Adaptive borehole-centric voxel model based on local inversion of logging data

Abstract

Methods for modeling downhole formations include drilling, with a drill string, a drilling interval of a borehole through the downhole formation. The methods include obtaining measurement data for at least one measurement interval along the borehole, generating an initial composite model for a predefined region associated with the at least one measurement interval, calculating a best-fit model for the initial composite model based on the measurement data, performing a geometric partitioning and a property-driven partitioning of the initial composite model to generate a final composite model, and calculating a best-fit model for the final composite model based on the measurement data.

Description

ADAPTIVE BOREHOLE-CENTRIC VOXEL MODEL BASED ON LOCAL INVERSION OF LOGGING DATACROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 568,054, filed March 21, 2024.BACKGROUND

[0002] The present disclosure relates to downhole and subsurface exploration systems and processes and, more particularly, to methods and systems for construction of voxel modes of near-borehole space.

[0003] In downhole and subsurface exploration, modeling of the formation and earth around a borehole may allow for improved drilling operations and / or for improved extraction and / or injection of material from / to subsurface formations (e.g., gas, water, oil, etc.). Modeling may be based, for example, on data and information collected during a drilling operation, based on information obtained from nearby wells, test or synthetic data, or other sources and combinations thereof, as will be appreciated by those of skill in the art. The information obtained during drilling may be obtained using one or more sensors that are arranged on a downhole tool. A while-drilling measurement may be taken using the sensors, and the data may be used to generate models that are representative of the formation through which the drilling operation is performed. Such measurements may be referred to as surveys.

[0004] Surveys are often performed using acquisition methodologies, such as seismic scanners, acoustic sensors, nuclear magnetic resonance sensors, and the like to generate maps and / or representations of underground structures and formations. These structures and formations are often analyzed to determine the presence of subterranean materials of interest (e.g., fluids and / or minerals). The information may be used to assess the underground structures and locate the formation(s) containing desirable subterranean materials. Data collected from the surveys and acquisition methodologies may be evaluated and analyzed to determine whether such subterranean materials are present, and if they are reasonably accessible. Conventionally, the data may be processed (e.g., by inversion) to generate a two-dimensional (2D) map or image of the downhole formation(s). Further, three-dimensional (3D) mapping is also possible. Forexample, a seismic volume is a 3D cube of values generated by various data acquisition tools and a position in the 3D cube is referred to as a voxel (i.e., volume element). Voxel mapping and modeling may improve the efficiency, costs, and operations associated both with downhole drilling and post-drilling operations (e.g., production). Further improvements on these processes may be desirable.SUMMARY

[0005] According to some embodiments, methods for modeling downhole formations are provided. The methods include obtaining measurement data for a series of measurement intervals along a borehole, calculating a best-fit model for a model interval associated with each measurement interval, generating an initial composite model based on the best-fit models, performing a geometric partition of the initial composite model to generate a plurality of geometric cells based on geometric criterion, and performing a property-driven partitioning of the geometric cells based on a property-driven criterion to generate a final composite model. The property-driven partitioning of the geometric cells comprises determining if each geometric cell is a terminal geometric cell or a non-terminal geometric cell, for each terminal geometric cell, setting the region of the composite model represented by the terminal geometric cell with a formation property value of the terminal geometric cell, and assigning the cell as a terminal cell, for each non-terminal geometric cell, dividing the non-terminal geometric cell into a plurality of sub-cells, and determining if each sub-cell is a terminal sub-cell, for each terminal sub-cell, setting the region of the composite model represented by the terminal subcell with a formation property value of the terminal sub-cell, and assigning the sub-cell as a terminal cell, and for each non-terminal sub-cell, further dividing until each cell or sub-cell is a terminal cell and setting a respective region of the composite model with a formation property value of the respective terminal cell. A final composite model is assembled based on a set of terminal cells.BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The following descriptions should not be considered limiting in any way. With reference to the accompanying drawings, like elements are numbered alike:

[0007] FIG. 1 depicts a schematic illustration of a borehole operation system that can incorporate embodiments of the present disclosure;

[0008] FIG. 2 depicts a block diagram of a processing system, which can be used for implementing more embodiments of the present disclosure;

[0009] FIG. 3A is a schematic illustration of a coordinate system employed in embodiments of the present disclosure and cells thereof;

[0010] FIG. 3B illustrates a cell and sub-cell arrangement as generated by processes in accordance with the present disclosure;

[0011] FIG. 4A is a schematic diagram of cells of a modeling process in accordance with an embodiment of the present disclosure;

[0012] FIG. 4B is a representative a cell structure of cells and sub-cells as assembled into an illustrative model of a portion of a formation in accordance with an embodiment of the present disclosure;

[0013] FIG. 5 a plot of cell structures as generated in accordance with embodiments of the present disclosure;

[0014] FIG. 6 is a flow process for generating a composite model of a subsurface formation in accordance with an embodiment of the present disclosure;

[0015] FIG. 7A illustrates a flow process for generating a composite model based on cell analysis in accordance with an embodiment of the present disclosure;

[0016] FIG. 7B is a subroutine of the flow process of FIG. 7A; and

[0017] FIG. 8 is a schematic illustration of a composite model generated in accordance with embodiments of the present disclosure.DETAILED DESCRIPTION

[0018] A detailed description of one or more embodiments of the disclosed apparatus and method are presented herein by way of exemplification and not limitation with reference to the Figures. Modern bottom hole assemblies (BHAs) are composed of several distributed components, such as sensors and tools, with each component performing data acquisition and / or processing of a special purpose. During a drilling operation, sensors and detectors may be used to determine the nature of a surrounding formation and / or to determine if the locationof the borehole is passing through an expected formation and / or within a specific formation (e.g., for production purposes). Such sensors and detectors may also or alternatively be used to determine physical properties relevant for drilling operations, such as, and without limitation, pressure, temperature, mechanical loading (e.g., accelerations, bending moments, torsional moments, axial forces, etc.), or directional information, such as drift / inclination or direction / azimuth. Data collected by such sensors and systems may be used for modeling of the formation(s) and earth surrounding a borehole.

[0019] FIG. 1 illustrates an embodiment of a system 100 for performing an energy industry operation (e.g., subsurface drilling, measurement, stimulation, and / or production). The system 100 includes a borehole string 102 that is shown disposed in a well or borehole 104 that penetrates at least one earth formation 106 during a drilling operation or other downhole operation. As described herein, the terms “borehole” or “wellbore” refers to a hole that makes up all or part of a drilled well. It is noted that the borehole 104 may include vertical, deviated, and / or horizontal sections, and may follow any suitable or desired path. As described herein, the term “formation” refers to the various features and materials (e.g., geological material) that may be encountered in a subsurface environment and that surround the borehole 104. It will be appreciated that the borehole 104 may pass through multiple different formations, and each formation may have different properties.

[0020] The borehole string 102 is operably connected to a surface structure or surface equipment such as a drill rig 108, which includes or is connected to various components such as a surface drive 110 (also referred to as top drive) and / or rotary table 112 for supporting the borehole string 102, rotating the borehole string 102, and lowering string sections or other downhole components into the borehole 104. In one example configuration, the borehole string 102 is configured as a drill string that includes one or more drill pipe sections 114 that extend downward into the borehole 104 and is connected to one or more downhole components (e.g., downhole tools), which may be configured as a bottomhole assembly (BHA) 116. The BHA 116 may be fixedly connected to the borehole string 102 such that rotation of the borehole string 102 causes rotation of the BHA 116.

[0021] The BHA 116 includes a disintegrating device 118 (e.g., a drill bit), which in this embodiment is intended or configured to be driven from the surface. In other configurations, the disintegrating device 118 may be driven from downhole (e.g., by a downhole mud motor or turbine). The system 100 may include components to facilitate circulating a drilling fluid120, such as drilling mud, through an inner bore of the borehole string 102 down to the disintegrating device 118. The drilling fluid 120 may pass through the disintegrating device 118, to drive operation thereof, and may enter an annulus between an exterior of the borehole string 102 and a wall of the borehole 104. For example, in this illustrative embodiment, a pumping device 122 is located at the surface to circulate the drilling fluid 120 from fluid source 124 (e.g., a mud pit) into the borehole 104 as the disintegrating device 118 is rotated (e.g., by rotation of the borehole string 102 and / or a downhole motor).

[0022] In the illustrative embodiment shown in FIG. 1, the system 100 includes a steering assembly 126 configured to steer or direct a section of the borehole string 102 and the disintegrating device 118 along a selected path. The steering assembly 126 may have any configuration suitable to direct or steer the borehole string 102. Examples of steering assemblies include, without limitation, steerable motor assemblies (e.g., bent housing motor assemblies), turbines, and rotary steerable assemblies or systems.

[0023] In one non-limiting embodiment, the steering assembly 126 is configured as a rotary steering assembly forming the BHA 116 or part of the BHA 116. The steering assembly 126 includes a non-rotating or slowly rotating sleeve 128 that includes one or more radially extendable pads 130 (e.g., extendable in a direction perpendicular to a longitudinal axis of the sleeve 128). The pads 130 may be located at different circumferential and / or axial locations on the sleeve 128 and may be adjustable individually or in combination to deflect the disintegrating device 118 by engaging the wall of the borehole 104. The sleeve 128 may be coupled to the borehole string 102 by a bearing assembly or other mechanism that allows rotation of the sleeve independent of the rotation of the borehole string, as will be appreciated by those of skill in the art.

[0024] The system 100 may also include a controller configured to operate or control operation of the pads 130 based on directional information derived from directional sensors located in the BHA 116 and / or the borehole string 102. Alternatively, or in combination, the steering may be based on instructions received from the surface. In some embodiments, the directional sensor(s) may be arranged at, in, or near the steering assembly 126. The directional sensor(s) can include one or more gyroscopes (e.g., gyroscope sensors or earth rate sensors), one or more magnetometers (i.e., magnetic field sensors), one or more accelerometers (e.g., acceleration sensors and / or gravitational sensors), and / or other sensors as will be appreciated by those of skill in the art (e.g., acoustic, nuclear magnetic resonance, etc.).

[0025] In this illustrative embodiment, the system 100 includes one or more sensor assemblies 132 configured to perform measurements of parameters related to position and / or direction of the borehole string 102, the disintegrating device 118, and / or the steering assembly 126. As shown in FIG. 1, the sensor assemblies 132 may be located at one or more of various locations, such as on the sleeve 128, at or near the disintegrating device 118, and / or on other components of the borehole string 102 and / or the BHA 116. For example, a sensor assembly 132 can be located on one or more stabilizer sections 134 of the steering assembly 126.

