SYSTEM AND METHOD FOR RAPID MUD LOSS DIAGNOSTICS IN FRACTURED MEDIA

Description

TECHNICAL FIELD

Embodiments of the disclosure generally relate to wellbore drilling operations, and more particularly to a semi-analytical solution for predicting lost circulation events in fractured media using a neural network.

BACKGROUND

A rock formation that resides under the Earth's surface is often called a “subsurface” formation. A subsurface formation that contains a subsurface pool of hydrocarbons, such as oil and gas, is usually referred to as a “hydrocarbon reservoir.” Hydrocarbons are typically extracted (or “produced”) from a hydrocarbon reservoir by way of a hydrocarbon well. A hydrocarbon well normally includes a wellbore (or “borehole”) that is drilled into the reservoir. For example, a hydrocarbon well may include a wellbore that extends into the rock of a reservoir to facilitate the extraction (or “production”) of hydrocarbons from the reservoir, the injection of fluids into the reservoir, or the evaluation and monitoring of the reservoir.

Wellbore drilling is a critical process to explore and recover natural resources, such as water, oil, and gas, for the oil and gas industry. During wellbore drilling, drilling mud (or “drilling fluid”), such as solids and fluid, is gradually pumped into the hydrocarbon well to enable hydrocarbons to be depleted by flowing up the wellbore through a wellbore annulus. Drilling mud is an important part of the drilling process. For example, the drilling mud may cool and lubricate a drilling bit and stabilize the borehole by providing hydrostatic pressure to prevent formation fluids from entering the wellbore. As another example, the drilling mud may carry cuttings and draining waste to the surface. Thus, the hydrocarbons may safely be extracted by flowing up the wellbore through the wellbore annulus. However, drilling mud loss may occur in a lost circulation event during the drilling process of penetrating a subsurface formation with complex rock properties, particularly in fractured, cavernous, or highly permeability media. Thus, the drilling mud uncontrollably flows into the surrounding formation, reducing the amount of drilling mud returning to the surface. For example, the drilling mud loss occurs when a mud weight essential to maintain wellbore stability and well control exceeds a pore pressure or a fracture resistance of the surrounding formation. The lost circulation event may be classified by the quantity of mud or fluid lost per hour meter³/hour (m³/h), such as complete loss (no return), severe loss (loss rate up to 15 m³/h), partial loss (loss rate up to 10 m³/h), and seepage loss (loss rate up to 1 m³/h). As a result, lost circulation may result in expensive operational costs which vary from a couple of barrels per hour to hundreds of barrels in minutes.

SUMMARY

Lost circulation events may be very costly to drilling operations because the lost circulation of drilling mud increases non-production time and operating costs and leads to various problems, such as wellbore instability, jamming of a drilling tool, blowout, or even loss of the well. An improper or untimely response usually causes loss of more drilling mud, time, and extra cost. For example, lost circulation may be associated with severe issues like formation damage caused by plugging of pore throats by mud particles, unsuccessful production tests, borehole instability, well control issues, substandard hydrocarbon production after well completion, and stuck pipe. Even if a lost circulation event is identified, it is usually identified much later than the beginning of the lost circulation event. Therefore, identifying a lost circulation event earlier may prevent the magnitude of lost drilling fluid. Establishing a prediction model to characterize a drilling mud loss behavior may mitigate and overcome the drilling mud loss problem. In particular, an efficient solution to characterize the lost circulation event behavior in various formations may assist in rapid decision-making of the lost circulation treatment plan, drilling engineering safety, and cost control.

The following presents a simplified summary of the disclosed subject matter in order to provide a basic understanding of some aspects of the subject matter disclosed herein. This summary is not an exhaustive overview of the technology disclosed herein. It is not intended to identify key or critical elements of the disclosed subject matter or to delineate the scope of the disclosed subject matter. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is discussed later.

In one or more embodiments, the present invention provides a method for modeling a drilling mud loss behavior for a reservoir. The method may receive mud loss data associated with the drilling mud loss behavior for the reservoir. The method may further identify, using the mud loss data, a plurality of uncertainty parameters associated with the drilling mud loss behavior for the reservoir. The method may further determine, using the mud loss data and a Latin Hypercube Sampling (LHS) algorithm, a plurality of lost circulation events associated with the drilling mud loss behavior for the reservoir. The method may further generate, using a semi-analytical function, a mud loss training dataset from the plurality of lost circulation events associated with the drilling mud loss behavior for the reservoir. The method may further train, using the mud loss training dataset, a machine learning model to predict a maximum loss volume, a maximum stopping time, and an equivalent hydraulic fracture aperture associated with the drilling mud loss behavior for the reservoir. The method may further determine, using the mud loss data, a new lost circulation event based on the plurality of uncertainty parameters associated with the drilling mud loss behavior for the reservoir, the new lost circulation event having a corresponding early loss volume and a corresponding early loss time. The method may further determine, using the trained machine learning model, a new maximum loss volume, a new maximum stopping time, and a new equivalent hydraulic fracture aperture associated with the new lost circulation event based on the plurality of uncertainty parameters and the new lost circulation event. The method may further determine an operation to adjust a parameter of a drilling mud for the reservoir based on the maximum loss volume, the maximum stopping time, and the equivalent hydraulic fracture aperture associated with the new lost circulation event.

In one or more embodiments, the present invention provides a system for modeling a drilling mud loss behavior for a reservoir. The system may include a processor and a computer-readable non-transitory storage medium including instructions that, when executed by the processor, cause to the processor to perform operations. The operations include receiving mud loss data associated with the drilling mud loss behavior for the reservoir. The operations further include identifying, using the mud loss data, a plurality of uncertainty parameters associated with the drilling mud loss behavior for the reservoir. The operations further include determining, using the mud loss data and a Latin Hypercube Sampling (LHS) algorithm, a plurality of lost circulation events associated with the drilling mud loss behavior for the reservoir. The operations further include generating, using a semi-analytical function, a mud loss training dataset from the plurality of lost circulation events associated with the drilling mud loss behavior for the reservoir. The operations further include training, using the mud loss training dataset, a machine learning model to predict a maximum loss volume, a maximum stopping time, and an equivalent hydraulic fracture aperture associated with the drilling mud loss behavior for the reservoir. The operations further include determining, using the mud loss data, a new lost circulation event based on the plurality of uncertainty parameters associated with the drilling mud loss behavior for the reservoir, the new lost circulation event having a corresponding early loss volume and a corresponding early loss time. The operations further include determining, using the trained machine learning model, a new maximum loss volume, a new maximum stopping time, and a new equivalent hydraulic fracture aperture associated with the new lost circulation event based on the plurality of uncertainty parameters and the new lost circulation event. The operations further include determining an operation to adjust a parameter of a drilling mud for the reservoir based on the maximum loss volume, the maximum stopping time, and the equivalent hydraulic fracture aperture associated with the new lost circulation event.

In one or more embodiments, the present invention provides a non-transitory computer-readable medium comprising instructions, when executed by a processor, cause the processor to perform operations. The operations include receiving mud loss data associated with the drilling mud loss behavior for the reservoir. The operations further include identifying, using the mud loss data, a plurality of uncertainty parameters associated with the drilling mud loss behavior for the reservoir. The operations further include determining, using the mud loss data and a Latin Hypercube Sampling (LHS) algorithm, a plurality of lost circulation events associated with the drilling mud loss behavior for the reservoir. The operations further include generating, using a semi-analytical function, a mud loss training dataset from the plurality of lost circulation events associated with the drilling mud loss behavior for the reservoir. The operations further include training, using the mud loss training dataset, a machine learning model to predict a maximum loss volume, a maximum stopping time, and an equivalent hydraulic fracture aperture associated with the drilling mud loss behavior for the reservoir. The operations further include determining, using the mud loss data, a new lost circulation event based on the plurality of uncertainty parameters associated with the drilling mud loss behavior for the reservoir, the new lost circulation event having a corresponding early loss volume and a corresponding early loss time. The operations further include determining, using the trained machine learning model, a new maximum loss volume, a new maximum stopping time, and a new equivalent hydraulic fracture aperture associated with the new lost circulation event based on the plurality of uncertainty parameters and the new lost circulation event. The operations further include determining an operation to adjust a parameter of a drilling mud for the reservoir based on the maximum loss volume, the maximum stopping time, and the equivalent hydraulic fracture aperture associated with the new lost circulation event.

