ONE-DIMENSIONAL CALCULATIONS FOR AXIAL PULLBACK FORCE DISTRIBUTIONS IN PIPES DURING DIRECTIONAL DRILLING INSTALLATIONS

Transcription

1 ONE-DIMENSIONAL CALCULATIONS FOR AXIAL PULLBACK FORCE DISTRIBUTIONS IN PIPES DURING DIRECTIONAL DRILLING INSTALLATIONS A. G. Chehab and I. D. Moore GeoEngineering Centre at Queen s RMC, Queen s University, Kingston, Ontario, Canada ABSTRACT This aer describes one dimensional modeling to estimate tensile stresses within ies during ullback. This is achieved by dividing the ie into elements, simulating the movement of the ulling head, and calculating gravity, friction, and drag forces alied on each element based on its location along the borehole. Estimates of axial force history along the ie throughout the insertion rocess are obtained by integrating the elemental forces over the ie length. The rocedure is used to study axial force distributions and cyclic resonse of ies during ulling oerations where the time history of movement of the ulling head is re-determined. RÉSUMÉ Cet article décrit modeler unidimensionnel our estimer des efforts de tension dans des ies endant le retrait. Ceci est réalisé en divisant la ie en éléments, en simulant le mouvement de la tête de traction, et en calculant la esanteur, le frottement, et les forces de résistance à l'avancement aliquées sur chaque élément basé sur son endroit le long du forage. Des évaluations de la force et de l'histoire axiales d'effort le long de la ie dans tout le rocédé d'insertion sont obtenues en intégrant les forces élémentaires au-dessus de la longueur de ie. Le rocédé est emloyé our étudier des distributions axiales de force et la réonse cyclique des ies endant des extractions où l'histoire de tems du mouvement de la tête de traction est déterminée à artir de l'installation de traction utilisée. Le rendement modelant est comaré aux données fournies ar des essais sur le terrain. 1. INTRODUCTION Horizontal directional drilling (HDD) is a technique for installing ies or utility lines below ground using a surface-monitored drilling rig that launches and laces a drill string at a shallow angle to the surface and has tracking and steering caabilities (ASTM F ). The oeration involves three main stages: Pilot Bore excavation: A ilot hole is first advanced using a drill rig oerating from the ground surface. A secially designed ti enables steering of the drill head until it is brought back to the surface at the desired location. To conform to the designed ath and avoid hitting other infrastructure, the drill head is usually monitored using a remote sensor. Back-reaming: The drill bit is relaced with a back-reamer that is ulled back to enlarge the borehole size u to the desired diameter. Multile reaming asses may be required deending on the soil tye and the required degree of borehole enlargement. Pull back: The new ie is attached to the drill string and ulled back into the borehole. The ulling rocess is carried out in stes or cycles. In each cycle, the ie head is ulled by the rig with a fairly constant seed for a secific distance that deends on the rig caacity and the length of the ulling rods. The ulling then stos and time is allowed for removal of each drill rod in turn. During the ullback oeration the ie is subjected to loading from the drill string as well as shear stresses between the outer surface of the ie and the surrounding environment (fluidic drag from the drilling mud, static or kinetic friction from the surrounding soil or materials at the ground surface). These loads roduce comlex axial stress distributions that vary both along the ie and with time. After insertion, the ie is released from the rig and left to recover for a short time eriod. Finally the ie is attached to existing infrastructure (such as manholes or hydrants) and laced into service. Even after installation, tensile stresses continue to vary along the ie and with time, esecially for olymer ies since viscoelastic strain recovery is revented once the ie is attached to its suly and termination oints. The axial stresses during insertion and those that occur over the service life of the new ie may influence the erformance of the ie selected. 1148

2 2. INSTALLATION LOADS 2.1 Load comonents During installation, the ie interacts with the borehole and the drilling mud. If a straight segment is considered (Figure 1), the main alied forces are due to gravity, friction between the ie and the ground surface or the borehole wall, and viscous drag from the drilling mud. 2.2 Gravity Forces The gravity force deends on the ie weight in case of dry installations and the net buoyant force, i.e. resultant of the ie weight and the buoyancy force resulting from submerging the ie in the drilling fluid (mud) in case of wet installations. For inclined segments, the net gravity or buoyancy force comonent along the ie axis contributes to the total tensile force alied to the ie, while the comonent normal to the ie axis contributes to the normal force roducing friction between the segment and the wall of the borehole. In dry installations, the ie segment will rest on the invert of the borehole. In wet installations however, buoyancy forces are usually higher than self weight and the segment is ushed u against the crown of the borehole. T Frictional forces Forces also develo due to friction between the ie and the borehole wall or the ground surface (for segments not yet in the borehole). While gravity forces may act with or against the ie movement direction, frictional forces always act against the ie movement. 