METHODS FOR OPTIMIZING PRODUCTION PACKER PLACEMENT IN HYDROCARBON WELLS FOR UNIFORM INFLOW PROFILE

Description

BACKGROUND

Well completion is the process of making a well ready for production or injection after drilling operations. Well completion involves preparing the bottom of the wellbore, installing production tubing and downhole tools, and other steps, such as running in and cementing a well casing. Inflow control devices (ICDs) paired with oil-swellable packers often perform water control during well completions. An inflow control device (ICD) is a passive component installed as part of the well completion to help optimize production by equalizing reservoir inflow along the length of the wellbore. A packer, also referred to as completion packer or well completion packer, is a device that is run (i.e., advanced) into a wellbore with a smaller initial outside diameter that expands to seal the wellbore after the packer is placed at a desired location in the wellbore. For example, the packer may employ flexible elastomeric elements. The packer is a key piece of downhole equipment that isolates and contains produced fluids and pressures within the production tubing string.

SUMMARY

In general, in one aspect, the invention relates to a method to perform a completion operation of a wellbore. The method includes determining a wellbore trajectory of the wellbore penetrating a reservoir, generating a grid cell set of interest surrounding the wellbore, wherein the grid cell set of interest comprises a plurality of consecutive grid cells that are penetrated by the wellbore in the reservoir, generating, from the grid cell set of interest and using a clustering algorithm, a plurality of grid cell clusters based on a grid cell position measure and a reservoir property of each grid cell, wherein each grid cell cluster corresponds to a flow compartment of the wellbore, and placing, during the completion operation and for said each grid cell cluster, a packer at a starting position and an ending position of the corresponding flow compartment.

In general, in one aspect, the invention relates to a data analysis system to facilitate a completion operation of a wellbore. The data analysis system includes a computer processor and memory storing instructions, when executed by the computer processor comprising functionality for determining a wellbore trajectory of the wellbore penetrating a reservoir, generating a grid cell set of interest surrounding the wellbore, wherein the grid cell set of interest comprises a plurality of consecutive grid cells that are penetrated by the wellbore in the reservoir, generating, from the grid cell set of interest and using a clustering algorithm, a plurality of grid cell clusters based on a grid cell position measure and a reservoir property of each grid cell, wherein each grid cell cluster corresponds to a flow compartment of the wellbore, and determining, for said each grid cell cluster, a starting position and an ending position of the corresponding flow compartment, wherein a packer is placed, during the completion operation and for said each grid cell cluster, at a starting position and an ending position of the corresponding flow compartment.

In general, in one aspect, the invention relates to a system that includes a wellbore penetrating a reservoir, and a data analysis system comprising a computer processor and memory storing instructions, when executed by the computer processor comprising functionality for determining a wellbore trajectory of the wellbore penetrating a reservoir, generating a grid cell set of interest surrounding the wellbore, wherein the grid cell set of interest comprises a plurality of consecutive grid cells that are penetrated by the wellbore in the reservoir, generating, from the grid cell set of interest and using a clustering algorithm, a plurality of grid cell clusters based on a grid cell position measure and a reservoir property of each grid cell, wherein each grid cell cluster corresponds to a flow compartment of the wellbore, and determining, for said each grid cell cluster, a starting position and an ending position of the corresponding flow compartment, wherein a packer is placed, during a completion operation and for said each grid cell cluster, at a starting position and an ending position of the corresponding flow compartment.

Other aspects and advantages of the claimed subject matter will be apparent from the following description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

Specific embodiments of the disclosed technology will now be described in detail with reference to the accompanying figures. Like elements in the various figures are denoted by like reference numerals for consistency.

FIGS. 1A and 1B show a system in accordance with one or more embodiments.

FIG. 2 shows a method flowchart in accordance with one or more embodiments.

FIGS. 3A-3G show an example in accordance with one or more embodiments.

FIG. 4 shows a computing system in accordance with one or more embodiments.

DETAILED DESCRIPTION

In the following detailed description of embodiments of the disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to one of ordinary skill in the art that the disclosure may be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description.

Throughout the application, ordinal numbers (for example, first, second, third) may be used as an adjective for an element (that is, any noun in the application). The use of ordinal numbers is not to imply or create any particular ordering of the elements nor to limit any element to being only a single element unless expressly disclosed, such as using the terms “before”, “after”, “single”, and other such terminology. Rather, the use of ordinal numbers is to distinguish between the elements. By way of an example, a first element is distinct from a second element, and the first element may encompass more than one element and succeed (or precede) the second element in an ordering of elements.

