METHOD AND SYSTEM FOR CONTROLLING A WASHOUT AREA

Abstract

A method for evaluating and controlling a washout region of a wellbore placed in a formation includes: obtaining information about the wellbore and the formation; establishing a washout indicator function as a function of time and location; computationally determining whether the washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation, at each depth in a specific depth range; and upon finding presence of the washout region in the specific depth range, quantifying the washout region. The washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary.

Description

BACKGROUND

Operations, such as geophysical surveying and logging are typically performed to locate and obtain hydrocarbons or mineral reserves. While technologies have advanced the chance of successful oil and gas operations, wellbore failures arise naturally and/or due to drilling of rocks. Various stress elements are known to affect the integrity of a wellbore. For example, the insufficient pressure in drilling fluid turns drilling fluid into a source of wellbore blockage. Dilation of a wellbore diameter in a portion of a wellbore, a washout region, should be accurately identified and managed because the washout region can cause a stagnant drilling fluid and ultimately result in a wellbore failure.

However, the accurate assessment and effective management of washout regions have been a challenge and have not yet been fully achieved by available technologies. Multi-arm caliper logs and fluid calipers are employed as after-the-fact techniques but require specialized equipment, a substantial amount of labor, suspension of operations, and associated costs. The dedicated run of these tools disrupts main drilling operations. On the technical side, the resolution of a multi-arm caliper is often too coarse for accurate identification of washout regions. Fluid calipers fail to work if there is lost circulation or a turbulent flow. Another limitation of fluid calipers is that they can only be used for estimating a washout size for cement casing. Accordingly, there exists a need for an effective assessment and control system of washout areas to prevent a wellbore failure.

SUMMARY

In general, in one aspect, embodiments relate to a method for evaluating and controlling a washout region of a wellbore placed in a formation. The method comprises: obtaining information about the wellbore and the formation; establishing a washout indicator function as a function of time and location; computationally determining whether the washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation, at each depth in a specific depth range; and upon finding presence of the washout region in the specific depth range, quantifying the washout region. The washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary.

In another aspect, embodiments relate to a system for evaluating and controlling a washout region of a wellbore placed in a formation. The system comprises: a hardware processor, operatively connected to an interface and a memory that: obtains information about the wellbore and the formation; establishes a washout indicator function as a function of time and location; computationally determines whether the washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation, at each depth in a specific depth range; and upon finding presence of the washout region in the specific depth range, quantifies the washout region; the interface for inputting and outputting a signal that the hardware processor processes; the memory that stores the information about the wellbore and the formation. The washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary.

In yet another aspect, embodiments relate to a non-transitory computer readable medium storing instructions executable by a hardware processor of a computer, the instructions comprising: obtaining information about a wellbore and a formation; establishing a washout indicator function as a function of time and location in the formation; computationally determining whether a washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation, at each depth in a specific depth range; and upon finding presence of the washout region, quantifying the washout region in the specific depth range. The washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary between the washout region and the formation.

Other aspects of the disclosure will be apparent from the following description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

Specific embodiments of the disclosed technology will now be described in detail with reference to the accompanying figures. Like elements in the various figures are denoted by like reference numerals for consistency.

FIGS. 1A and 1B show schematic perspective views of a reservoir region in which a system of controlling a washout area is implemented in accordance with one or more embodiments.

FIG. 2 shows a schematic cross-sectional view of a wellbore with a washout area in accordance with one or more embodiments.

FIGS. 3A to 3E show schematic representations of a wellbore with a washout area in accordance with one or more embodiments.

FIGS. 4A and 4B depict an image data that shows the wellbore with a washout area structured on a breakout failure criterion in accordance with one or more embodiments.

FIG. 5 shows an example implementation of the system in accordance with one or more embodiments.

FIG. 6 shows a block diagram of a computer system in accordance with one or more embodiments.

FIGS. 7A and 7B show flowcharts for controlling a washout area in accordance with one or more embodiments.

DETAILED DESCRIPTION

Specific embodiments of the disclosure will now be described in detail with reference to the accompanying figures. Like elements in the various figures are denoted by like reference numerals for consistency.

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

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

Throughout the application, the term “borehole” may be used to mean “wellbore” or vice versa.

The terms “deep” and/or “depth” may be used to mean a measured depth (MD), a length along the drilled wellbore. However, it may mean a true vertical depth (TVD) only if such interpretation is deemed necessary based on the context in which the term is used.

In general, embodiments of the disclosure include a system and a method for controlling a washout region in a wellbore using a computerized identification and quantification of the washout area. In some embodiments, for example, the computerized identification and quantification establishes a washout indicator function, using a time-dependent model, and determines presence or absence of a washout region in the well system 100. As such, the computerized identification and quantification of the washout area may continuously monitor for a risk of wellbore failure and manages to transmit an alert about the risk without delay. The identification and quantification may be performed by a computer in real-time or in near real-time, thus resulting in accurate and effective prevention of a wellbore failure even in dynamically changing environments.

In some embodiments, the system controls the washout area by detecting a predetermined condition in the washout area and adjusting a mud control system in response to the washout area characteristics. Specifically, the system performs computerized identification and quantification of the washout area and detects a level of expansion of the washout area and/or total volume thereof above certain levels. The quantified expansion of the washout area and distribution of the washout area exceeding a certain threshold level may direct the mud control system to alter mud weight, etc. to confine the washout area. Once stabilization of the washout area is observed, the corresponding setting may be kept. Furthermore, some embodiments enable the alteration of a drilling rate, e.g., rate of penetration (ROP) of the drilling operation, in digging of the wellbore.

Turning to FIG. 1A, FIG. 1A shows a schematic diagram in accordance with one or more embodiments. FIG. 1A illustrates a well system 100 including a (hydrocarbon) reservoir 104 located in a formation 106 and a series of wells. The formation 106 may include a porous or fractured rock formation that resides underground, beneath the earth's surface. In the case of the well system 100 being a region containing hydrocarbons, the reservoir 104 may include a portion of the formation 106 that includes a subsurface accumulation of oil and gas. The formation 106 and the reservoir 104 may include different layers of rock having varying characteristics, such as varying degrees of permeability, porosity, and resistivity.

The well system 100 may run various types of operations such as drilling, well production operations, well completion operations, well maintenance operations, and reservoir monitoring or surveys, assessments and development operations. While a wellbore failure may occur at any stage of these operations, early failures e.g., during drilling and well completion, lead to a significant loss of resources.

The production site 102, the injection site 110, and the drilling site 114 may exist in parallel at a given time (parallel operation) according to one or more embodiments. In other embodiments, the production site 102, the injection site 110, and the drilling site 114 may exist or run at different time periods. In parallel-operation scenarios, the extraction of hydrocarbons from the reservoir 104 may need to be coordinated with conditions of other components such as operations and situations at the drilling site 114. Thus, when the well system 100 involves multiple sites, or when operations become a large-scale implementation, it is necessary to have a system 116 that manages multiple components of the well system 100 to prevent wellbore failures. Even without any parallel operation, operators need to harmonize various activities, allocate sufficient resources timely, estimate well productivity, and monitor the well system 100 to prevent hazardous situations.

