Methods and Systems for Gas-Lift Anomaly Detection Using Integrated Unsupervised Learning Models

Hydrocarbon fluids can be localized in porous rock formations of the Earth's subsurface forming hydrocarbon reservoirs. Wells may be drilled for the purpose of extracting the hydrocarbon fluids from the hydrocarbon reservoirs. In some instances, hydrocarbon fluids are able to flow naturally through producing wells (i.e., wells configured for the production of hydrocarbons) because the pressure within the reservoir is high enough to propel the hydrocarbons to the surface. However, in other instances, for example, when a reservoir approaches depletion or is naturally a reservoir with low pressure, gas-lift may be utilized to produce the hydrocarbon fluids. In general, gas-lift uses a source of high-pressure gas to lower the bulk density of a fluid mixture with hydrocarbons and “lift” the mixture to the surface. In some examples, gas-lift systems use an external source of gas which is injected into production tubing located in the production well. In these examples, the injected gas mixes with the fluid mixture in the production tubing reducing the density of the fluid mixture, now entrained with injected gas, such that the overall fluid and injected gas mixture becomes light enough to flow to the surface using the available reservoir pressure. Gas-lift systems and their associated operation are instrumental in augmenting hydrocarbon recovery rates but can encounter issues. Issues during operation of a gas-lift system or process can diminish operational efficiency and, in severe cases, result in considerable damage to infrastructure (e.g., the well). As such, there exists a need to quickly determine whether an issue or operational fault has occurred in a gas-lift system or process.

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

Embodiments disclosed herein generally relate to a method for detecting an anomaly in a gas-lift system. The method includes obtaining gas-lift data from a gas-lift system and associated well, where the gas-lift system injects a gas into a fluid mixture of the well. The method further includes obtaining a set of operation parameters including an injected gas rate and an injected gas pressure. The method further includes determining, with a first machine learned model and a second machine learned model, a first and second anomaly metric each indicative of an anomaly in the gas-lift system or a flow of a production fluid from the well, respectively, based on the gas-lift data, where the production fluid includes the fluid mixture and the injected gas. The method further includes forming an aggregate anomaly prediction from the first anomaly metric and the second anomaly metric and adjusting, with a controller, the set of operation parameters based on, at least, the aggregate anomaly prediction.

Embodiments disclosed herein generally relate to a system that includes a gas-lift system that injects a gas into a fluid mixture of a well and a controller that can configure one or more configurable parameters of the gas-lift system and well. The one or more configurable parameters are included in a set of operation parameters. The controller is configured to: obtain gas-lift data from the gas-lift system and the well; determine, with a first machine learned model and a second machine learned model, a first and second anomaly metric each indicative of a presence of an anomaly in the gas-lift system or a flow of a production fluid from the well, respectively, based on the gas-lift data, where the production fluid includes the fluid mixture and the injected gas; form an aggregate anomaly prediction from the first anomaly metric and the second anomaly metric; and adjust the set of operation parameters based on, at least, the aggregate anomaly prediction.

Embodiments disclosed herein generally relate to a non-transitory computer-readable memory with computer-executable instructions stored thereon that, when executed on a processor, cause the processor to perform certain steps. The steps include obtaining gas-lift data from a gas-lift system and associated well and obtaining a set of operation parameters including an injected gas rate and an injected gas pressure. The steps further include determining, with a first machine learned model and a second machine learned model, a first and second anomaly prediction metric each indicative of an anomaly in the gas-lift system or flow of a production fluid from the well, respectively, based on the gas-lift data. The steps further include forming an aggregate anomaly prediction from the first predicted anomaly metric and the second anomaly metric and adjusting, with a controller, the set of operation parameters based on, at least, the aggregate anomaly prediction.

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

In the following detailed description of embodiments of the disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to one of ordinary skill in the art that the disclosure may be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description.

Throughout the application, ordinal numbers (e.g., first, second, third, etc.) may be used as an adjective for an element (i.e., any noun in the application). The use of ordinal numbers is not to imply or create any particular ordering of the elements nor to limit any element to being only a single element unless expressly disclosed, such as using the terms “before,” “after,” “single,” and other such terminology. Rather, the use of ordinal numbers is to distinguish between the elements. By way of an example, a first element is distinct from a second element, and the first element may encompass more than one element and succeed (or precede) the second element in an ordering of elements.

It is to be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. For example, a “sensor” may include any number of “sensors” without limitation.