In general, embodiments of the invention include a method and system for placing packers in the well completion where packer placement locations are determined in the ICD completions design using reservoir simulation models. The method of determining the packer placement utilizes a clustering analysis algorithm that examines three-dimensional reservoir properties (static and dynamic) surrounding the wellbore to identify the most optimal flow compartments. The method evaluates the variation of reservoir properties and detects similar and continuous sections that form coherent flow compartments.

One or more embodiments automate the decision process of completion packer placement, without user (e.g., reservoir engineers) intervention, at the optimum measured depths along the vertical, horizontal, or slanted well trajectory. The automated completion packer placement results in more uniform hydrocarbon production, reduced water-cut and delayed gas gusping across all sections and zones of a well. In some embodiments, the optimization and automation of packer placement minimizes the effort to design ICD completions for individual wells. In other embodiments, the optimization and automation of packer placement are performed simultaneously across multiple wells, which provides a significant reduction in the turnaround time for developing a field and business plan of the reservoir.

FIGS. 1A and 1B show schematic diagrams in accordance with one or more embodiments. In one or more embodiments, one or more of the modules and/or elements shown in FIGS. 1A and 1B may be omitted, repeated, combined and/or substituted. Accordingly, embodiments disclosed herein should not be considered limited to the specific arrangements of modules and/or elements shown in FIGS. 1A and 1B.

Specifically, FIG. 1A illustrates a well environment (100) that includes a hydrocarbon reservoir (“reservoir”) (102) located in a subsurface hydrocarbon-bearing formation (“formation”) (104) and a well system (106). In one or more embodiments of the disclosure, the reservoir (102) is a gas reservoir to produce condensate, referred to as a gas condensate reservoir. The hydrocarbon-bearing formation (104) may include a porous or fractured rock formation that resides underground, beneath the Earth's surface (“surface”) (108). In the case of the well system (106) being a hydrocarbon well, the reservoir (102) may include a portion of the hydrocarbon-bearing formation (104). The hydrocarbon-bearing formation (104) and the reservoir (102) may include different layers of rock (referred to as formation layers) having varying characteristics, such as varying degrees of permeability, porosity, capillary pressure, and resistivity. In the case of the well system (106) being operated as a production well, the well system (106) may facilitate the extraction of hydrocarbons (or “production”) from the reservoir (102).

In some embodiments, the well system (106) includes a wellbore (120), a well sub-surface system (122), a well surface system (124), and a well control system (“control system”) (126). The control system (126) may control various operations of the well system (106), such as well production operations, well completion operations, well maintenance operations, and reservoir monitoring, assessment and development operations. In some embodiments, the control system (126) includes a computer system that is the same as or similar to that of the computer system (400) described below in FIG. 4 and the accompanying description.

The wellbore (120) may include a bored hole that extends from the surface (108) into a target zone of the hydrocarbon-bearing formation (104), such as the reservoir (102). An upper end of the wellbore (120), terminating at or near the surface (108), may be referred to as the “up-hole” end of the wellbore (120), and a lower end of the wellbore, terminating in the hydrocarbon-bearing formation (104), may be referred to as the “down-hole” end of the wellbore (120). The wellbore (120) may facilitate the circulation of drilling fluids during drilling operations, the flow of hydrocarbon production (“production”) (121) (e.g., oil and gas) from the reservoir (102) to the surface (108) during production operations, the injection of substances (e.g., water) into the hydrocarbon-bearing formation (104) or the reservoir (102) during injection operations, or the communication of monitoring devices (e.g., logging tools) into the hydrocarbon-bearing formation (104) or the reservoir (102) during monitoring operations (e.g., during in situ logging operations).

In some embodiments, during operation of the well system (106), the control system (126) collects and records wellhead data (140) for the well system (106). The wellhead data (140) may include, for example, a record of measurements of wellhead pressure (P_wh) (e.g., including flowing wellhead pressure), wellhead temperature (T_wh) (e.g., including flowing wellhead temperature), wellhead production rate (Q_wh) over some or all of the life of the well system (106), and water cut data. In some embodiments, the measurements are recorded in real-time, and are available for review or use within seconds, minutes or hours of the condition being sensed (e.g., the measurements are available within 1 hour of the condition being sensed). In such an embodiment, the wellhead data (140) may be referred to as “real-time” wellhead data (140). Real-time wellhead data (140) may enable an operator of the well system (106) to assess a relatively current state of the well system (106), and make real-time decisions regarding development of the well system (106) and the reservoir (102), such as on-demand adjustments in regulation of production flow from the well.

