Employing artificial intelligence to enhance reservoir property estimation in waste sequestration wells

Abstract

A Physics-Informed Machine Learning (PMIL) model is used to determine reservoir response attributes based on injection operation and reservoir parameters. The model can be used to predict reservoir response to proposed injection operation parameters or to identify injection operation parameters based on a selected reservoir response goal.

Description

Attorney Docket: ADVA-047-PCTApp. No.: tbdTITLE:EMPLOYING ARTIFICIAL INTELLIGENCE TO ENHANCE RESERVOIR PROPERTY ESTIMATION IN WASTE SEQUESTRATION WELLSCROSS-REFERENCE TO RELATED APPLICATIONSThis is an International Patent Application filed under the auspices of the PCT claiming priority to U.S. Provisional Application Ser. No. 63 / 688217, filed August 28, 2024.TECHNICAL FIELD

[0001] The disclosure relates generally to injection operations at subterranean wells, specifically waste injection. The disclosure more particularly relates to machine learning and artificial intelligence modelling for estimating reservoir response attributes based on injection attributes.BACKGROUND

[0002] Global efforts towards environmentally safe waste disposal necessitate waste injection wells, such as cuttings reinjection (CRI) wells, be monitored for operational compliance, safety, continuity, and optimization of waste disposal and vaulting capacity.

[0003] Disposal of waste fluids by hydraulic fracturing injection into a target zone in a subterranean formation is known in the art. Typically, a waste injection well is useful for the storage or sequestration of waste from multiple injections, performed by injecting a plurality of batches of waste slurry into the formation in injection cycles. The waste slurry is injected into a target subterranean zone during a waste injection or disposal operation. Slurry waste is often injected repeatedly into the formations in batches.Attorney Docket: ADVA-047-PCT App. No.: tbd

[0004] Waste materials in non-slurry form are prepared into a slurry prior to injection. The waste materials can include wastes produced during exploration, drilling, completion, and production phases of oil and gas operations. Further, waste materials can be by-products of sewage treatment processes, biosolid waste fluids, waste organic materials, such as food and animal waste, or contaminated materials. Further, waste materials can come from post-industrial operation waste, carbon-bearing materials created for sequestration, and other sources as are known in the art.

[0005] Different types of wells are used for the disposal of waste and byproducts of energy production, including cuttings reinjection (CRI), Saltwater Disposal, and Waste Sequestration wells. CRI wells are commonly used to inject and emplace drill cuttings and other waste materials into the formations, through hydraulic fracturing. Unlike unconventional oil and gas production wells that may undergo hydraulic fracturing or re-fracturing treatment a few times in their lifetime, the CRI and waste sequestration wells are subjected to hydraulic fracturing on a daily, often twice a day, basis. As a result, it is crucial to confirm that the fracture is confined inside the formation and that the formation shows favorable responses following each injection. Similarly, waste sequestration wells play a crucial role for disposing of industrial wastes, and carbon dioxide sequestration. This means that both of these wells require accurate and dependable evaluation of subsurface properties to ensure safe and sustainable performance, while avoiding potential issues such as leakage or suboptimal usage of the reservoir capacity.

[0006] On one hand, accurate estimation of reservoir properties is critical for designing effective injection strategies, such as the optimal injection pressure and rate, use of polymers during injection and maximum solid content in the injected fluid. These secondary parameters are essential for optimal utilization of the reservoir capacity, long-term monitoring of storage performance and maintaining integrity. On the other hand, the consequences of inaccurateAttorney Docket: ADVA-047-PCT App. No.: tbd reservoir property estimation can be severe. Overestimations of capacity can lead to over-injection, risking fractures in the top and bottom barriers and potential leakage of stored materials. Underestimations can also result in suboptimal utilization of the reservoir, leading to economic inefficiencies. Moreover, inaccurate assessments can hinder the ability to predict long-term behavior and stability of the sequestration site, which is critical for ensuring environmental safety and regulatory compliance.BRIEF DESCRIPTION OF THE DRAWING

[0007] For a more complete understanding of the features and advantages of the present disclosure, reference is now made to the detailed description of the disclosure along with the accompanying figures in which corresponding numerals in the different figures refer to corresponding parts and in which:

[0008] FIG. 1 is a schematic of an exemplary well site for injection of fluids into a subterranean zone according to an aspect of the disclosure.

[0009] FIG. 2 is a schematic showing an exemplary methodological framework for creating a Phy sics -Informed Machine Learning model according to aspects of the disclosure.

[0010] FIG. 3 is a graphical representation of a distortion score elbow for K-means clustering according to aspects of the disclosure.

[0011] FIGS. 4A-J are plot charts showing the relationship between predicted attributes using the PMIL model verses observed values according to an aspect of the disclosure.

[0012] FIGS. 5A-B are bar charts showing the relative feature importance for predicting fracture closure pressure for a well according to aspects of the disclosure.

[0013] FIG. 6 is a flow chart showing an exemplary method for creating and implementing thePMIL model in accordance with aspects of the disclosure.Attorney Docket: ADVA-047-PCTApp. No.: tbdDETAILED DESCRIPTION OF EMBODIMENTS

[0014] The present disclosures are described by reference to drawings showing one or more examples of how the disclosures can be made and used. In these drawings, reference characters are used throughout the views to indicate like or corresponding parts. In the description which follows, like or corresponding parts are marked throughout the specification and drawings with the same reference numerals, respectively.Determining Reservoir Response from Post- Injection Data

[0015] Global efforts towards environmentally safe waste disposal necessitate cuttings reinjection (CRI) wells to be monitored for operational compliance, safety, continuity, and optimization of waste disposal wells and vaulting capacity. Pressure Transit Analysis (PTA) is a comprehensive and time-consuming analysis conducted on shut-in data collected post-injection to determine reservoir response to the injection and ensure compliance. An engineering team performs PTA on over 7,000 injection batches annually, which opens a venue for Al optimization. This paper presents a Physics Informed Machine Learning (PIML) method that enhances PTA accuracy, predicting reservoir properties to enhance CRI and waste disposal.

[0016] The methodology integrates standard PTA with machine learning informed by physical science and geomechanical principles. A Physics Informed Machine Learning (PIML) model using shut-in data was developed and trained, to enable early prediction of the behavior of hydraulic fractures and other reservoir properties prior to further injections. This model is validated against 35,000 injection batches and their corresponding PTA results from 10 wells over the last 5 years and allows for better storage capacity management and operational forecasting.Attorney Docket: ADVA-047-PCT App. No.: tbd

[0017] The application of the PIML model demonstrates a significant improvement in estimating the formation response prior to the injection operations, solely based on controllable parameters which can be changed at the surface. Results indicate that the model can predict injectivity, formation stress, fracture closure pressure and time, well head pressure at closure, bottom-hole instantaneous shut-in pressure, fracture half-length, skin and transmissivity with high confidence and accuracy, thus enabling more informed decision-making during the disposal process. Observations from multiple test scenarios confirm that the model reliably estimates critical reservoir characteristics under varying conditions. Conclusions drawn from these experiments suggest that incorporating machine learning with physical science principles substantially reduces the risks associated with hydraulic fracturing in waste disposal. Additionally, the ability to predict reservoir behavior ahead of injections can lead to better compliance with safety standards and reduced environmental impact, setting a new benchmark for operational practices in the industry.

[0018] Through introduction of a novel integration of physics-informed machine learning with conventional PTA techniques, this paper contributes new insights into the preemptive estimation of reservoir properties, potentially transforming operational protocols in underground waste disposal. The methodology and findings provide actionable intelligence that could influence future designs and operational strategies in the energy industry, enhancing both safety and efficiency.Exemplary Waste Injection Well

[0019] FIG. 1 is a schematic of an exemplary waste slurry injection operation. A target subterranean zone 10 is typically confined by upper 12 and lower boundary zones 14. Waste disposal must occur in the target zone without breach of containment into the upper or lower boundary zones. A formation may have multiple target zones layered between multiple boundary zones. Similarly, the formation may host several disposal wells. The zones, and particularly theAttorney Docket: ADVA-047-PCT App. No.: tbd target zone have associated parameters as is known in the art. For example, a zone has an associated permeability, porosity, formation pore pressure, formation stresses, Young’s modulus of elasticity, and Poisson’ s ratio. Further, the target zone, which is made up of particles or granules of materials, includes pore throats extending between the granules and connecting pore volumes in the formation. The pore throat size, or injection interval aperture size, is another parameter of the formation. Some parameters change over time or in response to well operations.

[0020] The waste injection well 20 has a wellbore 22 extending through the target zone 10. The wellbore 22 is typically cased along at least a portion of its depth. The casing 24 is typically cemented 26 in pace. One or more injection tubulars 28 are positioned in the wellbore. Injection occurs through the tubulars or along the annulus between the wellbore and tubular. Downhole tools, as is known in the ail, can be employed during injection and hydraulic fracturing operations such as packers 30, seals, valves, screens, and measuring and sensing equipment.

