WO2025166753A1

WO2025166753A1 - Methods and systems for seismic-conditioned process-based geological models using multi-point statistics

Info

Publication number: WO2025166753A1
Application number: PCT/CN2024/077010
Authority: WO
Inventors: Lin Ying Hu; Yupeng Li
Original assignee: Aramco Far East Beijing Business Services Co Ltd; Saudi Arabian Oil Co
Current assignee: Aramco Far East Beijing Business Services Co Ltd; Saudi Arabian Oil Co
Priority date: 2024-02-08
Filing date: 2024-02-08
Publication date: 2025-08-14
Anticipated expiration: 2026-08-08

Abstract

The methods may include defining cells that represent a subterranean region of interest (SROI) and obtaining seismic data and well data pertaining to the SROI. Each cell is associated with a location within the SROI and seismic constraint among the seismic data. The cells include informed cells and uninformed cells. Each informed cell is associated with each well datum. The methods may further include obtaining a process-based geological model (PBGM) of the SROI and determining a corresponding simulated seismic image (CSSI) based on the PBGM. Each cell is further associated with a facies among the PBGM and simulated seismic constraint among the CSSI. The methods may further still include determining a probability based on the location, seismic constraint, PBGM, CSSI, and well data for each uninformed cell, determining a seismic-conditioned PBGM based on the probabilities, and identifying a predicted location of hydrocarbons within the SROI based on the seismic-conditioned PBGM.

Description

METHODS AND SYSTEMS FOR SEISMIC-CONDITIONED PROCESS-BASED GEOLOGICAL MODELS USING MULTI-POINT STATISTICS

BACKGROUND

A process-based geological model, synonymous with a forward stratigraphic model, models geological processes that occurred over geological time to form a subterranean region of interest. To model the geological processes, which may include depositional and/or diagenetic processes, the process-based geological model relies on physics-and/or chemical-based simulations. Following adequate modeling, the process-based geological model may be used to identify a predicted location of hydrocarbons within the subterranean region of interest. Accordingly, a wellbore plan may be designed and a wellbore drilled such that the hydrocarbons may be produced to the surface of the earth for use as fuel.

SUMMARY

This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

In general, in one aspect, embodiments relate to a method. The method includes defining cells that represent a subterranean region of interest and obtaining seismic data and well data pertaining to the subterranean region of interest. Each cell is associated with a location within the subterranean region of interest and seismic constraint among the seismic data. The cells include informed cells and uninformed cells. Each informed cell is associated with each well datum. The method further includes obtaining a process-based geological model of the subterranean region of interest and determining a corresponding simulated seismic image based on the process-based geological model. Each cell is further associated with a facies among the process-based geological model and simulated seismic constraint among the corresponding simulated seismic image. The methods may further still include determining a probability based on the location, seismic constraint, process-based geological model, corresponding simulated seismic image, and well data for each uninformed cell, determining a seismic-conditioned process-based geological model based on the probabilities, and identifying a predicted location of hydrocarbons within the subterranean region of interest based on the seismic-conditioned process-based geological model.

In general, in one aspect, embodiments relate to a system. The system includes a computer system and an interpretation workstation. The computer system is configured to define cells that represent a subterranean region of interest and receive seismic data and well data pertaining to the subterranean region of interest. Each cell is associated with a location within the subterranean region of interest and seismic constraint among the seismic data. The cells include informed cells and uninformed cells. Each informed cell is associated with each well datum. The computer system is further configured to receive a process-based geological model of the subterranean region of interest and determine a corresponding simulated seismic image based on the process-based geological model. Each cell is further associated with a facies among the process-based geological model and simulated seismic constraint among the corresponding simulated seismic image. The computer system is further still configured to determine a probability based on the location, seismic constraint, process-based geological model, corresponding simulated seismic image, and well data for each uninformed cell and determine a seismic-conditioned process-based geological model based on the probabilities. The interpretation workstation is configured to identify a predicted location of hydrocarbons within the subterranean region of interest based on the seismic-conditioned process-based geological model.

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.

FIG. 1 displays cells in accordance with one or more embodiments.

FIG. 2 illustrates a seismic acquisition system in accordance with one or more embodiments.

FIG. 3 displays seismic data in accordance with one or more embodiments.

FIG. 4A displays a process-based geological model in accordance with one or more embodiments.

FIG. 4B displays a corresponding simulated seismic image in accordance with one or more embodiments.

FIG. 5 displays replicates in accordance with one or more embodiments.

FIG. 6 illustrates a well logging system in accordance with one or more embodiments.

FIG. 7A displays a seismic-conditioned process-based geological model in accordance with one or more embodiments.

FIG. 7B displays a seismic-conditioned corresponding simulated seismic image in accordance with one or more embodiments.

FIG. 8A displays a seismic-conditioned process-based geological model in accordance with one or more embodiments.

FIG. 8B displays a seismic-conditioned corresponding simulated seismic image in accordance with one or more embodiments.

FIG. 9 describes a method in accordance with one or more embodiments.

FIG. 10 illustrates a computer system in accordance with one or more embodiments.

FIG. 11 illustrates a drilling system in accordance with one or more embodiments.

FIG. 12 illustrates a system in accordance with one or more embodiments.

FIG. 13 describes a method 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 (e.g., first, second, third, etc. ) may be used as an adjective for an element (i.e., 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.

It is to be understood that the singular forms “a, ” “an, ” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a seismic constraint” includes reference to one or more of such constraints.

Terms such as “approximately, ” “substantially, ” etc., mean that the recited characteristic, parameter, or value need not be achieved exactly, but that deviations or variations, including for example, tolerances, measurement error, measurement accuracy limitations and other factors known to those of skill in the art, may occur in amounts that do not preclude the effect the characteristic was intended to provide.

It is to be understood that one or more of the steps shown in the flowcharts may be omitted, repeated, and/or performed in a different order than the order shown. Accordingly, the scope disclosed herein should not be considered limited to the specific arrangement of steps shown in the flowcharts.

Although multiple dependent claims are not introduced, it would be apparent to one of ordinary skill that the subject matter of the dependent claims of one or more embodiments may be combined with other dependent claims.

In the following description of FIGs. 1-13, any component described regarding a figure, in various embodiments disclosed herein, may be equivalent to one or more like-named components described regarding any other figure. For brevity, descriptions of these components will not be repeated regarding each figure. Thus, each and every embodiment of the components of each figure is incorporated by reference and assumed to be optionally present within every other figure having one or more like-named components. Additionally, in accordance with various embodiments disclosed herein, any description of the components of a figure is to be interpreted as an optional embodiment which may be implemented in addition to, in conjunction with, or in place of the embodiments described regarding a corresponding like-named component in any other figure.

Methods and systems are disclosed to identify a predicted location of hydrocarbons within a subterranean region of interest using a seismic-conditioned process-based geological model. To do so, the methods and systems may rely on a process-based geological model, corresponding simulated seismic image, seismic data, well data, and an unconventional multi-point statistics approach.

The process-based geological model may be synonymous with a forward stratigraphic model. The process-based geological model may be the result of physics-and/or chemical-based simulations that model geological processes (e.g., depositional and diagenetic processes) within the subterranean region of interest over geological time. Geological processes may include, without limitation, sediment erosion, sediment transport, sediment deposition, formation compaction, porosity reduction, fold deformation, diagenesis, and fluid maturation. Accordingly, the process-based geological model may be a geologically-realistic model.

