A Novel Automated Model for Evaluation of the Efficiency of Hole Cleaning Conditions during Drilling Operations  
[PERSON]  
1 Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals,  
Dhahramen 31261, Saudi Arabia; [EMAIL_ADDRESS]  
[PERSON]  
2 School of Earth Sciences & Engineering, Tomsk Polytechnic University, Lenin Avenue, Tomsk 634050, Russia; [EMAIL_ADDRESS]  
[PERSON]  
1 Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals,  
Dhahramen 31261, Saudi Arabia; [EMAIL_ADDRESS]  
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clean-up monitoring difficult [7; 8]. The factors affecting wellbore clean-up are divided into three groups. The first group includes the fluid flow rate and the fluid parameters such as the viscosity and density. Furthermore, these parameters are interdependent and can influence the behavior of a moving fluid. For example, the viscosity of a fluid refers to its resistance to flow and can influence its flow rate through a pipe or annulus. Assuming all other parameters remain constant, a fluid with high viscosity will flow more slowly than a fluid with low viscosity. Similarly, a fluid's density can impact its flow rate. A fluid with a higher density will require greater pumping force to move through a pipe or annulus, resulting in a delayed flow rate [9; 10]. The second group consists of the cuttings' parameters, which include the cutting density, size, and shape as well as the cuttings concentration in the annulus. The third group is operator factors and consists of the characteristics of the drill string with fluid swirl devices and its eccentric position in the wellbore, as well as the inclination of the wellbore itself. More importantly, optimizing the impact of these parameters can help sustain the carrying capacity of drilling fluids, leading to the improved design of wellbores [2; 11]. Moreover, in order to understand the factors that determine the effectiveness of hole cleaning, several studies have been carried out over the years. For instance, [PERSON] et al. proved that the rotation of the drill pipe is one of the most important parameters for cuttings' removal especially in laminar flow and transition flow [12]. Moreover, over the past few decades, numerous researchers have explored cuttings' transport and developed various mechanistic and semi-mechanistic models to explain flow characteristics [13; 14; 15]. [PERSON] et al. examined particle settling velocity, flow rate, fluid viscosity, and internal pipe rotation's influences on transport mechanisms within a 15 foot-long, 3.5 inch inner diameter vertical glass tube laboratory setup [16]. [PERSON] et al. developed an early mechanistic model for cuttings' transport [17]. [PERSON] et al. used numerical simulations to analyze 3D incompressible non-Newtonian drilling mud flow in a vertical well drilling model under steady flow conditions, focusing on laminar flow with a Reynolds number of 1150 based on the hydraulic diameter of the annular space [18]. [PERSON] et al. performed experiments with a multiphase flow loop, varying air and water flow rates and introducing cuttings into the annulus in different quantities. Data were collected under steady-state conditions, including liquid, gas, and cuttings' injection rates, frictional pressure drop, local pressures, and high-speed digital images to identify the solid, liquid, and gas distribution within the wellbore [19]. [PERSON] et al.