2.4 Drag forces Normal Friction Net Buoyancy Viscous Drag Figure 1. Installation forces on a straight ie segment Fluid drag is the shear force alied on the outer surface of the ie being installed as a result of the movement of the viscous drilling mud relative to the ie being installed. The drilling fluid is usually umed continuously during the drilling, reaming and ullback rocesses. Even if no fluid is umed during the ullback rocess, any advance of the ie through the mud confined in the T 1 borehole will cause the dislaced mud to flow out of bore, i.e. ast the ie and/or the drilling string. That relative movement will still cause some drag forces on the ie. Fluid drag deends mainly on the roerties of the slurry (drilling fluid containing soil cuttings), the annulus oening geometry and configuration (ie and borehole size and eccentricity), and the rate of mud flow relative to ie (uming rate and rate of ie advance). 2.5 Curves Force Comonents at Curves Pulling a ie segment through a curve not only causes bending stresses, but also magnifies the tensile force required to ull the segment. This is due to the additional normal force resulting when the ie is forced to conform to the curve (due to bending stiffness) as well as the associated friction (the castan effect, exlained below) Castan Effect When a flexible ie is ulled around a curve, extra normal force is created as a result of the change in the direction of the ulling force alied on the curved surface being considered, and friction between that curved surface and the ie Pie Bending/Stiffness Effect Bending stresses and additional normal forces develo in the ie segment when it is forced to conform to a horizontal or vertical curve. The tighter the radius of curvature, the higher the stresses and the normal forces that result. The additional normal forces lead to higher frictional forces and increased ulling forces. For large diameter steel ies, bending stresses and additional normal forces can be significant and should be considered. For olyethylene (PE) ie, the safe curve radii are usually dictated by the drilling rod caacity, since they are stiffer than PE ies and are subject to cyclic bending stresses as the curved drill string rotates. Research studies indicate that contributions from bending stiffness of PE ies to increases in ulling force are insignificant over well designed curves. For examle, Dareing and Ahlers (1991) analyzed the ullout force needed to remove drill strings from high curvature well bores, and concluded that the weighted cable or string model (that assumes zero flexural stiffness EI) rovides a reasonable aroximation of the ulling load, rovided there are no severe local curves. 3. EXISTING METHODS FOR LOAD CALCULATION 3.1 Introduction to ulling force equations This section reviews methods currently available for estimating tensile ull loads on ie installed using horizontal directional drilling (see Baumert and Allouche 22 for further discussion). 1149

3 3.2 Driscoie Method The Driscoie Method (Driscoie, 1993) is considered to be the simlest rocedure. The bore ath is broken into linear segments. The contribution of each segment to the total ull load is calculated using segment geometry (length L and angle θ). This method neglects the mud drag and load magnification at curves. 3.3 Drillath Method The Drillath Software (Drillath, 1996) is a three dimensional aroach discretizing the ie into segments that transmit axial forces only (i.e. strings). This neglects the mud drag and the ie stiffness effect, and relates the load magnification at curves to castan effect only. 3.4 PRCI Method The PRCI method (Huey et al, 1996) estimates the maximum ulling load for HDD installations. It assumes that the maximum load occurs toward the end of the ull, and accounts for both mud drag forces and the ie bending stiffness effect. 3.5 ASTM F Method The American Society for Testing and Materials rovides design equations for the estimation of ulling loads alied to the installed ie at the ie entry oint, the first bend, the second bend, and the ie exit oints. The ASTM equations are based on assumtions such as: The effect of the ie bending stiffness is neglected. The entry and exit oints have the same elevation (i.e. the ground surface is horizontal). The intermediate san (L2) is horizontal. 