STUDY ON THE STRESS AND STRAIN OF THE DRILL BITS USING THE FINITE ELEMENT METHOD

Stela Dinescu1, Ildikó Kertész (Brînaș)2, Marioara Vesa (Benea)3 1PhD, Lecturer, 2, 3 PhDStudent

University of Petroșani, Department of Mechanical, Industrial and Transportation Engineering

1. ABSTRACT

The well is a mining construction realized in the earth’s crust by a complex drilling operation which consists in rock removal and the transportation of detritus (debris) away from the well to the surface. Because the drill bit is the main component of the drilling equipment, in the paper we intended to perform a study of the stress and strain occurring in it, using the Finite Element Method (FEM). The tool used in this respect is the SOLODWORKS software package which, in addition to the achievement of an object design, enables the determination of the stress, strain and safety factor in a given loading condition.

2. FOREWORD

Well drilling is a technology used from ancient times and is employed in many fields [1], such as:

- geological exploration;- oi land gas extraction;- underground water extraction;- mining shaft sinking;- geotechnical research.The well is an excavation having a cylindrical shape. The wells can be vertical

or inclined ones. The well drilling is a complex operation which consists in rock removal and the

transportation of detritus (debris) away from the well to the surface. The drilling is performed with the equipment called drilling rig.

The drilling rigs can be: - heavy drilling rigs, with high actuating power, the drilling depth reaching

thousands of meters and the well diameter ranges from hundreds ofmillimetres to 7000 mm;

- small depth drilling rigs (lightweight drilling rigs) with reduced actuatingpower, and drilling depth less than 1000 – 2000 m, with small welldiameters.

The purpose of the drilling operation determines the kind of drill bit used, which differs in the manner in which the rock is removed on the bottom of the well, as follows:

- for the exploration wells, which aim to obtain samples of rocks, the rockcutting is performed in an annular cross section, using a bit named coringdrill bit (Figure 1), the drilling is called coring drilling and the rock sample

MultiScience - XXXII. microCAD International Multidisciplinary Scientific ConferenceUniversity of Miskolc, 5-6 September, 2018. ISBN 978-963-358-162-9

DOI: 10.26649/musci.2018.029

obtained is named core specimen, which is a cylindrical piece of rock, which is useful for the knowledge of the geological structure of the location’s subsurface [9].

- for the wells drilled with the purpose of extraction (oil, gas, water) or mining infrastructure (transport or ventilation shafts) the rock removal on the bottom of the well is made on full circular cross section, and the corresponding tool is the conventional drill bit (Figure 2). In both cases the drill bit is actuated through the drill string by the rotating table which is located at the top of the well and is a component of the drilling rig. The detritus is transported away using the so called drilling fluid or mud [7].

Fig.1 Coring drill bit

Fig.2 Conventional drill bit (tri-cone type)

The most frequently used drilling method is the rotary one, with debris transport

by fluid circulation. The drilling process is a continuous one, the rock removal and the detritus transportation being performed simultaneously. (Figure 3).

Fig.3 The principle of drill bit’s operation (1 – thrust force, 2 – torque, 3 – fluid flow, 4 – detritus,

5 – drill string, 6 – drill bit, 7 – bottom of well)

3. STUDY OF THE STRESS AND STRAIN OF THE DRILL BIT USING FEM

For the purpose of our study we selected the drill bit presented in Figure 4. In the screenshot we can see the main elements which are the subject of the considered analysis, in which we consider the drill bit fixed.

Fig.4 Establishment of fixed elements (the case of drill bit with PDC cutters)

Then we considered the drill bit laden by two kinds of loads. The first one is the

thrust force which is transmitted from the drill string towards the annular surface on the top of the bit’s main body. (Figure 5). We imposed a value of 2500 N.

The second one is spread among the cutters and it is due to the cutting resistance of the rock and it was considered as a pressure of 500000 N/m2 (Figure 6)

Fig.5 Thrust force on bit’s body

Fig.6 Pressure acting on cutters

We used a standard discretisation with mesh dimension between 10 and 0.5

mm. On the obtained geometrical model, we imposed the loads and constraints and the FEM analysis has been performed. [6], [4]. We considered three kinds of results presented in the following: strain (Figure 7), von Mises stress (Figure 8) and safety factor (Figure 9).

Fig.7 Strain map

Fig.8 von Mises map

Fig.9 Safety factor map

Considering the symmetry of the bit’s body, and of the corresponding loads, we selected the nodal region presented in Figure 10. For this region we plotted the variation of the von Mises stress relative to the corresponding nodes (Figure 11). The maximal value is 1.25x107 N/m2. By comparing this value with the yield value of the stress for the bit’s body material (alloy steel) which is 62.04x107 N/m2, [2] we observe that for considered loads it is no question of failure.

Fig. 10 Proposed region for highlighting the maximal stress

Fig.11 Plot of von Mises stress variation corresponding to the nodes of selected

region

In Figure 12 the safety factor variation for the same region is presented. The

minimal value of 49.5 is in the central peak of the bottom part of the bit’s body.

Fig.12 Variation of the safety factor

4. CONCLUSIONS

The Finite Element Method (FEM) based analysis is a tool of numerical

analysis used for solving problems for varied fields of engineering. As a design tool, the method allows the shift from the design process based on repetitive cycles design > prototype > testing towards a simplified process which uses virtual prototypes, the materialised prototype being necessary only for the validation of the final design.

We presented a FEM based study related to the stress and strain of a drill bit under the loading corresponding to those which occurs during the drilling process. We considered that the drill bit is loaded by a compression force (thrust) and pressure distributed among the buttons (cutters).

The maximal value of the von Mises stress is 1.25 x107 N/m2, which is inferior to the yield stress of the material, which is 62.04 x107 N/m2. This value of the stress occurs in the central peak of the bottom part of the bit’s body. The maximal strain (deformation) is de 3x10-3 mm and it occurs in the regions of PDC buttons insertion areas in the lateral extremity of the bit’s body.

Regarding the safety factor, it has a minimal value in the same region where the stress is maximal.

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