The disclosed methods and systems may be an improvement over other methods that identify a predicted location of hydrocarbons within a subterranean region of interest using a process-based geological model. By way of example, other methods may identify a predicted location of hydrocarbons within a subterranean region of interest using a calibrated process-based geological model. The calibrated process-based geological model may aim to honor the seismic data and/or well data not honored by the process-based geological model. However, to do so, the other methods may only indirectly use the seismic data and/or well data to tune one or more input parameters, through trial-and-error or automated inverse procedures, of the process-based geological model. The one or more input parameters may include, without limitation, paleo-topography parameters, sediment input rates, sediment transport rates, sea level changes, and tectonic subsidence history parameters. The other methods may improve the process-based geological model but are rarely able to satisfactorily calibrate the process-based geological model. Accordingly, the calibrated process-based geological model may be inaccurate in or have a high degree of uncertainty associated with locations within the subterranean region of interest where little-to-no data is available for validation.

To overcome the challenges associated with the other methods, the disclosed methods and systems rely on an unconventional multi-point statistics approach to condition or constrain a process-based geological model to seismic data. The unconventional multi-point statistics approach may be used for regionalized statistical geological pattern recognition and regeneration. The unconventional multi-point statistics approach may rely on Bayes’ law and a kernel function to condition the process-based geological model to seismic data.

The unconventional multi-point statistics approach differs from, and may be an improvement over, conventional multi-point statistics approaches in at least four ways. First, the process-based geological model need not be stationary (i.e., may be nonstationary) as required by conventional multi-point statistics approaches. For example, statistical parameters, such as correlation lengths, may vary spatially. Second, there is no need to partition a nonstationary process-based geological model into multiple pseudo-stationary process-based geological models as required by conventional multi-point statistics approaches. Third, the unconventional multi-point statistics approach is based on concrete probability schemes, such as Bayes’ law and a kernel function, unlike conventional multi-point statistics approaches that are based on arbitrary probability schemes and/or heuristic rules. Fourth, the unconventional multi-point statistics approach is memory economic as there is no need to build a search tree as conventional multi-point statistics approaches require. Accordingly, the unconventional multi-point statistics approach used in the disclosed methods may determine a more geologically-realistic process-based geological model by adequately conditioning the process-based geological model to seismic data.

In some embodiments, the process-based geological model may be conditioned to seismic data on a cell-by-cell basis. To do so, prior to seismic conditioning, cells that represent the subterranean region of interest that the process-based geological model and seismic data aim to characterize are defined. FIG. 1 illustrates cells 100 that represent a two-dimensional subterranean region of interest 105 in accordance with one or more embodiments. Though FIG. 1 displays the cells 100 (i.e., the simulation field or simulation grid) arranged in two dimensions, the cells 100 may be arranged in three dimensions to represent a three-dimensional subterranean region of interest 105 without departing from the scope of the disclosure. In other embodiments, simulations points (i.e., grid nodes) may represent the subterranean region of interest 105 instead of cells 100.

Each cell 100 is associated with a location, x, 110 within the subterranean region of interest 105. Though the location 110 is represented by the scalar variable x, a person of ordinary skill in the art will appreciate that the location 110 may be a vector x. By way of example, x= (x, y) as illustrated in FIG. 1. However, a person of ordinary skill in the art will appreciate that a location 110 within a three-dimensional subterranean region of interest 105 may be denoted x= (x, y, z) , where x and y denote mutually orthogonal horizontal axes and z denotes depth.

Continuing with FIG. 1, the cells 100 may include uninformed cells 115 and informed cells 120. Each uninformed cell 115 is displayed using white and each informed cell 120 is displayed using upward diagonal lines in FIG. 1 as shown by the key 125. Each informed cell 120 may be associated with a hard datum among hard data. The hard data may be data acquired or observed from the subterranean region of interest 105. In some embodiments, the hard data may be or include well data or interpretations derived from the well data. Each uninformed cell 115 may not be associated with a datum or may be associated with a soft datum among soft data. The soft data may be simulated or estimated data. Two or more neighboring uninformed cells 115 may form one or more random paths 140. Each uninformed cell 115 among each random path 140 may be among one or more sets of neighboring cells 130. FIG. 1 displays one set of neighboring cells 130 using downward diagonal lines as shown by the key 125. In some embodiments, each set of neighboring cells 130 may include uninformed cells 115 and/or informed cells 120. Each set of neighboring cells 130 may take any dimensionality, which may be the same or lower than the dimensionality of the subterranean region of interest 105. Further, each set of neighboring cells 130 may include any number of cells 100 and take any shape. Hereinafter, each set of neighboring cells 130 that includes an uninformed cell 115 among a random path 140 and cell data (e.g., each location x 110) associated with each set of those neighboring cells 130 is denoted a data event d 135. Further hereinafter, a set of neighboring cells 130 that may or may not include the uninformed cell 115 among the random path 140 but takes the same shape as the data event d 135 and cell data associated with the set of those neighboring cells 130 is denoted a replicate of the data event d 135. Additional cell data is introduced below.

Turning to FIG. 2, the subterranean region of interest 105 may be made up of layers of rock 200 separated by geological discontinuities 205. Further, in some embodiments, the subterranean region of interest 105 may include hydrocarbons stored within a reservoir 210, which is a type of geological discontinuity 205. Further illustrated in FIG. 2, a seismic acquisition system 215 may be configured to perform a seismic survey 220 over the subterranean region of interest 105 to acquire the seismic data.

The seismic acquisition system 215 may include a seismic source 225 and seismic receivers 230 positioned on or near the surface of the earth 235. While FIG. 2 specifically illustrates a surface seismic survey 220, a person of ordinary skill in the art will appreciate that other seismic surveys, such as vertical seismic profile (VSP) surveys, may be alternatively or additionally used to acquire the seismic data.

The seismic survey 220 may initially rely on the seismic source 225 configured to generate radiated seismic waves 240 (i.e., emitted energy, wavefield) . The type of seismic source 225 may depend on the environment in which it is used. For example, on land, the seismic source 225 may be a vibroseis truck or explosive charge. In water, the seismic source 225 may be an airgun. The radiated seismic waves 240 may radiate along and into the subterranean region of interest 105. The radiated seismic waves 240 may return to the surface of the earth 235 as refracted seismic waves (not shown) or may be reflected by the geological discontinuities 205 and return to the surface of the earth 235 as reflected seismic waves 245. The radiated seismic waves 240 may also propagate along the surface of the earth 235 as Rayleigh waves or Love waves, collectively known as “ground roll” 250. Vibrations associated with ground roll 250 do not penetrate far beneath the surface of the earth 235 and, hence, are not influenced by, nor contain information about, deep portions of the subterranean region of interest 105. Each seismic receiver 230 located on or near the surface of the earth 235 is configured to detect and record the radiated seismic waves 240, reflected seismic waves 245, refracted seismic waves, and ground roll 250 collectively as a seismic trace.

Denoting the two-dimensional position of the seismic source 225 as x_p= (x′_p, y′_p) and the two-dimensional position of each seismic receiver 230 as x_r= (x′_r, y′_r) , respectively, the seismic trace recorded by each seismic receiver 230 may then be denoted D (x′_p, y′_p, x′_r, y′_r, t) , where t denotes recording time (i.e., the time elapsed after the activation of the seismic source 225) . The collection of all seismic traces acquired during the seismic survey 220 may be described as the seismic data. As such, the seismic data may be initially collected in five dimensions.

The seismic data may be processed to remove near-surface effects, noise, seismic survey geometry irregularities, migration artifacts, etc. from the seismic data. The seismic data may be further processed to transform the seismic data from one domain to another domain, change the dimensionality of the seismic data, and/or determine one or more seismic attributes (hereinafter “attributes” ) of the seismic data. Attributes may include, without limitation, reflection amplitude, frequency, phase, reflectivity, and impedance.

