Drag-ReductionPerformanceEvaluationofControllableHybrid ...

Research ArticleDrag-Reduction Performance Evaluation of Controllable HybridSteering Drilling System

Jianyan Zou 1 Ping Chen1 Tianshou Ma1 Yang Liu2 and Xingming Wang3

1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum University Chengdu 610500China2School of Mechatronic Engineering Southwest Petroleum University Chengdu 610500 China3State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Chengdu University of Technology Chengdu 610059China

Correspondence should be addressed to Jianyan Zou 201711000078stuswpueducn

Received 28 November 2020 Revised 15 January 2021 Accepted 3 March 2021 Published 20 March 2021

Academic Editor Qilong Xue

Copyright copy 2021 Jianyan Zou et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+e excessive dragtorque and the backing pressure is an important factor that restricts the improvement of the penetration rateand the extension of the drilling in the sliding drilling process of extended-reach wells and horizontal wells To deal with thisproblem this paper developed a novel controllable hybrid steering drilling system (CHSDS) based on the friction-reducingprinciple of a rotating drill string +e CHSDS is composed of a gear clutch hydraulic system and measurement and controlsystem By controlling the meshing and separation of the clutch with the mud pulse signal the CHSDS has two working stateswhich leads to two boundary conditions Combined with the stiff-string drag torque model the effects of the drilling parameterson the friction-reducing performance of the CHSDS are analyzed systematically+e results show that the friction reduction effectin the inclined section is the most significant followed by that in the horizontal section whereas there is almost no impact in thevertical section Friction reduction increases with the rotary speed and the drilling fluid density whereas it decreases with theincrease in the surface weight-on-bit and the bit reaction torque Field tests confirm the separation and meshing function of theCHSDS +e developed controllable hybrid steering and friction-reducing technology provides an alternative approach for thesafe and high-efficiency drilling of horizontal wells

1 Introduction

Realizing economical and high-efficiency exploitation ofunconventional oil and gas resources depends on combininghorizontal drilling and hydraulic fracturing technologies [1]However owing to the limitations of the rig equipment andthe performance of horizontal well drilling tools the issuesof low drilling efficiency and long well construction periodare common in unconventional horizontal wells in China[2] Considering shale gas horizontal well drilling as anexample at a particular vertical depth and a domestichorizontal section that is shorter than that of North Americathe domestic drilling cycle is 36ndash4 times than that in NorthAmerica [3 4] +is is primarily because the ultrahigh dragand torque between the drill string and the wellbore wall and

the induced severe backing pressure effect have becomesome of the main technical bottlenecks restricting the op-timal and rapid drilling of horizontal wells in unconven-tional resources

To solve the above-mentioned drilling problemsscholars have started from the fundamental principles oftribology including lowering the friction coefficient re-ducing the normal contact force and altering the frictionalforce direction to conduct research on drag-reducingtechnologies in horizontal drilling [5 6] +us variousadvanced drag-reduction tools are developed and successfulfield applications are achieved such as drill pipe bearingsubs hydraulic oscillators rotary steering systems (RSSs)and drill string rocking systems [7ndash10] However all theabove methods have different degrees of limitation [11 12]

HindawiShock and VibrationVolume 2021 Article ID 6688656 13 pageshttpsdoiorg10115520216688656

A drill pipe bearing sub is affected by the wellbore qualityand the installation number resulting in a poor drag-re-duction effect [13ndash15] For instance a hydraulic oscillator islimited by the high circulating pressure loss and the shortservice life Moreover a high-frequency vibration can easilydamage downhole measuring instruments [16ndash18] An RSShas significant and potential risks of sticking and buryingassociated with its own structural defects and its service costis comparatively high [19ndash21] Large-scale applications andpromotions are yet to be realized for a drill string rockingsystem because the friction-reducing mechanism and theautomatic control technology are not thoroughly under-stood [22ndash24] +erefore a complete understanding of thedefects of the existing mechanical drag-reduction technol-ogy is developed and an in-depth study on the mechanismof friction reduction in horizontal wells is conducted Fi-nally based on the principle of friction reduction by a rotarydrill string a novel controllable hybrid steering drillingsystem (CHSDS) is developed which can switch freelybetween meshing and separation states by receiving re-motely controlled commands from the ground

In the evaluation of the effect of drag-reduction systemsit is necessary to determine the corresponding boundaryconditions and build a mechanical model according to theactual working state of the drilling system being examined[25] Because there are two working states of meshing andseparation in the actual drilling of the CHSDS the boundaryconditions of the traditional drag torquemodel are no longerapplicable +erefore the existing friction torque predictionmodel cannot be directly used to evaluate the drag-reductioneffect of the CHSDS

+erefore based on the actual working conditions of theCHSDS the boundary conditions of its separation ormeshing states and of the bit are determined +e drag-reduction performance of the CHSDS is analyzed bycombining with the classical drag torque model of the drillstring +e field test verifies the remote separation andmeshing functions of the CHSDS providing the basis for thedrag-reduction performance test and the subsequent ap-plication of the CHSDS

2 Operating Principle and Structure of CHSDS

21 Operating Principle of CHSDS During the slidingdrilling process of the conventional sliding steering drillingsystem the bottom hole assembly (BHA) is as shown inFigure 1(a) It comprises a bit bent sub positive displace-ment motor (PDM) and measurement while drilling(MWD) +e drill string does not rotate but slides along theaxis of the borehole wall +e deviation and azimuth anglesof the wellbore are changed by the sliding of the steering toolface thereby controlling the wellbore trajectory When theactual wellbore trajectory deviates from the designed oneand needs to be adjusted the rotary table is manuallycontrolled to rotate it an angle to rotate the tool face of thedrill tool assembly to the specified direction

