WO2025175409A1

WO2025175409A1 - Method and system for rock physics-based grid refinement of grid in forward stratigraphic modeling

Info

Publication number: WO2025175409A1
Application number: PCT/CN2024/077513
Authority: WO
Inventors: Wisam ALKAWAI; Xiaoxi Wang
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: 2024-02-19
Filing date: 2024-02-19
Publication date: 2025-08-28
Anticipated expiration: 2026-08-19

Abstract

The method may include obtaining an observed seismic dataset pertaining to a subterranean region of interest and determining from the dataset a seismic reflectivity series for a line transecting the region including a number of seismic reflectivity coefficients. The method may also include iteratively, until a convergence criterion is satisfied, obtaining a forward stratigraphic model (FSM), determining a number of FSM reflectivity coefficients from the FSM, and determining a refinement coefficient based on the number of seismic reflectivity coefficients and the number of FSM reflectivity coefficients. The method may further include updating the grid resolution of the FSM and obtaining an updated FSM using the updated grid resolution, determining an updated number of FSM reflectivity coefficients from the updated FSM, determining a calibrated FSM using the updated number of coefficients, and updating a location of a hydrocarbon reservoir based on the updated FSM.

Description

METHOD AND SYSTEM FOR ROCK PHYSICS-BASED GRID REFINEMENT OF GRID IN FORWARD STRATIGRAPHIC MODELING

BACKGROUND

Forward stratigraphic modeling is a method used to predict the sedimentary facies (i.e., the characteristics of a rock that distinguishes it from adjacent rock) of geologic layers with increasing burial depth. Sedimentary facies may result from the deposits of sediment over geological history. The output of forward stratigraphic modeling may include prediction of porosity, permeability and temperature. Such predictions may be made for each geologic layer and/or at regularly or irregularly spaced depths. The predicted values may be functions of facies dependent compaction models and cementation models (particularly of quartz) , in addition to changes in sea level, sediment supply, and subsidence/uplift. Forward stratigraphic modeling predictions are therefore the subject of considerable uncertainty.

To derive robust results from forward stratigraphic modeling, its predictions are often calibrated against data from wells, such as wireline logs and core data. When wells are spatially sparse (for example, in frontier areas) , calibration using seismic data may be performed instead or as well as calibration using wells. Rock properties from forward stratigraphic modeling predictions may be converted to acoustic impedance models using rock physics calculations. From acoustic impedance models a synthetic seismic dataset may be calculated and compared to an observed seismic dataset. However, seismic calibration encounters challenges due to resolution differences between synthetic and observed seismic data, particularly at increasing burial depths.

To obtain satisfactory calibration it may be necessary to discretize the predictions made by forward stratigraphic modeling to match the resolution for the seismic dataset. Discretization of a forward stratigraphic model (FSM) onto too coarse a scale may lead to loss of resolution and accuracy, while discretization onto too fine a scale may lead to computational inefficiency. Thus, there is a pressing need for a method to determine a preferred discretization for forward stratigraphic modeling.

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 may include obtaining, from a seismic acquisition system, an observed seismic dataset pertaining to a subterranean region of interest and determining, using a seismic processing system, from the observed seismic dataset a seismic reflectivity series for a line transecting the subterranean region of interest, where the seismic reflectivity series comprises a number of seismic reflectivity coefficients. The method may also include, using a forward stratigraphic modeler, iteratively, or recursively, until a convergence criterion is satisfied, obtaining a forward stratigraphic model (FSM) , wherein the FSM is generated using a grid resolution, determining a number of FSM reflectivity coefficients from the FSM, and determining a refinement coefficient based, at least in part, on the number of seismic reflectivity coefficients and the number of FSM reflectivity coefficients. The method further include, iteratively, or recursively, until a stopping criterion is satisfied, updating the grid resolution of the FSM based, at least in part, on the refinement coefficient to yield an updated grid resolution, obtaining an updated FSM, wherein the updated FSM is generated using the updated grid resolution, determining an updated number of FSM reflectivity coefficients from the updated FSM, updating the refinement coefficient based, at least in part, on the number of seismic reflectivity coefficients and the updated number of FSM reflectivity coefficients, and determining a calibrated FSM, using, at least in part, the updated number of FSM reflectivity coefficients. The method may still further include determining, using an interpretation workstation, a presence and a location of a hydrocarbon reservoir based, at least in part, on the updated FSM.