FIG. 3 displays processed seismic data 300 (hereinafter “seismic data” ) of a subterranean region of interest 105 in accordance with one or more embodiments. In some embodiments, the seismic data 300 may be a migrated seismic image or an image of one or more attributes. Each cell 100 that represents the subterranean region of interest 105 is further associated with a seismic constraint s 305 among the seismic data 300. In some embodiments, the seismic constraint 305 may be a value of the one or more attributes. Accordingly, in these embodiments, the seismic constraint 305 may be a vector s where s= (s₁, …, s_n) . The seismic constraint 305 may be additional cell data along with the location 110.

A process-based geological model may be conditioned to the seismic data 300. FIG. 4A displays a process-based geological model 400 of the subterranean region of interest 105 in accordance with one or more embodiments. The process-based geological model 400 may be the result of physics-and/or chemical-based simulations that model the geological processes that occurred over geological history to form the subterranean region of interest 105. For illustration of the disclosed methods and systems only, FIG. 4A displays a binary satellite image of a river delta as the process-based geological model 400. However, in practice, the process-based geological model 400 may be a model of a three-dimensional subterranean region of interest 105 or a cross section of the three-dimensional subterranean region of interest 105. Further, in some embodiments, the process-based geological model 400 may be a calibrated process-based geological model calibrated by tuning the one or more input parameters indirectly based on the seismic data 300 and/or well data. In other embodiments, the process-based geological model 400 may be a well-conditioned process-based geological model. Methods used to determine the well-conditioned process-based geological model are disclosed in the Supplemental Description section below.

The process-based geological model 400 may aim to characterize the subterranean region of interest 105 using facies. Accordingly, each cell 100 is further associated with a facies A 405 among the process-based geological model 400. By way of example, FIG. 4A displays two facies options as shown by the key 410. A water facies, such as a delta of a fluvial facies, is displayed in white. A land facies, such as a paludal (i.e., swamp) facies, is displayed in black. The spatial distribution of the facies 405 in FIG. 4A shows a trend with more land facies in the northwest area and more water facies in the southeast area based on the cardinal directions 415. Further, the spatial distribution of the facies 405 illustrates a variety of geometric patterns that represent geological features. The geological features may include, without limitation, small and large lakes, swamps, meandering rivers, marine deltas, marine bays, and beach deposits. However, a person of ordinary skill in the art will appreciate that the process-based geological model 400 may include any number of facies options without departing from the scope of the disclosure. Further, just as the seismic data 300 may be three-dimensional, a person of ordinary skill in the art will appreciate that the process-based geological model 400 may be three dimensional without departing from the scope of the disclosure. The facies 405 may be additional cell data along with the location 110 and seismic constraint 305.

A corresponding simulated seismic image may be determined from the process-based geological model 400. Accordingly, the process-based geological model 400 and corresponding simulated seismic image are coupled and, hereinafter, collectively referred to as “coupled training images. ”

In some embodiments, a rock-physics model may be derived or determined from the process-based geological model 400. The process of seismic forward modeling (hereinafter “forward modeling” ) may be applied to the rock-physics model to determine the corresponding simulated seismic image. Accordingly, the corresponding simulated seismic image may be simulated seismic data where the simulated seismic data characterizes or honors the process-based geological model 400.

FIG. 4B displays a corresponding simulated seismic image 420 of the subterranean region of interest 105 determined from the process-based geological model 400 displayed in FIG. 4A in accordance with one or more embodiments. Each cell 100 is further associated with a simulated seismic constraint among the corresponding simulated seismic image 420. Like the location x 110 and seismic constraint s 305, the simulated seismic constraint may be a vector. The simulated seismic constraint may be additional cell data along with the location 110, seismic constraint 305, and facies 405.

If the process-based geological model 400 displayed in FIG. 4A adequately characterizes or honors the subterranean region of interest 105, the seismic data 300 displayed in FIG. 3 and corresponding simulated seismic image 420 displayed in FIG. 4B should agree at all locations. However, the seismic data 300 and corresponding simulated seismic image 420 disagree at some locations. Accordingly, the process-based geological model 400 displayed in FIG. 4A may not adequately characterize or honor the seismic data 300 as the process-based geological model 400 should.

The unconventional multi-point statistics approach may be used to condition the process-based geological model 400 to the seismic data 300 to determine a seismic-conditioned process-based geological model. Hereinafter, this process may be referred to as a “seismic-conditioning process” or simply “seismic conditioning. ” The unconventional multi-point statistics approach may rely on Bayes’ law. In some embodiments, Bayes’ law may be denoted:

where the probability P (A|d, x, s) is the probability of the facies A 405 given the data event d 135, location x 110, and seismic constraint s 305. Note a joint event (x, A, d, s) may be a location x 110 where a data event d 135 surrounds the location x 110 and is associated with a facies A 405 and seismic constraint s 305.

Returning to Equation (1) , the three probabilities P on the right-hand side of Equation (1) are denoted the first probability, second probability, and third probability.

In some embodiments, the first probability P (A|d) of the facies A 405 given the data event d 135 may be approximated as the ratio:

where # (A, d) is the number of replicates of an event (A, d) and #d is the number of replicates of the data event d 135 among the process-based geological model 400. Accordingly, the first probability P (A|d) disregards the location x 110. Note that a replicate of the event (A, d) is a replicate of the data event d where each of the neighboring cells 130 within the replicate of the data event d is associated with the same facies A as the corresponding cell among the event (A, d) .

FIG. 5 illustrates replicates in accordance with one or more embodiments. FIG. 5 displays two dimensions. The first of the two dimensions includes the location x 110 as shown along the abscissa 500. The second of the two dimensions includes the seismic constraint s 305 as shown along the ordinate 505. The seismic data 300 is displayed as a solid line. The corresponding simulated seismic image 420 is displayed as a dashed line. By scanning the process-based geological model 400 (not shown in FIG. 5) and corresponding simulated seismic image 420, four replicates of the data event d 510 are identified among which there are two replicates of the event (A, d) 515 and two replicates of the eventwhereis not facies A 405. Accordingly, by way of example, the first probability P (A|d) is approximated as the ratiousing Equation (2) .

In some embodiments, the second probability P (x, s|A, d) of the location x 110 and seismic constraint s 305 given the facies A 405 and data event d 135 (collectively the event (A, d) ) is a probability density function (PDF) that may be approximated as:

where (x_i, s_i) is the location x_i and simulated seismic constraint of the ith replicate of the event (A, d) (as illustrated in FIG. 5) and g_σ [ (x, s) - (x_i, s_i) ] is a kernel probability density function (hereinafter simply “kernel function” ) centered at (x_i, s_i) with parameter vector σ. Application of the kernel function may be a smoothing operation.

In some embodiments, the third probability P (x, s|d) of the location x 110 and seismic constraint s 305 given the data event d 135 is a PDF that may be approximated as:

where (x_i, s_i) is the location x_i and simulated seismic constraint of the ith replicate of the data event d 135 (as illustrated in FIG. 5) .

If Equations (2) - (4) are implemented within Equation (1) , Equation (1) may be rewritten as:

Further, by way of example, if # (A, d) =2 and #d=4 as illustrated in FIG. 5, Equation (5) becomes:

In some embodiments, the kernel function in Equations (3) and (4) may be or include a multivariate Gaussian kernel function of conditional probability g_σ (t) (hereinafter simply “Gaussian kernel function” ) where:

In some embodiments, the Gaussian kernel function may be factorized as:

where σ_x and σ_s are standard deviations associated with the location x 110 and seismic constraint s 305, respectively. In some embodiments, factorization of the Gaussian kernel function may be performed due to the different nature and scale of the location x 110 and seismic constraint s 305. Accordingly, Equation (5) may be rewritten as:

whereis a location kernel function andis a seismic constraint kernel function.

