EP3948365A1 - Automatic calibration of forward depositional models - Google Patents
Automatic calibration of forward depositional modelsInfo
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- EP3948365A1 EP3948365A1 EP20718508.3A EP20718508A EP3948365A1 EP 3948365 A1 EP3948365 A1 EP 3948365A1 EP 20718508 A EP20718508 A EP 20718508A EP 3948365 A1 EP3948365 A1 EP 3948365A1
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Classifications
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- G—PHYSICS
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- G01V20/00—Geomodelling in general
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
-
- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B44/00—Automatic control systems specially adapted for drilling operations, i.e. self-operating systems which function to carry out or modify a drilling operation without intervention of a human operator, e.g. computer-controlled drilling systems; Systems specially adapted for monitoring a plurality of drilling variables or conditions
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/60—Analysis
- G01V2210/66—Subsurface modeling
- G01V2210/661—Model from sedimentation process modeling, e.g. from first principles
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- G01V2210/66—Subsurface modeling
- G01V2210/665—Subsurface modeling using geostatistical modeling
- G01V2210/6652—Kriging
Definitions
- This instant specification relates to techniques for predicting subterranean geological structures.
- a forward depositional modeling process usually includes several coupled or sequential sub-processes to simulate different depositional processes.
- Such a modeling procedure can numerically simulate fluid flow, sedimentation laws which govern erosion, transport, and deposition.
- Some sedimentation processes such as compaction and porosity reduction, fold deformation, diagenesis and fluid maturation can also be numerically simulated in the forward depositional modeling procedure.
- the output of the numerical forward depositional simulation can be the stratigraphic spatial architectures, such as the thickness of each formation, and the lithology or the geological facies within each formation.
- petrophysical properties of the simulated area such as porosity and permeability can also be derived in the final model.
- this document describes techniques for predicting subterranean geological structures.
- a method for geological modeling includes receiving a forward depositional model, determining a Latin Hypercube Sampling (LHS) stratigraphic model based on the projected forward depositional model, performing forward depositional modeling, transform the forward depositional model from time domain to stratigraphic-depth domain, determining one or more pseudo-wells based on the transformed model, determining a mismatch value based on the transformed forward depositional model and a collection of simulated physical value, and determining a kriging surrogate model based on the LHS stratigraphic model and the mismatch value.
- LHS Latin Hypercube Sampling
- the forward depositional model can be based on well log data descriptive of a drilled well path through a predetermined geographical area.
- the method can also include receiving the well log data descriptive of the drilled well path through the predetermined geographical area, and projecting, based on the well log data, the drilled well path to forward depositional model coordinates in the forward depositional model.
- the collection of simulated physical values can include a collection of at least one of hydraulic values, geological values, and sedimentological values.
- the method can also include determining a drilling path based on an identified set of predetermined input parameters, and drilling a well based on the determined drilling path.
- Determining a mismatch value based on the transformed forward depositional model and the collection of simulated physical values can include identifying a first collection of geological parameter values representative of geological properties measured at predetermined points along a drilled well path, determining a second collection of geological parameter values representative of simulated geological properties of the LHS stratigraphic model at the predetermined points along the drilled well path, determining a collection of difference values comprising differences between selected geological parameter values of the first collection and corresponding geological parameter values of the second collection, and providing the collection of differences as the mismatch value.
- a system for geographical modeling includes a control system having one or more processors, and a non-transitory computer- readable medium storing instructions executable by the one or more processors to perform operations including receiving a forward depositional model, determining a Latin Hypercube Sampling (LHS) stratigraphic model based on the projected forward depositional model, performing forward depositional modeling, transform the forward depositional model from time domain to stratigraphic-depth domain, determining one or more pseudo-wells based on the transformed model, determining a mismatch value based on the transformed forward depositional model and a collection of simulated physical values, and determining a kriging surrogate model based on the LHS stratigraphic model and the mismatch value.
- LHS Latin Hypercube Sampling
- a non-transitory computer-readable medium storing instructions executable by a processing device to perform operations includes receiving a forward depositional model, determining a Latin Hypercube Sampling (LHS) stratigraphic model based on the projected forward depositional model, performing forward depositional modeling, transforming the forward depositional model from time domain to stratigraphic-depth domain, determining one or more pseudo-wells based on the transformed model, determining a mismatch value based on the transformed forward depositional model and a collection of simulated physical values, determining a kriging surrogate model based on the LHS stratigraphic model and the mismatch value.
- LHS Latin Hypercube Sampling
- the forward depositional model can be based on well log data descriptive of a drilled well path through a predetermined geographical area.
- the operations can also include receiving the well log data descriptive of the drilled well path through the predetermined geographical area, and projecting, based on the well log data, the drilled well path to forward depositional model coordinates in the forward depositional model.
- the operations can also include determining a drilling path based on an identified set of predetermined input parameters, and drilling a well based on the determined drilling path.
- Determining a mismatch value based on the transformed forward depositional model and the collection of simulated physical values can also include identifying a first collection of geological parameter values representative of geological properties measured at predetermined points along a drilled well path, determining a second collection of geological parameter values representative of simulated geological properties of the LHS stratigraphic model at the predetermined points along the drilled well path, determining a collection of difference values including differences between selected geological parameter values of the first collection and corresponding geological parameter values of the second collection, and providing the collection of differences as the mismatch value.
- a system can provide models of subterranean geological structures that accurately reflect observed conditions.
- the system can perform the modeling using relatively fewer computing resources than previous techniques.
- the system can perform the modeling more quickly than previous techniques.
- the system can provide information that can increase the efficiency of drilling operations.