[0021] Surface equipment can include pumping equipment, such as an injection pump 36 positioned at the wellhead 32 to pump waste fluids into the wellbore under pressure. Associated manifolds and operational valving 34, such as controls, shut-in valves, safety valves and the like, are known in the art. A waste slurry source 40 provides waste slurry for injection. Additional sources (not shown) can be employed for flushing fluids, water, additives, chemicals, or other fluids for injection or for mixing with injected fluids. Although a tank is shown, it is understood that the sources can be vessels, trucks, piping systems, facilities and the like. For an injection of a batch of waste slurry, the slurry is held in a tank and flowed through surface lines and equipment (e.g., pump) to the wellhead. This surface equipment which contains the slurry during the batch injection process defines a surface slurry equipment volume. This surface slurry equipment volume may be used in determining or calculating a pre-flush or post-flush volume.Attorney Docket: ADVA-047-PCT App. No.: tbd

[0022] One or more operational controllers 50 communicate with and control the various surface equipment, such as the pump system 36, the valving 34, and slurry processing equipment 40. The controllers 50 can also communicate with the various sensors. The controllers are operable to control the various equipment in response to signals from manual source and from processors and computers associated with the PIML model or receiving data from the PMIL model. Communication can be wired or wireless, as is known in the art. The operational controllers can perform their control functions automatically in response to signals from another computerized system, such as a computer associated with the PIML model, a computer utilizing the PIML model outputs in addition to performing further analysis or tasks, or in response to measure well data.Injection Operations

[0023] Waste fluids or slurry are pumped into the wellbore and target zone under pressure. In some cases, the waste slurry is pumped into the formation at below fracturing pressure. In some case, the waste slurry is pumped into the formation at above fracturing pressure, thereby creating a plurality of fractures 50 in the target zone. Underground slurry injection for waste management is often carried out in cycles, consisting of injecting batches of waste slurry with intervening shut-in periods to allow fracture closure and pressure dissipation. Waste injection operations can be quite long-term. It is not atypical for injection cycles to be earned out multiple times per day, multiple days per week, and over a period of months or years. In some cases, a single batch can take long periods to be injected, such as weeks. A cycle or batch has known or measurable cycle parameters, such as batch volume, solids volume, solids concentration, viscosity, density, particle size, etc. The cycle parameters depend on the type and volume of waste and slurry being injected and can be selected based on the physical and fractural properties of the formation and or surface equipment constraints.Attorney Docket: ADVA-047-PCT App. No.: tbd

[0024] During fracturing waste slurry injection, the target zone is hydraulically fractured, creating and extending fractures through the formation. The waste slurry flows into the fractures and the waste solids are eventually trapped in and around the fractures when they close after cessation of pumping. Often, fracture is initiated hydraulically by clean water, then the waste slurry is injected downhole to fill and to propagate the initiated fracture. As cycles are repeatedly carried out, additional fractures are created, extended and filled.

[0025] Testing and parameter measurement is performed on the well to collect relevant data. For example, sensors 42 can measure conditions at or near the bottom of the wellbore, such as bottom hole pressure (BHP) and temperature. Similarly, uphole sensors 44 can measure wellhead pressure and temperature. Additional sensors, such as above-ground sensors 46 can measure pressures and temperatures at various locations in above-ground equipment. Slurry sensors 48 can be used to measure slurry parameters, such as solids content, viscosity, density, etc., as is known in the art. The sensors are used, for example, during fall-off tests, shut-in tests, pressure tests, tubing tests, injection operations, and the like. Sensors can be used to measure, directly or indirectly, pressure, temperature, opacity, light, reflected light, density, viscosity, flow rate, solids content, position, displacement, distance, speed, or acceleration, refraction, diffraction, reflection, biomass content, etc., as is known in the art.

[0026] After each injection cycle, the well is shut-in at cessation of pumping. A period of rest follows. Cumulative rest of a formation is the summed rest periods over a given time period (e.g., a week) or number of cycles. Upon shut-in, the disposal fractures close onto the disposed solids in the slurry and any build-up of pressure in the formation is dissipated. The waste fluid “leaks-off” after cessation of pumping, thereby reducing the formation pressure near the wellbore.Attorney Docket: ADVA-047-PCT App. No.: tbd

[0027] A shut-in or fall-off test is the measurement and analysis of pressure data taken after an injection well is shut-in. When the well is shut-in, pressure shut-in or fall-off data is collected. Pressure is measured over time to track the decrease in pressure after shut-in. Collection of such transient well-test data is well known in the art. Wellhead and bottom hole pressure rise during injection. If the well remains full of liquid after shut-in, the pressure can be measured at the surface and bottom hole pressure can be calculated. In some fracturing injection operations, the injection well goes into vacuum and the fluid level falls below the surface, so bottom hole pressure gauges or sonic devices can be employed. The term “test” does not imply that the injection procedure is performed only or primarily to take pressure drop-off or other measurements, although such tests are run under certain circumstances. A shut-in or fall-off test can be performed after an operational procedure, namely, fracturing injection of a batch of waste slurry.

[0028] Of concern is continuous monitoring of fracture growth and the formation stress, which incrementally increases over multiple injection cycles, to ensure compliance and fracture containment. The injection of successive slurry cycles leads to incremental in-situ stress increase, resulting from the additional solid volume added into the injection zone over the well lifetime.

[0029] One of the key formation properties is the formation fracture pressure, which can be used to select the proper pump horsepower, pump rates, and other operational parameters for designing a hydraulic fracturing operation. Fracture closure pressure is the fluid pressure needed to initiate the opening of a fracture, and, after a fracturing operation, the pressure at which the fractures close. Closure pressure is equal to the minimum in-situ stress of the formation because the pressure required to open a fracture is the same as the pressure required to counteract the stress in the rock perpendicular to the fracture orientation.Attorney Docket: ADVA-047-PCT App. No.: tbd

[0030] In hydraulic fracturing applications, conventional pressure shut-in or fall-off pressure analyses are the main methods for predicting fracture closure pressure and formation stress. Fracture closure pressure can be estimated using predictive and analytical methods. Predictive methods are used to predict fracture closure pressure by developing empirical equations based on the formation geophysical properties, overburden pressure, pore pressure, etc. Analytical methods are used to estimate the fracture pressure during or after running a shut-in or fall-off pressure test. Analytical methods are used to monitor fracture pressure development as the in-situ stresses reorient and reservoir properties change over time.Determining Reservoir Response to Injection Operations

[0031] As stated above, Pressure Transit Analysis (PTA) is a time-consuming analysis conducted on shut-in data collected post-injection to determine reservoir response to the injection and ensure compliance. The disclosure presents a Physics Informed Machine Learning (PIML) method that enhances PTA accuracy, predicting reservoir properties to enhance CRI and waste disposal.

[0032] Generally, PTA uses injection operation features and reservoir features to determine reservoir response attributes. The reservoir features include reservoir parameters, such as permeability, porosity, rock type, Poisson’s ratio, etc. These can be considered uncontrollable variables as they are determined by the reservoir itself and are largely unchangeable. Injection operation features include variables such as injection flow rate, injection pump pressure, injection volume, batch solids content, viscosity, etc. The injection operation features can be considered controllable variables as they are designed or selected by the operations team.

[0033] Traditionally, pressure transient analysis (PTA) techniques have been used to analyze and interpret the reservoir response attributes of each injection operation. However, these methods involve time consuming analysis. To save time and make the PTA manageable, simplifiedAttorney Docket: ADVA-047-PCT App. No.: tbd assumptions are made, such as presuming homogeneous reservoir conditions and singular(linear / radial) flow regimes. Unfortunately, these assumptions may not reflect the complex subsurface conditions leading to erroneous or inaccurate calculation of reservoir response attributes. To perform the PTA, considerable amount of pressure datapoints need to be captured, including post-injection and shut-in data, which is then used in identifying flow regimes and extracting information from each region of the data (e.g., near wellbore effects, fracturing behavior, fracture closure and post closure behavior). This makes estimating or predicting the reservoir response attributes to an injection operation beforehand, or designing for optimal injection scenarios extremely difficult, if not impossible.Artificial Intelligence and Machine Learning in Subsurface Engineering

[0034] Other techniques that have seen increasing demand and application in numerous fields, including subsurface engineering, are artificial intelligence (Al) and machine learning (ML). Traditional AI / ML approaches generally rely on modeling observed system behavior via a set of statistical and computational algorithms, often without considering the underlying physical principles governing the system. While this approach may work in many instances, it is not without limitations, as it can disregard physical relationships that have been established through centuries of scientific research, or estimations that lack validity and reliability in real-world applications. Consequently, it is preferable to combine the non-linear modeling capabilities of AI / ML algorithms with established physical laws, creating a hybrid model that can accurately represent the complex nature of the phenomena being observed.

[0035] Most AI / ML models used in different fields of science and engineering, including in the oil and gas industry, are data-driven and are not strictly bound to abide by underlying physical constraints. This can result in model estimations that violate basic physical principles such asAttorney Docket: ADVA-047-PCT App. No.: tbd conservation of mass, momentum and energy. Additionally, these models may overfit and lack generalizability to unseen data. To overcome these issues known physical constraints are incorporated into the models and reject any model estimation that does not meet these constraints. Models created in this manner are generally referred to as Physics Informed Machine Learning models. Alternatively, Physics-Informed Neural Networks (PINNs) are used to emphasize that the underlying ML model is a neural network. In such models, the physical constraints are typically represented by partial differential equations (PDEs) and are embedded into the loss function of the network to ensure that the predictions follow the governing physical constraints throughout the training process.

[0036] Physics-based preprocessing, physics-based architecture, and physics-based regularization are three distinct methods for incorporating physics into machine learning models. PIML models have been used in reservoir characterization, fracture behavior prediction, and optimization of injection strategies. For instance, PINNs have been used to model fluid flow in porous media, a hybrid approach has been used for estimating the average reservoir pressure from observed pressure transient data, and PIML has been applied to subsurface applications, showing improved predictive performance over traditional methods.

[0037] Studies have also shown the effectiveness of PIML in improving the accuracy of determining reservoir properties, such as estimating reservoir connectivity and forecasting production, modelling multiphase flow, and enhancing the accuracy of BHP estimations.Advantages of Using a PIML Model to Determine Reservoir Response Attributes

[0038] The disclosure presents a novel approach leveraging Physics-Informed Machine Learning (PIML) to enhance determining reservoir response attributes. The integration of Al with physicsbased models allows us to perform a more accurate and robust analysis by learning from data whileAttorney Docket: ADVA-047-PCT App. No.: tbd adhering to physical laws. This hybrid approach improves the precision of the reservoir property estimates while ensuring that the predictions are physically consistent and reliable, which in turn creates a significant advancement over traditional methods.

[0039] As with traditional PTA, a trained PIML model can be used to determine reservoir response attributes based on injection operation features and reservoir physical features. Unlike traditional PTA, the PIML model can perform these determinations in a vastly shorter amount of time (e.g., thousands of times faster). The PIML model, unlike traditional PTA, does not rely on short-cut assumptions or simplifications to save time or make the analysis feasible. For example, the PIML model does not presume singular flow regimes. Consequently, the PIML model does not inherently produce attributes with known shortcomings.

