SUBSURFACE KNOWLEDGE ENHANCEMENT USING DATA SCIENCE-CONSTRAINED INVERSE MODELLING

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to and the benefit of U.S. Provisional Patent Application No. 63/645,484, filed on May 10, 2024, which is incorporated by reference in its entirety.

BACKGROUND

Measurements of the subsurface (e.g., well logs, seismic, and core samples) may be inherently incomplete and uncertain. This is due to both limitations of the scope of data collection and the interpretive nature of the processing. As such, computer models of subsurface assets may contain errors. More particularly, the subsurface models are 3-dimensional in nature, containing estimations of porosity, permeability, surface tension with respect to fluids, etc. that vary with space.

The desired task is to infer more accurate 3D properties based on the flowing behaviors of one or more wells, using their measurements over time such as pressure and flow rates. This may be challenging for several reasons. For example, it may be challenging because calculating mismatches between the current model and the measurements involves physics simulations which are expensive in time and computing power. In addition, the problem is “ill-posed” (i.e., it contains many more changeable variables than available measurements). For example, the measured data is from existing wells and is spatially sparse. Moreover, solutions are non-unique, so variable combinations may fit the well data and still contain errors. Furthermore, changes to variables may not be consistent with prior geological understanding.

One approach to upgrade model accuracy is to use the flowing data from any available wells such as pressure and volumetric flow rates. Measurements from the field are compared to physics simulations with the model's parameters. The model's properties are then iteratively adjusted to minimize the difference between the physics simulations and field measurements. However, this process is challenging to complete. Firstly, there are many more possible adjustments than well measurements (i.e., data is sparse). Secondly, even though solutions are non-unique, the high complexity of the science (e.g., physics) makes it difficult to manually adjust the parameters to find any solution. Finally, manual adjustments made may be improbable given prior geological knowledge.

As these models are used to make capital expenditure and operational decisions (e.g., in the fields of petroleum, gas storage, geothermal, hydrogeology, and carbon sequestration), there is a need for an improved system and method for modelling a subsurface formation.

SUMMARY

A method for updating a model of a subsurface formation is disclosed. The method includes receiving input data for a subsurface formation. The method also includes creating an algorithm based upon the input data. The method also includes determining a plurality of 3D subsurface properties that are possible using the algorithm. The method also includes predicting one or more flowing characteristics of the subsurface formation based upon the 3D subsurface properties. The method also includes training a machine-learning (ML) model using the one or more predicted flowing characteristics.

A computing system is also disclosed. The computing system includes one or more processors and a memory system. The memory system includes one or more non-transitory computer-readable media storing instructions that, when executed by at least one of the one or more processors, cause the computing system to perform operations. The operations include receiving input data for a subsurface formation. The input data includes geological features, seismic data, seismic attributes, well logs, structural geometry, rock and fluid physics data, and/or initial conditions. The operations also include creating a probabilistic random forest based upon the input data. The operations also include determining a plurality of 3D subsurface properties that are possible using the probabilistic random forest. The 3D subsurface properties include porosity, permeability, and/or initial water saturation. The 3D subsurface properties are a function of one or more intervention variables. The one or more intervention variables are selected to intervene to modify a sampling from the probabilistic random forest. The operations also include predicting one or more flowing characteristics of the subsurface formation based upon the 3D subsurface properties. The one or more predicted flowing characteristics include pressure and/or flow rates at one or more wells. The operations also include training a machine-learning (ML) model using the one or more predicted flowing characteristics. The operations also include receiving one or more measured flowing characteristics. The one or more measured flowing characteristics include measured pressure and measured flow rates at the one or more wells. The operations also include adjusting the one or more intervention variables using the trained ML model to provide updated 3D subsurface properties. Adjusting the one or more intervention variables adjusts how the probabilistic random forest is sampled.