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

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts.

FIG. 1 illustrates a schematic diagram of a reservoir environment in accordance with one or more embodiments.

FIG. 2 illustrates a schematic diagram of drilling mud loss in accordance with one or more embodiments.

FIG. 3 illustrates a machine learning system in accordance with one or more embodiments.

FIGS. 4A-4C illustrate a plurality of distributions of three uncertainty parameters and cumulative mud-loss volume versus time for a dataset in accordance with one or more embodiments.

FIG. 4D illustrates a plurality of semi-analytical solutions of cumulative mud-loss volume versus time in accordance with one or more embodiments.

FIG. 5A illustrates a plot of transient loss volume versus time in accordance with one or more embodiments.

FIG. 5B illustrates a plot of maximum loss volume versus maximum stopping time in accordance with one or more embodiments.

FIG. 6 illustrates a plot of a plurality of early time solutions in accordance with one or more embodiments.

FIG. 7 illustrates a comparison of a plurality of performance functions of ANN for a training dataset and a validation dataset in accordance with one or more embodiments.

FIGS. 8A and 8B illustrate a plurality of comparisons of predicted output data versus expended output data for a training dataset and a validation dataset in accordance with one or more embodiments.

FIG. 9 illustrates a plot of a plurality of histogram error distributions for a plurality of prediction output parameters for a testing dataset in accordance with one or more embodiments.

FIG. 10 illustrates a Tornado error distribution of relative errors for a plurality of prediction output parameters for three field cases in accordance with one or more embodiments.

FIG. 11 illustrates a comparison of a plurality of predicted output parameters versus expected output parameters for three field cases in accordance with one or more embodiments.

FIG. 12 illustrates a flow chart that shows a method for predicting a plurality of output parameters for a lost circulation event in fractured media in accordance with one or more embodiments.

FIG. 13 illustrates a functional block diagram of a computer system in accordance with one or more embodiments.

While certain embodiments will be described in connection with the illustrative embodiments shown herein, the subject matter of the present disclosure is not limited to those embodiments. On the contrary, all alternatives, modifications, and equivalents are included within the spirit and scope of the disclosed subject matter as defined by the claims. In the drawings, which are not to scale, the same reference numerals are used throughout the description and in the drawing figures for components and elements having the same structure.

DETAILED DESCRIPTION

In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the inventive concept. In the interest of clarity, not all features of an actual implementation are described. Moreover, the language used in this disclosure has been principally selected for readability and instructional purposes, and may not have been selected to delineate or circumscribe the inventive subject matter, resort to the claims being necessary to determine such inventive subject matter. Reference in this disclosure to “one embodiment” or to “an embodiment” or “another embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosed subject matter, and multiple references to “one embodiment” or “an embodiment” or “another embodiment” should not be understood as necessarily all referring to the same embodiment.

This disclosure pertains to a system and method for modeling a drilling mud loss behavior for a reservoir. Techniques disclosed herein apply a semi-analytical workflow to predict lost circulation events by modeling a drilling mud loss behavior for the reservoir based on a neural network. Traditional approaches usually take preventive measures to limit lost circulation. For example, traditional approaches may treat the mud with loss of circulation materials (LCMs) or perform a mud leak off test and a formation integrity test. In another example, some traditional approaches may take precautions to minimize loss circulation during drilling by maintaining a proper mud weight, minimizing annular-friction pressure losses during drilling and tripping in, applying adequate hole cleaning, avoiding restrictions in an annular space, and using a setting casing to protect upper weaker formations within a transition zone. However, complete prevention of lost circulation is difficult because the penetration of a drill bit in subsurface formation, such as in fractured media, may cause lost circulation to reach a target zone. Embodiments of the disclosure include training a surrogate model using an Artificial Neural Network (ANN) based on a mud loss training dataset generated using a Latin Hypercube sampling algorithm and mud loss data from a reservoir. The mud loss training dataset includes a plurality of type curves developed based on a plurality of uncertainty parameters which are relevant to lost circulation events for the reservoir. As a result, the proposed semi-analytical workflow may use the surrogate model to predict a plurality output parameters of lost circulation events, such as average hydraulic fracture aperture w, maximum stop volume

V m max ,

and maximum stopping loss time t^max, during the drilling a reservoir.

Additionally, the semi-analytical workflow may determine one or more input parameters in the mud loss training dataset by using one or more semi-analytical functions, such as mud loss ordinary differential equations (ODE) solutions derived from previous experience. For example, the one or more semi-analytical functions include a first plurality of mud loss ODE solutions for Newtonian fluid flow into a horizontal fracture by combining the diffusivity equation and mass conservation in a one-dimensional (1D) radial system. As another example, the one or more semi-analytical functions include a second plurality of mud loss ODE solutions for non-Newtonian fluid flow or lost circulation material (LCM) exhibiting a yield-power law behavior. As a result, the semi-analytical workflow may be automated to generate an accurate, efficient, and robust model for predicting the plurality output parameters of lost circulation events, such as average hydraulic fracture aperture w, maximum stop volume

V m max ,

and maximum stopping loss time t^max from input mud loss data to significantly reduce the time of interpreting and analyzing mud loss information by minimizing human error due to subjectivity. As a result, the semi-analytical workflow may be integrated into a control system to characterize a lost circulation event behavior in fractured media for rapid decision-making of the lost circulation treatment plan, drilling engineering safety, and cost control. Additionally, the surrogate model may be integrated with real-time data acquisition systems to continuously monitor the performance of the drilling mud. The surrogate model may also be used to provide immediate feedback and suggest adjustments to the mud properties or pumping rates to maintain optimal conditions and prevent problems like severe lost circulation or wellbore instability. After drilling, the surrogate model may be implemented to analyze the performance of the drilling mud and the overall drilling operation to identify areas for improvement and optimize future drilling programs.

FIG. 1 is a diagram that illustrates a hydrocarbon reservoir environment (for example, reservoir environment or well environment) 100 in accordance with one or more embodiments. In the illustrated embodiment, reservoir environment 100 includes a hydrocarbon reservoir (“reservoir”) 116 located in a subsurface formation (“formation”) 106, and a hydrocarbon reservoir development system 110. Formation 106 may include a porous or fractured rock formation that resides underground, beneath the Earth's surface (“surface”) 108. Reservoir 116 may include a portion of formation 106 that contains (or that is determined to contain) a subsurface pool of hydrocarbons, such as oil and gas. Formation 106 and reservoir 116 may each include different layers of rock having varying characteristics (for example, varying degrees of permeability, porosity, lithology, geology, or fluid saturation). Hydrocarbon reservoir development system 110, such as a drilling system, may facilitate extraction (or “production”) of hydrocarbons from reservoir 116. Hydrocarbon reservoir development system 110 may include a drill string, a drill bit, a mud circulation system, and the like for use in extending wellbore 104 into formation 106.

In some embodiments, hydrocarbon reservoir development system 110 includes a hydrocarbon reservoir control system (“control system”) 114 and (one or more) well 102. Control system 114 may include hardware, software, or both for managing drilling operations or maintenance operations. For example, control system 114 may include one or more programmable logic controllers (PLCs) that include hardware, software, or both with functionality to control one or more processes performed by hydrocarbon reservoir development system 110. Specifically, a PLC may control valve states, fluid levels, pipe pressures, warning alarms, drilling parameters (for example, torque, weight on bit (WOB), stand pipe pressure (SPP), revolutions per minute (RPM), etc.), pressure releases, or any combination thereof throughout a drilling rig. In particular, a PLC may be a ruggedized computer system with functionality to withstand vibrations, extreme temperatures, wet conditions, dusty conditions, or any combination thereof, for example, around a drilling rig. In some embodiments, control system 114 includes a computer system that is the same as or similar to that of computer system 1300 described with regard to at least FIG. 13. Without loss of generality, the term “control system” may refer to a drilling operation control system that is used to operate and control the equipment, a drilling data acquisition and monitoring system that is used to acquire drilling process and equipment data and to monitor the operation of the drilling process, or a drilling interpretation software system that is used to analyze and understand drilling events and progress.

