## 8 Conclusions  
Hundreds of works are devoted to modeling the processes that take place during well drilling. However, they usually consider local effects, for example, wear of the bit cutting parts. Or, vice versa, the process is simulated in the entire well, for example, the drilling fluid flow, but with significant simplifications--the movement of the drill string is not considered. This happens because even the modeling of each process itself is a very complex and time-consuming task with many nuances. However, all the described processes strongly influence each other. Table 1 shows some of the works that consider simultaneously the modeling of two or more physical processes in a well. However, in industrial applications, it is required to consider all the processes that occur during drilling at once, wherein a simulation should not take much computational time, since it is usually used for multivariate calculations and optimization. To fulfill both these requirements is highly challenging. The complex model of the well drilling process considered in Section 7 can be called multiphysical. This class includes models in which phenomena of different natures are simultaneously considered: hydrodynamics, dynamics of deformable structures, heat, and mass transfer, etc. This circumstance makes it very difficult to develop such models for the following two reasons:  
* Expertise in each of the areas under consideration is needed for solving these problems. It is often difficult to find such expertise in one scientific group. * The computation time of the numerical solution of each of the considered subproblems should be comparable. Otherwise, the simulation does not make practical sense, since in practice it is always required to carry out multiple calculations corresponding to the various scenarios under consideration. * However, there is one important circumstance that facilitates the numerical solution of the problem under consideration. The mutual influence of the considered processes on each other is not so strong that special iterative procedures (e.g., [PERSON]'s method [137]) are required to ensure the convergence of the numerical process at each time step. It is enough to provide the data exchange between separate solvers at each time step. * The suggested multiphysical model is a first step on a way to model the complex physical processes in the well and their impact on each other. This topic needs further research to include more specific physical aspects in the model, for example, the wear of the bit cutting tools while leaving the model applicable for engineering calculations that are not very time-consuming to perform. Note also that in the present study the main emphasis is on modeling the processes that take place in the well itself during drilling. At the same time, if necessary, it is also possible to use advanced coupled models of processes occurring in the reservoir, surface equipment, etc. Studies devoted to these approaches are beyond the scope of this review. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Article** & **Drill String** & **Drilling Fluid** & **Drill Bit** & **Fluid Exchange with** & **Heat Exchange** \\  & **Dynamics** & **Circulation** & **Interaction with Rock** & **Soil (Mass Transfer)** & **with Soil** \\ \hline [PERSON] et al. [132], 2021 & – & + & – & + & + \\ [PERSON] et al. [133], 2009 & + & + & – & – & – \\ [PERSON] et al. [134], 2019 & – & + & – & – & + \\ [PERSON] et al. [135], 2017 & – & + & – & + & + \\ [PERSON] et al. [136], 2022 & – & + & – & + & + \\ [PERSON] et al. [86], 2021 & + & – & + & – & – \\ [PERSON] et al. [114], 2017 & + & + & + & + & + \\ [PERSON] et al. [115], 2020 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Complex modeling of well drilling processes. **Author Contributions:** Conceptualization, N.S. and S.L. ; methodology, S.L. ; software, M.C. ; investigation, S.L. and M.C. ; resources, N.S. ; writing--original draft preparation, M.C. ; writing--review and editing, N.S. and S.L. ; supervision, N.S.