- FIG. 1 is an example cross-sectional view of an example
- FIG. 2 shows a table of several example designs of input variables.
- FIG. 3 shows three examples of simulated models.
- FIG. 4A is a flow diagram of an example inverse depositional modeling workflow.
- FIG. 4B shows example conceptual models of example stratigraphic realizations.
- FIG. 4C shows an example conceptual mathematical representation of a surrogate model.
- FIG. 4D shows an example surrogate model represented as a mathematical surface.
- FIG. 5 is a flow diagram of an example Latin Hypercube sampling and physical transformation process.
- FIG. 6A is a flow diagram of an example spatial depth transformation process.
- FIG. 6B show example two and three-dimensional projections of example well trajectories.
- FIG. 7A is a flow diagram of an example mismatch determination process.
- FIG. 7B shows a graphical example of a time to spatial
- FIG. 7C shows an example grid values in a spatial transformation of a model.
- FIGs. 8 and 9 are flow diagrams of example mismatch determination processes.
- FIG. 10 is a flow diagram of an example parameter set generation process.
- FIG. 1 1 is a flow diagram of an example process for calibration of forward depositional models.
- IDM Depositional Modeling
- One of the challenges of some forward depositional modeling approaches is to optimize the various input parameters such that the simulated output would maximally match available prior observed data (such as from the data logs obtained from physical drilling operations).
- This document describes techniques for finding sets of appropriate input parameters, including the initial and boundary conditions that can provide consistency between the simulated deposits and prior observed data.
- a forward depositional modeling process usually includes several coupled or sequential sub-processes to simulate different depositional processes. Such modeling procedures can numerically simulate things such as fluid flows, sedimentation laws that govern erosion, transport, and deposition. Some sedimentation processes, such as compaction, porosity reduction, fold deformation, diagenesis and fluid maturation, can also be numerically simulated in the forward depositional modeling process.
- the output of numerical forward depositional simulation can be the stratigraphic spatial architectures (such as the thickness of each formation), the lithology, or the geological facies within formations. In some
- the petrophysical properties of a simulated area can also be derived.
- FIG. 1 is an example cross-sectional view of an example
- the experimental depositional environment is a carbonate depositional environment.
- a useful parameter for a forward depositional simulation is the growth rate of each rock type.
- the input parameters are usually a collection of initial topography parameters and other input parameters that describe the hydraulic or sedimentological dispersion characteristics of a selected geological area.
- a history of deformation and movement such as subsidence, may also be used as parameters for the forward depositional simulation to obtain realistic geological results.
- the spatial and temporal distribution of physical properties and their boundary conditions can also be used as model parameters.
- FIG. 2 shows a table 200 of several example designs of input variables.
- Each rock type such as those shown in the example depositional environment 100 of FIG. 1 , can be associated with a range for that rock type’s growth rate.
- the lagoon 1 10 can be associated with a growth rate of 10-80 meters per million years.
- the bank crest 120 can be associated with a growth rate of 40-1 10 meters per million years.
- the algal platform 130 can be associated with a growth rate of 0-70 meters per million years.
- the deep open marine 140 can be associated with a growth rate of 0-70 meters per million years.
- First step is doing a set of initial Latin Hypercube Sampling (LHS) designs.
- the table 200 presents an example of such initial LHS designs.
- LHS Latin Hypercube Sampling
- FIG. 3 shows three examples of simulated models and a key 301 for interpreting the models.
- the forward depositional modeling can be obtained with a batch process that uses the parameters as inputs. In some implementations, this process can be automatic, thus relieving huge amounts of labor. For example, 10, 20, 50, 100, or more models can be simulated and used for such experiments.
- a model 310 represents the facies-stacking pattern for a well (the true observed vertical profile from a well).
- Model 310 is based on observed data, for example, measurements obtained while drilling a well (a well log).
- the model shows various layers of bank crest 302, lagoon 303, algal platform 304, and deep ocean marine 305 layers.
- a model 320 represents a stacking pattern of a simulation produced from manual parameter inference (the vertical profile extracted from the simulated model using the proposed method).
- a model 330 represents a stacking pattern of a simulation result obtained from the processes (the vertical profile extracted from simulated model but the inverse parameters are manually inferred) that will be described in more detail in subsequent paragraphs.
- a comparison of the three models 310-330 shows that the model 330 more closely resembles the model 310 than does the model 320.
- a kriging surrogate modeling technique is then used to rank and identify relationships (correlations) between the initial collection of LHS designs and the mismatch values calculated from comparisons of models and wells.
- the efficient global search and expected is then used to rank and identify relationships (correlations) between the initial collection of LHS designs and the mismatch values calculated from comparisons of models and wells.
- improvement principle implemented in this technique can improve the likelihood that the next suggested design will reduce the uncertainty of the surrogate model built between the LHS design and the mismatch value.
- the process is run forward until the iteration meets various predetermined criteria, such as by determining that the mismatch value is less than a predetermined amount, or by determining that the process has iterated more than a predetermined maximum iteration count.
- various predetermined criteria such as by determining that the mismatch value is less than a predetermined amount, or by determining that the process has iterated more than a predetermined maximum iteration count.
- the maximum expected improvement is small enough, then the new mismatch value will be calculated from the surrogate model not the forward modeling simulation.
- any appropriate recognized input parameter for forward depositional modeling (such as initial bathymetry, input sediment composition, rates of fluvial discharge, transport efficiency) can be inferred automatically with a target to reproduce the prior observation data.