In some embodiments, the well sub-surface system (122) includes casing installed in the wellbore (120). For example, the wellbore (120) may have a cased portion and an uncased (or “open-hole”) portion. The cased portion may include a portion of the wellbore having casing (e.g., casing pipe and casing cement) disposed therein. The uncased portion may include a portion of the wellbore not having casing disposed therein. In some embodiments, the casing includes an annular casing that lines the wall of the wellbore (120) to define a central passage that provides a conduit for the transport of tools and substances through the wellbore (120). For example, the central passage may provide a conduit for lowering logging tools into the wellbore (120), a conduit for the flow of production (121) (e.g., oil and gas) from the reservoir (102) to the surface (108), or a conduit for the flow of injection substances (e.g., water) from the surface (108) into the hydrocarbon-bearing formation (104). In some embodiments, the well sub-surface system (122) includes production tubing installed in the wellbore (120). The production tubing may provide a conduit for the transport of tools and substances through the wellbore (120). The production tubing may, for example, be disposed inside casing. In such an embodiment, the production tubing may provide a conduit for some or all of the production (121) (e.g., oil and gas) passing through the wellbore (120) and the casing.

In some embodiments, the well surface system (124) includes a wellhead (130). The wellhead (130) may include a rigid structure installed at the “up-hole” end of the wellbore (120), at or near where the wellbore (120) terminates at the Earth's surface (108). The wellhead (130) may include structures for supporting (or “hanging”) casing and production tubing extending into the wellbore (120). Production (121) may flow through the wellhead (130), after exiting the wellbore (120) and the well sub-surface system (122), including, for example, the casing and the production tubing. In some embodiments, the well surface system (124) includes flow regulating devices that are operable to control the flow of substances into and out of the wellbore (120). For example, the well surface system (124) may include one or more production valves (132) that are operable to control the flow of production (121). For example, a production valve (132) may be fully opened to enable unrestricted flow of production (121) from the wellbore (120), the production valve (132) may be partially opened to partially restrict (or “throttle”) the flow of production (121) from the wellbore (120), and production valve (132) may be fully closed to fully restrict (or “block”) the flow of production (121) from the wellbore (120), and through the well surface system (124).

Keeping with FIG. 1A, in some embodiments, the well surface system (124) includes a surface sensing system (134). The surface sensing system (134) may include sensors for sensing characteristics of substances, including production (121), passing through or otherwise located in the well surface system (124). The characteristics may include, for example, pressure, temperature and flow rate of production (121) flowing through the wellhead (130), or other conduits of the well surface system (124), after exiting the wellbore (120).

In some embodiments, the surface sensing system (134) includes a surface pressure sensor (136) operable to sense the pressure of production (121) flowing through the well surface system (124), after it exits the wellbore (120). The surface pressure sensor (136) may include, for example, a wellhead pressure sensor that senses a pressure of production (121) flowing through or otherwise located in the wellhead (130). In some embodiments, the surface sensing system (134) includes a surface temperature sensor (138) operable to sense the temperature of production (121) flowing through the well surface system (124), after it exits the wellbore (120). The surface temperature sensor (138) may include, for example, a wellhead temperature sensor that senses a temperature of production (121) flowing through or otherwise located in the wellhead (130), referred to as “wellhead temperature” (Twh). In some embodiments, the surface sensing system (134) includes a flow rate sensor (139) operable to sense the flow rate of production (121) flowing through the well surface system (124), after it exits the wellbore (120). The flow rate sensor (139) may include hardware that senses a flow rate of production (121) (Qwh) passing through the wellhead (130).

In some embodiments, the well system (106) includes a data analysis system (160). For example, the data analysis system (160) may include hardware and/or software with functionality for generating one or more reservoir models regarding the hydrocarbon-bearing formation (104), and performing one or more reservoir simulations and generating optimal packer placements using the reservoir models. For example, the data analysis system (160) may store well logs and data regarding reservoir samples for performing simulations and/or generating optimal packer placements. For example, the reservoir samples may include core samples obtained from the reservoir. A data analysis system may further analyze the well log data, the reservoir sample data, seismic data, and/or other types of data to generate and/or update the one or more reservoir models. While the data analysis system (160) is shown at a well site, embodiments are contemplated where data analysis systems are located away from well sites. In some embodiments, the data analysis system (160) may include a computer system that is similar to the computer system (400) described below with regard to FIG. 4 and the accompanying description.