[0040] The PIML model is also capable of considering vast amounts of data points representing reservoir or injection operation features which are not considered in PTA, such as well log data, workover data, similar field data, maintenance records, equipment type, etc., leading to more accurate determination of reservoir response attributes based on past injection operations, prediction of anticipated reservoir response attributes based on proposed injection operations, and determination of proposed injection operation features based on a preferred reservoir response attribute. That is, the PIML model is more accurate in both interpreting historical data and planning and optimizing future operations.

[0041] This results in a PMIL model that is not only more robust and capable of handling the inherent complexities of subsurface formations but can also determine the response and sensitivity of uncontrollable variables (e.g., fracture half-length, transmissivity, etc.) to changes in controllable variables (such as the injection pressure or rate, solid content, viscosity, etc.), while respecting the underlying physical principles governing the system. This integration enhances theAttorney Docket: ADVA-047-PCT App. No.: tbd accuracy of the property estimation, thus improving the reliability of the decisions drawn based on these estimates, even before an injection is conducted. Additionally, such a model can be used in preliminary planning stages for estimating the operational limits, storage capacity and performance of future CRI or waste sequestration wells.Methodology[00421 The model setup used for this study started by gathering historical injection records and their corresponding PTA from tens of thousands of injection batches and their corresponding PTA results from multiple wells over multiple years. The data were subjected to rigorous pre-processing and data warehousing operations until the resulting dataset contained a common set of attributes amongst all wells. This section outlines the steps taken in preparing the data and setting up the PIML model for estimating reservoir property for CRI and waste sequestration wells. While the disclosure benefits from the creation of a working system by the inventors, it is understood that the details of training and operating a PIML model can and will vary, and that a model, once created should continue to be trained and enhanced.

[0043] FIG. 2 is a schematic of a methodological framework for producing an exemplary PIML. The various steps are discussed in greater detail below herein. The term PIML is used throughout, although it is recognized that the terms Al, or AI / ML can be used depending on preference and as various embodiments are understood by those of skill in the art.

[0044] FIG. 2 shows a methodological framework 52 for preparing a PIML. Injection records 54 and PTA results 56 are input to a unified input data 58. The data is the pre-processed 60 using processes such as data validation 62, data imputation 64, standardization 66, and normalization 68. Feature engineering 70 includes feature generation 72 and multicollinearity reduction 74. Feature generation includes log transformation 76 in some instances, polynomial features 78, and attributeAttorney Docket: ADVA-047-PCT App. No.: tbd ratios 80. Multicollinearity reduction 74 can include VIF analysis 82 and bidirectional OLS regression 84. Modelling 86 is performed after the pre-processing and feature engineering. Modelling 86 includes algorithm selection 88, data division 90, and splitting of data into training and testing portions 92. Custom extra trees regression 93 was selected in one embodiment as the best performing regression technique. Other regressions can be used. Using a selected regression, training 94, validation 95, estimation 96 was performed while also performing physical constraints validation 97. Finally, bootstrapping 98, explained herein, was performed with results used to inform controllable and uncontrollable data division.

[0045] Data Pre-processing and conditioning

[0046] The data used in one study was gathered from ten CRI wells over a span of five years. On average, each well was subjected to two injections per day. Each batch of data was manually analyzed by a team of experts and results were assembled in separate datasets for each well. The data included, but was not limited to, static reservoir properties or features (permeability, formation thickness, etc.), injection operational features (solid content, oil content, viscosity, density, injection rate, injection pressure, pre-post flush volume, batch volume, workover history, etc.) and reservoir response attributes (closure pressure, fracture half-length, transmissivity, etc.) This extensive dataset enabled a comprehensive analysis and training of the PIML model.

[0047] Table 1 shows a list of data used in the present study.

[0048] Table 1 - List of exemplary attributes.Attorney Docket: ADVA-047-PCTApp. No.: tbdData Cleaning and Standardization

[0049] The data cleaning process involved unifying different well data into a single source, removing invalid entries, and filling in missing values. For instance, viscosities reported in mixed units were standardized, and missing values for freshwater viscosities were imputed. Additionally, mixed batches were split into separate fluids to ensure consistency. In cases where data were missing for some of the entries (less than 100 missing values in the entire database), imputation techniques based on six nearest neighbors (KNN=6) were used to estimate the missing values, as opposed to using min, mean or maximum.

[0050] Subsequently, the data was split into smaller clusters that better represented the inherent properties of the data and thus would respond more uniformly. The number of clusters was determined based on the distortion score elbow method applied to K-Means algorithm.

[0051] FIG. 3 is a graphical representation of a distortion score elbow for K-means clustering according to aspects of the disclosure. A distortion score (sum of squared distances) elbow for K- mcans clustering was applied to the raw data. This plot suggests that choosing six clusters is likely to give the best separation of data points by balancing between having a low distortion score andAttorney Docket: ADVA-047-PCT App. No.: tbd not increasing the complexity unnecessarily. The data was further graphed onto a threedimensional representation of data points projected into Principal Component (PC) space and color coded by cluster number for the six clusters. The plot showed the clusters have good separation and overlap between clusters, highlighting the distinct groupings and spatial relationships among the data points.Feature Engineering

[0052] To enhance the accuracy of the models, a set of derived features was introduced to the model. These features included several engineered features, such as logarithmic transformation of permeability or that of apparent viscosity, as well as a second-degree polynomial feature generation model based on permeability, total injected slurry and maximum density. Since several of the parameters subjected to logarithmic transformation were small, the natural logarithm transformation, i.e., log (1 + x), was used to ensure that variance of these attributes is preserved, and the data is normally distributed. Additional feature engineering included determining derived attributed, such as the ratio of bottom-hole-pressure, to that of the well-head, or the ratio of solid contents, as well as the ratio of viscosity to density. These features, along with the initial attributes were subjected to subsequent processing and data cleaning practices described in this section.Standardization of data

[0053] To remove any bias or sway from the model, input data were standardized prior to use in the model. Standardization involved scaling the data to a common range (i.e., 0 to 1), for all observations in the dataset. Additionally, the mean value of each attribute was subtracted from that attribute, so that the new set of data has zero mean and unit variance, which aids in the convergence of the learning algorithms and improves the accuracy of the predictions. This step which resultedAttorney Docket: ADVA-047-PCT App. No.: tbd in Z-Normalized, also known as standardized, values is critical to ensure that the performance of the model is not affected by the relative scale of different attributes.

[0054] Data imputation techniques were used to handle missing values, ensuring that the dataset was complete and ready for analysis. Feature ranking and clustering techniques were also applied to identify the most important features in predicting closure pressure and other reservoir properties.Minimization of Multicollinearity

[0055] To minimize collinearity and interdependence of attributes, several pre-processing steps were performed, including Variance Inflation Factor (VIF) and bi-directional stepwise Ordinary Least Squares (OLS) regression. VIF analysis was performed for each predictor to quantify the degree of multicollinearity, with a VIF value exceeding 10 as the threshold indicating high multicollinearity. If an attribute exceeded this threshold, it was marked for exclusion from further analysis.

[0056] OLS regression was performed in a stepwise manner, where during the forward selection step, attributes were added one at a time and in the backward elimination, features that did not contribute significantly to the model were removed. Judgement on this level of contribution from each attribute was done based on their p-value, which shows the significance of the attribute in explaining the variance of the dependent variable. A threshold of 0.05 was used for the p-value and only attributes whose p-value was less than the threshold (i.e., those which indicated strong evidence against the null hypothesis) were retained.Machine Learning Algorithm Selection

[0057] An appropriate machine learning algorithm was selected, the physical constraints defined, and these components were integrated into a cohesive framework. To this end, fourteen different regressors were compared, including tree-based algorithms (random forest, decision tree, extraAttorney Docket: ADVA-047-PCT App. No.: tbd trees regressor, gradient boosting, Adaboost), neural network-based models (multi-layer perceptron), linear models (linear, ridge and lasso regression models, elastic net, stochastic gradient decent, and Bayesian ridge regression), support vector machines, and k- nearest neighbor regression. Among these models, the tree-based models, and in particular, the Extra-trees regressor model, performed better than others and resulted in the least Mean Squared Error (MSE) as well as the lowest Mean Absolute Error (MAE), and the highest value of R2. As a result, the extra-trees regressor was selected for one exemplary embodiment, although alternative embodiments can use other regressors.Controllable vs. Uncontrollable Features

[0058] Situations are encountered where the outcome of an operation is not known until the injection batch is carried out and PTA is conducted on the observed pressure data points. In this disclosure, features are divided into controllable and uncontrollable features. The controllable features are operational parameters that can be set or altered at the surface and are independent of each other, such as the injection rate, or viscosity of the injected fluids. Uncontrollable features refer to the dependent features, or reservoir parameters that change in response to the injected fluids. Examples of uncontrollable attributes include the fracture closure pressure, fracture halflength and transmissivity.

[0059] Error! Reference source not found, lists controllable and uncontrollable features defined and used here. A goal in designing the PIML model is to create a set of models that rely on a minimal set of attributes, namely the controllable attributes, and estimate the uncontrollable attributes. In doing so, the formation responses to the operational choices can be predicted, which in turn can help managing the risk and maximizing operational effectiveness.Attorney Docket: ADVA-047-PCTApp. No.: tbdBootstrap Estimation

[0060] ML models perform best when they are trained on a wide range of independent and noncorrelated attributes. As established above, controllable and uncontrollable variables are separated, thus allowing the model to estimate the dependent attributes with the least number of inputs. To increase model accuracy, however, dependent attributes are utilized for training the model and subsequent estimations.