An RSS can be classified into push-the-bit and point-the-bit according to the steering mode When the push-the-bitsystem operates it controls three wing ribs to push against

the well wall according to the actual well deviation azimuthdata and predetermined well trajectory this ensures the bitpoints to the direction to be drilled+e point-the-bit systemdepends on the biasing mechanism inside the RSS to bias themandrel therefore there is an angle between the axes of therotating drill string and borehole Finally rotary steering isrealized by the rotation angle of the drill bit As shown inFigure 1(b) the RSS rotates while drilling which transformsthe axial friction of the drill string into circumferentialfriction torque thus reducing the friction resistance of thedrill string

As can be seen from Figure 1(c) the steering method ofthe CHSDS is the same as the conventional sliding steeringdrilling method +e inclination and azimuth angles of thewell are controlled by a rotating turntable in the meshingstate In the drag-reduction drilling mode when the systemis in the separation state the upper drill string rotates toconvert the axial friction part of the drill string into thecircumferential friction torque+is significantly reduces thedrill string friction which is similar to rotary steeringdrilling +e lower drill string slide drills with the stable toolface +erefore the CHSDS includes three working modes

(1) Conventional sliding steering drilling mode(meshing)

(2) Conventional rotating drilling mode (meshing)(3) Controllable hybrid steering friction-reducing mode

(separation)

22 Structural Design of CHSDS +e CHSDS is mainlycomposed of a measurement and control system hydraulicsystem and clutch unit +e structure is shown in Figure 2

+e functions of the measurement and control systemare to detect the mud pressure pulse identify the groundcommand start the motor and solenoid valve drive circuitand move the piston in a predetermined direction of theground Moreover the system should realize effective sep-aration or engagement of the tool clutch device and effec-tively control the working mode of the drag-reduction toolon the ground

As shown in Figure 2(a) the measurement and controlsystem mainly includes pressure pulse detection signalfiltering and amplification AD conversion a micro-controller and a motor solenoid valve drive circuit

+e main roles of the hydraulic system are to execute theinstruction of the downhole microcontroller inject hy-draulic oil into a specified oil cylinder and drive the pistonto move in the predetermined direction It can be seen fromFigure 2(b) that it is mainly composed of a hydraulic cyl-inder motor and pump pressure relief valve 32 solenoidvalve check valve and double-acting oil cylinder

+e main objective of the clutch unit is to separate ortransfer the torque from the upper drill string to the lowerdrill string As shown in Figure 2(c) it mainly includes aninternal gear an outer gear a piston shaft a clutch outercylinder and a bearing bush +e hydraulic system drivesthe piston shaft to move back and forth to drive theseparation and meshing of the internal and outer gears to

2 Shock and Vibration

realize the separation and meshing functions of theCHSDS

+e principle prototype of the CHSDS is depicted inFigure 3

23 Functional Testing of CHSDS +e CHSDS function testis conducted to test whether it can realize the controlcommand on the ground and complete the separation ormeshing function in the downhole

231 Basic Parameters of Test Well +e depth of the testwell is 746m the depth of the deviation point is 545m themaximum deviation angle is 2215deg the length of the open-hole section is 201m and the drilling fluid density is1080 kgm3 +e BHA comprises a Φ2159 mm bit jointΦ172 mm drill collar Φ172 mm CHSDS switching jointand Φ127 mm drill pipe

232 Process and Results of CHSDS Function TestFigure 4 displays the CHSDS tripping in and out +eprocess of the CHSDS function test is as follows

(a) +e CHSDS is in the meshing state connected to theBHA and is subsequently implemented in thebottom hole

(b) +e pump strokes number per minute is kept at 40and the rotary speed is 30 rpm +e drilling tool islifted 9m and the hanging weight and the strokesnumber per minute are recorded

(c) +e pump strokes number per minute is kept at 40+e drilling stem is raised and lowered at a constantspeed and the hanging weight is recorded

(d) +e separation command is launched and subse-quently step (b) is repeated

(e) +e meshing command is launched +e CHSDS istripped out and disassembled to examine the datastored by the downhole microcontroller

+e test results are as follows

+e data in Table 1 show that the system can effectivelyexecute the separation command sent from the groundAfter tripping out it is found that the CHSDS cannot berotated with a chain clamp+is suggests that it is in a state ofmeshing +e disassembly of the CHSDS extracts the pulsesignal data stored in the microcontroller It is found that theCHSDS receives the command sent from the groundcompletely and accurately +e above results indicate thatthe CHSDS can accurately accept and identify ground mudpulse signals and effectively implement the meshing andseparation commands

3 Drag-Reduction Performance Modeling

+eCHSDS is developed according to the principle of rotarydrill string drag reduction and subsequently its functiontest is completed To better guide the field applications of theCHSDS it is necessary to predict and evaluate the drag-reduction performance +erefore the mathematical modelfor the CHSDS analysis is described below

31 Basic Assumptions In the analysis of the drill stringfriction based on Coulombrsquos theorem the solution of thenormal contact force is the key +e contact state betweenthe drill string and the borehole wall is uncertain because offactors therefore it is very difficult to accurately solve thenormal contact force +us it is necessary to make appro-priate assumptions about the contact and deformation of thedrill string [26ndash28]

(1) +e drill string is in continuous contact with theborehole wall the borehole wall is rigid and thedeformation of the drill string is within the elasticrange

(2) +e centerline of the drill string coincides with thewellbore track

(3) +e gravity normal force mud buoyancy andfriction force of the drill string unit are evenly dis-tributed on the drill string element

(4) +e drill string element is an arc with a constantcurvature in the spatial slanting plane

PDM+bent sub

Derrick Ground

BitDrill stringWellbore

MWD

(a)

RSSMWD

(b)

CHSDSPDM+

bent subMWD

(c)