[0026] The system 100 may include one or more of various tools or components configured to perform selected functions downhole such as performing downhole measurements / surveys (e.g., formation evaluation measurements, directional measurements, etc.), facilitating communications (e.g., mud pulser, wired pipe communication sub, etc.), providing electrical power and others (e.g., mud turbine, generator, battery, data storage device, processor device, modem device, hydraulic device, etc.). For example, the steering assembly 126 can be connected to one or more sensor devices, including, but not limited to, a gamma ray imaging tool 136. Such gamma ray imaging tool 136 may be used to measure formation density, for example.

[0027] In one embodiment, the system 100 includes a measurement device such as a logging while drilling (LWD) tool (e.g., for formation evaluation measurements) or a measurement while drilling (MWD) tool (e.g., for directional measurements), generally referred to as whiledrilling tool 138. Examples of LWD tools include nuclear magnetic resonance (NMR) tools, resistivity tools, gamma (density) tools, pulsed neutron tools, acoustic tools, and various others. Examples of MWD tools include tools measuring pressure, temperature, or directional data (e.g., magnetometer, accelerometer, gyroscope, etc.). The steering assembly 126 of the system 100 can include other components, such as a telemetry assembly (e.g., mud pulser, wired pipe communication sub, etc.) or other downhole and / or surface components, systems, or assemblies.

[0028] One or more downhole components and / or one or more surface components may be in communication with and / or controlled by a processor such as a downhole processing unit 140 and / or a surface processing unit 142. The downhole processing unit 140 may be part of the BHA 116 or may be otherwise arranged on or part of or disposed on the borehole string 102 (e.g., on a different sub than the BHA 116). The surface processing unit 142 may be arranged at the surface and associated with the drill rig 108. The surface processing unit 142 and / or thedownhole processing unit 140 may be configured to perform functions such as controlling drilling and steering, controlling the flow rate and pressure of the drilling fluid 120, controlling weight on bit (WOB), controlling rotary speed (RPM) of the rotary table 112 or the surface drive 110, transmitting and receiving data, processing measurement data, and / or monitoring operations of the system 100. The surface processing unit 142, in some embodiments, includes an input / output (I / O) device 144 (such as a keyboard and a monitor), a processor 146, and a data storage device 148 (e.g., memory, computer-readable media, etc.) for storing data, models, and / or computer programs or software that cause the processor to perform aspects of methods and processes described herein. The downhole processing unit 140 may include similar processor(s), memory, and / or programs / software, as will be appreciated by those of skill in the art.

[0029] In one non-limiting embodiment, the surface processing unit 142 is configured as a surface control unit which controls a borehole operation and / or various parameters such as rotary speed (RPM), weight-on-bit, fluid flow parameters (e.g., pressure and flow rate), directional steering control of a rotary steering assembly, and / or other parameters or aspects of the system 100, such as data processing and / or data log generation. The borehole operation may involve a human operator or may be performed automatically without interference of a human operator. The downhole processing unit 140, in some embodiments, may be or include a directional measurement controller or other processing device that controls aspects of operating the sensor assemblies 132, acquiring measurement data, and / or estimating directional parameters. The downhole processing unit 140 may also include functionality for controlling operation of the steering assembly 126 and / or other downhole components, assemblies, or systems. In one non-limiting embodiment, the method and processes described herein may be performed in the downhole processing unit 140 located within the borehole string 102 or the BHA 116.

[0030] In the embodiment of FIG. 1, the system 100 is configured to perform a drilling operation and a downhole measurement operation (e.g., surveys), and the borehole string 102 is a drill string. However, embodiments described herein are not so limited and may have any configuration suitable for performing an energy industry operation that includes or can benefit from directional measurements (e.g., completion operation, fracturing operation, production operation, re-entry operation, etc.).

[0031] It is understood that embodiments of the present disclosure are capable of being implemented in conjunction with any other suitable type of computing environment now known or later developed. For example, FIG. 2 depicts a block diagram of a processing system 200 (e.g., representative of portions of the surface processing unit 142 and / or the downhole processing unit 140 of FIG. 1), which can be used for implementing the techniques described herein. In examples, the processing system 200 has one or more central processing units 202a, 202b, 202c, etc. (collectively or generically referred to as processor(s) 202 and / or as processing device(s) 202). In aspects of the present disclosure, each processor 202 can include a reduced instruction set computer (RISC) microprocessor. The processor(s) 202, as shown, are coupled to system memory (e.g., random access memory (RAM) 204) and various other components via a system bus 206. As illustrated, read only memory (ROM) 208 is coupled to the system bus 206 and can include a basic input / output system (BIOS), which may be configured to control certain basic functions of the processing system 200.

[0032] Further illustrated in FIG. 2 are an input / output (I / O) adapter 210 and a network adapter 212 coupled to the system bus 206. The I / O adapter 210 can be a small computer system interface (SCSI) adapter that communicates with a memory, such as a hard disk 214 and / or a tape storage drive 216 or any other similar component(s). The RO adapter 210 and associated memory, such as the hard disk 214 and / or the tape storage device 216, may be collectively referred to herein as a mass storage 218. An operating system 220 for execution on the processing system 200 can be stored in the mass storage 218. The network adapter 212 may be configured to interconnect the system bus 206 with an outside network 222 enabling the processing system 200 to communicate with other systems and / or remote systems (e.g., internet, extranet, and / or cloud-based systems).

[0033] A display 224 (e.g., a display monitor), when configured as a surface processing unit, may be connected to the system bus 206 by a display adapter 226, which can include, for example, a graphics adapter to improve the performance of graphics intensive applications and a video controller. In one aspect of the present disclosure, the adapters 210, 212, and / or 226 can be connected to one or more RO busses that are connected to the system bus 206 via an intermediate bus bridge (not shown), as will be appreciated by those of skill in the art. Suitable I / O buses for connecting peripheral devices such as hard disk controllers, network adapters, and graphics adapters typically include common protocols, such as the Peripheral Component Interconnect (PCI). Additional input / output devices are shown connected to the system bus 206via a user interface adapter 228 and the display adapter 226. For example, as shown, a keyboard 230, a mouse 232, and a speaker 234 can be interconnected to the system bus 206 via the user interface adapter 228, which can include, for example, a Super I / O chip integrating multiple device adapters into a single integrated circuit.

[0034] In some aspects of the present disclosure, and as shown, the processing system 200 includes a graphics processing unit 236. Graphics processing unit 236 may be a specialized electronic circuit designed to manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display (e.g., display 224). In general, the graphics processing unit 236 is very efficient at manipulating computer graphics and image processing and has a highly parallel structure that makes it more effective than general-purpose CPUs for algorithms where processing of large blocks of data is done in parallel.

[0035] Thus, as configured herein, the processing system 200 includes processing capability in the form of the processors 202, storage capability including system memory (e.g., the RAM 204 and the mass storage 218), input means such as the keyboard 230 and the mouse 232, and output capability including the speaker 234 and the display 224. In some aspects of the present disclosure, a portion of system memory (e.g., RAM 204 and mass storage 218) may be configured to store an operating system (e.g., operating system 220) to coordinate the functions of the various components shown in the processing system 200 and / or systems external to the processing system 200 (e.g., aspects of a BHA or the like).

[0036] It will be appreciated that the processing system 200 of FIG. 2 is presently described as a surface system (e.g., surface processing unit 142 of FIG. 1). However, it will be appreciated that similar electronic components may be employed in downhole systems (e.g., as part of a BHA and / or downhole processing unit 140). In such configurations, certain features of the processing system may be omitted. For example, in a downhole BHA system, the user interface components may be omitted. Further, the system bus may be arranged to span multiple different downhole components and the network connection may be a communication means (e.g., telemetry, wired connection, wireless connection, or the like) that is configured to enable communication between a surface system and the downhole BHA system.

[0037] The processing system 200, whether arranged as a surface processing unit or downhole processing unit, may be in communication with one or more downhole components through a communication connection, such as mud-pulse telemetry or the like. In some configurations,as mentioned, wired connections may be employed, but use of wired pipe may be cost- prohibitive. As such, lower bandwidth solutions may still be relied upon for communication between downhole components and other downhole components or with components at the surface. It will be appreciated that communication between two downhole components may be through a wired connection and may not require telemetry. However, a substantial portion of downhole communication may employ telemetry transmission and the bandwidth of telemetrybased communication is limited. A low bandwidth for uplink and / or downlink can result in delays in a drilling operation. For example, due to the low bandwidth, it is difficult (e.g., time consuming) to transmit information (including data and / or commands) between the surface and downhole components or vice versa. As such, during an active drilling operation, it is not desirable to delay drilling for the purpose of data transmission, particularly if the data being transmitted merely confirms that a drilling trajectory or drilling plan is being maintained (e.g., no issues present).

[0038] The BHA and processing units (e.g., downhole or at the surface) may be used to construct models of the earth and earth formations around the borehole (e.g., rock structures, bed layers, faults, reservoirs, etc.). Embodiments of the present disclosure are directed to methods for construction of composite voxel models of a near-borehole space. The composite model, in accordance with some embodiments of the present disclosure, may be constructed from a series of individual models (e.g., formation models) obtained by inversion of logging data. For example, logging data employed by some embodiments of the present disclosure may include, without limitation, resistivity measurements, although other types of logging data may be used without departing from the scope of the present disclosure (e.g., acoustic, NMR, etc.). As such, a set or group of individual models may be aggregated and assembled into a composite model that is representative of a borehole and the formation surrounding such borehole.

[0039] The resulting or constructed composite model is a borehole-centric model and may have an adaptive size of voxels (cells or volume elements) within the composite model. Such adaptive size of the voxels can provide a trade-off between resolution and computer memory size needed to store the composite model. Further, by reducing the total memory requirements, data transmission may be improved, as less data may be required than otherwise if such adaptive size voxels were not used. For example, if some amount of processing is performed downhole, the amount of data required to transmit the composite model (or some precursor thereof) to the surface may be reduced through the processes described herein.

[0040] In accordance with some embodiments of the present disclosure, a voxel-type composite formation model is determined in a neighborhood of the borehole. The voxel-type composite model, as described herein, is obtained as a result of inversion of measurements having finite depth of investigation. In accordance with some embodiments, a composite model of a formation surrounding a borehole is obtained as a result of a sequence of inversion procedures performed on successive intervals along the borehole (i.e., a sequence of individual models). As a result of using measurements of finite depth and as originated from tools and / or sensors within the borehole, the resulting individual models and the resulting composite model will be borehole-centric and thus may be defined in a coordinate system associated with the borehole rather than defined by global coordinates.