3.6 Polak and Lasheen Mechanical Model Polak and Lasheen (22) develoed a model to calculate the interaction between the ie and the borehole and the resulting ulling loads. The model accounts for ie bending stiffness effect and the mud drag. It assumes that all bends in the borehole are shar with zero radius of curvature, which makes bending of the ie urely dominated by the oversize ratio (ratio of the borehole diameter to the ie diameter) and angle of change of direction. The assumtion may lead to substantial overestimation of the ulling load magnification at bends, esecially for low oversize ratios. 3.7 Emirical Design Table of in-bore resistance Baumert et al. (24) roosed a set of tables or emirical design charts to rovide estimates of ulling loads in the form of load er unit ulling length. The tables or charts can be generated using a large database of monitored installations in different soil tyes, borehole rofiles, ie diameters and various construction qualities. This aroach rovides reliminary design values and assumes linear increase of ulling load with distance. All the revious aroaches treat the installation loads as monotonic (not cyclic), and they are not able to rovide information on the cyclic nature of tensile ulling loads, nor the otential effect of soil stiffness on the ie-soil interaction during installation. Furthermore, they do not rovide the attern of axial force along the ieline both during and after installation. 4. MODEL DEVELOPMENT 4.1 Model introduction The model develoed in this study is caable of calculating the tensile stress at every oint in the ie being installed at any secific time during the installation rocess. It considers gravity forces, friction forces (in bore and on the ground surface), mud drag forces, and accounts for the load magnification at curves due to the castan effect. The ie is divided into a number of elements. The location and orientation of each element is determined at the end of each time ste and different elemental loads are calculated accordingly. 4.2 Borehole Profile: The model considers the standard and most common borehole rofile that consists of three straight segments and three curves as shown in Figure 2 (though it could readily be extended to consider more comlex boring geometries). Lengths L 1, L 2, L 3 rovide horizontal ositions of the entry, intermediate and exit segments. Angles β 1, β 2 and β 3 define the inclination of the three segments. Values R 1 R 12 and R 23 are the radii of curvature of the entry and intermediate curves. In addition, β o reresents the average ground surface inclination at the ie entry oint. No horizontal curves are accounted for in the basic model. Pie Exit β 3 R 23 Figure 2. A tyical borehole rofile. 4.3 Pie Movement β 2 R 12 L 3 L 2 L 1 Pie Entry The movement of every segment of the ie is associated with the movement of the ulling head, which deends on several factors such as the rig size, ulling seed, length of each ulling rod, and time required to remove ulled rods. β 1 R 1 115

4 As reviously stated, the ulling stage is usually carried out in stes, Figure 3. In each ste, the ie head is ulled with a constant seed for a distance usually equal to the length of a single ulling rod. The ulling then stos for several seconds to remove the drill segment that was recovered. The movement of the head is reresented by a steed ram function: Pie soil interaction leads to shear at the external surface of the ie, mainly due to friction between the ie and the borehole wall (µ bore) or ground surface (µ surface). Adhesion may also contribute in some cases. The maximum shear force that can be mobilized er unit length is given by: Max. Shear = α.a cont + µ.n [3] PL NPC.PL +. ( t NPC (TP + TR) ) tc < TP Move(t) = TP (NPC + 1).PL TP < tc < TP + TR [1] where α is the adhesion, A cont is the contact area er unit length, and µ is the coefficient of friction between the ie and the borehole wall or ground surface. For a straight element, the normal force er unit length N is given by: Head Move NPC=1 PL τ TP TR Cycle NPC=3 π N = ( γmud.od γie(od ID )).cosβ 4 For a Newtonian fluid with viscosity µ, flowing in a concentric annulus, the drag shear stress τ and the mud drag force er unit length are given by: [4] Figure 3. Time history of ie head movement t d R bh R µ V τ = 2R + 4 dl R ln R R R ln R R ( ) ( ) bh bh [5] Now, PL is the length ulled er cycle, TP and TR are the ulling time and rest time in each cycle, t is the time measured from the beginning of the rocess, and τ is the time measured from the beginning of each cycle. 