Figure 1 Comparison of CHSDS and conventional horizontal well drilling method

Shock and Vibration 3

(5) +e dynamic load of the drill string is not considered

32 Governing Equations It is necessary to consider theeffects of the borehole bending and drill string stiffness onthe tension and torque as well as the drilling fluid dampingand the axial and circumferential components of the frictionduring rotary drilling +erefore a mathematical model[29 30] is used to calculate the friction and the torque of thedrill string during drilling with the CHSDS

dMt

ds f1RoN + m0

dTt

ds+ kbEI

dkb

dsminus f2N minus Cv minus B + qm e

g middot e

t 0

minusd2Mb

ds2 + Ttkb + kn kbMt + knMb( 1113857 + Nn + f1Nb + qm e

g middot e

n 0

minusd kbMt + knMb( 1113857

dsminus kn

dMb

ds+ Nb minus f1Nn + qm e

g middot e

b 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

where

f1 ωRof

v2

+ ωRo( 11138572

1113969

f2 vf

v2

+ ωRo( 11138572

1113969

N

N2n + N

2b

1113969

C 2πμ

ln Dw2Ro

mo 2πωR3o

τ

v2

+ ωRo( 11138572

1113969 +2μ

Dw minus 2Ro

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦

B 2πRoτv

v2

+ ωRo( 11138572

1113969

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)

where Mt is the drill string torque Mb is the drill stringbending moment N middot m Tt is the axial tension of the drillstring N kb is the borehole curvature kn is the naturaltortuosity of the centerline of the boreholeradm E is theelastic modulusGPa I is the moment of inertia of thedrill string m4 Dw is the borehole diameter Ro is theoutside radius of the drill string m ω is the rotary angularvelocity of the drill string rads v is the axial velocity ofthe drill string ms qm is the weight per unit length of thedrill string kNm τ is the shear stress of the drilling fluidPa and μ is the dynamic viscosity of the drilling fluidN middot sm2

Because kn and kb are small and their product is minimalthe term containing the product of kn and kb can be ignored[31] Moreover when the minimum curvature method isused the measurement point adjacent to the borehole axis isa circular arc on a spatial inclined plane and the boreholetorsion is always in the close plane Furthermore kn 0 canbe seen from the definition of the close section plane [5]

e

g middot e

t cos α

e

g middot e

n kα

kb

sin α

e

g middot e

b minuskφ

kb

(sin α)2

e

g minuscos α e

t +kα

kb

sin α e

n +kφ

kb

(sin α)2

e

b

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where e

t e

n and e

b are the unit basis vectors of the naturalcoordinate system dimensionless e

g is the drill string

gravity basis vector dimensionless kα is the deviationrateradm kφ is the azimuth rate of change radm α is theinclination angle rad kf is the linear floating weight co-efficient of the drill string dimensionless

Simultaneously the FrenetndashSerret [32] equation (3) issubstituted into equation (1) and the following equation isobtained

dMt

ds f1RoN + m0

dTt

ds+ kbEI

dkb

dsminus f2N minus Cv minus B + qmkf cos α 0

minusd2Mb

ds2 + Ttkb + Nn + f1Nb + qmkf

kα

kb

sin α 0

minuskb

dMt

ds+ Nb minus f1Nn minus qmkf

kφ

kb

sin2 α 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)

33 Boundary Conditions +ere are two working states ofthe CHSDS meshing and separation Different workingstates correspond to different boundary conditions

331 Boundary Conditions of CHSDS Meshing StateWhen the CHSDS is in the meshing state like conventionalrotary drilling the drill string rotates as a whole and thewellhead torque and the bit reverse torque are known +ewellhead torque is the external torque exerted by the rotarytable or the top drive and the bit torque is the reverse torqueproduced by the PDM +erefore the boundary conditionsare as follows [33]


Mt s sN( 1113857 TOB

T s sN( 1113857 minusWOB1113896 (5)

where Mt(S SN) is the torque on the element N middot m SN isthe drill string length below the node m T(S SN) is thepull at the top of the drill string below the nodeN TOB isthe torque on the bit N middot m and WOB is the weight on thebit N

332 Boundary Conditions of CHSDS Separation StateWhen the CHSDS is separated in its working state theupper drill string rotates and the lower drill string slides+eboundary conditions are shown in Figure 5 Similar to theabove scenario the wellhead torque is the external torque

and the bit torque is the reverse torque generated by thePDM +erefore the upper boundary conditions of the drillstring below the CHSDS are as follows [33]


T s sN( 1113857 minusWOB

Mt s sT( 1113857 MTL

T s sTU( 1113857 T s sTL( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)

where Mt is the friction torque of the CHSDS bearingrotation N middot m T(S STU) is the pull force at the bottomof the drill string above the CHSDS N T(S STL) is thepull force at the bottom of the drill string below theCHSDS N ST is the installation position of the CHSDS

MOil tank Motorand

pump

Reliefvalve

Checkvalve

Double-actingcylinder

32 way solenoidvalve

Clutchsystem

Hydraulicdrive system

Measurementand control

system

Gear pairs meshing

Gear pairs separation

Hydraulic oil drivespiston movement

IO

Motor and solenoid valve drive circuitMCUAD

Power

Signal filter and amplifier

Pressure pulse signal

detection

(a)

(b)

(c)

Figure 2 Structure of CHSDS

Figure 3 Principle prototype of CHSDS


m and MTL is the torque at the bottom of the drill stringbelow the CHSDS N middot m

+e lower boundary conditions of the drill string abovethe CHSDS are

Mt s sT( 1113857 MTU

T s sTU( 1113857 T s sTL( 11138571113896 (7)

where MTU is the torque at the bottom of the drill stringabove the CHSDS N middot m

