**2.1 Corrected MSE**

Most of the recent MSE applications for completion optimization use surface drilling data which do not represent the MSE at the drill bit. The challenge posed by the use of surface drilling data consists of finding a way to eliminate costly and risky downhole equipment to measure the downhole MSE while ensuring accurate results. The solution for this challenge is to correct the surface drilling data by removing the frictional losses along the borehole. The Corrected Mechanical Specific Energy (CMSE), which is calculated in real time and uses surface drilling data, wellbore geometry, and drilling equipment parameters to estimate the friction losses along the drill string, was shown [4–6] to be a viable solution. This new technology uses advanced drilling and wellbore mechanics to estimate the multiple factors that create the frictional losses in real time and has been validated in multiple wells and basins.

Commonly available surface drilling data such as torque, weight on bit, rate of penetration and RPM are used as inputs to the model, along with the mud motor differential pressure and flow rates. Mud motor specifications, such as the maximum limits of differential pressure and flow rates, are also important inputs to normalize the computed Mechanical Specific Energy. When a Rotary Steerable Tool (RST) is used to steer the well, the Bottom Hole Assembly (BHA) information is a necessary input along with the wellbore survey to accurately perform the torque and drag analysis and to estimate the friction pressure losses along the wellbore. The friction pressure losses are then extracted from the surface MSE to compute the Corrected MSE.

The Drilling Efficiency (DE), which is the ratio of the energy required over energy spent in breaking a unit volume of the rock, is computed based on the CMSE and the Confined Compressive Strength (CCS) as shown below in Eq. (3)

$$DE = \frac{\text{CCS}}{\text{CMSE}} \tag{3}$$

 As shown in Eq. (4) CCS accounts for the typically increasing Unconfined Compressive Strength (UCS) rock strength with depth as well as the effects of the confining stresses (∆*<sup>p</sup>*) and angle of internal friction factor (θ) applied on the rock. By correlating the MSE with CCS through the DE and by fitting a trendline on the computed DE data-set, the pore pressure can be estimated by accounting for the variations of DE data-set from the DE trendline. The fit of the DE trendline should be calibrated with pore pressure measurements from DFIT tests and the DE trendline should be updated accordingly.

$$\text{CCS} = \text{UCS} + \Delta \mathbf{p} \left( \frac{\mathbf{1} + \sin \theta}{\mathbf{1} - \sin \theta} \right) \tag{4}$$

Once these friction losses are correctly estimated, they can be used to correct the MSE measured from surface drilling data which can be compared to measured downhole MSE. The principle of the predictive model is that torque and drag forces in a directional wellbore are primarily caused by sliding friction. Sliding friction force is calculated by multiplying the sidewall contact force with a friction coefficient. A lumped-parameter model provides the basis for the prediction of torque and drag. Both torque and drag are caused entirely by sliding friction forces that result from contact of the drill string with the wellbore. The frictional forces are subtracted from the surface MSE to accurately estimate the corrected MSE.