In some embodiments, control system 114 controls operations for developing reservoir 116. Although FIG. 1 illustrates control system 114 as being disposed at a location proximal to well 102, this may not be the case. For example, control system 114 may be provided at a remote location (for example, remote control center, core analysis lab, data center, server farm, and the like) that is remote from well 102. Control system 114 may control one or more formation evaluation operations (for example, well logging operations, core analysis operations, coring operations, and the like) used to acquire data from reservoir 116 and may control processing that automatically generates core description data based on core image data, and models and simulations generated based on data including image data of reservoir 116 that characterize the reservoir 116. Alternately, an external system may control to automatically generate core description data based on core image data of wellbore 104, and control system 114 may control and implement models and simulations generated based on the automatically generated core description data.

In some embodiments, control system 114 determines drilling parameters for well 102 in reservoir 116, determines operating parameters for well 102 in reservoir 116, controls drilling of well 102 in accordance with drilling parameters, or controls operating well 102 in accordance with the operating parameters. This may include, for example, control system 114 determining drilling parameters (for example, determining well location and trajectory) for reservoir 116, controlling drilling of well 102 in accordance with the drilling parameters (for example, controlling a well drilling system of the hydrocarbon reservoir development system 110 to drill well 102 at the well location and with wellbore 104 following the trajectory), determining operating parameters (for example, determining production rates and pressures for “production” well 102 and injection rates and pressure for “injection” well 102), and controlling operations of well 102 in accordance with the operating parameters (for example, controlling a well operating system of the hydrocarbon reservoir development system 110 to operate the production well 102 to produce hydrocarbons from reservoir 116 in accordance with the production rates and pressures determined for well 102, and controlling the injection well 102 to inject substances, such as water, into reservoir 116 in accordance with the injection rates and pressures determined for well 102).

In some embodiments, well 102 may include wellbore 104 that extends from surface 108 into a target zone of formation 106, such as reservoir 116. Wellbore 104 may be created, for example, by a drill bit boring along a path (or trajectory) through formation 106 and reservoir 116. In some embodiments, formation 106 may include various formation characteristics of interest, such as formation porosity, formation permeability, water saturation, irreducible water saturation, rock type, temperature, density, and the like. Porosity may indicate how much space exists in a particular rock within an area of interest in formation 106, where oil, gas, water, or any combination thereof may be trapped. Permeability may indicate the ability of liquids and gases to flow through the rock within the area of interest. Water saturation may indicate the fraction of water in a given pore space. Irreducible water saturation may indicate the ratio of irreducible total fluid volume to effective porosity for a formation within the area of interest. Rock type may indicate the type of rock for a formation with the area of interest. For example, tight chalk may have a greater strength property that requires a greater pump pressure for breaking the chalk. Temperature may indicate the temperature or the temperature gradient for a formation with the area of interest. Density may indicate the bulk density for a formation with the area of interest.

In some embodiments, reservoir environment 100 may include a logging system 112. Logging system 112 may include one or more logging tools 113, such as a nuclear magnetic resonance (NMR) spectrometer, for use in generating well logs and core sample data of formation 106. Logging tools 113 may provide a powerful way to characterize the fine-scale petrophysical properties data, such as density, porosity, permeability, rock type, water saturation, irreducible water saturation, etc. Logging tool 113 may be inserted into wellbore 104 or used in the laboratory to acquire measurements, such as well logs and core sample data as the tool traverses a depth interval 130, such as a targeted reservoir section of wellbore 104. The plot of the logging measurements versus depth may be referred to as a “log” or “well log.” Well logs may provide depth measurements of well 102 that describe such reservoir characteristics as formation porosity, formation permeability, resistivity, density, water saturation, total organic content (TOC), volume of kerogen, Young's modulus, Poisson's ratio, and the like. The resulting logging measurements may be stored, processed, or both, for example, by control system 114, to generate corresponding well logs for well 102. A well log may include, for example, a plot of a logging response time versus true vertical depth (TVD) across the depth interval 130 of wellbore 104.

Reservoir characteristics may be determined using a variety of different techniques. For example, certain reservoir characteristics, such as uncertainty parameters 154, may be determined via coring, such as physical extraction of rock samples, to produce core samples, logging operations, or both, such as wireline logging, logging-while-drilling (LWD), and measurement-while-drilling (MWD). Coring operations may include physically extracting a rock sample from a region of interest within wellbore 104 for detailed laboratory analysis. For example, when drilling an oil or gas well, a coring bit may cut plugs (or “cores” or “core samples”) from formation 106 and bring the plugs to the surface, and these core samples may be analyzed at the surface, such as in a lab, to determine various characteristics of the formation 106 at the location where the sample was obtained.

In some embodiments, reservoir environment 100 may include a mud loss monitor 140. Mud loss monitor 140 may be configured to implement a semi-analytical workflow to predict a plurality of lost circulation events 160 based on a surrogate model 164. In particular, surrogate model 164 may be generated using one or more machine learning algorithms, such as ANN 162. In some embodiments, control system 114 may be communicatively coupled to mud loss monitor 140 to drive the operation of mud loss monitor 140 under stored program control. For example, control system 114 may include a control computer that may incorporate wireless networking communication interfaces to deliver a graphical user interface or other user interface to a compatible browser, application, or app of a mobile computing device, and to receive input signals and commands relating to mud loss monitor 140 from control system 114.

In some embodiments, mud loss monitor 140 may be programmed to generate surrogate model 164 in multiple stages of the semi-analytical workflow. In particular, the semi-analytical workflow includes three stages: (1) a data acquisition stage; (2) a surrogate model development stage; and (3) a model validation stage. In the data acquisition stage, mud loss monitor 140 may be implemented to use a data generator 150 to obtain mud loss data 142 from reservoir 116 to determine a plurality of uncertainty parameters 154 which are relevant to lost circulation events for reservoir 116. Based on the plurality of uncertainty parameters 154, mud loss monitor 140 may apply the semi-analytical workflow to determine a plurality of lost circulation events 160 associated with mud loss data 142 from reservoir 116. As a result, data generator 150 is configured to generate encoded mud loss data 152 from the plurality of uncertainty parameters 154 and other additional parameters determined using the one or more semi-analytical functions 156 for the plurality of lost circulation events 160 for reservoir 116. In the surrogate model development stage, mud loss monitor 140 may be implemented to use a training dataset of the encoded mud loss data 152 and one or more machine learning algorithms, such as ANN 162, to train surrogate model 164 to predict a plurality of output parameters of the plurality of lost circulation events 160 for reservoir 116. Surrogate model 164 is trained to map a nonlinear relationship between the plurality of input parameters and the plurality of output parameters by modeling a lost circulation behavior for the reservoir. Thus, surrogate model 164 may be used to predict the plurality of output parameters for lost circulation events in new input data.