333 Bit Boundary Conditions In the process of drillingthe formation forces on the bit mainly include the reaction ofthe WOB reaction of the bit lateral force and the frictiontorque +erefore the boundary conditions of the interac-tion between the bit and the formation can be expressed asfollows [34 35]

Fwob(t) Wo + kfxo sin 2πnbfbitt( 1113857

Tbit(φ _φ) 13Dwμk Wo + kfxo sin nbφbit1113872 1113873

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(8)

where Wo is the average WOB kN and nb is the incentivefactor dimensionless related to the type of the bit In ad-dition xo is the cutting depth of one turn of the drill bit mkf is the formation stiffness Nm fbit is the fluctuation

frequency of the WOB Hz and μk is the dynamic frictioncoefficient dimensionless

4 Results and Discussion

41 Basic Parameters of Case Well

411 Well Trajectory and Casing Program +ewell depth ofthe designed three-dimensional (3D) horizontal well is5016m and the casing program profile and the well tra-jectory are presented in Figures 6 and 7

According to the 3D well trajectory the actual drillingdepth of the well is 5000m and the deviation angle firstincreases and then decreases in the shallow vertical sectionSimultaneously the deviation of the horizontal section of thewell initially decreases then increases and finally decreases+e length of the horizontal section is approximately1500m +e wellbore trajectory of this well is complex andthe friction is extremely large

412 Bottom Hole Assembly +e BHA is divided into twogroups one group contains the CHSDS and the other groupdoes not include the CHSDS Specifically

BHA 1 bit + PDM+bent sub + nonmagnetic drillcollar + drill collar +CHSDS+ drill pipe

Figure 4 Tool tripping in and tripping out

Table 1 Drag-reduction test results

State Pump strokes (strokesmin) Rotary speed (rpm) Tripping out load (kN) Tripping in load (kN) Static load (kN)Meshing 40 mdash 328 2946 mdashMeshing 40 30 mdash mdash 31084Separation 40 30 mdash mdash 300ndash302


BHA 2 bit + PDM+bent sub + nonmagnetic drillcollar + drill collar + drill pipe

413 Drilling Parameters +e drilling parameters are asfollows WOB of 80 kN displacement of 26 Ls drilling fluiddensity of 2200 kgm3 drilling fluid viscosity of 24mPamiddotsand drilling fluid dynamic shear force of 55 Pa

42 Performance Analysis of CHSDS

421 Analysis of CHSDS Drag-Reduction Effect

(i) Drag and Torque Distribution +e drag distributions ofBHA 1 BHA 2 and combined drilling conditions are cal-culated which are presented in Figure 8 +e load of thehook with the CHSDS is larger than that without theCHSDS which shows that the CHSDS can effectively reducethe friction of the drill string Figure 9 shows the variationcurves of the drag differences of BHA 1 and BHA 2 with thewell depth In the vertical section the drag difference ba-sically presents a horizontal line +us there is almost nodrag-reduction effect in the vertical section In the deviatedsection the drag difference approximately presents a high-slope straight line indicating that the drag-reduction effect issignificant In the horizontal section the drag difference isalmost linear with a slope less than the slope for the deviatedsection indicating that the drag-reduction effect in thehorizontal section is notable However it is slightly worsethan that in the inclined section In the combined drillingthe drag distribution of the drill string is very close to that ofBHA 1 +e main difference is that there is no rotating drillstring under the CHSDS

In directional drilling the rotary torque of BHA 1 issignificantly higher than that of BHA 2+e difference in thetorques is due to the friction torque generated by the ro-tation of the drill string above the CHSDS as shown inFigure 10 installation of the CHSDS has no effect on thetorque distribution of the lower drill collar +erefore re-gardless of BHA 1 or BHA 2 the lower drill string usesfriction to offset the bit reverse torque +erefore the torquedistribution of the lower drill string is consistent +e dif-ference is that the friction torque produced by the CHSDSbearing has a weak influence on the torque distribution ofthe lower drill string near the CHSDS In the combineddrilling the wellhead torque is greater than that of BHA 1whereas the torque distribution law is basically the same+edifference is that the drill string under BHA 1 does not

rotate therefore the friction torque is smaller than that inthe combined drilling

(ii) Friction Distributions of BHA 1 and BHA 2 +e frictiondistributions of BHA 1 and BHA 2 are shown in Figure 11+e friction force of BHA 1 is slightly larger than that ofBHA 2 in the vertical section this is because the contactforce between the drill string and the borehole wall is largerin the rotary drilling than that in the sliding drillingAccording to Figure 11 the friction forces produced by BHA1 and BHA 2 in the deviated section are 2531 kN and49465 kN respectively and those by BHA 1 are reduced by4883 compared to those by BHA 2 Because the curvatureof the deviated hole increases significantly the contact forcebetween the drill string and the borehole wall increasessignificantly Moreover based on the principle of friction-reducing resistance of the rotary drill string the axial frictionforce of the rotary drilling is smaller than that of the slidingdrilling Similarly the friction forces produced by BHA 1and BHA 2 in the horizontal section are 41295 kN and5727 kN respectively and BHA 1 produces 2789 smallerforce than BHA 2 +e contact force between the drill stringand the borehole wall increases significantly because of thebending and stiffness of the drill string in the deviatedsection In comparison the contact force in the horizontalsection is mainly generated by gravity +erefore the drag-reduction effect of the CHSDS in the inclined section isbetter than that in the horizontal section

