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.

Description

BACKGROUND

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.

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.

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.

A need therefore exists in the art for a more effective and computationally efficient approach to well placement planning

SUMMARY

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

In some embodiments, an aspect of the invention involves generating the coarse scale reservoir simulation model by upscaling a fine scale reservoir geology model.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

FIG. 4 illustrates a production system for performing one or more oilfield operations in accordance with implementations of various technologies and techniques described herein.

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.

FIG. 6 is a cross section of an automatically generated vertical well through a reservoir, with three completions corresponding to three feasible (porous) intervals.

FIG. 7 is a three dimensional model view of a single platform with S well trajectories connected to targets.

FIG. 8 is a plot of an objective function for a plurality of trials, illustrating the progress of an optimization workflow.

FIG. 9 is an illustration of a feasible region and bounding box used in a target driven vertical wells case study.

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.

FIG. 11 is a pattern control vector for a five spot pattern in a pattern driven vertical wells case study.

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

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.

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.

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.

Other variations and modifications will be apparent to one of ordinary skill in the art.

Hardware and Software Environment

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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 _i ≦x _i ≦u _i for i=1, . . . , n  (1)

g _j(x)≦0 for j=1, . . . , q  (2)

h _j(x)≦0 for j=1, . . . , m  (3)

where

• • x={x₁, . . . , x_n}⊂_n is a set of n control variables over which to optimize,
  • f: _n→ is the objective function,
  • l, u the lower and upper bounds respectively,
  • g: ⁿ→^q the inequality constraints, and
  • h: ⁿ→^m the inequality constraints.

The constraint functions (g, h) may be linear or non-linear with respect to the control variables.

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.

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.

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.

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.

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.

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).

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 Φ(x)≦0, where the constraint violation function Φ(x) is strictly positive for infeasible control vectors and less than or equal to zero for feasible ones, that is:

Φ(x)>0 if x∉

Φ(x)≦0 if x∈

where

• • is the feasible region.

In this transformed problem, control vectors may be compared using the lexicographic order comparison operator (<_CL) rather than simple comparison of the objective function values, that is:

$\left(f_1,{\Phi }_1\right){<}_{\mathrm{CL}}\left(f_2,{\Phi }_2\right)\iff \{\begin{array}{cc}\mathrm{if}& \left(x_1\notin \bigvee x_2\notin \right):{\Phi }_1<{\Phi }_2\\ \mathrm{else}& f_1<f_2\end{array}$

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 (<_SL) may be defined as follows:

$\left(f_1,{\Phi }_{l1},{\Phi }_{\mathrm{nI}1},{\Phi }_{\mathrm{nE}1}\right){<}_{\mathrm{SL}}\left(f_2,{\Phi }_{l2},{\Phi }_{\mathrm{nI}2},{\Phi }_{\mathrm{nE}2}\right)\iff \{\begin{array}{cc}\mathrm{if}& \left(x_1\notin {}_l\bigvee x_2\notin {}_l\right):{\Phi }_{l1}<{\Phi }_{l2}\\ \mathrm{else}\mathrm{if}& \left(x_1\notin {}_{\mathrm{nI}}\bigvee x_2\notin {}_{\mathrm{nI}}\right):{\Phi }_{\mathrm{nI}1}<{\Phi }_{\mathrm{nI}2}\\ \mathrm{else}\mathrm{if}& \left(x_1\notin {}_{\mathrm{nE}}\bigvee x_2\notin {}_{\mathrm{nE}}\right):{\Phi }_{\mathrm{nE}1}<{\Phi }_{\mathrm{nE}2}\\ \mathrm{else}& f_1<f_2\end{array}$

Put another way, when an optimization engine compares two control vectors x₁ and x₂, feasibility with respect to the linear constraints _l may first be determined. If either vector is infeasible then the vector with the lower constraint violation function (Φ) 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 _nI, and thereafter if necessary with respect to non-linear expensive constraints _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.

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).

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.

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.

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.

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.

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.

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 ₁ , . . . , x _n}⊂ⁿ

where each control variable assumes a value in the range:

0≦x_i≦1.

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.

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).

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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:

$\frac{\partial p}{\partial t}={\eta }_x\frac{{\partial }^2p}{\partial x^2}+{\eta }_y\frac{{\partial }^2p}{\partial y^2}+{\eta }_z\frac{{\partial }^2p}{\partial z^2}$

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:

$PI=\frac{{\mathrm{kk}}_{\mathrm{ro}}h}{{\mu }_oB_o\ln \left(r_e/r_w\right)+S}$

Also, in some embodiments, a pressure analytical saturation explicit (PASE) method may be used to extend the solution to waterflooding problems.

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.

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.

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.

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.

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.

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.

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.

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 (μ) and variance (σ²). 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:

ƒ_λ=μ−λσ

where μ and σ are respectively the mean and standard deviation of the objective function value resulting from the uncertain model, λ is the risk aversion factor, and ƒ_λ is the risk corrected objective function value. Optimization then involves maximizing ƒ_λ.

The risk aversion factor (λ) 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 λ=0 there would be a 50% probability that the objective function value f₀ would be greater than the mean μ, so an optimum median (50% confidence level) would be obtained by maximizing θ₀. If λ=1, there would be an 84% probability that the realized objective function value would be greater than ƒ₁. Therefore, it can be seen that a higher value for λ generally implies a more conservative decision.

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_λ, 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

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 _j =X _2(j-1)+1 and y_j=X_2(j-1)+2 for j=1, . . . , M

where X is the control vector and x_j, and y_j are the coordinates of the jth target.

As noted above, each control variable may have the following bounds:

0≦X_i≦1 for i=1, . . . , N

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_j, and y_j). A mapping from the control variable coordinate system to the project geographic coordinate system is then a straightforward rotation, scaling and translation.

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

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

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:

• 490—Tie point location of one well (2 control variables)
• 492—Azimuth of the pattern (1 control variable)
• 494—Pattern spacing (1 control variable)

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.

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.

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.

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.

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; andin 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; andperforming 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; andin 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; andin 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; andperforming 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; andprogram 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; andin 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; andperforming 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; andprogram 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; andin 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; andperforming 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.