Drag-Bit Performance Modeling
- T.M. Warren (Amoco Production Co.) | A. Sinor (Amoco Production Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling Engineering
- Publication Date
- June 1989
- Document Type
- Journal Paper
- 119 - 127
- 1989. Society of Petroleum Engineers
- 1.6.9 Coring, Fishing, 1.5 Drill Bits, 1.5.1 Bit Design, 1.6 Drilling Operations, 5.3.4 Integration of geomechanics in models
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Models for the forces required to remove a fixed volume of rock with a single cutter have been applied to different polycrystalline-diamond-compact (PDC) bit designs. The integration of the forces for each cutter over the bit face gives the torque and weight on bit (WOB) required for a particular rate of penetration (ROP). This paper presents the results of comparing such a model to laboratory drilling tests for four radically different bit designs in four different rocks. The geometry of each cutter on the bit was determined by detailed measurement of the bit with a three-axis coordinate measuring machine. Drilling tests were conducted by "reaming" rock with an 8 1/2-in. [21.6-cm] bit that was previously drilled with a 6 1/4-in. [15.9-cm] bit. Only the peripheral cutters engaged the rock during reaming. Additional tests were conducted in which the WOB and torque were recorded during drilling of a pilot hole into the top of a flat rock and during drilling through two different bed boundaries with constant ROP. The model predictions compared well to the measured data for both the reaming and pilot-hole tests.
Analysis of the drilling mechanics of large-cutter (>1/4 in. [>0.64 cm] in diameter) PDC bits is much easier than that of roller-cone bits because of their simpler geometry. At the same time, variations in PDC bit designs result in a wider range of performance than observed with roller-cone bits. PDC bit performance is extremely sensitive to formation properties and operating conditions. There is a fine balance between bit durability and designs that ball up in shales. This paper concentrates on the mechanical design parameters for PDC bits. Bit-cleaning considerations are discussed in a companion paper.1
The PDC bit model described in this paper was developed to aid bit selection and evaluation. The model also serves as a baseline to identify and to quantify additional factors that affect bit performance by comparing model predictions with actual data, either from the laboratory or from field drilling.
PDC Bit Model
The simple kinematics of a large-cutter drag bit allows the position of each cutter in space to be easily tracked for a given rotational speed and ROP. The volume of rock removed by each cutter can be calculated for a given steady-state ROP because each cutter on the bit remains at a constant position relative to a coordinate system that moves with the bit body.
The PDC bit model is a combination of rigorous geometrical relationships used to describe the kinematics of a particular bit geometry and single-cutter force and wear models. The single-cutter models predict such items as cutter forces, temperatures, and wear. These predictions are for a single cutter and are independent of the cutter's position on the bit. Detailed cutter placement information is used to integrate these single-cutter models for a specific bit. The assumptions used in the overall model development, in the individual force and wear models, in the method used to generate the cutter location coordinates, and in other model information can be found in Ref. 2.
Input to the model comprises detailed cutter geometries, formation properties, ROP, and rotational speed. The model calculates the volume of rock removed by each cutter, total WOB, bit torque, bit imbalance force, and total wear-flat area.
Example Model Results
A generic bit design is used to demonstrate the results obtained with the model. The 8 1/2-in. [21.6-cm] bit is composed of seven 1 1/2-in. [3.8-cm] cutters arranged on three blades located 120° apart. Fig. 1 shows the bit profile and the angular location of the cutters on the bit.
Table 1 shows the predicted results for drilling with this bit in Berea sandstone at 50 ft/hr [15 m/h] with a rotary speed of 120 rev/min and the cross-sectional area of each cutter engaged in the rock, volumes of rock removed, resultant force angles, effective side- and backrakes, and cutter velocities. These quantities result directly from geometrical considerations and are not influenced by the empirical force models. The circumferential, axial, and normal forces are calculated for each cutter on the basis of the empirical force models.
Summary data are printed below the individual cutter data. The WOB is the sum of the axial cutter forces, and the bit torque is the sum of the circumferential forces times the cutter-moment arm. The magnitude and the direction (relative to the position of Cutter 1) of the imbalance force are also calculated and will be discussed later.
Laboratory Drilling Tests
Laboratory drilling tests were conducted with four 8 1/2-in. [21.6-cm] -diameter bits (Fig. 2) to provide model validation data and to develop the force functions used in the model. Tests were conducted in Catoosa shale, Indiana limestone, Berea sandstone, and Carthage marble. The conditions of these tests are discussed in more detail by Warren and Armagost.1
Figs. 3 and 4 show the laboratory data and model predictions for three different rocks drilled with Bits B and C. Rock strengths of 2.6, 1.2, and 0.7 were used for the Carthage marble, Berea sandstone, and Catoosa shale, respectively, for the model results presented in these and following figures. Unless otherwise noted, a bit factor (BF) of 1.0 was used. The model for the large-cutter-bladed bit, Bit C, fit the data for all three rocks well. Examination of the bit after each test showed no balling on the cutters for any of the rocks when a flow rate of 450 gal/min [1.7 m3/min] was used.
Good predictions for the flat-faced bit were obtained in the sandstone and marble, but not in the shale. The bit was balled up after the test in shale (see Ref. 1). The balling caused the observed ROP to be considerably less than the model predicted. These data for Bits B and C indicate that the basic model performance is good as long as the cutters are cleaned.
Fig. 5 shows test data and the model predictions (BF=0.73) for drilling in shale at a range of rotary speeds from 60 to 180 rev/min with Bit D. The model fits these data very well, but in cases where poor cutter cleaning was suspected, it did not work as well for rotary speed response.
The bottomhole pattern was examined for most of the laboratory bit runs. The observed pattern was compared with the model predictions to help identify the amount of fracturing that occurs between the cuts made by individual cutters. Fig. 6 is a comparison between a bottomhole pattern predicted by the model and the pattern measured with a coordinate measuring machine. In general, the patterns show little evidence of fracturing but often show evidence of off-center rotation.
To provide a more rigorous test of the model, the 8 1/2-in. [21.6-cm] bit, Bit A, was used to ream a previously drilled 6 1/4-in. [15.9-cm] hole. In this way, the forces on the inner cutters were eliminated, while the outer cutters were loaded under the same conditions as if they were drilling. The ROP, torque, and model predictions (BF=1.22) for both drilling and reaming are shown in Fig. 7. The bit removed only 41% as much rock volume while reaming as while drilling. The model predictions of both torque and WOB were slightly low for the reaming case. This probably results from a higher relative imbalance force during reaming than during drilling.
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