In general, in one aspect, embodiments relate to system. The system may include a seismic acquisition system, a seismic processing system, a forward stratigraphic modeler, and an interpretation workstation. The seismic acquisition system may be configured to obtain an observed seismic dataset pertaining to a subterranean region of interest and the seismic processing system may be configured to determine, from the observed seismic dataset, a seismic reflectivity series for a line transecting the subterranean region of interest, wherein the seismic reflectivity series comprises a number of seismic reflectivity coefficients. The forward stratigraphic modeler may be configured to, iteratively, or recursively, until a convergence criterion is satisfied, obtain an FSM, wherein the FSM is generated using a grid resolution, determine a number of FSM reflectivity coefficients from the FSM, and determine a refinement coefficient based, at least in part, on the number of seismic reflectivity coefficients and the number of FSM reflectivity coefficients. The forward stratigraphic modeler may be further configured to, iteratively, or recursively, until a stopping criterion is satisfied, update the grid resolution of the FSM based, at least in part, on the refinement coefficient to yield an updated grid resolution, obtain an updated FSM using the updated grid resolution, determine an updated number of FSM reflectivity coefficients from the updated FSM, and update the refinement coefficient based, at least in part, on the number of seismic reflectivity coefficients and the updated number of FSM reflectivity coefficients, and determine a calibrated FSM, using, at least in part, the updated number of FSM reflectivity coefficients. The interpretation workstation may be configured to determine a presence and a location of a hydrocarbon reservoir based, at least in part, on the updated FSM.

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

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A shows a seismic acquisition system in accordance with one or more embodiments.

FIG. 1B shows a portion of a seismic dataset in accordance with one or more embodiments.

FIG. 2 shows a flowchart in accordance with steps of one or more embodiments of forward stratigraphic modeling.

FIG. 3 is a flowchart in accordance with steps of one or more embodiments.

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

FIG. 5 shows a flowchart in accordance with one or more embodiments.

FIG. 6 shows a flowchart in accordance with one or more embodiments.

FIG. 7 displays a computer system in accordance with one or more embodiments.

FIG. 8 shows a drilling 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 (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 “reflectivity series” includes reference to one or more of such reflectivity series.

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 method 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 method.

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. 1-8, any component described with regard to a figure, in various embodiments disclosed herein, may be equivalent to one or more like-named components described with regard to any other figure. For brevity, descriptions of these components will not be repeated with regard to 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 with regard to a corresponding like-named component in any other figure.

The predictions made by forward stratigraphic modeling may be used to map the distributions of facies (rock types) in two or three dimensions within a subterranean region of interest. Such facies maps may be used during the exploration and development phases of the lifespan of a hydrocarbon reservoir. For example, they may be used in selecting drilling targets for both production and injection wells. To mitigate the inherent uncertainty in the predictions made by forward stratigraphic modeling, the predictions may be calibrated using seismic datasets, particularly in areas with few logged wells. Accurate calibration requires that forward stratigraphic modeling is performed using a discretization in depth (or geological time) appropriate to the characteristics of the seismic dataset, specifically the number of non-negligible reflection coefficients present in the seismic reflectivity series.

Methods and systems are disclosed to determine a preferred discretization. The method involves calculating a refinement coefficient number based on the number of coefficients in a reflectivity series predicted by forward stratigraphic modeling and the number of coefficients in a reflectivity series obtained from an observed seismic dataset. Further, the method involves using the refinement condition number to adjust the discretization used in forward stratigraphic modeling, such that the resulting FSM have a similar amount of detail to that present in the corresponding seismic reflection series.

Embodiments disclosed herein utilize one or more seismic datasets as an input. FIG. 1A illustrates a seismic acquisition system used to acquire a seismic dataset. An example of a seismic dataset is displayed in FIG. 1B. The illustrated seismic acquisition system and the displayed seismic dataset are only intended to be illustrative and should not be construed as limiting the scope of the invention in any way.

FIG. 1A shows a seismic acquisition system (100) configured to acquire a seismic dataset pertaining to a subterranean region of interest (102) . The subterranean region of interest (102) may or may not contain a hydrocarbon reservoir (104) . The purpose of the seismic survey may be to determine whether a hydrocarbon reservoir (104) is present within the subterranean region of interest (102) . The seismic acquisition system (100) may be used in relation to an interpretation workstation (195) , a forward stratigraphic modeler (197) , and/or a seismic processing system (199) as more fully described below.

The seismic acquisition system (100) may use a seismic source (106) positioned on the surface of the earth (116) . On land, the seismic source (106) is typically a vibroseis truck (as shown) or, less commonly, explosive charges, such as dynamite, buried to a shallow depth. In water, particularly in the ocean, the seismic source may commonly be an airgun (not shown) that releases a pulse of high-pressure gas when activated. Whatever its mechanical design, the seismic source (106) , when activated, generates radiated seismic waves, such as those whose paths are indicated by the rays (108) . The radiated seismic waves may be bent ( “refracted” ) by variations in the speed of seismic wave propagation within the subterranean region of interest (102) and return to the surface of the earth (116) as refracted seismic waves (110) . Alternatively, radiated seismic waves may be partially or wholly reflected by seismic reflectors, at reflection points such as (124) , and return to the surface as reflected seismic waves (114) . Seismic reflectors may be indicative of the geological boundaries (112) , such as the boundaries between geological layers, the boundaries between different pore fluids, faults, fractures or groups of fractures within the rock, or other structures of interest in the seismic for hydrocarbon reservoirs.

