WO2020142257A1 - Procédé et système d'évaluation de variabilité dans des modèles de subsurface pour supporter la prise de décisions dans des exploitations d'hydrocarbures - Google Patents

Procédé et système d'évaluation de variabilité dans des modèles de subsurface pour supporter la prise de décisions dans des exploitations d'hydrocarbures Download PDF

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WO2020142257A1
WO2020142257A1 PCT/US2019/067764 US2019067764W WO2020142257A1 WO 2020142257 A1 WO2020142257 A1 WO 2020142257A1 US 2019067764 W US2019067764 W US 2019067764W WO 2020142257 A1 WO2020142257 A1 WO 2020142257A1
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data
metric
data set
region
feature space
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Thomas C. Halsey
Sumeet Trehan
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Exxonmobil Upstream Research Company
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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
    • E21B41/00—Equipment or details not covered by groups E21B15/00 - E21B40/00
    • 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
    • E21B2200/00—Special features related to earth drilling for obtaining oil, gas or water
    • E21B2200/22—Fuzzy logic, artificial intelligence, neural networks or the like

Definitions

  • This disclosure relates generally to the field of subsurface modeling, and methods of creating subsurface models for use in hydrocarbon operations, such as hydrocarbon exploration, development, and production operations. Specifically, this disclosure relates to methods and systems that evaluate the intrinsic and extrinsic variability in subsurface models to support decision making for hydrocarbon operations.
  • Upstream oil and gas operations require a rich set of decisions on multiple time and spatial scales. These decisions start in the hydrocarbon exploration or acquisition phase of an asset, continue through development planning choices, and persist through the lifetime of an asset. Hydrocarbon exploration, development, and production decision-making always proceeds in the context of considerable uncertainty, both above-ground uncertainties (e.g., facilities performance, markets, commodity prices, etc.) and subsurface uncertainties (e.g., oil in place, effectiveness of recovery mechanisms, key controls on producibility, etc.). For decision-making, operators typically rely on various models, such as subsurface models, to aid in predicting various outcomes.
  • above-ground uncertainties e.g., facilities performance, markets, commodity prices, etc.
  • subsurface uncertainties e.g., oil in place, effectiveness of recovery mechanisms, key controls on producibility, etc.
  • subsurface models may be used to represent subsurface regions, which may include a description of subsurface structures within the region and material properties for the region.
  • the subsurface model may be a geologic model or a reservoir model.
  • the subsurface model may represent measured data and/or interpreted data for the subsurface region, may be within a physical space or domain, and/or may include objects (e.g., horizons, faults, surfaces, volumes, and the like).
  • the subsurface model may also be discretized with a mesh or a grid that includes nodes and forms cells (e.g., voxels or elements) within the model.
  • subsurface properties may be represented as spatially extended, three-dimensional geocell ular models, with specific physical and chemical properties associated with each cell of the model.
  • each cell may be associated with a specific rock permeability and porosity as well as saturations of the three potential phases, oil, gas, and water. Additional information may be incorporated into the reservoir model, such as phase behavior for the hydrocarbon components, aquifer strength, and multiple phase flow parameters such as irreducible saturations.
  • the reservoir model can be used to simulate multiphase flow within the subsurface.
  • Subsurface modeling is widely utilized in hydrocarbon development and hydrocarbon production phases for hydrocarbon assets.
  • Hydrocarbon development involves determining capital and operating decisions, which relate to the plans for production from an asset.
  • one or more subsurface models are created, which are conditioned to seismic data, well logs, well test data, and any other available data to determine the underlying geological and statistical concepts for the subsurface region.
  • history matching is utilized in conventional approaches to manage production from an asset. History matching utilizes production data, such as flow rates, pressure data and/or temperature data, to condition the reservoir model and determine the reservoir model that matches the measured data. The assimilation of this data is utilized with a reservoir model to provide a more accurate future prediction based on the past production data.
  • U.S. Patent Application No. 2007/0016389 describes a method for performing history matching using a neural network.
  • the neural network provides a correlation between the calculated history match error and a selected set of parameters that characterize the well bore and/or the reservoir.
  • the neural network iteratively varies the value of the parameters to provide at least one set of history match parameters having a value that provides a minimum for the calculated history matching error.
  • the method is directed to minimizing the history match error.
  • U.S. Patent No. 7,725,302 describes a method for performing an oilfield operation using a user objective.
  • a one-dimensional (ID) reservoir model is generated and a three dimensional (3D) reservoir model is generated by distributing properties per unit of depth in the volume.
  • the 3D reservoir model is calibrated using historical response of the reservoir, thereby assisting the forecast of the response of the reservoir to a set of input data by applying the set of input data to the 3D reservoir model.
  • U.S. Patent No. 9,074,454 describes a method for performing reservoir engineering using horizons and positioning wellbore equipment in a well completion design based on an offset. Then, the method further includes calculating an absolute position of the wellbore equipment in the well completion design based on the offset and the location of the geological horizon.
  • U.S. Patent No. 9,135,378 describes a method of developing a reservoir traversed using a production indicator.
  • a position of a well to be drilled is determined by means of a production indicator map.
  • the method involves determining production indicators on a group of cells; determining production indicators on another group of cells; and interpolating production indicators for the other cells of the map. Then, the new well is positioned at the highest production indicator.
  • the reservoir model optimization approach merely addresses a conditioning problem that determines the reservoir model that best matches the historical production data.
  • the history matching process has to rely upon noisy production data to determine the model that best matches the historical data.
  • history matching which is limited in properly determining the subsurface structures within the reservoir, has evolved to include ensembles of reservoir models to address this deficiency. The ensemble of models still rely upon the noisy production data to attempt to provide insights on the reservoir model (or models, within the full ensemble).
  • the reservoir model may be underdetermined by the data, and as a result, a unique optimal solution may not exist for the data being used in the history matching approach.
  • this approach has the goal to select a model or models to use in the performance of further modeling, in support of some business objective.
  • this approach may reduce the number or range of the models being reviewed, which may limit the number of models to a narrower or constricted range and/or may not necessarily be suited for assisting in decision making processes.
  • the process of determining a model that matches the historical production data is time-consuming and cumbersome within the reservoir modeling and software systems currently practiced.
  • the ultimate goal of a subsurface model is to aid or support a business decision (e.g., to drill or to not drill), not to create a perfect (physically realistic) subsurface model. As such, it may not be desirable and even may be unnecessary to history match or condition the subsurface model. Instead, it may be desirable to utilize a“goal- oriented inference” type of modeling, which allows the use of uncertain models to optimally determine“quantities of interest” relevant to particular decisions, without necessarily reducing the underlying uncertainty of the full model.
  • U.S. Patent Application Publication No. 2018/0188403 describes a regression and classification system for use in subsurface models to support decision making for hydrocarbon systems.
  • the method creates multiple reservoir models for a subsurface region using a first data set (e.g., seismic, well log, production data).
  • a second data set e.g., subsurface measurements
  • the models are then used to create the remainder of the second data set.
  • a feature space is then created and elements of the feature space corresponding to each reservoir model are defined.
  • Production data is then disposed into the feature space, and a region of interest within the feature space is determined.
  • a metric such as expected ultimate recovery, is then evaluated for an operation decision (e.g., to drill a well or to not drill a well) in the region of interest in the feature space.
  • an operation decision e.g., to drill a well or to not drill a well
  • the method described in U.S. Patent Application Publication No. 2018/0188403 assumes that the decision metric can be viewed as a function in the feature space. As such, the method in U.S. Patent Application Publication No. 2018/0188403 fails to account for instances where the decision metric can take various values at a point, points, or region in the feature space.
  • the present techniques may provide a method for evaluating and performing a hydrocarbon operation for a subsurface region comprising: obtaining a metric for a hydrocarbon operation decision; obtaining a first data set associated with the subsurface region; creating an ensemble of reservoir models for the subsurface region using the first data set, wherein the ensemble of reservoir models comprises two or more reservoir models; creating a second data set associated with the subsurface region using the ensemble of reservoir models; creating a feature space and defining a plurality of elements of the feature space corresponding to each reservoir model; determining a region of interest within the feature space; inferring an intrinsic variability for the metric in the region of interest within the feature space; comparing the intrinsic variability for the metric with the extrinsic variability for the metric within the ensemble of reservoir models; evaluating the metric for the operational decision at the region of interest in the
  • Figure 1 is an exemplary flow chart in accordance with one or more embodiments of the present techniques.
