This paper reports applications of the D3 single cutter model developed by Dagrain (2001) [1,2] at University of Minnesota (UMN), based on the original phenomenological cutting model developed by Detournay and Defourny in 1992 [3].

This paper comes to present the continuity at the FPMs, of the researches performed at UMN. In the present paper, the D3 model has been used to model two different field cases studied in the past at the FPMs, in order to confirm the validity of the D3 model for simulating rock cutting with multi-cutters tools.

The model has also been applied to estimate the best parameters to use to optimize the cutting efficiency for both particular field cases. Finally some basic rules are given to design tools (drill bits or cutting chain) to minimize the specific energy and to maximize the rate of penetration. The model can also be used to estimate the power needed in rock cutting and drilling.


Since the introduction of the PDC in the petroleum industry in the late 70's, many researches have been conducted to understand the mechanical processes involved in rock cutting. Different models have been developed mainly motivated by the need to improve the design and the performances of the cutting and drilling processes.

In 2001, Dagrain [1] developed a new three-dimensional model for rectangular cutters that takes into account side effects occurring on the cutter extremities: the D3 model.

The D3 model

Based on the work previously done by Detournay et al (1992–1999) [3], Dagrain [1,2] analyzed cutting tests performed with different rectangular cutters, and developed a new rock-cutting model which takes into account the effect of the geometry of the cutters.

As described in [1,2] the total force F acting on a rectangular cutter can be decomposed into two groups of force components (Fig.1): forces related to cutting processes Fc and force related to frictional contact Ff.

  • Equation 1

The cutting forceFc is related to the cutting process. This force can be further decomposed in:

  1. A pure cutting forceFcv that acts on the cutting face of the cutter, and is proportional to the depth of cut.

  2. A geometrical cutting force Fcg that acts on the surfaces created by the cutting process, and is proportional to the square of the depth of cut.

The frictional force Ff acts at the interface between the rock and the cutter wear flat, and is related to the frictional contact on this interface. This force is proportional to the wear flat length ? and the width of the cutter w.

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