A non-transitory computer-readable medium is also disclosed. The medium stores instructions that, when executed by one or more processors of a computing system, cause the computing system to perform operations. The operations include receiving input data for a subsurface formation. The input data includes geological features, seismic data, seismic attributes, well logs, structural geometry, rock and fluid physics data, and/or initial conditions. The operations also include creating a probabilistic random forest based upon the input data. The operations also include determining a plurality of 3D subsurface properties that are possible using the probabilistic random forest. The 3D subsurface properties include porosity, permeability, and/or initial water saturation. The 3D subsurface properties are a function of one or more intervention variables. The one or more intervention variables include external variables and/or secondary input data that are selected to intervene to modify a sampling from the probabilistic random forest. The external variables are not used to train the probabilistic random forest. The secondary input data are used to train the probabilistic random forest. The operations also include predicting one or more flowing characteristics of the subsurface formation based upon the 3D subsurface properties. The one or more flowing characteristics are predicted using a physics simulator. The one or more predicted flowing characteristics include pressure and/or flow rates at one or more wells. The operations also include training a machine-learning (ML) model using the one or more predicted flowing characteristics. The trained ML model functions as a surrogate model for the physics simulator. The trained ML model includes a physics-informed neural operator, a Fourier neural operator, or any other model capable of functioning as the surrogate model. The operations also include receiving one or more measured flowing characteristics. The one or more measured flowing characteristics include measured pressure and measured flow rates at the one or more wells. The operations also include adjusting the one or more intervention variables using the trained ML model to provide updated 3D subsurface properties. Adjusting the one or more intervention variables adjusts how the probabilistic random forest is sampled. The one or more intervention variables are selected by an optimizer to minimize a mismatch between the one or more predicted flowing characteristics versus the one or more measured flowing characteristics.

It will be appreciated that this summary is intended merely to introduce some aspects of the present methods, systems, and media, which are more fully described and/or claimed below. Accordingly, this summary is not intended to be limiting.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the present teachings and together with the description, serve to explain the principles of the present teachings. In the figures:

FIG. 1 illustrates an example of a system that includes various management components to manage various aspects of a geologic environment, according to an embodiment.

FIG. 2 illustrates a flowchart of the method for generating (or updating) a model of a subsurface formation, according to an embodiment.

FIG. 3 illustrates a schematic view of the method in FIG. 2, according to an embodiment.

FIG. 4 illustrates a schematic view of another method for generating (or updating) a model of the subsurface formation, according to an embodiment.

FIGS. 5A and 5B illustrate results of applying method to a synthetic reservoir for updating the porosity field to match the cumulative oil and water production to historical data, according to an embodiment.

FIG. 6 illustrates a schematic view of a computing system for performing at least a portion of the method(s) described herein, according to an embodiment.

DETAILED DESCRIPTION

Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings and figures. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to one of ordinary skill in the art that the invention may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments.

It will also be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first object or step could be termed a second object or step, and, similarly, a second object or step could be termed a first object or step, without departing from the scope of the present disclosure. The first object or step, and the second object or step, are both, objects or steps, respectively, but they are not to be considered the same object or step.

The terminology used in the description herein is for the purpose of describing particular embodiments and is not intended to be limiting. As used in this description and the appended claims, the singular forms “a,” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and/or” as used herein refers to and encompasses any possible combinations of one or more of the associated listed items. It will be further understood that the terms “includes,” “including,” “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Further, as used herein, the term “if” may be construed to mean “when” or “upon” or “in response to determining” or “in response to detecting,” depending on the context.

Attention is now directed to processing procedures, methods, techniques, and workflows that are in accordance with some embodiments. Some operations in the processing procedures, methods, techniques, and workflows disclosed herein may be combined and/or the order of some operations may be changed.

System Overview

FIG. 1 illustrates an example of a system 100 that includes various management components 110 to manage various aspects of a geologic environment 150 (e.g., an environment that includes a sedimentary basin, a reservoir 151, one or more faults 153-1, one or more geobodies 153-2, etc.). For example, the management components 110 may allow for direct or indirect management of sensing, drilling, injecting, extracting, etc., with respect to the geologic environment 150. In turn, further information about the geologic environment 150 may become available as feedback 160 (e.g., optionally as input to one or more of the management components 110).

In the example of FIG. 1, the management components 110 include a seismic data component 112, an additional information component 114 (e.g., well/logging data), a processing component 116, a simulation component 120, an attribute component 130, an analysis/visualization component 142 and a workflow component 144. In operation, seismic data and other information provided per the components 112 and 114 may be input to the simulation component 120.