Keeping with FIG. 1A, the well system 100 may be constructed on an intelligent environment in which the system 116 for controlling a washout region 208 operates. The system 116 may centrally manage multiple components of the well system 100 by collecting information about the injection site 110, the production site 102, and the drilling site 114 and make changes to operations thereof. To detect and manage a washout region 208 in the wellbore 118, the system 116 may monitor and control conditions and operations of the drilling site 114.

In some embodiments, the system 116 for controlling a washout region may include software and hardware, such as a computer that is the same as or similar to that of the computer 602 described below in FIG. 6 and the accompanying description. The computer 602 may deliver communication signals to and receive data and/or feedback from each other. The computer 602 provides control signals to elements and components in the well system 100 according to one or more embodiments.

The wellbore 118 may facilitate the circulation of drilling fluids during drilling operations, the flow of hydrocarbon production e.g., oil and gas, from the reservoir 104 to the surface during production operations. The injection of substances, e.g., water, into the formation 106 is adjusted in accordance with results obtained monitoring operations e.g., in situ logging operations.

Referring to FIG. 1B, an exemplary drilling site 114 according to one or more embodiments is illustrated. As shown in FIG. 1B, the wellbore 118 may include a drilled hole that extends from the surface into a drilling target 128 of the formation 106 and the reservoir 104. The drilling site 114 may include a wellbore 118, a bottomhole assembly 122, a casing 142, a drilling rig 146, and a mud control system 148 as one or more implementations of the present disclosure.

Prior to the commencement of drilling, a wellbore plan, as a part of a well construction plan, may be generated. For example, a wellbore plan may include specifications relating to the wellbore trajectory 126, the density of drilling mud to be used, and the size of the drill bit 124 and the intended diameter (“caliper”) of the wellbore 118. Similarly, a completion plan may include specifications of the wall thickness and material of the casing 142 as well as the location and size of downhole and/or surface pumps. Typically, the wellbore plan is generated based on best available information from a geophysical model, geomechanical models encapsulating subterranean stress conditions, the wellbore trajectory 126 of any existing wellbores, and the existence of other drilling hazards, such as shallow gas pockets, over-pressure zones, and active fault planes. The wellbore plan is typically formulated using wellbore geometry information such as measurement of a wellbore diameter and an inclination angle. If casing 142 is used, the wellbore plan may include casing type or casing depths. Furthermore, the wellbore plan may consider other engineering constraints such as the maximum wellbore curvature (“dog-log”) that the drillstring 120 may tolerate and the maximum torque and drag values that the drilling system may tolerate.

The drillstring 120 may include one or more drill pipes connected to form conduit and a bottomhole assembly (BHA) disposed at the distal end of the drillstring 120. The BHA may include a drill bit 124 to cut into subsurface rock. The BHA may further include measurement tools, such as a measurement-while-drilling (MWD) tool and logging-while-drilling (LWD) tool. MWD tools may include sensors and hardware to measure downhole drilling parameters, such as the azimuth and inclination of the drill bit 124, the weight-on-bit, and the torque. The LWD measurements may include sensors, such as resistivity, gamma ray, and neutron density sensors, to characterize the rock formation 106 surrounding the wellbore 118. Both MWD and LWD measurements may be transmitted to the surface using any suitable telemetry system, such as mud-pulse or wired-drill pipe, known in the art.

Drilling may continue without any casing 142, when drilling reaches a deep location or when more compact rock is reached. During drilling of rocks, the mud control system 148 may start pumping mud from a mud tank on the surface through a drill pipe. Drilling mud serves various purposes, including pressure equalization, removal of rock cuttings, and the like.

At planned depth intervals, drilling may be paused and sections of casing 142 may be inserted, connected, and cemented into the wellbore 118. Casing string may be cemented in place by pumping cement and mud, separated by a “cementing plug,” from the surface through a drill pipe. Once the cement cures, drilling may recommence.

Due to the high pressures experienced by deep wellbores, a blowout preventer (BOP) may be installed at the wellhead to protect the drilling rig 146 and the surrounding environment from oil or gas releases.

As one or more examples, the drilling control unit 150 may incorporate a protocol that governs the wellbore plan as well as execution thereof. The drilling control unit 150 collects and records not only information about the wellbore plan, but also operation data of the drilling rig 146 during operation of the well system 100.

In some implementations, the drilling control unit 150 may comprise one or more hardware processors 605 in communication with a memory 606 that stores the wellbore plan, the geophysical and geomechanical models, information relating to drilling hazards, and instructions from the system 116. The drilling control unit 150 may further include dedicated software to determine the planned wellbore trajectory 126 and associated drilling parameters, the planned depths at which casing 142 will be inserted to support the wellbore 118 and prevent formation fluids entering the wellbore, and the drilling mud weights, densities, and types.

As a non-limiting example, sensors may be arranged to measure weight-on-bit, drill rotational speed (RPM), flow rate of the mud pumps (GPM), and rate of penetration of the drilling operation (ROP). Each sensor may be positioned or configured to measure a desired physical stimulus.

In one or more implementations of the present disclosure, the system 116 may obtain relevant data with sensors. In some embodiments, the quantity of produced gas and oil, the well pressure, the wellbore temperature, as well as analysis of data may be obtained.

In some embodiments, the measurements are recorded in real-time, and are available for review or use within seconds, minutes or hours of the condition being sensed. In such an embodiment, the analysis of data may reveal the current state of the well system 100 and may allow real-time decisions regarding the development and maintenance of the well system 100.

The protocol of the system 116 for controlling a washout region can include components for implementation of a cognitive environment, which can include machine learning, training of machines and use of trained machines. As an example, the protocol may be established and updated by one or more cloud-based components, for example, for purposes of computations, access, data storage, transmission of instructions to equipment, etc. As an example, the system 116 automates and accelerates complex functions such as simulation, analysis, and forecasting. Such advanced computational capabilities can be based on insights from lab and/or field measurements, datasets across a range of diverse sources. The system 116 may be made scalable such that it enables processing and imaging on a single workstation, on a massive compute cluster, cloud resources, etc.

The system 116 may collect information about the wellbore 118 and the formation 106. The information about the wellbore 118 and the formation 106 may include (A) in-situ stress measurement; (B) weight of mud within the specific depth range; and (C) strength properties of rocks in the formation, as explained later. Further, the information about the wellbore 118 and the formation 106 may include (D) for each depth in a specific depth range of the formation 106, a wellbore diameter, an inclination angle of the wellbore 118, and an azimuth of the wellbore 118. Additionally, the information about the wellbore 118 and the formation 106 may include (E) a pore pressure of rocks in the formation 106, and the wellbore plan.

Turning to FIG. 2, FIG. 2 shows a schematic cross-sectional view of the wellbore 118 with a washout region 208 in accordance with one or more embodiments.

