## 3 Development of a Novel Model Cutting Transport Ratio  
The cutting transport ratio (CTR) of the cuttings created by this study serves as the foundation for the innovative real-time indication of the progress of hole cleaning, which was developed by [PERSON] in 1974 and was used to assess how well the drilling fluid removes cuttings from the wellbore and was determined as the fluid transport velocity divided by the average mud annular velocity in a lab experiment [37]. The design of his experiment involved investigating various controlled variables. During his observations, it was discovered that some variables were more significant than others. Specifically, it was found that the average velocity and the rheological properties of the mud were the top two factors that affected the transport ratio, although the size of the simulated chips and the density of the mud also played important roles. Typically, the speed at which the cuttings move upwards differs from the velocity of the mud flowing in the annular space. This disparity indicates a tendency, particularly in turbulent flow, for the cuttings to slide back down the hole [37]. The researcher established a connection between the two speeds, which can be expressed as [37]:  
\[\mathrm{V_{C}}=V_{a}-V_{s} \tag{1}\]  
where the symbol \(\mathrm{V_{C}}\) refers to the upward velocity of the cuttings, while \(V_{a}\) (AV) represents the average velocity of the mud flow. On the other hand, \(V_{s}\) denotes the downward velocity at which the cuttings slip. To calculate the cutting transport ratio (CTR), both sides were divided by \(V_{a}\). \[\mathrm{CTR}=1-\frac{V_{s}}{V_{a}} \tag{2}\]  
Moreover, [PERSON] defined the transport percentage as achieving complete hole cleaning when the cuttings and mud reached the surface at equal speed. If there was any  
Figure 3: The use of iterative steady-state modelling with real-time parameters as inputs while drilling in real-time. delay in the amount of cuttings that reached the surface or if they arrived later than the mud, the transport percentage would be less than 100%. It is important to note that a CTR of 75% or higher is considered sufficient [37]. Additionally, having an excessively high CTR (above what is required for complete hole cleaning) can be detrimental. It results in reducing the equivalent circulating density (ECD), increasing penetration rates, and, overall, optimizing the efficiency of energy. However, the CTR was only tested in a vertical interval and investigated by the experiment design. Therefore, there is a need to develop a novel model that can be used for real-time evaluations and applied in various profiles, such as deviated and horizontal wells [37; 38]. Thus, the novel model transport ratio (CTR\({}_{\text{m}}\)) was developed starting from the effective mud weight (\(MW_{eff}\)) calculated using Equation (3) [22; 39]. \[MW_{eff}=MW\cdot CCA+MW \tag{3}\]  
where \(MW\) is the static drilling fluid density (lb/cf) and \(CCA\) is the cuttings concentration in an annulus as defined by Equation (4) [22; 39]. \[CCA=\frac{ROP\cdot OH^{2}}{1471\cdot GPM\cdot TR} \tag{4}\]  
where \(ROP\) is the rate of penetration (ft/hr), \(OH\) is the hole size diameter (inch), 1471 is the conversion factor, \(GPM\) is the pump flow rate (gal/min), and \(TR\) is the transport ratio, which can be replaced with 0.55 according to [39]. Furthermore, the ECD is determined based on the \(MW_{eff}\) in real time (ppg). To be precise, Equation (5) can be utilized to calculate the \(ECD\)[22; 39]. \[ECD=MW+\left(\left(\frac{0.085}{OH-OD_{pipe}}\right)\cdot\left(YP+\frac{PVVann }{300\left(OH-OD_{pipe}\right)}\right)\right)\cdot 7.481 \tag{5}\]  
where \(OD\) is the outer diameter of the drill pipe (inch), \(PV\) is the plastic viscosity (CP), \(YP\) is the yield point (cP), and \(V_{ann}\) is the annular velocity of the drilling fluid (ft/min) as defined by Equation (6).