A Novel Model for the Real-Time Evaluation of Hole-Cleaning Conditions with Case Studies

: The main challenge in deviated and horizontal well drilling is hole cleaning, which involves the removal of drill cuttings and maintaining a clean borehole. Insufﬁcient hole cleaning can lead to issues such as stuck pipe incidents, lost circulation, slow rate of penetration ( ROP ), difﬁcult tripping operations, poor cementing, and formation damage. Insufﬁcient advancements in real-time drilling evaluation for complex wells can also lead to drilling troubles and an increase in drilling costs. Therefore, this study aimed to develop a model for the hole-cleaning index ( HCI ) that could be integrated into drilling operations to provide an automated and real-time evaluation of deviated-and horizontal-drilling hole cleaning based on hydraulic and mechanical drilling parameters and drilling ﬂuid rheological properties. This HCI model was validated and tested in the ﬁeld in 3 wells, as it was applied when drilling 12.25 (cid:48)(cid:48) intermediate directional sections and an 8.5 (cid:48)(cid:48) liner directional section. The integration of the HCI in Well-A and Well-B helped achieve much better well drilling performance (50% ROP enhancement) and mitigate potential problems such as pipe sticking due to hole cleaning and the slower rate of penetration. Moreover, the HCI model was also able to identify hole-cleaning efﬁciency during a stuck pipe issue in Well-C, which highlights its potential usage as a real-time model for optimizing drilling performance and demonstrates its versatility.


Introduction
Drilling vertical and more directional wells for the oil and gas industry is necessary to meet demand for global resources [1].Drilling troubles are a constant, and most of these drilling problems are stuck pipe incidents due to improper hole cleaning, lost circulation, and well control incidents [2,3].Optimization of downhole cleaning during drilling can be achieved either by improving engineering aspects or by enhancing drilling fluid properties using suitable chemical additives, and most of the time, both are applied appropriately [3].In planning and designing the drilling of wells, drilling time and flat time must be suitably optimized to obtain the best drilling efficiency and cost effectiveness [4,5].Hole cleaning during drilling plays a significant role in reducing drilling time by ensuring an enhanced rate of penetration (ROP) and a flat time by minimizing tripping operations, pumping of sweep pills, time of circulation, and time spent running casing, while improving cementation integrity and efficiency [6].Improper hole cleaning causes drilling problems such as high or erratic trends of equivalent circulating density, torque and drilling drag, wellbore instability, high annulus pressure, lost circulation, tight hole sections encountered during tripping, and stuck pipe and well control incidents [7].Hole cleaning is an effective tool used to overcome wellbore instability during drilling in case cutting accumulation and shale sloughing and caving are encountered.Cutting accumulation and shale caving will lead to difficult tripping operations resulting from pipe sticking [8].In fact, approximately Energies 2023, 16, 4934 2 of 27 33% of stuck pipe incidents in deviated and horizontal directions are caused by inadequate downhole cleaning while drilling, making it a significant contributor to these types of events [4,9,10].Moreover, effective hole cleaning is a crucial aspect of maximizing production rates in a well, as it can significantly impact the success of subsequent techniques such as acidizing and CO 2 injection.By ensuring that the wellbore is adequately cleaned during drilling, the efficiency of these methods can be improved, reducing the risk of problems such as stuck pipe, borehole instability, and reduced production rates [11][12][13][14].More importantly, the upwards flow velocity exceeding the speed of solids settling in the drilling fluid is the main condition of cutting removal while drilling vertical wells [7].In the case of deviated and horizontal drilling, it is more difficult to fulfil this condition [8].As the angle of the borehole increases, the direction of settling of fractured rock particles from the borehole axis changes.As a result, cuttings begin to accumulate on the bottom wall of the borehole.The efficiency of clearing the cutting particles from deviated and horizontal drilling wells depends on the basic hydrodynamic indicators and technological parameters of the drilling regime, as in the case of vertical wells, and on the geometry of the annular space and borehole profile [2,3,15].The borehole profile is determined by the zenith angle, and the geometry of the annulus is determined by the eccentric position of the drill string [16][17][18].There are 3 zenith angle intervals that affect the degree of cleaning of the drilled cuttings: 0-10 • , 10-30 • , and 30-60 • [3,19].At small zenith angles (0-10 • ), the particles settle in the direction of the bottom hole due to gravity acting on them.At medium values of the zenith angle (10-30 • ), the density and viscosity of the cuttings increase, which leads to possible accumulation of sludge at the bottom-hole bottom.If the zenith angle reaches 30-60 • , the friction forces increase, and the particle sliding speed slows down, possibly even to a complete stop [20][21][22].The efficiency of cutting removal also depends on the flow velocity profile in the annulus.In the concentric annulus of a vertical well, the drilling fluid velocity and energy are uniformly distributed relative to the drill string.As a result, the drill string is arranged eccentrically in the borehole.Therefore, there is a shift in the velocity profile.The consequence of this is that the flow velocity above the drill string is maximum and the velocity on the left and right sides of the drill string space is minimum.Sludge build-up occurs, and "stagnation zones or dead zones" are formed [3,19].Another factor affecting bottom-hole cleaning is the velocity of the drilling fluid in the annulus.In laminar drilling-fluid mode, good cleaning of broken rock occurs when the rheological properties of the drilling fluid are properly selected.In turbulent mode, most of the solids are carried out of the borehole by the flow.The rheology of the drilling fluid has much less influence.However, the turbulent flow mode can be used only at a given flow rate of drilling pumps, low erosion of borehole walls, and high velocity of drilling fluid movement in the borehole space [23].Another factor that influences bottom-hole cleaning is the rheological properties of the drilling fluid.It is possible to control the rheological properties of drilling fluids by treatment with special chemical additives [24].Thus, the regulation of wellbore drilling performance is one of the main objectives of well drilling.All rheological characteristics of drilling fluids and hydrodynamic characteristics should be taken into account in a hydraulic well-drilling program [25][26][27].Correctly selected formulation and rheological properties of the solution along with optimal technological parameters of the drilling process will allow high productivity and quality of drilling work to be achieved.Moreover, effective hole cleaning is a crucial aspect of maximizing production rates in a well, as it can significantly impact the success of subsequent techniques such as acidizing and CO 2 injection.By ensuring that the wellbore is adequately cleaned during drilling, the efficiency of these methods can be improved, reducing the risk of problems such as stuck pipe, borehole instability, and reduced production rates [11][12][13][14].In addition, enhancing the effect of these parameters can assist in maintaining the carrying capacity of drilling fluids, which in turn can lead to an improvement in the design of wellbores [24].Numerous studies have been conducted to investigate the parameters that affect hole-cleaning effectiveness.Raed et al. showed that drill pipe rotation is crucial for cutting removal in laminar and transition flow [23].Meanwhile, multiple researchers have investigated cutting Energies 2023, 16, 4934 3 of 27 transport over the past few decades and created a variety of mechanistic and semimechanistic models to explain flow features [25][26][27].Mohammadsalehi et al. developed an extensive approach that utilized Larsen's model and Moore's correlation for estimating and identifying the minimum flow rate that is needed for cutting removal across all inclination angles, which range from 0 • to 90 • .This was done to determine and estimate the bare minimum flow rate necessary for cutting removal at each and every inclination angle [28].Recently, in a real-time evaluation, Al Rubaii et al. proved that optimizing the usage of the carrying-capacity index (CCI) and the concentration of cuttings in the annulus (CA) can considerably improve hole-cleaning effectiveness and boost ROP.These two variables are collectively referred to as the "concentration of cuttings in the annulus."The model offers drilling engineers and drilling supervisors an efficient technique for determining the appropriate mud characteristics for effective hole cleaning, as well as the maximum ROP that can be achieved based on the volume of cuttings in the annulus [24].Nonetheless, with regard to the cleaning of boreholes during drilling procedures, there appears to be a notable deficiency in some models regarding evaluating the drilling process in real time.Furthermore, these models are based on a limited number of parameters affecting the status of hole cleaning.Therefore, the main objective of this study is to introduce a newly developed hole-cleaning index (HCI) based on Robinson's model that was developed in 2004 [29] to achieve effective downhole cleaning by applying the required adjustment to optimize the drilling process.This method implements automated carrying-capacity indicator modifications.The developed HCI enables real-time monitoring and evaluation of the status of hole cleaning during drilling.The study extensively explains the status of hole-cleaning models, as demonstrated in Figure 1.The paper delineates diverse real-time models that function as indicators for assessing hole cleaning.Furthermore, the mathematical formulation of the novel HCI model is expounded, encompassing all pertinent variables essential for the real-time assessment of hole-cleaning conditions.The significance of the HCI model as a novel index model is underscored by its validation through field applications.
Energies 2023, 16, x FOR PEER REVIEW 3 of 29 investigate the parameters that affect hole-cleaning effectiveness.Raed et al. showed that drill pipe rotation is crucial for cutting removal in laminar and transition flow [23].
Meanwhile, multiple researchers have investigated cutting transport over the past few decades and created a variety of mechanistic and semimechanistic models to explain flow features [25][26][27].Mohammadsalehi et al. developed an extensive approach that utilized Larsen's model and Moore's correlation for estimating and identifying the minimum flow rate that is needed for cutting removal across all inclination angles, which range from 0° to 90°.This was done to determine and estimate the bare minimum flow rate necessary for cutting removal at each and every inclination angle [28].Recently, in a real-time evaluation, Al Rubaii et al. proved that optimizing the usage of the carrying-capacity index (CCI) and the concentration of cuttings in the annulus (CA) can considerably improve hole-cleaning effectiveness and boost ROP.These two variables are collectively referred to as the "concentration of cuttings in the annulus."The model offers drilling engineers and drilling supervisors an efficient technique for determining the appropriate mud characteristics for effective hole cleaning, as well as the maximum ROP that can be achieved based on the volume of cuttings in the annulus [24].Nonetheless, with regard to the cleaning of boreholes during drilling procedures, there appears to be a notable deficiency in some models regarding evaluating the drilling process in real time.Furthermore, these models are based on a limited number of parameters affecting the status of hole cleaning.Therefore, the main objective of this study is to introduce a newly developed hole-cleaning index (HCI) based on Robinson's model that was developed in 2004 [29] to achieve effective downhole cleaning by applying the required adjustment to optimize the drilling process.This method implements automated carrying-capacity indicator modifications.The developed HCI enables real-time monitoring and evaluation of the status of hole cleaning during drilling.The study extensively explains the status of hole-cleaning models, as demonstrated in Figure 1.The paper delineates diverse real-time models that function as indicators for assessing hole cleaning.Furthermore, the mathematical formulation of the novel HCI model is expounded, encompassing all pertinent variables essential for the real-time assessment of hole-cleaning conditions.The significance of the HCI model as a novel index model is underscored by its validation through field applications.