The location kernel functionmay be considered a weight given to the data event d 135 or event (A, d) at the location x_i. The larger the distance between the location x 110 and location x_i, the smaller the weight. This feature allows the unconventional multi-point statistics approach to use a nonstationary process-based geological model 400. The degree of nonstationarity is controlled by the standard deviation σ_x. If the standard deviation σ_x is small, a seismic-conditioned process-based geological model may be like the process-based geological model 400. If the standard deviation σ_x is large, all weights become similar and lead to stationarity even if the process-based geological model 400 is nonstationary.

The seismic constraint kernel functionmay be considered a weight given to the data event d 135 or event (A, d) associated with the simulated seismic constraint. The larger the distance between the seismic constraint s 305 and simulated seismic constraint, the smaller the weight. This feature allows the unconventional multi-point statistics approach to condition the process-based geological model 400 to the seismic data 300. The degree of conditioning is controlled by the standard deviation σ_s. If the standard deviation σ_s is small, a seismic-conditioned process-based geological model is closely conditioned to the seismic data 300.

The selection of the standard deviations σ_x and σ_s provides a way to balance the influence of the process-based geological model 400 and the seismic data 300 on the seismic-conditioned process-based geological model. By way of example, if the trend of the process-based geological model 400 is to be closely honored, the standard deviation σ_x should be small compared to the standard deviation σ_s. If the trend of the seismic data 300 is to be closely honored, the standard deviation σ_s should be small compared to the standard deviation σ_x.

In practice, the probability P (A|d, x, s) is determined for each uninformed cell 115 among the cells 100 that represent the subterranean region of interest 105. However, prior to determining the probability P (A|d, x, s) for each uninformed cell 115, each informed cell 120 is associated with a well datum among well data (i.e., hard data) . In some embodiments, a well datum may be associated with the informed cell 120 most closely associated with the location within the subterranean region of interest 105 that the well datum was collected or acquired from.

In some embodiments, a well logging system may be configured to acquire, at least in part, the well data. FIG. 6 illustrates a well logging system 600 in accordance with one or more embodiments. Prior to deploying the well logging system 600 downhole, a well 605 may be partially or completely drilled within the subterranean region of interest 105 using a rock coring system or drilling system. The well 605 may traverse layers of rock 200 separated by geological discontinuities 205 and/or other structural features before ultimately penetrating a location of hydrocarbons (e.g., a reservoir 210) . In some embodiments, the well logging system 600 may be lowered into the well 605 following the removal of the rock coring system or drilling system. The well logging system 600 may be supported by a truck 610 and derrick 615 above ground. For example, the truck 610 may carry a conveyance mechanism 620 used to lower the well logging system 600 into the well 605. The conveyance mechanism 620 may be used to lower the well logging system 600 into the well 605. The conveyance mechanism 620 may be a wireline, coiled tubing, or drillpipe that may include means to provide power to the well logging system 600 and a telemetry channel from the well logging system 600 to the surface of the earth 235. In some embodiments, the well logging system 600 may be translated along the well 605 to acquire a well log over an interval 625 of the well 605.

The well logging system 600 may be configured to collect the well data in the form of well logs. The well logs may include, without limitation, an acoustic log (which may be a sonic log) , density log, neutron porosity log, gamma ray log, current resistivity log, caliper log, and any combination or derivation thereof. Accordingly, the well logging system 600 may be or include without limitation, an acoustic logging tool (which may be a sonic logging tool) , density logging tool, neutron porosity logging tool, gamma ray logging tool, resistivity logging tool, caliper logging tool, and any combination thereof.

In other embodiments, a rock coring system may acquire rock cores while drilling the well 605. Each rock core may be transported to, stored within, and tested in a laboratory setting. Any laboratory rock core testing system may be configured to collect the well data in the form of rock core data. Accordingly, the well data may include wells logs and/or rock core data.

Each well datum among the well data may be associated with each informed cell 120. Accordingly, the well datum may be additional cell data included with a data event d 135.

In some embodiments, Equation (1) , (5) , or (9) may be applied to each uninformed cell 115 to determine the probability P (A|d, x, s) associated with each uninformed cell 115. In some embodiments, the probability P (A|d, x, s) may be determined for each uninformed cell 115 in series following a sequential simulation scheme where the uninformed cells 115 form or follow one or more random paths 140 as displayed in FIG. 1. In some embodiments, one or more previously-determined probabilities P (A|d, x, s) , one per uninformed cell 115, may be used, at least in part, to determine the probability P (A|d, x, s) for the current uninformed cell 115. For example, this may occur when the cell 100 associated with the one or more previously-determined probabilities P (A|d, x, s) is included with one or more data events d 135.

In some embodiments, the entire process-based geological model 400 and corresponding simulated seismic image 420 are scanned to determine the probability P (A|d, x, s) associated with each uninformed cell 115. In other embodiments, scanning may be limited to a certain area within the process-based geological model 400 and corresponding simulated seismic image 420 that surrounds the current uninformed cell 115 as weights of replicates distant from the current uninformed cell 115 may be negligible. The size of each area may be determined by σ_x and/or σ_s. In these embodiments, the disclosed methods may be performed faster than if the entire process-based geological model 400 and corresponding simulated seismic image 420 are scanned.

In some embodiments, the well datum for each informed cell 120 and a seismic-conditioned facies selected or drawn from the probability P (A|d, x, s) for each uninformed cell 115 may be the seismic-conditioned process-based geological model. Note the probability P (A|d, x, s) and/or the seismic-conditioned facies selected from the probability P (A|d, x, s) for each uninformed cell 115 may be referred to as a “realization. ”

FIG. 7A displays a seismic-conditioned process-based geological model 700a in accordance with one or more embodiments. By way of example, the seismic-conditioned process-based geological model 700a is the process-based geological model 400 displayed in FIG. 4A conditioned to the seismic data 300 displayed in FIG. 3. Further, Equation (9) is used where σ_x=60 and σ_s=0.1 and a seismic-conditioned facies 705 is selected from the probability P (A|d, x, s) associated with each uninformed cell 115 as shown by the key 707.

Upon comparison, the seismic-conditioned process-based geological model 700a adequately reproduces the geometric patterns shown in the process-based geological model 400 displayed in FIG. 4A.

For verification, a seismic-conditioned corresponding simulated seismic image may be determined from the seismic-conditioned process-based geological model 700a. FIG. 7B displays a seismic-conditioned corresponding simulated seismic image 710a in accordance with one or more embodiments. In some embodiments, a rock-physics model may be determined from the seismic-conditioned process-based geological model 700a and forward modeling applied to the rock-physics model to determine the seismic-conditioned corresponding simulated seismic image 710a. Upon comparison of the seismic-conditioned corresponding simulated seismic image 710a displayed in FIG. 7B, the corresponding simulated seismic image 420 displayed in FIG. 4B, and the seismic data 300 displayed in FIG. 3, the seismic-conditioned corresponding simulated seismic image 710a more closely agrees with the seismic data 300 than the corresponding simulated seismic image 420. Accordingly, the seismic-conditioned process-based geological model 700a may be adequately conditioned to the seismic data 300 while preserving the geometric patterns within the process-based geological model 400. Accordingly, the seismic-conditioned process-based geological model 700a may adequately characterize the subterranean region of interest 105.

FIG. 8A displays a seismic-conditioned process-based geological model 700b in accordance with one or more embodiments. By way of example, the seismic-conditioned process-based geological model 700b is the process-based geological model 400 displayed in FIG. 4A conditioned to the seismic data 300 displayed in FIG. 3. Further, Equation (9) where σ_x=60 and σ_s=0.01 and a seismic-conditioned facies 705 is selected from the probability P (A|d, x, s) associated with each uninformed cell 115 as shown by the key 707. Because the standard deviation σ_s is small, the seismic-conditioned process-based geological model 700b is closely conditioned to the seismic data 300.

