Abstract:
A method is presented for field planning. The method includes obtaining a shared earth model comprising the hydrocarbon field. The hydrocarbon field comprises an area of ground surface and a reservoir disposed beneath the area of ground surface. The method also includes obtaining a plurality of targets for the reservoir. Additionally, the method includes specifying one or more field planning parameters for accessing the plurality of targets from the surface. The method further includes determining a plurality of well site locations for an entirety of the hydrocarbon field using constraint optimization. The number of well site locations is minimized. The number of the plurality of targets accessible from the plurality of well site locations is maximized.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims the benefit of U.S. Provisional Patent Application 61/444,916 filed Feb. 21, 2011 entitled METHOD AND SYSTEM FOR FIELD PLANNING, the entirety of which is incorporated by reference herein. 
     
    
     FIELD OF THE INVENTION 
       [0002]    Exemplary embodiments of the present techniques relate to a method and system for field planning by selecting well site locations and their corresponding reservoir target groupings. 
       BACKGROUND 
       [0003]    This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present techniques. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present techniques. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art. 
         [0004]    Field planning involves the design of a drilling plan for an oilfield, or other hydrocarbon resource. One of the objectives of field planning is to maximize the total field production by selecting appropriate well sites for accessing a hydrocarbon reservoir. Selecting well sites is complicated by numerous considerations, such as environmental issues, maintaining safe distances around wells, and cost. Costs may include costs for facilities and for drilling over the life cycle of the reservoir. 
         [0005]    Field planning decisions are typically made over a long period of time, and further involve complexities arising from land use, planned well site locations, well trajectory design, and business considerations. The complexity of field planning decisions leads to complex models for which optimal solutions are difficult and tedious to obtain. 
         [0006]    One research article published on field planning presents a model of hierarchical planning and a scheduling decision tool including strategic, tactical and operational processes to address an optimal utilization and production of a gas field. See Udoh et al., “Applications of Strategic Optimization Techniques to Development and Management of Oil and Gas Resources,” 27th SPE meeting, (2003). 
         [0007]    The following paragraphs of this Background section provide specific examples of known techniques. U.S. Pat. No. 7,460,957 presents a method that automatically designs a multi-well development plan given a set of previously interpreted subsurface targets. The method focuses on how to calculate well paths from selected platforms or targets in order to optimize the drilling planning. 
         [0008]    U.S. Pat. No. 7,200,540 also presents a method that selects a possible set of well platform locations from automatically generated target locations. 
         [0009]    U.S. Patent Application Publication No. 2009/0119076 discloses a method for generating an invertible 3D hydrodynamic earth model. The model is allegedly suitable for defining target characteristics of a subsurface area formed by a plurality of formations and comprising drilling positions of potential and real wells. 
         [0010]    An initial three-dimensional (3D) earth model may be constructed by combining solutions for a set of single one-dimensional (1D) models. Each of the 1D models correspond to a real or potential well drilling position. 
         [0011]    Each of the 1D models also covers the entire respective aggregate of formations along the wellbore, with solutions for a relevant set of 2D earth models which are constructed only for single formations. The method further includes optimizing the constructed initial 3D earth model by defining an optimal set of formations and an optimal set of model parameters that may be calibrated. 
         [0012]    A method and system for application of the earth model construction method for predicting overpressure evolution before and during drilling are also provided. As the earth model constructed in accordance with the above method provides efficient inversion of data, in particular gathered while drilling, the prediction can be updated in real-time while drilling. This method allegedly ensures optimization of the drilling process and improves its safety. 
         [0013]    International Patent Application Publication No. WO2009/032416 discloses methods and systems to make completion design an integral part of the well planning process by enabling the rapid evaluation of completion performance. This integration may include an earth model and may specify well-path parameters, completion parameters, and other parameters in a simulation of operations using the earth model. The simulation generates well performance measures, which may be optimized depending on well performance technical limits. The optimization may be used to maximize an objective function. The system may include multiple users at the same or different locations (e.g. over a network) interacting through graphic user interfaces (GUI&#39;s). 
         [0014]    U.S. Patent Application Publication No. 2009/0056935 discloses a method to automatically design a multi-well development plan given a set of previously interpreted subsurface targets. This method allegedly identifies an optimal plan by minimizing the total cost as a function of existing and required new platforms, the number of wells, and the drilling cost of each of the wells. The cost of each well is a function of the well path and the overall complexity of the well. 
