Patent Publication Number: US-2018031721-A1

Title: Method and System for Generating a Subsurface Model

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Patent Application 62/368,605, filed Jul. 29, 2016, entitled METHOD AND SYSTEM FOR GENERATING A SUBSURFACE MODEL, the entirety of which is incorporated by reference herein. 
    
    
     FIELD OF THE INVENTION 
     This disclosure relates generally to the field of hydrocarbon operations, such as exploration and production and, more particularly, to subsurface modeling. Specifically, the disclosure relates to a method for constructing subsurface models for a subsurface region and using the subsurface model for reservoir simulations. The simulation results and/or the subsurface model are used for hydrocarbon operations, such as hydrocarbon exploration, hydrocarbon development and/or hydrocarbon production. 
     BACKGROUND 
     This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present disclosure. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art. 
     In exploration, development and/or production stages for resources, such as hydrocarbons, different types of subsurface models may be used to represent the subsurface structure, which may include a description of a subsurface structure and material properties for a subsurface region. For example, the subsurface model may be a watertight model, a geologic model or a reservoir model. The subsurface model may represent measured or interpreted data for the subsurface region, may be within a physical space or domain, and may include objects (e.g., horizons, faults, surfaces, volumes, and the like). The subsurface model may also be discretized with a mesh or a grid that includes nodes and forms blocks (e.g., cells, voxels or elements) within the model. By way of example, the watertight model may be created from a structural framework (e.g., organization of objects) and provide defined compartments or subvolumes. The geologic model may represent measured or interpreted data for the subsurface region, such as seismic data and/or well log data. The geologic model may be within a physical space or domain and may have material properties, such as rock properties. The reservoir model may be used to simulate flow of fluids within the subsurface region. Accordingly, the reservoir model may use the same grid and/or blocks as other models, or may resample or upscale the grid and/or blocks to lessen the computations for simulating the fluid flow. 
     The development of the reservoir model or geologic model may be problematic. For example, the process may include forming a grid from objects, such as horizons and faults. The resulting grid may not form closed compartments or subvolumes, which may be problematic for populating material properties into the objects and/or blocks. In particular, the objects may partially contact each other, thus, forming open areas or voids that are not closed compartments. Objects may also overlap. As a result, the material properties may have to be assigned manually (e.g., by a designer, modeler or user) to only one object or block at a time. In addition to being inefficient, the process may introduce errors and uncertainty through a manual process that is based on subjective decisions. 
     As an example, a meshed or gridded representation may include a large number of triangles to represent the subsurface region. In such a meshed representation, spurious assignments, holes and intersections may be a prevalent problem. If the meshes are created for the faults and horizons separately and then merged, the resulting mesh may include overlaps and gaps. Even one spurious intersection may be sufficient to render the mesh invalid for gridding, property assignment and simulation. Further, in repairing the mesh, conventional mesh repair approaches are based on different assumptions and designed for different topologies. 
     Conventional mesh repair approaches do not involve repairing certain types of object intersections, such as T-junctions, which involve multiple mesh elements intersecting along common edges. Indeed, conventional mesh repair algorithms are designed to eliminate T-junctions. Further still, conventional approaches require manual intervention to preserve T-junctions, while removing mesh overlaps and gaps. 
     Accordingly, there remains a need in the industry for methods and systems that are more efficient and may lessen problems associated with forming a subsurface model (e.g., a watertight model, a geologic model or a reservoir model) for use in hydrocarbon operations. Further, a need remains for efficient approaches to detect and repair mesh problems. The present techniques provide a method and apparatus that overcome one or more of the deficiencies discussed above. 
     SUMMARY 
     In one embodiment, a method for updating a subsurface model having one or more object for a subsurface region is described. The method may include: obtaining a subsurface model associated with the subsurface region and having a mesh formed from a plurality of nodes and forming a plurality of blocks (e.g., triangles or other mesh elements which have mesh shapes); identifying one or more areas of the mesh that need repair; applying to the identified areas of the mesh one or more of a local re-meshing operation, an edge-flipping operation, a collapsing operation and any combination thereof; outputting the updated subsurface model. 
     In one or more embodiments, a system for generating a subsurface model having one or more objects associated with a subsurface region is described. The system may include a processor; an input device in communication with the processor and configured to receive input data associated with a subsurface region; and memory in communication with the processor, the memory having a set of instructions. The set of instructions, when executed, are configured to: obtain a subsurface model associated with the subsurface region and having a mesh formed from a plurality of nodes and forming a plurality of blocks; identify one or more areas of the mesh that need repair; apply to the identified areas of the mesh one or more of a local re-meshing operation, an edge-flipping operation, a collapsing operation and any combination thereof; and output the updated subsurface model. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The advantages of the present invention are better understood by referring to the following detailed description and the attached drawings. 
         FIG. 1  is an exemplary flow chart in accordance with an embodiment of the present techniques. 
         FIG. 2  is an exemplary flow chart for repairing a mesh in accordance with an embodiment of the present techniques. 
         FIG. 3  is another exemplary flow chart for repairing a mesh in accordance with an embodiment of the present techniques. 
         FIG. 4  is yet another exemplary flow chart for repairing a mesh in accordance with an embodiment of the present techniques. 
         FIG. 5  is still another exemplary flow chart for repairing a mesh in accordance with an embodiment of the present techniques. 
         FIG. 6  is a block diagram of a computer system that may be used to perform any of the methods disclosed herein. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description section, the specific embodiments of the present disclosure 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 disclosure, this is intended to be for exemplary purposes only and simply provides a description of the exemplary embodiments. Accordingly, the disclosure is not limited to the specific embodiments described below, but rather, it includes all alternatives, modifications, and equivalents falling within the true spirit and scope of the appended claims. 
     Various terms as used herein are defined below. To the extent a term used in a claim 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. 
     The articles “the”, “a” and “an” are not necessarily limited to mean only one, but rather are inclusive and open ended so as to include, optionally, multiple such elements. 
     As used herein, the term “hydrocarbons” are generally defined as molecules formed primarily of carbon and hydrogen atoms such as oil and natural gas. Hydrocarbons may also include other elements or compounds, such as, but not limited to, halogens, metallic elements, nitrogen, oxygen, sulfur, hydrogen sulfide (H 2 S) and carbon dioxide (CO 2 ). Hydrocarbons may be produced from hydrocarbon reservoirs through wells penetrating a hydrocarbon containing formation. Hydrocarbons derived from a hydrocarbon reservoir may include, but are not limited to, petroleum, kerogen, bitumen, pyrobitumen, asphaltenes, tars, oils, natural gas, or combinations thereof. Hydrocarbons may be located within or adjacent to mineral matrices within the earth, termed reservoirs. Matrices may include, but are not limited to, sedimentary rock, sands, silicilytes, carbonates, diatomites, and other porous media. 
     As used herein, “hydrocarbon exploration” refers to any activity associated with determining the location of hydrocarbons in subsurface regions. Hydrocarbon exploration normally refers to any activity conducted to obtain measurements through acquisition of measured data associated with the subsurface formation and the associated modeling of the data to identify potential locations of hydrocarbon accumulations. Accordingly, hydrocarbon exploration includes acquiring measurement data, modeling of the measurement data to form subsurface models and determining the likely locations for hydrocarbon reservoirs within the subsurface. The measurement data may include seismic data, gravity data, magnetic data, electromagnetic data and the like. 