Status of Hole-Cleaning Models
Hole cleaning is a fundamental function of mud, and this function is also the most used and misunderstood.Cleaning of deviated holes is most challenging because of changing formation lithologies and the drill cuttings.In addition, when the cutting beds (cutting accumulation height) are at a hole inclination of 35-50 degrees, the drill cuttings are more likely to slide downwards, negatively affecting hole cleaning [30][31][32].

Status of Hole-Cleaning Models
Hole cleaning is a fundamental function of mud, and this function is also the most used and misunderstood.Cleaning of deviated holes is most challenging because of changing formation lithologies and the drill cuttings.In addition, when the cutting beds (cutting accumulation height) are at a hole inclination of 35-50 degrees, the drill cuttings are more likely to slide downwards, negatively affecting hole cleaning [30][31][32].
Even though increasing the mud flow rate can reduce the height of the bed of drill cuttings, it will not be very effective in directional wells [30,33,34].Pigott (1935) recommended that the concentration of the cuttings in the annulus must remain less than 5% to prevent stuck pipe problems [35,36].Newitt et al. (1961) found a precise equation for drilling cuttings volumetric concentration in the annulus for steady-state lifting of drill cuttings in a vertical tube [37].Mitchell (1992) developed an equation for quantifying average cutting concentration in the annulus while drilling and after stopping circulation while making a connection [38].Moreover, experimental investigations performed by Hussaini and Azar (1983) [39] and Azar (1990) [40] indicate that mud rheology also affects hole cleaning.The results of these investigations confirmed that the carrying efficiency of drilling mud increases when the percentage of the ratio between the mud yield point (YP) and the mud plastic viscosity (PV) is maximized.Larsen (1997) introduced a novel design model that facilitates the selection of appropriate hydraulic parameters by drilling engineers, thereby ensuring seamless drilling operations in high-angle boreholes ranging from 55 • to 90 • from the vertical.Empirical correlations were derived through a comprehensive experimental investigation of cutting transport in a flowloop with a full-scale diameter of 5 inches [41].Moreover, Thonhauser (1999) introduced a mechanical device that was built to measure the amount of cuttings produced from the wellbore and analyze the hole-cleaning behavior.It was designed to provide the basis for real-time interpretation to optimize the circulating strategy and schedule, and to correlate the measured cutting flux with wellbore stability problems and overall drilling performance [42].
Furthermore, determining the density and size of drill cuttings during drilling to estimate the slipping velocity of drill cuttings is critical and vital.Additionally, when the viscosity of drilling mud is high, the effectiveness of mud in cleaning the hole by removing the drilled cuttings will also be high.Pipe rotation significantly improves the efficiency of hole cleaning if the drill string has a high eccentricity for both vertical wells [43] and inclined hole sections, according to Sanchez et al. [44].
Ogunrinde and Dosunmu (2012) developed a model to estimate the optimum ROP and Q to be used during drilling to maintain proper hole cleaning [15].Samuel (2013) developed a modified model to predict drilling-string vibration during drilling to prevent damage or twisting-off of the BHA and associated poor hole cleaning [45].
Al-Azani et al. (2019) predicted real-time cutting concentration in the annulus by using ANNs, including back-propagation neural networks (BPNNs), radial basis functional networks (RBFNs), and SVMs, which are classified as artificial intelligence tools.The selected parameters were mud weight (MW), PV, YP temperature, mud pump flow rate (Q), rpm, ROP, pipe eccentricity, and inclination of the hole section.The results were validated with 116 experimental studies in the literature review domain.The accuracy was 0.9 R, and average absolute error (AAE) was less than 5% [1].Al-Rubaii et al. (2020) developed a new real-time model for cutting concentrations in annuli based on the influence of Q and ROP, and the model was applied to real-time data and validated with Newtis and API models [46].
The model showed acceptable accuracy and results.Al-Rubaii et al. (2018 and 2020) developed a new methodology for hole cleaning by improving ROP through evaluation and adjustment of the carrying-capacity index and accumulation of drill cuttings in the annulus of the drilled hole section simultaneously to improve drilling performance by more than 20% [24,46].
In addition, they modified the cutting carrying index by including cutting rise velocity with annular velocity and then applied the CCI to real-time data to monitor and evaluate the hole-cleaning efficiency and thereby optimize well and rig performance.Alawami et al. (2020) applied the hole-cleaning carrying-capacity index to real-time data to monitor and evaluate the hole-cleaning performance of drilled wells by using offline real-time data [10].Mahmoud et al. (2020) modified the CCI to make it applicable in cleaning deviated hole sections.They modified the original carrying-capacity index by considering the effect of inclination on the annular velocity and equivalent circulating density [47].Saihati et al. (2021) developed a predictive drilling torque model using machine learning techniques to monitor downhole conditions, such as poor hole-cleaning conditions [48].Huaizhong  a narrow annulus to maximize the rate of penetration of coiled tubing, which is partially underbalanced to solve the problem of wellbore instability.The outcomes of measurements were particle velocity, particle distribution, the phenomenon of collision of particles, and sinking and rising of particles.The obtained results were that the particle velocity declines with the increase in rotational speed and increases with the increase in flow rate [49].Ytrehus et al. (2019 and2021) used micronized barite to provide a lower-viscosity drilling fluid and nonlaminar flow, which is advantageous for particle transport in nearhorizontal sections.They found that low-viscosity fluids are more efficient than viscous fluids at higher flow rates and low drill-string rotation.Different fields have applied oil-based drilling fluids with similar weights and varying viscosities, and positive results have been shown for cutting transport performance, hole-cleaning abilities, and hydraulic frictional pressure drop [50,51].Pedrosa et al. (2022) investigated the influence of the rheological properties of three different types of fluids on the erodibility of the cutting bed.Three outcomes were measured: erodibility of the cutting bed, shear rates of different types of fluids, and flow rate dependency along the dune extent.The results showed that the cutting bed is eroded by dune movement [52].Shirangi et al. (2022) developed a new digital-twin methodology for predicting drilling fluid properties to perform real-time calculations for hole cleaning by combining several models, using the large amount of offset data integrated in the model [53].Elmgerbi et al. (2022) used two interconnected models to optimize drilling hydraulics.They used predictive and analytical models to predict, compute, and optimize surface drilling parameters [54].
Rathgeber (2023) examined the impact of pipe eccentricity, drill pipe rotation rates, pipe-to-hole area ratio, and wellbore flow area on cutting transport efficiency.The author additionally examined the influence of the ratio between the area of the pipe and the hole, as well as the area of flow within the wellbore, on the rotation of the drill pipe and the occurrence of flow channeling [55].Moreover, Tables 1 and 2 show a summary of major findings for other studies related to hole-cleaning chemistry and engineering.Several models and studies have been discussed in the preceding text.Notably, Ogunrinde and Dosunmu developed a model to estimate the optimal ROP and flow rate, which demonstrated high accuracy in real-time drilling operations [45].Similarly, Saihati et al. proposed a predictive drilling torque model [48], while Elmgerbi et al. utilised two interconnected models to optimise drilling hydraulics.Specifically, they employed predictive and analytical models to predict, compute, and optimise surface drilling parameters [54].These models have shown promising results in enhancing drilling efficiency and accuracy.Notwithstanding the plethora of models and studies available, the CCI model, as proposed by Robinson [29], exclusively takes into account the adequacy of vertical transportation of cuttings, without providing any insight into the actual quantity of cuttings present, and is restricted to application within the drill pipe.Consequently, it is imperative to devise an innovative model that takes into account all the significant variables that impact the state of hole cleaning.Additionally, the proposed approach should be authenticated by utilising real-time field data and historical data from previously drilled wells.The following two sections delineate the mathematical development of the novel HCI and its implementation and verifications in three wells.