422 Analysis of Influence Factors of CHSDSDrag-ReductionEffect

(i) Influence of CHSDS Installation Position on FrictionForce In the process of drilling with the PDM the reversetorque generated by the bit is offset by the friction torquebetween the drill string and the borehole wall below theCHSDS as shown in Figure 12 Under the same reversetorque condition of the bit the effects of different CHSDSinstallation positions on the drag-reduction effect aredepicted It can be seen from the figure that when theCHSDS installation position is close to the bit the drag-reduction effect is large If the CHSDS is installed extremelyfar from the drill bit the axial friction of the drill string in thehorizontal section is large whereas the drag-reduction effectis low If the CHSDS is installed extremely close to the drillbit the reverse torque of the drill bit cannot be offset and thetool surface will be unstable +erefore it is necessary to

CHSDS is in separation stateWellhead direction Bit direction

Mt (s = sT) = MTU

T (s = sTU) = T (s = sTL)

Mt (s = sT) = MTL


Figure 5 CHSDS separation state boundary conditions


ensure that the friction torque of the drill string can offset thereverse torque of the bit and the closeness between theCHSDS and the bit is associated with a good drag-reductioneffect

(ii) Influence of Rotational Speed on Friction According tothe principle of frictional decomposition the axial andtangential frictional forces are related to the axial and cir-cumferential speeds Figure 13 displays the friction curveobtained by changing the rotary speed under the conditionsof constant rate of penetration (ROP) WOB and bit torqueIt can be seen from the figure that the friction decreases withthe increase in the rotating speed in the inclined and hor-izontal sections According to the decomposition principleof the friction force of the drill string compound motion anincrease in the circumferential speed leads to a decrease inthe axial friction coefficient and therefore the axial frictionforce decreases However the influence of the rotating speedon the axial friction in the vertical section is not clear As canbe noted from the figure with the increase in the rotatingspeed the effect of drag reduction in the inclined section isthe best followed by that in the horizontal section However

the effect of drag reduction in the vertical section is notnotable

(iii) Effect of WOB on Friction +e change in the WOB willlead to a change in the contact force of the drill string in thecurved well section causing a change in the axial frictionforce of the drill string As displayed in Figure 14 in thevertical section the change in the WOB does not lead to achange in the friction force because the increase in the axialforce in the vertical section does not modify the contactforce In the deviated section the axial friction increases withthe increase in the WOB because the contact force betweenthe drill string and the wellbore increases with the increase inthe WOB In the horizontal section with the increase in theWOB the axial friction force of the drill string does notincrease significantly however the fluctuation amplitudeincreases significantly As theWOB of the horizontal sectionincreases the contact force of the smooth horizontal sectiondoes not increase whereas the contact force of the curvedsection increases significantly

(iv) Effect of Drilling Fluid Density on Friction +e density ofthe drilling fluid determines the floating weight of the drillstring and it changes the contact force of the drill string andthe wellbore+erefore it has an impact on the friction forceof the drill string From Figure 15 we can see that thedistribution curve of the drill string friction force with thevariation in the drilling fluid density With the increase inthe drilling fluid density the axial friction of the drill stringdecreases gradually because a high-density drilling fluid isassociated with a small floating weight of the drill stringFurthermore a small contact force between the drill stringand the borehole wall corresponds to a small friction force

43 Discussion of Simulation Results Based on Figure 11compared to the conventional sliding steering drilling thedrag-reduction effect of the CHSDS can reach 4883 in thedeviated section and 2789 in the horizontal section+is isbased on a given case of well-calculated parameters it is notuniversal Moreover because of the effect of the drag re-duction and well trajectory the installation position rotaryspeed WOB and drilling fluid present close relations Al-though the results of the calculations with different drillingparameters are not the same the simulation results can bequalitatively explained in that in the drilling process of aparticular horizontal well the deviated section of the CHSDShas a better drag-reduction effect than the horizontalsection

Because a 3D horizontal well drill string dynamic modelcalculation is complex and time-consuming it is not con-ducive to field promotion Considering that the axial velocityof the drill string during horizontal well drilling is very lowthe calculation of the drag torque during the drilling of thedrill string mainly focuses on the drill string static balanceinstead of the instantaneous dynamic response as a drillstring vibration [5 26 34] To simplify the calculation andignore the effect of the dynamic load a static model is usedwhich is different from the actual scenario

Φ50800 mm times 4700 mΦ66040 mm times 4700 m



Cement return height 200000 m


Figure 6 Casing program of horizontal well


In the process of horizontal well drilling the recom-mended drilling tool assembly is bit + PDM+bent sub+ nonmagnetic drill collar + drill collar +CHSDS+ drillpipe +e downhole function test is conducted for thesystem however it does not test its actual drag-reductioneffect during the drilling in horizontal and deviated sections+e simulated drag-reduction effect needs to be further

confirmed by field tests +e next steps will be to conduct thedownhole drag reduction performance test of the system andsubsequently perform a comparison with the model cal-culation results +is will be followed by the analysis andmodification of the model to improve the prediction ac-curacy as well as provision of a theoretical basis for thesubsequent application of the system

Vert

ical

dep

th (m

)

300 600 900 1200 1500 18000Horizontal displacement (m)

3500

3000

2500

2000

1500

1000

500

0

(a)

0

400

800

1200

1600

2000

Nor

th co

ordi

nate

s (m

)

ndash160 ndash120 ndash80 ndash40 0ndash200East coordinates (m)

(b)

Figure 7 Horizontal well trajectory (a) Vertical projection view (b) Horizontal projection view

Dra

g (k

N)

1000 2000 3000 4000 50000Well depth (m)

ndash400

ndash200

0

200

400

600

800

1000

BHA 1Combined drillingBHA 2

Figure 8 Drag force variation with well depth


Dra

g di

ffere

nce (

kN)

050

100150200250300350400450500550

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

Figure 9 Drag difference between BHA 1 and BHA 2

Torq

ue (k

Nmiddotm

)

1000 2000 3000 4000 50000Well depth (m)

