BHA modeling is another key component of well planning. A good well plan provides rigsite personnel with the predicted capabilities and tendencies of each planned BHA. BHA modeling should identify the response of each BHA to variations in operating parameters, such as weight-on-bit (WOB), hole angle, overgauge or undergauge hole, stabilizer wear, and formation tendencies. Modeling should also identify the directional response to BHA
design parameters, such as stabilizer diameter, drill collar length, or motor bend angle.
BHA modeling can also be used for calculating bending moments and stresses. In some applications, bending stress caused by hole curvature may be high enough to cause additional problems of fatigue or overload. Side forces on bits and stabilizers can also be calculated. These values are useful for motor component design work and as inputs into torque/drag and casing-wear programs.
Various types of directional prediction models exist, but all are based on the principle that directional control is accomplished when forces are applied to the bit that will cause it to drill in the desired direction. Two kinds of models are commonly used: equilibrium (constant hole curvature) models and drill-ahead models.
Equilibrium models are typically static beam models that solve for the hole curvature in which all bending moments and forces on the beams and BHA components are in equilibrium. A typical 2D model (Williamson and Lubinski, 1986) applies known loads (including weight-on-bit, buoyancy, and the weight of the BHA itself) and derived loads (bit side-loads resulting from formation anisotropy) to the BHA elements. Effects of rotation or dynamics are not considered. A single, empirically derived, bit-formation interaction factor is normally used. The premise of the model is that while both the bit and formation may have anisotropic properties, only the net effect can be measured. These models have proved to be reasonably accurate for a wide range of BHAs and formations.
Drill-ahead models (Larson and Azar, 1992) create a constantly changing wellbore path, the instantaneous direction of which is based on the combination of force vectors on the bit and anisotropy factors. Anisotropic cutting properties may be assigned to the bit, meaning that its ability to drill sideways in response to a given force is not the same as its ability to drill forward in response to the same force. Formation anisotropy properties may also be assigned, meaning that the formation is more easily drilled in one direction than another. Formation anisotropy properties are oriented with respect to the dip angle and direction of bedding planes. Three-dimensional forces resulting from rotation or reactive torque can also be applied in drill-ahead models. Such models are useful for analysis, but since the shape of the wellbore is generated in increments of inches rather than dozens of feet, these models are typically too computationally intensive for everyday well planning. Some drill-ahead models can be used to characterize the well post-mortem, thus optimizing future well plans.
Formation anisotropy is a variable that can significantly affect the directional characteristics of a BHA. The exact mechanism of formation anisotropy is not known. Lubinski (1953) theorized that formations have a higher drillability perpendicular to the bedding plane than parallel to it (Figure 2-11).
Figure 2-11 Formation drillability theory (after Lubinski, 1953)
This theory would seem to be supported by the science of rock mechanics, since it is known that the compressive strength of many rocks is anisotropic.
Rollins (1959) proposed that thinly laminated formations fracture perpendicular to the bedding plane, creating miniature whipstocks that force the bit updip. Murphey and Cheatham (1965) proposed the drill collar moment theory, suggesting that when a bit drills from a soft formation into a hard formation, the hard formation supports most of the bit load, causing a bending moment to be applied to the drill collar. The collar then would bow to the opposite side of the hole and point the bit updip.
Although the formation anisotropy mechanism may not be fully understood, the manner in which BHAs respond to formation anisotropy and dip can be observed. For well-planning purposes, detailed information from offset wells should be compiled. This information should consist of data from intervals in which consistent operating parameters have been used. Formation dip and direction may be obtained either from seismic information or by correlations of logs from several offset wells. BHA design, operating parameters, and hole curvature can be found in daily reports and well surveys. With these as input parameters, the BHA modeling program can solve for the remaining variable, which is the formation anisotropy factor. As field development progresses, factors should continually be evaluated, updated, and then applied to the planning of future wells. When BHAs do not exhibit the
predicted directional characteristics, parametric studies must be performed to isolate whether variation from plan resulted from formation anisotropy or some other effect, such as hole erosion or stabilizer wear. In nearly all cases, predictive BHA modeling requires disciplined integration of mechanical models with empirical field experience.