In some embodiments, encoded mud loss data 152 may include a plurality of input parameters, such as flow behavior index n, fluid yield stress τ₀, consistency factor m, pressure drop Δp, wellbore radius r_w, early mud loss volume

V m early ,

and early mud loss time t^early for the plurality of lost circulation events 160. As another example, encoded mud loss data 152 may include a plurality of output parameters, such as average hydraulic fracture aperture w, maximum stop volume

V m max ,

and maximum stopping loss time t^max, for the plurality of lost circulation events 160. The flow behavior index n is a parameter used to describe the flow characteristics of non-Newtonian fluids in rheology. The flow behavior index n may determine whether a fluid is shear-thinning (pseudoplastic), shear-thickening (dilatant), or Newtonian. For example, a flow behavior index of n=1 may identify Newtonian fluids. The viscosity is constant, and the shear stress is directly proportional to the shear rate. As another example, a flow behavior index of n<1may identify shear-thinning (pseudoplastic) fluids. The apparent viscosity decreases with an increasing shear rate. As another example, the flow behavior index of n>1 may identify shear-thickening (dilatant) fluids. The apparent viscosity increases with an increasing shear rate. The fluid yield stress τ₀ is a measure of the stress associated with a steady flow at an infinitely small shear rate for a fluid. The consistency factor m is a parameter used in a power-law model to describe the viscosity of non-Newtonian fluids. The consistency factor m represents the fluid's consistency and is a measure of the fluid's thickness or resistance to flow. The power-law model is used to characterize the flow behavior of non-Newtonian fluids based on Equation 1. The pressure drop Δp is the difference in pressure between two points in a fluid flow system. Wellbore radius r_w is an apparent wellbore radius of a wellbore which is generally equal to a casing radius at the reservoir section.

τ = m ⁢ γ ˙ n ( 1 )

where τ is shear stress, {dot over (γ)} is shear rate, m is consistency factor, n is flow behavior factor.

In some embodiments, in the model validation stage, mud loss monitor 140 may be implemented to apply a validation module 170 to validate surrogate model 164 using a testing dataset of the encoded mud loss data 152 to validate surrogate model 164 to improve the performance of predicting the plurality of lost circulation events 160 for reservoir 116. As a result, mud loss monitor 140 may be used to automate the semi-analytical workflow to determine a plurality of type-curves stored in database 172 for predicting a mud loss behavior, which includes an effective hydraulic aperture of natural fractures, a maximum loss volume, a maximum stopping time, and a leakage rate as a function of time, for reservoir 116 during drilling. Therefore, mud loss monitor 140 may use the semi-analytical workflow to determine an accurate and quick estimate of the effective hydraulic aperture of natural fracture, and predictions for a mud leakage behavior based on maximum loss volume and maximum stopping time. Such information may be used to make a preventive/corrective decision, such as an optimum drilling additive design for the lost circulation material (LCM). Furthermore, mud loss monitor 140 may use the semi-analytical workflow to minimize human error due to subjectivity and significantly reduce the time of interpreting and analyzing mud loss information, such as mud loss leakage rate as a function of time, fracture conductivity, etc., for various formations 106 during drilling reservoir 116. As a result, the semi-analytical workflow may be applied to various environmental and energy applications, such as geothermal energy, geological carbon dioxide (CO₂) sequestration, underground hydrogen storage, oil, and gas industries.

In some embodiments, in the data acquisition stage, data generator 150 is configured to obtain mud loss data 142 from reservoir 116 to determine the plurality of uncertainty parameters 154 for surrogate model 164. In some embodiments, mud loss data 142 may be generated using multiple sources. For example, mud loss data 142 may include experimental drilling data generated in simulations using a reservoir simulator. As another example, mud loss data 142 may include field drilling data collected for reservoir 116. In some embodiments, data generator 150 may be configured to apply an uncertainty analysis in the semi-analytical workflow to identify a plurality of relevant uncertainty parameters 154 using mud loss data 142 for reservoir 116. Each of the plurality of relevant uncertainty parameters 154 is a scalar parameter having a uniform distribution and a corresponding range identified based on a predetermined criterion or previous experience. The plurality of uncertainty parameters may vary with different subsurface environment conditions associated with reservoir 116. An example of the plurality of relevant uncertainty parameters 154 are shown in Table 1.

In some embodiments, data generator 150 is configured to use a Latin Hypercube sampling algorithm 158 to generate a plurality of lost circulation events 160 using the plurality of uncertainty parameters 154 associated with mud loss data 142 from reservoir 116. For example, the plurality of uncertainty parameters 154 include flow behavior index n, fluid yield stress τ₀, average hydraulic fracture aperture w, consistency factor m, pressure drop Δp, and wellbore radius r_w. Data generator 150 may use the Latin Hypercube sampling algorithm 158 to optimize the plurality of lost circulation events 160 for reservoir 116 based on a predetermined sampling number S. For example, in some embodiments the predetermined sampling number is 1500 which is determined based on output solutions of the one or more semi-analytical functions 156 for the plurality of lost circulation events 160. The Latin Hypercube sampling algorithm 158 is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution. In particular, the Latin Hypercube sampling algorithm 158 may be used to sample a function of N variables, such as the plurality of uncertainty parameters 154 associated with mud loss data 142 from reservoir 116, to determine a set of random numbers which are representative of the real variability. For example, assuming that m samples are to be sampled in an N-dimensional vector space, the Latin Hypercube sampling algorithm 158 may be implemented in a plurality of steps: (1) dividing the range of each variable into m equally probable intervals that do not overlap each other, so that each interval has the same probability; (2) randomly extracting a point from each interval in each dimension; and (3) randomly extracting the points selected in the step (2) from each dimension, and composing them into a vector. Thus, in some instances the LHC algorithm may perform better than other conventional random sampling algorithms because the LHC algorithm provides good space-filling properties and avoidance of the clustering effect to ensure a good coverage of the entire high-dimensional input space.

In some embodiments, for each of the plurality of lost circulation events 160, data generator 150 is configured to apply the one or more semi-analytical functions 156 to determine a respective mud loss volume as a function of time (V_m versus t, t^max and

V m max ) .

In some embodiments, the one or more semi-analytical functions 156 may include a plurality of mud loss ordinary differential equation (ODE) solutions derived from previous experience. For example, the one or more semi-analytical functions 156 includes a first plurality of mud loss ODE solutions for Newtonian fluid flow into a horizontal fracture by combining the diffusivity equation and mass conservation in a 1D radial system. As another example, the one or more semi-analytical functions 156 includes a second plurality of mud loss ODE solutions for non-Newtonian fluid flow or lost circulation material (LCM) exhibiting a yield-power law behavior.

In some embodiments, data generator 150 may evaluate the output solutions of the one or more semi-analytical functions 156 for the plurality of lost circulation events 160. For some output solutions, a lost circulation event fails to initiate when a pressure drop in an annulus does not overcome the yield stress of a drilling mud. Thus, data generator 150 may determine the plurality of lost circulation events 160 based on the output solutions of the one or more semi-analytical functions 156 and one or more selected conditions. For example, in some embodiments the plurality of lost circulation events 160 may include 1356 lost circulation events which are selected from the 1500 output solutions of the one or more semi-analytical functions 156 based on the predetermined sampling number S=1500.

In some embodiments, data generator 150 is configured to generate encoded mud loss data 152 by formulating the plurality of uncertainty parameters 154 and one or more additional parameters, such as early mud loss volume

V m early ,

early mud loss time t^early, maximum loss volume

V m max ,

and maximum stopping time t^max, associated with the plurality of lost circulation events 160 for reservoir 116. In some embodiments, data generator 150 may determine a cut-off threshold to design an early time solution of transient mud loss volume to transform V_m and t into

V m early

and t^early, respectively. Thus, a specified portion of the mud loss volume versus time is selected after determining the cut-off threshold. For example, data generator 150 is configured to determine an early time solution of transient mud loss volume by selecting the beginning 30% portion of the output solutions of the one or more semi-analytical functions 156. In some embodiments, data generator 150 is configured to apply a common logarithmic function to compress wide data value ranges for early mud loss volume

V m early ,

early mud loss time t^early, maximum loss volume

V m max ,

and maximum stopping time t^max.

