Methods and Systems for Continuous Bottomhole Pressure Estimation

Description

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Application No. 63/550,850 filed Feb. 7, 2024, entitled “METHODS AND SYSTEMS FOR CONTINUOUS BOTTOMHOLE PRESSURE ESTIMATION” by Sathish Sankaran and Hardikkumar Zalavadia, which is incorporated herein by reference as if reproduced in its entirety.

TECHNICAL FIELD

This disclosure relates to reservoir characterization and continuous bottomhole pressure (BHP) estimation of subterranean petroleum reservoirs.

BACKGROUND

Developing unconventional reservoirs has triggered a reimagination of reservoir engineering models and methodologies for agile asset development planning. The completion of horizontal wells with multi-stage fracturing has enabled the commercial production of hydrocarbon resources in ultra-low permeability rock. It is important to properly understand well performance across the whole life of the wells to optimally develop unconventional reservoirs and extract maximum economic value. Identifying key drivers and production behaviors is critical to generating robust production forecasting and enabling proper field development planning and production optimization through the most appropriate operational strategy. Thus, well performance evaluation based on BHP becomes an attractive tool for robust and continuous development planning for unconventional operators.

Bottomhole pressure (BHP) is an important parameter to optimize the performance of oil wells. BHP may be integrated into a modern workflow to characterize subsurface reservoirs, evaluate well production performance, and optimize artificial lift designs for unconventional reservoirs. BHP is a reservoir or formation pressure at the bottom of a wellbore, usually measured in pounds per square inch. For example, in a non-flowing well when wellbore fluid is not being circulated, BHP is caused by the hydrostatic pressure in an annulus exerted by the fluid in the wellbore and surface pressure. As another example, in a flowing well when wellbore fluid is being circulated, BHP is equal to the friction drop in the tubing plus the wellhead pressure. In recent years, permanent downhole gauges have been deployed in electrical submersible pump systems to monitor BHP for the wellbore. However, the deployment of permanent downhole pressure gauges is not an economically feasible solution for continuous measurement throughout the entire life span on all wells across the entire asset due to the high cost.

BHP is often a key parameter to optimize the performance of oil wells for well and reservoir surveillance in oil and gas production. In some embodiments, BHP may be an important downhole parameter controlled during drilling. For example, a drilling operator may carefully control fluid density at the surface in order to control BHP and other pressures associated with a wellbore, such as pump intake pressure (PIP), back pressure, etc. The operator may maintain a hydrostatic pressure of the drilling fluid in the wellbore above a formation or pore pressure to avoid well blow-out. Likewise, the density of the drilling fluid and the fluid flow rate may impact the effectiveness of the drilling fluid in carrying the cuttings to the surface. BHP may be measured by deploying a plurality of permanent downhole sensors in the wellbore to obtain continuous downhole measurement throughout the entire life span on all wells in a field. However, a high cost is usually associated with the deployment and maintenance of the plurality of downhole sensors in fields with large well counts, such as thousands of wells in a field.

Calculating accurate BHP is often an important task in petroleum engineering. BHP is required in a plurality of well performance forecasting techniques, such as rate-transient analysis (RTA), history matching using reservoir simulation, inflow-performance-relationship (IPR) estimation, etc. Understanding well production performance in petroleum reservoirs is useful for achieving optimal field development and maximizing value. It is desired to have a robust and scalable method for quantifying well productivity, which can be applied in a practical manner to all wells, overcoming the limitations of decline curve analysis (not representative of changing operating conditions) and analytical and numerical models (based on either simplifying assumptions, manual interpretation or not suitable for large scale usage).

A more practical approach is to estimate BHP from wellhead pressure by using a plurality of physics-based multi-phase flow correlations. For example, BHP may be estimated from surface pressure and rate measurements by applying steady-state multi-phase flow correlations to capture the pressure losses in a wellbore. The overall pressure losses can be expressed as the sum of the following pressure drop components-hydrostatic, frictional, acceleration, and any head added by artificial lift (e.g., ESP, rod pump, etc.). However, the plurality of physics-based multi-phase flow correlations are derived based on various empirical or mechanistic models using limited field datasets and assumptions only applicable to certain flow conditions. Thus, these empirical or mechanistic models are not generalized enough to fully characterize the fluid flow behaviors that are applicable to various flow patterns without constant manual selection and tuning. Therefore, there is a need for robust estimation of BHP with various changing wellbore configurations under different artificial lift designs and types throughout the life of the well.

BRIEF DESCRIPTION OF THE DRAWINGS

These drawings illustrate certain aspects of some of the embodiments of the present disclosure and should not be used to limit or define the claims.

FIG. 1 illustrates an example hybrid BHP modeling method using physics-based preprocessing and physics-based regularization, in accordance with certain embodiments.

FIG. 2 illustrates an example hybrid BHP modeling method for training and testing a two-step ML model for predicting a best physics correlation and a residual BHP correction, in accordance with certain embodiments.

FIG. 3 illustrates an example method for performing a two-step ML model for predicting BHP for a reservoir system, in accordance with certain embodiments.

FIG. 4 illustrates a block diagram of an exemplary control unit, in accordance with certain embodiments.

FIG. 5A illustrates an example comparison of actual gauge BHP data against BHP data based on a plurality of physics correlations for a public dataset, in accordance with certain embodiments.

FIG. 5B illustrates an example comparison of actual gauge BHP data against BHP data based on a plurality of ML-based methods for the public dataset, in accordance with certain embodiments.

FIG. 5C illustrates an example comparison of actual gauge BHP data against BHP data based on a plurality of physics augmented features (PAF) models for the public dataset, in accordance with certain embodiments.

FIG. 6A illustrates an example relative error for a plurality of wells with a classical physics-based correlation for a deep-water offshore dataset, in accordance with certain embodiments.

FIG. 6B illustrates an example relative error for a plurality of wells after applying one or more physics-preprocessing based ML models for the deep-water offshore dataset, in accordance with certain embodiments.

FIG. 6C illustrates an example comparison of actual gauge BHP data against predicted BHP data from a hybrid model for the deep-water offshore dataset, in accordance with certain embodiments.