Development of a Novel Hole-Cleaning Index
The novel real-time automated model of the status of hole cleaning developed in this study is based on the carrying-capacity index of cuttings developed by Robinson in 2004 [29].Ideally, Robinson created a model that utilizes the power law constant, mud weight, and annular velocity to estimate the changes in pressure differential at the bottom of a hole based on the mud weight and cuttings in the annulus.The calculation procedure assumes that annular pressure losses from drilling fluid flow remain constant, and the accuracy of current calculations is not considered precise enough to include them in this process.Therefore, the carrying capacity of the drilling fluid can be estimated using the carrying-capacity index (CCI), shown in Equation ( 1) [29].
where k is the consistency index, which can be obtained from Equation ( 2) based on [83-85], AV is the average annular velocity (ft/min), and MW is the drilling fluid density (pcf).
where n is the flow behavior index, PV is the plastic vicosity (cP), and YP is the yield point (lb/100 ft 2 ).More importantly, based on the Robinson results, when the borehole is effectively cleaned, the drilling rate initially decreases until the first drilled solids reach the surface.However, as these solids are removed, the bottom-hole pressure still increases, albeit at a slower rate.As more solids are eliminated due to good carrying capacity, the bottom-hole pressure starts to decrease.The first solids typically reach the surface when the bit reaches a depth of 11,100 ft.The ROP then decreases more gradually until the bit reaches a depth of 11,200 ft.At this point, enough drilled solids are being removed that the drilling rate actually increases, as illustrated in Figure 2a.In contrast, if the hole cleaning is poor, drilled solids continue to accumulate in the annulus, and the drilling rate does not show significant abrupt changes.This effect is demonstrated in terms of the pressure differential during drilling, as shown in Figure 2b [29].Although the sharpness and tumbling movement of the cuttings in the annulus can be used by the CCI to determine whether they are being carried properly in a vertical well, it does not reveal how many cuttings are actually present and is only applicable inside the drill pipe, in accordance with [29,86].Moreover, additional parameters, such as hydraulic velocities, must be taken into account to achieve a more accurate evaluation of hole-cleaning performance in deviated and horizontal drilling.The drilling fluid's rheological characteristics, which include the low-shear yield point (LSYP) parameter, are a significant factor [2].The calculated cutting slip and annular velocities must also be taken into account.Cutting slip is the difference between the velocities of the drilling fluid and the cuttings, whereas annular velocity is the velocity of the drilling fluid within the annulus Although the sharpness and tumbling movement of the cuttings in the annulus can be used by the CCI to determine whether they are being carried properly in a vertical well, it does not reveal how many cuttings are actually present and is only applicable inside the drill pipe, in accordance with [29,86].Moreover, additional parameters, such as hydraulic velocities, must be taken into account to achieve a more accurate evaluation of hole-cleaning performance in deviated and horizontal drilling.The drilling fluid's rheological characteristics, which include the low-shear yield point (LSYP) parameter, are a significant factor [2].The calculated cutting slip and annular velocities must also be taken into account.Cutting slip is the difference between the velocities of the drilling fluid and the cuttings, whereas annular velocity is the velocity of the drilling fluid within the annulus that exists between the drill string and the wellbore.These parameters can be used to calculate the amount of cuttings that are transported to the surface and how well holes are cleaned [53].Therefore, the novel index indicator considers all the important factors affecting the status of hole cleaning and is called the hole-cleaning index (HCI).It was developed starting from the CCI calculated using Equation (1) [29].Moreover, Appendix A shows a flowchart for the development of the HCI starting from CCI.
More importantly, in Equation ( 2), PV represents the mechanical friction between the drilling fluid solids and drilling fluid that causes resistance to flow [87].YP is the minimum value of stress that is required to move the fluid [48].R 3 is the viscometer reading at 3 rpm, and R 6 is the viscometer reading at 6 rpm, which can be used to predict the yield point at a low shear rate that can be defined as LSYP.Specifically, LSYP can contribute significantly to hole-cleaning efficiency and the ability to transport drill cuttings in the drilling of directional wells, and it is as critical and important as YP during well drilling.In drilling operations practices, it is highly recommended to have increased YP and a decreased LSYP [88].In addition, Bern et al. defined LSYP as the minimum yield stress for preventing solids settling (sagging) [89].The value of LSYP can be dramatically decreased by increasing the pH because the increase in pH readings can support the minimization of the bentonite's dispersion particles, and then, the particles of bentonite will not assist the fluid viscosity being established.Hence, the lifting capacity of drilling mud to transport the generated drill cuttings will be minimized [90].The standard API of measuring the low-shear yield point is defined as (LSYP = 2R 3 − R 6 ), which is used to estimate the proper yield stress [91].For a newly developed HCI, the LSYP was considered for better simulation of hole conditions and rheological drilling fluid influences during drilling operations.Therefore, PV and YP can be modified based on the LSYP, as shown in Equations ( 3) and (4), based on [2].
Generally, k describes the thickness of the fluid and is thus somewhat analogous to apparent viscosity [92].As the consistency index increases, the mud becomes thicker, based on [92].n determines whether the fluid becomes less or more viscous as the shear rate increases, in accordance with [92,93].The original expressions for k and n do not contain LSYP [83, 84,92].Here, the expressions for k and n of the developed real-time model take LSYP into account, and the LSYP term is a function of the viscometer readings at 3 and 6 rpm [4,84].Thus, the modified k m and n m that contain the modified PV m and modified YP m considering the LSYP can be obtained from Equations ( 5) and ( 6) [2,84].
In Equation (6), n m is expressed as a function of PV m , YP m , and LSYP as defined by the equation.Substituting Equation (5) into Equation ( 1) and replacing CCI with the new parameter HCI yields Equation (7).
Energies 2023, 16, 4934 Moreover, in Equation ( 7), the AV (as expressed in Equation ( 8)) is a drilling hydraulic parameter [29,84] that can be modified to include the effect of the hole inclination and the impact of the cutting rise velocity, cutting transport velocity, and cutting slip velocity defined by Equation ( 9).The modified annulus velocity (AV m ), which is equal to V transport , is defined by Equation ( 9) as the summation of the velocity corrected for the wellbore inclination effect (V corrected ) and cutting slip velocity (V slip ) based on [45,84], where V corrected and V slip are in (ft/min).V slip can be calculated by considering the axial and radial cutting slip velocities with the influence of inclination and azimuth, as mentioned by Azar [32,39] and Robello [86]; therefore, V slip = V sa cos(α) +V sr sin(β), where V sr is the redial cutting slip velocity and V sa is the axial cutting slip velocity.Moreover, in V slip , the weight of cuttings and cutting diameter (inch) can be considered and calculated as d C = 0.2 ROP DSR in accordance with [45,84,94].Finally, V corrected , including annular, cutting, and transport velocities, and V slip can be defined by Equations ( 10) and (11), respectively [2,45,84]. )) where Q is the mud pump flow rate (gal/min), OH is the hole size (in), OD is the drill pipe outside diameter (in) in the drilling-string design, α and β are the inclination and azimuthal directions of the hole (degrees), respectively, ROP is the drilling rate of penetration (ft/h), and DSR is the drill-string rotation (rpm).More importantly, the modified AV m is applicable inside the drill pipe and in the annulus according to [83,86].By combining Equation (8) to Equation (11), the transport velocity or the modified annular velocity can be expressed as indicated in Equation ( 12) [2,45,84].
where V ann is expressed as a function of Q, OH, and OD by Equation ( 13), which is the original annular mud velocity applied in the vertical hole section based only on [83].The modified annular velocity as defined in Equation ( 12) is a function of the flow rate and weight of the drilling fluid with cuttings, size of the drilled hole, outer diameter of the drill pipe, rate of penetration, drill-string rotation, modified plastic viscosity, modified yield point, viscometer reading at 3 rpm, viscometer reading at 6 rpm, wellbore inclination, and azimuthal directions [2,45,83,84].Based on [2,9,86], the MW in Equation ( 7) is replaced by the equivalent mud weight (EMW) (Equation ( 15)), which accounts for the weight of the cuttings' influence and is a function of ROP, OH, and Q ((Equation ( 14)).
drill pipe, rate of penetration, drill-string rotation, modified plastic viscosity, modified yield point, viscometer reading at 3 rpm, viscometer reading at 6 rpm, wellbore inclination, and azimuthal directions [2,45,83,84].Based on [2,9,86], the MW in Equation ( 7) is replaced by the equivalent mud weight (EMW) (Equation ( 15)), which accounts for the weight of the cuttings' influence and is a function of ROP, OH, and Q ((Equation ( 14)).Finally, the HCI is expressed as a function of PVm, YPm, LSYP, Km, nm, AVm, and EMW calculated using Equations ( 3)-( 6), (12), and (15) (see Figure 3).Equation ( 16) can be used to compute and finalize the modified HCI as a consequence: The application of HCI to determine the status of hole cleaning during drilling is based on the classification of the HCI value.As the HCI parameter developed in this study is based on CCI, the classification ranges for the HCI parameter are based on the ranges of CCI, in accordance with [29].CCI has two classification ranges of CCI > 1, which indicates proper hole-cleaning performance during drilling, and CCI < 1, which indicates insufficient hole cleaning [29].Classification of CCI was also adopted for the HCI parameter [29].An HCI value greater than 1 indicates proper hole cleaning, while an HCI value less than 1 indicates ineffective hole cleaning, which may lead to induced problems during drilling.More importantly, as illustrated in Figure 3, the HCI is a comprehensive metric and model that considers various parameters when assessing the effectiveness of hole cleaning.These parameters include rheological properties and density of the drilling fluid, as well as mechanical factors associated with drilling, such as well trajectory survey, mud velocities, rate of penetration, drill-string rotation, and cutting accumulation load.By considering these factors together, the HCI provides a more complete picture of the hole-cleaning conditions and can help identify potential issues that may arise during drilling.The use of the HCI in drilling operations can help optimize the drilling process and improve wellbore integrity.By monitoring the HCI and making adjustments to drilling parameters as needed, drilling teams can ensure that the wellbore is being cleaned effectively and that drilling operations are proceeding smoothly.