In some embodiments, each lost circulation event of encoded mud loss data 152 includes a pair of input data and output data for ANN 162. For example, input data includes a plurality of input parameters, such as flow behavior index n, fluid yield stress τ₀, consistency factor m, pressure drop Δp, wellbore radius r_w, early mud loss volume

V m early ,

and early mud loss time t^early for the plurality of lost circulation events 160. As another example, output data includes a plurality of output parameters, such as such as average hydraulic fracture aperture w, maximum loss volume

V m max ,

and maximum stopping time t^max, for the plurality of lost circulation events 160. For convergence of training ANN 162, input data and output data are normalized by min-max linear scale based on Equation 2.

X ¯ = X v ⁢ alue - X min X min max ( 2 )

where X_value is the value of each input/output, X_min is the minimum value of all events, and X_max is the maximum value.

In some embodiments, in the surrogate model development stage, mud loss monitor 140 is configured to implement the one or more machine learning algorithms, such as ANN 162, to train surrogate model 164 using encoded mud loss data 152. For example, surrogate model 164 is trained to predict a plurality of output parameters, such as average hydraulic fracture aperture w, maximum loss volume

V m max ,

and maximum stopping time t^max for the plurality of lost circulation events 160, based on a plurality of input parameters, such as flow behavior index n, fluid yield stress τ₀, consistency factor m, pressure drop Δp, wellbore radius r_w, early mud loss volume

V m early ,

and early mud loss time t^early for the plurality of lost circulation events 160. The plurality of input parameters are selected to accurately predict the plurality of output parameters of lost circulation events for reservoir 116. For example, the plurality of input parameters include five uncertainty parameters determined from the plurality of uncertainty parameters 154, such as flow behavior index n, fluid yield stress τ₀, consistency factor m, pressure drop Δp, and wellbore radius r_w. As another example, the plurality of input parameters include two time-dependent vector parameters, corresponding to early mud loss volume

V m early ⁢ { V m 1 , V m 2 , V m 3 , … , V m N }

early time t^early {t¹, t², t³, . . . , t^N}.

In some embodiments, data generator 150 is configured to apply a simple data split technique to separate the encoded mud loss data 152 (for example, n, τ₀, m, Δp, r_w, t^early,

V m early ,

w, t^max, and

V m max )

for reservoir 116 used for the training, validation, and testing of surrogate model 164 using ANN 162. An example embodiment of the data split technique may consider 70% of encoded mud data 152 for model training (for example, tuning of the model parameters), 15% of the encoded mud data 152 for validation (for example, performance validation for each different set of model parameters), and 15% of the encoded mud data 152 for testing the final trained model. However, the data split technique may result in the over-fitting problem of ANN 162 with limited generalization capabilities. For example, such a deployed model may underperform when predicting unseen samples. Although only example embodiments have been described in foregoing detail, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this disclosure.

In some embodiments, ANN 162 may be used to train surrogate model 164, such as a feed-forward network, on the training dataset of encoded mud loss data 152. Surrogate model 164 is trained to solve an optimization problem by minimizing an objective function based on the difference between expected output data and predicted output data. The network includes a plurality of computing layers, each computing layer including a plurality of neurons and a plurality of internal parameters, such as weights and biases, associated with the plurality of neurons. In particular, during a training process, pairs of the input data and the expected output data are passed into the network. The expected outputs may be predicted for the network in a forward propagation step when corresponding input data is provided. A difference is determined by comparing the predicted output data to the expected output data. Thus, the plurality of internal parameters of the network may be adjusted backward through the neural network in a back-propagation step to reduce the difference between expected output data and predicted output data. Thus, the neural network is updated after one iteration. The training process may include a plurality of iterations until a predetermined criterion is met. When the training process is complete, the trained neural network may be used to predict the corresponding output by providing new input data.

Turning to FIG. 3, FIG. 3 illustrates a machine learning system 300 in accordance with one or more embodiments. Machine learning system 300 may include one or more machine learning models, such as ANN 162. The input parameters may include flow behavior index n 312, fluid yield stress τ₀ 314, consistency factor m 316, pressure drop Δp 318, wellbore radius r_w 320, early mud loss volume

V m early

322, and early mud loss time t^early 324 for a plurality of lost circulation events in the training dataset of encoded mud loss data 152 (referring to FIG. 1). Machine learning system 300 may determine a respective average hydraulic fracture aperture w 332, a respective maximum loss volume

V m max

334, and a respective maximum stopping time t^max 336 for each of the plurality of lost circulation events in the training dataset of encoded mud loss data 152 (referring to FIG. 1). In some embodiments, machine learning system 300 may include a plurality of layers, such as an input layer 302, one or more hidden layers 304, and an output layer 306. Input layer 302 may be programmed to receive the plurality of input parameters from machine learning system 300. In some embodiments, the one or more hidden layers 304 may include six hidden layers from left to right, such as hidden layer A, hidden layer B, hidden layer C, hidden layer D, hidden layer E, and hidden layer F. For example, the hidden layer A is coupled between the input layer 302 and the hidden layer B. As another example, the hidden layer F is coupled between the hidden layer E and the output layer 306. Each of the one or more hidden layers 304 may be a convolutional layer, a pooling layer, a rectified linear unit (ReLU) layer, a softmax layer, a regressor layer, a dropout layer, or various other hidden layer types or combinations thereof. In particular embodiments, the number of hidden layers may be greater than or less than six. These hidden layers may be arranged in any order as long as they satisfy the input/output size criteria. Each layer comprises of a set number of image filters. The output of filters from each layer is stacked together in the third dimension. This filter response stack then serves as the input to the next layer(s). Each hidden layer may be featured by 20 neurons or any appropriate number of neurons. An example of an ANN architecture with the number of layers and neurons may be found in Table 2.

In some embodiments, the six hidden layers are configured as according to the following. The hidden layer A and the hidden layer B may be down-sampling blocks to extract high-level features from the input data set. The hidden layer D and the hidden layer E may be up-sampling blocks to output the classified or predicted output data set. The hidden layer C may perform residual stacking as a bottleneck between down-sampling blocks (for example, hidden layer A, hidden layer B) and up-sampling blocks (for example, hidden layer D, hidden layer E). The hidden layer F may include a softmax layer or a regressor layer to classify or predict a predetermined class or a value based on input attributes.

In some embodiments, in a convolutional layer, the input data set is convolved with a set of learned filters that are designed to highlight specific characteristics of the input data set. A pooling layer produces a scaled-down version of the output by considering small neighborhood regions and applying a desired operation filter (e.g., min, max, mean, etc.) across the neighborhood. A ReLU layer enhances a nonlinear property of the network by introducing a non-saturating activation function. One example of such a non-saturating function is to threshold out negative responses (that is, set negative values to zero). A fully connected layer provides high-level reasoning by connecting each node in the layer to all activation nodes in the previous layer. A softmax layer maps the inputs from the previous layer into a value between 0 and 1 or between −1 and 1. Therefore, a softmax layer allows for interpreting the outputs as probabilities and selection of classified facie with the greatest probability. In some embodiments, a softmax layer may apply a symmetric sigmoid transfer function to each element of the raw outputs independently to interpret the outputs as probabilities in the range of values between −1 and 1. A dropout layer offers a regularization technique for reducing network over-fitting on the training data by dropping out individual nodes with a certain probability. A loss layer (for example, utilized in training) defines a weight-dependent cost function that needs to be optimized (that is, bring the cost down toward zero) for improved accuracy. In some embodiments, each hidden layer is a combination of a convolutional layer, a pooling layer, and a ReLU layer in a multilayer architecture. As an example and not by way of limitation, each hidden has a convolutional layer, a pooling layer, and a ReLU layer.