In a typical reservoir simulation, a mathematical model of the reservoir includes a set of partial differential equations representing reservoir and well flows that are solved numerically. Numerical solution involves time and space/domain discretization replacing differential equations with difference equations. Time discretization refers to division of time into a sequence of time steps. In each time step, after discretization is solved iteratively, a non-linear system is linearized using Newton method, which may take several Newton iterations to converge. Space/domain discretization, also called grid generation, refers to division of the reservoir domain into a reservoir grid of small grid blocks. A grid is a tessellation of a set of contiguous polygonal (2D) or polyhedral (3D) objects referred to as grid blocks/cells/elements/control volumes. The grid generation is a process of discretization of the reservoir using both structured and more complex unstructured grid blocks to accurately represent the geometry of the reservoir. Local grid refinement (i.e., LGR where a finer grid is selectively embedded inside a coarse grid) is also a feature provided by many simulators to more accurately represent the near wellbore multi-phase flow effects.

Numerical schemes used in reservoir simulation are control volume distributed (CVD). Rock properties such as permeability and porosity, and flow properties such as pressure, temperature, and composition (saturation) are stored in in the reservoir model and assumed piecewise constant within a control volume (i.e., grid cell). However, reservoir and flow properties may jump by order of magnitude across the faces of the control volumes (i.e., grid cells). Consequently, property distribution in reservoir simulation is stair step, and rate of change of a property across grid cells depends on grid resolution. Lack of definition within a single grid cell and sharp changes in pressure and saturation across the grid cells create several physical, numerical, and convergence problems during the reservoir simulation.

In numerical simulation, dynamic interaction between hydrocarbon reservoirs and wells may be modeled using reservoir boundary conditions in the form of well controls to match historical data and/or define operational limits for reservoir forecasting. For example, the reservoir simulation may be used to predict or forecast field performance and ultimate recovery for various field development scenarios to evaluate the effects on recovery of different operational conditions and compare economics of different recovery methods.

The use of advanced well completion such as Inflow Control Valves (ICV) and Inflow Control Devices (ICD) is important to control fluid flow from sandface to the wellbore for each section across hydrocarbon wells. This type of completion becomes more significant in extended or multilateral wells due to increasing exposure and more contact with heterogeneous sections that exhibit different flow regimes in the reservoir. Downhole tools such as ICDs, ICVs and packers are used to balance the flow from different heterogeneous sections to prevent undesirable phenomena such as water/gas coning and early water breakthrough. The placement of packers creates isolated compartments across the wellbore corresponding to different reservoir sections where each section exhibits similar heterogeneity within itself. Determining the optimum depths is critical as it impacts subsequent optimizations of ICDs and ICVs settings. Evaluation of multiple well completion scenarios is performed using simulation tools to predict performance before applying the well completion in the field.

FIG. 1B illustrates a portion of the reservoir model (160a) for the well environment (100) depicted in FIG. 1A above. Specifically, the wellbore (130) depicted in FIG. 1A is shown as a horizontal or slanted oil producer well that penetrates a number of grid cells (104a, 104b, 104c, 104d, 104e, 104f, 104g, 104h, 104i, 104j) of the reservoir simulation model (160a). The reservoir model (160a) is analyzed by the data analysis system (160) to identify flow compartments (135a, 135b, 135c, 135d, 135e, 135f) and determine a placement of packers (131a, 131b, 131c, 131d, 131e, 131f, 131g) that seal the flow compartments from each other. The flow compartment is a segregated portion of fluid accumulation in the reservoir, e.g., due to hinderance by a geological barrier in the reservoir. In addition, ICDs (136a, 136b) are placed within the flow compartments (135d, 135e). The flow compartment is a section of the wellbore in a reservoir region with similar characteristics throughout. In other words, different regions with differing characteristics in the reservoir intersect with different flow compartments of the wellbore. A flow compartment may be created by enclosing the section of the wellbore by two sealing packers to limit the production from certain regions or depths in the reservoir.

FIG. 2 shows a flowchart in accordance with one or more embodiments disclosed herein. One or more of the steps in FIG. 2 may be performed by the components of the well environment (100) and the data analysis system (160), discussed above in reference to FIGS. 1A-1B. In one or more embodiments, one or more of the steps shown in FIG. 2 may be omitted, repeated, and/or performed in a different order than the order shown in FIG. 2. Accordingly, the scope of the disclosure should not be considered limited to the specific arrangement of steps shown in FIG. 2.

The flowchart shown in FIG. 2 illustrates a method to perform a completion operation of a wellbore. Initially in Block 200, a geologic survey operation and/or a well logging operation is performed to determine the wellbore trajectory penetrating the reservoir and determine the reservoir property throughout the reservoir. For example, seismic survey may be performed to determine permeability throughout the reservoir while sonic logging may be performed to determine permeability surrounding the wellbore. In addition, the wellbore trajectory may be mapped using seismic survey and/or measurement-while-drilling (MWD) logging.