In an example embodiment, the simulation component 120 may rely on entities 122. Entities 122 may include earth entities or geological objects such as wells, surfaces, bodies, reservoirs, etc. In the system 100, the entities 122 can include virtual representations of actual physical entities that are reconstructed for purposes of simulation. The entities 122 may include entities based on data acquired via sensing, observation, etc. (e.g., the seismic data 112 and other information 114). An entity may be characterized by one or more properties (e.g., a geometrical pillar grid entity of an earth model may be characterized by a porosity property). Such properties may represent one or more measurements (e.g., acquired data), calculations, etc.

In an example embodiment, the simulation component 120 may operate in conjunction with a software framework such as an object-based framework. In such a framework, entities may include entities based on pre-defined classes to facilitate modeling and simulation. A commercially available example of an object-based framework is the MICROSOFT® NET® framework (Redmond, Washington), which provides a set of extensible object classes. In the .NET® framework, an object class encapsulates a module of reusable code and associated data structures. Object classes can be used to instantiate object instances for use in by a program, script, etc. For example, borehole classes may define objects for representing boreholes based on well data.

In the example of FIG. 1, the simulation component 120 may process information to conform to one or more attributes specified by the attribute component 130, which may include a library of attributes. Such processing may occur prior to input to the simulation component 120 (e.g., consider the processing component 116). As an example, the simulation component 120 may perform operations on input information based on one or more attributes specified by the attribute component 130. In an example embodiment, the simulation component 120 may construct one or more models of the geologic environment 150, which may be relied on to simulate behavior of the geologic environment 150 (e.g., responsive to one or more acts, whether natural or artificial). In the example of FIG. 1, the analysis/visualization component 142 may allow for interaction with a model or model-based results (e.g., simulation results, etc.). As an example, output from the simulation component 120 may be input to one or more other workflows, as indicated by a workflow component 144.

As an example, the simulation component 120 may include one or more features of a simulator such as the ECLIPSE™ reservoir simulator (SLB, Houston Texas), the INTERSECT™ reservoir simulator (SLB, Houston Texas), etc. As an example, a simulation component, a simulator, etc. may include features to implement one or more meshless techniques (e.g., to solve one or more equations, etc.). As an example, a reservoir or reservoirs may be simulated with respect to one or more enhanced recovery techniques (e.g., consider a thermal process such as SAGD, etc.).

As an example, the simulation component 120 may include one or more features of a simulator such as SYMMETRY software (SLB, Houston, Texas). More particularly, SYMMETRY may process workflows in a single integrated environment with accurate thermodynamic fluid representation and consistent modeling across multiple disciplines including process, production, and HSE. The simulator integrates steady-state and transient (e.g., dynamic) analyses that can be tailored for each domain. This approach enables users to optimize processes in upstream, midstream, and downstream sectors while maximizing profits and minimizing capital expenditures. It may also help reduce emissions, energy consumption, and waste.

As an example, the simulation component 120 may include one or more features of a simulator such as PIPESIM (SLB, Houston, Texas). More particularly, PIPESIM is steady-state multiphase flow simulator that incorporates the three areas of flow modeling: multiphase flow, heat transfer and fluid behavior.

As an example, the simulation component 120 may include one or more features of a simulator such as OLGA™ (SLB, Houston, Texas). More particularly, OLGA™ is a dynamic multiphase flow simulator that models transient flow (e.g., time-dependent behaviors) to maximize production potential. Transient modeling is a component for feasibility studies and field development design. Dynamic simulation is useful in deep water and is used in both offshore and onshore developments to investigate transient behavior in pipelines and wellbores. Transient simulation with the OLGA™ simulator provides an added dimension to steady-state analysis by predicting system dynamics, such as time-varying changes in flow rates, fluid compositions, temperature, solids deposition, and operational changes.