In some embodiments, machine learning system 300 may include an activation function in a ReLU layer (for example, hidden layer F) to calculate the misfit function based on the difference between the predicted friction value and ground truth (for example, a value of “0”). In some embodiments, machine learning system 300 may use a simple data split technique to separate the input data, such as flow behavior index n 312, fluid yield stress τ₀ 314, consistency factor m 316, pressure drop Δp 318, wellbore radius r_w 320, early mud loss volume

V m early

322, and early mud loss time t^early 324, used for the training, validation, and testing of surrogate model 164. For example and not by way of limitation, the data split technique may consider 70% of the input data for model training (for example, tuning of the model parameters), 15% of the obtained input data for validation (for example, performance validation for each different set of model parameters), and 15% of the obtained input data for testing the final trained model. However, the data split technique may be appropriately adjusted (for example, by the user) to prevent over-fitting that results in ANN 162 with limited generalization capabilities (for example, models that underperform when predicting unseen sample data).

As shown in FIG. 1, in some embodiments, in the model validation stage, mud loss monitor 140 is configured to apply validation module 170 to validate surrogate model 164 using the validation dataset of the encoded mud loss data 152. For example, validation module 170 may apply a nested k-fold inner/outer cross-validation to tune and validate the optimal parameters of surrogate model 164. In some embodiments, the nested stratified inner/outer cross-validation may be a software and/or hardware system that includes functionality to mitigate the over-fitting problem of the model by applying a k-fold inner cross-validation and a k-fold outer cross-validation. The k-fold inner cross-validation and the k-fold outer cross-validation may have different values of the “k” parameter. In some example embodiments, the nested inner/outer cross-validation defines one or more machine learning algorithms and their corresponding models in a grid and evaluates one or more performance metrics of interest (for example, area under curve (AUC), accuracy, geometric mean, f1 score, mean absolute error, mean squared error (MSE), root mean square error (RMSE), sensitivity, specificity, etc.) to find the optimal parameters of ANN 162. Furthermore, mud loss monitor 140 is configured to apply validation module 170 to test surrogate model 164 using the test dataset of the encoded mud loss data 152. In addition, there will be other randomly distributed solutions generated based on random distributions. These randomly distributed solutions may be inserted into the one or more semi-analytical functions to generate different testing data for the same determined ranges of input data. For example, the testing dataset may contain 279 samples with the three targeted outputs, such as average hydraulic fracture aperture w, maximum loss volume

V m max ,

and maximum stopping time t^max. As a result, the performance of surrogate model 164 may be evaluated by calculating the one or more performance metrics of interest (for example, AUC, accuracy, geometric mean, f1 score, mean absolute error, MSE, RMSE, sensitivity, specificity, etc.). Thus, mud loss monitor 140 may be used to confirm the accuracy, applicability, and robustness of the surrogate model 164.

FIG. 2 illustrates a schematic diagram 200 of drilling mud loss in accordance with one or more embodiments. Lost circulation may occur in a process of mud-filtrate invasion in rock formations 232 penetrated by a mud-filled and overbalanced borehole 204 when a drilling bit 202 transverses a subterranean formation 230 in a wellbore 220. Arrows 210 indicate a circulating direction of mud 206 in borchole 204 from surface pumps then to the drilling pipe, open-hole, wellbore annulus, and back to surface. Subterranean formation 230 includes porous rocks in rock formations 232 with relatively high permeability or fractured rocks 234 in natural or drilling-induced fractures. The lost circulation may occur due to a mud leakage 208 from the wellborc. such as wellbore 220, to the surrounding formation, such as subterranean formation 230. driven by the pressure drop between the well-flowing pressure and the subterranean formation pressure. For example, the lost circulation may occur when the surrounding formation is inherently fractured, cavernous, or have relatively high permeability. As another example, the lost circulation may occur when the surrounding formation has natural fractures or induced fractures caused by excessive downhole pressures and setting intermediate casing too high. As another example, the lost circulation may occur due to improper drilling conditions. Losing mud into a reservoir drastically reduces an operator's ability to produce the zone. Thus, the lost circulation may significantly increase the non-productive time (NPT) and operational cost, mainly in relatively high temperature regions.

FIGS. 4A-4C illustrate a plurality of distributions of three uncertainty parameters and cumulative mud-loss volume versus time for a dataset in accordance with one or more embodiments. In particular, based on mud loss data for a reservoir, a plurality of uncertain parameters may be identified to predict a lost circulation event. For example, the plurality of uncertainty parameters include the flow behavior index n, fluid yield stress τ₀, average hydraulic fracture aperture w, consistency factor m, pressure drop Δp, and wellbore radius r_w. A Latin Hypercube sampling algorithm is applied to determine a plurality of lost circulation events (S=500) from mud loss data based on the plurality of uncertain parameters. FIG. 4A shows a first distribution 400 of three uncertainty parameters (average hydraulic fracture aperture w, fluid yield stress τ₀, and flow behavior index n) for a plurality of lost circulation events 402. FIG. 4B shows a second distribution 420 of three uncertainty parameters (average hydraulic fracture aperture w, consistency factor m, and pressure drop Δp) for the plurality of lost circulation events 402. FIG. 4C shows a third distribution 440 of three uncertainty parameters (average hydraulic fracture aperture w, flow behavior index n, and wellbore radius r_w) for the plurality of lost circulation events 402. As a result, the plurality of lost circulation events are generated to construct a near-random sample of the plurality of uncertainty parameters in a multi-dimensional space.

FIG. 4D illustrates a plurality of semi-analytical solutions of cumulative mud-loss volume versus time 460 in accordance with one or more embodiments. For the plurality of lost circulation events, a semi-analytical function, such as a mud loss ODE, may be applied to generate a mud loss behavior, such as a plurality of solutions 408 of cumulative mud-loss volume versus time. The mud loss behavior may be used to estimate maximum loss volume

V m max ,

and maximum stopping time t^max for the plurality of lost circulation events.

FIG. 5A illustrates a plot 500 of transient loss volume versus time in accordance with one or more embodiments. FIG. 5A shows a plurality of solutions 502 of transient loss volume versus time. For the plurality of solutions 502, a plurality of circular points 504 are extracted after applying a derivative equal to zero based on Equation 3. From the plurality of circular points 502, maximum loss volume

V m max

and maximum stopping time t^max may be calculated for the plurality of lost circulation events:

dV m dt ❘ max = 0 ( 3 )

where V_m is transient loss volume, and t is time.

FIG. 5B illustrates a plot 550 of maximum loss volume versus maximum stopping time in accordance with one or more embodiments. In particular, FIG. 5B shows a plurality of samples 506 of maximum loss volume

V m max

and maximum stopping time t^max for the plurality of lost circulation events. For example, a maximum loss volume

V m max

represents a final volume which the mud is lost for a corresponding lost circulation event at maximum stopping time t^max.

FIG. 6 illustrates a plot 600 of a plurality of early time solutions 604 in accordance with one or more embodiments. The plurality of early time solutions 604 are a plurality of selected cut-off solutions based on a predetermined cut-off threshold, such as the beginning 30% portion, for both time and loss volume from the original solutions of transient loss volume versus time using a semi-analytical function for a plurality of lost circulation events. Dots 602 represent maximum loss volume

V m max

and maximum stopping time t^max for the plurality of lost circulation events. In this one example, there may be 1356 output solutions of transient loss volume versus time using the semi-analytical function for the plurality of lost circulation events.

FIG. 7 illustrates a comparison 700 of a plurality of performance functions of ANN for an example training dataset and an example validation dataset in accordance with one or more embodiments. In particular, a first performance function 702 and a second performance function 704 may be evaluated using one or more metrics, such as MSE and RMSE, for a training dataset and a validation dataset, respectively. A circle 706 indicates a best-fitting model with a minimum error and maximum accuracy. The first performance function 702 suffers from an underfitting problem of the network. Furthermore, overfitting/underfitting regions both exist for performance function 704 where the best-fitting model is chosen after 477 iterations at circle 706.

FIGS. 8A and 8B illustrate a plurality of comparisons of predicted output data versus expended output data based on a best-fitting model for an example training dataset and an example validation dataset in accordance with one or more embodiments. FIG. 8A shows a first plurality of data samples associated with a comparison 800 of predicted output data versus expended output data based on the best fitting model for the training dataset. FIG. 8B shows a second plurality of data samples associated with a comparison 850 of predicted output data versus expended output data based on the best fitting model for the validation dataset. A black diagonal line 802 indicates the predicted output data matches the expected output data with no error. The majority of data samples assemble around diagonal line 802 of the plots, reflecting minor errors. It is also noted that the validation set is a blind set, which is used for checking overfitting or underfitting.

