## 1 Introduction  
The oil and gas industry is still one of the biggest economy drivers in the world [1]. The discovery, exploration, and exploitation of hydrocarbons (HC) from pre-salt carbonate hard rocks are key steps forward in this sector [2]. The pre-salt region in Brazil is recognized as the biggest set of recently discovered giant oil fields in the world [3]. However, more than ten years after its discovery, operations in the pre-salt carbonates continue to present challenges in terms of drilling, production, and also in relation to the reservoir characterization [4; 5]. Pre-salt carbonate reservoirs are highly complex and heterogeneous [2; 6; 7], a feature justified by the nature of the original deposition system and the subsequent diagOptimizing the drilling processes and reducing the costs of production are extremely important to maximize profitability in the oil and gas industry [8]. Due to the ongoing considerable demand for hydrocarbons on a global scale, the oil and gas industry has always tried to find novel solutions, especially for drilling operations, to diminish the operational costs [9; 10; 11]. Drilling operations are very expensive, challenging, and involve risks and different problems, especially with deep drilling and activities through hard formations [12; 13; 14; 15]. Due to these facts, the drilling process has gained notable technological improvements in recent years [16]. For example, current bottom hole assemblies have several sensors, which allow for the monitoring, steering, and optimization of the drilling process by measuring the geological and directional information of the borehole while drilling [17]. Industries within the sector are motivated to implement technologies that focus on cost and operational optimization [18; 19] and solve the challenges still found in petroleum exploration [20]. The rate of penetration (ROP) is one of the main parameters affecting the process of oil and gas well drilling optimization and the total drilling costs [1; 21; 22; 23; 24]. The ROP can be defined as the speed at which a drill bit breaks through a formation, deepening (advancing) the borehole [25], or as the volume of rock removed per unit area per unit time [22]. An ROP prediction can help in planning the drilling process and reducing the drilling costs [14; 26]. Finding an accurate method for ROP prediction has been one of the objectives of the oil and gas industry since the 1950s [27]. Due to the complex relationship between the parameters affecting the ROP, an accurate prediction of the ROP is very difficult to obtain [22; 28]. There are many drilling variables that affect the ROP, such as the weight-on-bit (WOB), drill string rotation speed (RPM), torque-on-bit (TOB), standpipe pressure (SPP), flow rate (FLOW), as well as the depth and lithology [27; 29; 30]. Increasing the ROP has been the main target of drilling in the O-G industry [31]. Excessive increases in the ROP can cause problems such as stuck pipes, poor hole cleaning, and drill bit tooth wear [26] in addition to drilling vibrations and fast drill bit warming [32; 33]. Therefore, there is an ideal (or optimized) value for the ROP for each situation and scenario, where decreases in the operation time and drilling costs are more likely to be achieved [34]. The mechanical specific energy (MSE) and ROP are two key factors for evaluating the efficiency of a drilling process [35]. The combination of both factors allows for the optimization of the drilling process [20]. The MSE has been utilized as a tool for evaluating the performance of the drilling process, where the maximum efficiency can be reached at the point where the MSE has the lowest value [36]. The MSE has been widely used to quantify the efficiency of the drilling process [37]. The concept of MSE was first introduced by [PERSON] in 1965 [38]. The MSE is defined as the energy required to remove a unit volume of rock [35; 36; 37; 39; 23]. The MSE has also been applied to formation lithology prediction [14; 39].