In an example embodiment, the management components 110 may include features of a commercially available framework such as the PETREL® seismic to simulation software framework (SLB, Houston, Texas). The PETREL® framework provides components that allow for optimization of exploration and development operations. The PETREL® framework includes seismic to simulation software components that can output information for use in increasing reservoir performance, for example, by improving asset team productivity. Through use of such a framework, various professionals (e.g., geophysicists, geologists, and reservoir engineers) can develop collaborative workflows and integrate operations to streamline processes. Such a framework may be considered an application and may be considered a data-driven application (e.g., where data is input for purposes of modeling, simulating, etc.).

In an example embodiment, various aspects of the management components 110 may include add-ons or plug-ins that operate according to specifications of a framework environment. For example, a commercially available framework environment marketed as the OCEAN® framework environment (SLB, Houston, Texas) allows for integration of add-ons (or plug-ins) into a PETREL® framework workflow. The OCEAN® framework environment leverages .NET® tools (Microsoft Corporation, Redmond, Washington) and offers stable, user-friendly interfaces for efficient development. In an example embodiment, various components may be implemented as add-ons (or plug-ins) that conform to and operate according to specifications of a framework environment (e.g., according to application programming interface (API) specifications, etc.).

FIG. 1 also shows an example of a framework 170 that includes a model simulation layer 180 along with a framework services layer 190, a framework core layer 195 and a modules layer 175. The framework 170 may include the commercially available OCEAN® framework where the model simulation layer 180 is the commercially available PETREL® model-centric software package that hosts OCEAN® framework applications. In an example embodiment, the PETREL® software may be considered a data-driven application. The PETREL® software can include a framework for model building and visualization.

As an example, a framework may include features for implementing one or more mesh generation techniques. For example, a framework may include an input component for receipt of information from interpretation of seismic data, one or more attributes based at least in part on seismic data, log data, image data, etc. Such a framework may include a mesh generation component that processes input information, optionally in conjunction with other information, to generate a mesh.

In the example of FIG. 1, the model simulation layer 180 may provide domain objects 182, act as a data source 184, provide for rendering 186 and provide for various user interfaces 188. Rendering 186 may provide a graphical environment in which applications can display their data while the user interfaces 188 may provide a common look and feel for application user interface components.

As an example, the domain objects 182 can include entity objects, property objects and optionally other objects. Entity objects may be used to geometrically represent wells, surfaces, bodies, reservoirs, etc., while property objects may be used to provide property values as well as data versions and display parameters. For example, an entity object may represent a well where a property object provides log information as well as version information and display information (e.g., to display the well as part of a model).

In the example of FIG. 1, data may be stored in one or more data sources (or data stores, generally physical data storage devices), which may be at the same or different physical sites and accessible via one or more networks. The model simulation layer 180 may be configured to model projects. As such, a particular project may be stored where stored project information may include inputs, models, results and cases. Thus, upon completion of a modeling session, a user may store a project. At a later time, the project can be accessed and restored using the model simulation layer 180, which can recreate instances of the relevant domain objects.

In the example of FIG. 1, the geologic environment 150 may include layers (e.g., stratification) that include a reservoir 151 and one or more other features such as the fault 153-1, the geobody 153-2, etc. As an example, the geologic environment 150 may be outfitted with any of a variety of sensors, detectors, actuators, etc. For example, equipment 152 may include communication circuitry to receive and to transmit information with respect to one or more networks 155. Such information may include information associated with downhole equipment 154, which may be equipment to acquire information, to assist with resource recovery, etc. Other equipment 156 may be located remote from a well site and include sensing, detecting, emitting or other circuitry. Such equipment may include storage and communication circuitry to store and to communicate data, instructions, etc. As an example, one or more satellites may be provided for purposes of communications, data acquisition, etc. For example, FIG. 1 shows a satellite in communication with the network 155 that may be configured for communications, noting that the satellite may additionally or instead include circuitry for imagery (e.g., spatial, spectral, temporal, radiometric, etc.).

FIG. 1 also shows the geologic environment 150 as optionally including equipment 157 and 158 associated with a well that includes a substantially horizontal portion that may intersect with one or more fractures 159. For example, consider a well in a shale formation that may include natural fractures, artificial fractures (e.g., hydraulic fractures) or a combination of natural and artificial fractures. As an example, a well may be drilled for a reservoir that is laterally extensive. In such an example, lateral variations in properties, stresses, etc. may exist where an assessment of such variations may assist with planning, operations, etc. to develop a laterally extensive reservoir (e.g., via fracturing, injecting, extracting, etc.). As an example, the equipment 157 and/or 158 may include components, a system, systems, etc. for fracturing, seismic sensing, analysis of seismic data, assessment of one or more fractures, etc.