FIGS. 7A, 7B, and 7C illustrate example well test and allocation based gas rate, oil rate, and water rate for a first well of a first onshore unconventional dataset, in accordance with certain embodiments.

FIG. 7D illustrates an example comparison of actual gauge BHP data against predicted BHP data from a hybrid model for a first well of the first onshore unconventional dataset, in accordance with certain embodiments.

FIGS. 8A, 8B, and 8C illustrate example well test and allocation based gas rate, oil rate, and water rate for a second well of a first onshore unconventional dataset, in accordance with certain embodiments.

FIG. 8D illustrates an example comparison of actual gauge BHP data against predicted BHP data from a hybrid model for a second well of the first onshore unconventional dataset, in accordance with certain embodiments.

FIGS. 9A and 9B illustrate example cumulative distribution of median absolute percentage error (MedAPE) between actual BHP data and hybrid BHP model predictions for all wells of a second onshore unconventional dataset, in accordance with certain embodiments.

FIG. 10 illustrates an example MedAPE of BHPs predicted by physics-based correlations as compared to the hybrid BHP model for allocation data and well test data for the second onshore unconventional dataset, in accordance with certain embodiments.

FIG. 11A illustrates an example MedAPE of the hybrid BHP model predictions by formation with distribution errors across all areas in a formation for the second onshore unconventional dataset, in accordance with certain embodiments.

FIG. 11B illustrates an example MedAPE of the hybrid BHP model predictions by area with distribution errors across all formations in an area for the second onshore unconventional dataset, in accordance with certain embodiments.

While embodiments of this disclosure have been depicted and described and are defined by reference to exemplary embodiments of the disclosure, such references do not imply a limitation on the disclosure, and no such limitation is to be inferred. The subject matter disclosed is capable of considerable modification, alteration, and equivalents in form and function, as will occur to those skilled in the pertinent art and having the benefit of this disclosure. The depicted and described embodiments of this disclosure are examples only, and not exhaustive of the scope of the disclosure.

DETAILED DESCRIPTION

Illustrative embodiments of the present disclosure are described in detail herein. In the interest of clarity, not all features of an actual implementation may be described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions may be made to achieve the specific implementation goals, which may vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of the present disclosure.

The present disclosure relates to methods and systems for continuous BHP estimation of subterranean petroleum reservoirs. In some embodiments, the modeling may include a hybrid methodology integrating a physics-based model and a machine learning model to provide BHP with high accuracy.

More specifically, the present disclosure provides methods including providing a hybrid BHP modeling method to determine a hybrid BHP model by applying a physics-based pre-processing approach and a physics-based regularization. In some embodiments, the BHP model may include a machine learning (ML) classification model and an ML regression model. The hybrid BHP modeling method may apply the ML classification model to determine the best physics correlation and corresponding BHP estimate based on a plurality of input attributes calculated from routine daily production data, such as static and dynamic parameters. For example, the static parameters include pressure-volume-temperature (PVT) fluid properties and reservoir properties. As another example, the dynamic parameters include multi-phase flow rate, wellhead pressure, gas to liquid ratio (GLR), water cut (WCT), etc. Likewise, the hybrid BHP modeling method may apply the ML regression model for determining a residual correction to update the BHP estimate based on the best physics correlation. Thus, the hybrid BHP modeling method may use the hybrid BHP model to develop a scalable workflow for estimating BHP from routinely available data.

In some embodiments, the hybrid BHP modeling method may implement a two-step machine learning model to predict the best physics correlation to obtain a BHP estimate and adjust that estimate based on a residual correction method. In some embodiments, the hybrid BHP model training may be implemented in two steps. In the first step, the hybrid BHP modeling method may calculate a plurality of multi-phase flow correlations from training data, such as routine daily production data. The routine daily production data may include both static parameters and dynamic parameters, such as PVT, wellhead pressure, wellhead temperature, multiphase flow rates, fluid description, wellbore configuration (e.g., deviation survey describing the curvilinear shape of the well, wellbore diameter, and pipe roughness), GLR, WCT, etc. Based on the plurality of multi-phase flow correlations, the hybrid BHP modeling method may use an ML classification model to determine a proper physics-based model associated with the best predicted multi-phase flow correlation. Thus, the hybrid BHP modeling method may use the best-predicted multi-phase flow correction to estimate the BHP based on the training data. In the second step, the hybrid BHP modeling method may use an ML regression model to predict a residual correction for the estimated BHP in the first step to determine a final BHP based on the training data.

In some embodiments, the hybrid BHP modeling method may apply the BHP model to determine BHP from testing data, such as new input field data (e.g., PVT, wellhead pressure, multiphase flow rates, fluid description, wellbore configuration, GLR, WCT, etc.). In some embodiments, the hybrid BHP model prediction may be implemented in two steps. In the first step, the hybrid BHP modeling method may use the ML classification model to determine a proper physics-based model associated with the best predicted multi-phase flow correlation. Thus, the hybrid BHP modeling method may use the best-predicted multi-phase flow correction to estimate the BHP based on the testing data. In the second step, the hybrid BHP modeling method may use the ML regression model to predict a residual correction for the estimated BHP in the first step to determine a final BHP based on the testing data. With continuous, mainly downhole telemetry, to provide mostly real-time field data of a wellbore, one application of the hybrid BHP modeling method is to use the real-time field data to predict the final BHP of the wellbore. The operator may modify the density or viscosity of the drilling fluid to modify a dynamic pressure in the wellbore in order to adjust the predicted final BHP.

Physics-Based Models

In some embodiments, permanent downhole sensors may continuously measure BHP for well and reservoir surveillance in oil and gas production. However, it may be uneconomical to deploy the permanent downhole sensors in fields with large well counts and maintain the permanent downhole sensors when they fail to have continuous downhole measurements. An alternative approach is to determine a BHP model to estimate BHP from wellhead pressure by using physics-based multi-phase flow correlations for a wellbore. A multi-phase flow is a simultaneous flow of fluids containing multiple thermodynamic phases. The multiple thermodynamic phases may include one or more chemical components, such as water, water vapor, and/or oil. In some embodiments, the flowing BHP may be estimated from surface measurements by using a plurality of multi-phase flow correlations based on one or more empirical and/or mechanistic models for the wellbore. However, the predicted BHP based on various multi-phase flow correlations often differ significantly from actual BHP measurements due to the complexities of multi-phase flows.