FIG. 9 illustrates a plot 900 of a plurality of histogram error distributions for a plurality of prediction output parameters for a testing dataset in accordance with one or more embodiments. In particular, the plurality of histogram error distributions are generated using a plurality of predicted output parameters, such as maximum loss volume

V m max

902, maximum stopping time t^max 904, and average hydraulic fracture aperture w 906, based on a best fitting mode for an example testing dataset which includes 279 samples. It is noted that the plurality of histogram error distributions show a symmetric normal distribution of the relative error values around a zero-error line 910. The relative error values conglomerate around the zero error line 910 with minimum skewness or bias, indicating that the best fitting is proper to predict lost circulation events for the testing dataset.

Application of the Semi-Analytical Workflow

The semi-analytical workflow may be used to develop an accurate, efficient, and robust surrogate model for predicting a plurality of output parameters, such as equivalent hydraulic fracture aperture w, maximum cumulative mud loss volume

V m max ,

and maximum stopping time t^max for the mud for a plurality of lost circulation event. The semi-analytical workflow may cope with a wide range of flow index values, where each flow index comprises a plurality of type curves. Therefore, the semi-analytical workflow may be used to reduce the time of interpreting and analyzing mud loss information during drilling by integrating the type-curves solution with machine learning to assess uncertainties. In terms of formation evaluation, the semi-analytical workflow helps to assess fracture conductivity from the behavior of leakage rate as a function of time. The semi-analytical workflow was applied to three field data cases, each of which are discussed infra.

Field Data Examples

Field data of lost circulation events generally contains noise. The most common way to quantify mud loss is by monitoring the pit volume changes or bottom-hole flow meter. The raw field data may be transformed into cumulative mud loss volume over transient time to be used as an additional validation step for a surrogate model. The selected field data examples included two zones of lost circulation in the Gulf of Mexico (GOM) and one well in North Sea. The semi-analytical workflow was used to train the surrogate model to predict three output parameters, such as equivalent hydraulic fracture aperture, maximum cumulative mud loss volume, and maximum stopping time. In particular, the surrogate model was tested on a plurality of lost circulation events from these three field data examples. A 30% logarithmically cut-off was applied to the data to determine early data solutions

V m early

and t^early for training the surrogate model.

FIG. 10 illustrates a Tornado error distribution 1000 of relative errors for a plurality of prediction output parameters for the three field cases in accordance with one or more embodiments. The semi-analytical workflow was used to train a surrogate model to predict three output parameters, such as equivalent hydraulic fracture aperture w 1006, 1016, 1026, maximum cumulative loss volume

V m max

1002, 1012, 1022, and maximum stopping time t^max 1004, 1014, 1024 for two zones, such as zone-1 and zone-2, in GOM and a well, such as well M18, in North Sea. The predicted output parameters overestimated the expected results with minor error values, except for underestimating negative relative error of maximum cumulative loss volume

V m max

1002 for the well in North Sea. Overall, the prediction errors of the predicted output parameters were within an acceptable range of ±10%.

FIG. 11 illustrates a comparison 1100 of a plurality of predicted output parameters versus expected output parameters for the three field cases in accordance with one or more embodiments. A plurality of output parameters, such as equivalent hydraulic fracture aperture w, maximum cumulative loss volume

V m max ,

and maximum stopping time t^max were determined using a surrogate model to be compared to the corresponding expected data for zone-1 in GOM 1102, zone-2 in GOM 1104, and well M18 in North Sea 1106. The predicted output parameters were consistent with the corresponding expected output parameters, which indicates the surrogate model is a reliable and accurate model for predicting lost circulation events for these three field cases.

FIG. 12 illustrates a flowchart of a process 1200 for predicting a plurality of output parameters for a lost circulation event in fractured media in accordance with one or more embodiments. In some embodiments, the process 1200 may be implemented to model a drilling mud loss behavior for a reservoir to determine a surrogate model for predicting lost circulation events for the reservoir. In particular, the surrogate model may be implemented to predict a plurality of output parameters, such as equivalent hydraulic fracture aperture w, maximum cumulative loss volume

V m max ,

and maximum stopping time t^max for lost circulation events for real-time mud loss data obtained for the reservoir. At Block 1205, the process 1200 may receive mud loss data associated with the drilling mud loss behavior for the reservoir. Mud loss data may be collected from a plurality of wells for the reservoir using multiple sources including experimental drilling data generated using a reservoir simulator, daily drilling reports, mud logging reports, final drilling reports, etc. For example, the mud loss data may be pre-processed by removing outliers and unwanted lost circulation events. At Block 1210, the process 1200 may usc the mud loss data to identify a plurality of uncertainty parameters associated with the drilling mud loss behavior for the reservoir. The plurality of uncertainty parameters include flow behavior index n, fluid yield stress τ₀, average hydraulic fracture aperture w, consistency factor m, pressure drop Δp, and wellbore radius r_w.

At Block 1215, the process 1200 may use the mud loss data and a Latin Hypercube Sampling (LHS) algorithm to determine a plurality of lost circulation events associated with the drilling mud loss behavior for the reservoir. In particular, the process 1200 may use the Latin Hypercube Sampling algorithm to optimize the plurality of lost circulation events for the reservoir based on a predetermined sampling number S. In some embodiments, the predetermined sampling number may be 1500.

At Block 1220, the process may use a semi-analytical function to generate a mud loss training dataset from the plurality of lost circulation events associated with the drilling mud loss behavior for the reservoir. For example, the semi-analytical function includes a mud loss ODE solution for Newtonian fluid flow into a horizontal fracture by combining the diffusivity equation and mass conservation in 1D radial system. As another example, the semi-analytical function includes a mud loss ODE solution for non-Newtonian fluid flow or LCM exhibiting a yield-power law behavior. Thus, the process 1200 may use the semi-analytic function to generate a plurality of output solutions based on the plurality of lost circulation events associated with the drilling mud loss behavior for the reservoir. Each of the plurality of output solutions includes a corresponding early loss volume, a corresponding early loss time, a corresponding maximum stopping loss volume, and a corresponding maximum stopping time. Furthermore, the process 1200 may evaluate the output solutions of the semi-analytical function for the plurality of lost circulation events and generate the mud loss training dataset by combining the plurality of output solutions and the respective plurality of uncertainty parameters based on a predetermined threshold, such as a 30% cut-off threshold.

In Block 1225, the process 1200 may use the mud loss training dataset to train a machine learning model to predict a maximum stopping loss volume, a maximum stopping time, and an equivalent hydraulic fracture aperture associated with the drilling mud loss behavior for the reservoir. The machine learning model may be a surrogate model trained by implementing an ANN. In particular, the machine learning model is trained using a plurality of input parameters, such as flow behavior index n, fluid yield stress τ₀, consistency factor m, pressure drop Δp, wellbore radius r_w, early mud loss volume

V m early ,

and early mud loss time t^early for a plurality of lost circulation events in the mud loss training dataset. The machine learning model is trained to predict a plurality of output parameters, such as equivalent hydraulic fracture aperture w, maximum cumulative loss volume

V m max ,

and maximum stopping time t^max for a corresponding input lost circulation event. The process 1200 may normalize the input and output parameters of the machine learning model using a min-max linear scale. Furthermore, the process 1200 may evaluate the machine learning model using a mean squared error (MSE) and a root mean square error (RMSE).

In Block 1230, the process 1200 may use the mud loss data to determine a new lost circulation event based on the plurality of uncertainty parameters associated with the drilling mud loss behavior for the reservoir. The new lost circulation event has a corresponding early loss volume and a corresponding early loss time. For example, the process 1200 may determine the plurality of input parameters for the new lost circulation event which is determined from real-time mud loss data during drilling.

