Torque and drag may be critical factors in determining whether the desired wellpath can actually be drilled and cased. Torque/drag models consider well trajectory, drillstring configuration, doglegs, friction factors, and casing depth to predict torque and drag in the well. Torque-and-drag modeling is used for various purposes, including:
• evaluating and optimizing wellpaths to minimize torque and drag
• fine-tuning wellpaths to minimize local effects, such as excessive normal loads
• providing normal force loads for inputs into other programs, such as casing wear models
• identifying depth or reach capabilities or limitations, both for drilling and running casing/tubing
• matching the strength of drillstring components to the loads (axial, torsional, or lateral) in the wellbore
• identifying the hoisting and torque requirements of the drilling rig
The most commonly used torque/drag models are based on the "soft-string"
model developed by Johancsik et al. (1983). The drillstring is modeled as a string or cable that is capable of carrying axial loads but not bending moments (Section 2-2.5). Friction is the product of normal forces and a coefficient of friction. The normal force at each calculation node has two components: (1) the buoyed weight of the pipe in drilling fluid, and (2) the lateral reaction force resulting from drillstring tension through curved sections of the wellbore. A simplified drillstring element, shown in Figure 2-7, has net axial forces and normal forces acting upon it.
Figure 2-7 Drillstring element for "softstring" torque-and-drag model (from Johancsik et al., 1983)
The equations for these forces are
(2-6)
(2-7)
(2-8) and
(2-9)
where FN is the net normal force, T is the axial tension at the lower end of the element, W is the buoyed weight of drillstring element, FF is the sliding friction force acting on the element, R is the characteristic radius of element, M is the torsion at the lower end of element, is the inclination angle at lower end of element, is the azimuth angle at lower end of element, f is the
coefficient of friction, and (T,M, , ) is the change in those values over the length of the element.
In Eq. 2-7, the product fFn can be positive or negative, depending on whether the drillstring is advancing into the hole or being pulled out of the hole.
If accurate friction factors are derived from existing field data, soft-string models yield reasonably accurate results for most sizes of drillpipe and hole curvatures. However, since the soft-string model does not consider the stiffness of the drillstring, its accuracy will degrade as drillpipe diameter increases and as hole curvature increases. Both of these increases result in high normal forces and increased torque/drag. Finite-element models that incorporate drillstring properties are available for such applications, and they may be necessary for modeling casing. Neither type of model can accommodate localized hole and drillstring/BHA mechanical interactions (for example, a stabilizer hanging up on a ledge or a dogleg). Such a model would require much more information about actual hole geometry than what is available. However, empirically derived macrolevel friction factors are adequate for predictive analysis, since these factors are calculated from wells that include similar localized geometry.
Friction factors should be derived from analogous case histories. The properties of the drilling fluid used in the baseline wells and the planned well should be similar. However, the ranges in Table 2-1 can be used as starting points if prior experience is unavailable (Johancsik et al., 1983; Rasmussen et al., 1991).
Table 2-1 Ranges of Friction Factors in the Casing and the Formation (from Johancsik et al., 1983 and Rasmussen et al., 1991)
Drilling Fluid f in casing f in formation Oil-based 0.16 to 0.20 0.17 to 0.25 Water-based 0.25 to 0.35 0.25 to 0.40 Brine 0.30 to 0.40 0.30 to 0.40
Field experience has shown that axial drillstring drag is reduced when the drillstring is rotated. Torque-and-drag models account for this mathematically by the use of velocity vectors (Dellinger et al., 1980) (Figure 2-8). The resultant velocity VR of a contact point on the drillstring is the vector sum of two components, circumferential velocity VC (caused by rotation) and axial velocity VA (affected by drilling rate or tripping speed).
Figure 2-8 Effect of drillstring rotation on axial friction (from Dellinger et al., 1980) The direction of the resultant frictional force is assumed to act in the direction opposite to that of resultant velocity VR ; therefore, its vector components will be in proportion to those of resultant velocity. The magnitude of resultant frictional force is simply the product of normal force F and friction coefficient f, and it does not vary with velocity. Since the magnitude of the vector sum of these components is a fixed quantity, as the circumferential component increases, the axial component must decrease.
Logically, as drillstring rotation speed increases, it increases the circumferential component, which decreases axial friction.
Well planning should include torque/drag modeling with worst-case friction factors to ensure that the drillstring can be advanced, rotated, slid if oriented drilling is necessary, and pulled out of the hole. Similar modeling should be used to ensure that friction will not prevent the casing from being run, and that the casing can be pulled if necessary. The torque and tension/compression at any point in the drillstring must be compared to the torsional, tension, and buckling capabilities of the drillstring and tool joints.
Table 2-2 contains properties for Range 2 drillpipe.
Table 2-2 Properties of Range 2 drillpipe (after API Publication RP7-G)
based on uniform wear, ft-lb Tensile data based on uniform wear load at minimum yield strength, lb.
in. lb/ft E 95 105 135 E 95 105 135
The results from torque/drag analysis are usually expressed graphically with torque and/or drillstring tension on one axis and measured depth on the other (Figure 2-9). The subject well is a build/hold/drop profile similar to that of Figure 2-1, with a 5000-ft tangent section at a 60° angle. A friction factor of 0.2 was used for cased holes and a factor of 0.3 was used for open holes.
Figure 2-9 Torque-and-drag analysis
The torque/drag analysis qualifies this well as drillable with the operating parameters used, and allows the selection of drillstring components with a reasonable safety margin as compared to loads. Axial load values never drop into the buckling region, even during sliding. Because of the relatively high hole angle, torque is nearly 20,000 ft-lb, dictating the use of 5-in., high-strength (S-135) drillpipe in the upper 6000 ft of the well. Maximum tension in the drillstring is about 340,000 lb, which leaves a reasonable safety margin below the yield strength of 487,000 lb. On the basis of torque/drag, this well is drillable with standard drillstring components and practices if the friction factors used in modeling are accurate and unusual hole problems do not occur.
During drilling, a log of predicted and actual torque and/or drag vs. depth should be maintained (Figure 2-10).
Figure 2-10 Log of actual vs. predicted drillstring torque
Such a log enables friction factors to be updated and verified; if actual friction factors are significantly different than planned, problems can be predicted and prevented instead of dealt with after the fact. The log will also show the effect of changing bit types or altering operational parameters.
Note the increase in overall torque when PDC bits are run rather than roller-cone rock bits. The log can also reveal deteriorating hole conditions, such as the buildup of cuttings and local hole features like doglegs. Remedial actions, whether preventive or after the damage occurs, could include (1) enhancing hole cleaning through higher flow rates, rotation, or modified drilling-fluid rheology, (2) making short trips to condition the hole, (3) reaming out ledges, key seats, or doglegs, (4) changing mud type, or (5) even altering the well profile or changing the casing or hole program.