In Block 201, a grid cell set of interest surrounding the wellbore is generated. Specifically, the grid cell set of interest includes consecutive grid cells that are penetrated by the wellbore in the reservoir.

In Block 202, a number of grid cell clusters are generated from the grid cell set of interest. Each grid cell cluster is a collection of grid cells forming a contiguous subset of the grid cell set of interest. In one or more embodiments, the grid cell clusters are generated using a clustering algorithm based on a grid cell position measure and one or more reservoir properties of each grid cell, such as permeability, porosity, residual oil saturation, fault transmissibility multiplier, etc. For example, the grid cell position measure may include a depth of the grid cell along the trajectory of the wellbore. In other example, the grid cell position measure may include the three dimensional coordinates of the grid cell in the physical space.

In one or more embodiments, the grid cell clusters are generated by first generating a multi-dimensional data set based on the grid cell of interest. Each data object in the multi-dimensional data set corresponds to one of the consecutive grid cells in the grid cell set of interest. The data object includes the grid cell position measure and the reservoir property of the corresponding grid cell, which are two of the multiple dimensions of the multi-dimensional data set. The data object may further include additional reservoir properties corresponding to the remaining dimensions of the multi-dimensional data set. By applying the clustering algorithm to the multi-dimensional data set, a number of data object clusters are generated. Each data object cluster is in the multi-dimensional data space and corresponds to a grid cell cluster in the three-dimensional physical space.

In one or more embodiments, the clustering algorithm includes a K-Means algorithm that determines an optimal target cluster count by first determining an aggregate silhouette coefficient value of the data object clusters, and then determining a target cluster count based at least on the aggregate silhouette coefficient value.

In Block 203, a number of flow compartments of the wellbore are identified based on the grid cell clusters. Specifically, for each grid cell cluster, a minimum value of the grid cell position measure and a maximum value of the grid cell position measure are extracted or otherwise determined from a corresponding data object cluster. Accordingly, the minimum value and the maximum value of the grid cell position measure defines the starting position and the ending position of a flow compartment.

In Block 204, during the completion operation, a packer is placed at a starting position and an ending position of each flow compartment.

In Block 205, further during the completion operation, an inflow control device is placed within at least one flow compartment.

In Block 206, the inflow control device is used to equalize reservoir inflow along the trajectory of the wellbore to facilitate production of the wellbore.

FIGS. 3A-3G show an implementation example in accordance with one or more embodiments. The implementation example shown in FIGS. 3A-3G is based on the system and method flowchart described in reference to FIGS. 1A-1B and 2 above.

Specifically, FIG. 3A shows a flowchart (300) that describes the optimization process of identifying flow compartments and packer placement. The implementation example relates to well trajectories of existing wells that require workover or recompletion, and new wells that have been planned as part of field development assessment and planning.

In Block 301 through Block 305, data preparation is performed by first obtaining a reservoir model containing the trajectory of the well, i.e., wellbore trajectory (Block 301). The reservoir model stores reservoir properties (e.g., permeability) in a form of spatially distributed values in a grided 3D space (Block 302). In addition, well log measurements from petrophysical evaluation (e.g., resistivity log, acoustic log, etc.) of the well is obtained (Block 303). The grid cells of the reservoir model that are intersected by the wellbore trajectory are identified by filtering out grid cells located away from the well (Block 304). The well logs are converted to a set of grid cells with 3D property around the wellbore trajectory (Block 305). The output of this data preparation is a set of consecutive grid cells, referred to as the grid cell set of interest, in a 3D space that define a region surrounding the wellbore. Each grid cell in the grid cell set of interest corresponds to a data object o formed by (a) reservoir properties stored in the reservoir model, (b) reservoir properties converted from the well log measurements, and (c) a grid cell position measure such as the depth of the grid cell along the wellbore trajectory. The data objects of all grid cells in the grid cell of interest collectively form a data set D, which is the output of the data preparation. The data set D is represented as a multi-dimensional data space where each reservoir property in the grid cell corresponds to one dimension of the multi-dimensional space and the depth of the grid cell corresponds to one additional dimension. Accordingly, each data object o in the data set D corresponds to one point in the multi-dimensional data space. For example, the multi-dimensional data space may be an n-dimensional Euclidean space where distances and centroids are determined based on coordinates of data object o in the n-dimensional Euclidean space.