- conditioning data for example, previously collected well log data
- data previously collected during well path drilling can be projected to forward depositional model grid coordinates. This process will transform the well path into a grid cell index in the simulation model for property extraction from the model, and for mismatch value calculation.
- LHS Latin Hyper- cube Sampling design
- FIG. 4A is a flow diagram 400 of an example inverse depositional modeling workflow.
- an initial LHS design is determined, for example, based on observed well log data.
- initial forward simulation is determined.
- the forward depositional modeling procedure can be considered a numerical experiment in experimental design notation. In some implementations, ignoring the knowledge of the inner functionality of the forward depositional modeling can allow the process to be treated as a black-box model in which only the relation of the input-output variables is considered.
- LHS Latin Hyper-cube Sampling
- This step is performed to transform the experimental design from uniform space to physical space and to write a set of forward depositional modeling parameter files for later surrogate modeling.
- forward modeling several recognized parameters are used in the inverse procedure.
- the parameters can be denoted as:
- X ⁇ x 1 , x 2 , - , x k ⁇ .
- D k design space or design domain
- Different samples from the domain can compose a sampling plan.
- X ⁇ x 1 , x 2 , ⁇ , x N ⁇ .
- a full set of parameter files can be generated based on the process described in this text.
- a forward modeling program can performed N times automatically using a batch script and the template. In the latter iteration(s), the identified parameter set from the optimization procedure is used to construct a parameter file and run the forward stratigraphic modeling process.
- the forward depositional model is constructed, it is compared with the prior observation data.
- the forward depositional model and the prior observation data may not be in same data or coordinate format.
- some pre-processing or decoding work on simulated runs can be done before doing comparison or mismatch operations.
- different forward engines and different pre-processing modules may be used to deal with different model output formats.
- the extraction from the simulated model may not follow the true well trajectory with sufficient precision.
- stratigraphic correlation is performed before well trajectories are compared, which provides a basis for property extraction along the true trajectory of the well path.
- a chronostratigraphic correlation is performed based on the formation marker of the well log data and the mean thickness of the model. This correlation process will project the well path to the same chronostratigraphic correlation as the simulated depositional model.
- the index of each cell can be searched and indexed given the well trajectory and the grid definition of the depositional model in spatial depth domain. Then, the properties along the trajectory are obtained from the simulation depositional model for use with later mismatch value calculations.
- an initial mismatch result is determined.
- the initial forward simulation can be compared to observed well log data to determine a measurement of how accurately (or not) the initial forward simulation emulates the observed data.
- the mismatch value guides the surrogate model building and optimization.
- a challenge for well log based calibration is related to the type and nature of the data to be calibrated.
- three types of mismatch value calculation approaches are described. They are for interval data such as formation thickness, continuous variable such as permeability and porosity and categorical variables such as lithofacies types or rock types. Those are three common and frequently used observation data types obtained from well log data.
- stop criteria are received.
- an iteration limit value can be obtained that represents the maximum number of iterations that the modeling process is allowed to perform, after which the best available model may be identified and provided as the final output of the process 400.
- a time limit can be obtained that represents the maximum amount of time that the modeling process is allowed to run, after which the best available model may be identified and provided as the final output of the process 400.
- a model mismatch threshold may be received that represents a mismatch value for a simulated model that would be considered sufficiently emulative of the observed data.
- a surrogate model is determined.
- the surrogate model is an approximation that emulates the relation between the difference of forward simulation and the observed data.
- the surrogate model is generally simpler and therefore less computationally intensive to run than the more fully featured forward simulation. In the reversion, there is only one surrogate model will be built.
- This surrogate model is updated after the initial set of (x,y).
- FIG. 4B shows example conceptual models of example stratigraphic realizations.
- FIG. 4C shows an example conceptual mathematical representation of a surrogate model.
- the simulated forward model output is compared with the prior observation hard data. This comparison provides a suggestion of how these models compare to the prior observation data, which are used as constraints.
- the comparison data can be called the response of experimental, y, which is a quantitative measure of a difference between the model and the measured data.
- S obs Assuming the availability of a well log of porosity along certain locations vertically in the study area, the well log data is denoted as S obs . A simulated well log of porosity can be obtained from the same location, denoted as S sim , then the difference between the well logs can be defined as a response variable of the stratigraphic model:
- the surrogate solution implements construction of a computationally cheap-to-evaluate“surrogate” model f(x) that emulates the computationally expensive response of forward stratigraphic model procedure f(x).
- f(x) is defined by a k-vector of design variables x e D.
- D represents the design space or design domain. Different samples from the domain will compose a sampling plan
- the learning data set ⁇ (x (1) , y ⁇ 1) ), (c (2) , y ⁇ 2) ), ... , (x (n) , y ⁇ n) ) ⁇ can be determined.
- the shape of the model being determined by the set of parameters w.
- An early step in this process is the selection of the vector w such that the model will fit the hard data.
- a minimum mismatch among the surrogate models is identified. Assuming that the surrogate model (expressed as the surface in FIG. 4D) has been built. From the fitted surface/surrogate model, minimum searching can be performed.
- this surrogate model (the surface) can be identified as being not good enough, and another LHS design and respective y variable should be added.
- the smallest mismatch value will be compared with a predefined stop criteria to decide for a subsequent stop action, such as that illustrated at 430.
- the obtained stratigraphic model can be compared to the prior observed data. This comparison can provide an indication of how these models are different in comparison to the prior observed data that are used as constraints. This will be the response of experiments, denoted as y which is a quantitative measure of the difference between a simulated model and the observed data.
- y' is the difference between each of simulated models and the current prior observation data set, which would be some thickness, or lithofacies record, or some porosity or permeability sequences.