4.4 Alied Loads At any time, the location of each element of the ie can be determined knowing the location of the ulling head and the location of the element with resect to the ulling head. Loads alied on each element are calculated knowing its location and the roerties of ie, mud and soil. The gravity force P gravity er unit length is given by: Pdrag = 2πR. τ [6] where R bh and R are the radii of the borehole and ie resectively, and V is the ie movement velocity. The ressure gradient d/dl can be solved, if flow rate Q of the drilling mud in the borehole annulus is known: π d 4 4 (R R i ) Q = R Ri 8µ dl ln(r /R i) 2 2 R bh R 2 + πv R 2ln( Rbh R ) [7] π P = ( γ 2 γ 2 2 gravity mud.od ie(od ID )).sinβ 4 [2] For an eccentric annulus, a modification factor that is a function of eccentricity can be alied to the calculated ressure loss (Haciislamoglu and Langlinas, 199). where OD and ID are the external and internal diameters of the ie, γ is the secific weight, and β is the inclination angle of the element under consideration. The first term in the equation accounts for buoyancy, whereas the second term accounts for the ie weight. For dry installation where no mud is used, γ mud can be set equal to zero. 4.5 Forces at Curves: The change in direction of the ie is associated with additional normal force N curve that is equal to: N T.d β [8] curve 1151

5 where dβ is the change in direction along the element under consideration. To account for the curve effect, N curve is added to N in Equation 3. In addition, all elemental forces are divided by (cos(dβ/2)-µ.cos(dβ/2)). 4.6 Pie-Soil Interaction: The interaction between the ie and the soil (borehole or ground surface) is assumed to exhibit elastolastic behaviour as shown in Figure 4. The relative movement between the ie and the surrounding soil is accomanied by linear increase in the interaction shear. This increase continues until the full shear limit given by Equation 3 is mobilized. Further relative dislacement takes lace as sliage at a constant shear force. Switching the direction of the relative movement will decrease the shear force linearly with a sloe equal to K. The sloe K deends on several factors including the soil roerties (modulus and Poisson s ratio), soil-mud cake, borehole geometry, borehole deth, and bedrock deth. 5. VALIDATION, RESULTS AND DISCUSSIONS To evaluate the model, calculations are first comared to those from other methods. The model was used to comute the tensile forces along a steel ie during a horizontal directional drilling installation reorted by Baumert et al. (22). A 1275 m long crossing to a deth of 5 m of a large diameter (61 mm) steel ie was chosen (figure 6). The borehole rofile consists of three segments, a -1 o entry segment, horizontal intermediate segment and a +1 o exit segment. Two curves of 75 m radius rovide transition between the segments. 1 o 1275 m R =75 m 1 o Figure 6. Profile of the crossing analyzed. Max. Shear Shear stress K K Pie-soil relative movement Figure 4. Assumed ie-soil shear interaction mechanism 4.7 Load Integration: The contribution of loads on an element n is given by: Baumert et al. (22) used the Driscoie, Drillath, and PRCI methods to evaluate the ulling force along the rofile for three sets of arameters reresenting uer bound values, lower bound, and intermediate or average values. The uer and lower bound arameters are given in Table 1. Table 1. Characteristics of tested soils. µ surface µ bore γ mud (kn/m 3 ) Low arameter set High arameter set P + P + P Tn = cos d β µ.sindβ gravity shear drag The total tensile force is comuted by integrating the loads over all the elements starting with the element at the ie tail where tension is zero. i.e. n n i= 1 T = T T n i T n n T 2 2 T 1 Figure 5. Total load accumulation over ie length 1 [9] [9] Figures 7a and 7b show the calculations of Baumert et al. (22) for uer and lower bound arameters, as well as calculations from the new model resented here (assuming zero adhesion). The redictions of the ASTM formulae are also shown. Both adhesion and mud drag are not considered in the calculations. The redictions of the model develoed in this study agree well with those of the Drillath and PRCI methods. All the methods roduce load er unit length in linear segments. The differences are mainly at curves, where the Driscoie method always redicts lower ulling loads since it does not account for load magnification at curves. Though the PRCI method accounts for the ie stiffness effect, it roduced values very close to those of the Drillath method since the curves are well designed with high radius of curvature. At low levels of ulling load, the PRCI redicts slightly higher load magnification at curves. However, the difference decreases as ulling load 1152

6 increases since the castan effect becomes the dominant factor. At very high ulling load, the Drillath method redicts higher load magnification at curves. The lots in Figure 7 rovide general estimates of the ulling loads along the ie. It is imortant though to anticiate how the load changes during test times (while rods are being removed), and how that is affected by the stiffness of the ie and the surrounding soil. For that urose, another roblem is now examined. Pull Load (kn) Pull Load (kn) (a) (b) Length of Pie in Bore (m) Length of Pie in Bore (m) Figure 7. Pulling load versus ulled length: (a) Lower bound (b) Uer bound DRISCOPIPE DRILLPATH PRCI ASTM DRISCOPIPE DRILLPATH PRCI ASTM HDDPIPE HDDPIPE µ surface =.3 µ bore =.4 K = 1 MN/m er 1 m of borehole