[0061] To achieve this, a gradual inclusion of dependent attributes is used in subsequent models. This approach, which can be referred to as “bootstrapping”, allows the user to achieve the most accurate models while still providing no more than the minimum data, i.e., the controllable attributes. The sequence of bootstrapping and the gradual introduction of dependent attributes is determined through an initial assessment of all dependent attributes to available attributes, followed by a ranking of dependent attributes to independent features. Least dependent attributesAttorney Docket: ADVA-047-PCT App. No.: tbd were then selected as the first target attributes and were introduced as input features for the next dependent attribute in the ranking. The uncontrollable (dependent) attributes listed in Error! Reference source not found, are listed based on their ranking.Physical Constraints

[0062] To ensure that the models follow physical laws, a custom Extra Trees Regressor class was created that utilized the standard extra trees regressor as its base estimator and used a set of physics informed constraints in its prediction phase. This physics-based post-processing approach ensured that the predictions from the model complied with the constraints and if violated, they were rejected. Exemplary constraints are addressed below.N on-Negativity Constraint:

[0063] Since pressure values cannot be negative, a non-negativity constraint is introduced to ensure that the fracture closure pressure is always positive.Relationship with Minimum Horizontal Stress

[0064] Fracture closure pressure is typically close to or slightly above the minimum horizontal stress in the formation. Hence, the predictions were constrained to be greater than or equal to the minimum horizontal stress.where m11M,,m. is the minimum horizontal stress.Maximum Pressure Constraint

[0065] In addition to the non-negativity constraint, the fracture closure pressure should be less than the maximum in-situ stress, which in a normal faulting regime, as was the assumption in the study, is usually the overburden stress or the maximum horizontal stress.Attorney Docket: ADVA-047-PCTApp. No.: tbd^closure — Max where aMaxis the maximum in-situ stress.Training and Validation

[0066] Standard practices for data preparation and division between training and validation sets were followed in the present work. Input data was randomly split into a training and a test set, with a proportion of 80-20, and the test data was not presented to the model during the training process. This means that 80% of the data was used for training the model, while the remaining 20% was reserved for testing its performance. This split should help in evaluating the generalizability of the model to new, unseen data, while preventing overfitting. All data points, regardless of their assignment to the training or test set, underwent identical scaling and standardization procedures.Model Performance

[0067] The initial results from the PIML model indicated good accuracy of reservoir property estimation compared to traditional PTA methods. Error! Reference source not found, show the relationship between the predicted attributes and the observed values. More specifically, FIG. 4A shows a plot of Expected verse Predicted Values for Injectivity (in barrels per day (bpd) / psi). FIGS. 4B-J are similar plots for expected verses predicted values for, respectively, bottom hole instantaneous shut-in pressure, formation stress, closure pressure, wellhead pressure at closure, closure time, skin factor, fracture half-length (feet), thermal conductivity to heat transfer coefficient (Kh / U), and leak off time to 1000 psi (hour).

[0068] Each point on the plot represents a single prediction from the Extra Trees Regressor model against its corresponding expected value. The red diagonal line represents the ideal scenario where the predicted values perfectly match the expected values, implying perfect model accuracy. Points located on this line indicate exact predictions, while deviations from this line highlight predictionAttorney Docket: ADVA-047-PCT App. No.: tbd errors. It can be observed that the Extra Trees Regressor is reasonably effective at predicting these target attributes, though there are areas where the model could be improved to enhance prediction accuracy.

[0069] As depicted in Error! Reference source not found., the PIML models achieved reasonably high accuracy without reliance on any of the reservoir properties or formation response attributes. The ten different models that were trained have been able to capture anywhere from 0.732 (Leakoff time, FIG. 4J) to 0.993 (Injectivity, Error! Reference source not found.A) of variance in the data in the unseen test datasets. The bootstrapping approach introduced here enables the model to establish the required features and foundations for estimating more complex and harder to capture attributes, such as fracture closure pressure (Error! Reference source not found.), after generating the less convoluted attributes, such as injectivity (Error! Reference source not found.-a) or formation stress (Error! Reference source not found.).

[0070] It is important to note that these models were subjected to rigorous pre-processing steps (e.g., VIF), which were subsequently repeated after introduction of each dependent variable (e.g., Injectivity, Bottom-hole Instantaneous Shut-in Pressure, etc.). This ensures that the models are free of multicollinearity and that predictions remain reliable and interpretable.Feature Importance

[0071] FIGS. 5A-B show the importance of various attributes in predicting fracture closure pressure using the Extra Trees Regressor model in one of the wells in the study. Feature importance quantifies the contribution of each feature to the prediction model, with higher values indicating greater significance. Feature importance analysis revealed that certain attributes, such as solid content Non- Aqueous-Fluids (NAF), weight of the water-based- md, and average well head pressure, played a critical role in predicting closure pressure. It is important to note that from anAttorney Docket: ADVA-047-PCT App. No.: tbd operational standpoint presence of NAFs is a major hurdle in CRI operations as it can result in foaming and pressure loss, and leads to lowered storage capacity of the well. This observation is backed by the feature importances observed in this study.

[0072] However, it is important to note that not all wells have to deal with NAF or large quantities of it. As a result, the feature importance pertaining to all wells in this study shows a slightly different behavior, in which fluid viscosity, solid content in water based mud (WBM) and density, play a more significant role than solid content of NAF.

[0073] FIG. 6 is a flow chart showing an exemplary method 100 for creating and implementing the PMIL model in accordance with aspects of the disclosure.

[0074] At 102 is a method for training an Al or PMIL model. At 104 sensors measure physical data at a well site. At 106 measured and known parameters related to the injectate slurry, or injectant, are acquired by measurement and / or determination, such as solids content, oil content, viscosity, density, etc. At 108 injection operational parameters are acquired or determined, such as injection flow rate, injection pressure, pump pressure, waste type, viscous pill volume, fluids volume, etc. At 110, reservoir response data is determined. For example, data can be calculated through a process such as Pressure Transit Analysis. Reservoir response attributes can include closure pressure, fracture half-length, bottom hole instantaneous shut-in pressure, injectivity, skin factor, wellhead pressure at fracture closure, leak-off time, etc. At 112, physical constraints on possible determinations of reservoir response attributes are identified, acquired, or determined.

[0075] At 114, the data acquired at the previous steps are input to an artificial intelligence or machine learning model and the model is trained. The data from previous steps may be provided to the model cumulatively, in part, in separated data sets, step-wise, or as otherwise known in theAttorney Docket: ADVA-047-PCT App. No.: tbd art. The model is trained as explained above and as known in the art. This results in a trained PIML per the explanations herein.

[0076] At 116, the trained PIML is employed. At 118, in some embodiments, the PIML, either directly or through or in combination with another computer or computerized network, communicates with and gives instructions to one or more equipment controllers capable of operating the well-site equipment. The operation of well equipment by controller is known in the art and not described in detail here.

[0077] In some embodiments, the PIML model is used to conduct feasibility studies, for example, in the pre-construction phase of a facility or pre-operational phase of an injection operation or series of operations. A method is provided for conducting feasibility studies for slurry injection wells by employing AI / ML models trained on historical and operational datasets. The training data includes reservoir physical features and injection operation features, for example: geological data, drilling parameters (rate of penetration, weight on bit, drilling time, lost circulation zones), well logs, water depth, anticipated well life, pressure and injection volume histories, waste type and generation rates. The training data further includes PT A data and reservoir response attributes. The AI / ML or PIML is capable of considering vastly more information and data than a manual function feasibility study. The AI / ML model processes this data to predict the following for the new location: estimate drilling programs and drilling costs, predict well storage capacity and operational life, determine pumping requirements and necessary additives, quantify equipment capacities, and generate economic forecasts (construction cost, operational balance, and lifecycle economics).

[0078] In other embodiments, the PIML is used to perform Long-Term Optimization and Predictive Maintenance. The disclosure provides for long-term optimization of injection wellAttorney Docket: ADVA-047-PCT App. No.: tbd performance. AI / ML models are trained using operational datasets such as: fluid properties, Waste nature, downhole pressures and temperatures, reservoir permeability, fracture geometry and propagation parameters, and formation integrity characteristics. The system outputs: predicted and updated well life and remaining capacity, updated injection parameter recommendations to extend operational life, and maintenance scheduling (valve replacement, tubing changeouts, packer resets, well clean-outs, reperforation, or shifting injection to new zones). This predictive maintenance framework ensures operational continuity and provides economic planning tools for asset owners.

[0079] In another embodiment, the PIML model is used to provide Adaptive Real-Time Operation and Control, such as by the process seen in FIG. 6 at process 120. The system incorporates an AI / ML-driven feedback loop for dynamic adjustment of injection operations. Data is taken in real time at the well during an injection operation at 122. Real-time inputs can include pressure trends and anomaly signals such as: sudden pressure increases, sudden pressure drops, and noisy or unstable pressure signals. The data is communicated to the PIML at 124, which performs an analysis to get reservoir responsive attributes. The determined attributes can be analyzed for negative outcomes or dangers of such, or for optimization opportunities, in which case, the PIML model, directly or through additional computers and networks, can communicate 126 to one or more controllers to effect one or more changes to the injection operation at 128. The AI / ML engine classifies these patterns into operational issues such as: well plugging, fracture breakout, and / or pump cavitation. Based on these classifications, the system automatically recommends or executes corrective actions including: adjusting injection rate, switching to water flush cycles, or reconfiguring pump operations. The reservoir response attributes and underlying measured data can then be communicated back to the PIML model as further training or learning, as indicated byAttorney Docket: ADVA-047-PCT App. No.: tbd the dotted lines. This closed-loop optimization improves operational stability, reduces downtime, and mitigates the risk of well damage.

[0080] As an example, a proposed set of injection operation parameters (flow rate, viscosity, solids content, etc.) can be input to the PIML, with the PIML then determining or predicting the resulting reservoir response attributes. As another example, the PIML can provide, at a user request, a proposed injection plan of one or more injections, specifying the proposed injection operation features, based on corresponding predicted reservoir response attributes. In another example, the PIML can provide an optimized injection plan including injection operation features based on a selected optimization or reservoir response goal, such as maximum solids disposal. In another embodiment, the PIML can provide a series of injection operations, over a long period of time, designed to maximize or optimize long term goals, such as maximizing reservoir capacity. Persons of skill in the art will recognize that certain of the enumerated steps can be performed in orders different than those shown, simultaneously, skipped when unnecessary, repeated, performed altematingly, etc. All of the permutations and combinations of process steps are not laid out in the interest of space and time constraints.