[0041] In accordance with some embodiments, the models (individual and / or composite) described herein may have different scales. For example, a first scale may be a size along the borehole (e.g., axial length along the borehole), which is much greater than a size in a transverse direction from the borehole. This scale difference may be due to the finite depth of investigation of measurements obtained during drilling. That is, for example, a drilled borehole will have a substantially long length (e.g., hundreds or thousands of meters) but the depth of investigation using while-drilling tools may be in the range of meters or even below. Further, for example, rapid local changes of formation (and thus changes in resistivity or other measurement) may require a relatively high resolution to model the variety of data, whereas large homogeneous regions can be represented by relatively large blocks of data without loss of quality. As a result, the composite models disclosed herein may have relatively thin and relatively thick layers (with thin layers having fine detail and thick layers being more homogenous). Furthermore, near the borehole, the data and thus the model is determined with greater certainty which, in turn, requires a higher resolution.

[0042] The processing and modeling processes described herein may be performed whiledrilling. That is, as a borehole is drilled through the earth, one or more sensors and / or systems (e.g., BHA 116 and associated tools) may be configured to collect data related to the formation that is being drilled through and surrounds the borehole. As the borehole is drilled, the borehole will extend or increase in axial length, and will typically have a relatively fixed diameter based on the disintegrating device 118 or drill bit and any components of the BHA 116. As the borehole 104 is increased in length, the sensors and other tools may collect data for interval sections of the borehole. As such, the borehole 104 may be modeled based on sets or collectionsof interval data. The interval data may be obtained by collecting data using the sensors of a downhole tool or system, such as resistivity data, acoustic data, NMR data, or the like during a drilling operation.

[0043] In one non-limiting example embodiment of the present disclosure, inversion of borehole measurement data (e.g., resistivity measurements) is performed interval-by-interval while-drilling. In such a process, a model of an interval may be obtained for a section or interval of data associated with a length of drilling along the borehole 104. That is, the model of the interval may have length associated with a drilled distance along a portion of the intended borehole trajectory. The individual model(s) may be of a class, for example and without limitation, such as one-dimensional layer cake, two-dimensional parametric, pixel-based, etc. Each model will provide a best-fit representation of formation properties that are to provide a minimum deviation between the measured data obtained during the drilling operation and synthetic data (i.e., calculated data that a hypothetical measurement tool would measure in a formation having said formation properties), such that the model is a best representation of the downhole conditions and properties. The synthetic data may be obtained in advance of the drilling operation, such as based on other wells in the region, based on information from surface measurements obtained prior to drilling, projected synthetic data generated in a lab based on anticipated formation distribution, or the like. That is, the modeling performed to obtain the models of each drilling interval may be a result of the real-world data collected downhole and the synthetic data that is expected or anticipated to be obtained. The goal is to select a model with a best-fit between the real-world data and the synthetic data, with the model providing a representation of the earth and downhole formation properties.

[0044] The resulting best-fit model is then associated with the drilled interval of the borehole 104. The drilled interval of the borehole 104 is a length interval of the borehole 104 and thus has an axial length in a direction of drilling. In accordance with some non-limiting embodiments, the interval of the model may be the same interval as the data interval. That is, the length or interval of the model may be set to be the length or interval of the borehole 104 from which the measurement data is collected to which the model is compared. In other configurations, the model interval may be a length or interval that is smaller or shorter in axial length along the borehole 104 than a drilled length of an interval from which data is collected. For example, the model interval may be contained within the data interval (relative to an axial length along the borehole). As a result, in some such configurations, the measured data at endsof the measured interval may be ignored or omitted from a match with the model interval. This operation or process may be repeated for sequential intervals of drilling, and thus a set of models representative of the borehole may be obtained. In configurations where the model interval is shorter than the data interval (also referred to as measurement interval), the end portions of the measurement interval that are not used for a specific model interval may be captured by one or more other / different model intervals that may have overlap with the specific measurement interval. The inversion procedure related to the models and measurement intervals may be repeated for each subsequent interval along the length of the borehole, and so on, which produces a sequence or series of models. The model intervals in the sequence are spatially sequential such that one model is next to an adjacent model or are arranged one after another along the borehole length and constitute an interval of the whole model (e.g., model of whole borehole or section of borehole of interest).

[0045] As noted above, the models can belong to different classes. For example, and without limitation, the models may be ID layer cake model, 2D parametric models, pixel-based models, 3D models, etc. In embodiments that employ layer cake models, for example, the models may have different numbers of layers from one model to the next within a sequence, or all models in a given sequence may have the same number of layers, but different boreholes or borehole intervals (as a whole) may be based on layer cake models of a different number of layers. By using the above processes of data collection, measurement, and inversion to find a best-fit model, every model of a sequence, has, at every point, a certain physical property (e.g., resistivity, such as anisotropic resistivity such as resistivity that includes horizontal resistivity and vertical resistivity).

[0046] In accordance with embodiments of the present disclosure, the modeling described above may be used to generate a composite model of the near-borehole space representative of a length of borehole 104 that is larger than any individual model of the composite model. That is, the composite model, which is formed of a series or sequence of models, may be used to illustratively or schematically model the earth formation(s) (e.g., materials, structures, faults, fractures, fluids, solids, etc.) around the region of the borehole which is drilled through the earth. In accordance with embodiments of the present disclosure, a two-step division or partitioning process may be performed. A first step is to geometrically partition the modeling into a set of geometric cells. The geometric cells may then be partitioned or aggregated based on a second step of property division. That is, once the geometric cells are generated, the cellsthereof may be separated or grouped based on one or more specific formation properties of interest. The second step may be referred to as a property-driven division and aggregation.

[0047] A process for developing a composite model of a near-borehole space in accordance with an embodiment of the present disclosure will now be described. In accordance with this example, the composite model is defined in an orthogonal curvilinear coordinate system (e.g., x, y, z) associated with a borehole. In such an orthogonal curvilinear coordinate system, the z- coordinate direction may be along the borehole 104 or in the direction of drilling of the borehole 104 (i.e., direction of trajectory); the x-coordinate direction may be perpendicular to both the trajectory and a horizontal direction and the y-coordinate direction is orthogonal to the z- coordinate direction and the x-coordinate direction to complete a right-handed Cartesian coordinate system with its origin on the borehole 104. FIG. 3 A illustrates an example of an orthogonal curvilinear coordinate system in accordance with this illustrative discussion. In FIG. 3 A, the plot 300 includes a line 302 that represents the borehole 104 or borehole trajectory. The --coordinate direction is along the line 302 and plane 304 is defined by two conditions, i.e., the line 302 is part of the plane 304 and the plane 304 is oriented perpendicular to the direction of gravity (i.e., the plane 304 is a horizontal plane). The x-coordinate direction is perpendicular to the line 302 and is antiparallel to the direction of gravity. The x-coordinate direction and the --coordinate direction together define plane 306. The y-coordinatc direction is orthogonal to the --coordinate direction and the x-coordinate direction to complete the right- handed Cartesian coordinate system. The y-coordinatc direction and the x-coordinate direction together define the plane 308.

[0048] For example, and in more detail, a selected point with coordinates (x, y, z) is defined as follows. Take the point on the trajectory (line 302) with measured depth (MD) equal to z and build the (right-handed) Cartesian coordinate system with origin at this point whose --axis is tangent to the trajectory in the direction of increasing of MD and whose x-axis is perpendicular to both the --axis and the horizontal direction (as defined by the plane 304). For definiteness, it is assumed that ex■ g < 0, where exis the corresponding unit vector in the x-coordinate direction and g is the gravity vector. The y-axis is defined uniquely by the x-axis and the --axis (i.e., the y-axis is defined as a direction normal to both the x-axis and the --axis to complete the right-handed Cartesian coordinate system). The selected point along the --axis is a point with coordinates (x, y, 0) in the constructed Cartesian coordinate system. If the borehole trajectory has moderate curvature (i.e., the curvature radius is greater than 100 m), which is always truefor real boreholes, then the coordinates of points near the borehole are defined uniquely. Each model of an interval and the composite model fills a domain that is a curvilinear parallelepiped [x0, xw] X [y0, yM] X [z0, zK] in the coordinate system.

[0049] In an example of construction of a composite model in accordance with an embodiment of the present disclosure, a drilling operation is performed to drill a section or interval of borehole 104 using a bottomhole assembly 116, disintegrating device 118, drill bit, or the like. As the borehole 104 is formed during the drilling operation, a measurement- while-drilling tool 138 and / or logging-while-drilling tool 138 may be used to collect data regarding the formation(s) 106 and material(s) through which the borehole 104 is being drilled. As the data is collected over an interval of drilling, the processes described above may be performed for each interval drilled. That is, for each section of drilling (e.g., drilled interval) a measurement interval of the same length may be obtained, with the measurement interval comprising a set of measurements taken by a tool and indicative of a property of the formation surrounding the borehole 104. Each measurement interval may be of the same length or length of measured depth (MD), although such uniform length of measurement interval is not intended to be limiting (i.e., non-uniform length measurement intervals may be employed). The measured depth (MD) is a depth or length of the borehole 104 from the earth surface or another reference point along the path of drilling. This is contrasted with true vertical depth which is a measurement of vertical depth at any given point along the borehole path. The collected data may include, for example and without limitation, resistivity data, acoustic wave velocity data, density, nuclear data, or any other physical property / characteristic of interest. For each measurement interval, a model of the measurement interval may be obtained.

[0050] The construction of the composite model begins by defining an initial domain (e.g., [x0, xw] X [y0, yM] X [z0, zK]), based on a depth of investigation of measurements taken and an interval along the borehole trajectory where the inversion results are available. The interval in the x-axis direction is [x0, xw] , the interval in the y-axis direction is [y0, yM] , and the interval in the --axis direction is [z0, zK]. Within this initial domain, the data may be divided into cells or voxels. For example, in the initial partitioning step, a primary partition may be made in every direction. The primary partitioning may be partially illustratively shown in FIG. 3A, where a set of cells 310 are formed having x, y, and z values, with a node of each cell 310 being representative of a volume of the whole cell 310. The node may be a single direction point (e.g., x, y, and z values).