In some embodiments, the complexities of the multi-phase flow in deviated wellbores necessitate the use of one or more simplified physics-based models and empirical correlations. In some embodiments, these physics-based models are developed using limited field datasets and assumptions only applicable to certain conditions. Thus, one or more factors, such as phase volume fractions and flow patterns, are used to determine a plurality of multi-phase flow correlations based on one or more empirical and/or mechanistic models for the wellbore. In some embodiments, one or more factors may be used, at least in part, to calculate a pressure gradient in a plurality of pipe segments that depend on forces such as gravity, friction, and acceleration. For example, the pressure gradient in a steady-state multiphase flow may be calculated using experimental or empirical, theoretical or mechanistic, and data-driven or ML methods.

Empirical Models

In some embodiments, a multi-phase fluid flow modeling workflow may be used to determine a plurality of multi-phase flow correlations by using an empirical model based on laboratory experiments and field trials. The empirical model may be determined with varying levels of complexity and accuracy, depending on the flow patterns considered. Some models represent all three phases (oil, gas, and water), while others lump them into a fully mixed liquid phase. The plurality of multi-phase flow correlations may be developed for various pipe configurations (vertical, inclined, and horizontal) and tubing types (smooth, rough) over specific ranges of liquid rates, gas to liquid ratios, and water cuts. For example, in some embodiments, the plurality of multi-phase flow correlations used for BHP calculation may have poor quality because the BHP is calculated by using experimental data and, typically, by extrapolating the empirical model outside a corresponding support range.

In some embodiments, the empirical model is developed under a corresponding condition for a wellbore or a formation and may lack generalizability and may not accurately predict a flow behavior outside of the corresponding condition. In some embodiments, the multi-phase flow correlations may be determined using the empirical model with simplifying assumptions on relevant physics associated with experimental data. For example, a gas phase may travel faster than a liquid phase under a condition in a vertical flow due to gas slippage. As another example, slips and/or flow patterns may be considered or ignored under a different condition in a vertical flow. An example of a selected single-phase and multi-phase flow correlations for fluid flow type and pipe flow configurations may be found in Table 1 below:

TABLE 1
Selected single-phase and multi-phase flow correlations
for fluid type and pipe flow configurations.

Phase	Type	Method
Single	Gas	Darcy-Weisbach
Phase Flow		Weymouth
		Panhandle A
		Panhandle B
		Cullender and Smith
	Liquid	Darcy-Weisbach
		Hazen Williams
Multi-	Vertical	Beggs and Brill (no slip)
Phase Flow	Flow	Beggs and Brill (with Darcy-Weisbach
		friction factor)
		Dukler, Wicks and Cleveland
		Duns and Ros
		Fancher and Brown
		Gray
		Gray (with Darcy-Weisbach friction factor)
		Hagedorn and Brown
		Orkiszewski
	Horizontal	Eaton Flanigan
	Flow	Eaton Dunkler Flanigan
		Beggs and Brill (no slip)
		Beggs and Brill (with Darcy-Weisbach
		friction factor)

Mechanistic Models

In some embodiments, a multi-phase fluid flow modeling workflow may be used to determine a plurality of multi-phase mechanistic flow correlations by using a mechanistic model based on heuristics or thumb rules without regard to the actual flow behavior. The mechanistic model may have some pre-determined physics embedded in the BHP estimation. The pre-determined physics may affect the accuracy of the BHP estimation when the underlying assumptions of the pre-determined physics are violated. For example, the mechanistic model may be determined by predicting a multi-phase flow behavior in a pipe for an isolated mechanism such as flow pattern, film thickness, or the velocity of gas bubbles in liquid columns. Thus, the mechanistic model often includes some physical phenomena with analytical or semi-empirical closure relations to predict the flow patterns and different parameters for each flow regime. In some embodiments, the mechanistic model may implement one or more modeled mechanisms based on simplifying assumptions about dominant flow patterns and transitions between different flow patterns. In some embodiments, the mechanistic model may implement one or more flow regime maps by combining one or more best features of existing correlations in a unified model.

In some embodiments, the mechanistic model may be developed based on a physics-based model. For example, selecting a representative physics-based flow correlation may determine the mechanistic model. Likewise, the mechanistic model may have some difficulties in modeling with low-liquid loading in an upward flow, a downward flow, and high gas flow rates because a plurality of closure parameters are not predicted accurately or have modeling deficiencies. Thus, the application of the mechanistic model may be limited by the underlying physics-based model and varying operational conditions. As a result, it may be difficult to use the mechanistic model as a fully generalized model for producing very robust BHP for different operational conditions, such as well geometry, fluid properties, and flow patterns.

In some embodiments, the mechanistic model may need to be manually calibrated across different operational conditions, such as well geometry, fluid properties, and flow patterns. For example, the mechanistic model may be selected by using an evidence-based approach to search for the best predictive model from a plurality of mechanistic models. As another example, the mechanistic model may be selected generically for a certain duration of time and not updated routinely when flow conditions change due to operational variations or reservoir behaviors. Thus, determining the mechanistic model may rely on a manual calibration against the observed BHP measurements for various operational conditions. In those instances, the mechanistic model may not be sufficient for an automated and scalable workflow to determine BHP for oil fields with large well counts. An example of selected mechanistic models for multi-phase flow and various pipe flow configurations may be found in Table 2 below:

TABLE 2
Selected mechanistic models for multiphase
flow and various pipe flow configurations.