In Block 306 through Block 309, clustering is performed after generating the data set D as the output of the data preparation. Clustering is performed to divide the grid cell set of interest to multiple consecutive portions, referred to as clusters, based on the measured depth and the value of the reservoir property of each grid cell in the grid cell set of interest. This process involves using a clustering analysis algorithm, e.g., K-Means algorithm, to group the grid cells within the grid cell set of interest into different clusters that define distinct flow compartments. More specifically, the clustering algorithm is applied to partition the data set D into N clusters, C₁, . . . , C_N. Based on the K-Means algorithm, a point in the multi-dimensional space is considered to be in a particular cluster if it is closer to that cluster's centroid in the multi-dimensional space than any other centroid of other clusters.

To perform the clustering, the number of clusters n is initialized to 1 at the beginning of the clustering process (Block 306). For each iteration, the KMEANS algorithm is performed (Block 308) to generate an additional cluster while the number of cluster n is determined as less than a target cluster count N (Block 307). The number of clusters n is then incremented. Upon the number of cluster n equals the target cluster count N, all the clusters iteratively generated are collected as the compartmentalized grid cell set of interest where each cluster corresponds to a flow compartment of the wellbore trajectory.

In the clustering analysis algorithm, the silhouette coefficient value is a measure of how similar an object, e.g., the measured depth and the value of the reservoir property of a grid cell, is to its own cluster, e.g., flow compartment, compared to other clusters. For each object o∈D, a (o) denotes the average distance between 0 and all other objects in the cluster to which o belongs, and b(o) denotes the minimum average distance from o to all clusters to which o does not belong. For o∈C_i(1≤i≤k); the silhouette coefficient of o is defined by the equations Eq. (1), Eq. (2), and Eq. (3) below where o′ denotes a different data object than o, k denotes the number of clusters in D, and dist (o, o′) denotes the distance between the objects o and o′.

a ⁢ ( o ) = ∑ o ′ ∈ C i , o ≠ o ′ dist ⁢ ( o , o ′ ) ❘ "\[LeftBracketingBar]" C i ❘ "\[RightBracketingBar]" - 1 Eq . ( 1 ) b ⁢ ( o ) = min C j : 1 ≤ j ≤ k , j ≠ i ∑ o ′ ∈ C j dist ⁢ ( o , o ′ ) ❘ "\[LeftBracketingBar]" C j ❘ "\[RightBracketingBar]" Eq . ( 2 ) s ⁡ ( o ) = b ⁡ ( o ) - a ⁡ ( o ) max ⁢ { a ⁡ ( o ) , b ⁡ ( o ) } Eq . ( 3 )

Typically, the silhouette coefficient value ranges from −1 to +1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters. The sum of all silhouette coefficient values of all objects o∈D is referred to as the aggregate silhouette coefficient value. To determine the optimal number of clusters, a range of clustering scenarios are evaluated by generating multiple compartmentalized grid cell set of interest using different values (i.e., as k in Eq. (1), Eq. (2), and Eq. (3)) of the target cluster count N to determine the aggregate silhouette coefficient value for each clustering scenario. The quality of the compartmentalized grid cell set in each scenario is measured using the aggregate silhouette coefficient value, and the scenario with the highest aggregate silhouette coefficient value is selected as the optimal solution where the target cluster count N of the optimal compartmentalized grid cell set is referred to as the final flow compartment count C.

In Block 310 through Block 311, packer placement is performed. To generate the packer placement for each flow compartment, the index of flow compartment i is initialized to 1 at the beginning of the packer placement (Block 309). For each iteration, the starting and ending positions of the flow compartment are assigned as packer placement positions (Block 311) while the index of flow compartment i is determined as less than the final cluster count C (Block 310). The index of flow compartment “i” is then incremented. Upon the index of flow compartment i equals the final flow compartment count C, all the assigned packer placement positions are collected as the final packer placement of the wellbore trajectory.

FIG. 3B shows an example perspective view of the reservoir (102) depicted in FIG. 1A above where the wellbore (130) is shown as having a slanted wellbore trajectory. The curved surface shown in the perspective view corresponds to a rock layer of the reservoir (102). As noted above, the reservoir model stores reservoir properties (e.g., permeability) in a form of spatially distributed values in a 3D grided space. In this context, the perspective view also represents the reservoir simulation model (160a) depicted in FIG. 1B above where the curved intersects grid cells (e.g., grid cell (104a)) where each grid cell stores corresponding value of rock permeability property identified according to the depicted grey scale. Although only one curved surface and one reservoir property (e.g., permeability) are shown in FIG. 3B, multiple rock layers and multiple reservoir properties may exist in the example reservoir and corresponding reservoir simulation model.