  • Figure 2 is an exemplary flow chart in accordance with one or more embodiments of the present techniques.
  • Figures 3A 3B , 3C, 3D, 3E, 3F, 3G, 3H, 31, 3J, 3K, 3U, and 3M are exemplary diagrams associated with an embodiment of the present techniques.
  • Figure 4 is a block diagram of a computer system that may be used to perform any of the methods disclosed herein.
  • Figure 5 is an exemplary diagram illustrating the variance in intrinsic an extrinsic variability for a decision metric M.
  • Figure 6 is an exemplary diagram illustrating a variogram of a decision metric M.
  • Figure 7 is an exemplary diagram illustrating a distribution of clusters.
  • hydrocarbon(s) refers to molecule(s) formed primarily of carbon and hydrogen atoms. Hydrocarbons may also include other elements or compounds, such as, halogens, metallic elements, nitrogen, oxygen, sulfur, hydrogen sulfide (H2S), and carbon dioxide (CO2). Hydrocarbons may be located within or adjacent to mineral matrices, termed reservoirs, within the earth. Matrices may include, but are not limited to sedimentary rock, shales, sands, carbonates, diatomites, and other porous media. Hydrocarbons may be produced from hydrocarbon reservoirs through wells penetrating a hydrocarbon containing formation. Hydrocarbons derived from a hydrocarbon reservoir may include, but are not limited to, oil, natural gas, petroleum, kerogen, bitumen, pyrobitumen, asphaltenes, tars, or combinations thereof.
  • hydrocarbon exploration refers to any activity associated with determining the location of hydrocarbons in subsurface regions.
  • Hydrocarbon exploration normally refers to any activity conducted to obtain measurements through acquisition of measured data associated with the subsurface formation and the associated modeling of the data to identify potential locations of hydrocarbon accumulations.
  • hydrocarbon exploration may include acquiring measurement data, modeling of the measurement data to form subsurface models, and determining likely locations for hydrocarbon reservoirs within the subsurface.
  • the measurement data may include seismic data, gravity data, magnetic data, electromagnetic data, and the like.
  • hydrocarbon development refers to any activity associated with planning of extraction and/or access to hydrocarbons in subsurface regions. Hydrocarbon development normally refers to any activity conducted to plan for access to and/or for production of hydrocarbons from the subsurface formation and the associated modeling of data to identify preferred development approaches and methods. Accordingly, hydrocarbon development may include modeling of subsurface formations and extraction planning for periods of production, determining and planning equipment to be utilized and techniques to be utilized in extracting hydrocarbons from the subsurface formation, and the like.
  • hydrocarbon operations refers to any activity associated with hydrocarbon exploration, hydrocarbon development, and/or hydrocarbon production.
  • hydrocarbon production refers to any activity associated with extracting hydrocarbons from a subsurface location through a well or other opening. Hydrocarbon production normally refers to any activity conducted to form the wellbore along with any activity in or on the well after the well is completed. Accordingly, hydrocarbon production includes not only primary hydrocarbon extraction, but also secondary and tertiary production techniques, such as injection of gas or liquid for increasing drive pressure or mobilizing the hydrocarbons; treating the well by, for example, chemicals or hydraulic fracturing the wellbore to promote increased flow; well servicing; well logging; and other well and wellbore treatments.
  • the term“subsurface model” refers to a model of a subsurface region and may include a reservoir model, a geomechanical model, a watertight model, and/or a geologic model.
  • the subsurface model may include subsurface data distributed within the model in two-dimensions (e.g., distributed into a plurality of cells, such as elements or blocks), three-dimensions (e.g., distributed into a plurality of voxels,), or four or more dimensions.
  • the term“geologic model” refers to a model (e.g., a two- dimensional model or a three dimensional model) of the subsurface region having static properties and includes objects, such as faults and/or horizons, and properties, such as facies, lithology, porosity, permeability, and/or the proportion of sand and shale.
  • the term“reservoir model” is a model (e.g., a two-dimensional model or a three-dimensional model) of the subsurface that in addition to static properties, such as porosity and/or permeability, also has dynamic properties that vary over the timescale of resource extraction, such as fluid composition, pressure, and/or relative permeability.
  • the term“extrinsic variability” refers to the variability in the metric of interest, such as expected ultimate recovery or decision-relevant metric, with change in the observed data.
  • the term“intrinsic variability” refers to the variability in the metric of interest based on the models that are consistent with the observed data (or part of the feature space)
  • a simulation refers to the process of performing one or more operations using a subsurface model and any associated properties to create simulation results.
  • a simulation my involve computing a prediction related to the resource extraction based on a reservoir model.
  • a reservoir simulation may involve, by execution of a reservoir-simulator computer program on a processor, computing composition, pressure, and/or movement of fluid as a function of time and space for a specified scenario of injection and production wells by solving a set of reservoir fluid flow equations.
  • a subsurface model is created in the physical space or domain to represent the subsurface region.
  • the subsurface model is a computerized representation of a subsurface region based on geophysical and geological observations made of regions on and / or below the surface of the Earth.
  • the subsurface model may be a numerical equivalent of a three-dimensional geological map complemented by a description of physical quantities in the domain of interest.
  • the subsurface model may include multiple dimensions.
  • the subsurface model may include a structural framework of objects, such as faults and horizons, and may include a mesh or grid of nodes to divide the structural framework and/or subsurface model into cells, which may include mesh elements or blocks in two-dimensions, mesh elements or voxels in three-dimensions or other suitable mesh elements in other dimensions.
  • a cell, such as block, mesh element or voxel, is a subvolume of the space, which may be constructed from nodes within the mesh.
  • Subsurface modeling is utilized in hydrocarbon development and hydrocarbon production phases for hydrocarbon assets.
  • Hydrocarbon development involves determining capital and operating decisions, which relate to the plans for production from an asset.
  • one or more subsurface models are created, which are conditioned to seismic data, well logs, well test data, and any other available data to determine the underlying geological and statistical concepts for the subsurface region. Accordingly, the subsurface models may be used to determine the fluid flow within the reservoir and from the respective production wells.
  • Reservoir modeling and simulation are utilized to support particular business decisions. While in the hydrocarbon development phase, the decisions are broad in scope, such as whether to pursue a project, or selections regarding facilities design and constraints, for example. While in the hydrocarbon production phase, the decisions are typically more specific, such as whether to drill a new well or a location for a new well, for example.
  • the present techniques relate to a system and method that identifies the intrinsic and extrinsic variability in ensemble of subsurface models to support decision making for hydrocarbon operations.
  • the present techniques may be used to addres the uncertainty in reservoir proeprties that determine future production from existing or potential wells.
  • the present techniques do not involve themselves in the inefficiencies of optimizing a reservoir model to match production data, as this effort in determining a large amount of highly granular model information, much of which is irrelevant to the hydrocarbon operations.
  • the resulting enhancements provided by the present techniques may then be used for various hydrocarbon operations, such as hydrocarbon exploration, hydrocarbon development and/or hydrocarbon production operations.
  • the present techniques utilize an ensemble of models to guide a hydrocarbon operations decision.
  • the hydrocarbon operations decision may be framed as a discrete decision (e.g., yes or no, or a one or zero).
  • a hydrcoarbon decision may be whether or not to drill an infill well in a field that is already under production.
  • a first data set which may be referred to as data set“A”, includes data that is used to condition two or more reservoir models that form the ensemble of reservoir models. This conditioning may be performed using a variety of techniques known in the art.
  • the first data set may include seismic data, well test data, and well log data that is used to generate the reservoir models.
  • the first data set may contain pre-production data such as seismic, well test, and well log data.
  • a second data set which may be referred to as data set“B”, includes data that is not used to condition the reservoir models, but instead defines a feature space (which may ultimately be simplified or reduced in dimension) in which the reservoir model results or operations data can be represented as points.
  • the second data set may include simulation results, production data, generated or observed seismic data, generated or observed well test data and/or generated or observed well log data.
  • the second data set may correspond to reservoir simulation output for an ensemble of models conditioned ot the pre-production data, supplemented by corresponding data for the actual field.
  • M a metric, which may be referred to as“M”, corresponding to some physical parameter of interest that supports the operations decisions.