- the operator diff is a difference operator. In some implementations, however, the operator might be differently defined depending on the nature of observation data.
- a new surrogate model design is obtained. If at 450, the new model’s improvement over the previous model is small enough, then at 452 a new mismatch value is calculated. If at 450, the new model’s
- a file is generated.
- the best surrogate model found during the previous steps can be saved to a storage medium such as an electronic document that can be saved, archived, and transported.
- forward modeling is performed based on the saved file.
- the stored model can be transported on a flash drive to another computer that is used for forward modeling, and that computer can read the flash drive as part of a process of forward modeling.
- FIG. 5 is a flow diagram of an example Latin Hypercube sampling and physical transformation process 500.
- the process 500 can be the step 410 of the example process 400 shown in FIG. 4A.
- an experimental variable total number is received.
- the experimental variable total number is the identified key parameter numbers from a modeler.
- the total number is four for FIG. 1 .
- an LHS design total number is obtained.
- the total number is the initial LHS design number.
- the total LHS design number is 100.
- the LHS design is performed.
- the results from the LHS design is in range of zero to one, or [0,1]
- the result is a matrix.
- the matrix dimension is determined from 510 and 515. For example, in the example of FIG. 2, the dimension is 4x100.
- the range of each target inverse variable is obtained.
- the grow rate for each sedimentary type can be obtained.
- the LHS design in geological space is obtained.
- Initial forward depositional modeling results from step 530 are saved in terms of geological time coordinates. For example, along the vertical direction, time increments are equal, and all the simulated properties such as thickness, facies type, or other continuous properties are saved inside this timeframe.
- a forward model parameter file template is obtained.
- the forward modeling program can be run from a parameter file or a template.
- a collection of designed keywords is identified from the template.
- the identified inverse target forward modeling parameter variables are tagged in the template.
- the tagged variables identify the variables to be replaced by the LHS design in parameter range space as illustrated in FIG. 5.
- each parameter file is obtained from a LHS design and can be enough to perform a normal forward run.
- FIG. 6A is a flow diagram of an example spatial depth transformation process 600.
- the process 600 may be performed based on the output of the example process 500 of FIG. 5.
- the time-to-spatial depth transformation can be done before extracting the simulated data values and compared with well log data, which is usually expressed in terms of depth.
- a stratigraphic model expressed in terms of geological time coordinates, is received.
- the output of the example process 500 of FIG. 5 can be received.
- information about the depths and thicknesses of geological layers can be extracted from the received model.
- this information can be saved as a part of the final model but not in explicit format.
- some decoding and extraction works are required to pick those information from the saved forward model which are varies from one forward to another forward modeling program.
- the stratigraphic model is transformed into spatial depth coordinates.
- the model may be analyzed to determine that the model describes a lagoon layer that is 10 meters think, a bank crest layer that is 100 meters thick, an algal platform that is 150 meters thick, and a deep open marine layer that is 90 meters thick.
- the spatial correlation in spatial depth coordinates is provided. After transforming the model from time to spatial space, at 650 the simulated properties of some pseudo-wells are extracted. The top depths of the wells, however, might not all have the same depth. At 660, a spatial stratigraphic correlation in spatial depth coordinates is performed for the extracted pseudo-wells. The spatial correlation causes the tops for all the wells to start from same depth. This correlation also causes a correct mismatch calculation from each property for all the wells. In reservoir, the observed wells have their respective spatial locations and respective trajectories. Such location and trajectory information can be projected to the numerical models, an example of which is shown as FIG 6B. FIG. 6B shows example two and three-dimensional projections of example well trajectories.
- FIG. 7A is a flow diagram of an example mismatch determination processes. After the model is transformed from time domain to spatial depth domain, for example as in the process 600 of FIG. 6A, a transformed stratigraphic correlation is applied to the simulation domain, which will ensure the model is saved in a simulated domain that is divided into small cells, and those cells (3D cubic cells) are the same size.
- FIG. 7B shows a graphical example of a time to spatial transformation of a model.
- FIG. 7C shows an example grid values in a spatial transformation of a model.
- FIGs. 7B and 7C show small examples to illustrate the process of time to spatial transformation in a model and in a well.
- Subfigures 750a and 760a show examples of simulated outputs from a traditional forward depositional model. The properties as recorded according simulation time increment along vertical direction.
- Subfigures 750b and 760b show examples of transformations of the simulated model from time record to spatial coordinates. The top or bottom might not occur at same spatial depth.
- Subfigures 750c and 760c show examples of stratigraphic correlation transformations. The model properties are saved in each cell.
- the formations are saved in a chronological order (such as by year) from oldest to newest.
- Properties such as thickness of the formation, facies type, and other (including continuous) measurements such as porosity, permeability, sand ratio, and combinations of these or any other appropriate property of the formation are saved in each time layer, which is simulated from substantially equally increased geological time.
- the model can be expressed in spatial depth domain. After the model is transformed from time domain to spatial depth domain, a stratigraphic correlation transformed is applied to the simulation domain, which will ensure that the model is saved in a“sugar-block” like conceptual arrangement of grid cells. In some implementations, the intention of this arrangement can be to provide easy and precise hard data extraction for later mismatch function calculations.
- Z rei represents the relative spatial depth in space domain
- Z Ch represents the stratigraphic bottom
- Z ct represents the stratigraphic top
- T represents the mean thickness between Z Cb and Z ct .
- FIG. 7A is a flow diagram of an example mismatch determination process 700.
- the process 700 can be performed on the data provided by the example process 600 of FIG. 6A.
- target formation thicknesses are received.