As mentioned, the system 100 may be used to perform one or more workflows. A workflow may be a process that includes a number of worksteps. A workstep may operate on data, for example, to create new data, to update existing data, etc. As an example, a may operate on one or more inputs and create one or more results, for example, based on one or more algorithms. As an example, a system may include a workflow editor for creation, editing, executing, etc. of a workflow. In such an example, the workflow editor may provide for selection of one or more pre-defined worksteps, one or more customized worksteps, etc. As an example, a workflow may be a workflow implementable in the PETREL® software, for example, that operates on seismic data, seismic attribute(s), etc. As an example, a workflow may be a process implementable in the OCEAN® framework. As an example, a workflow may include one or more worksteps that access a module such as a plug-in (e.g., external executable code, etc.).

Subsurface Knowledge Enhancement Using Data Science-Constrained Inverse Modelling

The present disclosure includes a system and method that can rapidly improve subsurface models and constrain solutions within a probabilistic geological framework. More particularly, the system and method may rapidly find multiple subsurface property distributions which match flowing well data and are geologically consistent. This may enable more profitable capital expenditures and efficient operations.

The 3D model may not be a single realization of spatial properties, but instead is a probabilistic framework. Any point in space can take on a range of property values with probabilities defined by a trained random forest. In particular, a computer program such as EMBER (Embedded Model Estimator) may be used to construct this forest. The computer program may use multiple secondary variables by combining geostatistics with random forests for three-dimensional reservoir property modeling.

The random forest, an ensemble of random trees, may be trained using the given sample data including various secondary variables such as seismic attributes, geometrical data, as well as two embedded variables generated, for example, from the cross-validated short and long-range kriging estimations.

After training the random forest, the secondary variables (plus two embedding variables) may be passed down to the trained random forest, and the approximated conditional distribution for the target variable (called the envelop) may be derived for each target location where the target variable is to be estimated. For a conditional simulation of the target variable, the sampling variable may be used to sample from the envelop.

A conditional simulation of the target variable may be run by modifying the sampling from the envelope using the multiple intervention variables and powers. Intervention variables are either external variables or the secondary input variables that are selected (e.g., by a user) to intervene to modify the sampling process. Intervention power refers to the correlation between the target and the forcing variable for generating sampling variables. The intervention variables and powers may be updated in order to match the production history and update the 3D subsurface models. The construction of the workflow in this way (1) reduces the number of parameters to be changed to update the 3D model and (2) constrains the solution to geological probability inherent in the forest.

The use of the computing program (e.g., EMBER) and the probabilistic model may assist by (1) directly incorporating primary geological measurements and interpretations, (2) constraining the property values to a range with a probability density function, and (3) reducing the dimensionality of the problem by constraining the search to bounded values of a few “intervention variables.” The random forest method described above may be coupled with machine learning (ML) estimation of the physics equations such as neural operators to allow for extremely rapid searching.

Exemplary Method

FIG. 2 illustrates a flowchart of the method 200 for generating (or updating) a model of a subsurface formation, according to an embodiment. The method 200 rapidly and efficiently finds 3D fields that are geologically consistent, matches the measured parameters, and addresses the non-unique nature of the problem. As mentioned above, the method 200 may (1) reduce the number of parameters to be changed to update the 3D model and/or (2) constrain the solution(s) to geological probability inherent in the forest. An illustrative order of the method 200 is provided below; however, one or more portions of the method 200 may be performed in a different order, simultaneously, repeated, or omitted. At least a portion of the method 200 may be performed with a computing system 600 (described below). FIG. 3 illustrates a schematic view of the method 200 in FIG. 2, according to an embodiment.

The method 200 may include receiving input data for a subsurface formation, as at 205. This is also shown at 305 in FIG. 3. The input data may be or include geological features, seismic data, seismic attributes, well logs, structural geometry, rock and fluid physics data, initial conditions, or a combination thereof.