For verification, a seismic-conditioned corresponding simulated seismic image may be determined from the seismic-conditioned process-based geological model 700b. FIG. 8B displays a seismic-conditioned corresponding simulated seismic image 710b in accordance with one or more embodiments. Upon comparison of the seismic-conditioned corresponding simulated seismic image 710b displayed in FIG. 8B, the corresponding simulated seismic image 420 displayed in FIG. 4B, and the seismic data 300 displayed in FIG. 3, the seismic-conditioned corresponding simulated seismic image 710b more closely agrees with the seismic data 300 than the corresponding simulated seismic image 420. Accordingly, the seismic-conditioned process-based geological model 700b may be adequately conditioned to the seismic data 300. Accordingly, the seismic-conditioned process-based geological model 700b may adequately characterize the subterranean region of interest 105.

FIG. 9 describes a method in accordance with one or more embodiments. In step 900, cells 100 that represent a subterranean region of interest 105 are defined. The subterranean region of interest 105 may be two or three dimensional. Accordingly, the cells 100 may be arranged in two or three dimensions. Each cell 100 is associated with a location x 110 within the subterranean region of interest 105. Further, the cells 100 include informed cells 120 and uninformed cells 115. Cells 100 represent a two-dimensional subterranean region of interest 105 in FIG. 1.

In step 905, seismic data 300 of the subterranean region of interest 105 is obtained. In some embodiments, a seismic acquisition system 215 may be configured to acquire the seismic data 300 as illustrated in FIG. 2. Each cell 100 is further associated with a seismic constraint s 305 among the seismic data 300 as displayed in FIG. 3.

In step 910, well data pertaining to the subterranean region of interest 105 is obtained. In some embodiments, a well logging system 600 may be configured to acquire, at least in part, the well data as illustrated in FIG. 6. Each informed cell 120 among the cells 100 is further associated with each of the well data (i.e., each well datum) . In practice, each well datum may be associated with the informed cell 120 most closely associated with the location within the subterranean region of interest 105 that the well datum was collected from.

In step 915, a process-based geological model 400 of the subterranean region of interest 105 is obtained. In some embodiments, a simulation system may be configured to determine or simulate the process-based geological model 400. To do so, the simulation system may model the geological processes within the subterranean region of interest 105 using physics-and/or chemical-based simulations. The simulation system may be or include a computer system, which is discussed relative to FIG. 10 below. Each cell 100 is further associated with a facies A 405 among the process-based geological model 400 as displayed in FIG. 4A.

In step 920, a corresponding simulated seismic image 420 of the subterranean region of interest 105 is determined based, at least in part, on the process-based geological model 400. In some embodiments, a rock-physics model is determined from the process-based geological model 400 and forward modeling applied to the rock-physics model to determine the corresponding simulated seismic image 420. Each cell 100 is further associated with a simulated seismic constraint among the corresponding simulated seismic image 420.

Step 925 is performed for each of the uninformed cells 115 in series. For each uninformed cell 115, a probability P (A|d, x, s) of the facies A 405 given a data event d 135, location x 110, and seismic constraint s 305 is determined based, at least in part, on the location x 110, seismic constraint s 305, process-based geological model 400, corresponding simulated seismic image 420, and well data. Equations (1) , (5) , or (9) may be used to determine the probability P (A|d, x, s) for each uninformed cell 115 by following one or more random paths 140 each formed by two or more uninformed cells 115. Note each data event d 135 includes a set of neighboring cells 130 that includes the uninformed cell of interest among the random path of interest as previously described and illustrated in FIG. 1.

In step 930, a seismic-conditioned process-based geological model 700a, b is determined based, at least in part, on the probability P (A|d, x, s) for each uninformed cell 115 and each well datum for each informed cell 120. In some embodiments, a seismic-conditioned facies 705 may be selected from the probability P (A|d, x, s) for each uninformed cell 115 as shown by the key 707. FIGs. 7A and 8A each display a seismic-conditioned process-based geological model 700a, b that includes a seismic-conditioned facies 705 for each uninformed cell 115.

In some embodiments, the seismic-conditioned process-based geological model 700a, b may be conditioned to the well data. Methods used to determine the well-conditioned seismic-conditioned process-based geological model are disclosed in the Supplemental Description section below.

In step 935, a predicted location of hydrocarbons within the subterranean region of interest 105 is identified based, at least in part, on the seismic-conditioned process-based geological model 700a, b. In some embodiments, an interpretation workstation may be configured to display the seismic-conditioned process-based geological model 700a, b such that an interpreter may visually identify a manifestation of the predicted location of hydrocarbons on the seismic-conditioned process-based geological model 700a, b.

Turning to systems, a computer system may be configured to perform steps 900, 905, 910, 915, 920, 925, and 930. FIG. 10 illustrates a computer system 1000 in accordance with one or more embodiments. Though the term “computer system” is used to describe the various parts of the computer system relative to FIG. 10, “interpretation workstation” may replace the term “computer system” without departing from the scope of the disclosure. The interpretation workstation may be configured to perform step 935.

The computer system 1000 is intended to depict any computing device such as 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 system 1000 may include an input device, such as a keypad, keyboard, touch screen, or other device that can accept user information, and an output device that displays information, including digital data, visual or audio information (or a combination of both) , or a graphical user interface (GUI) . Specifically, an interpretation workstation may include a robust graphics card for the detailed rendering of the seismic-conditioned process-based geological model 700a, b such that the seismic-conditioned process-based geological model 700a, b may be displayed and manipulated in a virtual reality system using 3D goggles, a mouse, or a wand to identify a manifestation of a predicted location of hydrocarbons within the subterranean region of interest 105.

The computer system 1000 can serve in a role as a client, network component, server, database, or any other component (or a combination of roles) of a computer system 1000 as required for seismic processing and interpretation. The illustrated computer system 1000 is communicably coupled with a network 1005. In some implementations, one or more components of each computer system 1000 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 system 1000 is an electronic computing device operable to receive, transmit, process, store, and/or manage data and information associated with the disclosed methods. According to some implementations, the computer system 1000 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) .

Because processing and interpretation may not be sequential, the computer system 1000 can receive requests over network 1005 from other computer systems 1000 or another client application and respond to the received requests by processing the requests appropriately. In addition, requests may also be sent to the computer system 1000 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 computer systems 1000.

Each of the components of the computer system 1000 can communicate using a system bus 1010. In some implementations, any or all of the components of each computer system 1000, both hardware or software (or a combination of hardware and software) , may interface with each other or the interface 1015 (or a combination of both) over the system bus 1010 using an application programming interface (API) 1020 or a service layer 1025 (or a combination of the API 1020 and service layer 1025. The API 1020 may include specifications for routines, data structures, and object classes. The API 1020 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 1025 provides software services to each computer system 1000 or other components (whether or not illustrated) that are communicably coupled to each computer system 1000. The functionality of each computer system 1000 may be accessible for all service consumers using this service layer 1025. Software services, such as those provided by the service layer 1025, 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 another suitable format. While illustrated as an integrated component of each computer system 1000, alternative implementations may illustrate the API 1020 or the service layer 1025 as stand-alone components in relation to other components of each computer system 1000 or other components (whether or not illustrated) that are communicably coupled to each computer system 1000. Moreover, any or all parts of the API 1020 or the service layer 1025 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 system 1000 includes an interface 1015. Although illustrated as a single interface 1015 in FIG. 10, two or more interfaces 1015 may be used according to particular needs, desires, or particular implementations of each computer system 1000. The interface 1015 is used by each computer system 1000 for communicating with other systems in a distributed environment that are connected to the network 1005. Generally, the interface 1015 includes logic encoded in software or hardware (or a combination of software and hardware) and operable to communicate with the network 1005. More specifically, the interface 1015 may include software supporting one or more communication protocols associated with communications such that the network 1005 or interface’s hardware is operable to communicate physical signals within and outside of the illustrated computer system 1000.