         [0015]    U.S. Pat. No. 6,549,879 discloses a systematic, computationally-efficient, two-stage method for determining well locations in a 3D reservoir model while satisfying various constraints including: minimum interwell spacing, maximum well length, angular limits for deviated completions, and minimum distance from reservoir and fluid boundaries. In the first stage, the wells are placed assuming that the wells can only be vertical. In the second stage, these vertical wells are examined for optimized horizontal and deviated completions. This solution is expedient, yet systematic, and it provides a good first-pass set of well locations and configurations. 
         [0016]    The first stage solution formulates the well placement problem as a binary integer programming (BIP) problem which uses a “set-packing” approach that exploits the problem structure, strengthens the optimization formulation, and reduces the problem size. Commercial software packages are readily available for solving BIP problems. 
         [0017]    The second stage sequentially considers the selected vertical completions to determine well trajectories that connect maximum reservoir pay values while honoring configuration constraints including: completion spacing constraints, angular deviation constraints, and maximum length constraints. 
         [0018]    The parameter to be optimized in both stages is a tortuosity-adjusted reservoir “quality.” The quality is preferably a static measure based on a proxy value such as porosity, net pay, permeability, permeability-thickness, or pore volume. These property volumes are generated by standard techniques of seismic data analysis and interpretation, geology and petrophysical interpretation and mapping, and well testing from existing wells. An algorithm is disclosed for calculating the tortuosity-adjusted quality values. 
       SUMMARY 
       [0019]    A method is presented for field planning. The method includes obtaining a shared earth model comprising the hydrocarbon field. The hydrocarbon field comprises an area of ground surface and a reservoir disposed beneath the area of ground surface. The method also includes obtaining a plurality of targets for the reservoir. Additionally, the method includes specifying one or more field planning parameters for accessing the plurality of targets from the surface. The method further includes determining a plurality of well site locations for an entirety of the hydrocarbon field using constraint optimization. The number of well site locations is minimized. The number of the plurality of targets accessible from the plurality of well site locations is maximized. 
         [0020]    In some embodiments, the method includes generating a cost function that optimizes for the number of well site locations and a number of accessible targets of the plurality of targets. The method also includes generating a plurality of target groups. 
         [0021]    A target group comprises a plurality of targets corresponding to a plurality of slots on a well site. Only one target group comprises each of the plurality of targets. 
         [0022]    Additionally, the method includes determining a plurality of well site locations. The plurality of well site locations are determined based on the cost function, and correspond to the plurality of target groups. 
         [0023]    Another exemplary embodiment of the present techniques provides a system for field planning. The system may include a plurality of processors, and a machine readable medium comprising code configured to direct at least one of the plurality of processors to generate a cost function that optimizes for the number of well site locations and a number of accessible targets of the plurality of targets. The code is also configured to direct at least one of the processors to generate the plurality of target groups. The code is further configured to direct at least one of the processors to determine a plurality of well site locations corresponding to the plurality of target groups based on the cost function. 
         [0024]    Another exemplary embodiment of the present techniques provides a method for producing hydrocarbons from an oil and/or gas field using a field planning method. The method for producing hydrocarbons may include obtaining a shared earth model comprising the hydrocarbon field. 
         [0025]    The hydrocarbon field comprises an area of ground surface and a reservoir disposed beneath the area of ground surface. The method also includes identifying a plurality of targets for the reservoir. 
         [0026]    Additionally, the method includes specifying one or more field planning parameters for accessing the plurality of targets from the surface. The method further includes determining a plurality of well site locations for an entirety of the hydrocarbon field using constraint optimization. The number of well site locations is minimized. The number of the plurality of targets accessible from the plurality of well site locations is maximized. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0027]    The advantages of the present techniques are better understood by referring to the following detailed description and the attached drawings, in which: 
           [0028]      FIG. 1A  is a schematic view of the reservoir, in accordance with an exemplary embodiment of the present techniques; 
           [0029]      FIG. 1B  is a view of an exemplary surface of a hydrocarbon field, in accordance with an exemplary embodiment of the present techniques; 
           [0030]      FIG. 2  is a process flow diagram of a method for field planning, in accordance with an exemplary embodiment of the present techniques; 
           [0031]      FIG. 3  is a block diagram of exemplary well site configurations, in accordance with an exemplary embodiment of the present techniques; 
           [0032]      FIG. 4  is a process flow diagram of an exemplary method for constraint optimization, in accordance with an exemplary embodiment of the present techniques; 
           [0033]      FIG. 5A  is a disjoint target groupset, in accordance with an exemplary embodiment of the present techniques; 
           [0034]      FIG. 5B  is a composite diagram of the exemplary surface overlaid on the target group assignment, in accordance with an exemplary embodiment of the present techniques; 
           [0035]      FIG. 6  is a block diagram of an exemplary cluster computing system that may be used in exemplary embodiments of the present techniques. 