At the surface, the refracted seismic waves (110) , reflected seismic waves (114) , and surface waves (118) , also known as “ground-roll” may be detected by seismic receivers (120) . On land, a seismic receiver (120) may be a geophone (that records the velocity of ground motion) or an accelerometer (that records the acceleration of ground motion) . In water, the seismic receiver may commonly be a hydrophone that records pressure disturbances within the water. Irrespective of its mechanical design or the quantity detected, seismic receivers (120) convert the detected seismic waves into electrical signals that may subsequently be digitized and recorded by a seismic recorder (122) as a time-series of samples. Such a time-series is typically referred to as a seismic “trace” and represents the amplitude of the detected seismic wave at a plurality of sample times. Usually, the sample times are referenced to the time of source activation and the sample times are referred to as “recording times” . Thus, zero recording time occurs at the moment the seismic source is activated.

Each seismic receiver (120) may be positioned at a seismic receiver location that may be denoted (x_r, y_r) where x and y represent orthogonal axes, such as North-South and East-West, on the surface of the earth (116) above the subterranean region of interest (102) . Thus, the refracted seismic waves (110) and reflected seismic waves (114) generated by a single activation of the seismic source (106) may be represented as a three-dimensional “3D” volume of data with axes (x_r, y_r, t) where t indicates the recording time of the sample, i.e., the time after the activation of the seismic source (106) .

Typically, a seismic survey includes recordings of seismic waves generated by one or more seismic sources (106) positioned at a plurality of seismic source locations denoted (x_s, y_s) . In some cases, a single seismic source (106) may be used to acquire the seismic survey, with the seismic source (106) being moved sequentially from one seismic source location to another. In other cases, a plurality of seismic sources, such as seismic source (106) may be used, each occupying and being activated ( “fired” ) sequentially at a subset of the total number of seismic source locations used for the survey. Similarly, some or all the seismic receivers (120) may be moved between firing of the seismic source (106) . For example, seismic receivers (120) may be moved such that the seismic source (106) remains at the center of the area covered by the seismic receivers (120) even as the seismic source (106) is moved from one seismic source location to the next. In other cases, such as marine seismic acquisition (not shown) the seismic source may be towed a short distance behind a seismic vessel and strings of receivers attached to multiple cables ( “streamers” ) are towed behind the seismic sources. Thus, a seismic dataset, the aggregate of all the seismic data acquired by the seismic survey, may be represented as a five-dimensional volume (four space dimensions and one time dimension) with coordinate axes (x_r, y_r, x_s, y_s, t) .

FIG. 1B shows an illustrative example of a processed seismic dataset (150) . The horizontal axis (152) indicates distance between the seismic source, such as seismic source (106) and the seismic receivers (120) recording each trace. Absolute separation between the seismic source (106) and the seismic receivers (120) increases from right to left. The vertical axis (154) indicates recording time, increasing from the top to the bottom. The amplitude of each recorded sample is shown on the grayscale (156) with dark colors indicating negative amplitudes and light colors indicating positive amplitudes. The display is a composite of a plurality of traces, each running vertically with their location on the horizontal axis indicating the distance of the corresponding receiver from the seismic source. Reflections from a plurality of geological layers can be seen manifested as in FIG. 1B as a series of curves arriving at increasing times to the left (large absolute offset) of FIG. 1B.

FIG. 2 illustrates a simplified workflow (200) for forward stratigraphic modeling, in accordance with one or more embodiments. A person of ordinary skill in the art will appreciate that many additions and refinements to the simplified workflow (200) are available within the art and the simplified workflow (200) shown here is only intended as an illustrative example and in no way should be construed as limiting the scope of the invention. The workflow (200) begins with the initial conditions of the geographic region (202) , such as a sedimentary basin, at a time in geological history. Typically, the initial geological time may be older than the oldest rock formations of interest. The initial conditions, or parameterization, may include the topography of the surface of the earth and the sea level at the initial geological time. The topography may include portions of the region initially above sea level, that may be eroded over geological time and form a source of sediment, as well as portions initially below sea level where sediment may be deposited.

Forward stratigraphic modeling may then advance in a loop (204) one geological time interval at a time. The duration of the geological time interval, that may for example be one million years or ten million years, may depend on the rate at which sedimentary conditions change, and/or may depend on the desired discretization or resolution of the output. For example, if sea level is stable and the rate of sediment influx constant over extended periods, then a large geological time interval may be appropriate. In contrast, if sea levels have varied rapidly over geological time and/or the rate of sediment influx has fluctuated rapidly, then a smaller geological time interval may be appropriate.

FSMs require inputs of various types. Input may include the rate of subsidence versus geological time, the sea level versus geological time, and the sediment influx rate and type versus geological time. Some of these inputs, such as subsidence and sediment influx may also vary spatially across the geographical region whereas others, such as sea level, may be spatially constant. In some cases, these inputs may be considered known perhaps from geological or geomorphological studies in adjacent areas. In other cases, these inputs may be considered provisional and subject to revision in a calibration procedure external to the workflow shown. For example, the predictions of forward stratigraphic modeling may be compared to observed values for the region of interest, and then the input parameter values adjusted until the predicted and observed values match to a satisfactory tolerance. In some embodiments, the list of inputs (206) may be supplemented by additional inputs, such as lateral tectonic stress values.