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

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

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

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

In general, embodiments of the disclosure include systems and methods for determining, at least, an anomaly in a gas-lift system or process. In some embodiments, a detected anomaly further undergoes a root cause analysis and can be assigned a class representative of a type of anomaly or issue in the gas-lift system or process. In one or more embodiments, anomaly detecting is performed on the gas-lift system or process in real time given one or more measurements of the gas-lift system or process such as gas injection flow rate, temperature, pressure, etc., where such measurements can be collected as gas-lift data.

In one or more embodiments, an anomaly in the gas-lift system or process is detected using two machine learning (ML) models based on the gas-lift data. In particular, the two ML models need not be trained using labelled data. That is, borrowing language commonly employed in the literature, the two ML models may be said to be “unsupervised” learning models. In one or more embodiments, the two ML models are an isolation forest (IF) and a one-class support vector machine (1CSVM). These ML models will be described in greater detail later in the instant disclosure.

In one or more embodiments, the two ML models each detect an anomaly in a gas-lift system or process based on the gas-lift data, resulting in two anomaly predictions that are aggregated according to an aggregation function to form an aggregated anomaly prediction (“aggregate anomaly prediction”). As will be demonstrated later, each of the ML models is capable of outputting quantitative information, such as a metric (e.g., a score) that can represent, for example, a level of divergence of a data point from those data points considered “normal” or a confidence level in a determination that a data point is anomalous. That is, the ML models need not only output a binary classification of “anomalous” and “non-anomalous” (i.e., “normal”). As a result, and as will be described in greater detail later in the instant disclosure, the two ML models can be uniquely integrated, for example, by forming an aggregate anomaly prediction dependent on their respective quantitative outputs in view of the gas-lift data.

In one or more embodiments, the two ML models may further be informed by a set of operation parameters that define configurable aspects of a well and accompanying gas-lift system. For example, the set of operation parameters may include well control parameters and gas-lift parameters, where the well control parameters define the state of hardware governing fluid flow in the well system or along any portion of the pipeline (e.g., a valve configured to be opened or closed, or partially closed) and the gas-lift parameters define the state of hardware governing aspects of a gas-lift process (e.g., gas injection rate). The collection of well control parameters and gas-lift parameters are referred to herein as a set of operation parameters. In one or more embodiments, based on the aggregate anomaly prediction, a command may be sent to update the set of operation parameters to new values or states to achieve a particular goal. Goals include, but are not limited to: optimizing the production of hydrocarbons from a well; operating the gas-lift system at a most economical setting in view of a desired hydrocarbon production rate; and restoring operation of the gas-lift system to a “normal” state in response to detecting an anomaly. With respect to restoring operation of a gas-lift system to a normal state in response to detecting an anomaly, embodiments disclosed herein may further produce a recommendation, or a recommended “treatment” (e.g., an action or sequence of actions), where application of the recommendation is expected to restore the operation of a gas-lift system to the normal state.

In general, a gas-lift system or process works to aid or increase hydrocarbon production in hydrocarbon production wells by injecting high-pressure gas, from the surface, down a casing annulus or coil tubing into fluids disposed in the production tubing. The fluid density and hydrostatic pressure of the fluid are reduced by the introduction of the injected gas thereby allowing the in-situ reservoir pressure to lift the lightened fluids. In one or more embodiments, a gas-lift system includes a source of gas and a gas pump. In other embodiments, a source of gas and gas pump (or other means of supplying pressurized gas) are external to a gas-lift system and the gas-lift system receives a high-pressure gas. Hereafter, a gas-lift system refers to the set of components and mechanical or electrical devices used in a gas-lifting operation.

In accordance with one or more embodiments, systems of the instant disclosure include a well site with a gas-lift system, including an oil and gas well (“well”) with access to a subsurface formation containing hydrocarbons or reservoir (“reservoir”) and a source of gas to be used for gas-lifting. In one or more embodiments, an external source of gas may be accessed by a gas-lift system including a gas pump. In one or more embodiments, the injected gas is nitrogen. The operation of the gas-lift system, including the source of gas and gas injection rate, is defined by one or more gas-lift parameters. The result of injecting gas into the well is sensitive to a number of factors, including the physical properties or characteristics of the well, the reservoir, and the various fluids that may be present in either the well or reservoir. The result of injecting gas into the well is further sensitive to the values or states of the parameters of the gas-lift parameters. In one or more embodiments, the set of gas-lift parameters is adjusted, automatically and in real time, to optimize gas-lifting via injection of gas into the well (e.g., using a controller and/or gas-lift optimization system described below).