FIG. 3C shows an example grid cell of interest (160b) of the wellbore (130) depicted in FIG. 3B above. The grid cells (104a, 104b, 104c, 104d, 104e) within the example grid cell of interest (160b) correspond to similarly named grid cells in the reservoir simulation model (160a) depicted in FIG. 1B above. In addition to reservoir properties obtained from the reservoir simulation model (160a), the grid cells (104a, 104b, 104c, 104d, 104e) within the example grid cell of interest (160b) also include measurement data retrieved from the well log (e.g., well log (141) depicted in FIG. 3D below) and corresponding depth value of each grid cell. In this context, each grid cell within the example grid cell of interest (160b) corresponds to one data object o that is represented as a point in the multi-dimensional data space of the data set D described above.

FIG. 3D shows an example permeability well log (141) along the wellbore trajectory of the wellbore (130) depicted in FIG. 3B above. The permeability values (e.g., 141a, 141b) at different depths along the wellbore trajectory are identified according to the depicted grey scale.

FIG. 3E shows example clusters (134a, 134b, 134c, 134d, 134e, 134f) along the wellbore trajectory of the wellbore (130) depicted in FIG. 3B above. The clusters (134a, 134b, 134c, 134d, 134e, 134f) are generated by grouping consecutive grid cells based on their similarity in permeability values and depth values. For example, the clusters (134a, 134b, 134c, 134d, 134e, 134f) may be generated by applying the K-Means algorithm to the data set D described above.

FIG. 3F shows example flow compartment (135a, 135b, 135c, 135d, 135e, 135f) along the wellbore trajectory of the wellbore (130) depicted in FIG. 3B above.

FIG. 3G shows example packers (131a, 131b, 131c, 131d, 131e, 131f, 131g) placed at optimum depths to enclose and isolate the flow compartments (135a, 135b, 135c, 135d, 135e, 135f). Additionally, Table 1 shows permeability values at different measured depths and the corresponding cluster ID.

The examples discussed in reference to FIGS. 3A-3G illustrate a method for optimizing and automating the placement of well completion packers in a reservoir. The method places packers at optimum depths to ensure isolating similar property sections into compartments. The method is applicable across a field where the completion of multiple wells is automated in an efficient manner. In a three-dimensional reservoir model, the method uses clustering analysis algorithm over the grid cells around the wellbore to identify optimum flow compartments. In the example described above, the K-Means clustering algorithm is used to detect the variation of permeability and to identify similar permeabilities that form distinct sections. Consecutive similar grid cells are grouped into a distinct flow compartment. The similarity is determined by the clustering algorithm based on permeability values and distances between the grid cells. The automation in this method enables rapid design of packers based on reservoir properties. The method not only save time but also optimize the number of compartments for each well using an objective criterion. The method can be applied simultaneously across a large number of wells, which provides significant reduction in the turnaround time for generating a full field development plans to guide the actual completions.

Moreover, this automated method can contribute to cost saving in sandstone and carbonate reservoirs to avoid short compartments and unnecessarily large number of costly packers. Taking $20,000 as an average cost of one basic ICD, extended wells can sometimes be over-equipped with many ICD's reaching 70 or more devices. The cost in such cases can reach $1,500,000 for completing one well with basic ICDs, or $7,000,000 for advanced ICD's. The method described above can reduce the required number of ICD's depending on the reservoir's characteristics surrounding the well. In reservoirs with slowly varying reservoir properties (e.g., permeability), the number of ICDs may be reduced to half, reducing significant cost compared to manual packer placement.

Embodiments may be implemented on a computer system. FIG. 4 is a block diagram of a computer system (402) used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure, according to an implementation. For example, the computer system may be used to model the reservoir, identify grid cells, perform clustering of grid cells to identify optimum flow compartments, and guide well completion such as packer placement. Embodiments disclosed herein capitalize on the reservoir models, and implement the workflow in FIG. 3A using the computer system of FIG. 4. This involves data preparation, grid cells filtering, converting logs to a set of grid cells, running the clustering analysis, flow compartments identification, placing packers, data visualization, etc. The illustrated computer (402) is intended to encompass any computing device such as a high performance computing (HPC) device, a server, desktop computer, laptop/notebook computer, wireless data port, smart phone, personal data assistant (PDA), tablet computing device, one or more processors within these devices, or any other suitable processing device, including both physical or virtual instances (or both) of the computing device. Additionally, the computer (402) may include a computer that includes an input device, such as a keypad, keyboard, touch screen, or other device that can accept user information, and an output device that conveys information associated with the operation of the computer (402), including digital data, visual, or audio information (or a combination of information), or a GUI.

The computer (402) can serve in a role as a client, network component, a server, a database or other persistency, or any other component (or a combination of roles) of a computer system for performing the subject matter described in the instant disclosure. The illustrated computer (402) is communicably coupled with a network (430). In some implementations, one or more components of the computer (402) may be configured to operate within environments, including cloud-computing-based, local, global, or other environment (or a combination of environments).