     As used herein, “hydrocarbon development” refers to any activity associated with planning of extraction and/or access to hydrocarbons in subsurface regions. Hydrocarbon development normally refers to any activity conducted to plan for access to and/or for production of hydrocarbons from the subsurface formation and the associated modeling of the data to identify preferred development approaches and methods. By way of example, hydrocarbon development may include modeling of the subsurface formation and extraction planning for periods of production; determining and planning equipment to be utilized and techniques to be utilized in extracting the hydrocarbons from the subsurface formation and the like. 
     As used herein, “hydrocarbon operation(s)” refers to any activity associated with hydrocarbon exploration, hydrocarbon development and/or hydrocarbon production. 
     As used herein, “hydrocarbon production” refers to any activity associated with extracting hydrocarbons from subsurface location, such as a well or other opening. Hydrocarbon production normally refers to any activity conducted to form the wellbore along with any activity in or on the well after the well is completed. Accordingly, hydrocarbon production or extraction includes not only primary hydrocarbon extraction, but also secondary and tertiary production techniques, such as injection of gas or liquid for increasing drive pressure, mobilizing the hydrocarbon or treating by, for example chemicals or hydraulic fracturing the wellbore to promote increased flow, well servicing, well logging, and other well and wellbore treatments. 
     As used herein, the term “framework” or “structural framework” means an organized assembly of objects (e.g., faults and/or horizons) within a specific volume known as an area or interest or volume of interest. The organization may include horizon order, truncation relationships and/or faulting order. The organized assembly of objects may include gaps between surfaces and/or voids within the specific volume. 
     As used herein, “watertight” means that a containing specific volume can be divided into one or more volume compartments with no overlapping volume compartments and with boundaries that have no holes. A watertight framework of faults and horizons divides a containing specified volume of interest into one or more volume compartments that have boundaries completely enclosing the compartments. Each fault and horizon is either a boundary of or contained within a volume compartment without any piece outside of a compartment. For example, in a watertight triangular mesh framework, every triangle face on the boundary of a compartment shares each of its edges with one other triangle to completely enclose the compartment. No two triangles may overlap partially. In some embodiment, no two triangles may overlap in their entirety. In another embodiment, this restriction is loosened only where two surfaces are merged. Contained within a volume compartment, there may be a partial fault that is not a boundary and does not completely subdivide the compartment, and a triangle face on the edge of the partial fault may not share an edge with another triangle. 
     As used herein, “triangle” refers to a polygon. Triangle may include quadrilateral or other polygons. 
     As used herein, “surface” refers to geologic features such as horizon and fault as well as technical features, such as model boundary, concession boundary, or artificial compartment boundary. A horizon separates two packages of rock. A fault is a discontinuity of rock packages. Often, a fault exhibits displacement. An artificial compartment boundary may be used for accounting purposes. 
     In hydrocarbon operations, a subsurface model is created in the physical space or domain to represent the subsurface region. The subsurface model is a computerized representation of a subsurface region based on geophysical and geological observations made on and below the surface of the Earth. The subsurface model may be a numerical equivalent of a three-dimensional geological map complemented by a description of physical quantities in the domain of interest. The subsurface model may include multiple dimensions and is delineated by objects, such as horizons and faults. The subsurface model may include a structural framework of objects, such as faults and horizons, and may include a mesh or grid of nodes to divide the structural framework and/or subsurface model into blocks, which may include cells in two-dimensions, voxels in three-dimensions or other suitable elements in other dimensions. A block, such as cell or voxel, is a subvolume of the space, which may be constructed from nodes within the mesh. In the subsurface model, material properties, such as rock properties (e.g., permeability and/or porosity), may be represented as continuous volumes or unfaulted volumes in the design space, while the physical space may be represented as discontinuous volumes or faulted volumes (e.g., contain volume discontinuities, such as post-depositional faults). 
     Within the subsurface models, a grid or mesh may be used to partition the model into different subvolumes, which may be used in hydrocarbon operations, such as reservoir simulation studies in reservoir exploration, development and/or production stages, as well as for representing a subsurface model description of a reservoir structure and material properties. Accordingly, the grid or mesh may be configured to form blocks that may represent material properties, such as rock and fluid properties, of a reservoir or may be used for numerical discretization of partial differential equations, such as fluid flow or wave propagation. 
     The representation and updating of subsurface models involves complex computational challenges. Subsurface models may include objects, such as surfaces (e.g., faults or horizons) that intersect each other in arbitrary ways, which are often represented by pillar-based or triangle mesh-based data structures. Both representations, however, fail to offer a fast, intuitive approaches for the updating of the model geometry. The updating of the model geometry is usually necessary given the uncertainty on the model construction, and so there is still a need for a model representation that offer both an efficient data storage and support for updating operations. 
     As a result, the present techniques involve a parametric-based representation for subsurface models. The model surfaces are decomposed into smaller, manageable surface patches that are then converted into parametric patches. The parametric patches have no intersections other than their boundaries, so the conversion of a patch to a mesh (e.g., a triangle mesh) is manageable. In a preferred embodiment, the boundaries are in parametric formats governed by control points. In some embodiments, the shape of the patch is controlled by a small set of control points, which may facilitate change to the model topology without the burden of working directly on the geometry based representation. By working directly on control points, the updating of the model topology and geometry may be performed with high-level operations, without involving specific knowledge of the underlying data structure. Thus, the present techniques may be used to enhance subsurface models, which may be used for hydrocarbon operations and, more particularly, to subsurface modeling. 
     The present techniques describe a method and system for enhancing the generation of a subsurface model (e.g., watertight model, geologic model and/or reservoir model). Geologic models are often used to determine properties and structures of the subsurface region, while reservoir models are often used to determine hydrocarbon reserves in place and serve as inputs to reservoir simulation programs that predict the behavior of rocks and fluids contained therein under various scenarios of hydrocarbon recovery. Construction of a geologic model or a reservoir model is a multistep process. For a subsurface model, a structural framework is created from subsurface measurements. The structural framework may include various objects, such as faults, horizons, and if necessary, one or more surfaces that bound the area of interest. The different objects are meshed to define closed volumes (e.g., zones, compartments, or subvolumes). Then, the closed volumes are partitioned into small blocks defined by the grid. Finally, properties are assigned to objects (e.g., surface transmissibility) and individual blocks (e.g., rock type and/or porosity) in the watertight model to form the subsurface model. If the initial model is a geologic model, it may be upscaled to form a reservoir model. 
     To enhance the subsurface model building process, the present techniques provide enhancements to the creation and generation of subsurface models. A first enhancement is a process for forming a watertight model, which involves performing extrapolation, intersection and/or cleanup of objects in the structural framework. As the structural framework may include one or more horizons and/or one or more faults, gaps or voids as well as overlaps may be present between objects. Thus, the inputted objects may not have a quality acceptable enough to be discretized and uniquely intersected. For example, in some regions of the structural framework, objects may be interpreted or extended too far and may penetrate each other. In other regions, objects may fail to intersect each other and need to be extrapolated to contact other objects. The present techniques utilize a structural framework or discrete volumetric representation of the objects based on polygon complexes (e.g., cubic complexes). The discrete volumetric representation includes a volumetric grid of the subsurface region. From the volumetric grid, the present techniques removes or carves away blocks until the topology is not preserved. Accordingly, a priority field (e.g., an unsigned distance field) is computed or determined, which may be constrained by surfaces (e.g., fault and/or horizon), and may be used to control the carving order. The carving may also utilize an isosurface approach that assigns a signed-distance field to the objects (e.g., a surface of the object). The distance field may focus the carving to the objects and their respective extensions. Moreover, the volumetric representation may also be utilized to address pinchouts between faults, horizons or combinations thereof, which often cause problems because there may be multiple, isolated or folded intersections instead of a simple intersection. Accordingly, the volumetric representation may use the morphological image processing operators of erosion and dilation to simplify the intersections. Erosion removes the outermost blocks from an object. Dilation adds additional blocks next to existing ones. Closing is the performance of dilation, followed by the performance of erosion. Opening is the performance of erosion, followed by dilation. Morphological operators provide a mechanism to close gaps as well as to remove outliers or noise. For example, if the volumetric representation is based on cubic complexes, erosion is applied to create a hole in a horizon close to a noisy intersection with a fault, and dilation is applied to fill the hole smoothly and create a simpler intersection. 