shows a schematic diagram in accordance with one or more embodiments. More specifically,illustrates a well site with gas-lift () including a well (). A gas-lift system “lifts” production fluids (), such as oil, gas, and/or water, to a well exit () by lowering the density of the production fluids () with high-pressure gas (). In one or more embodiments, the gas (), commonly nitrogen, is pumped from a gas source () using a gas pump () as part of a gas-lift system and is supplied into the well () through a surface gas injection valve (). In some embodiments, a gas-lift system may simply include one gas pump, though in other embodiments the gas-lift system may include several gas pumps. A gas-lift system further includes electronic controllers (not shown) which may be operated by a computer, such as the computer ofand its accompanying description. The gas source () can be of many shapes and sizes. In one or more embodiments, the gas source () and gas-lift system including a gas pump () are located near the well site (), as illustrated in. In other examples, the gas source () and gas pump () may be located at some distance from the well site (). A surface gas injection valve (), disposed at a surface () and connected to an annulus () of the well (), controls the flow of the gas () and injects the gas () into the annulus () with a user-defined pressure, which can be considered as high (e.g., 20 MPa), according to one or more embodiments. The annulus () consists of the space between a casing () and a main inner pipe () and is configured to isolate the gas (), allowing the gas () to flow the depth of the well () without mixing with other fluids. In one or more embodiments, the gas may instead be injected using coiled tubing threaded into the main inner pipe () instead of injecting the gas through the annulus (). Gas injection may involve defining the depth at which the gas is injected, e.g., into the main inner pipe (), to lift the fluids. For example, injecting gas with coiled tubing may involve defining the depth of the coil tubing landing for gas injection. The depth at with gas is injected in a gas-lift operation can affect the efficiency of the gas-lift operations and the quantity and rate of hydrocarbons extracted from the well. In some instances, depth(s) of injection are considered configurable gas-lift parameters. In other instances, depth(s) of injection are fixed and temporally invariant.

In the depiction of, the casing (), disposed in the well () against a wellbore () and typically formed of a durable material such as steel, extends to a depth above a reservoir (). The casing () isolates the subsurface fluids and supports a wellbore (), a drilled hole of the well (), up to the depth above the reservoir (). At the other end, the wellbore () extends through the reservoir () beneath the casing (). The reservoir () is disposed below the surface () of the Earth in porous rock formations and is the source of the production fluids (). The main inner pipe (), disposed in the wellbore (), extends from a well exit () to a depth proximate or intersecting the reservoir () and is a conduit for production fluids () to exit the well. In one or more embodiments, the main inner pipe () may be formed of tempered steel or equivalent. For the embodiment depicted in, the production fluids () may be oil and gas. The oil and gas flows from the reservoir () into the wellbore () and into the main inner pipe (). If the reservoir () has enough pressure, the oil travels upwards in the main inner pipe () to the surface (). Conversely, if the reservoir () does not have enough pressure to lift the oil and gas by itself, in a gas-lift system, external gas ()—where here “external” is used to distinguish the to-be-injected gas from gases originating from the wellbore—is injected into the well ().

In one or more implementations, at a given pressure that may be considered as high (e.g., 20 MPa), the external gas () enters the main inner pipe () through a downhole gas injection valve () and mixes with the production fluids () disposed in the main inner pipe (). The downhole gas injection valve () forms a hydraulic connection between the annulus () and the main inner pipe () and is configured to allow the flow of the external gas () from the annulus () into the main inner pipe (). In one or more embodiments, the downhole gas injection valve () forms a hydraulic connection between coil tubing which is disposed within the main inner pipe () and is configured to allow the flow of external gas () from the coil tubing into the main inner pipe (). In one or more embodiments, the downhole gas injection valve () is composed of stainless steel or the equivalent. The pressure of the injected gas (), combined with the lighter weight of the gas (), lowers the density of the production fluids () until the mixture becomes light enough to flow towards the well exit () and into a production tank (). The production tank () is a storage tank, disposed at the surface (), that collects and stores the production fluids () after the production fluids () exit the well (). In some instances, the production fluids () may be directly transported to (e.g., by a pipeline), or otherwise processed by, an oil and gas processing facility.