  • M may denote the decision-relevant metric or the decision itself.
  • Examples of such a metric may include the expected ultimate recovery from a reservoir (“EUR”), which is often used to guide hydrocarbon operation decisions, or expected incremental cumulative oil produced from hydrocarbon operation decision (e.g., as drilling or using an in-fill well).
  • EURO expected ultimate recovery from a reservoir
  • This metric can also be included as a position descriptor for the points in the feature space.
  • the present techniques involve analyzing the results of simulations of an ensemble of reservoir models (e.g., two or more reservoir models) to provide information on particular hydrocarbon operations.
  • the method may include various steps, such as assigning particular data to the data set A or data set B, obtaining or creating two or more reservoir models, using the reservoir models in simulations and analyzing the results in a feature space.
  • an ensemble of reservoir models may be created which are conditioned to a first data set (i.e., data set A), such as a pre-production data set.
  • a first data set i.e., data set A
  • Each model of the ensemble of models can be simulated to create a modeled version of data set B and the metric M.
  • Machine learning methods can then be used to build an approximate for the relationship between M and B, which can be used with the real-world data sets B to estimate the real-world value of the metric M.
  • the present techniques may be used to provide a direct map from the data-space to the metric that drives the decision. While the initial models may be conditioned with the first data set, no actual model purporting to represent the actual field (consistent with its production data) is ever consturcted.
  • the reservoir models may be conditioned to an initial data set (e.g., the first data set or data set A), which may include seismic data and appraisal well data, but not necessarily production data.
  • the reservoir models should include plausible geological scenarios consistent with the initial data set.
  • the models can be used to generate data set B, which define the highest dimensional feature space possible.
  • a feature space can be defined as a Cartesian space whose axes are the rates at selected times of the phases (oil, gas, water) produced at each well, as well as pressure information corresponding to the wells (e.g. bottom hole pressure).
  • Each of the reservoir model results for time in the range between 0 ⁇ t ⁇ T may be embedded into the feature space, which accounts for production information prior to the time of the new or updated hydrocarbon operation. Then, one or more points within the feature space corresponding to the measured or observed production data, possibly with synthetic noise added (e.g., a“truth case” of the measured production data time series over time in the range between 0 ⁇ t ⁇ T) can be added to the feature space, where the one or more points may have a spatial relationship within that space.
  • synthetic noise added e.g., a“truth case” of the measured production data time series over time in the range between 0 ⁇ t ⁇ T
  • the spatial relationship may be the forming of a region or area that is associated with the results within a distance threshold in the space of the measured or observed production data (e.g., actually observed production data).
  • machine learning classification or regression techniques e.g., k- means clustering, support vector models, or Kriging
  • k- means clustering, support vector models, or Kriging
  • This may involve regressing the value of the metric to the point, points, or region that represent the truth case from neighboring reservoir models (e.g., in the feature space or the higher dimensional space), which have been simulated (e.g., both prior to and subsequent to the time T); and/or may involve estimating a probability distribution function of the metric value for the preferred decision or may involve determining clusters from the data corresponding to the reservoir models.
  • the metric may be defined as a function in the feature space, with regression to the value of the function at the point, points, or region corresponding to the truth case, or it is possible to create a larger feature space by including the metric value as an axis, and then determine the metric at the truth case point or points using conventional regression methods, as noted above, in the sub-region occupied by reservoir model data in that larger space.
  • data set A may comprise seismic data indicating basic geologic structures, environments of deposition, and other seismically observable or inferable properties
  • data set B may comprise well log and well test data from one or more appraisal wells.
  • Two or more reservoir models may be created from data set A, and synthetic results from examination of these models may be used to create data corresponding to synthetic well log or well test results corresponding to the positions of the appraisal wells, these latter comprising data set B.
  • a feature space can be created by choosing a parameterization of these latter well log or well test results, using methods known to those skilled in the art, and using these parameters to define the axes of a Cartesian space.
  • Linear or non-linear transformations of these parameters may also be used to define the axes.
  • the measured well log or well test results from the appraisal well or wells, possibly with synthetic noise added, may then be placed in the feature space in which data set B is indicated; regression or classification techniques may then be used to characterize the expected value of a metric, such as EUR (Expected Ultimate Recovery), which may be computed from the models, at the point, points or region in feature space corresponding to the measured data (e.g., the truth case).
  • a metric such as EUR (Expected Ultimate Recovery)
  • the reservoir models are not conditioned or changed (subsequent to their initial formulation using data set A), as in conventional history matching operations, but are utilized in evaluating the performance of hydrocarbon operations. Also, the reservoir models are not filtered or reviewed to indicate that any particular reservoir model or models is determined to be the closest, in some quantitiatively defined sense, to the subsurface region (e.g., actual subsurface region). This is beneficial because the simulation of even a large number of models to determine the parameters that may be used to create data points in the feature space is more computationally efficient and less cumbersome than the“inverse problem” of trying to determine a reservoir model that matches the truth case data.
  • the prediction of the metric describing the outcome of that operation is determined by the evaluated metric of neighboring reservoir models in the feature space, following statistical methods to average over these behaviors to provide a robust solution in that particular feature space.
  • the regression method depends on the metric used, and thus may vary with the business decision being analyzed, even for the same ensemble of models.
  • the statistical regression techniques may weigh the different reservoir models differently in determining the metric or metrics describing the outcome of the hydrocarbon operations decision at the point or points or region corresponding to the truth case (e.g., within a zone or region near or within a threshold of the truth case). Accordingly, different reservoir models may contribute differently to different decisions, which is not the result if history matching is performed to identify a preferred, optimal, or best reservoir model.
  • the present techniques utilize the behavior for the models, which may be computed directly from their properties, such as production for times in the range 0 ⁇ t ⁇ T or t > T (in the production example) or EUR (in the development example). Because any property relevant to hydrocarbon operations of these models for any time may be determined by the simulation, the present techniques provide a mechanism to verify and to test the robustness of the present techniques.
  • One particular model may be chosen as a“synthetic truth case”, and the classification and regression method can be executed on the remaining models within the ensemble.
  • the value computed for the metric at the synthetic truth case may then be compared with the actual value of the metric for the chosen model, which is computable, thereby providing a test of the robustness and accuracy of the procedure for a particular ensemble of models, a particular choice of data sets A and B, and a particular metric used to evaluate an envisioned hydrocarbon operations decision.
  • the data for these model results may also be used to tune the feature determination and regression and/or classification algorithms prior to identification of the predicted behavior for the hydrocarbon operations being evaluated. For example, this may involve using methods, such as, Lasso regression and/or sensitivity analysis, to identify features, which are most informative for the metric of interest.
  • Feature space creation is commonly practiced in machine learning applications, and may follow standard supervised or unsupervised machine learning practices. Pre-existing domain knowledge about the subsurface region or its analog(s) in another geospatial area(s) and existing data may be used to assist in defining the feature space.
  • data set B includes a set of time series of production data from existing M wells at N time points within the time interval (0, T)
  • data set B may be considered to be embedded in a feature space of dimension greater than or equal to MN, depending on how many data observations are conducted at each well. Then, the dimension of the feature space may be changed by transforming data vectors in data set B into feature vectors via a feature map.
  • a feature map may be based on polynomial combinations of components in a data vector or alternatively functional data analysis (“FDA”) can be used to define a set of basis vectors and coefficients that approximate, within some specified accuracy, the full data set.
  • FDA functional data analysis
  • Another alternative configuration may include FDA that may be used to describe the features.
  • FDA involves representing the functional data (e.g., time series corresponding to multiphase flow rates at wells), by coefficients of the smoothing spline or low-dimensional representation of the smoothing spline coefficients.
  • a feature space may be infinite dimensional and a feature map need not be explicitly constructed. Regression or classification in the feature space can be performed using function kernels representing inner products in the feature space. In this case, choosing a kernel is equivalent to choosing feature map(s) and/or feature space(s). Radial basis functions are often used as kernels in practice.
  • a feature space there are multiple ways to construct a feature space, including direct use of the original data set B as well as possible linear or non-linear transformations of this data, which may result in an altered (e.g., a lower) dimensionality feature space.
  • feature space selection the feature space that provides the most confident and unbiased evaluation of the operations under consideration should be chosen. It follows that the feature space constructed, even for the same ensemble of reservoir or subsurface models, may be different based on the hydrocarbon operations decision to be evaluated. Visual display may be used to assist the selection of the feature space.