     As a second enhancement, the present techniques provide mesh quality assessment and repair for a processed structural framework, which may be at least partially watertight. Mesh quality assessment and repair may also be used to improve the quality of the watertight framework. As part of the mesh quality assessment and repair, hierarchical smoothing is utilized to address problems with mesh repair. Hierarchical smoothing involves (i) setting the order in which the surfaces are to be processed (e.g., based on truncation relationships defined by the watertight model); (ii) extracting the intersection among objects (e.g., intersection lines or contacts) as well as characteristic points of partial objects; and (iii) iteratively smoothing the objects. The smoothing of one object may set constraints for the smoothing of other objects when they share vertices along their intersections or contacts. 
     The mesh repair method provides interactive editing functionality for the watertight model. For example, the objects, such as surfaces, may be decomposed and converted into parametric patches that have no intersections other than their boundaries. This decomposition and conversion may facilitate the conversion of objects to polygon meshes (e.g., triangle or quadrangle meshes). The patch shape may be controlled by a small set of control points used to manipulate the watertight model. The watertight model may update or modify the topology and geometry with high-level operations on the control points without involving the knowledge of the underlying data structure. 
     In one or more embodiments, the present techniques may involve various steps to form the structural framework, the watertight model and resulting subsurface model. For example, the method may include computing of boundary surfaces to limit the model to the extent of the volume of interest. The computation of boundaries may include extracting boundaries and may be the output from the creation of the watertight model, which may be a set of objects (e.g., triangle or quadrangle meshes) and a set of volumes (e.g., compartments or groups of blocks). Further, the method may include computing volumes enclosed by objects. This computation may include recording the indices of the volumes or compartments in contact to each polygon mesh. Volume indices may be computed directly from a digital image or other suitable source. Then, the process may remove isolated faces or triangles. The isolated faces may be faces that are not adjacent to at least one volume. For example, polygons (e.g., triangles on the boundaries of faults, which may be above (below) the top (bottom) horizon, do not cope with such constraint, thus they may be detected and removed. 
     In addition, the method may include various steps to split or divide an object. For example, the method may include splitting surfaces based on adjacent volumes. In this method, an object may be split into smaller and manageable objects. The splitting process relies on volume indices to partition object in smaller objects, where each smaller object contains triangles adjacent to the same volume. Further, the method may include splitting surfaces based on faults. In this step, the faults may be re-meshed before being incorporated into the watertight model. Re-meshing faults may be performed when certain requirements as to fault&#39;s shape are satisfied, such as faults should not be shared by a non-convex surfaces. Accordingly, partial faults, horizons and boundary surfaces may be partitioned according to the fault network. A virtual extrusion of the fault is computed on the target surface, which splits the surface in two components. Also, the method may include splitting surface to remove holes or voids. Holes or voids may result from pinch-outs computations and/or from certain fault-fault intersections. As the voids may be problematic for re-meshing operations, the voids should be removed. As a result, objects or surfaces may be split in the voids, and each of the split objects may be re-meshing separately. 
     Moreover, the method may include some additional steps to re-orient objects, remove small objects, reassign small objects, and perform validation of the mesh. For example, the method may include re-orientating objects. For example, the polygon meshes may be oriented towards a specific direction or the outside of the model. As volumetric information is utilized to properly perform surface orientation, this operation may be performed during the conversion step, when the volumetric information is still available. The method may also include generating control points and reassigning or removing small objects from the model. The operation may be performed through a loop, which iteratively performs: (i) computing control points; (ii) computing contacts from the current control points; and (iii) removing invalid contacts. Further, the method may include validating the output mesh. 
     In one or more embodiments, the present techniques may involve various steps to repair the mesh. For example, once the watertight model is formed, the resulting meshes within the watertight model may still have certain geometric and topological deficiencies. These deficiencies may be a result of the parametric shape curves as well as distortions introduced during a parameterization process used in a re-meshing process to form the watertight framework. To remove these deficiencies, a method may be used that iteratively identifies inconsistencies and bad quality elements (e.g., nodes, edges and triangles) to produce a reliable output mesh. The repairing process performs on a local basis (e.g., on specific contacts of faults, horizons, or combination thereof) and on a global basis (e.g., on the watertight model) until no inconsistencies and/or bad quality elements are identified or until any repair may be applied without introducing additional damages to the mesh. In some embodiment, a tradeoff between different mesh quality measures is specified. 
     Further, various operations may be utilized to provide the enhancements to the watertight model in the mesh repair process. These operations may include edge splitting (e.g., by median length), removing one-manifold intersections, removing non-manifold vertexes, flipping cap triangles, flipping triangles with high dihedral angles, splitting cap triangles, removing small edges and splitting edges with boundary vertexes, or triangle merges. In some embodiments, these operations are performed on meshes based on quadrangles or sets of polygons may be used instead of triangles. Smoothing may be employed to the vertices of the mesh to enhance the mesh quality, which may be on a local basis (e.g., only over vertexes of intersecting polygons, such as triangles) and/or on a global (e.g., over all vertexes). The smoothing operation may also be utilized in the removal of polygon overlaps that are still be present in the watertight model after the one or more of the mesh repair operations are performed. 
     One of the mesh repair operations is edge splitting. The edge splitting operation may be utilized to obtain a mesh with an even distribution of polygon sizes. Accordingly, edges whose length is greater than a constant factor times the median edge length of whole mesh may be split, which is a global operation that may be performed on each of the edges within the watertight model. If the mesh configuration is triangular, each edge split operation gives rise to four triangles by connecting the created vertex to the two vertices of the triangles adjacent to the split edge that are not ends of the split edge. The edge splitting operation may be performed once the structural framework is formed into the watertight model and/or may be performed prior to other mesh repair operations. 
     Another of the mesh repair operation includes the removing one-manifold intersections operation. For the operation, boundary intersection between horizons and/or faults may result in 1-manifold structures, which are edges at the boundary of a fault that create a discontinuity in the horizon. At the lateral edge of a fault, throw tends to vanish. In some cases, the framework may exhibit artifacts such as finite throw or displacement at the edges of faults. A 1-manifold structure may need to be removed to avoid the creation of a throw in the boundary of a fault. The 1-manifold structures may be removed by collapsing the edges of the 1-manifold structure onto the corresponding fault and horizon. 
     Yet another of the mesh repair operations involves removing non-manifold vertexes. This operation may be used to simplify the mesh, which may involve removing unnecessary polygons. For example, the triangulation process can generate triangle patterns that are not relevant for the watertight model. Examples of such undesired patterns are triangles formed from three triangles. To remove the unnecessary triangles and simplify the mesh, the interior vertex and the adjacent triangles may be removed and replaced by one triangle. 