	Phase	Type	Method
	Multi-Phase Flow	Vertical Flow	Hasan and Kabir
			Taitel et al.
			Ansari et al.
			Aziz et al.
		Inclined Flow	Barnea
			Petalas and Aziz
		Horizontal Flow	Xiao et al.
			Taitel and Dukler

ML Models

In some embodiments, a multi-phase fluid flow modeling workflow may use an ML model for BHP estimation by leveraging data to capture complex relationships that traditional empirical and mechanistic models struggle to represent using surface measurements. Thus, the ML model may provide an attractive data-driven tool for BHP estimation to fill a gap left by empirical correlations and mechanistic models, capturing nuances in multiphase flow behavior that may be missed by traditional methods. For example, the ML model may be determined using a supervised ML algorithm, such as an artificial neural network, a support vector machine, a fuzzy inference system, a flow regime classification, and an expert system. In some embodiments, the ML model may be implemented to determine patterns or relationships associated with minor physics which may not be modeled using the empirical and/or mechanistic models.

In some embodiments, the ML model generated in the multi-phase fluid flow modeling workflow often suffers from bias in limited input data without generalization. Thus, the ML model is difficult to interpret the BHP estimation without a physics-based context. In some embodiments, the ML model may easily suffer from an over-fitting problem by capturing spurious trends and generating physically inconsistent BHP estimation. In some embodiments, the ML model may not capture relationships that are not available in training data associated with out-of-sample scenarios. For example, the ML model generated using training data based on a bubble flow regime may not adequately predict a slug flow regime behavior.

In some embodiments, since various multi-phase flow correlations have been developed with limited field datasets and assumptions only applicable for certain flow conditions, these empirical, mechanistic, or ML models are not generalized to fully characterize the fluid flow behaviors that are applicable for various flow patterns without constant manual selection and tuning. Therefore, there is a need for robust estimation of BHP with various changing wellbore configurations under different artificial lift designs and types throughout the life of the well.

Hybrid BHP Models

In some embodiments, a multi-phase fluid flow modeling workflow may use a hybrid BHP model to estimate BHP from routinely available field data, such as PVT, wellhead pressure, wellhead temperature, multiphase flow rates, fluid description, wellbore configuration (e.g., deviation survey describing the curvilinear shape of the well, wellbore diameter, and pipe roughness), GLR, WCT, etc. The hybrid BHP model may combine physics and data-driven methods to address the limitations of either pure physics or pure data-driven methods. For example, the hybrid BHP method may be used to predict gas-liquid flow pattern transition in pipes or correct for unmodeled physics. The multi-phase fluid flow modeling workflow may build the hybrid BHP model to calculate BHP based on one or more data-driven methods constrained by physics. For example, the multi-phase fluid flow modeling workflow may utilize downhole pressure measurements and machine learning to correct BHP estimates obtained from empirical correlations or mechanistic models. Using available pressure sensor data as training data, the hybrid BHP model may include a two-step ML model which is trained to predict BHP using physics-based preprocessing and physics-based regularization. Likewise, the hybrid BHP model may be implemented to predict BHP using testing data to function as a virtual gauge using routine field measurements. As a result, the hybrid BHP model may be more reliable and generalized than traditional models to improve the prediction accuracy of BHP. The hybrid BHP model may also account for unmodeled physics for a wide range of dynamic conditions that a flowing well would experience.

FIG. 1 illustrates an example hybrid BHP modeling method 100 using physics-based preprocessing 102 and physics-based regularization 104, in accordance with certain embodiments. The hybrid BHP modeling method 100 may combine the fidelity and interpretability of a best-matched physics-based model, such as a physics model 108, with the scalability and agility of an ML model, such as a data-driven model 110. A goal of hybrid BHP modeling method 100 may be to determine a BHP by constraining a solution space of data-driven model 110 using physics-based principles of physics model 108. In some embodiments, hybrid BHP modeling method 100 may include two key components: physics-based preprocessing and physics-based regularization.

In some embodiments, physics-based preprocessing 102 involves extracting relevant features using physical or empirical models. The hybrid BHP modeling method 100 may utilize a plurality of input parameters 106 to determine a plurality of BHP estimates 112 based on one or more physics-based models associated with a physics model 108. Based on the plurality of BHP estimates 112, hybrid BHP modeling method 100 may use one or more ML models associated with a data-driven model 110 to determine a plurality of final BHP estimates 114 based on the plurality of input parameters 106. The plurality of input parameters may include observed BHP measurements. Physics-based preprocessing 102 may include data preprocessing, feature extraction, and feature processing to determine updated input data, such as the plurality of BHP estimates 112 which includes physics-based preprocessed input data 122 for physics-based model 108 and ML-based input data 132 for data-driven model 110. For example, a physical correlation may be used to compute physics-based preprocessed data, such as physics-based BHP estimates 124, which may be used as an “engineered” feature within data-driven model 110. As another example, updated input data, such as the plurality of BHP estimates 112, may include a residual value which is a difference between the physics-based preprocessed data with actual measurements for training the one or more ML models associated with data-driven model 110. In some embodiments, the one or more physics-based models may be associated with multiple physics models 108 when no single physics model may work well under all operating conditions.

In some embodiments, physics-based regularization 104 involves a loss function for hybrid BHP modeling method 100 which is a weighted sum of both a data-driven loss and physics-based loss. For example, the loss function may include a least squared sum of errors between observed BHP measurements, such as input parameters 106, and BHP predictions, such as final BHP estimates 114. In some embodiments, final BHP estimates 114 may be a weighted sum of physics-based BHP estimates 124 and ML-based BHP estimates 134 by adjusting physics-based BHP estimates 124 based on a residual correction method 150. For example, the hybrid BHP modeling method 100 may use physics-based preprocessed input data 122 and physics model 108 to determine physics-based BHP estimates 124. As another example, the hybrid BHP modeling method 100 may use ML-based input data 132 and data-driven model 110 to determine ML-based BHP estimates 134. Because the hybrid BHP modeling method 100 may combine the fidelity and interpretability of a best-matched physics model 108 with the scalability and agility of data-driven model 110, a final hybrid BHP model may be more generalizable to out-of-sample scenarios compared to pure machine learning models. Likewise, the final hybrid BHP model also improves BHP prediction when physics model 108 is not accurate or only approximate. In some embodiments, a hybrid BHP model may include a physics-based machine learning (PIML) model, a physics-based neural network (PINN), and/or a theory guided neural network (TGNN), etc.