- the process 600 can provide a collection of information that describes formation thicknesses, and that information can be received for use at step 710.
- both the well log data and the simulated data can include a first layer, a second layer, and a third layer (and so on), each having its own thickness.
- a mismatch is calculated between target and simulated formation thicknesses.
- the well log data may indicate the presence of layers that are 100, 150, 75, and 120 meters thick, respectively, while a simulated model may describe layers that are 1 10, 100, 80, and 120 meters thick respectively.
- the mathematical differences between the two data sets can be compared to determine the amount of mismatch between the various layers, which in this example would be 10, 50,
- sequence stratigraphic framework for the target reservoir is established before forward depositional modeling is performed.
- target strata have already been identified by modelers and has already been noted as horizon data.
- Such frameworks expressed as horizons, which can also be recognized from the simulated model along a vertical direction from clear geological time definition.
- the process 700 identifies the top and bottom of the target well, denoted here as h obs .
- h obs the top and bottom of the target well
- h s l im a simulated thickness is calculated from the same top and bottom of same stratigraphy.
- the differences between the observation well and each simulated model are represented as:
- index / is the index of the simulated model.
- FIG. 8 is a flow diagram of an example mismatch determination process 800.
- the process 800 can be performed on the data provided by the example process 600 of FIG. 6A.
- target facies stacking patterns are received.
- the process 600 can provide a collection of information that describes how geological layer types are arranged on top of each other, and that information can be received for use at step 810.
- both the well log data and the simulated data can include a bank crest layer stacked upon a lagoon layer, stacked upon an algal platform layer, stacked upon a deep ocean marine layer (and so on).
- a mismatch is calculated between target and simulated formation thicknesses.
- the well log data may indicate the presence of a bank crest layer stacked upon a lagoon layer, stacked upon an algal platform layer, stacked upon a deep ocean marine layer, while a simulated model may describe a bank crest layer stacked upon an algal platform layer, stacked upon another bank crest layer, stacked upon an algal platform layer, stacked upon a deep ocean marine layer.
- the ordering differences between the two data sets can be compared to determine the amount of mismatch between the various layers.
- the simulated model may be expressed as mismatching the observed data by 10%, 20%, 1 %, or any other appropriately descriptive value.
- the first step is numerical coding of facies type of the research domain.
- the facies in the research domain can be [domits, sand, shale], and these values can be numerically transformed to be represented as [1 ,2,3]
- the facies codes can be transformed into an integer set, [1,2,— , K] with aim being to compare them numerically.
- S obs ⁇ k , k 2 , ⁇ , k n ]
- a simulated facies stacking sequence can also be extracted from the same well location from each simulated stratigraphic model, which is denoted as Sj im .
- the facies observation numbers from the simulated model are different from numbers obtained from the prior observed well data. Assuming that the observation facies number is m , the structure of the simulated formation can be represented as:
- Each simulated well is then re-sampled.
- the maximum facies observation number can be implemented whenever it is equal to m or n.
- the facies observation sequence can re-sampled according the maximum number of m or n. After the sequence is re-sampled, they are in same observation length.
- An indicator transformation is performed upon the layers:
- index i would be the simulated model
- index j would be the facies type found along a selected trajectory in the model. Then, the response variable y t from the sequence pairs is calculated as:
- FIG. 9 is a flow diagram of an example mismatch determination process 900.
- the process 900 can be performed on the data provided by the example process 600 of FIG. 6A.
- target (continuous) well logs are received.
- the process 600 can provide a collection of information that describes sensor data detected at various points along the length of a wellbore (which may be serpentine rather than perfectly linear or vertical), and that information can be received for use at step 910.
- corresponding simulated well logs are identified from simulated models. For example, the path of the actual well can be recreated in the simulated models, and simulated logs of the simulated well bore can be obtained.
- a mismatch is calculated between target and simulated well logs.
- the well log data may indicate the presence of bank crest for the first 100 meters, lagoon for the next 150 meters, algal platform for the next 50 meters, an another stretch of lagoon for the next 50 meters, while a simulated model may describe the presence of bank crest for the first 105 meters, lagoon for the next 200 meters, and deep ocean marine for the next 50 meters.
- the mathematical differences between the two data sets can be compared to determine the amount of mismatch between well logs, which can be expressed as a fractional value, a percentage value, or any other appropriate expression of mismatch between data sets.
- the simulated measurement can be determined for same well trajectory and denoted as:
- the simulated wells at the observation location might be different.
- a resampling can be done to a simulated pseudo-well extracted from each simulated well.
- the whole sequence can re sampled according the number n , and a final mismatch value y c l ont from the continuous measurements would be calculated as:
- index / represents the simulated model
- index j represents the measured property along the selected trajectory in each of the simulated models.
- a sequence calibration procedure can be adopted. For example, a certain stratigraphic formation thickness could be fitted first. After that, the categorical variables (such as facies or rock type) can be fitted, and then continuous measurements (such as porosity and permeability) can be fitted.
- FIG. 10 is a flow diagram of an example parameter set generation process 1000.
- a current surrogate model is received.
- the process 1000 can be used in a generally iterative process in which a number of surrogate models are produced and refined, and at 1010 one of the surrogate models produced in the current iteration can be received.
- the surrogate model received at 1010 can be the output of any one of the example processes 700, 800, or 900 of FIGs. 7A, 8, and 9.
- the LHS design having the relatively least degree of mismatch is identified based on the mismatch scores. This is the core technique from the optimization.
- the surrogate model will connect the input parameter and the mismatch value calculated from comparison of prior observation well log and the simulated model. Thus, it will surrogate the function of complex forward deposition simulation engine and save computing when searching for optimal input parameters for a best calibration of prior hard data.