     The flipping cap triangle operation is another mesh repair operation. This operation may be used to manage cap triangles. For example, the triangularization process may generate cap triangles, which may generate invalid configurations between contacts and may not be properly handled by the tetrahedralization process. Accordingly, the flipping cap triangle operation may identify cap triangles and removed by flipping the edge opposite to the cap angle, resulting in a locally performed operation. A cap triangle may occur at a concavity of the contact. Four vertices may involve the formation of two different sets of triangles. Any adjustment may lead to the creation of a cap triangle that intersects other triangles. Flipping these triangles may remove the spurious intersection. 
     Also, the mesh repair operations may include flipping triangles with high dihedral angles operation. In this operation, small angled triangles may be modified to repair the mesh. For example, with certain triangulation, triangles may share an edge whose dihedral angle between them is below a threshold. These small angles may be a result of the re-meshing phase. When the small angled triangles are created, the quality of the final mesh is sub-optimal and may result in intersections of triangles in the same mesh and/or problems in the tetrahedralization phase. The flipping triangles with high dihedral angles operation involves flipping of the shared edge between the triangles being analyzed and generating two new triangles, which has a dihedral angle between them that is smaller than the previous version. The threshold may be a constraint set by a user or predefined as a set of instructions. 
     In addition, splitting cap triangle operation is yet another mesh repair operation. As noted above, cap triangles have a negative impact on the quality of the mesh and should be managed or removed. However, when the edge appositive from the cap angle is incident to another surface (e.g., fault, horizon or boundary surface), the flipping procedure should not be performed because other the resulting pair may intersect other triangles. In some embodiment, the cap triangle is split into two new triangles rather than flipped with one of its neighbors. This is performed by dividing the edge appositive to the cap angle into two new edges. The new vertex is connected to the cap angle vertex, resulting in two new triangles being created. 
     Yet another mesh repair operation involves the remove small edge operation. The small edge triangles may be generated from a re-meshing process. The length of an edge may be predefined within a set of instructions, as s user-defined constraint or other suitable parameter. As small edges in triangles may be removed without substantially degrading the geometric shape of the underlying surface, the triangles in the mesh may be reformed to remove the small edge of the triangle, which may facilitate the tetrahedralization process. The operation may have a predefined length of an edge, which may be predefined within a set of instructions, and/or may be a user-defined constraint. The operation may involve collapsing the two end vertices. The collapse is performed to avoid triangle folding, thus ensuring no inconsistency is introduced to the mesh. 
     Another mesh repair operation is the splitting edges with boundary vertices operation. Similar to the splitting cap triangle operation, this operations may divide edges that are not on the boundary of the corresponding surface, but containing a vertex on a boundary. For example, one vertex should be on the boundary, but a second vertex from the same triangle is also placed on this boundary. Splitting the edge allows moving the second vertex off the boundary. 
     In one or more embodiments, a method for updating a subsurface model having one or more object for a subsurface region is described. The method may include: obtaining a subsurface model associated with the subsurface region and having a mesh formed from a plurality of nodes and forming a plurality of blocks (e.g., triangles or other mesh elements which have mesh shapes); identifying one or more areas of the mesh that need repair; applying to the identified areas of the mesh one or more of a local re-meshing operation, an edge-flipping operation, a collapsing operation and any combination thereof; outputting the updated subsurface model. 
     Further, the method may include other enhancements. For example, the method may include obtaining subsurface measurements associated with the subsurface region, generating a structural framework form the subsurface measurements, wherein the structural framework comprises a plurality of objects, wherein the plurality of objects include one or more of horizons, faults and any combination thereof and generating the subsurface model from structural framework; creating a geologic model from the subsurface model by assigning properties to one or more of the plurality of blocks; creating a reservoir model from the subsurface model by assigning properties associated with fluid flow to one or more of the plurality of blocks; simulating fluid flow within the reservoir model to create simulation results; outputting the updated subsurface model comprises providing a visualization of the subsurface model via a display and/or managing hydrocarbon production based on the simulation results. In addition, to apply the local re-meshing operation, the method may include: performing local re-meshing on the one or more identified area; performing a global vertex smoothing on the one or more identified area; and performing a local vertex smoothing on the one or more identified area; and/or wherein applying the local re-meshing comprises performing one or more of deleting interior nodes, relocating interior nodes, creating interior nodes, flipping interior blocks, splitting interior blocks, merging interior blocks, and any combination thereof. Also, to apply the edge flipping operation, the method may include: performing a first identification of self-intersections and low quality mesh shapes, splitting the low quality mesh shapes from the first identification, performing a second identification of self-intersections and low quality mesh shapes, and flipping the low quality mesh shapes from the first identification; and/or wherein performing a first identification of self-intersections and low quality mesh shapes comprises comparing angles formed within the mesh against a specified threshold to identify small dihedral angles below the threshold. Moreover, to apply the collapsing operation, the method may include: identifying small edges in the mesh shapes, collapsing the identified small edges, identifying high dihedral angles in mesh shapes, and flipping the identified high dihedral angles in the mesh shapes. 
     Beneficially, the present techniques provide various enhancements to the hydrocarbon extraction process. A framework may be generated with less effort, with less intervention and in a shorter time allowing the generation of a more realistic subsurface model, simulation and analysis of more complex models, and better quantification of risks and uncertainties. The present techniques may be further understood with reference to  FIGS. 1 to 6 , which are described further below. 
       FIG. 1  is an exemplary flow chart  100  in accordance with an embodiment of the present techniques. The flow chart  100  includes a method for creating a subsurface model from subsurface measurements. The method may include obtaining data and creating a watertight model from a structural framework for the subsurface region, as shown in blocks  102  to  106 , modifying the watertight model to form one or more subsurface models, as shown in blocks  108  to  110 , and using the subsurface model to perform simulations and for hydrocarbon operations, as shown in blocks  112  and  114 . 
     The method begins by obtaining data and creating a watertight model, as shown in blocks  102  to  106 . As shown in block  102 , subsurface measurements are obtained. The obtaining of subsurface measurements may include accessing measurements from a database associated with the subsurface region and/or performing one or more acquisition surveys to obtain subsurface measurements for the subsurface region. The performing one or more acquisition surveys may include acquiring and/or processing seismic data, core samples, wireline data, gravitational data, magnetic data and/or electromagnetic data. Then, as shown in block  104 , a structural framework associated with the subsurface measurements may be obtained. The obtaining of structural framework, which may be referred to as a volumetric representation, may include accessing a structural framework from a database, updating or modifying a structural framework with the subsurface measurements and/or creating a structural framework based on the subsurface measurement. The structural framework may include mesh elements, which may each include a block, such as a cell or a voxel, formed by the mesh and associated nodes. The mesh is a discretization of the objects and includes various nodes that may form mesh elements. For example, the mesh elements in a 3D grid may be a tetrahedron or hexahedron or a triangle or quadrilateral, and the geometrical classification may be the shape or type of the mesh element. A variety of known techniques exist for mesh generation in a volumetric domain (e.g., Delaunay tetrahedralization, or advancing front methods), which may be used in the present techniques. Accordingly, the present techniques may include finite-element grids, and/or even hybrid grids of several element types, such as prisms and tetrahedrals. 