       
    
    
     DETAILED DESCRIPTION 
       [0036]    In the following detailed description section, the specific embodiments of the present techniques are described in connection with preferred embodiments. However, to the extent that the following description is specific to a particular embodiment or a particular use of the present techniques, this is intended to be for exemplary purposes only and simply provides a description of the exemplary embodiments. Accordingly, the present techniques are not limited to the specific embodiments described below, but rather, such techniques include all alternatives, modifications, and equivalents falling within the true spirit and scope of the appended claims. 
         [0037]    At the outset, and for ease of reference, certain terms used in this application and their meanings as used in this context are set forth. To the extent a term used herein is not defined below, it should be given the broadest definition persons in the pertinent art have given that term as reflected in at least one printed publication or issued patent. Further, the present techniques are not limited by the usage of the terms shown below, as all equivalents, synonyms, new developments, and terms or techniques that serve the same or a similar purpose are considered to be within the scope of the present claims. 
         [0038]    “Computer-readable medium”, “tangible, computer-readable medium”, “tangible, non-transitory computer-readable medium” or the like as used herein refer to any tangible storage and/or transmission medium that participates in providing instructions to a processor for execution. Such a medium may include, but is not limited to, non-volatile media and volatile media. Non-volatile media includes, for example, NVRAM, or magnetic or optical disks. Volatile media includes dynamic memory, such as main memory. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, a hard disk, an array of hard disks, a magnetic tape, or any other magnetic medium, magneto-optical medium, a CD-ROM, a holographic medium, any other optical medium, a RAM, a PROM, and EPROM, a FLASH-EPROM, a solid state medium like a memory card, any other memory chip or cartridge, or any other tangible medium from which a computer can read data or instructions. When the computer-readable media is configured as a database, it is to be understood that the database may be any type of database, such as relational, hierarchical, object-oriented, and/or the like. 
         [0039]    The display device may include any device suitable for displaying the reference image, such as without limitation a CRT monitor, a LCD monitor, a plasma device, a flat panel device, or printer. The display device may include a device which has been calibrated through the use of any conventional software intended to be used in evaluating, correcting, and/or improving display results (for example, a color monitor that has been adjusted using monitor calibration software). 
         [0040]    Rather than (or in addition to) displaying the reference image on a display device, a method, consistent with the present techniques, may include providing a reference image to a subject. 
         [0041]    “Earth model” or “shared earth model” refer to a geometrical/volumetric model of a portion of the earth that may also contain material properties. The model is shared in the sense that it integrates the work of several specialists involved in the model&#39;s development (non-limiting examples may include such disciplines as geologists, geophysicists, petrophysicists, well log analysts, drilling engineers and reservoir engineers) who interact with the model through one or more application programs. 
         [0042]    “Exemplary” is used exclusively herein to mean “serving as an example, instance, or illustration.” Any embodiment described herein as “exemplary” is not to be construed as preferred or advantageous over other embodiments. 
         [0043]    “Reservoir” or “reservoir formations” are typically pay zones (for example, hydrocarbon producing zones) that include sandstone, limestone, chalk, coal and some types of shale. Pay zones can vary in thickness from less than one foot (0.3048 m) to hundreds of feet (hundreds of m). The permeability of the reservoir formation provides the potential for production. 
         [0044]    “Reservoir properties” and “reservoir property values” are defined as quantities representing physical attributes of rocks containing reservoir fluids. The term “reservoir properties” as used in this application includes both measurable and descriptive attributes. Examples of measurable reservoir property values include porosity, permeability, water saturation, and fracture density. Examples of descriptive reservoir property values include facies, lithology (for example, sandstone or carbonate), and environment-of-deposition (EOD). Reservoir properties may be populated into a reservoir framework to generate a reservoir model. 
         [0045]    “Well” or “wellbore” includes cased, cased and cemented, or open-hole wellbores, and may be any type of well, including, but not limited to, a producing well, an experimental well, an exploratory well, and the like. Wellbores may be vertical, horizontal, any angle between vertical and horizontal, deviated or non-deviated, and combinations thereof, for example a vertical well with a non-vertical component. 
         [0046]    Wellbores are typically drilled and then completed by positioning a casing string within the wellbore. Conventionally, the casing string is cemented to the well face by circulating cement into the annulus defined between the outer surface of the casing string and the wellbore face. The casing string, once embedded in cement within the well, is then perforated to allow fluid communication between the inside and outside of the tubulars across intervals of interest. 