[0081] It is understood by those of skill in the art that the PIML model is capable of performing in seconds a determination of, for example, reservoir response attributes, that would take a professional engineer, with computerized assistance, hours of work. It is also understood that the PIML is capable of taking into account, and running algorithms based on, a virtually unlimited number of data points across a wide range of controllable and uncontrollable variables, while a human endeavor would require a selection of only a limited data set expected to have the greatest effect on determining outcomes and using short-cut methods such as assumptions of characteristics or responses, or intentional simplification of complex factors. It is also understood that traditionalPage 1Attorney Docket: ADVA-047-PCT App. No.: tbd methods of performing Pressure Transit Analysis, and the like, often yield results so delayed as to prevent their use to prevent non-compliance, avoid reservoir- or well-damaging outcomes, or take timely corrective action, for example, during an injection operation.

[0082] It is also understood that the PIML model is capable of performing a task (e.g., predicting reservoir response attributes based on historical or anticipated injection operation features) much faster - orders of magnitude - than a computer reservoir model system which models a reservoir based on reservoir features. The added speed, efficiency and accuracy of the PIML model makes on-the-fly operational changes more feasible.Automated Equipment Operation

[0083] The methods can also include fully or partially automated equipment control. A network can provide connectivity between facilities, sensors, controllers, and the like. Equipment controllers are commercially available and known in the art and often comprise a computer device, having memory and processing, and various subsystems (communication, monitoring, metering, data management, safety overrides, etc.). Controllers control the equipment, performing tasks (e.g., on / off, power up / down, open / close, etc.) on the equipment. Controllers typically include user interfaces (e.g., screens) allowing monitoring, simple programming, and semi-automated equipment control. The controller provides connectivity to the network and computer control system, Common network protocols (e.g., LonWorks, BACnet, Modbus, etc.) can be used. Controllers can have multiple communication ports, wired and / or wireless, for connectivity to the network, and can communicate via Ethernet, OPC, BACnet IP, Modbus TCP, SNMP, or other protocol.

[0084] Relatedly, the network can include gateways associated with the sensor equipment (meters, sub-meters, smart meters, and Data Recorder meters, etc.), equipment controllers (e.g., generatorAttorney Docket: ADVA-047-PCT App. No.: tbd or pump gateways), etc. A gateway can be a physical unit connected to equipment or a software application running at some level of the network. Controllers can include or serve as gateways, providing connectivity integrally with other services of the device.

[0085] The network can have multiple sub-networks for various functions and controls. The network provides connectivity between facility equipment, sensor equipment, operator computers, the computer control system, etc. The network can employ multiple users, buildings, systems, etc. Network communication can be between: gateways and equipment; pieces of equipment; gateways; equipment and the internet; etc.

[0086] Exemplary equipment which can be controlled by a computerized control system, at the direction of the program, or associated control software, include electrical equipment, surface equipment, scrubbers, separators, mixers, blenders, agitators, filter separators, coalescers, knockout systems, piping, hoses, valving, tanks, pumps of all kinds, generators, actuators, dehydrators, thermal treatment systems, vacuum systems, compressors, stim equipment, and instrumentation and controls.

[0087] Automation is controlled by the controllers as informed by communications from, directly or indirectly, the Al model and associated computers. Based on real time or historical measured data, pulled from current monitoring or archives, and the current operation, the control system communicates operating instructions or tasks to the indicated equipment. For example, when a slurrification procedure is underway according to a design or schedule input to or created by the system, monitored sensor equipment may provide measured data regarding current slurry parameters (e.g., viscosity). The control system and software compares monitored and planned parameters, determines processes to correct current parameters to match the planned parameters. The system calculates necessary operating parameters for the correction (e.g., amounts, rates,Attorney Docket: ADVA-047-PCT App. No.: tbd materials, etc.) and determines corresponding tasks for facility equipment to undertake. In this example, the system corrects an errant slurry viscosity by communicating task instructions (e.g., by signals, data, computer code, etc.), via the network, to corresponding facility equipment, and operating the equipment to increase a fluid flow rate, activate a mixer, etc., to determined operating parameters (e.g., rates, speeds, percentage power, etc.). Further monitoring by the system can confirm achievement of planned viscosity or indicate a need for further tasks.

[0088] In an embodiment, the control system provides recommended tasks to the operator (e.g., increase water flow from a supply pipe to a suggested rate), communicated via the network to an operator station. In one embodiment, the operator then makes those changes manually or via local controller. In another embodiment, the operator either allows or disallows the recommended tasks. If allowed, the control system automatically operates the equipment accordingly. Operation of equipment requires connectivity and communication through the network and appropriate controllers and gateways. The controllers and gateways receive and interpret incoming messages and perform the action on the equipment. Thus, the computerized control service receives and analyzes incoming data, and if indicated takes one or more actions, communicates with facility equipment gateways and / or controllers, and actually alters and controls the operation of facility equipment, thereby changing the operating parameters of an on-going operation.Exemplary Embodiments

[0089] The following non-limiting examples of embodiments are provided in support of the disclosure and the appended claims.

[0090] Example 1. A method for controlling a fracturing injection operation in a well extending through a subterranean reservoir, the method comprising: sensing, using sensors at the well, current injection operation features; receiving the sensed current injection operation features at anAttorney Docket: ADVA-047-PCT App. No.: tbdAl model, the Al model trained using historical injection operation features, historical reservoir features, and historical reservoir response attributes from historical fracturing injection operations, the Al model incorporating physics-based constraints; predicting, using the Al model, reservoir response attributes based on the received current injection operation features; communicating, based on the predicted reservoir response attributes, a change to the current or future injection operation features; and making, at the well, the change to the current or future injection operation features.

[0091] Example 2. The method of example 1, wherein the historical injection operating features include reservoir parameters of at least one reservoir, the reservoir features including at least on of permeability, porosity, rock type, or Poisson’s ratio.

[0092] Example 3. The method of any preceding example, wherein the historical injection operation features include injection operation features from a plurality of fracturing slurry injection operations and include at least one of injection flow rate, injection pump pressure, injection volume, batch solids content, slurry viscosity, slurry density, pre-flush volume, post-flush volume, or batch volume.

[0093] Example 4. The method of any preceding example, wherein the historical reservoir response attributes include reservoir response attributes calculated from a plurality of fracturing slurry injection operations and include at least one of closure pressure, fracture half-length, transmissivity, bottom hole instantaneous shut-in pressure, skin factor, well head pressure at closure, closure time since shut-in, leak-off time, and formation stress.

[0094] Example 5. The method of any preceding example, wherein the sensors at the well include at least one sensor taken from the group comprising: bottom hole pressure, temperature,Attorney Docket: ADVA-047-PCT App. No.: tbd wellhead pressure, slurry parameter, solids content, viscosity, density, fall-off test, shut-in test, pressure test, tubing test, density, flow rate, and biomass content sensors.

[0095] Example 6. The method of any preceding example, wherein the physics-based constraints are used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.

[0096] Example 7. The method of any preceding example, wherein the physics-based constraints include at least one of a non-negativity constraint, a relationship between closure pressure and minimum horizontal stress, or a maximum pressure constraint.

[0097] Example 8. The method of any preceding example, wherein the Al model is a Physics- Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor or regression algorithm taken from the group consisting of: tree-based algorithms, random forest, decision tree, extra-trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron, linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent, Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.

[0098] Example 9. The method of any preceding example, wherein the Al model is a Physics- Informed Machine Learning (PIML) model, and wherein the PMIL model uses an extra-trees regressor model.

[0099] Example 10. A method for optimizing a fracturing injection operation in a well extending through a subterranean reservoir, the method comprising: inputting to an Al model one or more reservoir response attributes to optimize, the Al model trained using historical injection operation features, historical reservoir features, and historical reservoir response attributes fromAttorney Docket: ADVA-047-PCT App. No.: tbd historical fracturing injection operations, the Al model incorporating physics-based constraints; inputting to the Al model reservoir features of the subterranean reservoir; optimizing, using the Al model, the one or more reservoir response attributes based on the reservoir features of the subterranean reservoir; identifying, using the Al model, a first set of fracturing injection operation features corresponding to the optimized reservoir response attributes; running a first fracturing injection operation at the well, the first fracturing injection operation using the identified first set of fracturing injection operation features.

[0100] Example 11. The method of claim 10, wherein the historical injection operating features include reservoir parameters of at least one reservoir, the reservoir features including at least on of permeability, porosity, rock type, or Poisson’s ratio; wherein the historical injection operation features include injection operation features from a plurality of fracturing slurry injection operations and include at least one of injection flow rate, injection pump pressure, injection volume, batch solids content, slurry viscosity, slurry density, pre-flush volume, post-flush volume, or batch volume; and wherein the historical reservoir response attributes include reservoir response attributes calculated from a plurality of fracturing slurry injection operations and include at least one of closure pressure, fracture half-length, transmissivity, bottom hole instantaneous shut-in pressure, skin factor, well head pressure at closure, closure time since shut-in, leak-off time, and formation stress.

[0101] Example 12. The method of examples 10-11, wherein the physics-based constraints are used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.

[0102] Example 13. The method of examples 10-12, wherein the Al model is a Physics- Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor orAttorney Docket: ADVA-047-PCT App. No.: tbd regression algorithm taken from the group consisting of:, random forest, decision tree, extra-trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron, linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent, Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.

[0103] Example 14. The method of examples 10-13, wherein the Al model is a Physics- Informed Machine Learning (PIML) model, and wherein the PMIL model uses a regressor model taken from the group consisting of: a tree-based algorithm, a random forest algorithm, a decision tree algorithm, an extra-trees regressor algorithm, a gradient boosting algorithm, and an Adaboost algorithm.

[0104] Example 15. The method of examples 10-14, further comprising: identifying, using the Al model, a second set of fracturing injection operation features corresponding to the optimized reservoir response attributes; and running a second fracturing injection operation at the well, the second fracturing injection operation using the identified first set of fracturing injection operation features.

[0105] Example 16. The method of examples 10-15, further comprising: sensing, using sensors at the well, current injection operation features; receiving the sensed current injection operation features at the Al model; predicting, using the Al model, reservoir response attributes based on the received current injection operation features; communicating, based on the predicted reservoir response attributes, a change to the current or future injection operation features; and making, at the well, the change to the current or future injection operation features.