The computer system 1000 includes at least one computer processor 1030. Generally, a computer processor 1030 executes any instructions, algorithms, methods, functions, processes, flows, and procedures as described above. A computer processor 1030 may be a central processing unit (CPU) and/or a graphics processing unit (GPU) .

The computer system 1000 also includes a memory 1035 that stores data and software for the computer system 1000 or other components (or a combination of both) that can be connected to the network 1005. Although illustrated as a single memory 1035 in FIG. 10, two or more memories may be used according to particular needs, desires, or particular implementations of the computer system 1000 and the described functionality. In some embodiments, memory 1035 may receive (and store) the seismic data 300 from the seismic acquisition system 215, the well data 1040 from the well logging system 600, and the process-based geological model 400 from the simulation system as illustrated in FIG. 10. While memory 1035 is illustrated as an integral component of each computer system 1000, in alternative implementations, memory 1035 can be external to the computer system 1000.

The application 1045 is an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer system 1000, particularly with respect to functionality described in this disclosure. For example, application 1045 can serve as one or more components, modules, applications, etc. Further, although illustrated as a single application 1045, the application 1045 may be implemented as multiple applications 1045 on each computer system 1000. In addition, although illustrated as integral to each computer system 1000, in alternative implementations, the application 1045 can be external to each computer system 1000.

There may be any number of computer systems 1000, such as computer clusters, associated with, or external to, a seismic processing system and an interpretation workstation, where each computer system 1000 communicates over network 1005. 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 the computer system 1000, or that one user may use multiple computer systems 1000.

A wellbore planning system may be or include a computer system 1000. The wellbore planning system may be configured to design a wellbore plan based on the predicted location of hydrocarbons identified in step 935.

Following the design of the wellbore plan, a drilling system may be configured to drill a wellbore guided by the wellbore plan such that the wellbore penetrates the predicted location of hydrocarbons. FIG. 11 illustrates a drilling system 1100 in accordance with one or more embodiments. Although the drilling system 1100 shown in FIG. 11 is used to drill the wellbore 1105 guided by the wellbore plan (that includes a wellbore path 1110) on land, the drilling system 1100 may be a marine wellbore drilling system. Further, although the drilling system 1100 shown in FIG. 11 is used to drill a new wellbore 1105, the wellbore 1105 being drilled may be a sidetrack wellbore or an offset wellbore. As such, the example of the drilling system 1100 shown in FIG. 11 is not meant to limit the present disclosure.

As shown in FIG. 11, the wellbore 1105 may be drilled using a drill rig that may be situated on a land drill site, an offshore platform, such as a jack-up rig, a semi-submersible, or a drill ship. The drill rig may be equipped with a hoisting system, such as a derrick 615, which can raise or lower the drillstring 1115 and other tools required to drill the wellbore 1105. The drillstring 1115 may include one or more drill pipes connected to form conduit and a bottom hole assembly 1120 (BHA) disposed at the distal end of the drillstring 1115. The BHA 1120 may include a drill bit 1125 to cut into rock 200, including cap rock 200a. The BHA 1120 may further include measurement tools, such as a measurement-while-drilling (MWD) tool and logging-while-drilling (LWD) tool. MWD tools may include sensors and hardware to measure downhole drilling parameters, such as the azimuth and inclination of the drill bit 1125, the weight-on-bit, and the torque. The LWD measurements may include sensors, such as resistivity, gamma ray, and neutron density sensors, to characterize the rock 200 surrounding the wellbore 1105. Both MWD and LWD measurements may be transmitted to the surface of the earth 235 using any suitable telemetry system known in the art, such as a mud-pulse or by wired-drill pipe.

To start drilling, or “spudding in, ” the wellbore 1105, the hoisting system lowers the drillstring 1115 suspended from the derrick 615 of the drill rig towards the planned surface location of the wellbore 1105. An engine, such as a diesel engine, may be used to supply power to the top drive 1130 to rotate the drillstring 1115 via the drive shaft 1135. The weight of the drillstring 1115 combined with the rotational motion enables the drill bit 1125 to bore the wellbore 1105.

The near-surface rock 200 of the subterranean region of interest 105 is typically made up of loose or soft sediment or rock, so large diameter casing 1140 (e.g., “base pipe” or “conductor casing” ) is often put in place while drilling to stabilize and isolate the wellbore 1105. At the top of the base pipe is the wellhead, which serves to provide pressure control through a series of spools, valves, or adapters (not shown) . Once near-surface drilling has begun, water or drill fluid may be used to force the base pipe into place using a pumping system until the wellhead is situated just above the surface of the earth 235.

Drilling may continue without any casing 1140 once deeper or more compact rock 200 is reached. While drilling, a drilling mud system 1145 may pump drilling mud from a mud tank on the surface of the earth 235 through the drill pipe. Drilling mud serves various purposes, including pressure equalization, removal of rock cuttings, and drill bit cooling and lubrication.

At planned depth intervals, drilling may be paused and the drillstring 1115 withdrawn from the wellbore 1105. Sections of casing 1140 may be connected, inserted, and cemented into the wellbore 1105. Casing string may be cemented in place by pumping cement and mud, separated by a “cementing plug, ” from the surface of the earth 235 through the drill pipe. The cementing plug and drilling mud force the cement through the drill pipe and into the annular space between the casing 1140 and the wall of the wellbore 1105. Once the cement cures, drilling may recommence. The drilling process is often performed in several stages. Therefore, the drilling and casing cycle may be repeated more than once, depending on the depth of the wellbore 1105 and the pressure on the walls of the wellbore 1105 from surrounding rock 200.

Due to the high pressures experienced by deep wellbores 1105, a blowout preventer (BOP) may be installed at the wellhead to protect the rig and environment from unplanned oil or gas releases. As the wellbore 1105 becomes deeper, both successively smaller drill bits 1125 and casing 1140 may be used. Drilling deviated or horizontal wellbores 1105 may require specialized drill bits 1125 or drill assemblies.

The drilling system 1100 may be disposed at and communicate with other systems in the wellbore environment, such as the wellbore planning system 1150. The drilling system 1100 may control at least a portion of a drilling operation by providing controls to various components of the drilling operation. In one or more embodiments, the system may receive data from one or more sensors arranged to measure controllable parameters of the drilling operation. As a non-limiting example, sensors may be arranged to measure weight-on-bit, drill rotational speed (RPM) , flow rate of the mud pumps (GPM) , and rate of penetration of the drilling operation (ROP) . Each sensor may be positioned or configured to measure a desired physical stimulus. Drilling may be considered complete when a drilling target 1155 with the reservoir 210 is reached or the presence of hydrocarbons is established.

FIG. 12 illustrates a system 1200 in accordance with one or more embodiments. The system 1200 includes at least two of the seismic acquisition system 215, well logging system 600, simulation system 1205, computer system 1000, interpretation workstation 1000a, wellbore planning system 1150, and drilling system 1100. Each part of the system 1200 may be communicably coupled to any other part of the system 1200 via the network 1005 (not shown in FIG. 12) .

In some embodiments, the seismic acquisition system 215 may be configured to acquire the seismic data 300 as described relative to FIG. 2. In some embodiments, the well logging system 600 may be configured to acquire, at least in part, the well data 1040 as described relative to FIG. 6. In some embodiments, the simulation system 1205 may be configured to determine the process-based geological model 400.