  • Dimension reduction methods such as multi-dimensional scaling or nonlinear dimensionality reduction methods (e.g., manifold learning), such as those described and developed in the machine learning literature, may be used to reduce the dimension of the feature space to two or three-dimensional space for visual inspection.
  • Many such methods are described and known to those skilled in the art.
  • such methods may include those discussed in Friedman et al,“The elements of statistical learning”, vol. 1, Springer, Berlin: Springer series in statistics, 2001 and Suzuki et al., "Using Association Rule Mining and High-Dimensional Visualization to Explore the Impact of Geological Features on Dynamic Flow Behavior", SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, 2015.
  • specific knowledge about the subsurface region may be incorporated into feature space selection.
  • an understanding of the large scale reservoir structure and initial reservoir pressure e.g., part of data set A
  • This subset of data may be used to build the feature space.
  • certain information in data set B may be of greater physical significance than other information (e.g., the time when water breaks through at certain producers), this understanding might be used to reduce the number of data points that are used in defining the feature space. This selection may lower the dimensionality of the feature space.
  • the pressure differences between injector and producer pairs over time or the derivatives of production rates with respect to time may be used to enhance the feature space, which may increase the dimensionality of the feature space.
  • Signal processing tools which may involve wavelet analysis, may be used to find identifiable or primary characteristics of the time series in the frequency or time domain. These characteristics (e.g., coefficients of wavelet basis functions) can then be used to construct feature space. Similar procedures can be applied to spatial data along wellbores, for instance in the hydrocarbon development operations example previously discussed.
  • a tailored principal component analysis (“PC A”) or reduction method may be used, which is related to an objective or goal (e.g., parallel to the metric of interest and/or expanding the divergence of the metric of interest). Further, the method may involve performing machine learning, which may result in a lower dimensional space being used for visualization. In addition, the selection of features that amplify differences may be preferred. Moreover, the method may include using principal component analysis to reduce the feature space, which may be embedded into a higher dimensionality space for certain configurations.
  • the underlying geological drivers for performance of any particular decision relating to hydrocarbon operations may be further evaluated.
  • the present techniques may also involve combining the methods above with regression tree analysis of the underlying geological parameters (especially categorical choices in the construction of the ensemble of subsurface models, such as environment of deposition choices).
  • the regression tree analysis may be used to identify systematic correlations between particular geological unknowns and characteristics either of data set B or of one or more hydrocarbon operations decision outcomes.
  • a method for evaluating and performing a hydrocarbon operation for a subsurface region comprising: obtaining a first data set associated with a subsurface region, wherein the two or more reservoir models are based on a first data set; creating two or more reservoir models for a subsurface region from the first data set; obtaining a second data set associated with a subsurface region and the two or more reservoir models; obtaining production data associated with a subsurface region; disposing the production data and at least a portion of the second data set into a feature space; determining a region of interest within the feature space; evaluating the results of a hydrocarbon operation at the region of interest in the feature space; and determining whether to perform a hydrocarbon operation based on the evaluation of the region of interest.
  • the method may include various enhancements.
  • the method may include performing one or more regression techniques to evaluate the region of interest; wherein the first data set comprises one of seismic data, well log data and any combination thereof; wherein the second data set comprises one of generated or observed seismic data, generated or observed well log data, generated or observed well test data and any combination thereof; wherein the second data set comprises one of well log and well test data from appraisal wells; simulating each of the two or more reservoir models with the hydrocarbon operation being performed to create first simulation results, simulating each of the two or more reservoir models with the hydrocarbon operation not being performed to create second simulation results using the first data set; and wherein the second data set comprises the first simulation results and the second simulation results; simulating each of the two or more reservoir models with the hydrocarbon operation being performed to create simulation results; wherein the second data set comprises the first simulation results and the second simulation results; transforming the second data set to alter dimensionality of at least a portion of the second data set prior to disposing at least a portion of the second data set into the
  • the decision metric can be viewed as a function in the feature space.
  • the decision metric can take various values at a point, points, or region in the feature space, including but not limited to the point, points, or region corresponding to the truth case corresponding to a subsurface region.
  • This phenomenon can be referred to as the“intrinsic” variability of the decision metric, as contrasted with the “extrinsic” variablility corresponding to the differences in the determined decision metric for the two or more reservoir models, which may represent a sampling from the various possible values of the decision metric consistent with the points in the feature space corresponding to the two or more reservoir models.
  • Many mathematical, statistical, or machine learning methods may be used to regress to a value of the operational decision metric in the region of interest based on the lcoation in the feature space corresponding to the second data set obtained from the two or more reservoir models can also be used to determine a local variance in the region of interest of the operational decision metric. Examples include model-based regression (such as linear regression), Kriging, and random forest methods.
  • intrinsic or extrinsic variability may be defined, including but not limited to the first (mean) and second moment of the decision metric taken over the multiple reservoir models or using variograms of the decision metric as a function of distance in the feature space [0062]
  • the intrinsic variability of the decision metric may be smaller, comparable to, or larger than the extrinsic variability.
  • the intrinsic variability is comparable to or greater than than the extrinsic variability, it may be possible to estimate the decision metric at the point, points, or region corresponding to the subsurface region using weighted averages of the decision metric over all of the two or more reservoir models.
  • Another method of estimating the decision metric at the point, points, or region corresponding to the subsurface region is to use averages of the decision metric over a nearby cluster in the feature space of some subset of the two or more reservoir models.
  • the clustering of the two or more reservoir models into two or more clusters allows identification of regions of the feature space. For example, one may choose to evaluate the average (e.g., mean, median, or other statistical average) and variance cluster by cluster.
  • average e.g., mean, median, or other statistical average
  • variance cluster e.g., mean, median, or other statistical average
  • many clustering methods are known in the art, and an example of clustering methods in the feature space is sometimes referred to as “unsupervised learning”. See e.g., Hastie et al,“The Elements of Statistical Learning”, Springer, Chapter 14 (2001).
  • the degree to which the decision metric M changes within the region of interest of the feature space can be determined.
  • the intrinsic and extrinsic variability of M within the ensemble of models can then be compared, and this comparison can then be used to specify the mathematical, statistical, or machine learning method used to evaluate the operational decisional metric. For example, if the intrinsic varaiability (“I”) is significantly greater than the extrinsic variability (“E”) (i.e., I »E), then the original ensemble of models can be used for statistical inference of M. However, if the extrinsic variability is greater than the intrinsic variability (i.e., E >1), then the various statistical regression techniques described above may be utilized.
  • the clustering methods described above may be utilized.
  • the present techniques provide various enhancements to the hydrocarbon extraction process.
  • the present techniques avoid the slow and cumbersome process of determining the reservoir or subsurface model that preferably matches or assimilates additional data (data set B).
  • the techniques use information from the full ensemble of two or more reservoir models, and not just from one or more history matched models, to evaluate the results of a hydrocarbon operation, which may improve the accuracy of the determination of the results of a hydrocarbon operation under consideration.
  • the techniques allow two or more reservoir or subsurface models comprising the ensemble to be used differentially to support different hydrocarbon operations decisions, which may also improve the accuracy of the determination of the results of these different hydrocarbon operations.
  • the present techniques allow for a quantification of the variability in the decision metric, thus allowing for improved decision making.
  • the present techniques may be further understood with reference to Figures 1 to 4, which are described further below.
  • FIG. 1 is an exemplary flow chart 100 in accordance with one or more embodiments of the present techniques.
  • the flow chart 100 includes a method for analyzing the results of simulations of an ensemble of reservoir models to provide information on particular hydrocarbon operations decision in order to enhance hydrocarbon operations.
  • the method may include obtaining data and reservoir models for the subsurface region, as shown in blocks 102 to 104.
  • second data sets may be created along with an associated metric, as shown in blocks 106 to 110.
  • the measured data and computed metrics may be placed into the feature space, as shown in blocks 112 to 115.
  • a hydrocarbon operation may be evaluated and performed based on the review, as shown in blocks 116 to 122.
  • the method involves obtaining a first data set (e.g., data set“A”) for a subsurface region, which may include seismic data, well log data, well test data, well appraisal data, or production data, and obtaining two or more reservoir models for the subsurface region conditioned to this data, as shown in blocks 102 to 104.
  • a first data set e.g., data set“A” associated with a subsurface region and a metric (e.g., metric“M”) associated with a operational decision (e.g., potential hydrocarbon operations decision) are obtained.
  • the first data set may include seismic data, well test data and/or well log data
  • the metric may be a parameter associated with the results of a hydrocarbon operation.
  • the metric may correspond to a physical parameter of interest in supporting hydrocarbon operations decisions.
  • a metric may include the expected ultimate recovery from a reservoir (EUR) and/or expected incremental cumulative oil produced due to a hydrocarbon production decision.
  • two or more reservoir models may be created based on the first data set associated with the subsurface region. The determination of the metric may or may not influence the particular reservoir models chosen and/or constructed.
  • the reservoir models may be stored and obtained from memory or may be created to represent the subsurface region.
  • the reservoir models may be created from seismic data, well test data and/or well data, and may be subsequently conditioned to seismic data, well data, well test data and/or production data.
  • the reservoir models may include a mesh that forms various mesh elements.
  • the mesh elements may have one or more properties assigned to each mesh element. The properties may include transmissibility, rock type, porosity, permeability, rock compressibility, oil saturation, clay content and/or cementation factors, for example.
  • a portion of second data set associated with the subsurface region is obtained.
  • the portion of the second data set corresponding to measurements of the actual sub surface region is obtained.
  • the reservoir models may be used to create the remainder of the second data set at block 108.
  • a second data set is created from each of the two or more reservoir models.
  • the second data set may include simulation results, generated or observed seismic data (e.g., generated from the model of the subsurface region combined with seismic forward modeling methods known in the art) and/or generated or observed well log data (e.g., generated from the model of the subsurface region combined with modeling methods known in the art).
  • a feature space and defined elements of the feature space corresponding to each reservoir model is created.
  • the construction of the feature space may be included in which the second data set, or a portion thereof is included in the feature space.
  • the inclusion may involve construction of the feature space and specifying the elements in the feature space corresponding to each reservoir model.
  • the second data set for each reservoir model may be included into feature space, as shown in block 112.
  • a metric is determined for each reservoir model based on the second data set.
  • the metric may be computed from the reservoir model.
  • the difference between cumulative oil production corresponding to taking or not taking a particular hydrocarbon operations decision is a metric that can be computed using reservoir simulation methods known in the art.
  • the metric may correspond to a physical parameter of interest in supporting a hydrocarbon operations decision.
  • a metric may include the expected ultimate recovery from a reservoir (EUR), which is often used to guide hydrocarbon development decisions, or expected incremental cumulative oil produced from hydrocarbon production decisions (e.g., an in-fill well).
  • the hydrocarbon operation may include one or more hydrocarbon exploration operations, one or more hydrocarbon development operations and/or one or more hydrocarbon production operations.
  • the hydrocarbon production operation may involve installing or modifying a well or completion, modifying or adjusting drilling operations, decreasing fracture penetration, and/or to installing or modifying a production facility.
  • the measured data and computed metrics may be placed into the feature space, as shown in blocks 115 to 116.
  • the second data set associated with the subsurface region is disposed into feature space.
  • the measured data may include production data or other measured data from the subsurface region.
  • the second data set associated with the subsurface region may be used to determine a region of interest in feature space.
  • the measured data, and may be the metric, are used to identify a region of interest. The identification of a region of interest may involve determining a threshold or area surrounding a specific measured data point or points.
  • the variability of the metric M in the region of interest in the feature space may be inferred or determined.
  • the intrinsic variability of the metric M in the region of interest of a model may be inferred or determined.
  • the extrinsic variability of the metric M in two or more of the ensemble of models may be inferred or determined.
  • inferring the variability it is meant that the variability is estimated or approximated but is not necernerily exactly determined or measured.
  • the metric in the region of interest may be evaluated.
  • the type of evaluation used to evaluate the metric in the region of interest, which corresponds to a hydrocarbon operation, may depend on a comparison of the intrinsic variability (“I”) and the extrinsic variability (“E”). For example, if E is greater than I (i.e., E>I), the evaluation may involve performing regression techniques. These regression techniques may be one of the regression techniques noted above, for example. However, if I is significantly greater than E (i.e., I » E) simple statistical inference may be used with the original ensemble of models.
  • the evaluation may involve performing cluster anlaysis as described above.
  • the clustering may comprise clustering of the data in the feature space to determine an average value of M the cluster.
  • the hydrocarbon operation may be performed or not based on the evaluation, as shown in block 122.
  • the hydrocarbon operations may include hydrocarbon exploration operations, hydrocarbon development operations and/or hydrocarbon production operations.
  • the hydrocarbon operation may include installing or modifying a well or completion, modifying or adjusting drilling operations, decreasing or increasing fracture penetration, and/or installing or modifying a production facility.
  • the production facility may include one or more units to process and manage the flow of production fluids, such as hydrocarbons and/or water, from the formation.
  • this method provides an enhancement in the production, development and/or exploration of hydrocarbons.
  • the method may be utilized to enhance the decision for a hydrocarbon operation based on the metric being reviewed. Further, this method accounts for variability within and between the models without trying to lessen uncertainty in the reservoir models.
  • FIG. 2 is an exemplary flow chart 200 in accordance with one or more embodiments of the present techniques.
  • the flow chart 200 includes a method for analyzing the results of simulations of an ensemble of reservoir models to provide information on particular hydrocarbon operations to enhance operations.
  • the method may include obtaining data and reservoir models for the subsurface region, as shown in blocks 202 to 204.
  • a hydrocarbon operation may be evaluated through simulations of the reservoir models, as shown in blocks 205 to 210, and then a feature space is used with mathematical techniques to evaluate the hydrocarbon operation, as shown in blocks 212 to 220.
  • the hydrocarbon operation may be performed, as shown in block 222.
  • the method involves obtaining data for a subsurface region, and obtaining two or more reservoir models for the subsurface region, as shown in blocks 202 to 204.
  • production data is obtained for the subsurface region of interest.
  • the production data may include measured data from wells or other measured data.
  • two or more reservoir models may be created from other data associated with the subsurface region.
  • the other data used to create the reservoir models may include seismic data, well test data and/or well data (e.g., a first data set).
  • two or more reservoir models associated with the subsurface region are obtained, as shown in block 204.
  • the reservoir models may be obtained from memory, may have been used previously for other hydrocarbon operations decisions, or may be created to represent the subsurface region.
  • the reservoir models may be created from seismic data, well test data and/or well data, and may be subsequently conditioned to seismic data, well test data, well data and/or production data.
  • the reservoir models may include a mesh that forms various mesh elements.
  • the mesh elements may have one or more properties assigned to each mesh element. The properties may include transmissibility, rock type, porosity, permeability, rock compressibility, oil saturation, clay content and/or cementation factors, for example.
  • the present techniques may evaluate a hydrocarbon operation through simulations of the reservoir models, as shown in blocks 205 to 210.
  • a metric for a hydrocarbon operation is determined.
  • the metric may corresponding to a physical parameter of interest in supporting hydrocarbon operation decisions.
  • a metric may include the expected ultimate recovery from a reservoir (EUR) and/or expected incremental cumulative oil produced corresponding to a particular hydrocarbon operation.
  • a hydrocarbon operation is determined for evaluation.
  • the hydrocarbon operation may include one or more hydrocarbon exploration operations, one or more hydrocarbon development operations and/or one or more hydrocarbon production operations.
  • the hydrocarbon production operation may involve installing or modifying a well or completion, modifying or adjusting drilling operations, decreasing or increasing fracture penetration, and/or to installing or modifying a production facility.
  • each of the two or more reservoir models are simulated with the hydrocarbon operation and without the hydrocarbon operation, as shown in block 208.
  • the hydrocarbon operation may include large scale decisions, such as whether or not to develop a field at all, in which latter case the simulation without the hydrocarbon operation may essentially consist of not developing the field at all.
  • the performance of the simulation may include modeling fluid flow based on the reservoir model and the associated properties stored within the mesh elements (e.g., cells or voxels) of the respective reservoir model.
  • the simulation results may include the computation of time- varying fluid pressure and fluid compositions (e.g., oil, water, and gas saturation) and the prediction of fluid volumes produced or injected at wells.
  • the simulation results and/or the respective reservoir model may be outputted.
  • the outputting of the simulation results and/or the subsurface model may include displaying the simulation results and/or the reservoir model on a monitor and/or storing the simulation results and/or the reservoir model in memory of a computer system.
  • the simulations are performed once with the hydrocarbon operation being performed and once without the hydrocarbon operation being performed for each of the respective reservoir models. Once the simulations are performed, a metric for the hydrocarbon operation is determined based on a comparison of the simulation results, as shown in block 210
  • a feature space is used with mathematical techniques to evaluate the hydrocarbon operation, as shown in blocks 212 to 220.
  • the mathematical techniques may include estimate of the model form error or bias along with estimate of measurement noise.
  • a feature space is determined.
  • the feature space may be a higher dimensional space or may be a lower dimensional space with respect to some reference, e.g. that created by raw, unfit or unapproximated data alone.
  • the feature space may be used to highlight differences and to assist in evaluating the metric and/or hydrocarbon operations.
  • the simulation results or a portion of the simulation results are optionally transformed into the feature space, as shown in block 214.
  • This transformation may involve a mathematical representation or a graphical representation, which may depend on the size of the dimensionality.
  • a region of interest in the feature space is identified.
  • the region of interest may be identified by setting a threshold that defines the region as compared with a truth point or actual production data.
  • the region of interest may be extended or altered to account for noise.
  • the intrinsic variability of the decision metric in the region of interest in the feature space is inferred or determined.
  • the extrinsic variability of the decision metric in the region of interest in the feature space may also be inferred or determined.
  • the intrinsic and extrinsic variability may be compared, and this comparison may be used to choose the type of mathematical techniques, such as the type of regression technique, that is used to evaluate the decision metric and/or to evaluate the outcome of the hydrocarbon operation at the point, points or region corresponding to the region of interest.
  • the mathematical techniques may be similar to those noted above.
  • the hydrocarbon operation may be performed based on the evaluation, as shown in block 220.
  • the hydrocarbon operations may include hydrocarbon exploration operations, hydrocarbon development operations and/or hydrocarbon production operations.
  • the hydrocarbon operation may include installing or modifying a well or completion, modifying or adjusting drilling operations, decreasing fracture penetration, and/or to installing or modifying a production facility.
  • the production facility may include one or more units to process and manage the flow of production fluids, such as hydrocarbons and/or water, from the formation.
  • this method provides an enhancement in the production, development and/or exploration of hydrocarbons.
  • the method may be utilized to enhance the evaluation of the hydrocarbon operation by providing a region of interest that does not involve refining the reservoir models, but is directed to evaluating the hydrocarbon operations.
  • the present techniques may be utilized for evaluating drilling a new well.
  • the reservoir models and production data are obtained, as shown in blocks 202 and 204 of Figure 2, and used in the analysis for a determined hydrocarbon operation, such as drilling a new well, as shown in block 206.
  • the production data may be accumulated from an initial time To until time T (or Tdriii) that involves a decision to place a new well or to not place a new well.
  • the workflow to support the drill a new well decision may include various steps.
  • the reservoir models may be a suite of reservoir models used during the development phase as part of a scenario generation or scenario discovery process. It may be useful that the reservoir models span all plausible geological scenarios consistent with the development-phase data.
  • each reservoir model may be performed.
  • a first reservoir model is simulated with existing wells and facilities through a target time Tmax, but without the new well being reviewed.
  • the first reservoir model is simulated through target time Tmax with the new well inserted at decision time Tdriii. Similar simulations are also performed for the second reservoir model, and any other reservoir models being utilized in the evaluation.
  • the desirability of the decision to drill the new well is based on the production differences or comparisons between simulations with the new well and simulations without the new well for the respective models.
  • the production differences may be a production metric, such as differences in oil produced for a time in the range between Tdriii ⁇ t ⁇ Tmax (where t is time for the respective time step), an absolute production metric, or water breakthrough time or other facilities-related metric.
  • each reservoir model is tagged with a parameter related to the difference observed between simulations with the new well and simulations without the new well.
  • the feature space is determined and the simulation results are transformed into the feature space, based on the simulated production data for a time in the range between 0 ⁇ t ⁇ Tdriii, as shown in blocks 212 and 214.
  • the feature space accounts for production data prior to the time of the insertion (or non-insertion) of the well at change time Tdriii.
  • This feature space is one whose axes are a summary of all of the information in the various time series of production information; numerous technologies such as multidimensional scaling or principal component analysis exist to project the information embedded in the time series into a tractable and relatively low dimensional feature space.
  • machine learning classification and regression techniques are utilized to determine the optimal solution, as shown in blocks 216 to 220.
  • the identification of the point, points, or region in the feature space corresponds to the“truth case” of the actual production data time series over the range 0 ⁇ t ⁇ Tdriii.
  • the intrinsic variability of the decision metric within the“truth case” may be inferred or determined, and the extrinsic variability of the decision metric within the enseumble of models may be inferred or determined.
  • the intrinsic and extrinsic variabilities may be compared, and the comparison may be used to choose the standard machine learning classification or regression techniques (e.g.
  • k-means clustering support vector models, kriging
  • E > I this may be determined by regression of the value of the metric at the truth case point from neighboring simulation results from the respective reservoir models which have been simulated.
  • an estimate of a probability distribution function of the metric value for the truth case may also be utilized.
  • Another approach may be to use classification algorithms known in the statistical learning or machine learning art to determine if the point, points, or region corresponding to the truth case clusters or classifies with those reservoir models for which with the decision to add the well was successful or unsuccessful based on pre-determined economic and/or physical criteria. For example, where I > E or where I ⁇ E, it may be desirable to perform clustering within the data space, and then use the cluster that contains the truth space to average the values of the decision metric.
  • the method does not change or condition any reservoir model, nor does it identify any particular reservoir model as corresponding to the truth case.
  • the prediction of behavior at the truth case point is determined by the behaviors of neighboring reservoir models, following a statistical method to average over the behaviors to find a robust regression in that particular feature space.
  • the behavior for the time period in the range of 0 ⁇ t ⁇ Tdriii of the production data for any reservoir model may be used as a synthetic truth case, which provides a mechanism to test the robustness of the workflow, and tune both the feature determination and regression and/or classification algorithms prior to identification of the predicted behavior for the actual truth case.
  • Figure 3 The approach is summarized in Figure 3 below.
  • Figure 3A is an exemplary diagram 300 of a feature space determined by production data.
  • the data points such as data points 306, 308, 310 and 312 are represented along a first axis 302 of three phase flow rate and a second axis 304 of three phase flow rate.
  • Each reservoir model, as well as the truth case, corresponds to a point in the feature space determined by production data for time t ⁇ Tdriii.
  • the circle points, such as points 306, represent simulation results that provide acceptable performance with respect to some decision metric corresponding to a hydrocarbon operation
  • the triangle points, such as points 308, represent simulation results that provide unacceptable performance with respect to the same decision metric
  • the square points, such as points 310 represent simulation results that provide marginal performance
  • the diamond point 312 represents the actual flow rates.
  • the reservoir models are characterized by the performance of the well added at a decision time Tdriii, evaluated for times in the range between Tdriii ⁇ t ⁇ Tmax. The analysis estimates that the truth case exhibits acceptable performance, notwithstanding the fact that the apparently closest reservoir model in the feature space exhibits unacceptable performance.
  • the method and system may involve a modeling a hydrocarbon operation.
  • a first data set may include pre-production data, which is used to create the ensemble of reservoir models.
  • a second data set may include production history data for time less than the performance of the hydrocarbon operation.
  • the metric may be the total production for the time period after the hydrocarbon operation being performed compared to that without the hydrocarbon operation having been performed.
  • the first data set may include seismic data
  • the second data set may include appraisal well logs, which may be associated with various wells.
  • the metric may be the expected ultimate recovery from a reservoir (EUR). Implicitly, the hydrocarbon operation in this case is the decision to develop the field, possibly in more than one manner, or with more than one set of facility choices; versus the decision not to develop the field.
  • Figure 3B is an exemplary diagram 320, that shows the permeability K x of a sample realization of the subsurface region, which contains various wellbores that are configured to operate as producers or injectors.
  • This sample realization is a part of an ensemble of two hundred eighty-five reservoir models, which are generated by conditioning the reservoir models to pre-production data.