     At block  106 , a watertight model is created from the structural framework. The creation of the watertight model may include performing extrapolation, intersection and/or cleanup of objects in the structural framework. As noted above, the structural framework may include one or more horizons and/or one or more faults, which may have gaps or voids between objects. The creation of the watertight model may involve filling the gaps within the structural framework and then performing mesh repairs on the filled structural framework to create the watertight model. The filling the gaps within the structural framework may include generating a discrete volumetric representation of the objects within the structural framework based on polygon complexes (e.g., cubic complexes), which include a volumetric grid of the subsurface region. A discrete volumetric representation partitions the model into mutually exclusive blocks that span the entire volume of interest without gaps. Each surface can be mapped to a set of blocks. Furthermore, each surface can be mapped to a set of block faces. For hexahedral blocks, this constriction to block faces leads to cubic complexes, but the process applies to any kind of block. Then, blocks within the discrete volumetric representation may be removed based on constraints, such as maintaining the topology, and an object priority function (e.g., a priority field and/or an unsigned distance field). The filling of the structural framework may include using one or more morphological operators, such as erosion, dilation, opening and closing to address pitchouts within the volumetric representation. Erosion is the process of removing the outermost elements of an object. Dilation is the process of adding an additional element to the outermost elements of an object. Opening and closing are combinations of erosion and dilation. The performing the mesh repairs may include performing mesh quality assessment and repair for the filled structural framework, which may be a watertight model. The mesh quality assessment and repair may include hierarchical smoothing, which involves (i) setting the order in which the surfaces are to be processed (e.g., based on truncation relationships defined by the watertight model); (ii) extracting the intersection among objects (e.g., intersection lines or contacts) as well as characteristic points of partial objects; and (iii) iteratively smoothing the objects. The mesh repair may provide interactive editing functionality for the watertight model, such as decomposing object and converting the objects into parametric patches that have no intersections other than their boundaries. The mesh repair may include performing operations, such as edge splitting (e.g., by median length), removing one-manifold intersections, removing non-manifold vertexes, flipping cap triangles, flipping triangles with high dihedral angles, splitting cap triangles, removing small edges and splitting edges with boundary vertexes. 
     Once the watertight model is created, the watertight model may be modified to create one or more subsurface models, as shown in blocks  108  to  110 . At block  108 , a geologic model may optionally be created from the watertight model. The creation of the geologic model may include populating the blocks and/or objects within the watertight model with properties. The geologic model, which represents a specific portion of the subsurface region, may include one or more objects (e.g., horizons, faults, volumes, and the like) and may have material properties associated with the various objects. The material properties may include one or more of surface transmissibility, permeability, rock type, facies, porosity, fluid saturation, pressure and any combination thereof. At block  110 , the reservoir model may optionally be created based on the watertight model. The creation of the reservoir model may include creating the reservoir model directly from the watertight model or creating the reservoir model based on the geologic model, which is created from the watertight model. The creation of the reservoir model may include upscaling the underlying base model (e.g., the geologic model or watertight model) to provide a different scale for the reservoir model as compared with the underlying base model. Then, the creation of the reservoir model may include populating the blocks and/or objects within the model (e.g., the geologic model, watertight model, or upscaled model) with properties. The reservoir model, which represents a specific portion of the subsurface region, may include one or more objects (e.g., horizons, faults, volumes, and the like) and may have material properties associated with the various objects. 
     Once created, the subsurface model may be utilized to perform simulations and the model and associated results may be used for hydrocarbon operations, as shown in blocks  112  and  114 . At block  112 , a simulation is performed with the reservoir model and/or the geologic model to provide simulation results. The performing the simulation may include modeling fluid flow based on the reservoir model and the associated properties stored within the blocks of the reservoir model. The simulation results may include the computation of time-varying fluid pressure and fluid compositions (oil, water, and gas saturation) and the prediction of fluid volumes produced or injected at wells. The performing the simulation may include modeling structural changes based on the geologic model and the associated properties stored within the blocks of the geologic model. For example, reducing reservoir pressure may reduce porosity which may lead to a sagging overburden. The simulation results and/or the reservoir model may be outputted. The outputting of the simulation results and/or the subsurface model may include displaying the simulation results, the geologic model and/or the reservoir model on a monitor and/or storing the simulation results, the geologic model and/or the reservoir model in memory of a computer system. At block  114 , the simulation results may be utilized to manage the hydrocarbons. The hydrocarbon operations may include hydrocarbon exploration operations, hydrocarbon development operations and/or hydrocarbon production operations. For example, the simulation results, the geologic model and/or the reservoir model may be used to estimate or adjust reserves forecasts, reserves estimations and/or well performance prediction. As another example, the simulation results, the geologic model and/or the reservoir model may be used to adjust hydrocarbon production operations, such as installing or modifying a well or completion, modifying or adjusting drilling operations, decreasing fracture penetration, and/or to installing or modifying a production facility. The production facility may include one or more units to process and manage the flow of production fluids, such as hydrocarbons and/or water, from the formation. 
     Beneficially, this method provides an enhancement in the production, development and/or exploration of hydrocarbons. In particular, the method may be utilized to enhance development of a watertight model by providing an enhanced model with less computational effort, less interactive intervention, and/or in a shorter time. As a result, this may provide enhancements to production at lower costs and lower risk. 
     Regardless of how the watertight framework is obtained, mesh repair may also be performed on a subsurface model (e.g., reservoir model, geological model, and/or watertight model) to further enhance the process. Algorithms for mesh repairing are useful for many geometry processing applications. While conventional geometry processing approaches have a variety of techniques to repair meshes, the conventional approaches are not tailored to manage non-manifold meshes (e.g., meshes with T-junctions). Hence, subsurface models with many faults and horizons are not properly addressed by the conventional approaches. The present techniques provide a method, which is described further in  FIGS. 2 to 5  for mesh repair that is directed to handling subsurface models. 
     By way of example, a method of repairing a mesh in accordance with an embodiment of the present techniques is described. Given a set of faults and/or horizons, the first step in the method is to merge the set of faults and/or horizons into a single model, or volumetric representation. Then, the model may be subjected to a series of mesh repair operations, such as local re-meshing, edge flipping and collapsing. In each mesh repair operation, it should be verified that the operation (e.g., local re-meshing, edge flipping or collapsing) does not introduce undesirable topological change. For example, if the model includes a triangular mesh, the mesh repair operations may be utilized to remove small angles (e.g., angles within a mesh that are below a certain threshold) and replace the mesh at those locations with large angles, which may preferably be about 60 degrees. Accordingly, the method should include one or more checks, such as the link condition, and also verify if the gird is at the intersection between horizons and faults. 
       FIG. 2  is an exemplary flow chart for repairing a mesh in accordance with an embodiment of the present techniques. In this diagram  200 , a method of providing mesh repair to eliminate non-manifold edges and vertices and other problems with the mesh. This may be an exemplary method utilized in creating a watertight model in block  106 , utilized in creating a geologic model in block  108  and/or utilized in creating a reservoir model in block  110  of  FIG. 1 . In particular, the present techniques involves water-tightening, mesh repair, and smoothing. The method may include obtaining a model having objects, as shown in blocks  202  to  206 , applying one or more mesh repair operations (e.g., local re-meshing, edge flipping and/or collapsing), as shown in blocks  208  to  216 , and outputting the updated model, as shown in block  218 . 