At a high level, the computer (402) is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some implementations, the computer (402) may also include or be communicably coupled with an application server, e-mail server, web server, caching server, streaming data server, business intelligence (BI) server, or other server (or a combination of servers).

The computer (402) can receive requests over network (430) from a client application (for example, executing on another computer (402)) and responding to the received requests by processing the said requests in an appropriate software application. In addition, requests may also be sent to the computer (402) from internal users (for example, from a command console or by other appropriate access method), external or third-parties, other automated applications, as well as any other appropriate entities, individuals, systems, or computers.

Each of the components of the computer (402) can communicate using a system bus (403). In some implementations, any or all of the components of the computer (402), both hardware or software (or a combination of hardware and software), may interface with each other or the interface (404) (or a combination of both) over the system bus (403) using an application programming interface (API) (412) or a service layer (413) (or a combination of the API (412) and service layer (413). The API (412) may include specifications for routines, data structures, and object classes. The API (412) may be either computer-language independent or dependent and refer to a complete interface, a single function, or even a set of APIs. The service layer (413) provides software services to the computer (402) or other components (whether or not illustrated) that are communicably coupled to the computer (402). The functionality of the computer (402) may be accessible for all service consumers using this service layer. Software services, such as those provided by the service layer (413), provide reusable, defined business functionalities through a defined interface. For example, the interface may be software written in JAVA, C++, or other suitable language providing data in extensible markup language (XML) format or other suitable format. While illustrated as an integrated component of the computer (402), alternative implementations may illustrate the API (412) or the service layer (413) as stand-alone components in relation to other components of the computer (402) or other components (whether or not illustrated) that are communicably coupled to the computer (402). Moreover, any or all parts of the API (412) or the service layer (413) may be implemented as child or sub-modules of another software module, enterprise application, or hardware module without departing from the scope of this disclosure.

The computer (402) includes an interface (404). Although illustrated as a single interface (404) in FIG. 4, two or more interfaces (404) may be used according to particular needs, desires, or particular implementations of the computer (402). The interface (404) is used by the computer (402) for communicating with other systems in a distributed environment that are connected to the network (430). Generally, the interface (404) includes logic encoded in software or hardware (or a combination of software and hardware) and operable to communicate with the network (430). More specifically, the interface (404) may include software supporting one or more communication protocols associated with communications such that the network (430) or interface's hardware is operable to communicate physical signals within and outside of the illustrated computer (402).

The computer (402) includes at least one computer processor (405). Although illustrated as a single computer processor (405) in FIG. 4, two or more processors may be used according to particular needs, desires, or particular implementations of the computer (402). Generally, the computer processor (405) executes instructions and manipulates data to perform the operations of the computer (402) and any algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure.

The computer (402) also includes a memory (406) that holds data for the computer (402) or other components (or a combination of both) that can be connected to the network (430). For example, memory (406) can be a database storing data consistent with this disclosure. Although illustrated as a single memory (406) in FIG. 4, two or more memories may be used according to particular needs, desires, or particular implementations of the computer (402) and the described functionality. While memory (406) is illustrated as an integral component of the computer (402), in alternative implementations, memory (406) can be external to the computer (402).

The application (407) is an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer (402), particularly with respect to functionality described in this disclosure. For example, application (407) can serve as one or more components, modules, applications, etc. Further, although illustrated as a single application (407), the application (407) may be implemented as multiple applications (407) on the computer (402). In addition, although illustrated as integral to the computer (402), in alternative implementations, the application (407) can be external to the computer (402).

There may be any number of computers (402) associated with, or external to, a computer system containing computer (402), each computer (402) communicating over network (430). Further, the term “client,” “user,” and other appropriate terminology may be used interchangeably as appropriate without departing from the scope of this disclosure. Moreover, this disclosure contemplates that many users may use one computer (402), or that one user may use multiple computers (402).

In some embodiments, the computer (402) is implemented as part of a cloud computing system. For example, a cloud computing system may include one or more remote servers along with various other cloud components, such as cloud storage units and edge servers. In particular, a cloud computing system may perform one or more computing operations without direct active management by a user device or local computer system. As such, a cloud computing system may have different functions distributed over multiple locations from a central server, which may be performed using one or more Internet connections. More specifically, cloud computing system may operate according to one or more service models, such as infrastructure as a service (IaaS), platform as a service (PaaS), software as a service (SaaS), mobile “backend” as a service (MBaaS), serverless computing, artificial intelligence (AI) as a service (AIaaS), and/or function as a service (FaaS).

Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this invention. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims.