This study explores three distinct approaches to ROP modeling: deterministic, data-driven, and hybrid models. Deterministic or physics-based models rely on a fixed equation derived from drilling physical principles and have been the traditional workhorse of the industry. Newer, and more powerful data-driven models utilize machine learning and predictive analytics to enhance ROP prediction and optimization. However, the improved predictive accuracy achieved with statistical techniques comes at the expense of model interpretability. In order to overcome this disadvantage, a novel hybrid modeling technique is introduced.

A novel way to formulate hybrid models is discussed by presenting two broad strategies: ensembles of a single deterministic model (hybrid-One) and ensembles of several deterministic models (hybrid-N). They provide a means to encode the physics of drilling formulated in deterministic models into machine learning algorithms. Hybrid models also enable inference on ROP models which provide valuable insight.

Both classes of hybrid models predict ROP with a greater accuracy than physics-based models alone; purely data-driven models perform marginally better in most cases. On the other hand, hybrid models offer higher interpretability, as they are built from deterministic models. Inference using hybrid models has been discussed with a case study for Mission Canyon Limestone.

Hence, hybrid models are employed for ROP prediction and optimization by computing ideal drilling operating parameters - weight-on-bit, RPM, and flowrate - for each rock formation in the vertical section of a Bakken shale horizontal well. The study demonstrates the use of hybrid models for higher accuracy (than deterministic models) and higher interpretability (than machine learning models) - providing an optimal tradeoff.

1. Introduction

Rate of penetration (ROP) has been a focal point in drilling optimization for decades: the rate at which a well is drilled is a key indicator of drilling efficiency. Higher ROP implies faster drilling which in turn implies better rig performance and higher rig productivity. Given this inherent interest in ROP modeling, deterministic models have been developed over the past 50 years for ROP prediction based on laboratory experiments (Bingham, 1964; Bourgoyne Jr & Young Jr, 1974; Hareland & Rampersad, 1994; Motahhari, Hareland, & James, 2010). The performance of these models has been routinely questioned (Soares, Daigle, & Gray, 2016) since their applicability on new datasets is not guaranteed. Advances in computational power and machine learning over the past few years has seen the birth of many new data-driven ROP prediction models - models based purely on data statistics (C. Hegde, Daigle, Millwater, & Gray, 2017; C. Hegde & Gray, 2017). These models utilize machine learning algorithms for ROP prediction and have been shown to generalize well for different formations.

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