In situ rock at different locations within the formation 106 may experience differing states of stress. The stress state at a given location or point is characterized by various stress components, including normal stress or shear stress. As stress is a tensor, the force per unit area is associated with two directions, the direction of the applied force and the direction normal to the plane to which the force is applied. Normal stresses refer to the stress tensor components for which the two directions coincide and may be compressional or tensile, while shear stresses refer to stress tensor components where the two directions are normal to one another.

The stress state of in situ rock at each location may be caused, in part, by various geological phenonema, such as overburden weight, tectonics, thermal processes, or glacial rebound. The stress state of rock may also be caused by anthropomorphic activities that affect the in situ rock, such as drilling a wellbore, well completion strategies, mining tunnels, or hydrocarbon or other fluid recovery. In another example, drilling a wellbore may result in cracked or weakened in situ rock that relieves some of the stress present prior to drilling the well.

The material of the grains and the fluid saturating the pores of the rock may determine rock properties, which include the physical properties, mechanical behavior, or mechanical parameters of the rock. For example, physical properties may include porosity, permeability, or pore pressure. Porosity is defined as the fraction of the volume of the rock that is occupied by the pores. Mathematically, porosity is the open space in a rock divided by the total rock volume. For example, unconventional hydrocarbon reservoirs 104 may have a low porosity, e.g., under 5%.

Pore pressure (p_p) may be defined as the pressure that the fluids saturating the pores apply to the grains of the rock and may also be related to the confining stress. Confining stress σ_c is typically the stress caused by the weight of overburden rock. Effective stress σ_e may control the mechanical behavior of the rock and may be represented by a function of the pore pressure p_p and the confining stress acting on the rock. That is, in some embodiments, the effective stress σ_e may be modeled as:

$\begin{array}{cc}{\sigma }_e={\sigma }_c-\alpha p_p,& \mathrm{Equation}\left(1\right)\end{array}$

where α is Biot's coefficient of effective stress. The effective stress 6e may quantify the stress state of the rock, as the confining stress is supported partly by the grains and partly by the fluid in pore space. The Biot coefficient α may be defined as the volume of fluid change induced by the change in bulk volume when the rock is void of fluid and may be a value between zero and one.

The fluid-saturated pores of rock may present viscoelastic behavior, meaning that the fluid presents both viscous behavior and elastic behavior. Mechanical behaviors are defined by elastic behavior or plastic behavior depending on the magnitude of the applied force. In either the elastic or plastic range, grains may also consolidate or compact due to an applied force.

An externally applied mechanical stress can elastically and reversibly alter the grains of a rock, which is referred to as strain. Poisson's ratio v is an elastic property of a material, such as rock. Specifically, Poisson's ratio describes the proportional decrease/increase in a lateral measurement to the proportional increase/decrease in length in a sample of material that is elastically stretched/compressed.

The bulk compression modulus K, also referred to as the bulk modulus of elasticity, relates stress and compression, and may describe the ability of a rock to resist any change in its volume under compressional forces. That is, the bulk modulus may be defined as the radio of volumetric stress to volumetric strain.

Young's modulus E, also referred to as the modulus of longitudinal elasticity, describes the resistance of a material to stretching or compression during elastic deformation. The modulus of elasticity is a set of physical quantities that characterize the ability of any solid body to be elastically deformed under conditions where force is applied to it. That is, Young's modulus may be defined as the ratio of uniaxial tensile/compressive stress on a rock to the resulting extensional/compressional strain of the rock and may be measured in gigapascals (GPa).

The shear modulus G, also referred to as the modulus of rigidity, may be characterize as the ability of a rock to resist any change in its shape while maintaining its volume. G may be expressed by the ratio of shear stress to shear strain, defined as the alteration in the right angle between planes, whereon shear stresses are applied to two mutually orthogonal sites. Note that the relationship between Poisson's ratio v and Young's modulus E, bulk modulus K, and shear modulus G may be written as:

$\begin{array}{cc}G=\frac{E}{2\left(1+v\right)},& \mathrm{Equation}\left(2\right)\end{array}$ $\mathrm{and}$ $\begin{array}{cc}K=\frac{E}{3\left(1-2v\right)}.& \mathrm{Equation}\left(3\right)\end{array}$

The stress state of the rock may also affect its grains and pores. The general state of stress at a point within the formation 106 may be characterized by independent shear and normal stress components, represented by a stress tensor. For example, the in situ stress state may be the original stress status in the rock before excavations or other perturbations and may typically coincide with vertical and horizontal directions (components).

If the stresses acting on the rock are normal or perpendicular to the rock, the stresses may be referred to as “principal stresses.” The principal in situ stress tensor may consist of a vertical stress σ_V (e.g., the overburden stress), and two horizontal or axial stresses, σ_h and σ_H.

Defining effective stress σ_e using Equation (1) may be used to model an “isotropic” stress state of rock as only one principal stress (i.e., confining stress σ_c) is considered; however, an “anisotropic” stress state of a rock may be modeled by considering multiple principal stresses (e.g., confining stress σ_V and axial stress σ_h) when defining effective stress. An anisotropic stress state of in situ rock may be mimicked in a laboratory setting, which may also allow for the determination of mechanical and hydraulic rock properties, such as permeability k or diffusivity.

A minimum and maximum value for the drilling fluid pressure may be estimated by a wellbore stress failure criterion. A hoop stress is derived from the equation below.

$\begin{array}{cc}& \mathrm{Equation}\left(4\right)\end{array}$ ${\sigma }_{\theta \theta }=S_{\mathrm{Hmin}}\text{?}{S}_{\mathrm{Hmax}}-2\left(S_{\mathrm{Hmax}}-S_{\mathrm{Hmin}}\right)\cos 2\theta -2P_p-\Delta P-{\sigma }^{\Delta T}$ $\text{?}=\Delta P.$ $\text{?}\text{indicates text missing or illegible when filed}$

θ is measured from the azimuth of the maximum horizontal stress, S_Hmax, S_Hmin is the maximum and minimum horizontal stress; P_p is the pore pressure; ΔP is the difference between the wellbore pressure and the pore pressure, and σ^ΔT is the thermal stress of the wellbore by decrease of ΔT.

Drilling a vertical hole underground creates a vacuum in the formation 106 and disrupts the balance of forces within the formation 106. In practice, to prevent rocks from collapsing into a hollow created by drilling, mud must be added to put pressure on the wellbore wall.

The mechanical instability of the wellbore 118 is explainable by tensile failure and shear failure. If drilling mud places incompatible pressure toward the wellbore wall, the wall breaks in a peaked (e.g., compressed) area, leading to the emergence of a wellbore failure. Accordingly, mud weight is one parameter to be controlled to realize the wellbore's stability (“mud weight”). In other words, the insufficient wellbore pressure causes a washout region 208 in the wellbore 118. Characteristics of drilling mud such as its chemical properties and viscosities (“mud feature”) may affect the wellbore stability. Similarly, the wellbore trajectory 126 impacts the stress bearing of the wellbore 118 (“trajectory feature”).

Although not easily controllable, the petrophysical (e.g., pore pressure) and/or mechanical features of rocks, presence of weak formations 106, swelling or shrinking of shale as it contacts drilling fluid, are other modulators of the wellbore stability. Accordingly, the system 116 for controlling a washout area may determine values of these parameters based on information stored within the memory 606, or may receive information from the drilling control unit 150.