FIG. 2 illustrates an example hybrid BHP modeling method 100 for training and testing a two-step ML model for predicting the best physics correlation and a residual BHP correction in accordance with certain embodiments. The hybrid BHP modeling method 100 may build upon the physics-based preprocessing approach to develop a new scalable workflow for estimating accurate BHP 228 from input data 202. In some embodiments, in training step 210, hybrid BHP modeling method 100 may train an ML classification model 214 of the two-step ML model to determine a best-matched physics model 222 using a physics-based preprocessing approach 212 based on a plurality of physics models 220 to obtain a BHP estimate 224. Subsequently, in predicting step 250, hybrid BHP modeling method 100 may train an ML regression model 216 of the two-step ML model to determine a residual correction 226 which is used to adjust the BHP estimate 224 to match actual BHP measurements 218.

In some embodiments, hybrid BHP modeling method 100 may apply the two-step ML model as a hybrid BHP model to estimate accurate final BHP 228 from available field data, such as input data 202. Input data 202 may include routine daily production data, such as static parameters and dynamic parameters. Additionally, input data 202 may include wellbore configuration, such as a deviation survey describing the curvilinear shape of a well, wellbore diameter, and pipe roughness. In some embodiments, actual BHP measurements 218 may be collected for a few wells over a selected time range for training the hybrid BHP model. Having representative data samples covering the range of operation of a wellbore may enhance model prediction accuracy. In some embodiments, the static parameters may include PVT and reservoir properties in a wellbore. PVT may indicate a change in fluid properties as fluid flows through the reservoir, well and surface equipment under different pressure and temperature conditions. Static reservoir properties represent the elastic properties of unconventional reservoir rocks in a wellbore. The static reservoirs may include Young's modulus, porosity, permeability, face type, etc. The static reservoir properties may vary significantly between reservoirs or within a reservoir due to a wide variety of material composition and microstructures in a formation, such as organic-rich shales in an unconventional reservoir. Young's modulus may indicate the stiffness of a particular rock in a formation. Porosity may indicate how much space exists in a particular rock in a formation where oil, gas, and/or water may be trapped. Rock type may indicate the lithology information for a formation. Permeability may indicate the ability of liquids and gases to flow through a particular rock in a formation.

In some embodiments, the static parameters may be estimated from lab-based measurements, basin-wide equation of state, and early production data or flowback analysis. Ideally, the static parameters may be measured in the laboratory using a representative sample from the original fluid in the reservoir. In practice, most wells do not routinely characterize static parameters with full laboratory analysis. As most unconventional fields exhibit heterogeneous fluid properties for different locations and formations, extrapolating the static parameters from a few wells to represent the whole field without extensive fluid modeling may be inadequate, as it will often fail to capture such heterogencities.

In some embodiments, dynamic parameters may represent wellhead pressure, wellhead temperature, multi-phase flow rate, GLR, WCT, etc. Wellhead pressure may indicate pressure exerted by a well at the wellhead. The multi-phase flow rate may indicate a ratio of the mass of one phase of a mixture of oil, gas, and water to the total mass of the mixture passing through the cross-section of a pipeline per unit of time. GLR may indicate a ratio of a gas volume divided by a liquid volume at the same temperature and pressure. WCT may indicate a ratio of water produced compared to the volume of total liquids produced. In some embodiments, the dynamic parameters may be estimated by direct or indirect measurement of the volumes of gas and oil in a drilled rock cutting. In some embodiments, the best-matched physics model 222 may be selected from the plurality of physics models 220 based on usual heuristics and best practices. The plurality of physics models 220 may include a wide range of feasible flow patterns during the entire production period of a wellbore. In some embodiments, the plurality of physics models 220 may determine a flowing BHP from surface measurements by calculating a pressure drop resulting from a multi-phase flow within the wellbore, considering various geometries, flow conditions, and noisy measurements. The hybrid BHP modeling method 100 may effectively overcome the physical limitations of the plurality of physics models 220 by integrating the best-matched physics model 222, the ML classification model 214, and the ML regression model 216. For example, hybrid BHP modeling method 100 may generate a hybrid BHP model to accurately predict gas-liquid flow pattern transitions in pipes or correct for unmodeled physics in the wellbore.

In some embodiments, the hybrid BHP modeling method 100 may implement a two-step ML model to determine the best physics correlation based on the best-matched physics model 222 to obtain BHP estimate 224 and adjust BHP estimate 224 based on the residual correction 226. In some embodiments, in training step 210, the hybrid BHP model training may be implemented in two steps. In the first step, hybrid BHP modeling method 100 may include calculating a plurality of multi-phase flow correlations from input data 202, such as routine daily production data. The routine daily production data may include static and dynamic parameters, such as PVT, wellhead pressure, wellhead temperature, multiphase flow rates, fluid description, wellbore configuration, GLR, WCT, etc. Based on the plurality of multi-phase flow correlations, hybrid BHP modeling method 100 may use ML classification model 214 to determine a proper physics-based model, such as the best-matched physics model 222, associated with the best predicted multi-phase flow correlation based on a predetermined objective criterion, such as absolute error. Thus, hybrid BHP modeling method 100 may determine BHP estimate 224 based on the best-predicted multi-phase flow correction associated with the best-matched physics model 222 and input data 202. In the second step, hybrid BHP modeling method 100 may use ML regression model 216 to predict the residual correction 226 for BHP estimate 224 from the first step to determine a final BHP 228 based on input data 202.

In some embodiments, the hybrid BHP modeling method 100 may apply the BHP model to determine BHP from testing data 204, such as new input field data (e.g., PVT, wellhead pressure, multiphase flow rates, fluid description, wellbore configuration, GLR, WCT, etc.). In some embodiments, the hybrid BHP model prediction may be implemented in two steps. In the first step, the hybrid BHP modeling method 100 may use ML classification model 214 to determine a proper physics-based model associated with a best predicted multi-phase flow correlation. Thus, the hybrid BHP modeling method 100 may use the best-predicted multi-phase flow correction to determine a BHP estimate 224 based on testing data 204. In the second step, hybrid BHP modeling method 100 may use ML regression model 216 to predict the residual correction 226 for the BHP estimate 224 from the first step to determine a final BHP 228 based on testing data 204.