[0051] In such an example, an operator or user will select or make a choice of nodes (e.g., xpx2, ••• , Xjv-t) on the interval [x0, xw], with N being a natural number. For example, a first node location may be selected based on a drilling operation or the like, and then each subsequent node may be selected based on some predetermined step or interval, such as 4 m or 10 ft. Similarly, the nodes of the interval [y0, yM] may be represented by (e.g., y1;y2, • • • , y^-r) and the nodes of the interval [z0, zK] may be represented by (e.g., z1;z2, • • • , zK-1). with M and K being natural numbers. In accordance with embodiments of the present disclosure, the partitioning of the primary partition may be uniform or non-uniform such that each cell 310 may have the same dimension in each of the x, y, and z directions, or one direction may be different from the others, or each direction may have a different length. Each combination of nodes may define a unique location in three-dimensional space and represent a location relative to the borehole (line 302), within a given interval. For example, a first cell, based on the primary partitioning may be represented as having a central point of the node (i.e., coordinates), such that a first cell may be represented by (xi, yi, zi), with the specific points representing the center of the respective cell. Geometrically, the cells of the primary partition are curvilinear rectangles [Xi, xi+1] x [y yj+i] x [zk, zk+1].

[0052] FIG. 3B illustrates an example of a geometric partitioning of cells in the x-z plane. A primary geometric cell 312 is a cell generated from the initial partitioning of a volume into individual cells based on the initial model(s). Each cell 310 of the geometric partition may represent a volume of space (e.g., volume or section of an earth formation) that may be assigned a unique formation property value (e.g., resistivity) to the entire cell (or portions or sub-cells thereof). For example, based on an inversion of formation property data and finding a best-fit model, each specific geometric cell may be assigned a single formation property value that represents the entire geometric cell. Due to the nature of downhole formations, however, the geometric cell may actually encompass more than one formation type and / or more than one distinct formation property value. That is, the geometric division may encompass or include multiple different and distinct property values within a single geometric cell. Accordingly, if a composite model is based on the geometric partitioning, the granularity of the formation may not be as accurate as desired.

[0053] With a geometric partition performed and set of primary geometric cells 312 generated or identified, based on the set of nodes in each direction, a further processing step may be performed to increase the accuracy of the modeling that represents the formation. For example,with the set of primary geometric cells 312 based on models, as described above, each primary geometric cell 312 may be divided into a number of equal geometric sub-cells 314 in each direction, as shown in FIG. 3B. In accordance with some embodiments, the geometric sub-cells 314 may be equal in number in each of the coordinate directions (e.g., equal number of subcells along the x-axis, the y-axis, and the z-axis). However, in other embodiments, the number of geometric sub-cells 314 in each direction may be different, but the geometric sub-cells 314 in a given direction are each similar, such that each geometric sub-cell 314 in a given direction is equal in size as all other geometric sub-cells 314 in that same direction. Each geometric subcell 314 may be assigned a property value based on the modeling, which may be different from the original geometric cell (e.g., primary geometric cell 312) generated from the primary geometric partitioning or may be the same. The geometric sub-cells 314 may be partitioned or subdivided again through further processing to form a set of smaller sized geometric sub-cells 316. The smallest sized geometric sub-cells may be present in close proximity to the borehole (e.g., ’-axis), and the cell size of the geometric cells may increase in distance away from the borehole.

[0054] By subdividing the primary geometric cells 312 into geometric sub-cells 314 and / or smaller geometric sub-cells 316, it may be determined that some of the geometric sub-cells 314, 316 have the same property values, while other geometric sub-cells 314, 316 may have a property value different from other geometric sub-cells 314, 316 (and / or different from the primary geometric cell 312). This secondary step may be performed as described below, by performing a property-based partitioning of the geometric cells. If multiple geometric sub-cells 314, 316 have the same property value, or a property value within some predefined threshold of variance, then these geometric sub-cells 314, 316 may be aggregated into a larger geometric cell 312, 314, which may be the same size as the primary geometric cell 312 (e.g., if all geometric sub-cells 314 match the primary geometric cell 312) or may have a size smaller than the primary geometric cell 312, but larger than the individual geometric sub-cells 314 of the first division (or similarly larger than the second division geometric sub-cells 316). This process of dividing may be further expanded and the sub-cells may be further subdivided if necessary.

[0055] At the end of the geometric partitioning, the model of the formation will be comprised of a set of various different size cells, with smaller (meaning more accurate or precise) cells located closer in proximity to the borehole (and where the sensors are for measuring data). Asthe distance between the borehole and a cell increases, the granularity of the data decreases, due to physical and / or measurement constraints. That is, cells that are close to the borehole may be relatively small in dimension, and cells that are farther away from the borehole will generally increase in cell size. Accordingly, when the geometric partitioning is completed, an intermediate model that has relatively fine cell size is close to the borehole and more coarse cell sizes are present at greater distances from the borehole. This intermediate model may be further enhanced through analyzing property data of the cells and thus a more accurate cell division may be achieved based thereon, in accordance with embodiments of the present disclosure.

[0056] Referring now to FIG. 4A, a schematic diagram 400 of cells of a modeling process in accordance with an embodiment of the present disclosure is shown. As shown, a primary partition cell 402 may be obtained from a geometric partitioning, as described above (e.g., each end cell of a geometric partitioning). That is, the primary partition cell 402 may be one geometric cell from the geometric partitioning described with respect to FIG. 3 and further described herein.

[0057] The primary partition cell 402 may be assigned or have a property value assigned to it that is based on the interval modeling obtained from the while-drilling measurements. The primary partition cell 402 may represent a three-dimensional space of a downhole or subsurface formation that is grouped together to be represented within a model. As noted, however, the three-dimensional volume represented by the primary partition cell 402 may include multiple different features and / or properties. That is, the geometric division may not account for faults, formation boundaries or formation layers, fluid zones, or other subregions and / or transition zones that occur in real world downhole formations. For example, a formation boundary may pass directly through a geometric partition cell, and without further refinement, such formation boundary may be improperly estimated in a position that is separate from the actual location that is within a given geometric cell. Accordingly, the primary partitioning may be a first step in the disclosed process related to dividing (or not) geometric cells and thus achieving a greater accuracy and / or representation of the features of the downhole formation.

[0058] The primary partition cell 402 of the primary partition may be divided into a plurality of primary division sub-cells 404. As shown, in this non-limiting illustrative embodiment, the primary partition cell 402 is subdivided into six primary division sub-cells 404, represented as primary division sub-cells 404a-404f. Each primary division sub-cell 404a-404f may beassigned a formation property value (e.g., resistivity, etc.), based on the best-fit model, that is representative of the property of the smaller sized primary division sub-cell 404 as compared to the primary partition cell 402. That is, the primary division sub-cells 414a-404f represent cells that are generated from a first division of the primary partition cells 402.

[0059] Each primary division sub-cell 404 may be further subdivided into secondary division sub-cells 406 by a second division of the primary partition cells 402. For example, as an illustrative embodiment, the sixth primary division sub-cell 404f may be subdivided into secondary division sub-cells 406a-406c. It will be appreciated that each primary division subcell 404a-404e may be similarly subdivided into a set of secondary division sub-cells 406. Each secondary division sub-cell 406 may be assigned a property value. This process may be performed iteratively through further divisions resulting in tertiary sub-cells, quaternary subcells, etc. At each iteration and subdivision, the set of sub-cells may be compared. If all values of a given division of sub-cells are the same or within a predetermined threshold variance, the sub-cells may be reaggregated into a single larger sub-cell (or cell, such as back to a primary partition cell 402).

[0060] For example, if each of the primary division sub-cells 404 is the same with respect to a property of interest, then the primary division sub-cells 404 may be recombined or aggregated into a combined cell (e.g., recombined back to the primary partition cell 402). Similarly, if further subdivisions result in sub-cells (secondary, tertiary, etc.) having the same value or values within a predetermined threshold variance, then the sub-cells may be recombined into at least one level higher (e.g., a number of secondary division sub-cells may be rejoined to form a single primary division sub-cell). When it is determined that further divisions are unnecessary, because the sub-cells have the same property value, the formed primary partition cell or sub-cell may be referred to as a terminal cell. A terminal cell is a cell that represents a volume of a formation that has substantially the same physical properties (relative to a specific property of interest).

[0061] Referring now to FIG. 4B, a cell structure 408 of cells and sub-cells are shown as assembled into an illustrative schematic model of a portion of a formation. The cell structure 408 illustrates a primary partition cell 410 (which may be equivalent of a geometric cell), a set or group of primary division sub-cells 412, and a set or group of secondary division sub-cells 414. The cells and sub-cells 410, 412, 414 may be generated using the process described above with respect to FIG. 4A. That is, each of the cells and sub-cells 410, 412, 414 may have startedfrom a set of geometric cells (or all primary partition cells 41) may have be property-driven partitioned to form terminal cells that do not require addition partitioning and are distinct enough relative to a property of interest to not have such cells be combined together. Stated another way, each of the cells and sub-cells 410, 412, 414 do not benefit from further divisions and thus the larger terminal cells (e.g., primary partition cells 410) may represent a larger region, space, or volume of the formation as having a substantially uniform physical property.

[0062] Each of the cells and sub-cells 410, 412, 414 represents a region, space, or volume of a downhole formation that may be assigned a single representative value with respect to a formation property (e.g., resistivity, or other physical property). Each cell and sub-cell 410, 412, 414 may have a different property value than adjacent cells and sub-cells 410, 412, 414 (e.g., even between adjacent primary division sub-cells 412 and / or secondary division sub-cells 414). Each of the cells and sub-cells 410, 412, 414 has a generally uniform shape, with the specific dimensions being different at each level of division, with the primary partition cells 410 representing the largest individual portions of the formation having relatively uniform properties, the primary division sub-cells 412 represent smaller regions, and the secondary division sub-cells 414 represent even smaller regions, and so on. For example, if tertiary division sub-cells were generated in the process related to forming the cell structure 408 of cells and sub-cells, such tertiary division sub-cells would represent smaller regions than the secondary division sub-cells 414. It should be noted that for the discussion of this disclosure, that all cells, primary sub-cells, secondary cells, etc. are called “cells”. Additionally, if a cell is further divided, it still remains a cell. That is, for example, in FIG. 4B, there are shown four (4) primary partition cells 410, twelve (12) primary sub-cells 412, and twelve (12) secondary division sub-cells 414, all / each of which may be referred to as “cell.” In other words, some cells may comprise two or more cells (i.e., sub-cells).