As shown in FIG. 2, when the wellbore 118 is exposed to unbalanced stresses, the tension stress 202 placed by the maximum force 212 elevates the shear stress to the point upon which minimum force 214 is applied. A shear failure 210 may appear if drilling mud is poured into at a pressure lower than a safe mud window. The elevated compressive stress results in a break in the wellbore wall from which the washout region 208 arises. Field observations indicate that washout regions 208 usually become larger over time.

The system 116 for controlling a washout area may detect emergence and/or expansion of the washout region 208. In order to minimize the chance of wellbore failure, the system 116 transmits a control signal to the mud control system 148 that modifiable parameters should be adjusted, e.g., revision of the mud weight or the mud feature. The system 116 may determine which parameters among the modifiable parameters should be changed first.

The wellbore trajectory 126 may be revised in one or more embodiments. In some examples, the system 116, after finding that the wellbore trajectory 126 should be modified, transmits a command to the drilling control unit 150 at the drilling site 114 to reconstruct the wellbore trajectory 126 (e.g., the diameter of the wellbore 118 may be decreased).

In other examples, the system 116, after finding that the mud weight should be increased, transmits a control signal to the mud control system 148 to modify mud formulation, e.g., higher density of drilling mud being used.

Additionally, the system 116, if the wellbore plan should be revised, transmits a control signal to the drilling control unit 150 that a completion plan should specify an increased amount of cement or a thicker wall of the casing 142.

In yet other examples, the system 116, after determining that no change can be made to the modifiable parameters, may transmit a control signal that the wellbore trajectory 126 should be revised. In such circumstances, the system 116 may display an alert that actions are needed to handle the washout region 208.

Referring to FIGS. 3A to 3E, schematic representations of the wellbore 118 with a washout area is shown.

In FIG. 3A, an example washout region 208 is shown along with associated parameters. FIG. 3A shows one way how the system 116 for controlling a washout region may detect the washout region 208. When the washout region 208 arises, the washout region 208 may lead to a non-uniform shape and/or an increased volume of the wellbore 118. The washout region 208 may cause a difficulty in the establishment of the wellbore 118 and additional non-productive time in drilling operations. The washout regions 208 create pockets in parts of the wellbore 118 that can accumulate rock cuttings. The pockets may require a higher mud flow rate to avoid buildup of cuttings.

If the size of the washout region 208 is not determined precisely and quickly, the wellbore 118 will not be cleaned properly, and leads to more serious wellbore issues such as a stuck pipe. The unexplained status of the washout region 208 can also introduce uncertainty for engineers engaged in calculating the exact volume of cement to set the casing 142. It is therefore important to assess the size of the washout region 208 and calculate the washout-corrected flow rate and/or the cement volume in performing wellbore cleaning and cement casing operations.

FIG. 3B shows three locations specified by points X₁ 304, X₂ 306, and X₃ 308 in the formation 106 or in the wellbore 118. As illustrated, X₁ 304 is located inside the washout region 208, i.e., in the extended wellbore 118. X₂ 306 is located outside the wellbore 118. X₃ 308 is located at the boundary of the washout region 208 and the formation 106, or at the boundary of the wellbore 118 and the formation 106. Each point may be identified by a polar coordinate, for example, as X (r, θ). See FIG. 3B.

In one or more embodiments, the system 116 for controlling the washout region 208 establishes a washout indicator function ƒ_wo(r, θ, t) that computationally determines whether X is a point inside or outside the washout region 208 at time t. The washout indicator function returns: a negative value for a point within the formation 106; a positive value for a point within the washout region 208; and zero for a point on a boundary between the washout region 208 and the formation 106.

• • (i) ƒ_wo(r, θ, t)>0 if X is inside the washout region 208, e.g., point X₁ 304.Error!Reference source not found.
  • (ii) ƒ_wo(r, θ, t)<0 if X is outside the washout region 208, e.g., point X₂ 306.Error!Reference source not found.
  • (iii) ƒ_wo(r, θ, t)=0 if X is on the boundary between the washout region 208 and the formation 106, e.g., point X₃ 308.

To implement the washout indicator function ƒ_wo(r, θ, t), the system 116 collets information about (1) the shear strength of the rock at point X at time t. The shear strength parameters can be measured on a core plug in a laboratory or can be estimated using a well log. For example, unconfined compressive strength (UCS) and internal friction angle of the rock at a given depth can be time-invariant constants. The shear strength can be assumed to be the same near the wellbore 118 regardless of time. The system 116 may collect information stored at the memory 606, and the drilling control unit 150 at the drilling site 114. The information may be gathered as needed by the drilling control unit 150 of the drilling site 114 and be transmitted to the system 116, in some implementations.

In addition, the system 116 collects information about (2) the effective stress at point X at time t, using any wellbore stress models, e.g., the elastic model, poroelastic model, porothermoelastic model, etc. Under time-independent models such as the elastic model, the effective stresses stay the same regardless of t. For example, the effective stresses at point X at time t can be determined by methods such as those described in preceding paragraphs.

The system 116 applies (3) a rock breakout failure model (a.k.a. failure criterion) to predict whether the shear strength can withstand the effective stress. As an unlimited list, the system 116 may choose and apply a suitable rock breakout failure model under Mohr-Coulomb, Mogi-Coulomb, Drucker-Prager, modified Lade, Stassi d'Alia, Hoek-Brown, and/or the like.

In some embodiments, the poroelastic wellbore stress model may be adopted to determine the effective stress, and the Drucker-Prager failure criterion may be applied as the rock breakout failure model, to implement the function ƒ_wo(r, θ, t). Other pairs of a wellbore stress model and a rock failure criterion may be adopted. The effective stresses at point X at time t are computed under the poroelastic model by dividing the stress components into: effective tangential stress σ′_θθ; effective radial stress σ′_rr; effective axial stress σ′_zz; and shear stresses σ_rθ, σ_rz, σ_θz.

$\begin{array}{c}\mathrm{Equation}\left(5\right)\end{array}$ $J_2=\frac{1}{6}\left[{\left({\sigma }_{\mathrm{rr}}^{\prime }-{\sigma }_{\theta \theta }^{\prime }\right)}^2+{\left({\sigma }_{\theta \theta }^{\prime }-{\sigma }_{\mathrm{zz}}^{\prime }\right)}^2+{\left({\sigma }_{\mathrm{zz}}^{\prime }-{\sigma }_{\mathrm{rr}}^{\prime }\right)}^2\right]+{\sigma }_{r\theta }^2+{\sigma }_{\mathrm{rz}}^2+{\sigma }_{\theta z}^2$ $\begin{array}{cc}{S}_p=\frac{{\sigma }_{\mathrm{rr}}^{\prime }+{\sigma }_{\theta \theta }^{\prime }+{\sigma }_{\mathrm{zz}}^{\prime }}{3}& \mathrm{Equation}\left(6\right)\end{array}$

The failure envelope for the Drucker-Prager criterion is expressed, using A₀ and D₀, as rock strength parameters, as

$\begin{array}{cc}\sqrt{J_2}=3A_0{S}_p+D_0& \mathrm{Equation}\left(7\right)\end{array}$

The washout indicator function ƒ_wo(r, θ*, t*) may be provided by

$\begin{array}{cc}{f}_{\mathrm{wo}}\left(r,\theta ,t\right)=\sqrt{J_2}-3A_0{S}_p-D_0& \mathrm{Equation}\left(8\right)\end{array}$

The system 116 may determine the distribution of probabilities of the washout region 208 by obtaining values of the washout indicator function ƒ_wo(r, θ*, t*) after collecting information about (1) the shear strength of the rock at point X at time t, and (2) the effective stresses at point X at time t.