         [0047]    Exemplary embodiments of the present techniques relate to methods and systems for field planning. The techniques may determine multiple well site locations for accessing a hydrocarbon reservoir, while maximizing the number of reservoir targets accessible from the well site locations. 
         [0048]      FIG. 1A  is a schematic view  100 A of a hydrocarbon field, in accordance with an exemplary embodiment of the present techniques. The schematic view  100 A includes a reservoir  102 , surface  110 , wells  104 , targets  120 , and well sites  130 . The reservoir  102 , such as an oil or natural gas reservoir, can be a subsurface formation that may be accessed by drilling wells  104  from the surface  110  to reach one or more targets  120 . The wells  104  may be deviated, such as being directionally drilled to follow the subsurface of the reservoir  102 . 
         [0049]    The reservoir targets  120  may be pre-defined locations or regions within a gas or oil reservoir that a planned well trajectory will penetrate. The determination of the locations and the size of the targets  120  or target areas are typically performed based on some understanding and analysis of certain reservoir properties. These reservoir properties may include composition, quality, and connectivity to other areas of the reservoir  102 . The number of targets  120 , the spacing between targets  120 , may be determined based on an analysis of potential development strategies which may be facilitated by an exemplary embodiment of the present techniques. The targets  120  are also referred to herein as targeted areas. 
         [0050]    As shown, each well site  130  may include a number of wells  104 . The wells  104  may be drilled from slots on the well site  130 . Each well site  130  may include numerous slots, with each slot corresponding to one well  104 . Each target area  120  may be penetrated by a well path starting from the slot location on the well site  130 . The number of slots on the well site  130  is typically limited by drilling constraints. 
         [0051]    Field planning includes selecting the locations of well sites  130 . Well site selection involves several input considerations. These considerations include, in part, the cost of well-site construction, environmental impacts, the number of wells  104  to adequately drain the reservoir  102 , as well as selection of reservoir targets  120  to correctly position the well sites  130 . 
         [0052]    One environmental consideration may be the avoidance of surface obstacles.  FIG. 1B  is a view of an exemplary surface  110  of the hydrocarbon field, in accordance with an exemplary embodiment of the present techniques. 
         [0053]    The surface  110  includes a number of exemplary obstacles, including a residential area  122 , a river  124 , a road  126 , and a pipeline  128 . It should be understood that these exemplary obstacles are not an exhaustive list. The surface  110  may also include other obstacles, both man-made and natural. The well sites  130  may be selected to maintain a predetermined distance from the surface obstacles. 
         [0054]    In field planning, there are numerous trade-offs between considerations for a single well site  130  (location, well design, well drilling costs, well trajectory design, etc.) and the economic considerations of producing and developing a hydrocarbon field over its full life cycle. One goal of field planning is to place the well site  130  as close as possible to the reservoir targets  120  in order to reduce the cost of drilling. Another goal is to minimize the number of reservoir targets  120  that are not accessible due to the surface and/or drilling constraints. 
         [0055]    In a typical scenario, field planning is done on an ad-hoc basis, where each well site  130  is selected, planned, and built as resources, e.g., surface space, become available. However, this approach typically leads to unexpected costs and missed opportunities. 
         [0056]    For example, a set of reservoir targets may be selected based on available surface locations for a well site. The well site  130  may be then chosen in an appropriate surface location so that the horizontal reach to each reservoir target  120  does not exceed a predefined distance. 
         [0057]    A set of well trajectories starting from the slots of the well site  130  can then be designed according to well path algorithms and other engineering constraints. In addition to maintaining safe distances from obstacles on the surface  110 , field planning also takes into account maintaining minimum distances between the paths of the wells  104  and geological features of the overburden. 
         [0058]    As the development of the hydrocarbon field progresses, the same process may be repeated for a new subset of reservoir targets  120  and a new well site  130 . However, proceeding in this way over the life cycle of the hydrocarbon field may lead to reservoir targets  120  becoming isolated. Such a scenario may result in increased construction costs. 
         [0059]    For example, the reservoir  102  may include twenty reservoir targets  120 . Each well site  130  may include five slots, which optimally, may be accessed by four well sites  130 . The first three well sites  130  may be located as described above, accessing fifteen of the reservoir targets  120 . However, the final five reservoir targets  120  may be isolated such that a single well site  130  cannot access all five targets  120 . In such a case, two or more additional well sites  130  may be constructed, but the cost may be prohibitively expensive. 
