## 2 Materials and Methods
### Workflow Used by Companies to Control Torsional Vibration and Stick-Slip
#### 2.7.2 Flowcharts and Workflows Used by the Companies  
Naming three different companies as #A, #B, and #C, Company #A, for instance, based on mitigating stick-slip real-time drilling parameter indications, mainly by decreasing WOB and increasing RPM. However, FLOW is not seen as a key parameter for stick-slip mitigation. Table 10 details the workflow and further information used by Company #A. Company #B uses a more comprehensive workflow compared to Company #A. Its action plan is shown by a flowchart, as shown in Figure 6. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Real-Time Indications**} & \multicolumn{2}{c}{**Real-Time Actions**} \\ \hline \(\bullet\) & Real-Time Indications; & \\ \(\bullet\) & Cyclical torque and RPM fluctuations & \(\bullet\) & Decrease WOB; \\  & on the rotary table; & \(\bullet\) & Increase RPM; \\  & Loss of tool face control, poor & \(\bullet\) & Amount depends on the size of the \\  & directional control; & & assembly. Guideline is \(\pm\)10\% of the \\  & Reduced or erratic rate of penetration; & & maximum specified for the bit. \\  & Interference with mud pulse telemetry & & maximum specified for the bit. \\  & signals—signal loss. & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Workflow Company #A. The flowchart begins with a condition stating that if vibration persists, one should decrease the WOB by 5 [%] and increase the RPM by 10 [%]. This adjustment can be repeated up to three times unless the RPM limit is exceeded. After three repetitions, there is an overall decrease of 16 [%] and an increase of 33 [%] for the WOB and RPM, respectively, compared to the original values. For iterative adjustments, Equation (5) represents the calculation of the overall total percentage of adjustment. \[\mathrm{M}=\mathrm{C}(1+\mathrm{i})^{t} \tag{5}\]  
where \"M\" is the final RPM or WOB value; \"C\" is the initial RPM or WOB value; \"i\" is the percentage increase; and \"\(t\)\" is the number of interactions. If vibration and/or stick-slip persist above a specific desired and possible value, the next step involves disengaging the effective drilling followed by picking off the bottom and circulating. After the drill-string gets stabilized, drilling should then be resumed with a 10 [%] increase in RPM and a 15 to 20 [%] decrease in WOB, though it is unclear whether this reduction is from the original value or the adjusted value from the initial changes. If the adjustments are cumulative, the total changes after the second stage would equate to a 33-39 [%] decrease in WOB and a 46 [%] increase in RPM compared to the original values. This is a considerable adjustment, and it is fair to mention that the operational limit of WOB and RPM could end up by being exceeded. If vibration persists after this second stage of adjustments, the drill bit is withdrawn again, and WOB is reduced by 25 [%] below the original value while RPM is increased by 15 [%] above the original value. If vibration does not continue after these steps, drilling can proceed. Company #C also uses a more comprehensive flowchart than Company #A. It is similar to Company #B but with less room for parameter adjustment than Company #B, specifically with RPM and WOB, as shown in Figure 7.  
Figure 6: Workflow and flowchart used by Company #B. The company #C flowchart begins with monitoring vibration and stick and slip status. For stick-slip conditions, operations are classified into two main states: (1) red state and (2) purple state. In the red state, Step 1 involves increasing RPM by 10 to 50 [rev/min] while maintaining or decreasing the WOB by 2 to 5 [klbf] (10 to 20 [kN] or 0.9 to 2.5 [tf]). Step 2 requires repeating Step 1, except when the WOB or RPM limits are reached, at which point the drill bit should be picked off the bottom and the wellbore cleaned (circulation) before restarting over again with lower WOB and higher RPM. The purple state follows a similar sequence but requires a decrease in WOB along with an increase in RPM. Step 2 of the purple state is identical to step 2 in the red state.