The method 200 may also include creating a probabilistic random forest based upon the input data, as at 210. This is also shown at 310 in FIG. 3.

The method 200 may also include determining a plurality of 3D subsurface properties using the probabilistic random forest, as at 215. This is also shown at 315 in FIG. 3. The 3D subsurface properties may be referred to as an ensemble. The 3D subsurface properties may be or include porosity, permeability, initial water saturation, or a combination thereof. The 3D subsurface properties may be a function of one or more intervention variables that increase and/or decrease weights of the input data for generating a sampling variable. The one or more intervention variables may be or include external variables and/or secondary input data that are selected to intervene to modify a sampling from the probabilistic random forest. The external variables may not be used to train the probabilistic random forest. The secondary input data may be used to train the probabilistic random forest.

The method 200 may also include predicting one or more flowing characteristics based upon the 3D subsurface properties, as at 220. This is also shown at 320 in FIG. 3. The flowing characteristics may be predicted (e.g., simulated) using a physics simulator (e.g., a reservoir simulator). The simulator may be designed to predict three-dimensional fields of pressure and saturation, as well as pressure and flow rates at the wells over various time intervals. The pressure and flow rates at the wells serve as inputs for computing the objective function.

The method 200 may also include training a machine-learning (ML) model using the predicted characteristic(s), as at 225. This is also shown at 325 in FIG. 3. The ML model may be or include a physics-informed neural operator and/or a Fourier Neural Operator or PINO. For example, Deep Neural Networks (DNNs), Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM), Physics informed Neural Networks (PINN), Graph Neural Networks (GNNs), and/or any variants may be used. The ML model may replace reservoir simulation to expedite the process of determining the objective function, which measures the difference between the simulated result compared to the measured data at the wells.

The method 200 may also include receiving one or more measured flowing characteristics, as at 230. This is also shown at 330 in FIG. 3. The measured flowing characteristics may be or include pressure and/or flow rates at the wells.

The method 200 may also include adjusting one or more intervention variables using the ML model to update the 3D subsurface properties, as at 235. This is also shown at 335 in FIG. 3. The intervention variables may adjust how the random forest is sampled to provide the 3D subsurface properties. So, for each location, there may be a range of possible 3D subsurface property values, and the intervention variables may change which value is selected within the range. The intervention variables may be selected (e.g., by an optimizer) to minimize the mismatch between the predicted flowing characteristics (i.e., the flowing ML-physics surrogate) versus the measured flowing characteristics (i.e., the actual measured data production). In other words, the intervention variable(s) may be adjusted until one or more (e.g., best) matches are found to the measured characteristic(s). The adjusted intervention variables may be referred to as solutions.

The method 200 may also include displaying the updated 3D subsurface properties, as at 240.

The method 200 may also include performing a wellsite action, as at 245. The wellsite action may be based upon or in response to updated 3D subsurface properties. The wellsite action may be or include generating and/or transmitting a signal (e.g., using a computing system) that instructs or causes a physical action to occur at a wellsite. The wellsite action may also or instead include performing the physical action at the wellsite. The physical action may include selecting where to drill a wellbore, drilling the wellbore, varying a weight and/or torque on a drill bit that is drilling the wellbore, varying a drilling trajectory of the wellbore, varying a concentration and/or flow rate of a fluid pumped into the wellbore, or the like.

Another Method

FIG. 4 illustrates a schematic view of another method for generating (or updating) a model of a subsurface formation, according to an embodiment. The method 400 may be similar to the method 200 in FIG. 2, except that it may provide a prior-and-posterior range of results after the history matching/inverse modeling process. The coupling of a geologically-derived random forest and a machine learning physics simulation proxy is a new combination that addresses a problem in reservoir engineering.