[0106] Example 17. A method for conducting a feasibility study for a fracturing injection facility for performing multiple fracturing injection operations in a subterranean reservoir, the method comprising: inputting, to an Al model, reservoir features for a selected reservoir, the Al modelAttorney Docket: ADVA-047-PCT App. No.: tbd trained using historical injection operation features, historical reservoir features, and historical reservoir response attributes from historical fracturing injection operations, and historical injection operation economic features, the Al model incorporating physics-based constraints; predicting, using the Al model, reservoir response attributes based on a series of injection operation features for the reservoir features of the selected reservoir; determining, for the fracturing injection operation, a proposed series of fracturing injection operations, and at least one of: drilling costs, predicted well storage capacity, predicted well operational life, pumping requirements, equipment capacities, and economic forecasts.

[0107] Example 18. The method of example 17, further comprising: performing the proposed series of fracturing operations at the subterranean reservoir.

[0108] Example 19. The method of examples 17-18, wherein the historical injection operation economic features are taken from the group consisting of: geological data, drilling parameters, rate of penetration, weight on bit, drilling time, lost circulation zones, well logs, water depth, historical well life, pressure and injection volume histories, waste types, generation rates, drilling programs, drilling costs, well storage capacities, well operational lives, pumping requirements, equipment capacities, construction costs, operational balances, and lifecycle economics.

[0109] Example 20. The method of examples 17-19, wherein the physics-based constraints are used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.

[0110] Example 21. The method of examples 17-20, wherein the AT model is a Physics- Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor or regression algorithm taken from the group consisting of:, random forest, decision tree, extra-trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron,Attorney Docket: ADVA-047-PCT App. No.: tbd linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent, Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.

[0111] Example 22. The method of examples 17-21, wherein the Al model is a Physics- Informed Machine Learning (PIML) model, and wherein the PMIL model uses a regressor model taken from the group consisting of: a tree-based algorithm, a random forest algorithm, a decision tree algorithm, an extra-trees regressor algorithm, a gradient boosting algorithm, and an Adaboost algorithm.

[0112] Example 23. A method for conducting a long-term optimization program for a fracturing injection facility performing multiple fracturing injection operations in a subterranean reservoir, the method comprising: inputting, to an Al model, reservoir features for a selected reservoir, the Al model trained using historical injection operation features, historical reservoir features, and historical reservoir response attributes from historical fracturing injection operations, the Al model incorporating physics-based constraints; predicting, using the Al model, reservoir response attributes based on a series of injection operation features for the reservoir features of the selected reservoir; determining, for the fracturing injection operation, a proposed series of fracturing injection operations for optimizing at least one of: well operational life, well injection capacity, and number of fracturing injection operations on the well.

[0113] Example 24. The method of example 23, further comprising: performing the proposed series of fracturing injection operations at the well.

[0114] Example 25. The method of examples 23-24, further comprising: inputting to the Al model injection operation features from one or more of the performed fracturing injection operations; updating the proposed series of fracturing injection operations with updated injection operation features, thereby extending the operational life of the well.Attorney Docket: ADVA-047-PCT App. No.: tbd

[0115] Example 26. The method of examples 23-25, further comprising: using the Al model, determining a maintenance schedule for well equipment.

[0116] Example 27. The method of examples 23-26, wherein the historical injection operating features include reservoir parameters of at least one reservoir, the reservoir features including at least on of permeability, porosity, rock type, or Poisson’s ratio; wherein the historical injection operation features include injection operation features from a plurality of fracturing slurry injection operations and include at least one of injection flow rate, injection pump pressure, injection volume, batch solids content, slurry viscosity, slurry density, pre-flush volume, post-flush volume, or batch volume; and wherein the historical reservoir response attributes include reservoir response attributes calculated from a plurality of fracturing slurry injection operations and include at least one of closure pressure, fracture half-length, transmissivity, bottom hole instantaneous shut-in pressure, skin factor, well head pressure at closure, closure time since shut-in, leak-off time, and formation stress.

[0117] Example 28. The method of examples 23-27, wherein the physics-based constraints are used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.

[0118] Example 29. The method of examples 23-28, wherein the Al model is a Physics- Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor or regression algorithm taken from the group consisting of:, random forest, decision tree, extra-trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron, linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent,Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.Attorney Docket: ADVA-047-PCT App. No.: tbd

[0119] Example 30. A system for controlling a fracturing injection operation in a well extending through a subterranean reservoir, the system comprising: at least one sensor positioned at the well for sensing current injection operation features; memory storing an Al model trained using historical injection operation features, historical reservoir features, and historical reservoir response attributes from historical fracturing injection operations, the Al model incorporating physics-based constraints; one or more processors operatively coupled to the at least one sensor and the memory, the one or more processors configured to: predict, using the Al model, reservoir response attributes based on the received current injection operation features; communicate, based on the predicted reservoir response attributes, a change to the current injection operation features or future injection operation features; and effect a change in the injection operation features at the well.

[0120] Example 31. The system of example 30, wherein the historical injection operating features include reservoir parameters of at least one reservoir, the reservoir features including at least on of permeability, porosity, rock type, or Poisson’s ratio.

[0121] Example 32. The system of examples 30-31, wherein the historical injection operation features include injection operation features from a plurality of fracturing slurry injection operations and include at least one of injection flow rate, injection pump pressure, injection volume, batch solids content, slurry viscosity, slurry density, pre-flush volume, post-flush volume, or batch volume.

[0122] Example 33. The system of examples 30-32, wherein the historical reservoir response attributes include reservoir response attributes calculated from a plurality of fracturing slurry injection operations and include at least one of closure pressure, fracture half-length,Attorney Docket: ADVA-047-PCT App. No.: tbd transmissivity, bottom hole instantaneous shut-in pressure, skin factor, well head pressure at closure, closure time since shut-in, leak-off time, and formation stress.

[0123] Example 34. The system of examples 30-33, wherein the sensors at the well include at least one sensor taken from the group comprising: bottom hole pressure, temperature, wellhead pressure, slurry parameter, solids content, viscosity, density, fall-off test, shut-in test, pressure test, tubing test, density, flow rate, and biomass content sensors.

[0124] Example 35. The system of examples 30-34, wherein the physics-based constraints are used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.

[0125] Example 36. The system of examples 30-35, wherein the physics-based constraints include at least one of a non-negativity constraint, a relationship between closure pressure and minimum horizontal stress, or a maximum pressure constraint.

[0126] Example 37. The system of examples 30-36, wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor or regression algorithm taken from the group consisting of: tree-based algorithms, random forest, decision tree, extra-trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron, linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent, Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.

[0127] Example 38. The system of examples 30-37, wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model uses an extra-trees regressor model.Computerized Systems and ComponentsAttorney Docket: ADVA-047-PCT App. No.: tbd

[0128] Computer and Computerized Systems. The systems, methods, and other embodiments according to the disclosure include computerized systems requiring the performance of one or more methods or steps performed on or in association with one or more computer.

[0129] The term computer as used herein and in the claims is not and is not intended to be a means- plus-function term or element. A computer is a programmable machine having two principal characteristics, namely, it responds to a set of instructions in a well-defined manner and can execute a pre-recorded list of instructions (e.g., a program). A computer according to the present disclosure is a device with a processor and a memory. For purposes of this disclosure, a computer includes a server, a personal computer, (i.e., desktop computer, laptop computer, netbook), a mobile communications device, such as a mobile “smart” phone, and devices providing functionality through internal components or connection to an external computer, server, or global communications network (such as the internet) to take direction from or engage in processes which are then delivered to other system components.

[0130] Those of skill in the art recognize that other devices, alone or in conjunction with an architecture associated with a system, can provide a computerized environment for carrying out the methods disclosed herein. The method aspects of the disclosure are computer implemented and, more particularly, at least one step is carried out using a computer.

[0131] General-purpose computers include hardware components. A memory or memory device enables a computer to store data and programs. Common storage devices include disk drives, tape drives, thumb drives, and others known in the art. An input device can be a keyboard, mouse, hand-held controller, remote controller, a touchscreen, and other input devices known in the art. The input device is the conduit through which data and instructions enter a computer. An output device is a display screen, printer, or other device letting the user sense what the computer hasAttorney Docket: ADVA-047-PCT App. No.: tbd accomplished, is accomplishing, or is expected to accomplish. A central processing unit (CPU) is the “brains” of the computer and executes instructions and performs calculations. For example, typical components of a CPU are an arithmetic logic unit (ALU), which performs arithmetic and logical operations and a control unit (CU) which extracts instructions from memory, decodes and executes them, calling on the ALU when necessary. The CPU can be a micro-processor, processor, one or more printed circuit boards (PCBs). In addition to these components, others make it possible for computer components to work together or in conjunction with external devices and systems, for example, a bus to transmit data within the computer, ports for connectivity to external devices or data transmission systems (such as the internet), wireless transmitters, read and readwrite devices, etc., such as are known in the art.

[0132] A server is a computer or device on a network that manages network resources. There are many different types of servers, including remote, live and network access servers, data servers, member servers, staging servers, etc. A server can be hardware and / or software that manages access to a centralized resource or service in a network. For purposes of this disclosure, the term “server” also includes “virtual servers” which can be hosted on actual servers.

[0133] A computer network or data network is a communications network allowing computers to exchange data, with networked devices passing data to each other on data connections. Network devices that originate, route, and terminate data are called nodes. The connections (links) between nodes are established using wire or wireless media. Nodes can include hosts, such as PCs, phones, servers, and networking hardware. Devices are networked together when one device is able to exchange information with the other device whether or not they have a direct connection to each other. Computer networks support applications such as access to the World Wide Web (WWW) or internet, shared use of application and storage servers, printers, and useAttorney Docket: ADVA-047-PCT App. No.: tbd of email and instant messaging applications. Computer networks differ in the physical media to transmit signals, protocols to organize network traffic, network size, topology, and organizational intent.

[0134] Artificial Intelligence (Al) is a known term of the art referring to machines programmed in software to mimic human intelligence, or perform tasks normally requiring human perception and intelligence, using rules-based systems, logic-based reasoning, or machine learning.

[0135] Machine Learning (ML) is a subset of Al and a term of the art referring to machines or computers which use algorithms to “learn” or be trained in relationships between data sets and make inferences about new data, focusing on pattern recognition. ML allows the machine to make decisions or predictions without explicit, coded instructions. Machine learning can include the use of artificial neural networks or deep learning. Generally, deep learning relies on distributed “networks” of mathematical operations that provide the ability to learn the relationships between complex and voluminous data. Deep learning may require large amounts of data and computational resources.