In some embodiments, the computer system 1000 may be configured to receive the seismic data 300 from the seismic acquisition system 215, the well data 1040, at least in part, from the well logging system 600, and the process-based geological model 400 from the simulation system 1205. Accordingly, the seismic data 300, well data 1040, and process-based geological model 400 may be transferred to, stored on, and processed by the computer system 1000.

The computer system 1000 may be further configured to determine the corresponding simulated seismic image 420 based, at least in part, on the process-based geological model 400.

The computer system 1000 may be still further configured to determine the seismic-conditioned process-based geological model 700a, b based, at least in part, the seismic data 300, well data 1040, process-based geological model 400, corresponding simulated seismic image 420, and the unconventional multi-point simulation approach.

In some embodiments, the seismic-conditioned process-based geological model 700a, b may be transferred to and stored on the interpretation workstation 1000a. In some embodiments, the interpretation workstation 1000a may be configured to identify a predicted location of hydrocarbons within the subterranean region of interest 105 using the seismic-conditioned process-based geological model 700a, b. To do so, the interpretation workstation 1000a may display a detailed rendering of the seismic-conditioned process-based geological model 700a, b such that an interpreter may identify a manifestation of the predicted location of hydrocarbons within the seismic-conditioned process-based geological model 700a, b.

In some embodiments, the identified predicted location of hydrocarbons may be transferred to, stored on, and processed by the wellbore planning system 1150. The wellbore planning system 1150 may be configured to design a wellbore plan based, at least in part, on the identified predicted location of hydrocarbons.

In some embodiments, the designed wellbore plan may be transferred to, stored on, and used by the drilling system 1100. The drilling system 1100 may be configured to drill a wellbore within the subterranean region of interest 105 guided by, at least in part, on the designed wellbore plan. The wellbore may penetrate the predicted location of hydrocarbons within the subterranean region of interest 105 such that the hydrocarbons may be produced to the surface of the earth 235 to be used as fuel.

In summary, the disclosed methods and systems may be used to condition a process-based geological model 400 to seismic data 300. To do so, the disclosed methods may rely on an unconventional multi-point statistics approach based on Bayes’ law as described mathematically in Equations (1) - (9) . The seismic-conditioned process-based geological model 700a, b may adequately characterize a subterranean region of interest 105 while honoring the seismic data 300.

SUPPLEMENTAL DESCRIPTION

In some embodiments, the process-based geological model 400, calibrated process-based geological model, or seismic-conditioned process-based geological model 700a, b may be conditioned to the well data. FIG. 13 describes a method for generating a well-conditioned process-based geological model using an adjustable search template. While the various steps in FIG. 13 are presented and described sequentially, one of ordinary skill in the art will appreciate that some or all of the steps may be executed in a different order, combined or omitted, and/or executed in parallel.

In step 1300, well data 1040 pertaining to the subterranean region of interest 105 is obtained. More specifically, the well data 1040 may be acquired at one or more wells 605 in the subterranean region of interest 105. Examples of the well data 1040 may include well logs, rock core data, and/or cutting data. For more information on the well data 1040, see FIG. 6 above and the accompanying description. A subterranean region of interest 105 may be a portion of a geological area or volume desired or selected for further analysis (e.g., for simulating one or more depositional and/or diagenetic processes) .

In step 1305, one or more facies A 405 for the subterranean region of interest 105 are determined using the well data 1040.

In step 1310, the process-based geological model 400 of the subterranean region of interest 105 is obtained. The process-based geological model 400 may be a grid model where various cells 100 are assigned a facies A. FIG. 4A displays a process-based geological model 400.

In some embodiments, the process-based geological model 400 is generated by performing one or more physics-based simulations to model one or more geological processes. The simulation results may be represented as facies A 405 in a three-dimensional grid of cells 100. In some embodiments, the grid cell size in the process- based geological model 400 may be defined based on spatial variability of various heterogeneous features.

Returning to FIG. 13, in step 1315, a simulation grid of cells is determined using the process-based geological model 400. In some embodiments, for example, a simulation grid of cells is the same size as the process-based geological model 400. Various cells 100 in the simulation grid may be associated with little-to-no data prior to well conditioning.

In step 1320, the well data 1040 and/or one or more facies A 405 among the process-based geological model 400 are assigned to one or more cells 100 in the simulation grid of cells. In some embodiments, each well datum among the well data 1040 is assigned to each informed cell 120. For example, the well data 1040 may be scattered throughout the subterranean region of interest 105 such that a well datum among the well data 1040 is assigned to its closest respective cell 100.

In step 1325, an initial template size is selected for a search template. The search template may be a predetermined area in the simulation grid of cells 100 that is used to search a portion of the process-based geological model 400. During the well-conditioning process, the search template may have a default or selected size that may be rescaled through the well-conditioning process. A larger search template may include more data (e.g., well data 1040 or previously-simulated data) that may better capture long range heterogeneity in a sampling region. On the other hand, a smaller template size may have better performance for determining a number of replicates of a data event d 135 (hereinafter “replicate event” ) of a searched geological event in the process-based geological model 400. As such, the initial template size may be used for the initial search of the process-based geological model 400.

In step 1330, a random path 140 is determined through the simulation region. The random path 140 may be used to implement a stochastic simulation method based on a multiscale regionalized direct sampling scheme. Using the selected search template, a portion of the simulation grid of cells 100 may be subsequently selected as the simulation region for performing the geological simulation or well-conditioning procedure. Moreover, by sampling from a simulation region around each cell 100 (i.e., a certain area) instead of the entire process-based geological model 400, the well- conditioning process may be memory economic. Using the random path 140, the well-conditioned process-based geological model may honor the well data 1040 in the simulation region while also reproducing spatial geological features at various scales.

In step 1335, a sampling portion around an uninformed cell 115 along the random path 140 is determined in the process-based geological model 400.

In step 1340, a geological event is determined that is associated with one or more geological processes that are being simulated. A geological event may be the data event d 135 that includes the cell data among the neighboring cells 130 of a simulation region defined by a search template of a predetermined uninformed cell 115 that is undergoing analysis. In some embodiments, a geological event may be identified using the well data 1040.

In step 1345, one or more replicate events are determined for a geological event in a sampling portion based on a similarity analysis. After sampling a geological event in the process-based geological model 400, replicate events are searched within a simulation region of the process-based geological model 400. By sampling an alleged replicate event, a geological property is assigned at the center of the replicate to the uninformed cell 115 being simulated. To determine whether an alleged replicate event corresponds to a particular geological event, one or more similarity metrics are used to compare the geological event and the alleged replicate event. For example, similarity between two geological eventsandmay be determined using the following equations:

where i=1, 2, ..., n, s’ corresponds to a predetermined similarity metric function, and a_i corresponds a similarity metric threshold. The similarity metric s’ may take a value between [0, 1] . When the calculated similarity s’ is close to 0, two geological events are more similar. When the metric’s distance is closer to 1, the two geological events are more different.

In step 1350, a well-conditioned facies is assigned to a selected uninformed cell 115 of the simulation grid. After a replicate event is found in the simulation region, the facies A 405 at its center is directly assigned to the selected uninformed cell 115 of the simulation grid. If no such replicate events are found within the simulation region, the selected uninformed cell 115 may remain empty temporarily until assigned a well-conditioned facies at a later stage in the geological simulation with an adjusted search template (e.g., such as a reduced search template) .

In step 1355, a determination is made whether all uninformed cells 115 are visited along each of the one or more random paths 140. In particular, the one or more random paths 140 may traverse multiple sampling regions until the entire process-based geological model 400 has been traversed. For example, the process-based geological model 400 may be fully well-conditioned after completing iterative simulations. After the well-conditioning process is complete, another well-conditioning process may be performed, such as when new well data 1040 is acquired that pertains to the subterranean region of interest 105. If any uninformed cells 115 remain unassigned, the well-conditioning process may proceed to step 1360. Otherwise, the well-conditioning process may proceed to step 1365.