FIG. 3 illustrates an example method for performing a two-step ML model for predicting BHP for a reservoir system, in accordance with certain embodiments. Method 300 of FIG. 3 may be used by the hybrid BHP modeling method 100 of FIG. 1 and FIG. 2. Method 300 starts at step 305, where hybrid BHP modeling method 100 (referring to FIG. 1) may receive field data and a plurality of physics-based models for a wellbore. For example, the field data may include both static parameters and dynamic parameters, such as PVT, wellhead pressure, wellhead temperature, multiphase flow rates, fluid description, wellbore configuration, GLR, WCT, etc. The plurality of physics-based models may include both empirical and/or mechanistic models (Table 1 and Table 2).

At step 310, hybrid BHP modeling method 100 (referring to FIG. 1) may train an ML classification model to determine the best correlation using the plurality of physics-based models. In some embodiments, hybrid BHP modeling method 100 (referring to FIG. 1) may calculate a plurality of multi-phase flow correlations using the field data and the plurality of physics-based models for the wellbore. Based on the plurality of multi-phase flow correlations, hybrid BHP modeling method 100 (referring to FIG. 1) may train the ML classification model to determine the best correlation associated with a proper physics-based model based on a predetermined objective criterion, such as absolute error.

At step 315, hybrid BHP modeling method 100 (referring to FIG. 1) may use the ML classification model to determine the best correlation based on the field data for the wellbore. For example, the ML classification model may be determined using a supervised ML algorithm, such as an artificial neural network, a support vector machine, a fuzzy inference system, a flow regime classification, and an expert system.

At step 320, hybrid BHP modeling method 100 (referring to FIG. 1) may use the best correlation to determine a BHP estimate based on the field data for the wellbore.

At step 325, hybrid BHP modeling method 100 (referring to FIG. 1) may train an ML regression model to determine a residual correction using the BHP estimate and the field data for the wellbore. In some embodiments, the BHP estimate may be compared to observed BHP measurements to determine input data for training the ML regression model. The ML regression model may be implemented to determine patterns or relationships associated with minor physics, which are modeled using the empirical and/or mechanistic models.

At step 330, hybrid BHP modeling method 100 (referring to FIG. 1) may use the ML regression model to determine a final BHP using the BHP estimate and the residual correction for the wellbore.

Particular embodiments may repeat one or more steps of the method of FIG. 3, where appropriate. Although this disclosure describes and illustrates particular steps of the method of FIG. 3 as occurring in a particular order, this disclosure contemplates any suitable steps of the method of FIG. 3 occurring in any suitable order. Moreover, although this disclosure describes and illustrates an example method to perform a two-step ML model for predicting BHP for a reservoir system, including the particular steps of the method of FIG. 3, this disclosure contemplates any suitable method including any suitable steps, which may include all, some, or none of the steps of the method of FIG. 3, where appropriate. In some embodiments, although this disclosure describes and illustrates particular components, devices, or systems carrying out particular steps of the method of FIG. 3, this disclosure contemplates any suitable combination of any suitable components, devices, or systems carrying out any suitable steps of the method of FIG. 3.

FIG. 4 illustrates a block diagram of an exemplary control unit 400, in accordance with certain embodiments. In certain example embodiments, control unit 400 may be configured to create and maintain a first database 408 that includes information concerning a reservoir system. In other embodiments, the control unit 400 is configured to create and maintain database 408 with information concerning one or more fluid systems. In certain example embodiments, control unit 400 is configured to use information from database 408 to train one or many machine learning algorithms 412, including, but not limited to, artificial neural network, random forest, gradient boosting, support vector machine, or kernel density estimator. In some embodiments, control system 402 may include one more processors, such as processor 404. Processor 404 may include, for example, a microprocessor, microcontroller, digital signal processor (DSP), application specific integrated circuit (ASIC), or any other digital or analog circuitry configured to interpret and/or execute program instructions and/or process data. In some embodiments, processor 404 may be communicatively coupled to memory 406. Processor 404 may be configured to interpret and/or execute non-transitory program instructions and/or data stored in memory 406. Program instructions or data may constitute portions of software for carrying out fluid system modeling, as described herein. Memory 406 may include any system, device, or apparatus configured to hold and/or house one or more memory modules; for example, memory 406 may include read-only memory, random access memory, solid state memory, or disk-based memory. Each memory module may include any system, device or apparatus configured to retain program instructions and/or data for a period of time (e.g., computer-readable non-transitory media).

Although control unit 400 is illustrated as including two databases, control unit 400 may contain any suitable number of databases and machine learning algorithms. Control unit 400 may be communicatively coupled to one or more displays 416 such that information processed by sensor control system 402 may be conveyed to operators at or near the pipeline or flowline or may be displayed at a location offsite.

Modifications, additions, or omissions may be made to FIG. 4 without departing from the scope of the present disclosure. For example, FIG. 4 shows a particular configuration of components for control unit 400. However, any suitable configurations of components may be used. For example, components of control unit 400 may be implemented either as physical or logical components. Furthermore, in some embodiments, functionality associated with components of control unit 400 may be implemented in special purpose circuits or components. In other embodiments, functionality associated with components of control unit 400 may be implemented in a general purpose circuit or components of a general purpose circuit. For example, components of control unit 400 may be implemented by computer program instructions. In some embodiments, the two-step ML model may be implemented by computer program instructions.

To facilitate a better understanding of the present disclosure, the following examples of certain aspects of preferred embodiments are given. The following examples are not the only examples that could be given according to the present disclosure and are not intended to limit the scope of the disclosure or claims.