The list of inputs (206) to forward stratigraphic modeling may then be used to determine the type and thickness of sediments deposited (208) during the geological time interval currently being considered. Information about the sediment type may include its chemical composition, such as the relative amounts of quartz and calcium carbonate, and grain size, e.g., muds, silts, sands, conglomerates, and breccia. In addition, sediment type may include information on origin and depositional environment, e.g., silts, sands, aeolian (wind-laid) , lacustrine (lake deposits) , fluvial (river) , estuary, and various types of marine deposits (e.g., lagoon, beach, reef, shelf, and deep ocean) .

To determine the compaction, porosity and permeability of each sedimentary layer (212) , mathematical models (210) for each property may be employed. In order to provide the inputs to these stages of lithification and recrystallization, the mathematical models should estimate a realistic degree of compaction and cementation. The list of inputs (206) may include estimate of the physical properties of interest for each sedimentary layer (212) . Rock physics and rock chemistry models defining input values may consist of cementation, which may depend on chemistry, temperature and pressure, as well as compaction, which may depend on grain size, composition and pressure. The physical properties of each sedimentary layer (212) define the lithification of each layer, estimating the rock properties for the current geological time for each facies across the region of interest.

In step (214) , when each geological layer has been estimated, the FSM is updated for the current geological time in step. This includes updating the 3D porosity model, the 3D facies model, the 3D permeability model, as well as estimating the uncertainty for each of these physical parameters.

Following the update of the physical parameters of the 3D FSM in step (214) , the next geologic time step may be undertaken, up until the current geologic time. The next geologic time step may or may not make use of the same geologic time interval as the previous time step, depending on the fluctuations in sea level, sediment depository rate and type, and subsidence rate occurring during the next geologic time interval.

The acoustic impedance model may be determined after the end of the forward stratigraphic modeling, using different rock physics. These rock physics may include relationships between the physical parameters of porosity and permeability, and the seismic parameters of density and velocity. From the density and velocity the definition of acoustic impedance may be used to create the acoustic impedance model.

FIG. 3 displays a flow chart (300) in accordance with one or more embodiments. In step (312) , using a forward stratigraphic modeling system, an FSM of a subterranean region of interest is calculated. Further, in step (314) using one or more rock physics models and a discretization interval, an acoustic impedance model is calculated from the FSM, using the definition of acoustic impedance. A noise level should be defined when defining the acoustic impedance model from the FSM in step (314) . This way an impedance value may only be considered distinct whenever the difference between impedance values is bigger than this noise level. A unique acoustic impedance model is introduced this way.

In step (316) an acoustic impedance model 1D may be determined by selecting values corresponding to points along a vertical line extending downwards from a surface location into depth. In step (318) this 1D acoustic impedance profile may further be transformed into a modeled 1D reflectivity series as a function of depth, using the definition of an acoustic reflection coefficient as a function of acoustic impedance.

In step (304) a 1D seismic trace may be extracted from seismic the data for the subterranean region of interest (102) for the same surface location at which the modeled 1D reflectivity series was calculated in step (318) . In step (308) a seismic source wavelet may be extracted from the seismic data (150) , and then in step (306) an observed 1D reflectivity series may be obtained by deconvolving the wavelet from the trace. This deconvolution can be done in various ways. In the current disclosure the deconvolution is done by a method called the Z-transform, for which the deconvolution becomes an equivalent operation to solving an algebraic expression. Regardless of the deconvolution method employed, the result of deconvolving the extracted source wavelet from the 1D seismic trace will be an observed 1D seismic reflectivity series.

In step (320) the number of modeled reflectivity coefficients of the modeled 1D reflectivity series may be determined from the FSM. We may denote this number as C_FSM. Similarly in step (310) the number of observed reflectivity coefficients may be determined from the observed 1D seismic reflectivity series and denoted C_SEIS. Although the number of observed reflectivity coefficients C_SEIS is obtained from a seismic trace in the time domain it may be compared with the number of modeled reflectivity coefficients C_FSM obtained from a reflectivity model in the depth domain. In step (322) this comparison may give an indication of the appropriate change in vertical resolution required in the FSM, or input in a new forward stratigraphic modeling. More specifically, the ratio

may be used as part of such an updated resolution. This ratio may give an indication of the resolution change necessary to resample the FSM to apply it for seismic synthetic modeling. Alternatively, the ratio may indicate the resampling rate necessary for another iteration, or recursion, of forward stratigraphic modeling, followed by application of the resulting FSM in seismic synthetic modeling. This seismic synthetic modeling may lead to a selection of a candidate synthetic seismic model. We denote the ratio o to be the refinement coefficient.

If, in step (324) a stopping criterion is reached, in the form of meeting a discretization criterion, then the refinement coefficient, R, resulting from the last iteration may be used as the resolution of the FSM in a convergence criterion. If the discretization criterion is not met, in step (324) , then the discretization interval is updated in step (326) , based on the refinement coefficient determined in step (322) , and a new discretization is used to create an acoustic impedance model in step (314) with an updated resolution of the existing FSM. The coefficient number used for the refinement coefficient will therefore be chosen between the previous or updated number of FSM reflectivity coefficients, together with the number of seismic reflectivity coefficients. If the discretization criterion in step (324) is met, but the convergence criterion is not satisfied in step (328) , the FSM may be updated in step (330) . This is followed by the calculation of a new acoustic impedance model in step (312) . For both options, seismic synthetic data may be generated using the acoustic impedance model. The seismic synthetic data may be compared with seismic data from the region of interest, obtained in step (302) , and this way the convergence criterion may again be re-evaluated in step (328) . The iterations end, in step (328) , when the convergence criterion is met.