Field Applications Using the Novel Hole-Cleaning Index
The following flowchart exemplifies the estimation of the novel HCI model in real time (see Figure 4).Specifically, the flowchart demonstrates how the novel HCI model can be estimated in real time, with input data collected from various sources, including the monitoring operation, surface data, and operation report data.Three wells, namely Well-A, Well-B, and Well-C, were selected for this purpose.Furthermore, the performance of the HCI model was evaluated, and the importance, assumptions, and limitations of using the model in real-time are discussed.Finally, recommendations are provided to further improve the accuracy and efficiency of the model.

Case study and Data Description
Validation of the new HCI was demonstrated while directionally drilling 12.25″ intermediate sections of two offshore wells (Well-A and Well-B) and an 8.5″ liner section of another offshore well, Well-C, which experienced a stuck pipe incident.The 3 sections were highly deviated sections starting at 30 degrees and ending up nearing horizontal or 90 degrees inclination at the top of the reservoir.Figure 5 provides a clear schematic view of the three wells, including their respective sections.In the case of Well-A, the novel HCI model was utilized to evaluate the hole-cleaning conditions in the intermediate section at depths ranging from X100 to X1000 ft.For Well-B, the model was utilized to evaluate the hole-cleaning conditions at depths ranging from X100 to X520 ft.In the case of Well-C, which experienced a stuck pipe incident, the novel HCI model was utilized to evaluate hole cleaning in a stuck pipe incident due to the cutting accumulation at depths ranging from X1200 to X2200 ft.In this study, the formation and drilling cutting properties were carefully considered to ensure the effectiveness of the drilling process while utilizing the novel HCI model.

Case Study and Data Description
Validation of the new HCI was demonstrated while directionally drilling 12.25 intermediate sections of two offshore wells (Well-A and Well-B) and an 8.5 liner section of another offshore well, Well-C, which experienced a stuck pipe incident.The 3 sections were highly deviated sections starting at 30 degrees and ending up nearing horizontal or 90 degrees inclination at the top of the reservoir.Figure 5 provides a clear schematic view of the three wells, including their respective sections.In the case of Well-A, the novel HCI model was utilized to evaluate the hole-cleaning conditions in the intermediate section at depths ranging from X100 to X1000 ft.For Well-B, the model was utilized to evaluate the hole-cleaning conditions at depths ranging from X100 to X520 ft.In the case of Well-C, which experienced a stuck pipe incident, the novel HCI model was utilized to evaluate hole cleaning in a stuck pipe incident due to the cutting accumulation at depths ranging from X1200 to X2200 ft.In this study, the formation and drilling cutting properties were carefully considered to ensure the effectiveness of the drilling process while utilizing the novel HCI model.For Well-A and Well-B, the formation was composed of sandstone, limestone, and shale, with formation temperatures ranging from 140 to 155 °F.The formation porosity ranged from 0.15 to 0.25.The washout, which is the enlargement of the wellbore diameter due to the erosion of the formation, ranged from 10% to 30%.The properties of the drilling cuttings were also critical to the success of the drilling process.The density of the drill cuttings ranged from 20 to 24 ppg.The size of the drill cuttings ranged from 0.2 to 0.375 inches.Table 3 summarizes key characteristics of the drilled formations and cuttings produced during drilling of these sections.The two sections were drilled using an oil-based drilling fluid.For Well-C, the formation and drilling cutting properties were critical to the success of the drilling process.The formation temperature had a range of 155-175 °F, the porosity ranged from 0.10 to 0.15, and the washout had a range of 10-30%.The drill cuttings had a density of 20-24 ppg and a size of 0.15-0.3inches.The section was drilled using an Innovert oil-based mud.Table 4 summarizes the drilling fluid properties used to drill these sections.For Well-A and Well-B, the formation was composed of sandstone, limestone, and shale, with formation temperatures ranging from 140 to 155 • F. The formation porosity ranged from 0.15 to 0.25.The washout, which is the enlargement of the wellbore diameter due to the erosion of the formation, ranged from 10% to 30%.The properties of the drilling cuttings were also critical to the success of the drilling process.The density of the drill cuttings ranged from 20 to 24 ppg.The size of the drill cuttings ranged from 0.2 to 0.375 inches.Table 3 summarizes key characteristics of the drilled formations and cuttings produced during drilling of these sections.The two sections were drilled using an oil-based drilling fluid.For Well-C, the formation and drilling cutting properties were critical to the success of the drilling process.The formation temperature had a range of 155-175 • F, the porosity ranged from 0.10 to 0.15, and the washout had a range of 10-30%.The drill cuttings had a density of 20-24 ppg and a size of 0.15-0.3inches.The section was drilled using an Innovert oil-based mud.Table 4 summarizes the drilling fluid properties used to drill these sections.
In addition to the properties of the formation and drilling cuttings, several important parameters were carefully monitored and recorded during the drilling operations to ensure the accuracy and effectiveness of the HCI model.These parameters included the rheological properties of the drilling fluid, mechanical drilling parameters, hole section directional survey, and hydraulic velocities.To facilitate the analysis and interpretation of the data, tables were created to summarize the various parameters recorded during drilling operations.The other rheological properties of the drilling fluid, mechanical drilling parameters, hole section directional survey, and hydraulic velocities required for calculation of the HCI are listed in Table 5, Table 6, and Table 7 for Well-A, Well-B, and Well-C, respectively.These data were crucial for the calculation of the HCI, which required accurate and up-to-date information on the position and orientation of the drill bit.Calculating the HCI played a critical role in maintaining effective hole cleaning and preventing stuck pipe incidents.Moreover, a polycrystalline-diamond-cutter (PDC) drilling bit with 6 nozzles of 16/32 size, hydraulic horsepower of 2.5-3.8, and total bit flow area of 1.17 square inches was employed to drill the sections under study in both wells.The other components of the bottom-hole assembly are listed in Table 8 for 12.25 and 8.5 deviated sections.The results of applying the novel HCI model were tested in two wells.The HCI system underwent testing and validation in the field.Implementing the new HCI model and its automation proved to be a valuable addition to drilling best practices, minimizing potential problems caused by insufficient hole cleaning.The results of the field application are explained below for Well-A and Well-B.

Well-A
The first case study considered in this work involves a well identified as Well-A, where the HCI was employed during drilling to optimize hole cleaning.The changes in HCI and other drilling parameters of this case are shown in Figure 6.In Well-A, during drilling at a depth of X500, the HCI value is more than 1.1, indicating that the wellbore is clean, without accumulation of any cuttings.The crew also did not observe any other indication of the accumulation of cuttings.At a depth of X760 ft, the HCI value begins to continuously decrease from 1.17 to less than 1.1 at a depth of X840 ft, as shown in Figure 6.As indicated, the decrease in HCI is not caused by an increase in ROP.Hence, the crew decided to clean the hole by increasing the pumping rate of the drilling fluid from 750 to 915 gal/min, which increased the HCI from less than 1.1 to more than 1.15.The results of applying the novel HCI model were tested in two wells.The HCI system underwent testing and validation in the field.Implementing the new HCI model and its automation proved to be a valuable addition to drilling best practices, minimizing potential problems caused by insufficient hole cleaning.The results of the field application are explained below for Well-A and Well-B.