For the points X* (r*, θ*) located on the boundary between the washout region 208 and the formation 106 at time t*, the washout indicator function ƒ_wo(r, θ, t) equals zero (as described in (iii) above). In some embodiments, given the washout indicator function ƒ_wo(r, θ, t), a borehole angle θ*, and a time t*, the system 116 may compute a radial distance r* such that the value of the washout indicator function becomes 0, ƒ_wo(r*, θ*, t*)=0. By finding the root of the washout indicator function ƒ_wo(r, θ, t), the boundary between the washout region 208 and the formation 106 (i.e., X₃) may be identified. The problem of finding r* may be recast as finding a root r* of the single variable function ƒ_wo(r, θ*, t*). For convenience, if ƒ_wo(r, θ*, t*) is always negative, i.e., no washout in the direction of θ* at time t*, then r* is assigned the value of radius R of the wellbore 118.

In some implementations, the system 116 may estimate the washout region 208, once the boundary radius r* is obtained through the root finding calculation ƒ_wo(r*, θ*, t*)=0. The system 116 may apply the washout indicator function ƒ_wo(r, θ, t) to simulate the multi-arm caliper log as it can determine the radius r* of the wellbore 118 in any direction.

Turning to FIG. 3C, as shown in FIG. 3C, the system 116 may calculate a cross-sectional area of the washout region 208 at a given time t*, obtaining the relevant information related to (1) the shear strength of the rock at point X at time t, and (2) the effective stresses at point X at time t, and computing the radius r* when the washout indicator function ƒ_wo(r, θ, t) becomes 0. The cross-section of the wellbore 118 with the washout region 208 may be divided into n sections, and each section has an angle of Δθ 312. That means there are n discrete angles θ_i 316 (θ₁, θ₂, . . . , θ_n) around the wellbore 118, where

$\begin{array}{cc}{\theta }_i=\left(i-1\right)\times \mathrm{\Delta \theta }& \mathrm{Equation}\left(9\right)\end{array}$ $\left(i=1\dots n\right)$

The system 116 may identify the radial distance r_i 314 by the root finding calculation ƒ_wo(r*, θ* t*)=0, for each section with angle θ_i 316. If there is no washout region 208 in the direction θ_i 316, the system 116 determines that r_i 314 is the original radius R 302 of the wellbore 118, i.e., r_i=R.

Table 1 shows an example set of information about the wellbore 118 and the formation 106 that the system 116 may obtain from available data in the well system 100 to perform the root finding calculation ƒ_wo(r*, θ*, t*)=0.

TABLE 1
Formation, wellbore, and drilling mud data.
	Parameters	Value	Unit
	True vertical depth	3300	Ft
	Wellbore diameter	12.25	inch
	Wellbore inclination angle	60	degree
	Wellbore azimuth	0	degree
	Overburden stress gradient	0.88	psi/ft
	Maximum horizontal stress	0.8	psi/ft
	gradient
	Maximum horizontal stress	0	degree
	azimuth
	Minimum horizontal stress	0.6	psi/ft
	gradient
	Pore pressure gradient	0.44	psi/ft
	Young's modulus	300	ksi
	Poisson's ratio	0.22	unitless
	Undrained Poisson's ratio	0.46	unitless
	Formation permeability	0.001	md
	Biot's coefficient	0.96	unitless
	Drucker-Prager parameter A	0.071	unitless
	Drucker-Prager parameter D	875	psi
	Drilling mud weight	10	ppg
	Drilling mud viscosity	1	cP

The information contained in Table 1 enables the system 116 to identify the boundary between the washout region 208 and the formation 106, using the time-dependent poroelastic wellbore stress model in conjunction with the Drucker-Prager failure criterion. As shown in Table 1, the system 116 may use real-time parameters about the inclination of the wellbore 118 and drilling mud, including the mud weight being used in the wellbore 118. Those skilled in the art will appreciate that the values shown in Table 1 are for example purposes only and that any suitable values may be used to calculate parameters (i.e., area, volume) of the washout region(s).

Referring to FIG. 3D, the system 116 may identify a cross-sectional area demarcated by the boundary between the washout region 208 and the formation 106 and an original circumference of the wellbore 118 at each depth in a specific depth range. The system 116 may divide the cross-sectional area into n sections and compute each area of the sections.

The system 116 may compute the area of the triangle formed by three points O, B 320 (angle θ_i 316), C 322 (angle θ_i+1 318) by the following:

$\frac{r_i\times r_{i+1}\times \sin \mathrm{\Delta \theta }}{2}$

As such, the system 116 may calculate within the area of i-th the section between the point B 320 and the point C 322 by the following:

$\begin{array}{cc}{a}_i=\frac{r_i\times r_{i+1}\times \sin \mathrm{\Delta \theta }}{2}-\frac{\Delta \theta \times R^2}{2}& \mathrm{Equation}\left(10\right)\end{array}$

The second term on the right-hand side in Equation (10) is the area inside the original wellbore radius R 302 within the section.

In some embodiments, when r_i 314 equals r_i+1 318 and the original radius R 302, r_i=r_i+1=R, the system 116 determines that the area is 0, i.e., a_i=0.

Accordingly, the total area of n sections, the cross-sectional area demarcated by (a) the boundary between the washout region 208 and the formation 106 and (b) the original circumference of the wellbore 118, at each depth within the specific depth range, is provided by a summation of the sections at each depth in the specific depth range:

$\begin{array}{cc}A=\sum _{i=1}^n{a}_i& \mathrm{Equation}\left(11\right)\end{array}$

To achieve higher accuracy in approximation of the washout region 208, the system 116 may adopt a smaller Δθ 312.

Having the ability to identify all the points demarcating the washout region 208 separate from intact regions of the formation 106, the system 116 may calculate the area of the washout region 208 with precision. Troublesome steps of counting the number of grid points (or pixels) in the washout region 208, dividing it by the total number of grid points (or pixels), and multiplying the result with the total area are saved. The present disclosure reduces error-prone steps as well as deviation from the actual size of the washout region 208. The system 116 calculates the area of the washout region 208, using Equations (5) to (11) that depends only on Δθ, which is a constant, and delivers stable estimations according to one or more embodiments.

Referring to FIGS. 4A and 4B, FIG. 4A shows the washout region 208 of the wellbore 118 mounting to 5.46 in² after 5 minutes of wellbore drilling according to one or more embodiments. Likewise, FIG. 4B shows the washout region 208 totaling 7.80 in² after 1 day of wellbore drilling.