FIG. 4 illustrates the calculation of the two types of reflectivity series used in this disclosure. Flowchart (400) depicts simulated facies from forward stratigraphic modeling. The discretization interval along a 1D vertical trace of the FSM is illustrated (404) . The discretization interval determines the noise threshold of the resulting acoustic impedance model in step (406) . The calculation of the acoustic impedance model in step (406) from the FSM determined in step (402) using rock physics and the discretization interval is depicted in 1D in step (404) . One such trace of a 1D acoustic impedance profile from a surface point is extracted. The definition of the reflectivity coefficient from acoustic impedances is used to create the modeled 1D reflectivity series (408) from the surface location as a function of depth.

3D seismic data (410) from the region of interest is depicted. From the 3D seismic data (410) are extracted both the seismic source wavelet (414) and a 1D seismic amplitude trace (412) from the same surface point where the 1D acoustic impedance profile was picked from the FSM. The 1D seismic amplitude trace (412) is then deconvolved, either by using the Z-transform or an alternative algorithm, by the seismic source wavelet (414) . The result of this deconvolution is an observed 1D reflectivity series (416) as a function of time. This observed 1D reflectivity series (416) may or may not be transformed into a reflectivity series as a function of depth, identifying total time with total local depth from the FSM. However, what is used from the observed 1D reflectivity series (416) is the length, which may help indicate an updated resolution of the FSM. This resolution may or may not be finer than the previous resolution and may differ between windows as a function of depth. Specifically, the ratio o between the length C_SEIS of the observed 1D reflectivity series (416) and the length C_FSM of the modeled 1D reflectivity series (408) , may give a good indication of a useful resolution change in the existing FSM model for the next iteration. Alternatively, the ratio o may give a good estimate for a useful resolution change in a new forward stratigraphic modeling for the region of interest, in the process of calibrating the FSM.

The update of the discretization interval based on the refinement coefficient initially affects the resolution of the acoustic impedance model. FIG. 5, however, shows how this change of discretization interval, in step (326) , may affect the number C_FSM of reflection coefficients of the modeled 1D reflectivity series (408) . In (500) a depiction is shown of the effect of a coarser sampling resulting from the refinement coefficient, determined in step (326) , on a 1D acoustic impedance profile (502) to cause the sampling (506) . Their respective modeled 1D reflectivity series (408) are shown (504) and the observed 1D reflectivity series (508) .

FIG. 6 depicts a flow chart (600) in accordance with one or more embodiments. In Step 602, the observed seismic dataset may be obtained from the subterranean region of interest, using the seismic acquisition system (100) .

In Step 604, the seismic reflectivity series for a line transecting the subterranean region of interest may be determined from the observed seismic dataset, using the seismic processing system (199) . The reflectivity series may include a number of seismic reflectivity coefficients. The reflectivity series may be determined, in part, by performing deconvolution on a seismic trace from the observed seismic dataset. The seismic trace from the dataset may be a depth migrated seismic trace. The seismic trace from the dataset may be deconvolved by the extracted source wavelet from the data. Deconvolution may include applying a Z-transform. Performing deconvolution on the seismic trace may include decomposing the seismic trace into a plurality of sample windows.

Steps (606) through (620) may be performed iteratively, or recursively, until a convergence criterion is satisfied. In some embodiments the convergence criterion may include a distance from a synthetic seismic dataset to the observed seismic dataset. In other embodiments the convergence criterion may be the completion of a predefined number of iterations. In one such embodiment, the predetermined number of iterations is greater than one. In other such embodiments, the predetermined number of iterations is one.

In Step 606, using the forward stratigraphic modeler (197) , we may obtain an FSM, wherein the FSM may be generated using a grid resolution. The FSM may be obtained by performing forward stratigraphic modeling. Each time step 606 is performed, a different grid resolution is used resulting in generation of a different FSM.

In Step 608, using the forward stratigraphic modeler (197) , a number of FSM reflectivity coefficients may be determined from the FSM. Determining the number of FSM reflectivity coefficients may include performing rock physics transformations.

In Step 610, using the forward stratigraphic modeler (197) , a refinement coefficient may be determined, based, at least in part, on the number of seismic reflectivity coefficients and the number of FSM reflectivity coefficients. In some embodiments, the refinement coefficient may be a ratio of the number of seismic reflectivity coefficients to the number of FSM reflectivity coefficients. In other embodiments, the refinement coefficient may be a difference of the number of seismic reflectivity coefficients to the number of FSM reflectivity coefficients. This refinement coefficient is a global variable that is used in Step 612, and may be updated in Step 618.