Well-A
The first case study considered in this work involves a well identified as Well-A, where the HCI was employed during drilling to optimize hole cleaning.The changes in HCI and other drilling parameters of this case are shown in Figure 6.In Well-A, during drilling at a depth of X500, the HCI value is more than 1.1, indicating that the wellbore is clean, without accumulation of any cuttings.The crew also did not observe any other indication of the accumulation of cuttings.At a depth of X760 ft, the HCI value begins to continuously decrease from 1.17 to less than 1.1 at a depth of X840 ft, as shown in Figure 6.As indicated, the decrease in HCI is not caused by an increase in ROP.Hence, the crew decided to clean the hole by increasing the pumping rate of the drilling fluid from 750 to 915 gal/min, which increased the HCI from less than 1.1 to more than 1.15.The crew also reported a decrease in erratic torque, which is an indication of removing the solids that had accumulated earlier at the bottom of the well.The crew members attempted to increase the drilling rate depending on the real-time estimation of the HCI.The changes in the drilling parameters and the associated HCI for this case are shown in Figure 7.The crew noted that the HCI indicates proper hole cleaning by evaluating the hole-cleaning conditions at depths between X120 and X150 ft.Thus, they decided to increase ROP by applying more weight on bit (WOB) to increase well drillability, as shown in Figure 7.When ROP is increased, the HCI decreases due to an increase in the concentration of cuttings in the wellbore, as indicated in Figure 7.The crew also reported a decrease in erratic torque, which is an indication of removing the solids that had accumulated earlier at the bottom of the well.The crew members attempted to increase the drilling rate depending on the real-time estimation of the HCI.The changes in the drilling parameters and the associated HCI for this case are shown in Figure 7.The crew noted that the HCI indicates proper hole cleaning by evaluating the hole-cleaning conditions at depths between X120 and X150 ft.Thus, they decided to increase ROP by applying more weight on bit (WOB) to increase well drillability, as shown in Figure 7.When ROP is increased, the HCI decreases due to an increase in the concentration of cuttings in the wellbore, as indicated in Figure 7.According to the driller, this trend also correlates with an increase in the drilling torque.As HCI values are still greater than 1.0 at a depth of ×300, which is the minimum limit for proper hole cleaning, the driller decided to maintain the same ROP of 280 ft/h for drilling deeper sections.The crew did not report any stuck pipe problems during drilling, and they were able to increase the drilling rate of this section based on the application of the HCI.More importantly, Figures 6 and 7 clearly illustrate the substantial discrepancy between the accuracy of the CCI and the novel HCI model in evaluating hole-cleaning conditions.The figures demonstrate that the CCI was not applicable and produced highly inaccurate results when compared to the highly accurate and reliable novel HCI model.In Figure 5, the CCI values ranged from 2.2 to 2.5 at depths from X400 to X430 ft, whereas the HCI values for the same depths ranged from 1.01 to 1.2.This significant difference highlights the limitations of the CCI and emphasizes the importance of utilizing the advanced HCI model for accurate and reliable hole-cleaning evaluation, particularly in deviated and horizontal wells.

Well-B
The second well of this study is identified as offset Well-B, where HCI was used to evaluate the deficiency of hole cleaning due to cutting accumulation and HCI was not employed for hole-cleaning efficiency.The drilling parameters and HCI are shown in Figure 8.The driller noted that the HCI is stable at approximately 1.13 for more than 100 ft, from X320 to X420 ft.At X420 ft, ROP decreases considerably from 300 to 200 ft/h due to drilling through a hard formation.According to the driller, this trend also correlates with an increase in the drilling torque.As HCI values are still greater than 1.0 at a depth of ×300, which is the minimum limit for proper hole cleaning, the driller decided to maintain the same ROP of 280 ft/h for drilling deeper sections.The crew did not report any stuck pipe problems during drilling, and they were able to increase the drilling rate of this section based on the application of the HCI.More importantly, Figures 6 and 7 clearly illustrate the substantial discrepancy between the accuracy of the CCI and the novel HCI model in evaluating hole-cleaning conditions.The figures demonstrate that the CCI was not applicable and produced highly inaccurate results when compared to the highly accurate and reliable novel HCI model.In Figure 5, the CCI values ranged from 2.2 to 2.5 at depths from X400 to X430 ft, whereas the HCI values for the same depths ranged from 1.01 to 1.2.This significant difference highlights the limitations of the CCI and emphasizes the importance of utilizing the advanced HCI model for accurate and reliable hole-cleaning evaluation, particularly in deviated and horizontal wells.