The system 116 may generate a map, as depicted in FIGS. 4A and 4B, using a set of information about the wellbore 118 and the formation 106, which is summarized in Table 1. FIGS. 4A and 4B show areas having different value ranges of the function ƒ_wo(r, θ*, t*) as defined by Equation (8) for t=5 min (FIG. 4A) and t=1 day (FIG. 4B). In FIGS. 4A and 4B, areas with positive values 402, 404 indicate washout regions. Negative values 406, 408, 410 indicate stable regions. For example, the system 116 may identify the location of the washout region 208 and the formation 106, using the polar coordinate of boundary points X₃ (r, θ). As seen in areas with positive values 402, 404 (especially, areas shown with dense diagonal bars 402), the washout regions 208 become more severe over time, increasing the cross-sectional washout area by 43% after 1 day.

Moving back to FIG. 3E, FIG. 3E shows the calculation of the volume of the washout region 208. As some example implementations, the system 116 may use results of the washout area calculation described above, and obtain the location and size of cross-sectional washout areas A₁, A₂, . . . , A_n at corresponding depths z₁, . . . , z_n. The system 116 may determine the distribution of the washout region 208 and determine a volume of the washout region 208 in the specific depth range (depths ranging z₁, . . . , z_n), by totaling, for all depths z₁, . . . , z_n in the specific depth range, the summation of the sections at each depth A₁, A₂, . . . , A_n. In some embodiments, the wellbore 118 may include vertical portions, inclined portions, and horizontal legs.

The volume of the washout regions in the specific depth range is provided by:

$\begin{array}{cc}V=\frac{1}{2}\sum _{i=1}^{n-1}\left(z_{i+1}-z_i\right)\left(A_i+A_{i+1}\right)& \mathrm{Equation}\left(12\right)\end{array}$

Turning to FIG. 5, FIG. 5 illustrates an implementation of the system 116 in which the area and volume of the washout regions 208 in the specific depth range is determined. Data from the wellbore trajectory 126 are plotted in the Geometry track in FIG. 5. Data relevant to the shear strength and poroelastic properties of the rock are plotted in the Rock Properties track, and data relevant to the formation stresses and pore pressure are plotted in the In-Situ Stresses track. Drilling mud data are plotted in the Drilling Mud track.

The Cohesion 544 and Friction Angle 546 in the Rock Properties track are relevant to the shear strength of the rock. The poroelastic wellbore stress model uses the Geometry, Rock Properties, In-Situ Stresses, and Drilling Mud data to calculate the effective stresses at point X (r, θ) at time t. The effective stresses in conjunction with the Mohr-Coulomb failure criterion are utilized in the poroelastic wellbore stress model to compute the washout area (the cross-sectional area 536, 538 of the washout region 208 at each depth in a specific depth range) and the washout volume data. Accordingly, the volume of the washout region 208 is obtained and shown in the Washout Area and the Cum Washout Volume tracks. As shown in FIG. 5, the volume of the washout region 208 steadily increases over time.

FIG. 6 depicts a block diagram of a computer system used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures as described in this disclosure, according to one or more embodiments. The illustrated computer 602 is intended to encompass any computing device such as a server, desktop computer, laptop/notebook computer, wireless data port, smart phone, personal data assistant (PDA), tablet computing device, one or more processors within these devices, or any other suitable processing device, including both physical or virtual instances (or both) of the computing device.

The computer 602 can serve in a role as a client, network component, a server, a database or other persistency, or any other component (or a combination of roles) of a computer system for performing the subject matter described in the instant disclosure. The illustrated computer 602 is communicably coupled with a network 630. In some implementations, one or more components of the computer 602 may be configured to operate within environments, including cloud-computing-based, local, global, or other environment (or a combination of environments).

At a high level, the computer 602 is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some implementations, the computer 602 may also include or be communicably coupled with an application server, e-mail server, web server, caching server, streaming data server, business intelligence (BI) server, or other server (or a combination of servers).

The computer 602 can receive requests over network 630 from a client application (for example, executing on another computer 602 and responding to the received requests by processing the said requests in an appropriate software application. In addition, requests may also be sent to the computer 602 from internal users (for example, from a command console or by other appropriate access method), external or third-parties, other automated applications, as well as any other appropriate entities, individuals, systems, or computers.

Each of the components of the computer 602 can communicate using a system bus. In some implementations, any or all of the components of the computer 602, both hardware or software (or a combination of hardware and software), may interface with each other or the interface 604 (or a combination of both) over the system bus using an application programming interface (API) 612 or a service layer 613 (or a combination of the API 612 and service layer 613. The API 612 may include specifications for routines, data structures, and object classes. The API 612 may be either computer-language independent or dependent and refer to a complete interface, a single function, or even a set of APIs. The service layer 613 provides software services to the computer 602 or other components (whether or not illustrated) that are communicably coupled to the computer 602. The functionality of the computer 602 may be accessible for all service consumers using this service layer. Software services, such as those provided by the service layer 613, provide reusable, defined business functionalities through a defined interface. For example, the interface may be software written in JAVA, C++, or other suitable language providing data in extensible markup language (XML) format or another suitable format. While illustrated as an integrated component of the computer 602, alternative implementations may illustrate the API 612 or the service layer 613 as stand-alone components in relation to other components of the computer 602 or other components (whether or not illustrated) that are communicably coupled to the computer 602. Moreover, any or all parts of the API 612 or the service layer 613 may be implemented as child or sub-modules of another software module, enterprise application, or hardware module without departing from the scope of this disclosure.

The computer 602 includes an interface 604 for inputting and outputting a signal that the hardware processor 605 processes. Although illustrated as a single interface 604 in FIG. 6, two or more interfaces 604 may be used according to particular needs, desires, or particular implementations of the computer 602. The interface 604 is used by the computer 602 for communicating with other systems in a distributed environment that are connected to the network 630. Generally, the interface 604 includes logic encoded in software or hardware (or a combination of software and hardware) and operable to communicate with the network 630. More specifically, the interface 604 may include software supporting one or more communication protocols associated with communications such that the network 630 or interface's hardware is operable to communicate physical signals within and outside of the illustrated computer 602.

The computer 602 includes at least one hardware processor 605. Although illustrated as a single hardware processor 605 in FIG. 6, two or more processors may be used according to particular needs, desires, or particular implementations of the computer 602. The hardware processor(s) 605 may be an integrated circuit for processing instructions. For example, the hardware processor(s) 605 may be one or more cores, or micro-cores of a processor.

Generally, the hardware processor 605 executes instructions and manipulates data to perform the operations of the computer 602 and any algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure.

The computer 602 also includes a memory 606 that holds data for the computer 602 or other components (or a combination of both) that can be connected to the network 630. For example, memory 606 can be a database storing data consistent with this disclosure. Although illustrated as a single memory 606 in FIG. 6, two or more memories 606 may be used according to particular needs, desires, or particular implementations of the computer 602 and the described functionality. While the memory 606 is illustrated as an integral component of the computer 602, in alternative implementations, memory 606 can be external to the computer 602.