In Block 1235, the process 1200 may use the trained machine learning model to determine a new maximum stopping loss volume, a new maximum stopping time, and a new equivalent hydraulic fracture aperture associated with the new lost circulation event based on the plurality of uncertainty parameters and the new lost circulation event.

In Block 1240, the process 1200 may determine an operation to adjust a parameter of a drilling mud for the reservoir based on the maximum stopping loss volume, the maximum stopping time, and the equivalent hydraulic fracture aperture associated with the new lost circulation event. The operation includes adjusting a property of the drilling mud or adjusting a pumping rate of the drilling mud. The process 1200 may predict a drilling mud behavior of leakage rate as a function of time for the reservoir based on the new maximum stopping loss volume, the new maximum stopping time, and the new equivalent hydraulic fracture aperture associated with the new lost circulation event. For example, the process 1200 may use the drilling mud behavior of leakage rate as a function of time for the reservoir to assess fracture conductivity for the reservoir.

Particular embodiments may repeat one or more steps of the process of FIG. 12, where appropriate. Although this disclosure describes and illustrates particular steps of the process of FIG. 12 as occurring in a particular order, this disclosure contemplates any suitable steps of the process of FIG. 12 occurring in any suitable order. Moreover, although this disclosure describes and illustrates an example process to model a drilling mud loss behavior for a reservoir using a semi-analytical workflow, including the particular steps of the process of FIG. 12, this disclosure contemplates any suitable process including any suitable steps, which may include all, some, or none of the steps of the process of FIG. 12, where appropriate. Furthermore, although this disclosure describes and illustrates particular components, devices, or systems carrying out particular steps of the process of FIG. 12, this disclosure contemplates any suitable combination of any suitable components, devices, or systems carrying out any suitable steps of the process of FIG. 12.

FIG. 13 is a functional block diagram of a computer system (or “system”) 1300 in accordance with one or more embodiments. In some embodiments, system 1300 is a programmable logic controller (PLC). System 1300 may include memory 1304, processor 1306 and input/output (I/O) interface 1308. Memory 1304 may include non-volatile memory (for example, flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM)), volatile memory (for example, random access memory (RAM), static random access memory (SRAM), synchronous dynamic RAM (SDRAM)), or bulk storage memory (for example, CD-ROM or DVD-ROM, hard drives). Memory 1304 may include a non-transitory computer-readable storage medium (for example, non-transitory program storage device) having program instructions 1310 stored thereon. Program instructions 1310 may include program modules 1312 that are executable by a computer processor (for example, processor 1306) to cause the functional operations described, such as those described with regard to control system 114 or method 1200.

Processor 1306 may be any suitable processor capable of executing program instructions. Processor 1306 may include a central processing unit (CPU) that carries out program instructions (for example, the program instructions of the program modules 1312) to perform the arithmetical, logical, or input/output operations described. Processor 1306 may include one or more processors. I/O interface 1308 may provide an interface for communication with one or more I/O devices 1314, such as a joystick, a computer mouse, a keyboard, or a display screen (for example, an electronic display for displaying a graphical user interface (GUI)). I/O devices 1314 may include one or more of the user input devices. I/O devices 1314 may be connected to I/O interface 1308 by way of a wired connection (for example, an Industrial Ethernet connection) or a wireless connection (for example, a Wi-Fi connection). I/O interface 1308 may provide an interface for communication with one or more external devices 1316. In some embodiments, I/O interface 1308 includes one or both of an antenna and a transceiver. In some embodiments, external devices 1316 include logging tools, lab test systems, well pressure sensors, well flowrate sensors, or other sensors described in connection with control system 114.

Further modifications and alternative embodiments of various aspects of the disclosure will be apparent to those skilled in the art in view of this description. Accordingly, this description is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the general manner of carrying out the embodiments. It is to be understood that the forms of the embodiments shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed or omitted, and certain features of the embodiments may be utilized independently, all as would be apparent to one skilled in the art after having the benefit of this description of the embodiments. Changes may be made in the elements described herein without departing from the spirit and scope of the embodiments as described in the following claims. Headings used herein are for organizational purposes only and are not meant to be used to limit the scope of the description.

It will be appreciated that the processes and methods described herein are example embodiments of processes and methods that may be employed in accordance with the techniques described herein. The processes and methods may be modified to facilitate variations of their implementation and use. The order of the processes and methods and the operations provided may be changed, and various elements may be added, reordered, combined, omitted, modified, and so forth. Portions of the processes and methods may be implemented in software, hardware, or a combination of software and hardware. Some or all of the portions of the processes and methods may be implemented by one or more of the processors/modules/applications described here.

As used throughout this application, the word “may” is used in a permissive sense (that is, meaning having the potential to), rather than the mandatory sense (that is, meaning must). The words “include,” “including,” and “includes” mean including, but not limited to. As used throughout this application, the singular forms “a,” “an,” and “the” include plural referents unless the content clearly indicates otherwise. Thus, for example, reference to “an element” may include a combination of two or more elements. As used throughout this application, the term “or” is used in an inclusive sense, unless indicated otherwise. That is, a description of an element including A or B may refer to the element including one or both of A and B. As used throughout this application, the phrase “based on” does not limit the associated operation to being solely based on a particular item. Thus, for example, processing “based on” data A may include processing based at least in part on data A and based at least in part on data B, unless the content clearly indicates otherwise. As used throughout this application, the term “from” does not limit the associated operation to being directly from. Thus, for example, receiving an item “from” an entity may include receiving an item directly from the entity or indirectly from the entity (for example, by way of an intermediary entity). Unless specifically stated otherwise, as apparent from the discussion, it is appreciated that throughout this specification discussions utilizing terms such as “processing,” “computing,” “calculating,” “determining,” or the like refer to actions or processes of a specific apparatus, such as a special purpose computer or a similar special purpose electronic processing/computing device. In the context of this specification, a special purpose computer or a similar special purpose electronic processing/computing device is capable of manipulating or transforming signals, typically represented as physical, electronic or magnetic quantities within memories, registers, or other information storage devices, transmission devices, or display devices of the special purpose computer or similar special purpose electronic processing/computing device.

At least one embodiment is disclosed and variations, combinations, and/or modifications of the embodiment(s) and/or features of the embodiment(s) made by a person having ordinary skill in the art are within the scope of the disclosure. Alternative embodiments that result from combining, integrating, and/or omitting features of the embodiment(s) are also within the scope of the disclosure. Where numerical ranges or limitations are expressly stated, such express ranges or limitations may be understood to include iterative ranges or limitations of like magnitude falling within the expressly stated ranges or limitations (for example, from about 1 to about 10 includes, 2, 3, 4, etc.; greater than 0.10 includes 0.11, 0.12, 0.13, etc.). The use of the term “about” (or its variants) means ±10% of the subsequent number, unless otherwise stated.

Use of the term “optionally” with respect to any element of a claim means that the element is required, or alternatively, the element is not required, both alternatives being within the scope of the claim. Use of broader terms such as comprises, includes, and having may be understood to provide support for narrower terms such as consisting of, consisting essentially of, and comprised substantially of. Accordingly, the scope of protection is not limited by the foregoing but is defined by the claims that follow, that scope including all equivalents of the subject matter of the claims. Each and every claim is incorporated as further disclosure into the specification and the claims are embodiment(s) of the present disclosure.

While several embodiments have been provided in the present disclosure, it should be understood that the disclosed systems and methods might be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted, or not implemented.

In addition, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, modules, techniques, or methods without departing from the scope of the present disclosure. Other items shown or discussed as coupled or directly coupled or communicating with each other may be indirectly coupled or communicating through some interface, device, or intermediate component whether electrically, mechanically, or otherwise.

Many other embodiments will be apparent to those of skill in the art upon reviewing the foregoing description. The scope of the subject matter of the present disclosure therefore should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein.”