Well-B
The second well of this study is identified as offset Well-B, where HCI was used to evaluate the deficiency of hole cleaning due to cutting accumulation and HCI was not employed for hole-cleaning efficiency.The drilling parameters and HCI are shown in Figure 8.The driller noted that the HCI is stable at approximately 1.13 for more than 100 ft, from X320 to X420 ft.At X420 ft, ROP decreases considerably from 300 to 200 ft/h due to drilling through a hard formation.
However, as the hole was appropriately cleaned, the driller decided to apply more WOB to increase ROP again to approximately 300 ft/h.The crew noted that the HCI gradually decreases when the ROP begins to increase, indicating the accumulation of cuttings.Hence, the driller was forced to increase the pumping rate of the drilling fluid from approximately 730 to almost 845 gal/min, as indicated in Figure 8, to maintain a clean hole while drilling at a higher rate without encountering any stuck pipe problems.
As the driller was aware that the bit would penetrate a soft formation at a depth of X160 ft, he decided to reduce WOB from 37 to 18 Klbf to prevent a significant increase in ROP.As indicated in Figure 9, even though WOB was significantly decreased to approximately 1/3 rd of its value, ROP in this soft formation increased only slightly from 200 to 240 ft/h.Even the HCI increased with this change, which did not lead to cutting accumulation.However, as the hole was appropriately cleaned, the driller decided to apply more WOB to increase ROP again to approximately 300 ft/h.The crew noted that the HCI gradually decreases when the ROP begins to increase, indicating the accumulation of cuttings.Hence, the driller was forced to increase the pumping rate of the drilling fluid from approximately 730 to almost 845 gal/min, as indicated in Figure 8, to maintain a clean hole while drilling at a higher rate without encountering any stuck pipe problems.
As the driller was aware that the bit would penetrate a soft formation at a depth of X160 ft, he decided to reduce WOB from 37 to 18 Klbf to prevent a significant increase in ROP.As indicated in Figure 9, even though WOB was significantly decreased to approximately 1/3 rd of its value, ROP in this soft formation increased only slightly from 200 to 240 ft/h.Even the HCI increased with this change, which did not lead to cutting accumulation.The drilling rate increases again from 240 ft to approximately 285 ft, accompanied by a decrease in HCI values from 1.14 to 1.06 without any change in WOB, owing to the penetration of another softer formation.Despite this decrease in HCI, the driller decided not to reduce WOB to decrease the drilling rate, as an HCI value of 1.06 is still in the safe zone to obtain appropriately clean holes.In addition to the discrepancies observed in Well-A, the CCI was also found to be unreliable in Well-B, producing inaccurate values when compared to HCI.Furthermore, it is crucial to take into account additional parameters such as hydraulic velocities to achieve a more comprehensive and accurate evaluation of holecleaning performance, particularly in deviated and horizontal drilling.The accurate measurement and tracking of hydraulic velocities are critical in ensuring the effective removal  However, as the hole was appropriately cleaned, the driller decided to apply more WOB to increase ROP again to approximately 300 ft/h.The crew noted that the HCI gradually decreases when the ROP begins to increase, indicating the accumulation of cuttings.Hence, the driller was forced to increase the pumping rate of the drilling fluid from approximately 730 to almost 845 gal/min, as indicated in Figure 8, to maintain a clean hole while drilling at a higher rate without encountering any stuck pipe problems.
As the driller was aware that the bit would penetrate a soft formation at a depth of X160 ft, he decided to reduce WOB from 37 to 18 Klbf to prevent a significant increase in ROP.As indicated in Figure 9, even though WOB was significantly decreased to approximately 1/3 rd of its value, ROP in this soft formation increased only slightly from 200 to 240 ft/h.Even the HCI increased with this change, which did not lead to cutting accumulation.The drilling rate increases again from 240 ft to approximately 285 ft, accompanied by a decrease in HCI values from 1.14 to 1.06 without any change in WOB, owing to the penetration of another softer formation.Despite this decrease in HCI, the driller decided not to reduce WOB to decrease the drilling rate, as an HCI value of 1.06 is still in the safe zone to obtain appropriately clean holes.In addition to the discrepancies observed in Well-A, the CCI was also found to be unreliable in Well-B, producing inaccurate values when compared to HCI.Furthermore, it is crucial to take into account additional parameters such as hydraulic velocities to achieve a more comprehensive and accurate evaluation of holecleaning performance, particularly in deviated and horizontal drilling.The accurate measurement and tracking of hydraulic velocities are critical in ensuring the effective removal The drilling rate increases again from 240 ft to approximately 285 ft, accompanied by a decrease in HCI values from 1.14 to 1.06 without any change in WOB, owing to the penetration of another softer formation.Despite this decrease in HCI, the driller decided not to reduce WOB to decrease the drilling rate, as an HCI value of 1.06 is still in the safe zone to obtain appropriately clean holes.In addition to the discrepancies observed in Well-A, the CCI was also found to be unreliable in Well-B, producing inaccurate values when compared to HCI.Furthermore, it is crucial to take into account additional parameters such as hydraulic velocities to achieve a more comprehensive and accurate evaluation of hole-cleaning performance, particularly in deviated and horizontal drilling.The accurate measurement and tracking of hydraulic velocities are critical in ensuring the effective removal of drilling cuttings from the wellbore and preventing incidents such as stuck pipe incidents.