The application 607 is an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer 602, particularly with respect to functionality described in this disclosure. For example, application 607 can serve as one or more components, modules, applications, etc. Further, although illustrated as a single application 607, the application 607 may be implemented as multiple applications 607 on the computer 602. In addition, although illustrated as integral to the computer 602, in alternative implementations, the application 607 can be external to the computer 602.

There may be any number of computers 602 associated with, or external to, a computer system containing computer 602, wherein each computer 602 communicates over network 630. Further, the term “client,” “user,” and other appropriate terminology may be used interchangeably as appropriate without departing from the scope of this disclosure. Moreover, this disclosure contemplates that many users may use one computer 602, or that one user may use multiple computers 602.

Further, the computing system may include one or more output device(s), such as a screen (e.g., a liquid crystal display (LCD), a plasma display, touchscreen, cathode ray tube (CRT) monitor, projector, or other display device), a printer, external storage, or any other output device. One or more of the output device(s) may be the same or different from the interface 604.

In some embodiments, data may be presented through the interface 604 provided by the computer 602. The interface 604 may include a GUI that displays information on a display device, such as a computer monitor or a touchscreen on a handheld computer device. The GUI may include various GUI widgets that organize what data is shown as well as how data is presented to a user. Furthermore, the GUI may present data directly to the user, e.g., data presented as actual data values through text, or rendered by the computer 602 into a visual representation of the data, such as through visualizing a data model.

For example, a GUI may first obtain a notification from a software application 607 requesting that a particular data object be presented within the GUI. Next, the GUI may determine a data object type associated with the particular data object, e.g., by obtaining data from a data attribute within the data object that identifies the data object type. Then, the GUI may determine any rules designated for displaying that data object type, e.g., rules specified by a software framework for a data object class or according to any local parameters defined by the GUI for presenting that data object type. Finally, the GUI may obtain data values from the particular data object and render a visual representation of the data values within a display device according to the designated rules for that data object type.

Data may also be presented through various audio methods. In some embodiments, data may be rendered into an audio format and presented as sound through one or more speakers operably connected to a computer 602.

Software instructions in the form of computer readable program code to perform embodiments of the disclosure may be stored, in whole or in part, temporarily or permanently, on a non-transitory computer readable medium such as a CD, DVD, storage device, a diskette, a tape, flash memory, physical memory, or any other computer readable storage medium. Specifically, the software instructions may correspond to computer readable program code that, when executed by a processor(s) 605, is configured to perform one or more embodiments of the disclosure.

Referring to FIGS. 7A and 7B, these FIGS. show flowcharts in accordance with one or more embodiments. Specifically, FIGS. 7A and 7B describe a general method for controlling a washout region in a wellbore placed in a formation. One or more blocks in FIGS. 7A and 7B may be performed by one or more components (e.g., the hardware processor 605 of the system 116 of the well system 100) as described in FIGS. 1A, 1B, 6. While the various blocks in FIGS. 7A and 7B are presented and described sequentially, one of ordinary skill in the art will appreciate that some or all of the blocks may be executed in different orders, may be combined or omitted, and some or all of the blocks may be executed in parallel. Furthermore, the blocks may be performed actively or passively.

Initially, at Step 702, the system 116 for controlling a washout region 208 obtains information about the wellbore 118 and the formation 106. More specifically, in Step 702, the system 116 determines in-situ stresses and pore pressure from well logs, leak-off tests, and measurements from offset wells or from real-time drilling data. Further, Step 702 also involves extracting the formation rock's physical and mechanical properties, and strength properties from well logs and core samples or from real-time drilling data. In some embodiments, the system 116 collects information that is relevant to the shear strength of the rock at point X at time t within the formation 106. Such data may be stored in memory 606 of the system 116. Additionally, the information may be gathered as needed by the mud control system 148 and the drilling control unit 150 at the drilling site 114, in some implementations. Moreover, the system 116 collects information about the effective stress at point X at time t, using any wellbore stress models, e.g., the elastic model, poroelastic model, porothermoelastic model, etc.

Step 702 also includes obtaining the mud weight used in the field or from the mud program design, and determining the wellbore geometry, i.e., depth, borehole diameter, inclination angle, and azimuth from the well survey log or from the well trajectory design.

At Step 704, the system 116 establishes a washout indicator function as a function of time and location (point X (r, θ) at time t) in the formation 106. See FIG. 3B. In one or more embodiments, the system 116 generates the washout indicator function based on a rock breakout failure model (i.e., failure criterion) and predicts whether the shear strength can withstand the effective stress. As a suitable rock breakout failure model, the system 116 may select Mohr-Coulomb, Mogi-Coulomb, Drucker-Prager, modified Lade, Stassi d'Alia, Hoek-Brown, and/or the like. In one or more embodiments, the system 116 for controlling the washout region 208 may establish the washout indicator function ƒ_wo(r, θ, t) using any pair of wellbore stress model and rock failure criterion. The failure envelope for the Drucker-Prager criterion is expressed as Equation (7) above.

At Step 706, the system 116 computationally determines whether the washout region 208 exists. In some embodiments, the system 116 calculates the washout indicator function on a cross section of the wellbore 118 and the formation 106, at each depth in a specific depth range as shown in FIG. 3C.

If the washout region exists, at Step 708, the system 116 quantifies the washout region 208 in the specific depth range upon finding presence of the washout region 208. When a washout region does not exist, the method ends.

Continuing with FIG. 7A, at Step 710, the system 116 may set a target of mud weight to be used in the wellbore 118 once the washout region 208 has been found to exist. The target of mud weight may be selected by the system 116 to prevent worsening (expansion) of the washout region 208. Alternatively, the system 116 may set the target of mud weight once the washout region 208 is determined to be increasing at a predetermined rate range. The system 116 may transmit an instruction to the mud control system 148 to change mud weight. In some examples, the system 116 may determine whether or not to change features of drilling fluid or drilling mud (e.g., mud viscosity). The system 116 may transmit a command to recommend a change of the mud formulation, e.g., higher density of drilling mud being used.

Referring to Step 712, the system 116 may alter a drilling rate in digging of the wellbore 118. The drilling speed (ROP) is automatically set to ensure that the rate is appropriate for prevention of the washout region 208 or expansion of the washout region 208, in light of characteristics of the formation 106. Real time downhole monitoring sensors may provide information for the system 116 to determine (adjust) optimal drilling parameters.

At Step 714, the system 116 transmits an alert of: the washout region 208 of a predetermined size range; and the washout region 208 expanding at a predetermined rate range according to one or more embodiments. If the system 116 has determined that the washout region 208 of the predetermined size range is likely to cause a wellbore failure (such as a blockage of the wellbore 118 by stalled mud flow), the system 116 may transmit the alert to inform a user of the system 116 of the washout region 208 reaching the predetermined size range. Similarly, if the washout region 208 expanding at the predetermined rate range has been found, the system 116 may transmit an alert about the expansion of the washout region 208.