[0136] A (control) gateway is a network node that acts as an entrance to another network. In homes, the gateway is the ISP (internet service provider) that connects the user to the internet. In enterprises, the gateway node often acts as proxy server and firewall. The gateway is also associated with a router, which uses headers and forwarding tables to determine where packets are sent, and a switch, which provides the actual path for the packet in and out of the gateway.

[0137] A (control) gateway for the particular purpose of connection to identified cloud storage, often called a cloud storage gateway, is a hardware-based and / or software-based appliance located on the customer premises that serves as a bridge between local applications and remote cloudbased storage and are sometimes called cloud storage appliances or controllers. A cloud storageAttorney Docket: ADVA-047-PCT App. No.: tbd gateway provides protocol translation and connectivity to allow incompatible technologies to communicate transparently. The gateway can make cloud storage appear to be an NAS (network attached storage) filer, a block storage array, a backup target, a server, or an extension of the application itself. Local storage can be used as a cache for improved performance. Cloud gateway product features include encryption technology to safeguard data, compression, de-duplication, WAN optimization for faster performance, snapshots, version control, and data protection.

[0138] A “bridge” connects two (local) networks, often connecting a local network using an internet router.

[0139] A router forwards data packets along networks and is connected to at least two networks, commonly two LANs, WANs, or a LAN and its ISP’s network. Routers are located at “gateways,” the places where two or more networks connect. Routers use headers and forwarding tables to determine paths for forwarding packets and use protocols to communicate with each other to configure a route between hosts.

[0140] The disclosure includes one or more databases for storing information relating to aspects of the disclosure. The information stored on a database can, for example, be related to a private subscriber, a content provider, a host, a security provider, etc. One of ordinary skill in the art appreciates that “a database” can be a plurality of databases, each of which can be linked to one another, accessible by a user via a user interface, stored on a computer readable medium or a memory of a computer (e.g., PC, server, etc.), and accessed by users via global communications networks (e.g., the internet) which may be linked using satellites, wired technologies, or wireless technologies.

[0141] Data services can include applications for data processing, querying, and manipulation. For example, a Structured Query Language (SQL) or commercially available APACHE (trade name)Attorney Docket: ADVA-047-PCT App. No.: tbdHADOOP (trade name) can be used. Data storage and services can be performed on-site or remotely, accessible via network, and allow a user to access, manage, upload and download data, and query the databases and data services as needed.

[0142] In computer networking, “cloud computing” is used to describe a variety of concepts involving a large number of computers connected through a network (e.g., the Internet). The phrase is often used in reference to network-based services, which appear to be provided by real server hardware, but which are in fact served by virtual hardware, simulated by software running on one or more machines. Virtual servers do not physically exist and can therefore be moved around, scaled up or down, etc., without affecting the user.

[0143] In common usage, “the cloud” is essentially a metaphor for the internet. “In the cloud” also refers to software, platforms, and infrastructure sold “as a service” (i.e., remotely through the internet). The supplier has actual servers which host products and services from a remote location, so that individual users do not require servers of their own. End-users can simply log-on to the network, often without installing anything, and access software, platforms, etc. Models of cloud computing service are known as software as a service, platform as a service, and infrastructure as a service. Cloud services may be offered in public, private, or hybrid networks. Google, Amazon, Oracle Cloud, and Microsoft Azure are well-known cloud vendors.

[0144] Software as a service (SaaS) is a software delivery model in which software and associated data are centrally hosted on the Cloud. Under SaaS, a software provider licenses a software application to clients for use as a service on demand, e.g., through a subscription, time subscription, etc. SaaS allows the provider to develop, host, and operate a software application for use by clients who just need a computer with internet access to download and run the software application and / or to access a host to ran the software application.Attorney Docket: ADVA-047-PCT App. No.: tbd The software application can be licensed to a single user or a group of users, and each user may have many clients and / or client sessions.

[0145] Typically, SaaS systems are hosted in datacenters whose infrastructure provides a set of resources and application services to a set of multiple tenants. A “tenant” can refer to a distinct user or group of users having a service contract with the provider to support a specific service. Most SaaS solutions use a multi-tenant architecture where a single version of the application, having a single configuration (i.e., hardware, operating system, and network) is used by all tenants (customers). The application can be scaled by installation on several machines. Other solutions can be used, such as virtualization, to manage large numbers of customers. SaaS supports customization in that the application provides defined configuration options allowing each customer to alter their configuration parameters and options to choose functionality and “look and feel.”

[0146] SaaS services are supplied by independent software vendors (ISVs) or Application Service Providers (ASPs). SaaS is a common delivery model for business applications (e.g., office and messaging, management, and development software, and for accounting, collaboration, management information systems (MIS), invoicing, and content management.

[0147] SaaS is an advantage to end-users in that they do not need to provide hardware and software to store, back-up, manage, update, and execute the provided software. Since SaaS applications cannot access the user’s private systems (databases), they often offer integration protocols and application programming interfaces (API) such as http (hypertext transfer protocol), REST (representational state transfer), SOAP (simple object access protocol), and JSON (JavaScript Object Notation).ConclusionAttorney Docket: ADVA-047-PCT App. No.: tbd

[0148] The disclosure is provided in support of the methods claimed or which may be later claimed. Specifically, this support is provided to meet the technical, procedural, or substantive requirements of certain examining offices. It is expressly understood that the portions or actions of the methods can be performed in any order, unless specified or otherwise necessary, that each portion of the method can be repeated, performed in orders other than those presented, that additional actions can be performed between the enumerated actions, and that, unless stated otherwise, actions can be omitted or moved. Those of skill in the art will recognize the various possible combinations and permutations of actions performable in the methods disclosed herein without an explicit listing of every possible such combination or permutation. It is explicitly disclosed and understood that the actions disclosed, both herein below and throughout, can be performed in any order (xyz, xzy, yxz, yzx, etc.) without the wasteful and tedious inclusion of writing out every such order.

[0149]

[0150] The words or terms used herein have their plain, ordinary meaning in the field of this disclosure, except to the extent explicitly and clearly defined in this disclosure or unless the specific context otherwise requires a different meaning. If there is any conflict in the usages of a word or term in this disclosure and one or more patent(s) or other documents that may be incorporated by reference, the definitions that are consistent with this specification should be adopted.

[0151] The words “comprising,” “containing,” “including,” “having,” and all grammatical variations thereof are intended to have an open, non-limiting meaning. For example, a composition comprising a component does not exclude it from having additional components, an apparatus comprising a part does not exclude it from having additional parts, and a method having a stepAttorney Docket: ADVA-047-PCTApp. No.: tbd does not exclude it having additional steps. When such terms are used, the compositions, apparatuses, and methods that “consist essentially of’ or “consist of’ the specified components, parts, and steps are specifically included and disclosed.

[0152] The indefinite articles “a” or “an” mean one or more than one of the component, part, or step that the article introduces. The terms “and,” “or,” and “and / or” shall be read in the least restrictive sense possible. Each numerical value should be read once as modified by the term “about” (unless already expressly so modified), and then read again as not so modified, unless otherwise indicated in context.

[0153] Whenever a numerical range of degree or measurement with a lower limit and an upper limit is disclosed, any number and any range falling within the range is also intended to be specifically disclosed. For example, every range of values (in the form “from a to b,” or “from about a to about b,” or “from about a to b,” “from approximately a to b,” and any similar expressions, where “a” and “b” represent numerical values of degree or measurement) is to be understood to set forth every number and range encompassed within the broader range of values.

[0154] While the foregoing written description of the disclosure enables one of ordinary skill to make and use the embodiments discussed, those of ordinary skill will understand and appreciate the existence of variations, combinations, and equivalents of the specific embodiments, methods, and examples herein. The disclosure should therefore not be limited by the above described embodiments, methods, and examples. While this disclosure has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments as well as other embodiments of the disclosure will be apparent to persons skilled in the art upon reference to theAttorney Docket: ADVA-047-PCT App. No.: tbd description. It is, therefore, intended that the appended claims encompass any such modifications or embodiments.

[0155] The particular embodiments disclosed above are illustrative only, as the present disclosure may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. It is, therefore, evident that the particular illustrative embodiments disclosed above may be altered or modified and all such variations are considered within the scope of the present disclosure. The various elements or steps according to the disclosed elements or steps can be combined advantageously or practiced together in various combinations or sub-combinations of elements or sequences of steps to increase the efficiency and benefits that can be obtained from the disclosure. It will be appreciated that one or more of the above embodiments may be combined with one or more of the other embodiments, unless explicitly stated otherwise. Furthermore, no limitations arc intended to the details of construction, composition, design, or steps herein shown, other than as described in the claims.

Claims

Attorney Docket: ADVA-047-PCTApp. No.: tbdIt is Claimed1. A method for controlling a fracturing injection operation in a well extending through a subterranean reservoir, the method comprising: sensing, using sensors at the well, current injection operation features; receiving the sensed current injection operation features at an Al model, the Al model trained using historical injection operation features, historical reservoir features, and historical reservoir response attributes from historical fracturing injection operations, the Al model incorporating physics-based constraints; predicting, using the Al model, reservoir response attributes based on the received current injection operation features; communicating, based on the predicted reservoir response attributes, a change to the current or future injection operation features; and making, at the well, the change to the current or future injection operation features.

2. The method of claim 1, wherein the historical injection operating features include reservoir parameters of at least one reservoir, the reservoir features including at least on of permeability, porosity, rock type, or Poisson’s ratio.

3. The method of claim 1, wherein the historical injection operation features include injection operation features from a plurality of fracturing slurry injection operations and include at least one of injection flow rate, injection pump pressure, injection volume, batch solids content, slurry viscosity, slurry density, pre-flush volume, post-flush volume, or batch volume.Attorney Docket: ADVA-047-PCT App. No.: tbd4. The method of claim 1 , wherein the historical reservoir response attributes include reservoir response attributes calculated from a plurality of fracturing slurry injection operations and include at least one of closure pressure, fracture half-length, transmissivity, bottom hole instantaneous shut-in pressure, skin factor, well head pressure at closure, closure time since shut- in, leak-off time, and formation stress.