- prior data from the deposition model can be collected through seismic surveys, well logs, and others processes. In the examples described in this document, the focus has been on the calibration of well log data. However, in other examples, the inverse general principle is substantially the same, with differences in the calibration of different data is the mismatch value calculation that is used.
- LHS design is in [0, 1] space. It will transformed to geological space and will be used to construct one parameter set for procedure 1050.
- a parameter set based on the outputs of 1032 or 1042 is determined.
- the parameter set can be generated for use in a forward stratigraphic modeling process.
- Surrogate-based optimization techniques make use of the construction of a computationally inexpensive“surrogate” model f(X) that emulates the computationally expensive response of a forward model procedure /(x).
- Each design sample x' from the sample design domain will be a set of input forward depositional model parameters and will get one simulated stratigraphic model S s l im after feeding to a specified forward engine /(x). That is, based on the available of forward depositional modeling program, some simulated models can be obtained and they can be denoted as:
- a generic structure f(X, W) is selected, and the shape of the surrogate model is based on the set of parameters W. So, first step in this sub process is selecting a vector tVsuch that the model will best fit the hard data.
- This prediction will be generally consistent with the observed data (initial sampling plan and the calculated observations from the simulated model), and therefore will be generally consistent with the calculated correlation parameters. Hence, a prediction (given our correlation parameters and the prediction) that increases the likelihood that the sample data will be chosen to be used for next surrogate modeling construction iteration.
- An efficient global optimization (EGO) process is designed for the global optimization of computationally expensive-to-evaluate numerical models.
- the EGO algorithm is adopted to find a representative input parameter set in its super-dimensional space.
- An initial design (as discussed previously) is determined. Then the algorithms will sequentially visit a current global maximum of expected improvement to the current surrogate model and updates the kriging surrogate model at each iteration.
- the workflow can be performed by evaluating y‘ at initial set using the LHS design, estimating a covariance function using the initial design samples, determining the expected
- the location of the maximum improvement is the next sampled point x + , which will bring best improvement to the surrogate model.
- Kriging is then performed for this picked location, and the predication is added to the measured data.
- a stopping criterion is then identified based on the maximum expected improvement.
- Hypercube Sampling could be used.
- the kriging-based surrogate modeling is adopted and the training data sets obtained in step previous step will be used, as discussed previously.
- FIG. 1 1 is a flow diagram of an example process 1 100 for calibration of forward depositional models, such as those described in the previous paragraphs.
- a forward depositional modelling program is received.
- the forward depositional modellings can be done through software programs.
- a Latin Hypercube Sampling (LHS) design is determined based on the projected forward depositional model input variables.
- the LHS design is transformed to a collection of simulated physical values.
- the collection of simulated physical values can be a collection of at least one of hydraulic values, geological values, and sedimentological values.
- the forward depositional model is transformed from time domain to stratigraphic-depth domain.
- one or more pseudo-wells are determined (extracted) based on the simulated model.
- the extracted pseudo-wells’ locations should be the same as the prior observed or drilled wells in the study area.
- a mismatch value is determined based on the transformed forward depositional model and the collection of simulated physical values. In some implementations, determining a mismatch value based on the
- transformed forward depositional model and the collection of simulated physical values can include identifying a first collection of geological parameter values representative of geological properties measured at predetermined points along a drilled well path, determining a second collection of geological parameter values representative of simulated geological properties of the first stratigraphic model at the predetermined points along the drilled well path, determining a collection of difference values representing differences between selected geological parameter values of the first collection and corresponding geological parameter values of the second collection, and providing the collection of differences as the mismatch value.
- a kriging surrogate model is determined based on a collection of the LHS designs (which are x variables), the mismatched values (calculated from the comparison of all the simulated forward models and drilled wells which are y values). The surrogate model will connect x and y together with a function.
- the surrogate model and the iteration criteria are checked, and at 1 130 a determination is made. If the surrogate model is determined to be insufficient, then the process 1 100 continues at 1 1 16. If, however, the surrogate model is determined to be good, then at 1 140 a minimum mismatch search is performed based on the current surrogate model.
- a new LHS design is determined based on the current minimum mismatch search result. For example, a new LHS design can be obtained in order to improve the surrogate model if the surrogate model surface is not good enough.
- the EGO algorithm can ensure that the next suggested LHS design improves the surrogate model over previously determined models.
- a parameter set is generated for forward stratigraphic modeling. For example, when a new LHS design is suggested, that design can provide x for the surrogate model function.
- the y ean be calculated by running the forward depositional model and comparing the simulated output with the observation.
- Implementations of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them.
- implementations of the described subject matter can be implemented as one or more computer programs, that is, one or more modules of computer program instructions encoded on a tangible, non-transitory, computer-readable computer-storage medium for execution by, or to control the operation of, data processing apparatus.
- the program instructions can be encoded in/on an artificially generated propagated signal, for example, a machine-generated electrical, optical, or electromagnetic signal that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus.
- the computer- storage medium can be a machine-readable storage device, a machine- readable storage substrate, a random or serial access memory device, or a combination of computer-storage mediums.
- the terms“data processing apparatus,”“computer,” or“electronic computer device” refer to data processing hardware and encompass all kinds of apparatus, devices, and machines for processing data, including by way of example, a programmable processor, a computer, or multiple processors or computers.
- the apparatus can also be, or further include special purpose logic circuitry, for example, a central processing unit (CPU), a field programmable gate array (FPGA), or an application specific integrated circuit (ASIC).