         [0060]    Further, surface location constraints may complicate field planning in this manner. For example, instead of the remaining targets  120  being isolated as described above, the remaining targets may be accessible from a single well site location. However, the surface area above the targets  120  may be in the residential area  122 , or too close to the river  124 . As a result, a suitable site location may not be easily found without compromising other engineering or drilling constraints. In such a scenario, the opportunity for exploiting the remaining targets  120  may be lost. 
         [0061]    Accordingly, typical approaches to field planning may result in higher costs and missed opportunities. However, in an exemplary embodiment of the present techniques, the well sites  130  for the entire field may be identified so as to maximize the number of accessible reservoir targets  120 . In such an embodiment, clustering and optimization processes may be used to plan well site locations for the entire hydrocarbon field. Advantageously, such a method may maximize the number of accessible reservoir targets  120 , attenuate overall costs of field development, and limit environmental impact. 
         [0062]    In one embodiment, an interactive environment may be used to rapidly evaluate current field development and well path planning on the basis of environmental, geological, and engineering constraints. In such an embodiment, many alternative scenarios for field development may be quickly evaluated. Further, the method may be repeated throughout the life cycle of the hydrocarbon field. 
         [0063]    Additionally, the method may allow a user to obtain optimal field configurations in which constraints can be set while minimizing total cost and maximizing reservoir productivity. The constraints may include the number of available targets, number of slots per well site  130 , and minimum avoidance distance to ground and geological features. 
         [0064]      FIG. 2  is a process flow diagram of a method  200  for field planning, in accordance with an exemplary embodiment of the present techniques. The method  200  may begin at block  202 , where a three dimensional (3D) shared earth model may be obtained. In some embodiments, the shared earth model may be generated. The shared earth model may include one or more hydrocarbon fields with potential reservoirs  102 , and geographic maps for ground surface of the fields. 
         [0065]    The maps may indicate man-made and natural objects such as residential areas  122 , rivers  124 , and roads  126 . The maps may also include near-ground objects such as pipelines  128 , or other hazard regions. Additionally, geological features (e.g. salt bodies and faults), existing well site platforms, and well paths may also be included. 
         [0066]    At block  204 , a set of reservoir targets  120  may be obtained. The reservoir targets  120  may include target areas in the reservoir  102 , which are reachable from a surface location with planned drillable well trajectories identified. 
         [0067]    At block  206 , field planning parameters may be specified. The field planning parameters may include well site configuration, maximum horizontal reach, well trajectory constraints, anti-collision constraints, and quality of penetration of the reservoir  102 . Other parameters, such as environmental constraints, minimal stand-off distance to surface or subsurface objects may also be specified. In one embodiment of the present techniques, a user, such as a geoscientist or drilling engineer, may define field planning parameters as part of an optimization process. 
         [0068]    Further examples of field planning parameters include Dogleg Severity, which indicates the degree of well path curvature. Dogleg Severity is typically used by drilling engineers to ensure a viable well trajectory can be achieved. Other parameters may be used for controlling a well trajectory, such as Hold and Curve to Target and Specify Angle to Target. The optimization process is described below with reference to block  208 . 
         [0069]    The well site configuration parameters may specify the number of slots, spacing between slots, orientation of the well site  130 , etc. The orientation of the well site is described with reference to  FIG. 3 , which is a block diagram of two exemplary well site configurations  302 ,  304 , in accordance with an exemplary embodiment of the present techniques. The well site configuration  302  includes a 9-slot well site  130 , accommodating a maximum of 9 well bores starting from the given slot locations. Each of the black dots represents one well slot  320 . The spacing of slots  320  on each row may be 20 feet apart. The spacing between rows may be 45 feet apart. 
         [0070]    For example, the well site configuration  304  includes 12 slots  320 , arranged in a three by four matrix, with equal spacing for rows and columns. The well site configuration  304  is also rotated 45 degrees from north. 
         [0071]    Referring back to  FIG. 2 , the maximum horizontal reach may specify a constraint on distance between the well site  130  and the reservoir targets  120 . The maximum horizontal reach may specify a range within which potential targets  120  may be selected for a particular well site  130 . The horizontal reach typically correlates to drilling costs. As such, limiting the horizontal reach from the well site  130  limits the drilling cost. 
         [0072]    Well trajectory constraints may specify basic trajectory parameters such as dog-leg severity, kick-off depth, hold distances and trajectory type. Anti-collision or inter-well constraints may also be imposed through well-to-well distance functions. 
