This paper presents a complete model and an experimental validation of the drilling response of roller-cone bits. Firstly, a new phenomenological model for roller-cone bits is obtained, i.e. a set of relations between the weight-on-bit W, the torque-on-bit T, the rate of penetration V, and the angular velocity Ω. Afterwards, a series of laboratory tests at atmospheric pressure reported by Karasawa et al. (2002) are used to validate the model as well as to estimate the intrinsic specific energy ε, which is obtained via E-S diagram. Initially developed for PDC bits, the E−S diagram has been shown to be a robust tool to assess drilling response. The results here reported suggest that the intrinsic specific energy ε, which can be obtained independently of the degree of bit wear, and q are correlated at atmospheric pressure for both milled and insert roller-cone bits.
One of the biggest challenges of the oil and gas wells drilling has been the fact that it is impossible to know precisely what is happening downhole. The rock strength, drilling efficiency and the bit condition are some examples of valuable information that should be assessed during the drilling process. In this regard, there is a constant effort in the drilling industry to develop better and more accurate methods to evaluate drilling conditions as well as to obtain in-situ rock properties. Although PDC bits are more aggressive and represent the new generation, roller-cone bits are still commonly used in hard and abrasive formations, which are often found in deep reservoirs. Methods for simulating drilling action of roller-cone bits have been explored for more than 40 years. Several authors have proposed bitrock interaction laws for roller-cone bits, which are based on three distinct concepts: force balance, energy balance and empirical correlation [1, 2, 3, 4, 5]. Based on the force balance concept, Burgess & Lesso (1985)  developed an interpretation technique called Mechanical Efficiency Log (MEL) to obtain the tooth wears, drilling efficiency and the in-situ shear strength of the rock. Although this technique has been validated by laboratory testing data and for some field data, this approach is only intended for soft sedimentary formations and for roller-cone bits with milledteeth. Initially, developed by Warren (1987) , the penetration rate model, which is based on the empirical concept, was explored by several authors [8, 9] to identify in-situ rock strength. Because of the presence of empirical terms that are difficult to determine, Pessier & Fear (1992)  proposed a new approach to estimate the rock strength. This method uses the concept of energy balance to obtain the minimum specific energy E sm, which is linked to the rock strength [4, 10]. Along the same line, a new technique to identify E sm, using the drill-off test, was proposed by Hoberock & Bratcher (1996) . Recently, Karasawa et al. (2002) [12,13] developed a generalized model for both milled and inserttooth bits to estimate the rock strength as well as the tooth wear.