- the data processing apparatus or special purpose logic circuitry (or a combination of the data processing apparatus or special purpose logic circuitry) may be hardware- or software-based (or a combination of both hardware- and software-based).
- the apparatus can optionally include code that creates an execution environment for computer programs, for example, code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of execution environments.
- code that constitutes processor firmware for example, code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of execution environments.
- the present disclosure contemplates the use of data processing apparatuses with or without conventional operating systems, for example LINUX, UNIX, WINDOWS, MAC OS, ANDROID, or IOS, or any other suitable conventional operating system.
- a computer program may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages.
- a computer program can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.
- a computer program may, but need not, correspond to a file in a file system.
- a program can be stored in a portion of a file that holds other programs or data, for example, one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, for example, files that store one or more modules, sub programs, or portions of code.
- a computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. While portions of the programs illustrated in the various figures are shown as individual modules that implement the various features and functionality through various objects, methods, or other processes, the programs may instead include a number of sub-modules, third- party services, components, libraries, and such, as appropriate. Conversely, the features and functionality of various components can be combined into single components, as appropriate. Thresholds used to make computational determinations can be statically, dynamically, or both statically and
- Described implementations of the subject matter can include one or more features, alone or in combination.
- a method for geological modeling includes receiving a forward depositional model, determining a Latin
- Hypercube Sampling stratigraphic model based on the projected forward depositional model, performing forward depositional modeling, transform the forward depositional model from time domain to stratigraphic- depth domain, determining one or more pseudo-wells based on the
- the forward depositional model can be based on well log data descriptive of a drilled well path through a predetermined geographical area.
- the method can also include receiving the well log data descriptive of the drilled well path through the predetermined geographical area, and projecting, based on the well log data, the drilled well path to forward depositional model coordinates in the forward depositional model.
- the collection of simulated physical values can include a collection of at least one of hydraulic values, geological values, and sedimentological values.
- the method can also include determining a drilling path based on an identified set of predetermined input parameters, and drilling a well based on the determined drilling path.
- Determining a mismatch value based on the transformed forward depositional model and the collection of simulated physical values can include identifying a first collection of geological parameter values representative of geological properties measured at predetermined points along a drilled well path, determining a second collection of geological parameter values representative of simulated geological properties of the LHS stratigraphic model at the predetermined points along the drilled well path, determining a collection of difference values comprising differences between selected geological parameter values of the first collection and corresponding geological parameter values of the second collection, and providing the collection of differences as the mismatch value.
- a system for geographical modeling includes a control system having one or more processors, and a non-transitory computer- readable medium storing instructions executable by the one or more processors to perform operations including receiving a forward depositional model, determining a Latin Hypercube Sampling (LHS) stratigraphic model based on the projected forward depositional model, performing forward depositional modeling, transform the forward depositional model from time domain to stratigraphic-depth domain, determining one or more pseudo-wells based on the transformed model, determining a mismatch value based on the transformed forward depositional model and a collection of simulated physical values, and determining a kriging surrogate model based on the LHS stratigraphic model and the mismatch value.
- LHS Latin Hypercube Sampling
- a non-transitory computer-readable medium storing instructions executable by a processing device to perform operations includes receiving a forward depositional model, determining a Latin Hypercube Sampling (LHS) stratigraphic model based on the projected forward
- depositional model performing forward depositional modeling, transforming the forward depositional model from time domain to stratigraphic-depth domain, determining one or more pseudo-wells based on the transformed model, determining a mismatch value based on the transformed forward depositional model and a collection of simulated physical values, determining a kriging surrogate model based on the LHS stratigraphic model and the mismatch value.
- the forward depositional model can be based on well log data descriptive of a drilled well path through a predetermined geographical area.
- the operations can also include receiving the well log data descriptive of the drilled well path through the predetermined geographical area, and projecting, based on the well log data, the drilled well path to forward depositional model coordinates in the forward depositional model.
- the operations can also include determining a drilling path based on an identified set of predetermined input parameters, and drilling a well based on the determined drilling path.
- Determining a mismatch value based on the transformed forward depositional model and the collection of simulated physical values can also include identifying a first collection of geological parameter values representative of geological properties measured at predetermined points along a drilled well path, determining a second collection of geological parameter values representative of simulated geological properties of the LHS stratigraphic model at the predetermined points along the drilled well path, determining a collection of difference values including differences between selected geological parameter values of the first collection and corresponding geological parameter values of the second collection, and providing the collection of differences as the mismatch value.
- Implementations of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them.
- implementations of the described subject matter can be implemented as one or more computer programs.
- Each computer program can include one or more modules of computer program instructions encoded on a tangible, non- transitory, computer-readable computer-storage medium for execution by, or to control the operation of, data processing apparatus.
- the program instructions can be encoded in/on an artificially generated propagated signal.
- the signal can be a machine generated electrical, optical, or electromagnetic signal that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus.
- the computer-storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of computer- storage mediums.
- a data processing apparatus can encompass all kinds of apparatus, devices, and machines for processing data, including by way of example, a programmable processor, a computer, or multiple processors or computers.
- the apparatus can also include special purpose logic circuitry including, for example, a central processing unit (CPU), a field programmable gate array (FPGA), or an application specific integrated circuit (ASIC).
- the data processing apparatus or special purpose logic circuitry can be hardware- or software-based (or a combination of both hardware- and software-based).
- the apparatus can optionally include code that creates an execution environment for computer programs, for example, code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of execution environments.
- the present disclosure contemplates the use of data processing apparatuses with or without conventional operating systems, for example, LINUX, UNIX, WINDOWS, MAC OS, ANDROID, or IOS.