Table 9 summarizes the impact of the implementation of HCI on well performance when enhanced hole cleaning was performed in Well-A.The HCI had an average value greater than 1, and the CA was 0.024 in Well-A, whereas it was less than 0.04 in Well-B.The ultimate results show average ROP improvement in Well-A due to proper hole-cleaning achievement.In deviated Well-C, the HCI model proved its effectiveness in evaluating stuck pipe incidents due to cutting accumulation.The third well of the study, which was identified as offset Well-C, was used to evaluate the performance of the HCI in these situations.The HCI was not employed for hole-cleaning efficiency in this well, but it was utilized to evaluate the stuck pipe incident caused by cutting accumulation.The drilling parameters and HCI values for Well-C are shown in Figure 10.As seen in the Figure 10, the driller noted an increase in cutting accumulation at depths ranging from X1200 to X1380 ft.Moreover, the driller observed that the HCI remained stable at approximately 0.55 to 0.8 for more than 700 ft, from X1520 to X2200 ft.Furthermore, at X1590 ft, the rate of penetration (ROP) decreased significantly from 200 to 100 ft/h due to the cutting accumulation, ultimately resulting in a stuck pipe incident.The driller was then forced to stabilize the pumping rate of the drilling fluid at almost 600 gal/min, as indicated in Figure 10.The HCI model was crucial to indicating and evaluating the hole conditions leading to the stuck pipe incident.By utilizing the HCI model, drilling teams can quickly identify and mitigate issues, preventing incidents such as stuck pipes and reducing nonproductive time, resulting in more efficient and cost-effective drilling operations.The effectiveness of the HCI model in evaluating stuck pipe incidents demonstrates its potential to significantly improve drilling operations.Table 10 summarizes the impact of the implementation of the HCI on well performance when hole cleaning during a stuck pipe accident in Well-C was evaluated.The HCI had an average value greater than 0.75, and the CA was 0.02 in Well-C.Table 10 summarizes the impact of the implementation of the HCI on well performance when hole cleaning during a stuck pipe accident in Well-C was evaluated.The HCI had an average value greater than 0.75, and the CA was 0.02 in Well-C.

The Importance, Assumptions, and Limitations of Utilizing the Novel HCI Model in Real Time
The proposed HCI model sets itself apart from existing models that rely solely on laboratory data and lack the ability to provide real-time predictions.HCI utilizes a combination of real-time, surface, and operational data to produce instant predictions with high accuracy.This allows for the early identification and mitigation of abnormalities, leading to reduced drilling costs and operational time.In addition, the HCI model addresses the limitations of existing drilling operation models by providing instant predictions based on a combination of real-time, surface, and operational data.The automated flowchart shown in Figure 11 demonstrates the effectiveness of the HCI model in enhancing hole-cleaning performance and overall drilling efficiency.This innovative approach has the potential to significantly improve drilling operations, resulting in reduced costs and increased resource extraction.By leveraging the HCI model, drilling abnormalities can be identified and mitigated at an early stage, leading to reduced drilling costs and minimized operational time.As a result, the HCI model significantly enhances drilling performance efficiency.The HCI model has become an increasingly important index for hole cleaning in the oil and gas industry due to its ability to support consistent rig-site data capture and reporting across all operations, implement consistent data-quality methods and procedures, and support multiple units of measure.Additionally, the HCI enables operations engineers to remotely oversee drilling, provides accurate historical operations and performance data to well planners for statistical risk analysis, facilitates informed decision making, and enables live monitoring of drilling operation processes.
The HCI model also allows for the verification of best practices in drilling, drives continuous improvement across teams and basins, enforces procedural compliance, and elevates operational excellence.Furthermore, the HCI model ensures that data are always decision-ready, benchmarks drilling team performance, recognizes areas of improvement, and sets goals for footage per day, connections, and tripping.With analytics to minimize slide The HCI model has become an increasingly important index for hole cleaning in the oil and gas industry due to its ability to support consistent rig-site data capture and reporting across all operations, implement consistent data-quality methods and procedures, and support multiple units of measure.Additionally, the HCI enables operations engineers to remotely oversee drilling, provides accurate historical operations and performance data to well planners for statistical risk analysis, facilitates informed decision making, and enables live monitoring of drilling operation processes.
The HCI model also allows for the verification of best practices in drilling, drives continuous improvement across teams and basins, enforces procedural compliance, and elevates operational excellence.Furthermore, the HCI model ensures that data are always decision-ready, benchmarks drilling team performance, recognizes areas of improvement, and sets goals for footage per day, connections, and tripping.With analytics to minimize slide percentage, optimize drilling parameters, and mine offset wells for the bestperforming BHAs, the HCI model contributes to safer, better, and faster drilling of wells.Additionally, it enables automated alerts and on-screen index indicators to avoid costly hazards, streamlines decision making, and accelerates ROP, while reducing drilling costs by leveraging next-generation directional guidance and rotary automation.
Despite its advantages, the HCI model also has limitations that must be taken into consideration.These include rig pump limitations.Q refers to the maximum flow rate that can be provided by the rig pumps.The top drive is another critical component that may place limitations on RPM.The design of the drill string and BHA can also impact the effectiveness of the HCI model, as can the performance of mud solid control equipment and mud system capacity.Finally, the quality and accuracy of sensor data acquisition can also affect the effectiveness of the HCI model, as any errors or inaccuracies in the data can lead to incorrect conclusions and decisions.Furthermore, the HCI model is based on certain assumptions, which include no total lost circulation incidents, no well control incidents, and no wellbore instability.These assumptions are critical to the accurate and effective use of HCI in the oil and gas industry and must be considered when applying the model to operational decision making.