     The process begins by obtaining objects for a subsurface region, as shown in blocks  202  to  206 . In block  202 , objects for a subsurface region are obtained. The objects may include one or more horizons, faults, and model boundaries, and any combination thereof. The obtaining of objects may include accessing one or more objects from a database, updating or modifying objects from subsurface measurements and/or creating objects based on the subsurface measurements. Then, a model for the subsurface region is obtained, as shown in block  204 . The obtaining the model may include creating the model and/or accessing the model from memory. At block  206 , the objects are inserted into the model. The insertion of the object may include inputting specified surfaces, an area of interest, and relationships between surfaces and then forming a first framework that may or may not be watertight. In another embodiment, a framework is generated by another means as block  204  and inputted at block  206 . 
     Once the model is created, one or more mesh repair operations (e.g., local re-meshing, edge flipping and/or collapsing) may be applied to the mesh to repair various problematic mesh locations, as shown in blocks  208  to  216 . At block  208 , areas of the mesh that need repair are identified. The identification of areas for mesh repair may include conversion of the mesh to tetrahedral grid, pairwise check for triangle intersection, or quality measures such as dihedral angles or triangles with two edges on the same intersection. The area of the mesh may include one or more blocks, one or more nodes or other mesh elements. Then, a local re-meshing operation may be applied to one or more of the identified areas in block  210 . The local re-meshing operation may include may include deleting interior vertices, relocating interior vertices, and/or creating interior vertices as well as flipping interior triangles, splitting interior triangles, and/or merging interior triangles. The local re-meshing operation is described further below in  FIG. 3 . Then, an edge flipping operation may be applied to one or more of the identified areas in block  212 . The edge flipping operation may include adjusting the edges between two triangles that share a common edge. The edge flipping operation is described further below in  FIG. 4 . At block  214 , a collapsing operation may be applied to one or more of the identified areas. The collapsing operation may include adjusting two adjacent triangles into a single triangle. The collapsing operation is described further below in  FIG. 5 . Then, at block  216 , a determination is made whether the mesh repair is complete. If the mesh repair is not complete, the process may identify areas of mesh that need repair in block  208 . Alternatively, one or more of the mesh repair operations in blocks  210 ,  212  and  214  may be utilized to perform additional mesh repair. If the mesh repair is complete, the updated model is outputted, as shown in block  218 . The outputting of the updated model may include storing the updated model in memory and/or displaying the updated model. 
       FIG. 3  is another exemplary flow chart for repairing a mesh in accordance with an embodiment of the present techniques. In this diagram  300 , a method of performing a local re-meshing operation is described. The local re-meshing, which may be an exemplary method utilized in performing a local re-meshing operation in block  210  of  FIG. 2 , may be utilized to mesh a piece of surface wholly contained contacts or intersection lines. In a preferred embodiment, a piece of surface is deformed by moving points (e.g., control points) on the surface, which necessitates remeshing to preserve mesh quality and validity without spurious intersections. The method may include obtaining a model having objects, as shown in blocks  302 , applying local re-meshing, as shown in blocks  304  and  306 , applying global vertex smoothing, as shown in blocks  308  and  310 , applying local vertex smoothing, as shown in blocks  312  and  314 , and outputting the updated model, as shown in block  318 . 
     The process begins by obtaining a model for the subsurface region having a mesh and objects, as shown in block  302 , and applying local re-meshing, as shown in blocks  304  and  306 . At block  302 , a model for the subsurface region having a mesh and objects is obtained. The obtaining of the model may include accessing the model from a database, updating or modifying an existing model and/or creating a new model based on the subsurface measurements. Then, a local re-meshing may be performed, as shown in block  304 . The local re-meshing may include deleting interior vertices, relocating interior vertices, and/or creating interior vertices as well as flipping interior triangles, splitting interior triangles, and/or merging interior triangles. At block  306 , the self-intersections are identified. The identification of self-intersections may include selecting a triangle and testing a plurality of the remaining triangles for intersection. In another embodiment, the triangles are used as constraints during the generation of a tetrahedral mesh which fails when triangles intersect. 
     Once the local re-meshing is complete, global vertex smoothing is applied, as shown in blocks  308  and  310 . At block  308 , a global vertex smoothing may be performed. The global vertex smoothing may include plain smoothing or hierarchical smoothing where specified vertices in the interior of pieces surfaces and on surface intersections remain fixed. At block  310 , the self-intersections are identified. The identification of self-intersections may include selecting a triangle and testing a plurality of the remaining triangles for intersection. In another embodiment, the triangles are used as constraints during the generation of a tetrahedral mesh which fails when triangles intersect. 
     Upon completion of the global vertex smoothing, local vertex smoothing is applied, as shown in blocks  312  and  314 . At block  312 , a local vertex smoothing may be performed. The local vertex smoothing may include a single surface, for example. At block  314 , the self-intersections are identified. The identification of self-intersections may include selecting a triangle and testing a plurality of the remaining triangles for intersection. In another embodiment, the triangles are used as constraints during the generation of a tetrahedral mesh which fails when triangles intersect. 
     Once the local vertex smoothing is complete, a determination is made whether the local re-meshing is complete, as shown in block  316 . If the local re-meshing is not complete, the process may identify additional areas of mesh that are to be subjected to the local re-meshing and return to block  304 . If a first piece of surface is moved not only in its interior but also on its boundary, then at least one other piece of another surface may need to be re-meshed because contacts or surface intersections were deformed. In some embodiment, these deformations are small and no further action is required. In a preferred embodiment, other surfaces are analyzed for mesh quality, intersection, and validity. If the local re-meshing is complete, the updated model is outputted, as shown in block  318 . The outputting of the updated model may include storing the updated model in memory and/or displaying the updated model. The updated model may be then be subjected to other mesh repair operations. 
       FIG. 4  is yet another exemplary flow chart for repairing a mesh in accordance with an embodiment of the present techniques. In this diagram  400 , a method of performing an edge flipping operation is described. The edge flipping, which may be an exemplary method utilized in performing an edge flipping operation in block  212  of  FIG. 2 , may be utilized to improve mesh quality by flipping a pair of triangles with at least one small dihedral angle, to remove a spurious intersection by flipping a pair of triangles that includes a cap triangle or to remove a spurious intersection by splitting a cap triangle. The method may include obtaining a model having objects, as shown in blocks  402 , identifying low quality mesh shapes and splitting the identified low quality mesh shapes, as shown in blocks  404  and  406 , identifying self-intersections and low quality mesh shapes and flipping the low quality mesh shapes, as shown in blocks  408  and  410 , and identifying self-intersections and low quality mesh shapes and determining if the edge flipping operation is compete, as shown in blocks  412  to  416 . 
     The process begins by obtaining a model for the subsurface region having a mesh and objects, as shown in block  402 , and identifying low quality mesh shapes and splitting the identified low quality mesh shapes, as shown in blocks  404  and  406 . At block  402 , a model for the subsurface region having a mesh and objects is obtained. The obtaining of the model may include accessing the model from a database, updating or modifying an existing model and/or creating a new model based on the subsurface measurements. Then, self-intersections and low quality mesh shapes are identified, as shown in block  404 . The identification of the self-intersections and low quality mesh shapes may include selecting a triangle and testing a plurality of the remaining triangles for intersection and/or may include associating the triangle with a flag and/or indicator. In another embodiment, the triangles are used as constraints during the generation of a tetrahedral mesh which fails when triangles intersect, as well as computing the triangle angles and comparing them against a specified threshold to identify triangles with small dihedral angles. At block  406 , the identified self-intersections and low quality mesh shapes are split. The splitting of the identified self-intersections and low quality mesh shapes may include determining a flag or indication for the respective triangles. Further, the splitting of the identified self-intersections and low quality mesh shapes may not be performed if the splitting changes the topology of the mesh such as creating a hole, a spurious intersection or a new contact with a previously not-contacted surface. 