5. The method of claim 1, wherein the sensors at the well include at least one sensor taken from the group comprising: bottom hole pressure, temperature, wellhead pressure, slurry parameter, solids content, viscosity, density, fall-off test, shut-in test, pressure test, tubing test, density, flow rate, and biomass content sensors.

6. The method of claim 1, wherein the physics-based constraints arc used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.

7. The method of claim 1, wherein the physics-based constraints include at least one of a nonnegativity constraint, a relationship between closure pressure and minimum horizontal stress, or a maximum pressure constraint.

8. The method of claim 1 , wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor or regression algorithm taken from the group consisting of: tree-based algorithms, random forest, decision tree, extra- trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron,Attorney Docket: ADVA-047-PCT App. No.: tbd linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent, Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.

9. The method of claim 1, wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model uses an extra-trees regressor model.

10. A method for optimizing a fracturing injection operation in a well extending through a subterranean reservoir, the method comprising: inputting to an Al model one or more reservoir response attributes to optimize, the Al model trained using historical injection operation features, historical reservoir features, and historical reservoir response attributes from historical fracturing injection operations, the Al model incorporating physics-based constraints; inputting to the Al model reservoir features of the subterranean reservoir; optimizing, using the Al model, the one or more reservoir response attributes based on the reservoir features of the subterranean reservoir; identifying, using the Al model, a first set of fracturing injection operation features corresponding to the optimized reservoir response attributes; running a first fracturing injection operation at the well, the first fracturing injection operation using the identified first set of fracturing injection operation features.

11. The method of claim 10, wherein the historical injection operating features include reservoir parameters of at least one reservoir, the reservoir features including at least on of permeability, porosity, rock type, or Poisson’s ratio;Attorney Docket: ADVA-047-PCT App. No.: tbd wherein the historical injection operation features include injection operation features from a plurality of fracturing slurry injection operations and include at least one of injection flow rate, injection pump pressure, injection volume, batch solids content, slurry viscosity, slurry density, pre-flush volume, post-flush volume, or batch volume; and wherein the historical reservoir response attributes include reservoir response attributes calculated from a plurality of fracturing slurry injection operations and include at least one of closure pressure, fracture half-length, transmissivity, bottom hole instantaneous shut-in pressure, skin factor, well head pressure at closure, closure time since shut-in, leak-off time, and formation stress.

12. The method of claim 10, wherein the physics-based constraints are used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.

13. The method of claim 10, wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor or regression algorithm taken from the group consisting of:, random forest, decision tree, extra-trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron, linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent, Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.

14. The method of claim 10, wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model uses a regressor model taken from the groupAttorney Docket: ADVA-047-PCTApp. No.: tbd consisting of: a tree-based algorithm, a random forest algorithm, a decision tree algorithm, an extra-trees regressor algorithm, a gradient boosting algorithm, and an Adaboost algorithm.

15. The method of claim 10, further comprising: identifying, using the Al model, a second set of fracturing injection operation features corresponding to the optimized reservoir response attributes; and running a second fracturing injection operation at the well, the second fracturing injection operation using the identified first set of fracturing injection operation features.

16. The method of claim 10, further comprising: sensing, using sensors at the well, current injection operation features; receiving the sensed current injection operation features at the Al model; predicting, using the Al model, reservoir response attributes based on the received current injection operation features; communicating, based on the predicted reservoir response attributes, a change to the current or future injection operation features; and making, at the well, the change to the current or future injection operation features.

17. A method for conducting a feasibility study for a fracturing injection facility for performing multiple fracturing injection operations in a subterranean reservoir, the method comprising: inputting, to an Al model, reservoir features for a selected reservoir, the Al model trained using historical injection operation features, historical reservoir features, and historical reservoirAttorney Docket: ADVA-047-PCT App. No.: tbd response attributes from historical fracturing injection operations, and historical injection operation economic features, the Al model incorporating physics-based constraints; predicting, using the Al model, reservoir response attributes based on a series of injection operation features for the reservoir features of the selected reservoir; determining, for the fracturing injection operation, a proposed series of fracturing injection operations, and at least one of: drilling costs, predicted well storage capacity, predicted well operational life, pumping requirements, equipment capacities, and economic forecasts.

18. The method of claim 17, further comprising: performing the proposed series of fracturing operations at the subterranean reservoir.

19. The method of claim 17, wherein the historical injection operation economic features are taken from the group consisting of: geological data, drilling parameters, rate of penetration, weight on bit, drilling time, lost circulation zones, well logs, water depth, historical well life, pressure and injection volume histories, waste types, generation rates, drilling programs, drilling costs, well storage capacities, well operational lives, pumping requirements, equipment capacities, construction costs, operational balances, and lifecycle economics.

20. The method of claim 17, wherein the physics-based constraints are used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.Attorney Docket: ADVA-047-PCT App. No.: tbd21. The method of claim 17, wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor or regression algorithm taken from the group consisting of:, random forest, decision tree, extra-trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron, linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent, Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.

22. The method of claim 17, wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model uses a regressor model taken from the group consisting of: a tree-based algorithm, a random forest algorithm, a decision tree algorithm, an extra-trees regressor algorithm, a gradient boosting algorithm, and an Adaboost algorithm.

23. A method for conducting a long-term optimization program for a fracturing injection facility performing multiple fracturing injection operations in a subterranean reservoir, the method comprising: inputting, to an Al model, reservoir features for a selected reservoir, the Al model trained using historical injection operation features, historical reservoir features, and historical reservoir response attributes from historical fracturing injection operations, the Al model incorporating physics-based constraints; predicting, using the Al model, reservoir response attributes based on a series of injection operation features for the reservoir features of the selected reservoir;Attorney Docket: ADVA-047-PCT App. No.: tbd determining, for the fracturing injection operation, a proposed series of fracturing injection operations for optimizing at least one of: well operational life, well injection capacity, and number of fracturing injection operations on the well.

24. The method of claim 23, further comprising: performing the proposed series of fracturing injection operations at the well.

25. The method of claim 24, further comprising: inputting to the Al model injection operation features from one or more of the performed fracturing injection operations; updating the proposed series of fracturing injection operations with updated injection operation features, thereby extending the operational life of the well.

26. The method of claim 23, further comprising: using the Al model, determining a maintenance schedule for well equipment.

27. The method of claim 23, wherein the historical injection operating features include reservoir parameters of at least one reservoir, the reservoir features including at least on of permeability, porosity, rock type, or Poisson’s ratio; wherein the historical injection operation features include injection operation features from a plurality of fracturing slurry injection operations and include at least one of injection flow rate, injection pump pressure, injection volume, batch solids content, slurry viscosity, slurry density, pre-flush volume, post-flush volume, or batch volume; andAttorney Docket: ADVA-047-PCT App. No.: tbd wherein the historical reservoir response attributes include reservoir response attributes calculated from a plurality of fracturing slurry injection operations and include at least one of closure pressure, fracture half-length, transmissivity, bottom hole instantaneous shut-in pressure, skin factor, well head pressure at closure, closure time since shut-in, leak-off time, and formation stress.

28. The method of claim 23, wherein the physics-based constraints are used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.

29. The method of claim 23, wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor or regression algorithm taken from the group consisting of:, random forest, decision tree, extra-trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron, linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent, Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.

30. A system for controlling a fracturing injection operation in a well extending through a subterranean reservoir, the system comprising: at least one sensor positioned at the well for sensing current injection operation features; memory storing an Al model trained using historical injection operation features, historical reservoir features, and historical reservoir response attributes from historical fracturing injection operations, the Al model incorporating physics-based constraints;Attorney Docket: ADVA-047-PCT App. No.: tbd one or more processors operatively coupled to the at least one sensor and the memory, the one or more processors configured to: predict, using the Al model, reservoir response attributes based on the received current injection operation features; communicate, based on the predicted reservoir response attributes, a change to the current injection operation features or future injection operation features; and effect a change in the injection operation features at the well.

31. The system of claim 30, wherein the historical injection operating features include reservoir parameters of at least one reservoir, the reservoir features including at least on of permeability, porosity, rock type, or Poisson’s ratio.

32. The system of claim 30, wherein the historical injection operation features include injection operation features from a plurality of fracturing slurry injection operations and include at least one of injection flow rate, injection pump pressure, injection volume, batch solids content, slurry viscosity, slurry density, pre-flush volume, post-flush volume, or batch volume.

33. The system of claim 30, wherein the historical reservoir response attributes include reservoir response attributes calculated from a plurality of fracturing slurry injection operations and include at least one of closure pressure, fracture half-length, transmissivity, bottom hole instantaneous shut-in pressure, skin factor, well head pressure at closure, closure time since shutin, leak-off time, and formation stress.Attorney Docket: ADVA-047-PCT App. No.: tbd34. The system of claim 30, wherein the sensors at the well include at least one sensor taken from the group comprising: bottom hole pressure, temperature, wellhead pressure, slurry parameter, solids content, viscosity, density, fall-off test, shut-in test, pressure test, tubing test, density, flow rate, and biomass content sensors.

35. The system of claim 30, wherein the physics-based constraints are used to reject any Al model prediction that does not meet the physics-based constraints, or are represented by partial differential equations embedded into a loss function of the Al model.

36. The system of claim 30, wherein the physics-based constraints include at least one of a non-negativity constraint, a relationship between closure pressure and minimum horizontal stress, or a maximum pressure constraint.

37. The system of claim 30, wherein the Al model is a Physics-Informed Machine Learning (PIML) model, and wherein the PMIL model includes a regressor or regression algorithm taken from the group consisting of: tree-based algorithms, random forest, decision tree, extra- trees regressor, gradient boosting, Adaboost, neural network-based models, multi-layer perceptron, linear models, linear, ridge and lasso regression models, elastic net, stochastic gradient decent, Bayesian ridge regression, support vector machines, and k-nearest neighbor regression.

38. The system of claim 30, wherein the Al model is a Physics-Informed Machine Learning(PIML) model, and wherein the PMIL model uses an extra-trees regressor model.

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