[0063] Although illustratively shown in FIGS. 3A-3B and 4A-4B as two-dimensional blocks (square in shape), such representation is not intended to be limiting. For example, each cell / sub- cell of a cell structure in accordance with an embodiment of the present disclosure may be a three-dimensional structure (e.g., cubic or the like), such as voxels. Further, although the cells and sub-cells are illustrated as squared (e.g., equal length sides), such geometry is not intended to be limiting. For example, in a two-dimensional space, the cells / sub-cells may take any geometric shape, but may, preferably be squares, rectangles, triangles, or other polygons. Further, in cylindrical coordinate systems and / or spherical coordinate systems, the cells / sub-cells may take the shape of cylindrical shells, spherical shells, or the like, and have related geometric cells. A preference may be given toward polygons such that all space of a formation is captured within a cell or sub-cell of a measurement or model interval. If the cells / sub-cells take a circular shape, there may be spaces between adjacent circles that is not captured by such circular shapes. In such configurations, overlapping cells may be employed. However, due to the modeling and estimation nature of this modeling, such circular shapes may be usable. In three-dimensional space, similar considerations may be made to ensure that the entire formation over a given interval is represented within one or more cells or sub-cells.

[0064] Referring now to FIG. 5, a plot 500 of cell structures as generated in accordance with embodiments of the present disclosure is shown. The plot 500 is illustrated as extending along a trajectory 502. The trajectory 502 represents a central axis or centerline passing through a drilled borehole within or through a downhole formation. Based on the above-described cell structure process, the plot 500 may be generated by assembling and / or arranging the cells and sub-cells about the trajectory 502, thus resulting in a representation or composite model of the downhole formation(s) and features. As shown, the plot 500 includes cell structures having primary partition cells 504, primary division sub-cells 506, and secondary division sub-cells 508. As the cells reduce in size (or are further divided), a more precise or accurate the representation of the formation is achieved. The plot 500 may be illustrative of an example of the formed final composite model that is generated in accordance with the teachings herein. That is, the plot 500 and the cells 504-508 may represent a composite model achieved through geometric partitioning and then property-driven partitioning.

[0065] As shown, the secondary division sub-cells 508 may be present or generated where features or changes in formation properties occur, such as between different formation materials (e.g., rock types), at faults or formation beds, or the like. The primary division subcells 506, one step larger than the secondary division sub-cells 508, may represent relatively complicated divisions between downhole formations and materials, but with less variability or changing occurring than with the secondary division sub-cells 508. The secondary division sub-cells 508 may provide more detail at locations where the formation properties change more rapidly or frequently. The primary partition cells 504 represent sections of substantially uniform physical properties (e.g., similar or uniform rock types, no faults, or the like). The primary partition cells may be based on geometric cells (i.e., no change from a geometric cell) or may be generated by aggregating geometric cells into a larger cell. As a result, larger primarypartition cells 504 may be generated or present along the trajectory 502, even if the geometric partitioning resulting in relatively smaller cells to initially be generated.

[0066] As described above, each cell or sub-cell 504, 506, 508 of the plot 500 may be obtained from a best-fit model over a given interval along the trajectory 502. A series of intervals along the trajectory 502 is used to generate a composite model that represents a section of the borehole and the surrounding earth formation(s). In some embodiments, the section of borehole may be the entire length of the borehole from the surface to a distal end (e.g., at a drill bit during a drilling operation) or may be some sub-section or portion thereof. The composite model of the present disclosure represents a length along the borehole trajectory of interest and may be formed of one or more individual models taken over intervals that are equal to or less than the total length of the composite model along the length of the trajectory. In one nonlimiting example, the plot 500 may represent such composite model as output from processes as described herein.

[0067] The above-described illustrations and description represent the illustrative output of a process in accordance with an embodiment of the present disclosure. The mathematical construction of the composite model will now be described.

[0068] During drilling, a series or set of models (M1;M2, ••• , ML) is obtained. Each modelrepresents a model of a drilled interval or a portion thereof. The modelsare selected as best- fit models for a particular drilled interval. The drilled interval is a length of borehole over which data is collected in a while-drilling manner. Drilled intervals of modelsM2, ••• , MLmay be overlapping or separated. The data is then analyzed to determine the best-fit model that represents the earth formation surrounding the borehole for the particular drilled interval. The best-fit modeling may be combined with a geometric partitioning, to process the cells from the geometric partitioning with a property-driven partitioning, which can result in a highly accurate composite model of a downhole formation surrounding a borehole.

[0069] For example, a given modelmay represent a best-fit model of data that matches measured data obtained over a specific measured interval during a drilling operation. The model interval (e.g., length) may be equal to or less than a length of a drilled interval over which data is collected. Each modelmay be associated with a model interval [abbi] along the trajectory of the borehole and is defined in some neighborhood of the measured interval along the drilling trajectory and in a transverse direction. In embodiments where a physicalproperty of interest is resistivity, it will be appreciated that the resistivity models applied for inversion of logging-while-drilling (LWD) electromagnetic (EM) measurements (e.g., layer cake models, other parametric models, or pixel-based models) are defined in a larger three dimensional space around the borehole but make sense only in some neighborhood of the borehole in view of the finite depth of investigation of the EM tools.

[0070] A set or series of model intervals [at, bt] may be arranged one after another such that, in the --axis direction, each model interval [abbi] abuts or overlaps an adjacent model interval [abbi] . In some embodiments, there may be no overlapping between the adjacent model intervals. For example, a first model interval [a(, bt] may be arranged adjacent with and not overlap with a second model interval [a[+1, b(+1]. That is, in some embodiments, each model interval may be unique and represent a unique set of measured data and thus may represent a unique portion of the formation surrounding the borehole. In other embodiments, the model intervals may overlap. For example, a portion of the interval length of model interval [a bt] may share a portion or overlap with a portion of an adjacent model interval [a[+1, b(+1].

[0071] The domain of the composite model is defined as follows. In the transverse direction, the square [x0, xw]X[TO- TM]=[—D, D] X [—£), £)] is taken, where D is the depth of investigation (e.g., measured depth, along the borehole trajectory from the surface) of the measurements from which the models were obtained. Along the borehole, the interval [z0, zK] is the minimal interval that contains the intervals of all interval models. That is, the interval [z0, zK] represents the length (z direction) of the composite model in the --axis direction along the trajectory of the borehole.

[0072] In a non-limiting example, for a composite model based on formation property measurement obtained while-drilling, the formation property of the composite model at an arbitrary point [x, y, z] in the domain [x0, xw] X [y0, yM] X [z0, zK] is defined as follows. For each interval model, the weight of the individual interval modelin the composite model is defined depending on a distance from a point (e.g., origin, selected point along the borehole trajectory, etc.) to the interval of the model

[0073] In this definition of the weight of a given model Mt, w(z) is a decreasing non-negative function defined for positive values of - As such, in this example, the formation property is defined as:where pt(x, y, z) is the formation property in the model. It will be appreciated that different averaging formulas may be applied, without departing from the scope of the present disclosure. Such different averaging may be different based on the same formation property (e.g., resistivity) or the specific averaging and weighting may be based on the specific formation property of interest, as will be appreciated by those of skill in the art.

[0074] As a first step, the region of interest along the borehole is partitioned into geometric cells, as described above. As a result, small geometric cells maybe present close to the borehole and the cell size may gradually or in a step-wise manner increase in size as the distance from the borehole increases. During the geometric partitioning, a geometric criterion may be applied to potentially subdivide or partition a given geometric cell. For example, if the size of a geometric cell is greater than a threshold or predetermined size criteria and / or the geometric cell is within a threshold or predetermined distance from the borehole, the geometric cell may be processed with a geometric division. When the geometric division and processing is complete, each cell may be designated as a primary partition cell to be processed with a property-driven partitioning.

[0075] In the property-driven partitioning, if a primary partition cell of the initial division satisfies a predetermined or predefined geometric criterion or requirement (e.g., size of cell), the primary partition cell may be divided into sub-cells. For example, a primary partition cell may be analyzed, and if the geometric criterion is satisfied, the analyzed primary partition cell may be subdivided by a first division into primary division sub-cells, as described above. For example, and without limitation, the geometric criterion may be related to the size of the cell in questions. If the size of the primary partition cell is determined to be greater than a predefined, predetermined, or threshold value and / or the position of the primary partition cell is close (in distance / proximity) to the borehole, then property-driven partitioning may be performed. If one or both of these criteria, in this example, are satisfied, then the primary partition cell may be divided into a set of primary division sub-cells. If the resulting primarydivision sub-cells also meet the geometric criterion (or some other criterion), then these primary division sub-cells may also be divided into secondary division sub-cells. This process may be performed recursively until the cells or sub-cells no longer satisfy the criterion for division or partitioning. The geometric division makes it possible to reveal the features of the composite model in the area where such divisions are important and such divisions can be determined with high certainty. That is, smaller and smaller sub-cells may be generated by this process to achieve a desired level of accuracy in the composite model to represent the downhole formation, conditions, etc. If a cell (e.g., primary partition cell) or sub-cell (e.g., primary division sub-cell, secondary division sub-cell, etc.) does not satisfy the criterion for further division, then the cell / sub-cell may be designated as a terminal cell.

[0076] Accordingly, after the property-driven division is performed, each of the cells and subcells of the composite model are indicated as terminal cells. A terminal cell, as discussed above, is a cell or sub-cell that does not justify further division because each portion of the cell / sub- cell is the same or substantially similar with respect to a property of interest, and thus further dividing would result in a set of sub-cells that are each of the same or substantially similar physical property. The resulting set of terminal cells may then have a formation property value set for the individual cells / sub-cells as the formation property at the center of the respective cell. With each cell / sub-cell having a defined physical property, the composite model may be completed with a representation of the downhole formation and features thereof.

[0077] Referring again to FIG. 5, an example of a portion of a composite model (plot 500), as generated by the embodiments described herein is shown. A borehole axis (e.g., direction) is indicated by line 502. A set of cells are indicated surrounding the line 502 with primary partition cells 504, primary division sub-cells 506, and secondary division sub-cells 508 illustrated. The sections represented by the primary partition cells 504 are sections of formation that are generally similar in nature and did not require addition divisions or were aggregated from groups of smaller geometric cells and / or determined to be aggregated based on a property- driven partitioning operation. Accordingly, the primary partition cells 504 may not have satisfied the geometric criterion or were aggregated into terminal cells having the size and shape of the primary partition cells 504. It will be appreciated that each primary partition cell 504 may have a unique formation property value. Stated another way, the primary partition cells 504 may not be identical to each other, but rather merely represent regions of substantially uniform formation properties within the respective regions of the primary partition cells 504.