     Once the splitting of the low quality mesh shapes is complete, the method performs identifying self-intersections and low quality mesh shapes and flipping the low quality mesh shapes, as shown in blocks  408  and  410 . At block  408 , self-intersections and low quality mesh shapes are identified. The identification of the self-intersections and low quality mesh shapes may include selecting a triangle and testing a plurality of the remaining triangles for intersection. In another embodiment, the triangles are used as constraints during the generation of a tetrahedral mesh which fail when triangles intersect, as well as computing the triangle angles and comparing them against a specified threshold to identify triangles with small dihedral angles. At block  410 , the identified self-intersections and low quality mesh shapes are flipped. The flipping of the identified self-intersections and low quality mesh shapes may include selecting pairs of triangles where a first triangle of the pair either exhibits a self-intersection, an intersection with another surface, and/or at least one small dihedral angle. Also, the flipping of the identified self-intersections and low quality mesh shapes may not be performed if the flipping changes the topology of the mesh where a hole is created, a hole is filled, or a spurious contact is created. 
     Upon completion of the flipping of the identified self-intersections and low quality mesh shapes, the identification of self-intersections and low quality mesh shapes and determination whether the edge flipping operation is compete is performed, as shown in blocks  412  to  416 . The self-intersections and low quality mesh shapes are identified, as shown in block  412 . The identification of the self-intersections and low quality mesh shapes may include selecting a first triangle and comparing it against a plurality of remaining triangles. In another embodiment, the triangles are used as constraints for filling the model with tetrahedral which fails when triangles have spurious intersections. Then, a determination is made whether the edge flipping is complete, as shown in block  414 . If the edge flipping is not complete, the process may identify additional areas of mesh that are to be subjected to the edge flipping and return to block  404 . In some embodiments, a determination whether edge flipping is complete may be based on a mesh quality measure, such as minimal edge length or minimal dihedral angle. In another embodiment, a determination may be made based on the detection of at least one spurious intersection by analyzing a plurality of triangle pairs for intersection or by attempting to fill the mesh with tetrahedra constrained by a plurality of mesh triangles. If the edge flipping is complete, the updated model is outputted, as shown in block  416 . The outputting of the updated model may include storing the updated model in memory and/or displaying the updated model. The updated model may be then be subjected to other mesh repair operations. 
       FIG. 5  is still another exemplary flow chart  500  for repairing and improving a mesh in accordance with an embodiment of the present techniques. In this diagram  500 , a method of performing a collapsing operation is described. The collapsing, which may be an exemplary method utilized in performing a collapsing operation in block  214  of  FIG. 2 , may be utilized to improve mesh quality by combination of neighboring mesh vertices which removes mesh elements with short edges and/or small areas. The method may include obtaining a model having objects, as shown in blocks  502 , identifying small edges and collapsing the small edges, as shown in blocks  504  and  506 , identifying high dihedral angles in the mesh shapes and flipping the identified high dihedral angles in the mesh shapes, as shown in blocks  508  and  510 , and determining if the collapsing operation is compete, as shown in block  512  and  514 . 
     The process begins by obtaining a model for the subsurface region having a mesh and objects, as shown in block  502 , and identifying small edges and collapsing the small edges, as shown in blocks  504  and  506 . At block  502 , a model for the subsurface region having a mesh and objects is obtained. The obtaining of the model may include accessing the model from a database, updating or modifying an existing model and/or creating a new model based on the subsurface measurements. Then, small edges in the mesh shapes are identified, as shown in block  504 . The identification of the small edges in the mesh shapes may include computing the length of a plurality of edges for a plurality of mesh elements and comparing these lengths against a specified threshold. In another embodiment, the area of a specified mesh element may serve as a proxy for edge length. In yet another embodiment, one of the ratio between mesh element perimeter and mesh element or the ratio between minimal edge length and mesh perimeter is used to identify collapse candidates. At block  506 , the identified small edges are collapsed. The collapsing of the identified small edges may include selecting the mesh elements that contain either one of the two vertices forming the short edge, replacing these two vertices with one representative vertex, and re-meshing the mesh elements using the representative vertex instead of the two original ones. The representative vertex may be obtained by selection of either of the two vertices or by computation, for example, by forming the average of said two vertices. Further, the collapsing of the small edges may not be performed if the collapsing changes the topology of the mesh by creation of spurious mesh intersection, by creation of new contacts, or formation of a hole. 
     Once the collapsing of the small edges is complete, the method performs identifying high dihedral angles in the mesh shapes and flipping the identified high dihedral angles in the mesh shapes, as shown in blocks  508  and  510 . At block  508 , high dihedral angles in the mesh shapes are identified. The identification of the high dihedral angles in the mesh shapes may include computing a plurality of interior angles for a plurality of mesh shapes or by detection of mesh shapes with aspect ratios exceeding a specified threshold. At block  510 , the identified high dihedral angles in the mesh shapes are flipped. The flipping of the identified high dihedral angles in the mesh shapes may include select a mesh shape with dihedral angles and one of its neighbors and re-meshing said two shapes. Also, the flipping of the identified high dihedral angles in the mesh shapes may not be performed if the flipping changes the topology of the mesh by creation of a hole, new contact, and/or spurious intersection. 
     Upon completion of the flipping of the identified high dihedral angles in the mesh shapes, the determination whether the collapsing operation is compete is performed, as shown in blocks  512  and  514 . The determination is made whether the collapsing is complete, as shown in block  512 . In one embodiment, determination is made by performing blocks  504  to  510  to a specified plurality of surfaces or elements thereof. In another embodiment, a quality measure is formed for a specified plurality of surfaces or elements thereof and the workflow is iterated until a specified quality is reached or until a specified number of iteration is reached. If the collapsing is not complete, the process may identify additional areas of mesh that are to be subjected to the collapsing operations and return to block  504 . If the collapsing is complete, the updated model is outputted, as shown in block  514 . The outputting of the updated model may include storing the updated model in memory and/or displaying the updated model. The updated model may be then be subjected to other mesh repair operations. 
     Persons skilled in the technical field will readily recognize that in practical applications of the disclosed methodology, it is partially performed on a computer, typically a suitably programmed digital computer. Further, some portions of the detailed descriptions which follow are presented in terms of procedures, steps, logic blocks, processing and other symbolic representations of operations on data bits within a computer memory. These descriptions and representations are the means used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. In the present application, a procedure, step, logic block, process, or the like, is conceived to be a self-consistent sequence of steps or instructions leading to a desired result. The steps are those requiring physical manipulations of physical quantities. Usually, although not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated in a computer system. 
     It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise as apparent from the following discussions, it is appreciated that throughout the present application, discussions utilizing the terms such as “processing” or “computing”, “calculating”, “comparing”, “determining”, “displaying”, “copying,” “producing,” “storing,” “adding,” “applying,” “executing,” “maintaining,” “updating,” “creating,” “constructing” “generating” or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system&#39;s registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices. 
     Embodiments of the present techniques also relate to an apparatus for performing the operations herein. This apparatus may be specially constructed for the required purposes, or it may comprise a general-purpose computer selectively activated or reconfigured by a computer program stored in the computer (e.g., one or more sets of instructions). Such a computer program may be stored in a computer readable medium. A computer-readable medium includes any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computer). For example, but not limited to, a computer-readable (e.g., machine-readable) medium includes a machine (e.g., a computer) readable storage medium (e.g., read only memory (“ROM”), random access memory (“RAM”), magnetic disk storage media, optical storage media, flash memory devices, etc.), and a machine (e.g., computer) readable transmission medium (electrical, optical, acoustical or other form of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.)). 