length Drilling mud: γ mud = 14 kn/m 3 Q = 25 L/s µ =.1 a.s Head movement: TP = 2 s TR = 15 s PL = 8.8 m The viscolastic constitutive model develoed for HDPE by Zhang and Moore (1997) is used to model the mechanical resonse of the ie during installation. Figure 8 shows the ulling stress history at the ie head during installation. Looking at the general trend, it can be noticed that the ulling stress increases as more ie is ulled into the borehole. The rate of increase in the stress is not constant and a different sloe in the stress history results when the ie reaches a new region (a curve or a linear segment). Towards the end of each cycle, a dro in stress during rest times can be observed Pulling Stress at Head (MPa) Time (s) Figure 8. Pulling stress history at the ie head. The change of ie stresses during the 2 th ulling cycle is analyzed to further investigate the cyclic loading that occurs during the ulling force history. The reduction of the stress at the ie head is clearly observed during the 15 s rest eriod between 685 s and 7 s, as shown in Figure 9. A high density olyethylene ie with 4 mm outer diameter and 1 mm thickness is to be installed underground using horizontal directional drilling. The following set of arameters defines the 2 m oeration: Boreath rofile (referring to Figure 2): L 1 = 6 m L 2 = 8 m L 3 = 6 m β 1 = -1 o β 2 = 1 o β 3 = 12 o R 1 = 8 m R 12 = 9 m R 23 = 85 m β o = 2 o Borehole Diameter = 7 mm Pie-soil interaction: 1153

7 Pulling Stress at Head (MPa) This reduction no only occurs near the ie head but, to a lesser extent, along the entire ie as Figure 1 demonstrates. This occurs because of relaxation of the elements that are restrained by the soil from creeing. The level of axial stress dro deends on several factors including the stress level achieved, the ie material behaviour, the soil stiffness, and time at rest. Tensile stress (MPa) Figure 9. Pie head stress during the 2 th ulling cycle Figure 1. Change of stress along the ie during the rest eriod after the 2 th ulling cycle. When the head recommences moving during a load cycle, the ie recovers the load lost during the rest eriod (Figure 9). After that romt stress increase, further change deends on ie-borehole interaction. 6. CONCLUSION Head Moving At rest Time (s) Location on ie (m) At 685 sec At 69 sec At 7 sec A new model was develoed to calculate tensile force and stress over the ie length at any given time, knowing the history of ie movement during installation. Gravity forces, ie-soil interaction forces, and viscous drag force due to mud flow ast the ie are considered. Pie-soil interaction is included, emloying a simle model accounting for adhesion, friction, and soil stiffness. Model erformance was successfully evaluated through comarisons to redictions from established methods. A further examle roblem demonstrated that the model rovides details of cyclic loading history accounting for nonlinear, time deendent olymer behaviour. Develoment and use of this model is art of a comrehensive research rogram to calculate the short and long term behaviour of high density olyethylene ies during and after HDD installations. ACKNOWLEDGEMENT This work is art of a Strategic Research roject funded by the Natural Sciences and Engineering Research Council of Canada. Dr Moore s osition at Queen s University is suorted by the Canada Research Chairs rogram. REFERENCES ASTM International, Designation: F , Standard guide for use of maxi-horizontal directional drilling for lacement olyethylene ie or conduit under obstacles, including river crossings, 1-17 Baumert, M.E. and Allouche, E.N. 22. Methods for estimating ie ullback loads for horizontal directional drilling (HDD) crossings, Journal of Infrastructure Systems, ASCE, 8(1): Baumert, M.E., Allouche, E.N., and Moore I.D. 24. Exerimental investigation of ull loads and borehole ressures during horizontal directional drilling installations, Canadian Geotechnical Journal, ASCE, 41: Dareing, D.W. and Ahlers, C.A Tubular bending and ull-out forces in high curvature well bores, Journal of Energy Recourses Technology, 113: Drillath TM, Theory and user s manual, Infrasoft L. L. C., Houston, Texas, USA. Driscoie Technical exertise alication of driscoie in directional drilling and river-crossings, Technical Note #: 41. Huey, D.P., Hair, J.D. and McLeod K.B Installation loading and stress analysis involved with ielines installed in horizontal directional drilling, Proceedings of the No-Dig Conference New Orleans, North American Society for Trenchless Technology. Haciislamoglu, M. and Langlinais, J Non- Newtonian flow in eccentric annuli, Journal of Energy Ressources Technology, 112(3): Polak, M.A. and Lasheen, A. 22. Mechanical modelling for ies in horizontal directional drilling, Tunneling and Underground Sace Technology, 16(1): S47-S55. Zhang, C. and Moore, I.D Nonlinear mechanical resonse of high density olyethylene. Part II: Uniaxial constitutive modeling, Polymer Engineering and Science, 37(2):