For example, the user of the system 116 may adjust cementing operation to pump more cement if the washout region 208 is very large to fill up the empty space. In scenarios where the washout region 208 is significantly enlarged, the system 116 may prompt the user to change a drilling plan. In some implementations, the system 116 may identify the location of the boundary of the washout region 208 and the formation 106, based on the washout indicator function ƒ_wo(r, θ*, t*) using the polar coordinate of boundary points X₃ (r, θ).

Referring to FIG. 7B, FIG. 7B explains the steps the system 116 performs in quantifying the washout region 208. In other words, FIG. 7B expands on Step 708 of FIG. 7A. In one or more embodiments, in Step 722, the system 116 may identify a cross-sectional area demarcated by the boundary between the washout region 208 and the formation 106 and the original circumference of the wellbore 118 at each depth in the specific depth range. For example, the washout indicator function determines the location of the washout region 208 based on the following characteristics.

• • (i) ƒ_wo(r, θ, t)>0 if X is inside the washout region 208, e.g., point X₁ 304.Error!Reference source not found.
  • (ii) ƒ_wo(r, θ, t)<0 if X is outside the washout region 208, e.g., point X₂ 306.Error!Reference source not found.
  • (iii) ƒ_wo(r, θ, t)=0 if X is on the boundary (or at an interface) between the washout region 208 and the formation 106, e.g., point X₃ 308.

As shown in FIG. 3D, the system 116 may compute the area of the triangle formed by three points O B 320 (angle θ_i 316), C 322 (angle θ_i+1 318) and calculate the area of the washout region 208. In Step 722, for each depth in the borehole section of interest, the washout area calculation method described above is used to calculate the area of the washout regions.

At Step 724, the system 116 may divide the cross-sectional area into n sections and compute each area of the sections by Equation (10).

At Step 726, the total area of the washout region 208 on the cross-section in FIG. 3D is provided by Equation (11). The system 116 may obtain a summation of the sections at each depth.

At Step 728, the system 116 may determine the distribution of the washout region 208 and determine a volume of the washout region 208, by computing Equation (12). The system 116 may total, for all depths in the specific depth range (depths ranging z₁, . . . , z_n), the summation of the sections at each depth A₁, A₂, . . . , A_n.

Advantageously, embodiments disclosed herein provide two calculation based methods to determine a more exact size and area/volume of wash out regions. The methods disclosed herein are based on computational modeling, and thus do not require specialized equipment and can be performed in real time or in planning phase. Washouts lead to non-uniform borehole shape and increase the borehole volume, causing difficulties and non-productive time in drilling operations. The washouts create pockets in different sections of the open hole that can accumulate rock cuttings, thereby requiring a higher mud flow rate to avoid buildup of cuttings. If the washout sizes are not properly determined and accounted for, the wellbore can be inadequately cleaned, leading to more severe wellbore issues such as stuck pipe. The addition of washout volume can also introduce uncertainty for engineers to calculate the exact volume of cement to set casing. It is therefore important to know the size of borehole washout in borehole cleaning and cement casing operations to calculate the washout-corrected flow rate and cement volume.

While the disclosure has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the disclosure as disclosed herein. Accordingly, the scope of the disclosure should be limited only by the attached claims.

Claims

1. A method for evaluating and controlling a washout region of a wellbore placed in a formation, comprising: obtaining information about the wellbore and the formation;establishing a washout indicator function as a function of time and location;computationally determining whether the washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation, at each depth in a specific depth range; andupon finding presence of the washout region in the specific depth range, quantifying the washout region,wherein the washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary between the washout region and the formation.

2. The method of claim 1, wherein the quantifying the washout region comprises: identifying a cross-sectional area demarcated by the boundary between the washout region and the formation and an original circumference of the wellbore at each depth in the specific depth range;dividing the cross-sectional area into sections and computing each area of the sections;obtaining a summation of the sections at each depth in the specific depth range; anddetermining a volume of the washout region, by totaling for all depths in the specific depth range, the summation of the sections at each depth.

3. The method of claim 2, wherein the information about the wellbore and the formation comprises: in-situ stress measurement;weight of mud within the specific depth range; andstrength properties of rocks in the formation.

4. The method of claim 3, wherein the information about the wellbore and the formation further comprises: for each depth in the specific depth range, a wellbore diameter, an inclination angle of the wellbore, and an azimuth of the wellbore.

5. The method of claim 3, wherein the information about the wellbore further comprises: a pore pressure of rocks in the formation.

6. The method of claim 1, wherein the washout indicator function is based on a wellbore stress model and a rock breakout failure criterion.

7. The method of claim 3, wherein the washout indicator function identifies the washout region using Mohr-Coulomb failure criterion.

8. The method of claim 2, further comprising: setting a target of mud weight to be used in the wellbore.

9. The method of claim 2, further comprising: altering a drilling rate for digging the wellbore.

10. The method of claim 2, further comprising: transmitting an alert of at least one of the following: the washout region of a predetermined size range; and the washout region expanding at a predetermined rate range.

11. A system for evaluating and controlling a washout region of a wellbore placed in a formation, comprising: a hardware processor, operatively connected to an interface and a memory that: obtains information about the wellbore and the formation;establishes a washout indicator function as a function of time and location in the formation;determines whether the washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation at each depth in a specific depth range; andupon finding presence of the washout region, quantifies the washout region in the specific depth range;the interface for inputting and outputting a signal that the hardware processor processes; andthe memory that stores the information about the wellbore and the formation,wherein the washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary between the washout region and the formation.

12. The system of claim 11, wherein the hardware processor quantifies the washout region by: identifying a cross-sectional area demarcated by the boundary between the washout region and the formation and an original circumference of the wellbore at each depth in the specific depth range;dividing the cross-sectional area into sections and computing each area of the sections;obtaining a summation of the sections at each depth in the specific depth range; anddetermining a volume of the washout region, by totaling for all depths in the specific depth range, the summation of the sections at each depth.

13. The system of claim 12, wherein the information about the wellbore and the formation comprises: in-situ stress measurement;weight of mud within the specific depth range; andstrength properties of rocks in the formation.

14. The system of claim 13, wherein the information about the wellbore and the formation further comprises: for each depth in the specific depth range, a wellbore diameter, an inclination angle of the wellbore, and an azimuth of the wellbore.

15. The system of claim 13, wherein the information about the wellbore and the formation further comprises: a pore pressure of rocks in the formation.

16. The system of claim 11, wherein the washout indicator function is based on a wellbore stress model and a rock breakout failure criterion.

17. The system of claim 15, wherein the washout indicator function identifies the washout region using Mohr-Coulomb failure criterion.

18. The system of claim 12, wherein the hardware processor further: sets a target of mud weight to be used in the wellbore.

19. The system of claim 12, wherein the hardware processor further: alters a drilling rate in digging the wellbore.

20. A non-transitory computer readable medium storing instructions executable by a hardware processor of a computer, the instructions comprising: obtaining information about a wellbore and a formation;establishing a washout indicator function as a function of time and location in the formation;computationally determining whether a washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation, at each depth in a specific depth range; andupon finding presence of the washout region, quantifying the washout region in the specific depth range,wherein the washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary between the washout region and the formation.