0

5

10

15

Combined drillingBHA1BHA2

Figure 10 Relationship between torque and well depth

Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

14

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

BHA1BHA2

Figure 11 Distribution of friction force with and without CHSDS


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m

Figure 12 Influence of tool installation position on friction

Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm

Figure 13 Effect of rotational speed on friction

Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN

Figure 14 Effect of WOB on friction


5 Conclusion

To cope with the extreme friction torque and backing pressureduring sliding drilling of extended-reach wells and horizontalwells a novel controllable hybrid steering drilling system hasbeen developed and field function tests and numerical simu-lations have been carried out According to the test and analysisresults the following conclusions are drawn

(1) Based on the principle of reducing the friction of arotary drill string a novel controllable hybridsteering drilling system is developed and the designfunction was verified by field test

(2) According to the working mode of the CHSDS twotypes of boundary conditions in the meshing andseparation states are determined Combined with stiff-string model the drag-reduction effect and the influ-ence of the drilling parameters on the CHSDS areanalyzed

(3) +e simulation results show that the drag-reductioneffect in the inclined section is the best reaching4883 followed by that in the horizontal sectionreaching 2789 whereas the vertical section presentslittle drag-reduction effect

(4) Under the same conditions as the rotation speed anddrilling fluid density increase the axial friction of thedrill string decreases However as WOB and dis-tance between the CHSDS and the drill bit increasethe axial friction of the drill string increases

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the National Science andTechnology Major Project of China (Grant no2016ZX05022-01) and the China Postdoctoral ScienceFoundation Funded Project (Grant no 2020M673576XB)+e authors express their deep gratitude for the invaluablesupport of the institution

References

[1] M Kenomore M Hassan H Dhakal and A Shah ldquoEco-nomic appraisal of shale gas reservoirsrdquo in Proceedings of theSPE Europec Featured at 80th EAGE Conference andExhibition Copenhagen Denmark June 2018

[2] Z F Xiang Z X Quan L Z Bin et al ldquoPractice of drillingoptimization system in the development of unconventional oiland gas resources in Chinardquo China Petroleum Explorationvol 25 no 2 pp 96ndash109 2020

[3] S H Fang B Jing H Bing et al ldquoUnconventional shale gasdrilling comparison in Sichuan basin China different ap-proaches aim for same targetrdquo in Proceedings of the OffshoreTechnology Conference-Asia Kuala Lumpur Malaysia March2014

[4] Z J Cheng Z H Bo Z Y Bin and N X Ming ldquoOptimal andfast drilling technology for shale gas horizontal well and itsapplicationrdquo in Proceedings of the SPEIATMI Asia Pacific Oiland Gas Conference and Exhibition Jakarta Indonesia Oc-tober 2017

[5] W X Ying N H Jian W R He L T Ke and X J GuoldquoModeling and analyzing the movement of drill string whilebeing rocked on the groundrdquo Journal of Natural Gas Scienceand Engineering vol 39 pp 28ndash43 2017

[6] L Yang C Ping W X Ming and M T Shou ldquoModelingfriction-reducing performance of an axial oscillation toolusing dynamic frictionModelrdquo Journal of Natural Gas Scienceand Engineering vol 33 pp 397ndash404 2016

[7] J Garcia S Banks M John P Vertex B Robert andR Resources ldquoField-verified modeling compares weighttransfer methods in horizontal wellsrdquo in Proceedings of the

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3

Figure 15 Effect of drilling fluid density on friction


SPEIADC Drilling Conference and Exhibition +e Hague+e Netherlands March 2019

[8] I Rostahno M Yi P Ashok E V Oort B Potash andC Mullin ldquoA methodology for selecting optimal pipe rockingregimes during slide drillingrdquo in Proceedings of the SPEAAPGSEG Unconventional Resources Technology ConferenceDenver CO USA July 2019

[9] N Alnahash M Alghofaili S Aramco A A Khalifah andM Ali ldquoDrilling optimization approach in performanceenhancement and cost reduction using a friction-reductiontool in challenging applicationsrdquo in Proceedings of the SPEInternational Petroleum Technology Conference DhahranSaudi Arabia January 2020

[10] L Yang C Ping M T Shou andW X Ming ldquoAn evaluationmethod for friction-reducing performance of hydraulic os-cillatorrdquo Journal of Petroleum Science and Engineeringvol 157 pp 107ndash116 2017

[11] E Maidla and M Haci ldquoUnderstanding torque the key toslide-drilling directional wellsrdquo in Proceedings of the IADCSPE Drilling Conference Dallas TX USA March 2004

[12] L Yang M T shou C Ping and Y Chuan ldquoMethod andapparatus for monitoring of downhole dynamic drag andtorque of drill-string in horizontal wellsrdquo Journal of PetroleumScience and Engineering vol 164 pp 320ndash332 2018

[13] S Y Nao D X Rong and W J Jin ldquoAntifriction tool and itsapplicationrdquo Oil Drilling amp Production Technology vol 27pp 78ndash80 2005

[14] J E McCormick T Long andM Frilot ldquoInaccessible drillingtargets and completions operation made possible by the al-leviation of excessive torque and dragrdquo in Proceedings of theSPE Middle East Drilling Technology Conference andExhibition Manama Bahrain October 2009

[15] J E McCormick G Osorio J Andachi and M BarthldquoAdjustable gauge stabilizer and torque and drag reductiontools reduce overall drilling times by at least 20 a casestudyrdquo in Proceedings of the SPE Middle East Oil and GasConference Manama Bahrain September 2011

[16] M Warner and R A Hall ldquoBenefits of using downhole vi-bratory casing tools in the niobraracodell formationsrdquo inProceedings of the IADCSPE Drilling Conference andExhibition Fort Worth TX USA March 2016