In accordance with one or more embodiments, one or more downhole sensors () are disposed within the well (). The one or more downhole sensors () measure downhole fluid and process properties such as downhole gas injection rate, downhole production rate (which may be multiphase; i.e., flow rates for water, oil, and gas), downhole pressure, downhole temperature, and downhole gas concentration. In one or more embodiments, the downhole sensors () are grouped together and located on the side of the wellbore (), as illustrated in. In other examples, the downhole sensors () may be separated and located anywhere below the surface (). Downhole sensors () may further be disposed within the reservoir () and measure properties of the reservoir such as reservoir temperature and reservoir pressure.

In accordance with one or more embodiments, one or more surface sensors () are disposed at, or above, the surface () of the well (). The one or more surface sensors () measure fluid and process properties at the surface () such as surface pressure, gas injection pressure, gas injection rate, and gas injection temperature. In one or more embodiments, the surface sensors () are grouped together and located in the vicinity of the well exit (), as illustrated in. In other examples, the surface sensors () may be separated and located anywhere at or above the surface (). In one or more embodiments, the downhole sensors () or surface sensors () further include an acoustic sensor, such as a geophone, acquiring acoustic data that is added to the well data. In one or more embodiments, the downhole sensors () or surface sensors () further include at least one contamination sensor, configured to detect a presence, and possibly a concentration of contaminant in a produced hydrocarbon. The data measured by the downhole sensors () and surface sensors () are recorded and/or stored using a data collection unit (). In one or more embodiments, the data collection unit () is located in the vicinity of the well exit (), as illustrated in. In other examples, data collection unit () may be located separate from the well but in communication using either wired relays or a remote signal. One or more measurements acquired using the sensors, as described above, can be collected as well data.

Configuring a gas-lift system (including, for example, the operating conditions of a gas pump ()) for optimal gas-lift is a difficult and laborious task. Further, the state and behavior of a well site with gas-lift () may be transient according to conditions at the environment of the site (e.g., changing weather conditions in an offshore well) or within the reservoir (e.g., seismic activity and changing temperature and pressure). Gas-lift stability, in particular, is challenging to maintain. Gas-lift stability refers to the ability of a gas-lift system to maintain consistent and efficient operations over time without experiencing issues that could disrupt production. Instabilities in gas-lift operations can lead to reduced production rates, increased operational costs, and potential damage to equipment. To provide gas-lift stability, issues must be quickly detected and addressed. As such, embodiments disclosed herein, among other things, detect anomalies representative of issues and provide recommendations for restoring the operation of the gas-lift system to, at least, a normal or stable state.

A notable example of gas-lift instability is a slug flow, in which large pockets of gas and liquid alternate in the production tubing, causing rapid changes in pressure and flow rates. A slug flow may lead to inefficient lifting, decreased production, and wear on well equipment. The gas injection rate is typically balanced in order to create sufficient buoyancy to lift the fluids without causing excessive gas breakout at the surface. Over-injecting gas might lead to inefficient gas usage, while under-injecting gas could result in poor production rates. The gas-to-liquid ratio may also play a significant role in gas-lifted hydrocarbon production, as injecting too much gas may lead to inefficient fluid separation at the surface, while injecting too little gas may result in poor lifting performance. The opening and closing pressures of the surface gas injection valve () and the downhole gas injection valve () determine when gas injection starts and stops. Properly setting these pressures may help maintain an effective gas-lift cycle. Further, it may be advantageous, in some embodiments, for the hydrocarbon production rate itself to be adjusted according to different circumstances. For instance, the hydrocarbon production rate may be intentionally reduced while a maintenance action is performed. As another example, the hydrocarbon production rate may be desired to change based on current demand.

Thoughdepicts a well that may be considered typical for onshore wells, the elements shown and described are also generally applicable to offshore (and “rigless”) wells. Consequently,should not be considered as limiting as embodiments disclosed herein can be readily applied to offshore and rigless well sites although not depicted.

Regarding the components of a well site with gas-lift, the various systems and facilities may each have associated data that describe the status of the given system or facility. Additionally, the systems and/or facilities of a well site with gas-lift can have associated parameters that define and control one or more aspects of their operation. For example, features of the well site with gas-lift may be recorded in measurements collectively referred to as “well data.” In one or more embodiments, the well data may include “gas-lift data” from the gas-lift system (e.g., gas injection rates) and “reservoir data” from the reservoir. The well data may describe both static properties of the well (i.e., properties generally invariant to the passage of time), such as its diameter, end of tubing depth, perforation depth, and geographical location (among others not listed) and dynamic properties of the well (i.e., properties that can fluctuate/change temporally) such as the wellhead pressure, gas-to-oil ratio, fluid density inside the well, fluid temperature inside the well, fluid pressure inside the well, water cut, and liquid flowing rate (among others not listed). The reservoir data may describe both static properties of the reservoir, such as its depth, extent, and geographical location (among others not listed) and dynamic properties of the reservoir such as its temperature, pressure, salinity, porosity, resistivity, radioactivity, and fluid density inside the reservoir (among others not listed).