[0078] In regions that have variable or changing physical properties, the geometric criterion may be satisfied (e.g., close to the trajectory 502 and / or of a sufficiently large cell size), resulting in the division of some primary partition cells 504 into the primary division sub-cells 506. Similarly, the primary division sub-cells 506 may be different from adjacent primary division sub-cells 506 and / or groups of primary division sub-cells 506 may be different from other groups of primary division sub-cells 506. Finally, in this example, if the primary division sub-cells 506 satisfy a geometric criterion (e.g., size and / or proximity to trajectory 502), the primary division sub-cells 506 may be divided again into the secondary division sub-cells 508, with similar considerations thereof. The result is a composite model (plot 500) that illustrates features of a downhole formation that has fine detail where necessary to indicate changes, and less fine detail where the formation is uniform, and thus does not require the fine detail of the primary division or secondary division sub-cells 506, 508.

[0079] Referring now to FIG. 6, a flow process 600 in accordance with an embodiment of the present disclosure is shown. The flow process 600 may be used to generate a composite model aggregated from a collection of interval models and provide an accurate representation of the earth formations surrounding a borehole. The flow process 600 may incorporate features shown and described above.

[0080] At block 602, a drilling operation is performed. The drilling operation may be any type of drilling operation through the earth and may include a disintegrating device 118 configured to destroy material of the earth and form a borehole 104 therein. The disintegrating device 118 may be a drill bit although other types of systems and devices may be used to destroy and remove material to form a borehole 104. The disintegrating device 118 may be disposed on the end of a string 102 of tubulars or otherwise deployed into the formed borehole 104. Other tools may be arranged uphole from the disintegrating device 118 and arranged along or on the string 102. The tools may be part of a BHA 116 or the like and may include, without limitation, logging and / or measurement tools 138 for while-drilling measurement and data collection.

[0081] At block 604, the tools arranged downhole may be used to collect data regarding the formation and materials surrounding the borehole 104. For example, logging-while-drilling and / or measurement- while-drilling sensors and tools 138 may be used to collect data of the surrounding formation 106 as the drilling operation is performed. The logging-while-drilling and / or measurement- while drilling sensors and / or tools 138 may include nuclear magnetic resonance (NMR) tools, resistivity tools, gamma (density) tools, pulsed neutron tools, acoustictools, and various others as will be appreciated by those of skill in the art. The data collected may be representative of various formation properties associated with the specific tool, such as density, resistivity, porosity, etc. the data collected may be separated into intervals. For example, each interval may be a specific distance of drilling, and the data may be representative of the formation information surrounding the borehole 104 along the specific drilled interval.

[0082] At block 606, a set of interval models are generated. That is, for each drilled interval, the data collected is processed (e.g., inverted by an inversion) to generate an interval model representative of the drilled interval and its surrounding formation. As such, each drilled interval may be assigned one (or more) interval models. Each interval model may be different from adjacent (along the borehole) interval models.

[0083] At block 608, the interval models are aggregated and stacked to form an initial composite model. The initial composite model is a collection or set of the interval models arranged sequentially along the length of the borehole 104 (full borehole or a portion thereof). The initial composite model will thus have modeled data for points along a length of borehole 104 that covers one or more of said drilling intervals. The initial composite model will be formed of a collection of cells or voxels, generally referred to herein as cells. Each cell represents a portion or volume of the formation 106 surrounding the borehole 104 and may be two-dimensional or three-dimensional. Each cell will have a value assigned to it based on the interval model from which it is derived at block 606. That is, in the formation of the composite model at block 608, the interval models of block 606 are used to assign each cell a value of a particular formation property of interest (e.g., density, resistivity, porosity, etc.). As a result, the initial composite model is formed of a set of cells that represent the formation 106 surrounding the borehole 104, and each cell has a specific value of a specific formation property assigned thereto. The value of the cell may be set as the center point of the cell or may be the average of the interval model over the given cell, and then such average value is set at the center point of the cell. It will be appreciated that other processes or mechanisms of assigning the value of each cell may be employed without departing from the scope of the present disclosure. However, the result of block 608 is the aggregation of the models generated at block 606 such that all cells of the initial composite model have a value assigned thereto. As such, an initial composite model may be output from block 608.

[0084] At block 610, geometric partitioning is performed on the initial composite model generated at block 608. That is, the data obtained and aggregated into the initial compositemodel may be distributed over a set of cells that are geometrically assigned along the borehole (or trajectory thereof). The information of the initial composite model is then assigned to each respective geometric cell, such that each geometric cell provides a representation of a region of a downhole formation. As discussed above, during the geometric partitioning, cells are formed in a sequence around the borehole. Due to the nature of the information obtained to generate the initial composite model (blocks 604-608), the geometric cells closest to the borehole will be the smallest in size, and then have the finest detail associated therewith. As the distance increases in a direction away from the borehole (e.g., normal to a borehole trajectory), the cell size of the geometric cells will increase.

[0085] In the geometric division of block 610, if a geometric cell of the initial geometric division satisfies some geometric criterion, for example, its size is greater than a certain value and / or it is close to the wellbore, then the geometric cell is divided into a number of equal geometric sub-cells in each direction. If the resulting geometric sub-cells also meet the geometric criterion, then these geometric sub-cells are also divided (recursively). The geometric division of block 610 makes it possible to reveal the features of the model in the area where such features are important and can be determined with high certainty. After the geometric division, some of the initially formed geometric cells are designated as terminal because they did not satisfy the geometric criterion. In contrast, the geometric cells that satisfy the geometric criterion are divided into geometric sub-cells which in turn may be further divided. For all terminal cells, the formation property value is defined as the formation property at the center of the respective terminal cell and the region of formation represented thereby.

[0086] At block 612, the geometric cells are further processed by performing a property-driven partitioning. These initial geometric cells are all primary partition cells and represent a partitioning of the data obtained downhole using the interval models. The collection of primary partition cells is reviewed to determine if all cells are terminal. If the cells are all terminal, the process will move to block 614 and output a final composite model that is representative of the section of borehole encompassed by the composite model. However, it is initially assumed that all primary partition cells are not terminal, and thus each primary partition cell (formerly a geometric cell) will be analyzed to determine if such primary partition cell should be subdivided or aggregated with adjacent cells. Accordingly, as an initial step, each cell may be designated as non-terminal. During the property-driven partitioning of block 612, each nonterminal cell is divided into a number of sub-cells that occupy the same space as the undividednon-terminal cell. That is, a collection of sub-cells is generated for each non-terminal cell, with the sub-cells, as a whole, representing the same region, space, or volume as the non-terminal cell from which they are subdivided.

[0087] In the property-driven partitioning of block 612, each sub-cell that is generated from a prior larger cell (e.g., primary partition cell, or further divisions) will be analyzed to determine if the sub-cells satisfy one or more criteria. If the cells are all within a certain threshold or are substantially similar, the sub-cells may be aggregated back into the prior complete cell. If the cells are aggregated, the aggregated cell may be designated as a terminal cell. Alternatively, if even one sub-cell is sufficiently different from all other sub-cells of a given non-terminal cell, then the aggregation is not performed, and the sub-cells are then kept as-is. In accordance with some embodiments, these separated cells will not be designated as terminal cells. Rather, the process will be iteratively performed to inquire whether all cells are terminal or not. In this example, if some sub-cells are divided out and not indicated as terminal and an analysis of the sub-cells will be performed again. As such, block 612 may be recursively performed until all cells are designated as terminal cells.

[0088] In the property-driven partitioning the procedure may refer to a division criteria and / or an aggregation criteria, to determine if a cell should be sub-divided or multiple cells (or subcells) should be aggregated. The division criterion (DC) is formulated for terminal cells (which may be a primary partition cell, a sub-cell, or further divisions thereof). The terminal cell undergoes a trial division by Nx, Ny, Nzparts in the respective directions. The formation property is evaluated at the centers of the new sub-cells of the trial division. If the difference between these values is greater than a certain threshold and the cell size is greater than a certain threshold, then the cell is said to meet the Division Criterion and will be divided into sub-cells based on the trial division. Otherwise the formation property of the cell is set to the average formation property of the sub-cells which are not divided, and thus the cell remains terminal.

[0089] Additionally, an aggregation criterion (AC) may be used if all sub-cells of a cell are terminal and variation of the formation property between the sub-cells is less than a certain threshold. In this case, the AC will indicate that the sub-cells of the cell is said to meet the AC and the sub-cells will be aggregated or joined together to form a larger cell therefrom. After this aggregation of the sub-cells, the cell itself becomes terminal and the formation property is set to the average formation property of the sub-cells.

[0090] When no further divisions and / or aggregations are necessary and all cells / sub-cells are designated as terminal, then the output of the final composite model performed at block 614. The may final composite model be a displayed graphically or may be arranged as a set of data that is designated as complete and the data may be transmitted to the surface for additional processing (e.g., to take the transmitted data and generate a graphical display or the like).

[0091] The flow process 600 may be performed entirely downhole and during a drilling operation. That is, in real time, data may be collected and processed and a composite model may be generated. In such configurations, the output of the final composite model will be formed of sets of cells of differing sizes, with coarse or large cells used for parts of a formation having generally uniform properties, and small or more fine cells only being present in locations where high definition and distinction is necessary (e.g., at bed boundaries, faults, changes in materials, etc.). As a result, the total data size of the final composite model may be less than if all cells were of a small size to provide the detail required. As a contrast, such a process results in a model that includes relatively large cells (low resolution) for regions that do not require higher resolution, and then in areas that require higher resolution, the cells may be divided into sub-cells to provide the high resolution necessary for detailed information to be transmitted.

[0092] Referring now to FIGS. 7A-7B, a flow process 700 for generating a composite model in accordance with an embodiment of the present disclosure is shown. FIG. 7A represents a flow process 700 for generating a composite model (e.g., starting at block 612 of flow process 600) and FIG. 7B illustrates a subroutine or subprocess of the flow process 700. As an initial step, as shown at block 610 of flow process 600, a geometric partition is obtained, as described above (e.g., blocks 602-610). As noted above, some of the geometric cells may be designated as terminal cells at the geometric partitioning step, while other cells may not be labeled as terminal based on the geometric criterion. However, every portion of the modeled subregion is represented by one or more cells wherein one of these cells is labeled as terminal based on the geometric criterion. The flow process 700 may be illustrative of an example of the property- driven partitioning of the present disclosure, although other processes may be employed without departing from the scope of the present disclosure. As noted above, at the conclusion of the geometric partitioning each geometric cell may be relabeled as a primary partition cell, although such terminology is merely for clarity of processes and is not intended to be limitingon the specific nature of a given cell. Rather, the term primary partition cell is used to reference the initial step of the property-driven partitioning.

