This paper presents a mathematical method for the computation of torsional resonance frequencies in a drillstring. The torsional resonance frequencies in a drillstring are readily calculated from the nominal drillstring dimensions. A high degree of accuracy is achieved when a correction factor to the torsional propagation velocity in drillpipe due to the offsets at the drillpipe joints is incorporated into the calculations. The theory and computer program were tested against data recorded in a 1000m deep, nearly vertical well. Torsional spectra were recorded with the bit off bottom at 450m, 550m, and 1000m and while drilling. Well defined torsional resonances were observed for frequencies up to 40 Hz. The calculated resonance frequencies are in very good agreement with all experimental data.

The paper describes Statoils experiences in drilling extended reach (ERD) wells, to primarily serve remote parts of widespread reservoirs and experiences in drilling horizontal and complicated wells, specially designed for optimal drainage of complex reservoirs. Several world records in extended reach drilling, conducted from the Statfjord "C" platform are summarized. The latest ERD well drilled has a horizontal reach of 7290 m. Included are also the latest plans of implementing these techniques in developing new fields. A brief summary is given on the achievements within the industry regarding other special well types, such as dual lateral, snaky, multiple arm, etc. Furthermore the paper describes technical challenges of drilling complex wells and how planning is done to cope with these challenges. Some limitations to the drilling are highlighted and solutions to drilling problems related to torque, drag, buckling, hole cleaning and surveying are given. Cost-Benefit considerations regarding ERD, horizontal and complex wells are discussed. Reducing number of platforms and/or leave out subsea templates due to ERD wells are considerable cost reducing factors. Reducing the total number of wells from a platform due to horizontal and/or complex well profiles is another major cost reducing factor. The oilfields developed in the 1970-80s had relatively significant limitations to the drainage area from each platform. The Statfjord and Gullfaks fields were initially planned to be developed with maximum 60 degree inclination wells, resulting in a maximum horizontal reach of 3000 m at the Statfjord field and 2100 m at the Gullfaks field reservoir depths. To drain the fields in an optimum way based on the technology available, called for three GBS platforms on each field. Developments and improvements in drilling technology, engineering research and field experiences have, since then, pushed the limits for available well profiles and horizontal reach distances dramatically. The purpose of drilling extended reach, horizontal and complex design wells is to drain the field in the most cost effective way. The use of these new techniques can make old nonprofitable fields profitable, prolong an existing field's economic life and make new questionable field discoveries worth developing. Today's techniques enable the reservoir, dip angles, faults and structural geology to be design factors for optimal placement of the wellpath. P. 505^

Summary This paper addresses the various aspects of torque and drag problems encountered in drilling extended-reach wells. It discusses how to use torque and drag calculations and measurements to plan long-reach well profiles, to execute drilling operations that minimize torque and drag effects, to monitor hole cleaning, and to plan jarring operations. Introduction In extended-reach drilling, a limitation on the horizontal displacement occurs because of frictional forces between the drillstring and the borehole wall. Drag is measured as the difference between the static weight of the drillstring and the tripping weight. Similarly, a difference between the torque applied at the rig floor and the torque available at the bit occurs owing to friction. Torque and drag problems are often associated with each other and maybe profound in extended-reach and horizontal wells. As Sheppard et al. stated, a variety of sources of drag and torque loss exist: differential sticking, key seating, hole instabilities, poor hole cleaning, and the general frictional interaction associated with side forces along the drillstring. Therefore, drag and torque measurements may be used to monitor operations to optimize performance. In extended-reach drilling at Statoil, torque and drag problems have initiated use of more sophisticated well profile and use of torque as an indicator of hole-cleaning problems. Understanding of torque and drag problems has been applied to the well planning process. As a result, problems are often not found in wells with horizontal displacements up to 5000 m. Another interesting implementation of drag knowledge in operational procedures is described in a paper on the influence of drag on hydraulic jar efficiency. In this paper, we discuss torque and drag problems in extended-reach wells, how knowledge of torque and drag is used in operational procedures, and to what extent the planning phase can help avoid operational problems. Although always referring to extended reach, the same principles are valid for horizontal,'S'-shaped, and designer wells. Well Profiles Optimizing well profiles to minimize torque and drag problems has been discussed in many publications (e.g., Refs. 1, 4, and 8 through 10). Sheppard et al. thoroughly discussed the catenary curve principle for well drilling. Alfsen et al. discussed a modified catenary principle; Banks et al. included the concept of tortuousity and reached the important conclusion that making a smooth well path is key for successfully drilling extremely long-reach wells. To reduce friction in any well, a good mud program design is important. Friction factors down to 0.16 simulations have proved to give a best fit with measurements. The torque and drag program used in the work described here has been used extensively at Statoil together with measurements of actual data. Confidence in the calculations has been achieved, and they have been used to monitor and improve operational practice. Minimizing dogleg severity and even making changes in dogleg severity have been implemented in our procedures. Several papers have been published on long-reach well drilling from the Statfjord C platform. After a 6000-m horizontal displacement was reached in Well 33/09-C03, it was recognized that the well profile would need to be optimized to reach the planned depth for Well C02-7200-m horizontal displacement. The catenary curve, proposed as a possible solution to the torque and drag problems, is the solution to the following problem. A cable with weight per length, W, has a horizontal force at left Point A, FH, and a tangential force at right Point P(x, y), FT. The horizontal component of the force at Point P is in the opposite direction of the force at Point A. The solution to the above problem is given in the x-y plane as where An interesting feature of the catenary curve is the zero contact force between the drillstring and the borehole wall. Consequently, the catenary curve could theoretically give zero friction between the borehole wall and the drillstring. Several difficulties exist in using this approach for drilling a well. First, the effective force at the bottom of the well results in drillstring compression as opposed to the tension given in the theoretical curve. Furthermore, the catenary curve will lead to a much longer well path than more traditional well profiles. Thus, a slight modification of the catenary curve must be made. An important feature of the catenary curve was kept in the well plans for Wells 33/09-C24 and 33/09-C02 in the Statfjord field: the very slow build rate in the shallow part of the well with a slowly increasing build rate as well depth increases. The sailing angle of 80 to 84 is therefore much higher than the traditional 60 . Figs. 1 and 2 describe the well-path planning process with the resulting torque calculations. The catenary curve is compared with traditional constant-build curves with 1.5 /30- and 2.5 /30-m build rates. A much lower sailing angle is achieved with the traditional curve design. As a result, as Fig. 2 shows, the measured depth (MD) of the actual well path is longer than with traditional shapes. The friction along the drillstring is lower, however, and a higher torque at the bit is a welcome result. The success of reducing wall contact and thereby the total friction was reported in Ref. 4 and is shown in the simulations of comparison of wall contact force in Fig. 3. Well 33/09-C03 has a standard profile; Well 33/09-C02has a modified catenary profile. Note the difference in scale in the two parts of Fig. 3. The very high normal force in Well 33/09-C03 compared with the33/09-C02 profile will give similar marked higher friction and thus higher torque loss. The well profile used in Statfjord Wells C24 and C2 may lead to enhanced problems with formation stability and differential sticking owing to the high sailing angle. However, wherever these problems can be handled, the modified catenary curve will give a lower friction than traditional well profiles. Monitoring Hole Cleaning The confidence in torque and drag simulation programs may give unexpected benefits. When long-reach wells are drilled, the torque and drag simulation curves may be used to monitor hole cleaning. Deviations from properly modeled torque and drag simulations may indicate hole-cleaning problems. Fig. 4 shows torque simulations in Well 33/09-C02 and actual measured torque in the 12 1/4-in. section. The three smooth curves are the acceptable, planned, and actual torque simulations, respectively. The marked change in simulation curves at about 2600 m was caused by a bit change. An aggressive bit must be simulated with a higher torque on bit than a less aggressive bit. P. 800^

