A Benchmark of Regression Modeling Methods to Predict Drilling Operation Parameters in Oil Wells in Colombia
Authors: Caicedo Torres Pedro M. , Roa Prada Sebastián , Mantilla Hernández Hernán D. , Saavedra Trujillo Néstor F. 
Published: January 2025

Abstract
The rate of penetration is an important factor for the optimization of the drilling operation. Precise approximation of the rate of penetration allows for the management of consumption costs, providing better planning of future wells since the optimization of the rate of penetration allows the target depth to be reached at a lower cost, in addition to meeting operational and environmental requirements. Excessive values of rate of penetration can cause problems such as pipe clogging, poor hole cleaning, and bit tooth wear, which counteract the benefits of fast drilling, therefore achieving an optimal rate of penetration value is essential. The variables that affect rate of penetration can be divided into two subgroups of controllable and uncontrolled variables. Controllable variables can be modified during the drilling operation, while uncontrollable variables cannot be altered simply for economic and environmental reasons. Over the past few decades, researchers have come up with several mathematical relationships to model the correlation between rate of penetration and different drilling variables. Some important models of rate of penetration were introduced by authors such as Galle and Woods, Bingham, and Bourgoyne and Young, in 1963, 1965 and 1974, respectively. Experimental models depend on several constants, which change from field to field. These constants depend on the properties of the formation, such as pressure and rock type, which must be determined from the field data. In addition, in some traditional models, the effects of parameters such as the weight on the drill bit and the rotational speed of the drill bit on the ROP are assumed to be linear, and poor hole cleaning at very high drilling speeds is not taken into account. Despite some advantages of traditional rate of penetration models, these limitations increase calculation error and wasted time. Therefore, researchers have considered machine learning methods as a suitable alternative for the estimation of the rate of penetration. In this study, records of time-based drilling parameters were used, corresponding to the different sensors that measure the drilling parameters, were used to develop rate of penetration estimation models. The methodology includes two main steps: (i) Apply statistical techniques with the use of data on drilling parameters and drilling performance from databases provided by the oil industry. (ii) Compare the factors involved in the process of processing data obtained in the databases provided by the oil industry that allow the validation or estimation of the rate of penetration prediction. The machine learning techniques used include linear regression, polynomial regression, decision trees, and support vector regression. At the state petroleum company ECOPETROL, information from the different sensors is first collected via data communication protocols and sent to a master unit to be processed into relevant dimensions (i.e., to create operational variables). To record information accurately, the sensors are calibrated at regular intervals. The results indicated that a degree 3 polynomial regression achieved the highest performance compared to other developed models. The results of this study can serve as a practical guide for the management and planning of future well drilling.