Drilling rate models have been used extensively to increase drilling efficiency by introducing the optimum operational and bit design parameters for known formation types. Several authors have attempted to develop drilling rate models through investigating the effect of the associated parameters for rollercone bits. Among them, the two-term model developed by Warren in 1981 produces accurate results in the presence of a sufficient hydraulic level at the bit as well as with no bit wear effects. It was found that the hydraulic energy at the bottom of the hole can significantly influence the rate of penetration by removing the generated cuttings. In a real drilling operation, the generated cuttings might not be properly removed due to insufficient hole cleaning underneath the bit. Consequently, some portion of the bit’s energy will be spent on re-grinding of the cuttings which reduces the drilling rate. This paper presents the integration of a simple normalized hydraulics model in the two-term rollercone bit ROP model and verifying it through utilizing laboratory data. The modified model can be applied to estimate correct rate of penetration values considering available hydraulic level at the bit. It can also help determine the required hydraulic energy for a given set of operational parameters and a known formation type.


The applied weight on the bit (WOB) causes each single tooth to penetrate into the rock until the resistant force becomes equal to the force on the tooth. The volume of the rock that is fractured due to tooth penetration depends upon the geometry, rock properties and depth of tooth penetration. During the rock fracturing phenomenon, each single tooth continues to penetrate until the shear stress that is generated due to weight on the bit is equalized by the rock shear strength.

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