         [0073]    Finally, constraints around quality of penetration of the reservoir as defined by properties of the targets  120  may also be imposed. Such quality constraints may include minimum net sand or net pay penetrated by the well path. The quality constraints may also include path segments within selected reservoir target regions. 
         [0074]    At block  208  well site locations for accessing the reservoir targets  120  may be determined. The well site locations may be determined in a manner that minimizes the drilling cost and maximizes production of the hydrocarbon field. A modeling process may be used to determine the well site locations such that all the reservoir targets  120  are fully utilized. The well site locations may be determined in a manner meets the specified parameters, and limits the total cost of field development. 
         [0075]    The modeling process may use an optimization process to accomplish the following objectives: a) divide the targets  120  into one or more disjoint groups so that all targets in the same group would be reached by the same well site  130 ; and b) for each group, locate the well site  130  such that the environmental impact is limited, and drilling can be performed within the given geological and engineering constraints. 
         [0076]    At block  210 , well drilling activities may be performed. The wells  104  may be drilled at one or more of the determined well site locations. Well site locations may be selected for conducting detailed well drilling activities according to each development stage of the field. For each well  104  at the selected locations, the potential production, bore stability, torque, drag, and the like, may be evaluated. Drilling completion and performance processes, such as described in patent application WO2009/032416 titled “Well performance Modeling in a collaboration well planning environment” by T. Benish, et al., may also be performed. 
         [0077]    If the condition of the ground and reservoir changes over the life cycle of the field, a new field plan may be generated. For example, the acquisition of new acreage, or identification of new targets  120  field may affect the original field planning. Once those changes may be identified, the method  200  may repeat again from block  206 , where new parameters may be specified for a new field planning. 
         [0078]    Referring back to block  208 , the constraint optimization is a process where the value of a given function f: R n →R is to be maximized or minimized over a given set D in R n . The function f is called the objective function, and the set, D, the constraint set. The objective is to maximize (or minimize) f(x) subject to x in D. The constraint optimization method typically is defined and formulated such that constraints are expressed as a number of weighted cost functions. The aim of constraint optimization is to find a solution where total cost is maximized (or minimized) such that imposed constraints are satisfied. 
         [0079]    In an exemplary embodiment of the present techniques, constraints may be imposed as cost functions. Constraints for the design and construction of well sites  130  and well trajectories can be assigned cost functions such that a minimum cost is assigned to preferred values. The preferred construction, implementation, or design cost may be determined independent from all other considerations and constraints. 
         [0080]    In contrast, a maximum or unacceptably high cost may be assigned to a design, for example, that violates a constraint. A well path exceeding a specified dog leg severity, or placing the well site  130  in an environmentally restricted area may have unacceptably high costs. When the cost functions are collectively analyzed, the objective function of the optimization is to find the set of well sites  130  and well trajectory that reduce the cost while still fulfilling the reservoir penetration requirements, i.e. hitting all targets or target areas in acceptable locations. 
         [0081]    The result from the optimization process may provide a field planning solution. The solution may include, but is not limited to: identifying a set of well sites  130  on the ground to enable well planning that reaches the selected targets  120 , and minimizes the total field development cost, while solving the problem of target-slot assignments and well path trajectory constraints. This solution can be used as a blueprint for current field planning and field development. During the long period of field development, drilling activity may be conducted according to the availability of resources. As the field development progresses, the ground surface or reservoir condition may change. The optimization process described in block  208  may be repeated to find a field planning solution based on the newly acquired ground surface information as well as reservoir conditions. One embodiment of this optimization process is described with reference to  FIG. 4 . 
         [0082]    One task of an exemplary method may be to divide the available targets  120  into distinct groups based on constraints such as number of slots per drill center, maximum reach per well, etc. To lower cost, the objective may be formulated to minimize the number of well sites  130  since each well site  130  can only accommodate a fixed number of targets  120 . 
         [0083]    Such a method may also cluster reservoir targets  120  into a set of disjoint target groups such that each target group would correspond to a well site on the ground surface  110 . Constraint optimization algorithms and/or clustering optimization algorithms may be applied to determine preferred locations of well sites for the targets  120  to be drilled. Additionally, the total field development cost may be lowered while solving the problem of target-slot assignments and well path trajectory constraints. 
         [0084]      FIG. 4  is a process flow diagram of an exemplary method  400  for constraint optimization, in accordance with an exemplary embodiment of the present techniques. The method  400  may begin at block  402 , where a cost function for the well site construction is created. 
         [0085]    The cost function may be represented as a data grid, denoted herein as DG, on the surface map. Each cell in the data grid may represent a potential well site location. Accordingly, each cell may be assigned the properties and conditional constraints for a particular location. 