  • the ensemble of realizations represents uncertainty in the earth parameters, such as the porosity, the proximal/distal/medial grain size, the net-to-gross ratio (NTG) and the stacking pattern.
  • Figure 3E is an exemplary diagram 346 of the ensemble of the 285 models, which represent different clusters associated with different scenarios.
  • the x-axis indicate observed historical data (dii) while the y-axis indicate quantity of interest (Qol).
  • the subsurface region is assumed to contain ten producer wells and three injector wells.
  • the metric for hydrocarbon operation which is denoted by . corresponds to an infill drilling decision (e.g., a categorical variable (e.g., 0 or 1)).
  • this infill well e.g., if drilled
  • this infill well may be brought online (e.g., start producing hydrocarbons) at a time six years from the beginning of the time steps. All the wells are assumed to be bottom hole pressure-controlled.
  • Figure 3B shows the location of the six (e.g., out of thirteen) wells 322, 323, 324, 325 and the infill well 326 in the hydrocarbon system.
  • Figure 3C is an exemplary diagram 330, which shows the oil production rate for well 325 in Figure 3B in the units of barrels per day (bbl/d).
  • the oil production rate during the history corresponds to the time period from the beginning of the hydrocarbon production to six years, which is shown as the history from zero years to six years (noted by the vertical dashed line), which is also plotted separately in exemplary diagram 340 of Figure 3D.
  • the oil production forecast corresponds to the time period from six years to twenty seven years, which is shown as the oil production rate from six years to twenty-seven years.
  • the oil production rate from different realizations in the ensemble are indicated by curves and the oil production rate for the specific realization shown in Figure 3B is highlighted by the darker curve.
  • the unit of the oil production rate in axis 332 and 342 is bbl/d, while the unit of time in axis 334 and 344 is years.
  • a comparison of the existing history-matching-based approach with the approach in the present disclosure may be performed.
  • d £/ denotes the data vector of the observables, such as the rates (q) and the bottom-hole pressure (BHP) at time tj
  • dH denotes the observables during the history
  • dF denotes the observables during the forecasting period
  • g(m) denotes the forward simulator.
  • the vector of observables may be predicted (including the flow rates) and the associated uncertainty during the forecast time window.
  • the forecasted rates (and the associated uncertainty) may then be used to compute the metric Z as shown in equation (e2) below:
  • the mapping J is based on the fact that geological models with similar well connectivity have similar time series, and hence, similar metric (Z). [0093] To construct the mapping, J, a four step procedure may be used. In the first step, the reservoir simulation is performed for all 285 realizations in the ensemble. While performing the reservoir simulation, it is assumed that the infill well was drilled and comes online at six years. Second, the entire reservoir simulation is performed again for all 285 realizations in the ensemble. However, this time, it is assumed that infill drilling was not performed. As a result, for each realization in the ensemble, incremental hydrocarbon production may be computed (e.g., due to infill drilling) and the associated economic impact.
  • the reservoir simulations may be performed by one or more reservoir simulator, as is known in the art.
  • e FDA is noise and Fi, represents the basis, such as cubic B-spline basis.
  • FIG. 3F The results from functional PCA technique are shown in exemplary diagram 350 in Figure 3F, diagram 352 in Figure 3G and diagram 354 in Figure 3H, where the x-axis show the time in years, while the y-axis show the oil production rate during the history (with shutin removed) in bbl/d.
  • Figure 3G shows the oil production rate for well 325 of Figure 3B.
  • Figure 3G shows the reconstructed oil production rate for well 325 in Figure 3B after represententing dH (for each realization in the ensemble) using the approximation shown in equation (e5).
  • Figure 3H shows the reconstructed oil rate (for well 325 in Figure 3B) after representing dH (for each realization in the ensemble) using functional PCA approximations shown in equation (e6).
  • the above dataset is used to learn the mapping J.
  • the technique may be used in this example to leam the form of the mapping J is random forest. See, e.g., Breiman, L. (2001),“Random forests”, Machine learning, 45(1), 5-32. This reference provides more details on random forest.
  • Random forest is a (e.g., non-parameteric) decision-tree-based supervised learning technique. It involves segmenting the feature-space into multiple homogenous regions. The segmentation is determined by minimizing the following equation (e7) in a top-down greedy approach:
  • Z n denote average value of metric Z in a given region, such as R1 or R2 or R3.
  • the recursive segmentation provides a mechanism to capture the nonlinear interactions between the features.
  • the segmentation concept is shown in Figure 31 that includes the exemplary diagram 360.
  • Figure 31 shows different realizations (of the ensemble) in two-dimensional representation of yH.
  • the realizations represent drill or do not drill decisions.
  • the darker points denote the realizations for which the metric Z suggests to drill the infill well, while the lighter points denote the realizations for which the metric Z suggests not to drill the infill well.
  • the domain (of yH) is divided into regions Rl, R2 and R3 as indicated by the lines dividing the points.
  • the random-forest-based binary classifier (J) for the metric Z e.g., drill or do not drill
  • the dataset for the previously constructed e.g., tuple ⁇ yH, Z ⁇ i
  • the original dataset is split into two (unequal) parts. The first part is referred to as the training set, while the second part is referred to as the test set.
  • the training set (shown in equation e8 below) contains 255 randomly selected realizations from the ensemble.
  • the training set is used to construct the random-forest-based binary classifier J.
  • Figure 3J is an exemplary diagram 370, which shows the oil production rate for well 325 of Figure 3B for all the realizations in the training set.
  • the oil production rate (on the y-axis) is shown in bbl/d and the time (on x-axis) is shown in years.
  • Figure 3K is an exemplary diagram 372, which shows a histogram of the metric Z for all the realizations in the training set.
  • the y-axis denotes the frequency of the metric Z (0 on the x-axis denotes the decision to not drill the infill well, and 1 denotes the decision to drill the infill well).
  • test set shown in equation e9 below.
  • Figure 3L is an exemplary diagram 374, shows the oil production rate for well 325 of Figure 3B for all the realizations in the test set.
  • the oil production rate (on the y- axis) is shown in bbl/d, and time (on the x-axis) is shown in years.
  • Figure 3M is an exemplary diagram 376, which shows the histogram of the metric Z for all the realizations in the test set.
  • the y-axis denotes the frequency of the metric Z (e.g., 0 on the x-axis denotes the decision to not drill the infill well, and 1 denotes the decision to drill the infill well).
  • the binary classifier J by construction, has no information about the feature-space yH or the metric Z for the realizations in the test set.
  • the test set acts as a blind test to validate the prediction quality of the random-forest-based binary classifier J.
  • the value of the metric Z, predicted by Jon the test set, is denoted by Z * p red. .
  • the prediction quality of J is measured by comparing Z * p red. with the actual metric Z as shown by the confusion matrix in Table 1 below:
  • the metric Z can be a categorical variable (with multiple classes) or a real-valued variable such as EUR or NPV.
  • different machine learning algorithms for classification such as the neural networks, support vector machines) or regression techniques (such as neural networks or Gaussian Process) can be used.
  • a Bayesian calibration approach in the data-space dH or a low dimensional representation of the data-space yH can be used.
  • Such a Bayesian calibration approach may involve expressing the binary/multiclass classifier or regression function (in case the metric Z is a real-valued variable) as shown in equation (elO) below:
  • J is the mapping from the data-space to the Qol-space
  • x denotes calibration inputs to the mapping J
  • d is the bias/model-form error
  • e denotes the residual uncertainty.
  • the form of the mapping / and d can be defined using machine-leaming-based algorithms.
  • the largest dimensionality space, th emodel space may include values of 10 7 to 10 10 different geological paramters, such as permeability in a reservoir model cell, or the transmissibility of a particular fault.
  • the data space (from the first data set, data set A), by contrast, may only inlcude 10 5 to 10 6 parameters.
  • the dimension of the model space is expected to be subtantially greater than the dimension of the data space.
  • each manifold in the model space of models consistent with a particular data set B will have its onw value of M.
  • the variation of the decision metric, M, over the manifold of the model space i.e., the intrinsic variability
  • M the variation of the decision metric
  • the intrinsic variability is a variability that cannot be resolved from the data set B. If the intrinsic variability is large, then its existence casts into question the validity of any attempt to infer M, and thus the ability to make a correct decision from the ensemble of models.