The following Steps, step (612) through step (620) may be performed iteratively, or recursively, until a stopping criterion is satisfied. In some embodiments the stopping criterion may include the refinement coefficient satisfying a refinement criterion. In other embodiments the stopping criterion may be the completion of a predefined number of iterations. In one such embodiment, the predetermined number of iterations is greater than one. In other such embodiments, the predetermined number of iterations is one.

In Step 612, the grid resolution of the FSM may be updated based, at least in part, on the refinement coefficient. This refinement coefficient was determined in Step 610. Frequently, the refinement coefficient will be greater than one, because the number of seismic reflectivity coefficients are often greater than the number of FSM reflectivity coefficients. In some embodiments however, the refinement coefficient may be smaller than one. In some embodiments, the updated grid resolution replaces a prior used grid resolution (e.g., an updated grid resolution of Step 612 may replace the grid resolution of Step 606) . As used herein, an “updated grid resolution” may refer to any grid resolution that has been updated, and a “grid resolution” may refer to either a grid resolution that has not been updated or a grid resolution that has been updated.

In Step 614 an updated FSM may be obtained, wherein the updated FSM is generated using the updated grid resolution. In some embodiments, this updated FSM replaces the FSM obtained in Step 606.

In Step 616 an updated number of FSM reflectivity coefficients may be determined from the updated FSM. The updated number of FSM reflectivity coefficients may be determined using rock physics transformations.

In Step 618 a refinement coefficient may be determined, based, at least in part, on the number of seismic reflectivity coefficients and the updated number of FSM reflectivity coefficients. The refinement coefficient may comprise a ratio of the number of seismic reflectivity coefficients to the number of FSM reflectivity coefficients.

In Step 620 a calibrated FSM may be determined, using, at least in part, the updated number of FSM reflectivity coefficients. The calibrated FSM may be a candidate FSM determined using rock physics transformations. The candidate FSM may comprise a candidate synthetic seismic model, determining, at least in part, a synthetic seismic dataset.

A convergence criterion may be evaluated based on the synthetic seismic dataset and the observed seismic dataset. A set of input parameters to the FSM may be updated on the basis of the convergence criterion.

In Step 622, using the interpretation workstation (195) , a presence and a location of a hydrocarbon reservoir may be determined, based, at least in part, on the updated FSM.

Optionally, in Step 624, a wellbore trajectory may be planned, using a wellbore planning system, to intersect the location, and a wellbore may be drilled, using a drilling system, guided by the wellbore trajectory.

Several of the systems described in this application, such as the seismic acquisition system (100) , the seismic processing system (199) , the wellbore planning system, the interpretation workstation (195) , and the forward stratigraphic modeler (197) , may be implemented by making use of a computer system. While each of these systems may be implemented on dedicated computer hardware and software, such computer hardware may be implemented and/or at a high level include components such as those depicted in the computer system described in FIG. 7.

The computer system in FIG. 7 displays a computer system (700) 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. The illustrated computer system (700) 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 system (700) 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 system (700) , including digital data, visual, or audio information (or a combination of information) , or a GUI.

The computer system (700) 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 computer system (700) is communicably coupled with a network (702) . In some implementations, one or more components of the computer system (700) 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 (700) 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 system (700) 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 system (700) can receive requests over network (702) from a client application (for example, executing on another computer system (700) ) 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 system (700) 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 system (700) can communicate using a system bus (704) . In some implementations, any or all of the components of the computer system (700) , both hardware or software (or a combination of hardware and software) , may interface with each other or the interface (706) (or a combination of both) over the system bus (704) using an application programming interface (API) (708) or a service layer (710) (or a combination of the API (708) and service layer (710) . The API (708) may include specifications for routines, data structures, and object classes. The API (708) 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 (710) provides software services to the computer system (700) or other components (whether or not illustrated) that are communicably coupled to the computer system (700) . The functionality of the computer system (700) may be accessible for all service consumers using this service layer. Software services, such as those provided by the service layer (710) , 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 the computer system (700) , alternative implementations may illustrate the API (708) or the service layer (710) as stand-alone components in relation to other components of the computer system (700) or other components (whether or not illustrated) that are communicably coupled to the computer system (700) . Moreover, any or all parts of the API (708) or the service layer (710) 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 (700) includes an interface (706) . Although illustrated as a single interface (706) in FIG. 7, two or more interfaces (706) may be used according to particular needs, desires, or particular implementations of the computer system (700) . The interface (706) is used by the computer system (700) for communicating with other systems in a distributed environment that are connected to the network (702) . Generally, the interface (706) includes logic encoded in software or hardware (or a combination of software and hardware) and operable to communicate with the network (702) . More specifically, the interface (706) may include software supporting one or more communication protocols associated with communications such that the network (702) or interface′shardware is operable to communicate physical signals within and outside of the illustrated computer system (700) .

The computer system (700) includes at least one computer processor (712) . Although illustrated as a single computer processor (712) in FIG. 7, two or more processors may be used according to particular needs, desires, or particular implementations of the computer system (700) . Generally, the computer processor (712) executes instructions and manipulates data to perform the operations of the computer system (700) and any algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure.