In one or more embodiments, the external gas source—where “external” is used to distinguish the to-be-injected gas from any gas originating in the wellbore—and gas pump (and other elements, components, and or facilities of a gas-lift system) have an associated set of gas-lift parameters. The set of gas-lift parameters may include gas injection parameters that define the aspects of the gas injection into the well. The gas injection parameters may include defining a rate of gas injection, a fluid conduit medium (e.g., coil tubing or tubing annulus), and a depth at which gas is to be injected. To clarify, the selection or identification of the element(s) through which gas is injected into the well are referenced herein as a “fluid conduit medium,” and examples of fluid conduit mediums include coiled tubing and using an annular volume in the wellbore around the main pipe, i.e., a tubing annulus. A volume of injected gas may be defined by the injection parameters as well, though it is noted that a volume may be considered equivalent with a rate through integration of the rate over time. In accordance with one or more embodiments, the gas-lift parameters may include configurable parameters more commonly associated with the well rather than the gas-lift system such as valve states that control the rate of production fluids from the well.

In one aspect, embodiments disclosed herein relate to a system for determining the set of gas-lift parameters that optimize the gas-lifting at a well site with gas-lift. Optimizing the gas-lifting may refer to several goals, depending on the circumstances of the well site with gas-lift. For example, in one or more embodiments, optimizing gas-lifting may include detecting and mitigating against issues that result in decreased production or operational states that can be damaging to well equipment.

In accordance with one or more embodiments, gas-lift data from a well environment with a gas-lift system is processed with two machine learning (ML) models to, at least, detect an anomaly in the gas-lift system or process. As will be described below, these ML models are capable of operating on high-dimensional data without labelled training data. Consequently, these models can provide quick and accurate determinations allowing for real-time, or near-real time, recommendations and adjustments to be made to the operation of a gas-lift system and/or well operation to optimize or restore the gas-lift processes.

Machine learning, broadly defined, is the extraction of patterns and insights from data. The phrases “artificial intelligence,” “machine learning,” “deep learning,” and “pattern recognition” are often convoluted, interchanged, and used synonymously throughout the literature. This ambiguity arises because the field of “extracting patterns and insights from data” was developed simultaneously and disjointedly among a number of classical arts like mathematics, statistics, and computer science. For consistency, the term machine learning (ML) will be adopted herein, however, one skilled in the art will recognize that the concepts and methods detailed hereafter are not limited by this choice of nomenclature.

In accordance with one or more embodiments, the ML models are unsupervised anomaly detection models. Sometimes, in the literature, the subject of anomaly detection is further partitioned into the subgroups of outlier detection novelty detection. The primary distinction between outlier detection and novelty detection is that the training data for outlier detection is thought to contain some outliers (although these outliers are not labelled or otherwise distinguished from any other data points) and the training data for novelty detection is considered to be free of outliers (or anomalies). Herein, no distinction between outlier detection and novelty detection is made and only the more general term of anomaly detection is used. This is because, in part, the anomaly detection models specified herein are readily applicable to both tasks of outlier detection and novelty detection. For example, and as will be described later in the instant disclosure, a one-class support vector machine (1CSVM) can be defined to accept, as a hyperparameter during training, an expected proportion of outliers in a given set of training data. As such, this model generalizes to both outlier detection and novelty detection where setting such a training hyperparameter to 0 indicates the specific case of novelty detection. In accordance with one or more embodiments, the first ML model is an isolation forest (IF) and the second ML model is a one-class support vector machine (1CSVM). More details regarding these anomaly detection models are provided later in the disclosure. In general, these ML models are configured according to one or more “hyperparameters” which further describe the models. For example, hyperparameters providing further detail about the IF may include, but are not limited to, the number of decision trees in the forest and the configuration of a bootstrapping process, if used. The selection of hyperparameters may be informed through evaluation of a model performance metric (e.g., precision, recall, etc.) if a portion of labelled data is provided, however, labelled data is not a requirement to train and use these models. The processes of training, validating, and testing the ML models are described in greater detail later in the disclosure.