     Furthermore, as will be apparent to one of ordinary skill in the relevant art, the modules, features, attributes, methodologies, and other aspects of the invention can be implemented as software, hardware, firmware or any combination of the three. Of course, wherever a component of the present invention is implemented as software, the component can be implemented as a standalone program, as part of a larger program, as a plurality of separate programs, as a statically or dynamically linked library, as a kernel loadable module, as a device driver, and/or in every and any other way known now or in the future to those of skill in the art of computer programming. Additionally, the present invention is in no way limited to implementation in any specific operating system or environment. 
     Further, one or more embodiments may include methods that are performed by executing one or more sets of instructions to perform modeling enhancements in various stages. For example, the method may include executing one or more sets of instructions to perform comparisons between thresholds current statuses or indications along with transmitting data between modules, components and/or sensors. 
     As an example,  FIG. 6  is a block diagram of a computer system  600  that may be used to perform any of the methods disclosed herein. A central processing unit (CPU)  602  is coupled to system bus  604 . The CPU  602  may be any general-purpose CPU, although other types of architectures of CPU  602  (or other components of exemplary system  600 ) may be used as long as CPU  602  (and other components of system  600 ) supports the inventive operations as described herein. The CPU  602  may execute the various logical instructions according to disclosed aspects and methodologies. For example, the CPU  602  may execute machine-level instructions for performing processing according to aspects and methodologies disclosed herein. 
     The computer system  600  may also include computer components such as a random access memory (RAM)  606 , which may be SRAM, DRAM, SDRAM, or the like. The computer system  600  may also include read-only memory (ROM)  608 , which may be PROM, EPROM, EEPROM, or the like. RAM  606  and ROM  608  hold user and system data and programs, as is known in the art. The computer system  600  may also include an input/output (I/O) adapter  610 , a communications adapter  622 , a user interface adapter  624 , and a display adapter  618 . The I/O adapter  610 , the user interface adapter  624 , and/or communications adapter  622  may, in certain aspects and techniques, enable a user to interact with computer system  600  to input information. 
     The I/O adapter  610  preferably connects a storage device(s)  612 , such as one or more of hard drive, compact disc (CD) drive, floppy disk drive, tape drive, etc. to computer system  600 . The storage device(s) may be used when RAM  606  is insufficient for the memory requirements associated with storing data for operations of embodiments of the present techniques. The data storage of the computer system  600  may be used for storing information and/or other data used or generated as disclosed herein. The communications adapter  622  may couple the computer system  600  to a network (not shown), which may enable information to be input to and/or output from system  600  via the network (for example, a wide-area network, a local-area network, a wireless network, any combination of the foregoing). User interface adapter  624  couples user input devices, such as a keyboard  628 , a pointing device  626 , and the like, to computer system  600 . The display adapter  618  is driven by the CPU  602  to control, through a display driver  616 , the display on a display device  620 . Information and/or representations of one or more 2D canvases and one or more 3D windows may be displayed, according to disclosed aspects and methodologies. 
     The architecture of system  600  may be varied as desired. For example, any suitable processor-based device may be used, 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 use any number of suitable structures capable of executing logical operations according to the embodiments. 
     In one or more embodiments, the method may be implemented in machine-readable logic, such that a set of instructions or code that, when executed, performs the instructions or operations from memory. The computer system may include a processor; an input device in communication with the processor and configured to receive input data associated with a subsurface region; and memory in communication with the processor, the memory having a set of instructions. The set of instructions, when executed, are configured to: obtain a subsurface model associated with the subsurface region and having a mesh formed from a plurality of nodes and forming a plurality of blocks; identify one or more areas of the mesh that need repair; apply to the identified areas of the mesh one or more of a local re-meshing operation, an edge-flipping operation, a collapsing operation and any combination thereof; and output the updated subsurface model. 
     Further, the set of instructions may also be configured to: obtain subsurface measurements associated with the subsurface region, generate a structural framework form the subsurface measurements, wherein the structural framework comprises a plurality of objects, wherein the plurality of objects include one or more of horizons, faults and any combination thereof, and generate the subsurface model from structural framework; create a geologic model from the subsurface model by assigning properties to one or more of the plurality of blocks; create a reservoir model from the subsurface model by assigning properties associated with fluid flow to one or more of the plurality of blocks; simulate fluid flow within the reservoir model to create simulation results; provide a visualization of the subsurface model via a display and/or visualize the simulation results for hydrocarbon operations. Further, to perform the local re-meshing operation, the set of instructions may be configured to: perform local re-meshing on the one or more identified area, perform a global vertex smoothing on the one or more identified area, and perform a local vertex smoothing on the one or more identified area; and/or perform one or more of deleting interior nodes, relocating interior nodes, creating interior nodes, flipping interior blocks, splitting interior blocks, merging interior blocks, and any combination thereof. To perform the edge flipping operation, the set of instructions may be configured to: perform a first identification of self-intersections and low quality mesh shapes, split the low quality mesh shapes from the first identification, perform a second identification of self-intersections and low quality mesh shapes, and flipping the low quality mesh shapes from the first identification; and/or compare angles formed within the mesh against a specified threshold to identify small dihedral angles below the threshold to perform the identification of self-intersections and low quality mesh shapes. To perform the collapsing operation, the set of instructions may be configured to: identify small edges in the mesh shapes; collapse the identified small edges; identify high dihedral angles in mesh shapes; and flip the identified high dihedral angles in the mesh shapes. 
     For example, the memory may store an instance of the digital image and a list of model objects associated with a subsurface region. The model objects may represent a volume part (e.g., a compartment) or one of the input surfaces, such as faults, horizons and boundary surfaces. The set of instructions may be configured to create watertight model from the digital image, which includes objects, such as surfaces. The set of instructions may be used to generate a triangle mesh, if necessary, from the digital image. 
     As another example, the memory may store an instance of the volumetric representation associated with a subsurface region. The set of instructions configured to adjust the objects within the volumetric representation for pinch-outs. In particular, the set of instructions may be configured to split the conversion of narrow layers in three sets of instructions: (1) detection of collapsed parts of layers, (2) removal of volume parts and (3) splitting of surface patches for consistent representation of pinch-outs through contacts. The detection of collapsed sets of instructions may be utilized before volume detection. The collapsed results may be stored in memory, and read after volume detection. Once read, the volume detection post-processing may be configured to verify that the collapsed results are properly represented. An additional set of instructions may be configured to perform surface patching. 
     It should be understood that the preceding is merely a detailed description of specific embodiments of the invention and that numerous changes, modifications, and alternatives to the disclosed embodiments can be made in accordance with the disclosure here without departing from the scope of the invention. The preceding description, therefore, is not meant to limit the scope of the invention. Rather, the scope of the invention is to be determined only by the appended claims and their equivalents. It is also contemplated that structures and features embodied in the present examples can be altered, rearranged, substituted, deleted, duplicated, combined, or added to each other. 
     The foregoing description is directed to particular embodiments of the present invention for the purpose of illustrating it. It will be apparent, however, to one skilled in the art, that many modifications and variations to the embodiments described herein are possible. All such modifications and variations are intended to be within the scope of the present invention, as defined by the appended claims.