The computer system (700) also includes a memory (714) that holds data for the computer system (700) or other components (or a combination of both) that may be connected to the network (702) . For example, memory (714) may be a database storing data consistent with this disclosure. Although illustrated as a single memory (714) in FIG. 7, two or more memories may be used according to particular needs, desires, or particular implementations of the computer system (700) and the described functionality. While memory (714) is illustrated as an integral component of the computer system (700) , in alternative implementations, memory (714) may be external to the computer system (700) .

In addition to holding data, the memory may be a non-transitory medium storing computer readable instruction capable of execution by the computer processor (712) and having the functionality for carrying out manipulation of the data including mathematical computations.

The application (716) is an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer system (700) , particularly with respect to functionality described in this disclosure. For example, application (716) can serve as one or more components, modules, applications, etc. Further, although illustrated as a single application (716) , the application (716) may be implemented as multiple applications (716) on the computer system (700) . In addition, although illustrated as integral to the computer system (700) , in alternative implementations, the application (716) may be external to the computer system (700) .

There may be any number of computers associated with, or external to, a computer system (700) , each computer communicating over network (702) . 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, or that one user may use multiple computers.

In some embodiments, the computer system (700) 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) .

FIG. 8 shows the drilling system (800) in accordance with one or more embodiments. As shown in FIG. 8, the wellbore (822) following the wellbore trajectory (804) may be drilled by a drill bit (806) attached by the drillstring (808) to a drill rig (820) located on the surface (816) of the earth. The drill rig (820) may include framework, such as a derrick (812) to hold drilling machinery. A top drive (814) sits at the top of the derrick (812) and provides clockwise torque via a drive shaft (830) to the drillstring (808) in order to drill the wellbore (822) . The drillstring (808) may comprise a plurality of sections of drillpipe attached at the uphole end to the drive shaft (830) and downhole to a bottomhole assembly ( “BHA” ) (818) . The BHA may be composed of a plurality of sections of heavier drillpipe and one or more measurement-while-drilling ( “MWD” ) tools configured to measure drilling parameters, such as torque, weight-on-bit, drilling direction, temperature, etc., and one or more logging-while-drilling ( “LWD” ) tools configured to measure parameters of the rock surrounding the wellbore (822) , such as electrical resistivity, density, sonic propagation velocities, gamma-ray emission, etc.

The wellbore (822) may traverse a plurality of overburden (810) layers and one or more cap-rock (828) layers to a hydrocarbon reservoir (802) within the subterranean region of interest (102) , and specifically to a drilling target (824) within the hydrocarbon reservoir (802) . The wellbore trajectory (804) may be a curved or a straight trajectory. All or part of the wellbore trajectory (804) may be vertical, and some part of the wellbore trajectory (804) may be deviated or have horizontal sections. One or more portions of the wellbore (822) may be cased with casing (826) in accordance with the wellbore plan.

To start drilling, or “spudding in” the well, the hoisting system lowers the drillstring (808) suspended from the derrick (812) towards the planned surface location of the wellbore. An engine, such as a diesel engine, may be used to supply power to the top drive (814) to rotate the drillstring (808) . The weight of the drillstring (808) combined with the rotational motion enables the drill bit (806) to bore the wellbore.

The near-surface is typically made up of loose or soft sediment or rock, so large diameter casing (826) , e.g., “base pipe” or “conductor casing, ” is often put in place while drilling to stabilize and isolate the wellbore. At the top of the base pipe is the wellhead, which serves to provide pressure control through a series of spools, valves, or adapters. 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 (816) of the earth.

Drilling may continue without any casing (826) once deeper, or more compact rock is reached. While drilling, a drilling mud system (838) may pump drilling mud from a mud tank on the surface (816) 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 (808) withdrawn from the wellbore. Sections of casing (826) may be connected and inserted and cemented into the wellbore. Casing string may be cemented in place by pumping cement and mud, separated by a “cementing plug, ” from the surface (816) 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 and the wellbore wall. 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 and the pressure on the wellbore walls from surrounding rock.

Due to the high pressures experienced by deep wellbores, 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 becomes deeper, both successively smaller drill bits and casing string may be used. Drilling deviated or horizontal wellbores may require specialized drill bits or drill assemblies.

A drilling system (800) may be disposed to communicate with other systems in the well environment. The drilling system (800) 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 (824) is reached, or the presence of hydrocarbons is established.

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:

obtaining, from a seismic acquisition system, an observed seismic dataset pertaining to a subterranean region of interest;

determining, using a seismic processing system, from the observed seismic dataset a seismic reflectivity series for a line transecting the subterranean region of interest, wherein the seismic reflectivity series comprises a number of seismic reflectivity coefficients;

using a forward stratigraphic modeler:

iteratively, or recursively, until a convergence criterion is satisfied:

obtaining a forward stratigraphic model (FSM) , wherein the FSM is generated using a grid resolution,

determining a number of FSM reflectivity coefficients from the FSM,

determining a refinement coefficient based, at least in part, on the number of seismic reflectivity coefficients and the number of FSM reflectivity coefficients,

iteratively, or recursively, until a stopping criterion is satisfied:

updating the grid resolution of the FSM based, at least in part, on the refinement coefficient to yield an updated grid resolution;

obtaining an updated FSM, wherein the updated FSM is generated using the updated grid resolution;

determining an updated number of FSM reflectivity coefficients from the updated FSM; and

updating the refinement coefficient based, at least in part, on the number of seismic reflectivity coefficients and the updated number of FSM reflectivity coefficients, and

determining a calibrated FSM, using, at least in part, the updated number of FSM reflectivity coefficients,

determining, using an interpretation workstation, a presence and a location of a hydrocarbon reservoir based, at least in part, on the updated FSM.
The method of claim 1, further comprising:

planning, using a wellbore planning system, a wellbore trajectory to intersect the location;and

drilling, using a drilling system, a wellbore guided by the wellbore trajectory.
The method of claim 1, wherein determining the calibrated FSM comprises:

determining a candidate FSM using the forward stratigraphic modeler and a set of input parameters;

determining a candidate synthetic seismic model from the candidate FSM using rock physics transformations;

determining a synthetic seismic dataset based, at least in part, on the candidate synthetic seismic model;

evaluating the convergence criterion based on the synthetic seismic dataset and the observed seismic dataset; and

updating the set of input parameters.
The method of claim 1, wherein determining the seismic reflectivity series comprises performing deconvolution of a seismic trace from the observed seismic dataset.
The method of claim 4, wherein performing deconvolution comprises applying a Z-transform.
The method of claim 4, wherein performing deconvolution of a seismic trace comprises decomposing the seismic trace into a plurality of sample windows.
The method of claim 4, wherein the seismic trace comprises a depth migrated seismic trace.
The method of claim 1, wherein determining the number of FSM reflectivity coefficients or determining the updated number of FSM reflectivity coefficients comprises performing rock physics transformations.
The method of claim 1, wherein the refinement coefficient comprises a ratio of the number of seismic reflectivity coefficients to a coefficient number, and wherein the coefficient number is selected from a group consisting of: the number of FSM reflectivity coefficients, and the updated number of FSM reflectivity coefficients.
The method of claim 1, wherein the stopping criterion comprises the refinement coefficient satisfying a refinement criterion.
A system, comprising:

a seismic acquisition system, configured to obtain an observed seismic dataset pertaining to a subterranean region of interest;

a seismic processing system, configured to determine, from the observed seismic dataset,a seismic reflectivity series for a line transecting the subterranean region of interest, wherein the seismic reflectivity series comprises a number of seismic reflectivity coefficients;

a forward stratigraphic modeler, configured to:

iteratively, or recursively, until a convergence criterion is satisfied:

obtain an FSM, wherein the FSM is generated using a grid resolution,

determine a number of FSM reflectivity coefficients from the FSM, and,

determine a refinement coefficient based, at least in part, on the number of seismic reflectivity coefficients and the number of FSM reflectivity coefficients,

iteratively, or recursively, until a stopping criterion is satisfied:

update the grid resolution of the FSM based, at least in part, on the refinement coefficient to yield an updated grid resolution;

obtain an updated FSM, wherein the updated FSM is generated using the updated grid resolution;

determine an updated number of FSM reflectivity coefficients from the updated FSM; and

update the refinement coefficient based, at least in part, on the number of seismic reflectivity coefficients and the updated number of FSM reflectivity coefficients, and

determine a calibrated FSM, using, at least in part, the updated number of FSM reflectivity coefficients,

determine, using an interpretation workstation, a presence and a location of a hydrocarbon reservoir based, at least in part, on the updated FSM.
The system of claim 11, further comprising:

a wellbore planning system, configured to plan a wellbore trajectory to intersect the location; and

a drilling system, configured to drill a wellbore guided by the wellbore trajectory.
The system of claim 11, wherein determining the calibrated FSM comprises:

determine a candidate FSM using the forward stratigraphic modeler and a set of input parameters;

determine a candidate synthetic seismic model from the candidate FSM using rock physics transformations;

determine a synthetic seismic dataset based, at least in part, on the candidate synthetic seismic model;

evaluate the convergence criterion based on the synthetic seismic dataset and the observed seismic dataset; and

update the set of input parameters.
The system of claim 11, wherein determining the seismic reflectivity series comprises performing deconvolution of a seismic trace from the observed seismic dataset.
The system of claim 14, wherein performing deconvolution comprises applying a Z-transform.
The system of claim 14, wherein performing deconvolution of a seismic trace comprises decomposing the seismic trace into a plurality of sample windows.
The system of claim 14, wherein the seismic trace comprises a depth migrated seismic trace.
The system of claim 11, wherein determining the number of FSM reflectivity coefficients or determining the updated number of FSM reflectivity coefficients comprises performing rock physics transformations.
The system of claim 11, wherein the refinement coefficient comprises a ratio of the number of seismic reflectivity coefficients to a coefficient number, and wherein the coefficient number is selected from a group consisting of: the number of FSM reflectivity coefficients, and the updated number of FSM reflectivity coefficients.
The system of claim 11, wherein the stopping criterion comprises the refinement coefficient satisfying a refinement criterion.