In accordance with one or more embodiments,depicts the determination of an aggregate anomaly prediction () for a gas-lift system or process. As depicted in, two machine learning (ML) models, namely, a first ML model () and a second ML model () are each used to determine an anomaly metric. Specifically, the first ML model () is an isolation forest (IF) and the second ML model () is a one-class support vector machine (1CSVM). In one or more embodiments, the IF and 1CSVM models are specifically designated selected herein for the task of anomaly detection in gas-lift systems or processes because of their distinct operational strengths in view of the described gas-lift data. In particular, the IF is effective in identifying anomalies by isolating data points. The IF works on the principle that anomalies are few and different, such that they can be isolated more quickly than normal points. In other words, and as will be described alter, anomalies are expected to have shorter average path lengths when averaged over the decision trees of the forest. Further, the IF is particularly good at handling large datasets and can efficiently detect anomalies without the need for extensive data labelling (or any data labelling). Continuing, the 1CSVM creates a boundary in a high-dimensional space such that data points that fall outside this boundary are considered anomalies. The IF and 1CSVM can each process large amounts of data more quickly and efficiently than conventional methods, making them suitable for real-time anomaly detection tasks. By providing accurate and timely detections of anomalies, these ML models can support real-time recommendations leading to more efficient gas-lift operations and optimized hydrocarbon production. Additionally, once trained, these ML models can be continually updated and improved as new data is collected, allowing them to adapt to changing conditions in the well environment, reservoir, and gas-lift system.

As seen in, the first ML model () and the second ML model () process, as inputs, gas-lift data (). In accordance with one or more embodiments, the gas-lift data () includes temperature data (), pressure data (), an injected gas rate (), a hydrocarbon production rate (), and in some instances, one or more derived quantities (). The temperature data () can include temperature measurements acquired from one or more sensors disposed on the well (e.g., subsurface sensor) or as part of the gas-lift system. The pressure data () can include pressure measurements acquired from one or more sensors disposed on the well or as part of the gas-lift system. The injected gas rate () indicates the rate at which the gas-lift system injects the external gas into the well, as described above with respect to. The hydrocarbon production rate () represents a measurement of the hydrocarbons or production fluid produced from the well. In some instances, the gas-lift data () further includes one or more derived quantities (). A derived quantity is a quantity or value developed using at least one measured value. For example, a derived quantity may include a ratio of the hydrocarbon production rate () to the injected gas rate (). Another example consists of a polynomial expansion (e.g., taking the square), up to a given order, of one or more measured values. Derived quantities may be developed, tested, and/or selected as part of a feature engineering process when training the ML models. Feature engineering and training are described in greater detail later in the instant disclosure.

In accordance with one or more embodiments, and as seen in, each of the first ML model () and the second ML model () process the gas-lift data () and output an anomaly metric. Specifically, the first ML model () returns a first anomaly metric () and the second ML model () returns a second anomaly metric (). In accordance with one or more embodiments, the first and second anomaly metrics (,) are aggregated to form an aggregate anomaly prediction () using an aggregation function.

In accordance with one or more embodiments, the first ML model () is an isolation forest (IF) and the first anomaly metric () is an anomaly score based on a normalized path length of a given data point through the decision trees of the IF. The IF will be described in greater detail later in the instant disclosure, however, for now it suffices to say that an IF is composed of one or more decision trees and that a data point can traverse through each tree until, conventionally, terminating at a so-called leaf node. The number of edges (or nodes) traversed by the data point though a decision tree indicates the path length of that data point through the decision tree. The average path length across all decision trees in an isolation forest may serve as an anomaly score. However, in many instances, it is desirable to normalize the average path length in some manner because the average path length or path lengths through the individual decision trees are sensitive to the number of datapoints used to train the IF. In accordance with one or more embodiments, the anomaly score s of a data point according to a trained IF is

where x is a data point being scored, n is the number of data points used while training the IF, h(x) is the path length of data point x through decision tree t, T is the total number of decision trees in the IF, and c(n) is a function that returns the average path length of an unsuccessful search in a binary search tree given a data set of n instances. Specifically, c(n) is given as

where H is the harmonic number and it can be estimated by ln(i)+0.5772156649 (Euler's constant). Thus, given a data point, a trained IF (where the trained IF need not be trained using labelled training data) can return an anomaly score for that data point.