In step 1360, the template size is reduced. For example, the well-conditioning process may start with a large search template to capture large scale geological features in the process-based geological model 400. The size of the search template may be progressively reduced to represent smaller scale features. In some embodiments, the template size is changed level-by-level or even cell-by-cell from its edges to the center of the search template. In some embodiments, for example, search templates are nested such that template sizes shrink progressively throughout the well-conditioning process. Template sizes may also be automatically selected based on a desired computing time for the well-conditioning process. For example, a predetermined number of template sizes, such as three total sizes, may be selected accordingly.

In step 1365, a well-conditioned process-based geological model is generated based, at least in part, on the well-conditioned facies for each uninformed cell 115.

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.

Claims

A method comprising:

defining a plurality of cells that represents a subterranean region of interest,

wherein each of the plurality of cells is associated with a location x within the subterranean region of interest, and

wherein the plurality of cells comprises informed cells and uninformed cells;

obtaining, from a seismic acquisition system, seismic data of the subterranean region of interest,

wherein each of the plurality of cells is further associated with a seismic constraint s among the seismic data;

obtaining well data pertaining to the subterranean region of interest,

wherein each of the informed cells is associated with each of the well data;

obtaining, from a simulation system, a process-based geological model of the subterranean region of interest,

wherein each of the plurality of cells is further associated with a facies A among the process-based geological model;

determining a corresponding simulated seismic image of the subterranean region of interest based, at least in part, on the process-based geological model,

wherein each of the plurality of cells is further associated with a simulated seismic constraint among the corresponding simulated seismic image;

for each of the uninformed cells in series, determining a probability P (A|d, x, s) of the facies A given a data event d, the location x, and the seismic constraint s based, at least in part, on the location x, the seismic constraint s, the process-based geological model, the corresponding simulated seismic image, and the well data,

wherein the data event d comprises neighboring cells among the plurality of cells;

determining a seismic-conditioned process-based geological model based, at least in part, on the probability P (A|d, x, s) for each of the uninformed cells and each of the well data for each of the informed cells; and

identifying, using an interpretation workstation, a predicted location of hydrocarbons within the subterranean region of interest based, at least in part, on the seismic-conditioned process-based geological model.
The method of claim 1, further comprising designing, using a wellbore planning system, a wellbore plan based, at least in part, on the predicted location of hydrocarbons.
The method of claim 2, further comprising drilling, using a drilling system, a wellbore guided, at least in part, by the wellbore plan.
The method of claim 1, wherein determining the corresponding simulated seismic image comprises:

determining a rock-physics model based, at least in part, on the process-based geological model; and

determining, using forward modeling, the corresponding simulated seismic image based, at least in part, on the rock-physics model.
The method of claim 1, wherein determining the probability P (A|d, x, s) comprises:

determining a first probability P (A|d) of the facies A given the data event d;

determining a second probability P (x, s|A, d) of the location x and the seismic constraint s given the facies A and the data event d based, at least in part, on the location x, the seismic constraint s, the process-based geological model, and the corresponding simulated seismic image;

determining a third probability P (x, s|d) of the location x and the seismic constraint s given the data event d based, at least in part, on the location x, the seismic constraint s, the process-based geological model, and the corresponding simulated seismic image; and

determining the probability P (A|d, x, s) based, at least in part, on the first probability P (A|d) , the second probability P (x, s|A, d) , and the third probability P (x, s|d) .
The method of claim 5, wherein determining the first probability P (A|d) comprises:

determining a number of replicates of an event (A, d) ;

determining a number of replicates of the data event d; and

determining the first probability P (A|d) as a ratio of the number of replicates of the event (A, d) and number of replicates of the data event d.
The method of claim 5, wherein determining the second probability P (x, s|A, d) comprises applying

wherein # (A, d) is a number of replicates of an event (A, d) ,

wherein (x_i, s_i) is the location and the simulated seismic constraint of an ith replicate of the event (A, d) , and

wherein g_σ [ (x, s) - (x_i, s_i) ] is a kernel function.
The method of claim 7, wherein the kernel function comprises a Gaussian kernel function.
The method of claim 1, wherein determining the probability P (A|d, x, s) comprises applying

wherein #d is a number of replicates of the data event d,

wherein # (A, d) is a number of replicates of an event (A, d) ,

wherein x_i is the location of an ith replicate of the event (A, d) or the data event d,

wherein s_i is the simulated seismic constraint of the ith replicate of the event (A, d) or the data event d,

whereinis a location kernel function, and

whereinis a seismic constraint kernel function.
The method of claim 5, wherein determining the third probability P (x, s|d) comprises applying

wherein #d is a number of replicates of the data event d,

wherein (x_i, s_i) is the location and the simulated seismic constraint of an ith replicate of the data event d, and

wherein g_σ [ (x, s) - (x_i, s_i) ] is a kernel function.
The method of claim 1, wherein determining the probability P (A|d, x, s) comprises applying

wherein # (A, d) is a number of replicates of an event (A, d) ,

wherein #d is a number of replicates of the data event d,

wherein (x_i, s_i) is the location and the simulated seismic constraint of an ith replicate of the event (A, d) or the data event d, and

wherein g_σ [ (x, s) - (x_i, s_i) ] is a kernel function.
The method of claim 1, wherein determining the probability P (A|d, x, s) for each of the uninformed cells in series comprises following a random path formed by the uninformed cells.
The method of claim 1, wherein determining the seismic-conditioned process-based geological model comprises selecting a seismic-conditioned facies from the probability P (A|d, x, s) for each of the uninformed cells.
The method of claim 1, further comprising calibrating the process-based geological model by tuning one or more input parameters based, at least in part, on the seismic data and the well data.
A system comprising:

a computer system configured to:

define a plurality of cells that represents a subterranean region of interest,

wherein each of the plurality of cells is associated with a location x within the subterranean region of interest, and

wherein the plurality of cells comprises informed cells and uninformed cells,

receive, from a seismic acquisition system, seismic data of the subterranean region of interest,

wherein each of the plurality of cells is further associated with a seismic constraint s among the seismic data,

receive well data pertaining to the subterranean region of interest,

wherein each of the informed cells is associated with each of the well data,

receive, from a simulation system, a process-based geological model of the subterranean region of interest,

wherein each of the plurality of cells is further associated with a facies A among the process-based geological model,

determine a corresponding simulated seismic image of the subterranean region of interest based, at least in part, on the process-based geological model,

wherein each of the plurality of cells is further associated with a simulated seismic constraint among the corresponding simulated seismic image,

for each of the uninformed cells in series, determine a probability P (A|d, x, s) of the facies A given a data event d, the location x, and the seismic constraint s based, at least in part, on the location x, the seismic constraint s, the process-based geological model, the corresponding simulated seismic image, and the well data,

wherein the data event d comprises neighboring cells among the plurality of cells, and

determine a seismic-conditioned process-based geological model based, at least in part, on the probability P (A|d, x, s) for each of the uninformed cells and each of the well data for each of the informed cells; and

an interpretation workstation configured to identify a predicted location of hydrocarbons within the subterranean region of interest based, at least in part, on the seismic-conditioned process-based geological model.
The system of claim 15, further comprising the seismic acquisition system configured to acquire the seismic data.
The system of claim 15, further comprising a well logging system configured to acquire, at least in part, the well data.
The system of claim 15, further comprising the simulation system configured to determine the process-based geological model.
The system of claim 15, further comprising a wellbore planning system configured to design a wellbore plan based, at least in part, on the predicted location of hydrocarbons.
The system of claim 19, further comprising a drilling system configured to drill a wellbore guided, at least in part, by the wellbore plan.