Example 1

FIG. 5A illustrates an example 500 comparison of actual gauge BHP data against BHP data based on a plurality of physics correlations for a public dataset, in accordance with certain embodiments. In this example, the hybrid BHP modeling method is applied on a well from the Volve public dataset. In particular, FIG. 5A shows the BHP 502 computed from 11 different physics-based correlations 506 against actual gauge BHP data 504. The 11 physics-based correlations 506 include Baxendell and Thomas, Beggs and Brill, Duns and Ros, Fancher and Brown, Gray, Hagedorn and Brown, Mukherjee and Brill, Orkiszewski, Poetmann and Carpenter, Homogencous liquid, and Homogeneous no slip. However, there is no single correlation that may predict the BHP accurately without the need for tuning, nor any correlation is able to accurately model for the entire duration. Notably, a well event 508 around 1200 days changes the BHP behavior substantially. In practice, this requires continuous evaluation of the best physics correlation based on well conditions that must be done before tuning the selected correlation, which is not feasible in large fields.

FIG. 5B illustrates an example comparison 520 of actual gauge BHP data 504 against BHP data based on a plurality of ML-based methods 536 for the public dataset, in accordance with certain embodiments. In some embodiments, FIG. 5B shows a plurality of BHP results computed from 3 different ML-based methods 536, such as BHP 522 for ordinary least squares (OLS), BHP 524 for Lasso, and BHP 526 for support vector regression (SVR). The data 528 for the first 2 years was used for training the plurality of ML models which are later used to predict for the rest of the well life. The BHP 522 for the OLS model suffers from over-fitting with several unnecessary features. However, the BHP 524 for the Lasso model and the BHP 526 for the SVR model show significant improvement in prediction accuracy, such as a lower error and a better error distribution. In some embodiments, the BHP 524 for the Lasso model provides the best prediction (RMSE=184 psi) with the simplest model. While the BHP accuracy significantly improved during the early time, there is still a large bias for most of the prediction period. Thus, in this example, neither the pure physics nor pure data-driven method adequately predicts BHP without additional effort.

FIG. 5C illustrates an example comparison 550 of actual gauge BHP data 504 against BHP data based on a plurality of physics augmented features (PAF) models 566 for the public dataset, in accordance with certain embodiments. The hybrid BHP modeling method may determine the plurality of physics augmented features by calculating BHP from various physics-based correlations. An augmented training dataset may be formed by combining the plurality of physics augmented features with other features, such as liquid production rate, wellhead pressure, GLR, WCT, and variants of these features. Thus, the hybrid BHP modeling method may use the augmented training dataset to train the plurality of PAF models based on 3 different ML-based methods, such as OLS, lasso, and SVR. The data 558 for the first 2 years is used for training the plurality of PAF models 566, which are later used to predict the rest of the well life. In some embodiments, FIG. 5C shows a plurality of BHP results computed from 3 different PAF models 566, such as BHP 552 for PAF-OLS, BHP 554 for PAF-Lasso, and BHP 556 for PAF-SVR. The BHP 554 for the PAF-Lasso model produces the most accurate results with an RMSE of 141 psi. The overall accuracy of the model during prediction can be seen to improve significantly as compared to using pure physics or data driven models.

Example 2

FIG. 6A illustrates an example relative error 600 for a plurality of wells with a classical physics-based correlation for a deep-water offshore dataset, in accordance with certain embodiments. In this example, the hybrid BHP modeling method is applied to a deep-water offshore field with 5 wells. The physics-based correlations show good accuracy overall; however, they show higher frictional drops linearly at high rates. A generalized linear model is used as a suitable physics-based method based on the flow/fluid type as a feature in addition to the liquid rate. The relative error 602 for all wells is in a range from 0.35% to 1.16%. An example of the MedAPE in BHP compared to the actual gauge data using the physics-based model may be found in Table 3.

TABLE 3
Error metric (MedAPE) for 5 wells in a deep-water offshore field
using a pure physics-based correlations and a hybrid BHP model

	Well 1	Well 2	Well 3	Well 4	Well 5

Physics Model	0.86%	1.57%	0.5%	1.16%	0.35%
(MedAPE)
Hybrid Model	0.44%	0.15%	0.28%	0.1%	0.33%
(MedAPE)

FIG. 6B illustrates an example relative error 620 for a plurality of wells after applying one or more physics-preprocessing based ML models for the deep-water offshore dataset, in accordance with certain embodiments. The hybrid BHP model 622 shows improved accuracy overall compared to the pure physics-based model in FIG. 6A. The relative error for all wells is in a range from 0.1% to 0.44%. An example of the MedAPE in BHP compared to the actual gauge data using the hybrid BHP model may be found in Table 3.

FIG. 6C illustrates an example comparison 650 of actual gauge BHP data 652 against predicted BHP data 654 from a hybrid model for the deep-water offshore dataset, in accordance with certain embodiments. The predicted BHP data 654 from the hybrid method is very consistent with the actual gauge BHP data 652.

Example 3

FIGS. 7A, 7B, and 7C illustrate example well test and allocation based gas rate, oil rate, and water rate for a first well of a first onshore unconventional dataset, in accordance with certain embodiments. In this example, the hybrid BHP modeling method applies a 2-step ML model to determine BHP from field data in two wells from a major US onshore unconventional play that exhibits multi-phase flow. The two-step ML model is trained using field data until the end of 2020 for both wells using five correlations for an ML classification model, and then the residual is predicted by an ML regression model for the best model predicted by the ML classification model. FIG. 7A shows the allocation based gas rate 702 and well test based gas rate 704 for a first well of the first onshore unconventional dataset. FIG. 7B shows the allocation based oil rate 712 and well test based oil rate 714 for the first well of the first onshore unconventional dataset. FIG. 7C shows the allocation based water rate 722 and well test based water rate 724 for the first well of the first onshore unconventional dataset. The period after 2020 is used for blind testing the performance of the 2-step ML model for both wells.

FIG. 7D illustrates an example comparison of actual gauge BHP data 736 against predicted BHP data from a hybrid model for well 1 of the first onshore unconventional dataset, in accordance with certain embodiments. In some embodiments, the hybrid BHP modeling method is applied to predict BHP using allocation based production data 732 and well test based production data 734 to compare their impact on model performance. The best accuracy from a physical correlation is 14% for each well. As a result, the hybrid BHP modeling method shows very good accuracy on predicted BHP for the test period as compared to simply using any standard correlation.