Summary. A mechanism that couples longitudinal and torsional drillstring vibrations at the bit was studied. Torsional vibrations are associated with dynamic variations of the rotational bit speed. When a roller bit runs over a multilobed pattern, these speed variations have been shown to affect the input of longitudinal vibrations. The theory for this coupling mechanism is verified experimentally by high-rate data of near-bit accelerations and torque recorded in a 1000-m [3,280-ft] -deep well. Introduction Several publications have dealt with vibrations in drillstrings. As discussed in the literature, vibrations influence the drilling situation and can result in a lower rate of penetration or may cause fatigue failures. On the other hand, a thorough understanding of the vibrations can enable predictions of downhole conditions on the basis of top measurements. The theory presented here is an attempt to explain some phenomena seen in experiments performed at Ullrigg, a full-scale offshore-type research drilling rig. These experiments comprise both real drilling and "drilling" with an exciter system, which induces a longitudinal, sinusoidal vibration with a constant amplitude at the bit. The experimental setup with data transmission system is thoroughly described in Ref. 1. Frequency spectra on drilling data gathered at Ullrigg often contain small side lobes near the most dominant frequency components. The sources for these side lobes are also discussed here. Theory It is assumed here that the axial motion of the bit can be described by an elevation function, s(s theta), where s theta is the angular displacement of the bit. Assuming also that the shape and orientation of the downhole patterns do not change or at least change very slowly with time implies that ,............................(1) where n is an integer. The axial force through the bit, or weight on bit (WOB), can formally be written as ,............................(2) where F denotes the mean force and F denotes the dynamic or fluctuating force. The torque on bit (TOB) may also be separated into a mean torque, tau, and a dynamic part that is represented by ,............................(3) Because of this dynamic torque, the rotation rate of the bit will fluctuate about a mean value omega: ,............................(4) where omega = omega(tau) may be regarded as a dynamic torsional response to the input torque tau. Now, turning to the special case where the downhole patterns are pure sinusoidal three-lobed patterns with amplitude s1, the axial bit motion can be written as .............................(5) Note that Eq. 5 is correct only with a three-cone roller bit and if the roller radius is much smaller than the pattern curvature radius. This requirement is reasonably well satisfied for the exciter system, where s1 = 2 mm [0.08 in.]. In the first linear approximation, it is assumed that the dynamic variations of force and bit speed are negligibly small--i.e., .............................................(6) and .............................................(7) The input for axial and torsional vibrations is then decoupled and may be written as .......................................(8) and ........................................(9) The negative sign appears because the torque input--i.e., the torque transfer from the formation to the bit--is minus the TOB. Hence, the dynamic torque input is positive when the bit is running downward on a negative slope: ds/ds theta less than 0. Eq. 8 has been used in several earlier publications on drillstring vibrations. Experiments have revealed, however, that the assumptions for this first linear approximation are poorly satisfiedi.e., the dynamic force, F, and the dynamic speed, omega, are not negligibly small. Hence the displacement, ,...................................(10) and the torsional excitation moment, ,............................(11) SPEDE

Extensional vibrations in drillstrings have been studied with both linear elastic theory and experiments in a 1000m deep vertical well. A hardwire MWD-tool suitable for rotary drilling has been used to transmit near bit accelerations, weight on bit and torque at a rate of 556 measurements per second. New understanding of the vibration damping process has been achieved, and the damping effects are shown to have critical influence on the vibrations. By including frequency dependent damping the theoretical results agree better with experimental results than it does with constant damping.