
during optimization and used to compute f.sub..lamda., the risk
corrected objective function value. During uncertain optimization,
the objective function is generally evaluated N times during every
trial, which may result in a significant computational overhead
during uncertain optimizations, and further providing additional
benefits when such computations are avoided as a result of
feasibility evaluations that declare a WPP infeasible prior to
computation of an objective function.
Case Study--Target Driven Vertical Wells
[0141] As one example of the herein-described embodiments, consider
the problem of finding an optimal placement of vertical wells
driven by target quality. The control variables that make up the
control vector may be directly associated with target coordinates.
For this exercise, the easting and northing (X, Y) of the target
locations may be considered. A vertical well at this location may
potentially penetrate the entire reservoir being considered. Thus,
to define a target location and hence a vertical well, a control
vector may be defined including two control variables, one for X
and one for Y. For this example consider eight targets, or vertical
wells. If M represents the number of targets, then the length of
the control vector (N) is given by N=2M. It then follows that:
x.sub.j=X.sub.2(j-1)+1 and y.sub.j=X.sub.2(j-1)+2 for j=1, . . . ,
M
where X is the control vector and x.sub.j, and y.sub.j are the
coordinates of the jth target.
[0142] As noted above, each control variable may have the following
bounds:
0.ltoreq.X.sub.i.ltoreq.1 for i=1, . . . , N
[0143] These values may be mapped to the bounds of a feasible
region of the control variable, as illustrated in FIG. 9. Each
candidate target may have a feasible region (e.g., region 470)
defined by an irregular polygon (or polygons). A rotated bounding
box 472 encloses the feasible region, and the axes of the bounding
box correspond to the two control variables defining the target
coordinate (x.sub.j, and y.sub.j). A mapping from the control
variable coordinate system to the project geographic coordinate
system is then a straightforward rotation, scaling and
translation.
[0144] FIG. 10 illustrates the result of optimizing 8 vertical
wells 480 in an anticlinal structure. Since M=8 in this example,
the total number of control variables is 16. While production for
these 8 producers is computed by the reservoir simulator operating
on the upscaled reservoir model, the productivity of each well is
influenced by the fine scaled heterogeneity of the geological model
as illustrated here in FIG. 10 by the permeability property
represented by cells 482. Also, note the distribution of the wells
that reflects the distribution in reservoir quality rock, avoidance
of infeasible regions (water table), and minimizes the interference
between the wells.
Case Study--Target Driven Deviated Wells
[0145] The next example is also dictated by target quality.
However, rather than having vertical wells, this example
illustrates the optimization with a single platform and four
deviated S-Wells (e.g., as shown in FIG. 7). In this case, the
number of targets (M) is 4 yielding 8 control variables to describe
the targets, as in the vertical well example. However, the tie
point location for the platform may also be specified, thereby
requiring an additional two control variables for total of 10.
Case Study--Pattern Driven Vertical Wells
[0146] In another example, a pattern driven strategy, specifically
a five spot pattern, is illustrated in FIG. 11. In this case
discovering the optimal pattern parameters is generally more of an
issue that identifying specific targets. For basic pattern
geometry, the following parameters may be discovered, as
illustrated in FIG. 11: [0147] 490--Tie point location of one well
(2 control variables) [0148] 492--Azimuth of the pattern (1 control
variable) [0149] 494--Pattern spacing (1 control variable)
[0150] Thus, a basic five spot pattern may be optimized with as few
as four control variables. This can also be made more complex if
one allows for an asymmetric aspect ratio in the pattern, or
deviated wells as in the previous example. An illustration of an
optimized five spot pattern is shown in FIG. 12.
[0151] Presented herein therefore is a framework for automated well
placement planning as part of the field development planning
workflow that in some embodiments may be performed quickly and
using modest computing resources (e.g., performed in minutes using
desktop hardware and software). The framework in some embodiments
automatically designs a well placement plan that optimizes an
objective function (e.g., NPV or recovery) in the presence of
subsurface uncertainty and operational risk tolerance. Also, in
some embodiments, a production forecast of the well placement plan
may also be computed rigorously with an analytical or
semi-analytical reservoir simulator. Engineering, financial,
operational and geological constraints may also be incorporated
into the computed plan.
[0152] The aforementioned methodology has many applications in the
field of development planning context. For example, in some
embodiments, multiple field development planning scenarios can be
rapidly screened, and may be used in connection with selecting new
wells, sidetracking existing wells and/or completing existing
wells. In brownfields with hundreds of existing wells, infill
locations can be quickly identified. Additional applications and
uses of the herein-described techniques will be apparent to one of
ordinary skill in the art having the benefit of the instant
disclosure.
[0153] 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.
* * * * *