- a computer program which can also be referred to or described as a program, software, a software application, a module, a software module, a script, or code, can be written in any form of programming language.
- Programming languages can include, for example, compiled languages, interpreted languages, declarative languages, or procedural languages.
- Programs can be deployed in any form, including as stand-alone programs, modules, components, subroutines, or units for use in a computing
- a computer program can, but need not, correspond to a file in a file system.
- a program can be stored in a portion of a file that holds other programs or data, for example, one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files storing one or more modules, sub programs, or portions of code.
- a computer program can be deployed for execution on one computer or on multiple computers that are located, for example, at one site or distributed across multiple sites that are interconnected by a communication network. While portions of the programs illustrated in the various figures may be shown as individual modules that implement the various features and functionality through various objects, methods, or processes, the programs can instead include a number of sub-modules, third-party services, components, and libraries. Conversely, the features and functionality of various
- Thresholds used to make computational determinations can be statically, dynamically, or both statically and dynamically determined.
- Computers suitable for the execution of a computer program can be based on one or more of general and special purpose microprocessors and other kinds of CPUs.
- the elements of a computer are a CPU for performing or executing instructions and one or more memory devices for storing instructions and data.
- a CPU can receive instructions and data from (and write data to) a memory.
- a computer can also include, or be operatively coupled to, one or more mass storage devices for storing data.
- a computer can receive data from, and transfer data to, the mass storage devices including, for example, magnetic, magneto optical disks, or optical disks.
- a computer can be embedded in another device, for example, a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable storage device such as a universal serial bus (USB) flash drive.
- PDA personal digital assistant
- GPS global positioning system
- USB universal serial bus
- Computer readable media suitable for storing computer program instructions and data can include all forms of permanent/non-permanent and volatile/nonvolatile memory, media, and memory devices.
- Computer readable media can include, for example, semiconductor memory devices such as random access memory (RAM), read only memory (ROM), phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory devices.
- Computer readable media can also include, for example, magnetic devices such as tape, cartridges, cassettes, and internal/removable disks.
- Computer readable media can also include magneto optical disks and optical memory devices and technologies including, for example, digital video disc (DVD), CD ROM, DVD+/-R, DVD-RAM, DVD-ROM, HD-DVD, and BLURAY.
- the memory can store various objects or data, including caches, classes, frameworks, applications, modules, backup data, jobs, web pages, web page templates, data structures, database tables, repositories, and dynamic information. Types of objects and data stored in memory can include parameters, variables, algorithms, instructions, rules, constraints, and references.
- the memory can include logs, policies, security or access data, and reporting files.
- the processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.
- Implementations of the subject matter described in the present disclosure can be implemented on a computer having a display device for providing interaction with a user, including displaying information to (and receiving input from) the user.
- display devices can include, for example, a cathode ray tube (CRT), a liquid crystal display (LCD), a light- emitting diode (LED), and a plasma monitor.
- Display devices can include a keyboard and pointing devices including, for example, a mouse, a trackball, or a trackpad.
- User input can also be provided to the computer through the use of a touchscreen, such as a tablet computer surface with pressure sensitivity or a multi-touch screen using capacitive or electric sensing.
- a computer can interact with a user by sending documents to, and receiving documents from, a device that is used by the user.
- the computer can send web pages to a web browser on a user’s client device in response to requests received from the web browser.
- GUI graphical user interface
- GUI can be used in the singular or the plural to describe one or more graphical user interfaces and each of the displays of a particular graphical user interface. Therefore, a GUI can represent any graphical user interface, including, but not limited to, a web browser, a touch screen, or a command line interface (CLI) that processes information and efficiently presents the information results to the user.
- a GUI can include a plurality of user interface (Ul) elements, some or all associated with a web browser, such as interactive fields, pull-down lists, and buttons. These and other Ul elements can be related to or represent the functions of the web browser.
- Implementations of the subject matter described in this specification can be implemented in a computing system that includes a back end component, for example, as a data server, or that includes a middleware component, for example, an application server.
- the computing system can include a front-end component, for example, a client computer having one or both of a graphical user interface or a Web browser through which a user can interact with the computer.
- the components of the system can be interconnected by any form or medium of wireline or wireless digital data communication (or a combination of data communication) in a
- Examples of communication networks include a local area network (LAN), a radio access network (RAN), a metropolitan area network (MAN), a wide area network (WAN), Worldwide Interoperability for Microwave Access (WIMAX), a wireless local area network (WLAN) (for example, using 802.1 1 a/b/g/n or 802.20 or a combination of protocols), all or a portion of the Internet, or any other communication system or systems at one or more locations (or a combination of communication networks).
- the network can communicate with, for example, Internet Protocol (IP) packets, frame relay frames, asynchronous transfer mode (ATM) cells, voice, video, data, or a combination of communication types between network addresses.
- IP Internet Protocol
- ATM synchronous transfer mode
- the computing system can include clients and servers.
- a client and server can generally be remote from each other and can typically interact through a communication network.
- the relationship of client and server can arise by virtue of computer programs running on the respective computers and having a client-server relationship.
- Cluster file systems can be any file system type accessible from multiple servers for read and update. Locking or consistency tracking may not be necessary since the locking of exchange file system can be done at application layer.
- any claimed implementation is considered to be applicable to at least a computer-implemented method; a non-transitory, computer-readable medium storing computer-readable instructions to perform the computer-implemented method; and a computer system comprising a computer memory interoperably coupled with a hardware processor configured to perform the computer-implemented method or the instructions stored on the non-transitory, computer-readable medium.
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