[0093] The primary partition is formed of a set of primary partition cells that are derived from the geometric partitioning of the initial composite model. The primary partition cells are obtained from inversion of measured data during a drilling operation and finding a best-fit model for each interval and dividing the interval into the set of primary partition cells, with each primary partition cell representing a volume, space, or portion of a formation around a borehole. Because the primary partition cells are derived from the geometric partitioning, the set of primary partition cells of the process are not identical. That is, some of the primary partition cells may be volumetrically larger or smaller than other primary partition cells, based on the geometric divisions performed during the geometric partitioning (e.g., block 610 of flow process 600). To improve the resolution of the initial composite model beyond the improvements provided by the geometric partitioning, the flow process 700 (e.g., property- driven partitioning at block 612 of flow process 600) may be performed to subdivide the primary partition cells to obtain more precise model data, and thus the accuracy of a final composite model as representative of real-world downhole conditions may be obtained.

[0094] As described herein, FIG. 7A is illustrative of a procedure referred to in this description as the property-driven partitioning. For every primary partition cell of the primary partition, the cell may be processed using a process referred to as Procedure A. The flow process 700 may call flow process Procedure B indicated by block 712 which is shown in FIG. 7B which may recursively call Procedure A. The procedures refer, in part, to the Division Criterion (DC) and Aggregation Criterion (AC), with such criterion as defined in this disclosure.

[0095] At block 702, a cell from the geometric partitioning is selected as a primary partition cell of the primary partition and the selected primary partition cell is investigated. If, at inquiry 702, it is determined that the selected primary partition cell is a not a terminal cell (e.g., not designated as terminal during the geometric partitioning), the process 700 proceeds to inquiry 706. At inquiry 706, an inquiry is made to determine if the cell output from inquiry 702 meets the AC. If yes, the sub-cells of the selected primary partition cell are aggregated back into the cell from which they were derived (block 708) and the aggregated cell is designated as a terminal cell and is then finalized for entry as part of the final composite model (block 710). If the cell does not meet the AC, then the sub-cells are not regrouped, and rather are kept separate as distinct sub-cells.

[0096] At block 704, if the cell does not meet the AC at block 706, Procedure A is then started / re-started for all sub-cells of the non-terminal primary partition cell. That is, first, for each of the sub-cells of the non-terminal cell (e.g., non-terminal from the geometric partitioning) the inquiry 702 is made to determine if said sub-cell is terminal or not. For each of the sub-cells that is not terminal, inquiry 706 is to be made if the sub-cell meets the AC. This recursive process proceeds until all cells are designated as terminal or meet the AC.

[0097] The AC of block 706 is employed if all sub-cells of a cell (in the recursive partitioning) are designated as terminal cells and variation of the value of the formation property between the terminal cells is less than a certain threshold. Under such condition, the cell (or sub-cell) is said to meet the AC (“yes” at block 706) and the sub-cells of the partitioning will be aggregated or rejoined together to form the original cell from which they were partitioned (block 708). After this step (Aggregation), the cell itself becomes a terminal cell and the formation property value of this terminal is set to the average formation property of the sub-cells that were determined during the trial partition step.

[0098] If, at block 702, it is determined that the cell being analyzed from the geometric partition was designated as a terminal step during the geometric partitioning, then flow process 700 enters block 712. Referring to FIG. 7B, in Procedure B (block 712), a trial division is made of the terminal cell, at block 714. At block 714, each terminal geometric cell may be preliminarily divided into sub-cells, and a formation property for each of these preliminary sub-cells may be calculated for the center of each sub-cell. Then, at block 716, each of these preliminary sub-cells will be compared against the Division Criterion (DC). The Division Criterion (DC) is formulated for all terminal geometric cells. Under the Division Criterion, the terminal geometric cell (and thus a terminal primary partition cell) may undergo a trial division by Nx, Ny, N- parts in the respective directions, to form a set of sub-cells that occupy the space defined by the cell (or sub-cell) from which they are divided or partitioned (i.e., from the terminal geometric cell). The formation property (e.g., resistivity) is evaluated (e.g., evaluated by inversion) at the centers of the new sub-cells based on the initial composite model. If the difference between these values relative to each other is greater than a certain threshold and the cell size is greater than a certain threshold, then the cell is said to meet the Division Criterion and will be divided (yes at block 716). Otherwise (no at block 716), the formation property of the cell is set to the average resistivity of the sub-cells. That is, if each cell is within a certainrange of other cells of the division, then each of the cells is assigned the same formation property value.

[0099] Accordingly, if the preliminary sub-cells satisfy the DC (yes at block 716), then the sub-cells are kept separate as distinct sub-cells (block 718). At this stage, each of these subcells may then be passed through Procedure A (block 720; FIG. 7A). If, however, at block 716, the sub-cells do not meet the DC, then the preliminary division is removed, and the cell is not subdivided. The formation property is set for the non-divided cell (block 722) based on the average formation property value of the sub-cells from the trial partition. These cells / sub-cells may then be designated as terminal cells (block 724). Whether the geometric cell is processed through block 704 (non-terminal geometric cell) or block 712 (terminal geometric cell), the output will be a terminal property-driven cell of an optimized size, position, and property value. The final property-driven terminal cells are output from blocks 706, 708, and 712 and are collected to generate the final composite model at block 710. The optimization is achieved through running the flow processes 600, 700, described herein, which results in a final composite model that comprises cells and sub-cells of various sizes, locations, and property values, based on the actual downhole conditions, with smaller cells being representative of finer details, such as around the borehole and / or at locations of changes in a downhole property (e.g., faults, bed, boundaries, etc.).

[0100] Based on the above, a process is provided for generating a composite model of a downhole formation having different levels of detail, where sections of formation having generally uniform properties are represented by larger cells, and areas where changes in formation properties occur, the cells may be smaller and finer to provide sufficient detail of the local changes in formation properties. As such, a collection of data (cells and sub-cells) may be generated that provides an accurate representation of a formation and downhole conditions with a mixture of different size data blocks. The different size data blocks allow for a total reduction in data / bandwidth while maintaining a high level of detail where appropriate.

[0101] Upon completion of the modeling, and obtaining the best-fit model for the final composite model, a steering operation may be modified, updated, established, or performed to drill in a desired direction of drilling based on the best-fit model for the final composite model. That is, as the modeling and processing is performed, a preferred path or trajectory of drilling may be obtained based on the best-fit model for the final composite model, which can then be used to generate informed directional drilling decisions. Stated another way, in accordance withsome embodiments of the present disclosure, an optimized drilling trajectory or steering may be determined based on the processes described herein. As such, improved drilling operations may be achieved via implementation of embodiments of the present disclosure.

[0102] FIG. 8 illustrates a partial final composite model 800 of a downhole formation. The data of FIG. 8 is similar to that of FIG. 5, with a trajectory 802 representing a central axis or centerline passing through a drilled borehole within or through a downhole formation. As shown, different formations 804, 806, 808, 810, 812 may be identified in the composite model 800. Generally, the formations 804, 806, 808, 810, 812 may be represented by relatively large cells (or voxels) for the majority of their volume. However, where the different formations 804, 806, 808, 810, 812 are adjacent to each other, a finer granularity of data may be required, and thus the smaller sub-cells (primary division, secondary division, etc.) may be used to identify and indicate these finer detail changes in the subsurface formation. These distinctions between the various formations 804, 806, 808, 810, 812 are also illustratively shown in the plot 500 of FIG. 5. That is, the level of detail provided by the primary partition cells 504, the primary division sub-cells 506, and the secondary division sub-cells 508 may correspond to the proximity to the trajectory 802 and / or associated with changes between the different formations 804, 806, 808, 810, 812. Accordingly, the details of the downhole conditions may be accurately modeled through implementation of embodiments of the present disclosure. This may be in comparison to systems and processes that use uniformly sized cells in the modeling of the downhole conditions, and may further provide such detail while also reducing total data content by aggregation of cells that are similar in property.

[0103] Advantageously, in accordance with embodiment of the present disclosure, improvements to modeling of subsurface formation are provided. The composite modeling described herein is generated by best-fit interval models that are then assembled to form a composite model. The composite model will then be iteratively processed for each cell of the composite model. The interval models are generated from measurements that are taken during a drilling operation, with the measurements obtained over a predefined measurement interval. A best-fit model is obtained for each interval to create a set of interval models, with the interval of the interval models being equal to or smaller than a measurement interval. Each interval model is then stacked with all other interval models to generate a preliminary composite model. The preliminary composite model is then divided or partitioned into cells. Each cell of the preliminary composite model is analyzed to determine if it is a terminal cell (no furtherdivisions required) or if the cell should be subdivided. A terminal cell represents a region of uniform physical property. Each of the subdivided cells is then analyzed, and the sub-cells may be terminal cells, or may be further subdivided until terminal cells are obtained. A final composite model is formed based on the determination of all cells of the composite model being terminal cells.

[0104] Accordingly, a composite model comprising a set of cells (or voxels) may be generated that has cells of different sizes, which can provide advantages to data transmission from downhole tools to a surface tool or system. Advantageously, the described operations and processes may be performed entirely downhole or a combination of downhole and surface processes. Further, embodiments of the present disclosure may be partially or wholly performed downhole during a drilling operation. That is, during active drilling, and for each interval drilled, the processes described herein may be used and a composite model of the formation may be generated. Advantageously, the processes described herein can provide for a model and representation of features of a near-wellbore space and use moderate computer memory for storage due to the partitioning and cell generation described herein.

[0105] Set forth below are some embodiments of the foregoing disclosure:

[0106] Embodiment 1: A method for modeling a downhole formation, the method comprising: drilling, with a drill string, a drilling interval of a borehole through the downhole formation; obtaining measurement data for at least one measurement interval along the borehole; generating an initial composite model for a predefined region associated with the at least one measurement interval; calculating a best-fit model for the initial composite model based on the measurement data; performing a geometric partitioning and a property-driven partitioning of the initial composite model to generate a final composite model; and calculating a best-fit model for the final composite model based on the measurement data.

[0107] Embodiment 2: The method of any preceding embodiment, wherein the measurement data is obtained by one or more measurement tools in the drill string and the predefined region is based on a depth of detection of the one or more measurement tools.