In accordance with one or more embodiments, the second ML model () is a one-class support vector machine (1CSVM) and the second anomaly metric () is signed distance from a decision boundary or hyperplane that has been learned, through training, to separate normal (“inlier”) and anomalous (“outlier”) data points. Thus, depending on the sign of a distance associated with a data point, the datapoint can be classified as normal or anomalous and the absolute value of the distance represents a type of confidence that the data point is normal or is anomalous. A greater description of the 1CSVM is provided later in the instant disclosure, however, for now it suffices to say that similar to the IF, the output of the 1CSVM (used, for example, as the second anomaly metric ()) is quantitative in accordance with one or more embodiments.

With these descriptions of the first anomaly metric () and the second anomaly metric () in mind, various aggregation functions can be used to form the aggregate anomaly prediction (). For example, in one implementation, the aggregation function forms the aggregate anomaly prediction () as the weighted sum of the first anomaly metric () and the second anomaly metric (). In other implementations, the possible values of an instance of gas-lift data () are said to span a data space (e.g., hyperspace) and the data space is partitioned into two or more regimes. For example, in one or more embodiments, the data space is partitioned into a first regime and a second regime, the first and second regimes being mutually exclusive and their union exhausting the data space. In such an implementation, the first anomaly metric () can be selected and used as the aggregate anomaly prediction () when the gas-lift data () resides within the first regime. Similarly, in such an implementation, the second anomaly metric () is selected and used as the aggregate anomaly prediction () when the gas-lift data () resides within the second regime. That is, in one or more implementations, the first and second ML models (,) can be said to have complementary modalities of discrimination, where one model is more apt (or more accurate) at detecting an anomaly under a certain set of conditions (i.e., encompassed and defined by a regime in the data space) relative to the other model. In other implementations, the data space is partitioned into three regimes, where, for example, the aggregate anomaly prediction () is set equal to the first anomaly metric () when the gas-lift data () resides within the first regime, the aggregate anomaly prediction () is set equal to the second anomaly metric () when the gas-lift data () resides within the second regime, and the aggregate anomaly prediction () is set equal to a weighted sum of the first and second anomaly metrics (,) when the gas-lift data () resides within the third regime. In instances where the aggregation function represents a weighted sum of the first anomaly metric () and the second anomaly metric (), the weights assigned to each model may be given according to a regime in which the input resides. In another example, a confidence level (e.g., the magnitude of the signed distance output by the 1CSVM) is associated with at least one of the first anomaly metric () and the second anomaly metric (). In this example, the aggregation function can consist of a weighted average of the first anomaly metric () and the second anomaly metric (), where the weights correspond to the confidence level of at least one of the predictions. For example, in one or more embodiments, the weight assigned to the first anomaly metric () and the weight assigned to the second anomaly metric () when the aggregation function is a weighted average is wand w, respectively. Further, the confidence level associated with the first anomaly metric () and the confidence level associated with the second anomaly metric () is cand c, respectively, where cand cneed not sum to 1 and, in some instances, either cand ccan be based on the other. Using this notation, in one or more embodiments, the weights used in the aggregation function are determined using the softmax function as

In one or more embodiments, the first ML model () and the second ML model () operate synergistically. That is, the first ML model () and the second ML model () do not necessarily operate independently. For example, in one or more embodiments, the first ML model () and the second ML model () operate in a hierarchical manner where one model's output informs the focus or parameter settings of the other. For example, in some embodiments, the first ML model () processes gas-lift data () to determine a first anomaly metric (). Then, the gas-lift data () and the first anomaly metric () are processed, as inputs, by the second ML model () to produce the second anomaly metric (). In this case, the second anomaly metric () can be directly taken as the aggregate anomaly prediction (). In other embodiments, the first ML model () processes gas-lift data () to determine a first anomaly metric () and rather than passing the first anomaly metric () as an input to the second ML model (), the first anomaly metric () is used to inform (or adjust) the parameters of the second ML model (). For example, consider notation where the first ML model () is represented as a function ƒthat produces an output ygiven an input x, the function parameterized by parameters β(i.e., y=ƒ(x:β)). Likewise, consider a notation where the second ML model () is represented as a function ƒthat produces an output ygiven an input x, the function parameterized by parameters β(i.e., y=ƒ(x:β)). Thus, in some embodiments, the informed nature of the second ML model (), being informed by the first ML model (), can be represented mathematically as y=ƒ(x:β(y)). That is, the parameterization of the second ML model () is dependent on the output (i.e., first anomaly metric ()) of the first ML model (). In one or more embodiments, the input and/or parameterization of the first ML model () is based on the output of the second ML model () and, similarly, the input and/or parameterization of the second ML model () is based on the output of the first ML model (). In these embodiments, an initial (or null) output can be used to initialize either of the first or second ML models (,) and the subsequent output can be used to as input (and/or parameterization) to the other ML model. This may form an iterative process of interaction between the first ML model () and second ML model () that proceeds until a stopping criterion such as a number of iterations.