To capture the full value of BHA modeling, it must be used for more than simply specifying the BHA configuration that is sent out to the rigsite. BHA modeling should be used to make rig personnel aware of BHA responses to design and operating parameters. Knowing the response of BHAs to these parameters will enable the directional driller to vary BHA configuration or operating parameters to control directional tendencies, as well as to have BHAs available to respond to contingencies. Finally, modeling should be used to establish operating guidelines. In particular, the maximum dogleg in which each BHA can be rotated should be identified.
Hydraulics
Although annulus hydraulic pressure-loss calculations for directional wells are similar to calculations in vertical wells, the mechanism of cuttings transport is different. The physical model itself differs in that the drillstring can be assumed to be offset to the low side of the hole for almost the entire length of the well. Drillstring eccentricity affects velocity profiles along the cross section of the annulus; a low-velocity zone occurs in the vicinity of the least annular clearance. Cuttings transport is also significantly affected by hole angle because the gravitational velocity component acts radially on solids instead of axially. Both drilled cuttings and weighting solids are affected. The low-velocity zone and gravitational component are both factors that contribute to the buildup of cuttings on the low side of the hole (Thomas et al., 1982; Slavomir and Azar, 1986). For these reasons, directional wells require higher-than-normal circulation rates to facilitate cuttings removal.
Flow rates increased by 50%, as compared to vertical wells, are not uncommon, depending on hole angle and the cuttings-carrying capacity of the mud. Drillstring rotation is also critical to cuttings removal. Pipe rotation mechanically agitates the cuttings, lifting them up off bottom into the high-velocity flowstream (Lockett et al., 1993).
Throughout most of the well, the drillstring is lying on one side of the wellbore; thus, differential sticking is of greater concern than in vertical wells. Stuck pipe is generally the most common form of trouble in directional wells, and prevention and remediation of stuck pipe should be addressed by training all rig personnel in proper operating practices and optimum drilling-fluid properties. During drilling, the presence of cuttings beds must be monitored by the tracking of changes in circulating pressure and torque and drag; remedial action must be taken when predetermined levels are reached.
Equivalent circulating density (ECD) is also of greater concern in directional wells. ECD is defined as the sum of hydrostatic pressure resulting from the column of mud (and cuttings) in the annulus, plus the pressure drop in the annulus during circulating. The higher flow rates required in directional wells result in a high circulating-pressure drop in the annulus, and the angle of the
wellbore with respect to in-situ formation stress will generally result in a formation fracture at a lower ECD than in a vertical hole. Both of these factors narrow the range of safe drilling-fluid weight. In fact, as illustrated in Figure 2-12, it is possible for the pore pressure and fracture gradient to be such that some high-angle wells cannot be safely drilled (Guild et al., 1994).
Figure 2-12 Safe drilling-fluid weight range decreases as hole angle increases The relationship between mud weight, ECD, fracture gradient, and hole angle is a key screening criterion when evaluating the feasibility of a directional well and a key factor in planning casing design and hole intervals.
Large-diameter drillpipe is commonly used in directional wells. A good starting point is to specify one size larger than would be used in vertical wells. This practice provides two benefits relative to hydraulics: (1) the larger inside diameter (ID) greatly reduces the pressure drop through the bore, allowing higher flow rates to be used without an increase in surface pressure, and (2) the larger outside diameter (OD) increases annular velocity at a given flow rate, which improves hole cleaning. An additional benefit is the larger pipe's higher torsional capacity, which, as seen in the next section, can be necessary in high-angle wells.
The ideal drilling fluid for directional wells should exhibit good lubricity and cuttings-carrying capacity, minimum solids and ECD, and maximum formation inhibition. Since some of these properties may be mutually exclusive, iterative analysis with the appropriate models may be necessary for determining which of the many parameters (hole cleaning, formation stability, torque/drag, etc.) must be given priority and which can be successfully de-emphasized. Some drilling fluids are engineered specifically
for directional wells, and drilling-fluid companies should be consulted for specific recommendations regarding flow rates and optimum rheology.