[17] T J Lin Y Zhi L You et al ldquoVibration analysis of new drillstring system with hydro- oscillator in horizontal wellrdquoJournal of Mechanical Science amp Technology vol 30pp 2443ndash2451 2016

[18] T Mcintosh K J Gervais J G Gervais R Schultz andJ Whitworth ldquoA vibratory tool study on extended reachhorizontals during coiled tubing drillout in the eagle fordshalerdquo in Proceedings of the SPEICoTA Coiled Tubing andWell Intervention Conference and Exhibition Houston TXUSA March 2016

[19] O Hummes S Janwadkar J Powers et al ldquoEvolution of highbuild-rate RSS changes the approach to unconventional oiland gas drillingrdquo in Proceedings of the SPE Annual TechnicalConference and Exhibition Denver CO USA October 2011

[20] C Gillan S Boone G Kostiuk C Schlembach J Pinto andM Leblanc ldquoApplying precision drill pipe rotation and os-cillation to slide drilling problemsrdquo in Proceeedings of the SPEIADC Drilling Conference and Exhibition Amsterdam +eNetherlands March 2009

[21] C Gillan S Boone M LeBlanc R Picard and T FoxldquoApplying computer based precision drill pipe rotation andoscillation to automate slide drilling steering controlrdquo in

Proceedings of the SPE Canadian Unconventional ResourcesConference Calgary Alberta November 2011

[22] W X Ying Development of Torque Clutch Drilling Tool andEvaluation of Drag Reduction Performance Southwest Pe-troleum University Chengdu China 2017

[23] H L Xiang Z J Chuan and L Wei ldquoApplication evaluationof the PIPE ROCK twist drill string systemrdquo Natural GasIndustry vol 38 pp 73ndash78 2018

[24] C Pehlivanturk J D Angelo C D Zhou C D Mei andE V Oort ldquoSlide drilling guidance system for directionaldrilling path optimizationrdquo in Proceedings of the SPEIADCInternational Drilling Conference and Exhibition +e Hague+e Netherlands March 2019

[25] V S Tikhonov A I Safronov K R Valiullin andO S Bukashkina ldquoDevelopment of universal application fordrillstring dynamics simulationrdquo in Proceedings of the SPERussian Oil and Gas Technical Conference and ExhibitionMoscow Russia October 2014

[26] R F Mitchell and R Samuel ldquoHow good is the torquedragmodelrdquo in Proceedings of the SPEIADC Drilling Conferenceand Exhibition Amsterdam+e Netherlands February 2009

[27] G D Li and HW Jun ldquoA review of down-hole tubular stringbuckling in well engineeringrdquo Petroleum Science vol 12pp 443ndash457 2015

[28] L Z Feng Z C Yue and S G Ming ldquoResearch advances anddebates on tubular mechanics in oil and gas wellsrdquo JournalPetroleum Science and Engineering vol 151 pp 194ndash2122017

[29] L J Yuan and L Z Feng Prediction and Diagnosis of Sucker-Rod Pumping Systems in Directional Wells SPE 57014 So-ciety of Petroleum Engineers Dallas TX USA 1999

[30] L Z Feng L X Sheng Z D Qian and Z S Nan A SteadyTension-Torque Model for Drillstring in Horizontal Wells SPE26295 Society of Petroleum Engineers Dallas TX USA 1993

[31] H G Lu Study on Drillstring Torsional Vibration in ExtendedReached Well University of Petroleum Dongying China2002

[32] H S Ho ldquoAn improvedmodeling program for computing thetorque and drag in directional and deep wellsrdquo ldquo in Pro-ceedings of the SPE Annual Technical Conference andExhibition Houston TX USA October 1988

[33] W X Ming P Chen H W Zhi and Z J Yan ldquoDevelopmentof torque clutch drilling tool and evaluation of drag reductionperformancerdquo Advances in Mechanical Engineering vol 10pp 1ndash20 2018

[34] MW DykstraNonlinear Drill String Dynamics University ofTulsa Tulsa OK USA 1996

[35] H Y Bao D Q Feng Z W Ping C Z Feng andW W Chang ldquoDynamic characteristics analysis of drillstringin the ultra-deep well with spatial curved beam finite ele-mentrdquo Journal of Petroleum Science and Engineering vol 82pp 166ndash173 2012


A drill pipe bearing sub is affected by the wellbore qualityand the installation number resulting in a poor drag-re-duction effect [13ndash15] For instance a hydraulic oscillator islimited by the high circulating pressure loss and the shortservice life Moreover a high-frequency vibration can easilydamage downhole measuring instruments [16ndash18] An RSShas significant and potential risks of sticking and buryingassociated with its own structural defects and its service costis comparatively high [19ndash21] Large-scale applications andpromotions are yet to be realized for a drill string rockingsystem because the friction-reducing mechanism and theautomatic control technology are not thoroughly under-stood [22ndash24] +erefore a complete understanding of thedefects of the existing mechanical drag-reduction technol-ogy is developed and an in-depth study on the mechanismof friction reduction in horizontal wells is conducted Fi-nally based on the principle of friction reduction by a rotarydrill string a novel controllable hybrid steering drillingsystem (CHSDS) is developed which can switch freelybetween meshing and separation states by receiving re-motely controlled commands from the ground

In the evaluation of the effect of drag-reduction systemsit is necessary to determine the corresponding boundaryconditions and build a mechanical model according to theactual working state of the drilling system being examined[25] Because there are two working states of meshing andseparation in the actual drilling of the CHSDS the boundaryconditions of the traditional drag torquemodel are no longerapplicable +erefore the existing friction torque predictionmodel cannot be directly used to evaluate the drag-reductioneffect of the CHSDS