In summary, the synergistic operation of the first ML model () and the second ML model () can be implemented in a variety of ways in accordance with one or more embodiments, such as using the outputs of one model as inputs or contextual modifiers (e.g., dependent parametrization) for the other and/or iterative processes that continually refines the model predictions. Further, the aggregate anomaly prediction () can be formed using one or more of the first and second anomaly metrics (,). For example, in instances where the first and second ML models (,) interact iteratively, the aggregate anomaly prediction () can be set equal to either the first or second anomaly metric (,) upon determination of convergence in the predictions.

Benefits of synergistic operation are described with respect to specific ML model types. Consider the case where the first ML model () is an isolation forest (IF) and the second ML model () is a one-class support vector machine (1CSVM). In accordance with one or more embodiments, the IF and 1CSVM are specified for their complementary detection processes. For example, while isolation forests are generally efficient in quickly isolating anomalies, they may not always be precise in high-dimensional spaces where anomalies are not well-separated. One-class support vector machines, on the other hand, excel in these environments. By combining these two models, the methods and systems disclosed herein leverage the rapid detection capability of isolation forests and the high-dimensional precision of one-class support vector machines. Moreover, the synergistic integration of these models can be implemented either sequentially or in parallel. In a sequential setup, one model's output can refine the input for the other (as described above), enhancing the overall accuracy. In parallel processing, both models independently analyze the data, and their results are aggregated (e.g., a weighted sum) to make the final decision on anomalies. Additionally, the synergistic integration of these models allows for cross-validation and feedback. In particular, results from each model can be used to cross-validate the findings of the other. For instance, if both models independently identify the same data point as an anomaly, it can be considered with higher confidence. Conversely, if there's a discrepancy (e.g., one model identifies a data point as anomalous while the other model identifies it as normal), it can trigger a deeper analysis (e.g., a root cause analysis, described later in the instant disclosure). Additionally, because these models operate based on distinct processes, they can extract different insights from the same dataset. This dual extraction of insights provides a more comprehensive understanding of the data. Finally, embodiments disclosed herein can use adaptive thresholding strategies where the sensitivity of anomaly detection is adjusted based on the outputs of both models. Here, this is stated to be particularly useful in dynamic operational environments like gas-lift systems.

In some implementations, methods and systems of the instant disclosure are effectuated as a gas-lift monitoring system. Turning to,depicts an instance of a gas-lift monitoring system () in accordance with one or more embodiments. As seen in, the gas-lift monitoring system () interacts with a well (e.g., Well A ()) with access to a reservoir (e.g., Reservoir C ()). One or more sensors (e.g., Sensors A ()) are disposed on or within the well. The sensors may include one or more temperature sensors, pressure sensors, vibration sensors, and flow rate sensors (including multiphase flowrate devices (e.g., MPFM)), among other sensors.

Sensor data, and other data related to the well (e.g., Well A ()) is collected as well data (e.g., Well Data A ()). Additional data, associated with the reservoir (e.g., Reservoir C ()) is collected as reservoir data (e.g., Reservoir Data C ()). Reservoir data can be collected using one or more sensors associated with the well, one or more sensors associated with the reservoir, data collected as part of a drilling process (e.g., logging while drilling data), data collected apart from a drilling process (e.g., seismic survey), or any combination thereof.

The well (e.g., Well A ()) is coupled with a gas-lift system (e.g., Gas-lift System B ()) for effectuating a gas-lift process on the well. That is, the well (e.g., Well A ()) is associated with or otherwise can access the gas-lift system. The gas-lift system can, at least, set the values of configurable parameters of a gas-lift process applied to the well. Configurable gas-lift parameters are defined as a set of gas-lift parameters (e.g., Set of Gas-lift Parameters B ()). In some embodiments, the gas-lift system (e.g., Gas-lift System B ()) includes a computer system that is the same as or similar to that of computer system depicted in.