[0108] Embodiment 3: The method of any preceding embodiment, wherein the geometric partitioning is based on a distance from the borehole.

[0109] Embodiment 4: The method of any preceding embodiment, wherein the geometric partitioning is recursively executed until a geometric criterion is met.

[0110] Embodiment 5: The method of any preceding embodiment, wherein the geometric criterion comprises a threshold cell size and wherein, if a cell is larger than the geometric criterion, the cell will be divided into multiple smaller geometric cells.

[0111] Embodiment 6: The method of any preceding embodiment, wherein the property-driven partitioning is recursively executed until a division criterion and / or an aggregation criterion is met.

[0112] Embodiment 7: The method of any preceding embodiment, wherein the geometric partitioning of the initial composite model creates a geometrically partitioned composite model and the property-driven partitioning is performed of the geometrically partitioned composite model.

[0113] Embodiment 8: The method of any preceding embodiment, wherein the property-driven partitioning comprises comparing a formation property value of two or more adjacent cells or sub-cells to determine if a variation between the compared formation property value is within a threshold value.

[0114] Embodiment 9: The method of any preceding embodiment, further comprising: steering the drill string in a direction that based on the best- fit model for the final composite model.

[0115] Embodiment 10: The method of any preceding embodiment, wherein the final composite model only comprises cells that meet a criterion that is related to one or more formation property values assigned to the cells and one or more formation property values assigned to their adjacent cells.

[0116] Embodiment 11 : The method of any preceding embodiment, wherein the measurement data is obtained during drilling of the drilling interval.

[0117] Embodiment 12: The method of any preceding embodiment, wherein the best-fit model is calculated downhole in the drill string.

[0118] Embodiment 13: The method of any preceding embodiment, wherein at least one of the best-fit model for the initial composite model and the best-fit model for the final composite model is calculated by a numeric inversion of the measurement data.

[0119] Embodiment 14: The method of any preceding embodiment, wherein the numeric inversion comprises calculating synthetic measurement data with at least one of the initial composite model and the final composite model and comparing the synthetic measurement data with the measurement data.

[0120] Embodiment 15: A drilling system comprising: a drill string configured to drill a borehole through a downhole formation; at least one sensor arranged on the drill string and configured to obtain measurement data; and a bottom hole assembly configured to perform the method of any of embodiments 1-14.

[0121] Embodiment 16: A method for modeling a downhole formation, the method comprising: obtaining measurement data for a series of measurement intervals along a borehole; calculating a best-fit model for a model interval associated with each measurement interval; generating an initial composite model based on the best-fit models; performing a geometric partition of the initial composite model to generate a plurality of geometric cells based on geometric criterion; performing a property-driven partitioning of the geometric cells based on a property-driven criterion to generate a final composite model, wherein the property- driven partitioning of the geometric cells comprises: determining if each geometric cell is a terminal geometric cell or a non-terminal geometric cell; for each terminal geometric cell, setting the region of the composite model represented by the terminal geometric cell with a formation property value of the terminal geometric cell, and assigning the cell as a terminal cell; for each non-terminal geometric cell, dividing the non-terminal geometric cell into a plurality of sub-cells, and determining if each sub-cell is a terminal sub-cell, for each terminal sub-cell, setting the region of the composite model represented by the terminal sub-cell with a formation property value of the terminal sub-cell, and assigning the sub-cell as a terminal cell; and for each non-terminal sub-cell, further dividing until each cell or sub-cell is a terminal cell and setting a respective region of the composite model with a formation property value of the respective terminal cell; and assembling a final composite model based on a set of terminal cells.

[0122] Embodiment 17: The method of any preceding embodiment, wherein a length of the model interval is equal to or less than a length of the respective measurement interval.

[0123] Embodiment 18: The method of any preceding embodiment, wherein the geometric criterion comprises a threshold cell size, wherein if a cell is larger than the geometric criterion the cell will be divided into multiple smaller geometric cells.

[0124] Embodiment 19: The method of any preceding embodiment, wherein geometric cells that are divided into sub-cells based on the geometric criterion are compared against the geometric criterion to determine if the sub-cells satisfy the geometric criterion, and if the size of the sub-cell is larger than the threshold of the geometric criterion, the sub-cell is further divided.

[0125] Embodiment 20: The method of any preceding embodiment, wherein each terminal cell has a formation property value assigned to the terminal cell, and the formation property value is set at the center of the respective terminal cell.

[0126] Embodiment 21: The method of any preceding embodiment, wherein the property- driven criterion is a comparison of a formation property value of two or more adjacent cells or sub-cells to determine if a difference between the compared formation property value is within a threshold value.

[0127] Embodiment 22: The method of any preceding embodiment, further comprising aggregating the adjacent cells or sub-cells into a single cell when the compared formation property value is within the threshold value.

[0128] Embodiment 23: The method of any preceding embodiment, further comprising separating the adjacent cells or sub-cells into separate cells or sub-cells when the compared formation property value is not within the threshold value.

[0129] Embodiment 24: The method of any preceding embodiment, wherein the formation property value is a resistivity value.

[0130] Embodiment 25: The method of any preceding embodiment, wherein the terminal cells are voxels.

[0131] Embodiment 26: The method of any preceding embodiment, wherein the final composite model is a three-dimensional representation of a downhole formation.

[0132] Embodiment 27: The method of any preceding embodiment, wherein the obtaining of measurement occurs during a drilling operation.

[0133] Embodiment 28: The method of any preceding embodiment, wherein the processing of the geometric cells occurs downhole in a downhole tool.

[0134] Embodiment 29: The method of any preceding embodiment, wherein the processing of the geometric cells occurs during the drilling operation.

[0135] Embodiment 30: The method of any preceding embodiment, further comprising transmitting the final composite model to the surface from a downhole tool.

[0136] Embodiment 31: The method of any preceding embodiment, wherein each interval model is a ID layer cake model, a 2D parametric models, a pixel-based model, or a 3D model.

[0137] Embodiment 32: The method of any preceding embodiment, further comprising storing the final composite model in memory located in a downhole tool.

[0138] Embodiment 33: The method of any preceding embodiment, wherein the best-fit model for each model interval is a model that best represents the measurement data collected over a respective measurement interval.

[0139] Embodiment 34: The method of any preceding embodiment, wherein the generating of the initial composite model comprises stacking the best-fit models in an arrangement along a borehole trajectory sequentially relative to the drilling operation.

[0140] Embodiment 35: The method of any preceding embodiment, wherein the geometric cells are curvilinear rectangles.

[0141] The use of the terms “a” and “an” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. Further, it should be noted that the terms “first,” “second,” and the like herein do not denote any order, quantity, or importance, but rather are used to distinguishone element from another. The terms “about”, “substantially” and “generally” are intended to include the degree of error associated with measurement of the particular quantity based upon the equipment available at the time of filing the application. For example, “about” and / or “substantially” and / or “generally” can include a range of ± 8% of a given value.

[0142] The teachings of the present disclosure may be used in a variety of well operations. These operations may involve using one or more treatment agents to treat a formation, the fluids resident in a formation, a borehole, and / or equipment in the borehole, such as production tubing. The treatment agents may be in the form of liquids, gases, solids, semi-solids, and mixtures thereof. Illustrative treatment agents include, but are not limited to, fracturing fluids, acids, steam, water, brine, anti-corrosion agents, cement, permeability modifiers, drilling muds, emulsifiers, demulsifiers, tracers, flow improvers etc. Illustrative well operations include, but are not limited to, hydraulic fracturing, stimulation, tracer injection, cleaning, acidizing, steam injection, water flooding, cementing, etc.

[0143] While the invention has been described with reference to an exemplary embodiment or embodiments, it will be understood by those skilled in the art that various changes may be made, and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention is not limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the claims. Also, in the drawings and the description, there have been disclosed exemplary embodiments of the invention and, although specific terms may have been employed, they are unless otherwise stated used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention therefore not being so limited.

Claims

What is claimed is:

1. A method for modeling a downhole formation, the method comprising: drilling, with a drill string, a drilling interval of a borehole through the downhole formation; obtaining measurement data for at least one measurement interval along the borehole; generating an initial composite model for a predefined region associated with the at least one measurement interval; calculating a best-fit model for the initial composite model based on the measurement data; performing a geometric partitioning and a property-driven partitioning of the initial composite model to generate a final composite model; and calculating a best-fit model for the final composite model based on the measurement data.

2. The method of claim 1, wherein the measurement data is obtained by one or more measurement tools in the drill string and the predefined region is based on a depth of detection of the one or more measurement tools.

3. The method of any of claims 1-2, wherein the geometric partitioning is based on a distance from the borehole.

4. The method of any of claims 1-3, wherein the geometric partitioning is recursively executed until a geometric criterion is met.

5. The method of claim 4, wherein the geometric criterion comprises a threshold cell size and wherein, if a cell is larger than the geometric criterion, the cell will be divided into multiple smaller geometric cells.

6. The method of any of claims 1-5, wherein the property-driven partitioning is recursively executed until a division criterion and / or an aggregation criterion is met.

7. The method of any of claims 1-6, wherein the geometric partitioning of the initial composite model creates a geometrically partitioned composite model and the property- driven partitioning is performed of the geometrically partitioned composite model.

8. The method of any of claims 1-7, wherein the property-driven partitioning comprises comparing a formation property value of two or more adjacent cells or sub-cells to determine if a variation between the compared formation property value is within a threshold value.

9. The method of any of claims 1-8, further comprising: steering the drill string in a direction based on the best-fit model for the final composite model.

10. The method of any of claims 1-7, wherein the final composite model only comprises cells that meet a criterion that is related to one or more formation property values assigned to the cells and one or more formation property values assigned to their adjacent cells.

11. The method of any preceding claim, wherein the measurement data is obtained during drilling of the drilling interval.

12. The method of any preceding claim, wherein the best-fit model is calculated downhole in the drill string.

13. The method of any preceding claim, wherein at least one of the best- fit model for the initial composite model and the best-fit model for the final composite model is calculated by a numeric inversion of the measurement data.

14. The method of claim 13, wherein the numeric inversion comprises calculating synthetic measurement data with at least one of the initial composite model and the final composite model and comparing the synthetic measurement data with the measurement data.

15. A drilling system comprising: a drill string configured to drill a borehole through a downhole formation; at least one sensor arranged on the drill string and configured to obtain measurement data; anda bottom hole assembly configured to perform the method of any of claims 1-14.

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