Conclusions
In this study, a hole-cleaning index (HCI) was developed to optimize hole cleaning and positively impact well drilling ability by considering various parameters, such as drilling fluid properties, hydraulic velocities, and hole properties.Several points can be summarized as follows: the developed HCI model was rigorously tested and validated in the field in 3 wells, and the results demonstrated a remarkable improvement in well drilling performance by up to 50%.This significant improvement highlights the advanced capabilities of the HCI model and its ability to accurately evaluate hole-cleaning performance and optimize drilling operations.

•
The limitations of the CCI were observed in all three wells, namely Well-C, Well-B, and Well-A, further emphasizing the unreliable nature of this model in evaluating holecleaning performance.In contrast, the HCI model proved to be highly accurate and reliable in all three wells.Moreover, accurate measurement and tracking of hydraulic velocities and the drilling fluid's rheological characteristics are crucial to achieving a more comprehensive and accurate evaluation of hole-cleaning performance, particularly in deviated and horizontal drilling.Furthermore, the HCI was applied in Well-C and showed a highly accurate result from its evaluation of the hole-cleaning condition.

•
The implementation of the new HCI model can also lead to cost savings by preventing incidents such as stuck pipe and reducing non-productive time, resulting in more efficient drilling operations.Therefore, the adoption of the new HCI model can have a significant impact on drilling operations, promoting safer, more efficient, and more cost-effective drilling practices.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.The data are not publicly available due to the internal law of Saudi Aramco "On Export Control".

Acknowledgments:
The College of Petroleum and Geosciences at King Fahd University of Petroleum and Minerals and the School of Earth Sciences and Engineering at Tomsk Polytechnic University are acknowledged for their support and permission to publish this work.

Conflicts of Interest:
The authors declare no conflict of interest.

Figure 1 .
Figure 1.The flowchart outlining the various topics discussed and the systematic order in which they are presented.

Figure 1 .
Figure 1.The flowchart outlining the various topics discussed and the systematic order in which they are presented.

Figure 2 .
Figure 2. The CCI effect on differential pressure (a) and ROP (b) based on [29].

Figure 2 .
Figure 2. The CCI effect on differential pressure (a) and ROP (b) based on [29].

Figure 3 .
Figure 3.The input and output for the novel HCI model as a real-time evaluation indicating the hole-cleaning condition.

Figure 3 .
Figure 3.The input and output for the novel HCI model as a real-time evaluation indicating the hole-cleaning condition.

Figure 4 .
Figure 4. Flowchart to estimate the novel HCI model in real time.

Figure 4 .
Figure 4. Flowchart to estimate the novel HCI model in real time.

Energies 2023 , 29 Figure 5 .
Figure 5.A schematic view of the wells and the sections used: (a) Well-A; (b) Well-B; (c) Well-C.

Figure 5 .
Figure 5.A schematic view of the wells and the sections used: (a) Well-A; (b) Well-B; (c) Well-C.

Figure 6 .
Figure 6.Changes in HCI and the drilling parameters for Well-A.

Figure 6 .
Figure 6.Changes in HCI and the drilling parameters for Well-A.

Figure 7 .
Figure 7. Changes in HCI and the drilling parameters for Well-A.

Figure 7 .
Figure 7. Changes in HCI and the drilling parameters for Well-A.

Figure 8 .
Figure 8. Changes in HCI and the drilling parameters for Well-B.

Figure 9 .
Figure 9. Changes in HCI and the drilling parameters for Well-B.

Figure 8 .
Figure 8. Changes in HCI and the drilling parameters for Well-B.

Figure 8 .
Figure 8. Changes in HCI and the drilling parameters for Well-B.

Figure 9 .
Figure 9. Changes in HCI and the drilling parameters for Well-B.

Figure 9 .
Figure 9. Changes in HCI and the drilling parameters for Well-B.

Energies 2023 , 29 Figure 10 .
Figure 10.Changes in HCI and the drilling parameters for Well-C.

Figure 10 .
Figure 10.Changes in HCI and the drilling parameters for Well-C.

Figure 11 .
Figure 11.Field data were employed in an automated manner to analyze hole cleaning with the novel HCI model to increase drilling performance efficiency.

Figure 11 .
Figure 11.Field data were employed in an automated manner to analyze hole cleaning with the novel HCI model to increase drilling performance efficiency.

Table 1 .
Major findings in the field of hole-cleaning chemistry.
Rheology By increasing mud density, hole-cleaning efficiency can be increased [66] Sargani et al.Rheology CCI showed a high value at a 60/40 oil-water ratio [7] Alsaba et al.Rheology MgO showed the highest improvement in hole cleaning, while TiO 2 resulted in the lowest improvement [67]

Table 2 .
Major findings in the field of engineering.
FactorsDrill-string rotation in a deviated hole with an appropriate flow rate can remove the bed of cuttings, and an optimal hole cleaning can be achieved

Table 3 .
Formation and drilling cutting properties for Well-A, Well-B, and Well-C.

Table 3 .
Formation and drilling cutting properties for Well-A, Well-B, and Well-C.

Table 4 .
The drilling fluid characteristics for Well-A, Well-B, and Well-C.

Table 5 .
Well-A measured and calculated parameters.

Table 6 .
Well-B measured and calculated parameters.

Table 7 .
Well-C measured and calculated parameters.

Table 8 .
Bottom-hole assembly (BHA) used to drill the 12.25 and 8.5 deviated sections.

Bottom Hole Assembly (BHA) for 8.5
Results and Analysis 4.2.1.The Application of the Novel HCI Model in Well-A and Well-B The Application of the Novel HCI Model in Well-A and Well-B

Table 9 .
Impact of employing HCI on well performance.The Application of the Novel HCI Model in Well-C in the Case of a Stuck Pipe

Table 10 .
Impact of employing HCI on Well-C performance in the case of a stuck pipe.

Table 10 .
Impact of employing HCI on Well-C performance in the case of a stuck pipe.