  • the intrinsic variability can be contrasted with the extrinsic variability, that is the variability of M corresponding to the full range of dataset B values as seen in Figure 5.
  • the intrinsic variability captures that portion of the variability in the decision metric, M, as a function of the second data set, data set B, that is irreducible, and arises from the high dimensionality of the model space.
  • the extrinsic variability corresponds to the variability in M that is observable across values of dataset B.
  • Intrinsic variability may be difficult ot measure, as it may require a large number of samples (generated using unbiased sample) such that each sample has an identical (or almost- identical) data vector but different reservoir model parameters. Thus, as it is difficult to generate samples that are located at identical, or extremely close, locations in the data space, it may be difficult to directly determine the intrinsic variability.
  • Most machine learning methods can provide an estimate and a variability at each location at which regression is conducted; however, variability for an inference method inlcudes all statistical sources of variability arising from the intrinsic inaccuracy of the regression method. Thus, such statistical variances will, at best, be upper bounds on the intrinsic variability.
  • An alternate method is to use a variogram of the metrics M, i.e., the low-dimensional representation of observables in the mistory match period and the output.
  • M the low-dimensional representation of observables in the mistory match period
  • insight can be obtained into the extent to which such variations decline with distance, which can give an estimate of the intrinsic variability, provided that the intrinsic variability is significantly less than the extrinsic variability.
  • This approach is based only on the results from simulating the ensemble of reservoir models, and is thus independent of the statistical method used to build inferences for a particular element of a test set.
  • clustering approaches may be used.
  • the method would be to characterize clusters within the space spanned by the low-dimensonal representation of the data vector, and ascribe the best decision based on the majority result within that cluster.
  • An example of such clusters are shown in Figure 7. This involves clustering (or classifying) the ensemble of realizations based on the low-dimensional representation of the data vector in the history match period.
  • the number of clusters can be identified using techniques such as elbow method or silhouette score.
  • Embodiments of the present techniques also relate to an apparatus for performing the operations herein.
  • This apparatus may be specially constructed for the required purposes, or it may comprise a general-purpose computer selectively activated or reconfigured by a computer program stored in the computer (e.g., one or more sets of instructions).
  • a computer program may be stored in a computer readable medium.
  • a computer-readable medium includes any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computer).
  • a computer-readable (e.g., machine-readable) medium includes a machine (e.g., a computer) readable storage medium (e.g., read only memory (“ROM”), random access memory (“RAM”), magnetic disk storage media, optical storage media, flash memory devices, etc.), and a machine (e.g., computer) readable transmission medium (electrical, optical, acoustical or other form of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.)).
  • ROM read only memory
  • RAM random access memory
  • magnetic disk storage media e.g., magnetic disks, optical storage media, flash memory devices, etc.
  • a machine (e.g., computer) readable transmission medium electrical, optical, acoustical or other form of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.)
  • modules, features, attributes, methodologies, and other aspects of the invention can be implemented as software, hardware, firmware or any combination of the three.
  • a component of the present invention is implemented as software, the component can be implemented as a standalone program, as part of a larger program, as a plurality of separate programs, as a statically or dynamically linked library, as a kernel loadable module, as a device driver, and/or in every and any other way known now or in the future to those of skill in the art of computer programming.
  • the present invention is in no way limited to implementation in any specific operating system or environment.
  • FIG. 4 is a block diagram of a computer system 400 that may be used to perform any of the methods disclosed herein.
  • a central processing unit (CPU) 402 is coupled to system bus 404.
  • the CPU 402 may be any general-purpose CPU, although other types of architectures of CPU 402 (or other components of exemplary system 400) may be used as long as CPU 402 (and other components of system 400) supports the inventive operations as described herein.
  • the CPU 402 may execute the various logical instructions according to disclosed aspects and methodologies.
  • the CPU 402 may execute machine-level instructions for performing processing according to aspects and methodologies disclosed herein.
  • a computer system 400 may also include a graphical processing unit(s) (GPU(s)) 414.
  • GPU(s) graphical processing unit
  • the computer system 400 may also include computer components such as a random access memory (RAM) 406, which may be SRAM, DRAM, SDRAM, or the like.
  • the computer system 400 may also include read-only memory (ROM) 308, which may be PROM, EPROM, EEPROM, or the like.
  • RAM 406 and ROM 408 hold user and system data and programs, as is known in the art.
  • the computer system 400 may also include an input/output (I/O) adapter 410, a communications adapter 422, a user interface adapter 424, and a display adapter 418.
  • the I/O adapter 410, the user interface adapter 424, and/or communications adapter 422 may, in certain aspects and techniques, enable a user to interact with computer system 400 to input information.
  • the I/O adapter 410 preferably connects a storage device(s) 412, such as one or more of hard drive, compact disc (CD) drive, floppy disk drive, tape drive, etc. to computer system 400.
  • the storage device(s) may be used when RAM 406 is insufficient for the memory requirements associated with storing data for operations of embodiments of the present techniques.
  • the data storage of the computer system 400 may be used for storing information and/or other data used or generated as disclosed herein.
  • the communications adapter 422 may couple the computer system 400 to a network (not shown), which may enable information to be input to and/or output from system 400 via the network (for example, a wide-area network, a local-area network, a wireless network, any combination of the foregoing).
  • User interface adapter 424 couples user input devices, such as a keyboard 428, a pointing device 426, and the like, to computer system 400.
  • the display adapter 418 is driven by the CPU 402 to control, through a display driver 416, the display on a display device 420.
  • system 400 may be varied as desired.
  • any suitable processor-based device may be used, including without limitation personal computers, laptop computers, computer workstations, and multi-processor servers.
  • embodiments may be implemented on application specific integrated circuits (ASICs) or very large scale integrated (VLSI) circuits.
  • ASICs application specific integrated circuits
  • VLSI very large scale integrated circuits
  • the method may be implemented in machine-readable logic, such as a set of instructions or code that, when executed, performs the instructions or operations from memory.
  • the computer system includes a processor; an input device and memory.
  • the input device is in communication with the processor and is configured to receive input data associated with a subsurface region.
  • the memory is in communication with the processor and the memory has a set of instructions, wherein the set of instructions, when executed, are configured to: obtain a first data set associated with a subsurface region, wherein the two or more reservoir models are based on a first data set; create two or more reservoir models for a subsurface region from the first data set; obtain a second data set associated with a subsurface region and the two or more reservoir models; obtain production data associated with a subsurface region; dispose the production data and at least a portion of the second data set into a feature space; determine a region of interest within the feature space; evaluate the region of interest or a business-relevant metric in the feature space; and determine whether to perform a hydrocarbon operation based on the evaluation of the region of interest or of the business-relevant metric.
  • the system may include various enhancements.
  • the system may include the set of instructions, when executed by the processor, configured to: perform one or more regression techniques to evaluate the region of interest; wherein the first data set may comprise one of seismic data, well test data, well log data, production data, and any combination thereof; wherein the second data set may comprise one of generated or observed seismic data, generated or observed well log data, generated or observed well test data, generated or observed production data and any combination thereof; may simulate each of the two or more reservoir models with the hydrocarbon operation being performed to create first simulation results, may simulate each of the two or more reservoir models with the hydrocarbon operation not being performed to create second simulation results, wherein the second data set may comprise the first simulation results and the second simulation results; transform the second data set to alter dimensionality of the second data set, or portion of the second data set, prior to disposing the second data set, or a portion of the second data set, into the feature space; wherein the hydrocarbon operation may comprise adding a new well to access the subsurface region.
  • the second data set may contain production data (for instance in the hydrocarbon production applications), it does not need to contain production data.
  • the second data set e.g., data set B
  • the second data set may be limited to well log and well test data from appraisal wells, because in this example there is no production data.
  • certain examples may involve using production data in the first data set (e.g., data set A), such as production data up to a certain time that is used to condition the initial ensemble of reservoir models, for example.

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Abstract

L'invention concerne un procédé et un système pour évaluer la variabilité intrinsèque et extrinsèque d'une métrique de décision dans un ensemble de modèles de subsurface pour aider à prendre une décision d'exploitation d'hydrocarbures.
PCT/US2019/067764 2018-12-31 2019-12-20 Procédé et système d'évaluation de variabilité dans des modèles de subsurface pour supporter la prise de décisions dans des exploitations d'hydrocarbures WO2020142257A1 (fr)

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