Result of Applying the Method

FIGS. 5A and 5B illustrate results of applying method 200 to a synthetic reservoir for updating the porosity field to match the cumulative oil and water production to historical data, according to an embodiment. M ore particularly, FIG. 5A shows cumulative oil production, and FIG. 5B shows cumulative water production. The lines 510 represent historical data (e.g., a reference solution), the lines 520 represent the results from the initial porosity model, and the lines 530 represent the results from the updated porosity model. By utilizing the method 200, both cumulative oil and water productions more closely align with the historical data. Notably, the water breakthrough time has been improved. Although the results may not match the historical data, the updated porosity model is geologically consistent. Moreover, this improved model can serve as a better initial field for use in various history matching algorithms.

Exemplary Computing System

In some embodiments, the methods of the present disclosure may be executed by a computing system. FIG. 6 illustrates an example of such a computing system 600, in accordance with some embodiments. The computing system 600 may include a computer or computer system 601A, which may be an individual computer system 601A or an arrangement of distributed computer systems. The computer system 601A includes one or more analysis modules 602 that are configured to perform various tasks according to some embodiments, such as one or more methods disclosed herein. To perform these various tasks, the analysis module 602 executes independently, or in coordination with, one or more processors 604, which is (or are) connected to one or more storage media 606. The processor(s) 604 is (or are) also connected to a network interface 607 to allow the computer system 601A to communicate over a data network 609 with one or more additional computer systems and/or computing systems, such as 601B, 601C, and/or 601D (note that computer systems 601B, 601C and/or 601D may or may not share the same architecture as computer system 601A, and may be located in different physical locations, e.g., computer systems 601A and 601B may be located in a processing facility, while in communication with one or more computer systems such as 601C and/or 601D that are located in one or more data centers, and/or located in varying countries on different continents).

A processor may include a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device.

The storage media 606 may be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment of FIG. 6 storage media 606 is depicted as within computer system 601A, in some embodiments, storage media 606 may be distributed within and/or across multiple internal and/or external enclosures of computing system 601A and/or additional computing systems. Storage media 606 may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAM s), erasable and programmable read-only memories (EPROM s), electrically erasable and programmable read-only memories (EEPROM s) and flash memories, magnetic disks such as fixed, floppy and removable disks, other magnetic media including tape, optical media such as compact disks (CDs) or digital video disks (DVDs), BLURAY® disks, or other types of optical storage, or other types of storage devices. Note that the instructions discussed above may be provided on one computer-readable or machine-readable storage medium, or may be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media is (are) considered to be part of an article (or article of manufacture). An article or article of manufacture may refer to any manufactured single component or multiple components. The storage medium or media may be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions may be downloaded over a network for execution.

In some embodiments, computing system 600 contains one or more subsurface modelling module(s) 608. In the example of computing system 600, computer system 601A includes the subsurface modelling module 608. In some embodiments, a single subsurface modelling module may be used to perform some aspects of one or more embodiments of the methods disclosed herein. In other embodiments, a plurality of subsurface modelling modules may be used to perform some aspects of methods herein.

It should be appreciated that computing system 600 is merely one example of a computing system, and that computing system 600 may have more or fewer components than shown, may combine additional components not depicted in the example embodiment of FIG. 6, and/or computing system 600 may have a different configuration or arrangement of the components depicted in FIG. 6. The various components shown in FIG. 6 may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits.

Further, the steps in the processing methods described herein may be implemented by running one or more functional modules in information processing apparatus such as general purpose processors or application specific chips, such as ASICs, FPGAS, PLDs, or other appropriate devices. These modules, combinations of these modules, and/or their combination with general hardware are included within the scope of the present disclosure.

Computational interpretations, models, and/or other interpretation aids may be refined in an iterative fashion; this concept is applicable to the methods discussed herein. This may include use of feedback loops executed on an algorithmic basis, such as at a computing device (e.g., computing system 600, FIG. 6), and/or through manual control by a user who may make determinations regarding whether a given step, action, template, model, or set of curves has become sufficiently accurate for the evaluation of the subsurface three-dimensional geologic formation under consideration.

The foregoing description, for purposes of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or limiting to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. Moreover, the order in which the elements of the methods described herein are illustrated and described may be re-arranged, and/or two or more elements may occur simultaneously. The embodiments were chosen and described in order to best explain the principles of the disclosure and its practical applications, to thereby enable others skilled in the art to best utilize the disclosed embodiments and various embodiments with various modifications as are suited to the particular use contemplated.