         [0086]    A cell can be classified according to its cost as a criterion to determine a well site location. Some cells could have extremely high cost because the area may be restricted for use. The cost of construction at other cells may depend on the geographic locations, as well as the related cost of drilling activities. 
         [0087]    At block  404 , disjoint target group sets may be generated. A disjoint target group set may include a set of reservoir targets  120  organized into groups. The target group set is referred to as disjoint because each target  120  may be included in only one group. Different approaches may be used to generate the disjoint target group sets. 
         [0088]    In one embodiment, a clustering of disjoint target groups may depend upon the mathematical functions of the constraint optimization algorithms: a stochastic method, such as ‘genetic algorithm’, may randomly generate a new set of target groups based on previous iterations by the permutation of certain parameters. Other deterministic algorithms may define new target groups based on the calculated converging trend to the optimal solutions. 
         [0089]    Disjoint target group sets are described with reference to  FIG. 5A , which is a disjoint target group set  500 A, in accordance with an exemplary embodiment of the present techniques. The target group  540  may be a collection of reservoir targets  520  that are reachable by well trajectories from the same well site  130 . Each reservoir target  520  may be limited to one target group  540 . 
         [0090]    The reservoir targets  520  in each group may also satisfy other field planning constraints. For example, each target group may only include reservoir targets  520  that satisfy the maximum horizontal reach constraint. Additionally, if there are nine slots on each well site  130 , nine targets  520  may be assigned to each target group  540 . 
         [0091]      FIG. 5B  is a composite diagram  500 B of the exemplary surface  110  overlaid on the disjoint target group set  500 A, in accordance with an exemplary embodiment of the present techniques. Well site platforms  550  are shown in viable locations for the associated target groups  540 . 
         [0092]    In some cases, it may not be possible to fully utilize all slots on all the well sites  130 . In such cases, the number of targets  520  in each group  540  may be as close as possible to, but may not exceed the maximum number of slots available on the well sites  130 . As such, the total number of target groups may be minimized. 
         [0093]    As the optimization process continues, a disjoint target group set may change, along with the number of target groups in the set. In an exemplary embodiment of the present techniques, the target groups  540  may be generated using a clustering algorithm. If a well site location cannot be found for the target group  540 , an extra cost may be added, for example, as a penalty. Similarly, an extra cost may be added for each missing target-slot assignment if a selected well site location cannot reach all of the targets  520  in the same target group  540 . 
         [0094]    Additionally, the well site locations may be determined such that drillable well trajectories from the well site  130  to each target  520  can be achieved. For example, for each target  520  a viable well trajectory may be planned based on drilling physics from one of the slots of the well site  130 . All field planning parameters, described above, may be imposed. 
         [0095]    Additionally, in planning the well trajectories from potential well site locations, potential subsurface geo-hazards such as faults, salt formations, over pressured zones or unstable intervals may be avoided. As stated previously, the trajectories may also be planned to maintain safe distances from other planned or existing well paths. 
         [0096]    The well planning process is typically is performed in an iterative process wherein the field planning parameters are modified on successive iterations. For example, parameters that relate to drilling difficulty and cost may be modified. In some cases, even the well site location may be moved to accommodate a successful planning. In an exemplary embodiment of the disclosed techniques, this iterative process may be performed by visualizing the 3D shared earth model on a computer with visualization capabilities. 
         [0097]    At block  410 , it may be determined whether well site locations may be determined for all the target groups  540 . If not, blocks  406 - 410  may be repeated for another disjoint target group set. 
         [0098]    If so, at block  412 , a cost for the target group set may be determined, based on the constraint function described above. At block  414 , it may be determined whether the cost, for example, meets a specified threshold. 
         [0000]    If the specified threshold is not met, blocks  406 - 412  may be repeated for another disjoint target group set. If the threshold is met, the method  400  may stop. 
         [0099]    The method  400  may stop once a first successful disjoint target group set is found. In other embodiments of the present techniques, multiple successful sets may be considered. From these multiple sets, a solution may be selected based on a total cost or other criterion optimized to a preferred value. Additionally, there may be several well sites  130  and well trajectory configurations which satisfy all given constraints. As such, other criteria may be used for further evaluation. 
         [0100]    As stated previously, it may not be possible to locate a well site  130  such that all of the targets  520  in a target group  540  are penetrated by wells. In such a scenario, a threshold may be specified for the number of target groups  540  with unfilled slots. If a target group set exceeds this threshold, it may not be further considered. The method may iterate back to blocks  406  for another target group set. 