FIGS. 8A, 8B, and 8C illustrate example well test and allocation based gas rate, oil rate, and water rate for a second well of the first onshore unconventional dataset, in accordance with certain embodiments. FIG. 8A shows the allocation based gas rate 802 and well test based gas rate 804 for the second well of the first onshore unconventional dataset. FIG. 8B shows the allocation based oil rate 812 and well test based oil rate 814 for the second well of the first onshore unconventional dataset. FIG. 8C shows the allocation based water rate 822 and well test based water rate 824 for the second well of the first onshore unconventional dataset. The period after 2020 is used for blind testing the performance of the 2-step ML model for both wells.

FIG. 8D illustrates an example comparison of actual gauge BHP data 836 against predicted BHP data from a hybrid model for the second well of the onshore unconventional dataset, in accordance with certain embodiments. In some embodiments, the hybrid BHP modeling method is applied to predict BHP using allocation based production data 832 and well test based production data 834 to compare their impact on model performance. The best accuracy from a physical correlation is 14% for each well. As a result, the hybrid BHP modeling method shows very good accuracy on predicted BHP for the test period as compared to simply using any standard correlation. The well test and allocation based rates do not have a significant impact on model performance. Well test data performs slightly better for the first well while allocation based production rates perform slightly better for the second well. Regardless of the source of production rates, it is worth noting that the 2-stage BHP ML model outperforms the classical way of determining BHPs. An example of the MedAPE in BHP for two wells using hybrid BHP models with allocation rates and well test rates may be found in Table 4.

TABLE 4
Error Metric (MedAPE) for 2 wells using hybrid BHP models
trained with allocation rates and well test rates

	MedAPE with Allocation Data:	MedAPE with Test Data

Well 1	6.93%	6.87%
Well 2	6.32%	8.05%

Example 4

FIGS. 9A and 9B illustrate example cumulative distribution 902 and probability distribution 904 of MedAPE between actual BHP data and hybrid BHP model predictions for all wells of a second onshore unconventional dataset, in accordance with certain embodiments. In this example, the hybrid BHP modeling method applies a 2-step ML model to determine BHP from field data for approximately 3300 wells in a U.S. onshore unconventional basin in order to prove the generalization ability and robustness for field scale applications. Both classification and regression models have been implemented using an Extreme Gradient Boosting (XGBoost) algorithm with 80% of the data used for training and 20% for validation. The training data set includes data until the end of 2022 and testing done for 10 months in 2023 across all the wells. FIGS. 9A and 9B show a relatively low error between the actual BHP data and the hybrid BHP model predictions on the test set for all wells. The hybrid BHP predictions have a MedAPE value of 4.20% at 20th percentile of the cumulative distribution (P20). The hybrid BHP predictions have a MedAPE value of 5.81% at 50th percentile of the cumulative distribution (P50). The hybrid BHP predictions have a MedAPE value of 8.40% at 80th percentile of the cumulative distribution (P80). An example of the P20, P50, and P80 estimates of MedAPE of the hybrid BHP model may be found in Table 5.

TABLE 5
P20, P50 and P80 estimates of MedAPE of the 2-stage BHP model

	Cumulative Distribution	Median Absolute Percentage
	Probability	Error (MedAPE)

	P20	4.20%
	P50	5.81%
	P80	8.40%

FIG. 10 illustrates an example MedAPE of BHPs predicted by physics-based correlations as compared to the hybrid BHP model for allocation data and well test data for the second onshore unconventional dataset, in accordance with certain embodiments. The MedAPE value for the hybrid BHP method 1010 is compared to a plurality of MedAPE values for several classical physics-based models, such as Mukherjee and Brill 1012, Orkiszewski 1014, Hagedorn and Brown 1016, Duns and Ros 1018, and Beggs and Brill 1020. Likewise, for each physics-based model, the MedAPE value for allocation data 1002 is compared to the MedAPE value for well test data 1004. In general, the hybrid BHP method 1010 outperforms other classical methods significantly because the hybrid BHP method 1010 may determine the best correlation to be applied and then correct for any unexplained physics from selected correlation using an ML regression model. It is noted that a model which is trained with multiple wells has better predictability of correlations and residuals due to a large number of training samples that capture enough variance in well conditions across the field.

FIG. 11A illustrates an example MedAPE of the hybrid BHP model predictions by formation with distribution errors across all areas in a formation for the second onshore unconventional dataset, in accordance with certain embodiments. The error metric distributed by formation shows a similar distribution, which confirms that the hybrid BHP model does not bias any particular formation.

FIG. 11B illustrates an example MedAPE of the hybrid BHP model predictions by area with distribution errors across all formations in an area for the second onshore unconventional dataset, in accordance with certain embodiments. The error metric distributed by area shows a similar distribution, which confirms that the hybrid BHP model does not bias any particular area.

Modifications, additions, or omissions may be made to the systems and apparatuses described herein without departing from the scope of the disclosure. The components of the systems and apparatuses may be integrated or separated. Moreover, the operations of the systems and apparatuses may be performed by more, fewer, or other components. Additionally, operations of the systems and apparatuses may be performed using any suitable logic comprising software, hardware, and/or other logic. As used in this document, “each” refers to each member of a set or each member of a subset of a set.

Modifications, additions, or omissions may be made to the methods described herein without departing from the scope of the present disclosure. For example, the steps may be combined, modified, or deleted where appropriate, and additional steps may be added. Additionally, the steps may be performed in any suitable order without departing from the scope of the present disclosure.

Although the present disclosure has been described with several embodiments, a myriad of changes, variations, alterations, transformations, and modifications may be suggested to one skilled in the art, and it is intended that the present disclosure encompass such changes, variations, alterations, transformations, and modifications as fall within the scope of the appended claims. Therefore, the present disclosure is well adapted to attain the ends and advantages mentioned as well as those that are inherent therein. 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. Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. 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 and spirit of the present disclosure. Also, the terms in the claims have their plain, ordinary meaning unless otherwise explicitly and clearly defined by the patentee. The indefinite articles “a” or “an,” as used in the claims, are each defined herein to mean one or more than one of the element that it introduces.

A number of examples have been described. Nevertheless, it will be understood that various modifications can be made. Accordingly, other implementations are within the scope of the following claims.