         [0101]    In an exemplary embodiment of the disclosed techniques, successive iterations may use results from prior iterations to determine new target group sets. For example, unassigned targets  520  from a previous iteration may be re-grouped to a neighboring target group  540 . Re-assigning targets  520  as such may result in a new well site location, that also honors the other field planning parameters. 
         [0102]    The method of selecting a new clustering of target groups  540  may depend upon the mathematical functions of the constraint optimization algorithms: a stochastic method, such as ‘genetic algorithm’, may randomly generate a new set of target groups  540  based on previous iterations by the permutation of certain parameters. Other deterministic algorithms may define new target groups  540  based on the calculated converging trend to the optimal solutions. 
         [0103]    The techniques discussed herein may be implemented on a computing device, such as that shown in  FIG. 6 .  FIG. 6  shows an exemplary computer system  600  on which software for performing processing operations of embodiments of the present techniques may be implemented. A central processing unit (CPU)  601  is coupled to a system bus  602 . The CPU  601  may be any general-purpose CPU. The present techniques are not restricted by the architecture of CPU  601  (or other components of exemplary system  600 ) as long as the CPU  601  (and other components of system  600 ) supports operations according to the techniques described herein. 
         [0104]    The CPU  601  may execute the various logical instructions according to the disclosed techniques. For example, the CPU  601  may execute machine-level instructions for performing processing according to the exemplary operational flow described above in conjunction with  FIGS. 2 and 4 . As a specific example, the CPU  601  may execute machine-level instructions for performing the methods of  FIGS. 2 and 4 . 
         [0105]    The computer system  600  may also include random access memory (RAM)  603 , which may be SRAM, DRAM, SDRAM, or the like. The computer system  600  may include read-only memory (ROM)  604  which may be PROM, EPROM, EEPROM, or the like. The RAM  603  and the ROM  604  hold user and system data and programs, as is well known in the art. The programs may include code stored on the RAM  604  that may be used for modeling geologic properties with homogenized mixed finite elements, in accordance with embodiments of the present techniques. 
         [0106]    The computer system  600  may also include an input/output (I/O) adapter  605 , a communications adapter  614 , a user interface adapter  608 , and a display adapter  609 . The I/O adapter  605 , user interface adapter  608 , and/or communications adapter  611  may, in certain embodiments, enable a user to interact with computer system  600  in order to input information. 
         [0107]    The I/O adapter  605  may connect the bus  602  to storage device(s)  606 , such as one or more of hard drive, compact disc (CD) drive, floppy disk drive, tape drive, flash drives, USB connected storage, etc. to computer system  600 . The storage devices may be used when RAM  603  is insufficient for the memory requirements associated with storing data for operations of embodiments of the present techniques. For example, the storage device  606  of computer system  600  may be used for storing such information as computational meshes, intermediate results and combined data sets, and/or other data used or generated in accordance with embodiments of the present techniques. 
         [0108]    The communications adapter  611  is adapted to couple the computer system  600  to a network  612 , which may enable information to be input to and/or output from the system  600  via the network  612 , for example, the Internet or other wide-area network, a local-area network, a public or private switched telephone network, a wireless network, or any combination of the foregoing. The user interface adapter  608  couples user input devices, such as a keyboard  613 , a pointing device  607 , and a microphone  614  and/or output devices, such as speaker(s)  615  to computer system  600 . The display adapter  609  is driven by the CPU  601  to control the display on the display device  610 , for example, to display information pertaining to a target area under analysis, such as displaying a generated representation of the computational mesh, the reservoir, or the target area, according to certain embodiments. 
         [0109]    The present techniques are not limited to the architecture of the computer system  600  shown in  FIG. 6 . For example, any suitable processor-based device may be utilized for implementing all or a portion of embodiments of the present techniques, including without limitation personal computers, laptop computers, computer workstations, and multi-processor servers. Moreover, embodiments may be implemented on application specific integrated circuits (ASICs) or very large scale integrated (VLSI) circuits. In fact, persons of ordinary skill in the art may utilize any number of suitable structures capable of executing logical operations according to the embodiments. In one embodiment of the present techniques, the computer system may be a networked multi-processor system. 
         [0110]    While the present techniques may be susceptible to various modifications and alternative forms, the exemplary embodiments discussed above have been shown only by way of example. However, it should again be understood that the present techniques are not intended to be limited to the particular embodiments disclosed herein. Indeed, the present techniques include all alternatives, modifications, and equivalents falling within the true spirit and scope of the appended claims.