+erefore based on the actual working conditions of theCHSDS the boundary conditions of its separation ormeshing states and of the bit are determined +e drag-reduction performance of the CHSDS is analyzed bycombining with the classical drag torque model of the drillstring +e field test verifies the remote separation andmeshing functions of the CHSDS providing the basis for thedrag-reduction performance test and the subsequent ap-plication of the CHSDS

2 Operating Principle and Structure of CHSDS

21 Operating Principle of CHSDS During the slidingdrilling process of the conventional sliding steering drillingsystem the bottom hole assembly (BHA) is as shown inFigure 1(a) It comprises a bit bent sub positive displace-ment motor (PDM) and measurement while drilling(MWD) +e drill string does not rotate but slides along theaxis of the borehole wall +e deviation and azimuth anglesof the wellbore are changed by the sliding of the steering toolface thereby controlling the wellbore trajectory When theactual wellbore trajectory deviates from the designed oneand needs to be adjusted the rotary table is manuallycontrolled to rotate it an angle to rotate the tool face of thedrill tool assembly to the specified direction

An RSS can be classified into push-the-bit and point-the-bit according to the steering mode When the push-the-bitsystem operates it controls three wing ribs to push against

the well wall according to the actual well deviation azimuthdata and predetermined well trajectory this ensures the bitpoints to the direction to be drilled+e point-the-bit systemdepends on the biasing mechanism inside the RSS to bias themandrel therefore there is an angle between the axes of therotating drill string and borehole Finally rotary steering isrealized by the rotation angle of the drill bit As shown inFigure 1(b) the RSS rotates while drilling which transformsthe axial friction of the drill string into circumferentialfriction torque thus reducing the friction resistance of thedrill string

As can be seen from Figure 1(c) the steering method ofthe CHSDS is the same as the conventional sliding steeringdrilling method +e inclination and azimuth angles of thewell are controlled by a rotating turntable in the meshingstate In the drag-reduction drilling mode when the systemis in the separation state the upper drill string rotates toconvert the axial friction part of the drill string into thecircumferential friction torque+is significantly reduces thedrill string friction which is similar to rotary steeringdrilling +e lower drill string slide drills with the stable toolface +erefore the CHSDS includes three working modes

(1) Conventional sliding steering drilling mode(meshing)

(2) Conventional rotating drilling mode (meshing)(3) Controllable hybrid steering friction-reducing mode

(separation)

22 Structural Design of CHSDS +e CHSDS is mainlycomposed of a measurement and control system hydraulicsystem and clutch unit +e structure is shown in Figure 2

+e functions of the measurement and control systemare to detect the mud pressure pulse identify the groundcommand start the motor and solenoid valve drive circuitand move the piston in a predetermined direction of theground Moreover the system should realize effective sep-aration or engagement of the tool clutch device and effec-tively control the working mode of the drag-reduction toolon the ground

As shown in Figure 2(a) the measurement and controlsystem mainly includes pressure pulse detection signalfiltering and amplification AD conversion a micro-controller and a motor solenoid valve drive circuit

+e main roles of the hydraulic system are to execute theinstruction of the downhole microcontroller inject hy-draulic oil into a specified oil cylinder and drive the pistonto move in the predetermined direction It can be seen fromFigure 2(b) that it is mainly composed of a hydraulic cyl-inder motor and pump pressure relief valve 32 solenoidvalve check valve and double-acting oil cylinder

+e main objective of the clutch unit is to separate ortransfer the torque from the upper drill string to the lowerdrill string As shown in Figure 2(c) it mainly includes aninternal gear an outer gear a piston shaft a clutch outercylinder and a bearing bush +e hydraulic system drivesthe piston shaft to move back and forth to drive theseparation and meshing of the internal and outer gears to





















PDM+bent sub

Derrick Ground


MWD

(a)

RSSMWD

(b)

CHSDSPDM+

bent subMWD

(c)





dMt

ds f1RoN + m0

dTt

ds+ kbEI

dkb


g middot e

t 0

minusd2Mb


g middot e

n 0


dsminus kn

dMb


g middot e

b 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

where

f1 ωRof

v2

+ ωRo( 11138572

1113969

f2 vf

v2

+ ωRo( 11138572

1113969

N

N2n + N

2b

1113969

C 2πμ

ln Dw2Ro

mo 2πωR3o

τ

v2

+ ωRo( 11138572

1113969 +2μ

Dw minus 2Ro

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦

B 2πRoτv

v2

+ ωRo( 11138572

1113969

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)



e

g middot e

t cos α

e

g middot e

n kα

kb

sin α

e

g middot e

b minuskφ

kb

(sin α)2

e

g minuscos α e

t +kα

kb

sin α e

n +kφ

kb

(sin α)2

e

b

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where e

t e

n and e





dMt

ds f1RoN + m0

dTt

ds+ kbEI

dkb


minusd2Mb


kα

kb

sin α 0

minuskb

dMt


kφ

kb

sin2 α 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





T s sN( 1113857 minusWOB1113896 (5)







T s sTU( 1113857 T s sTL( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)


MOil tank Motorand

pump

Reliefvalve

Checkvalve



Clutchsystem



system

Gear pairs meshing



IO


Power



detection

(a)

(b)

(c)







T s sTU( 1113857 T s sTL( 11138571113896 (7)





⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(8)
























Mt (s = sT) = MTU


Mt (s = sT) = MTL




















Vert

ical

dep

th (m

)


3500

3000

2500

2000

1500

1000

500

0

(a)

0

400

800

1200

1600

2000

Nor

th co

ordi

nate

s (m

)


(b)


Dra

g (k

N)

1000 2000 3000 4000 50000Well depth (m)

ndash400

ndash200

0

200

400

600

800

1000




Dra

g di

ffere

nce (

kN)

050

100150200250300350400450500550

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)


Torq

ue (k

Nmiddotm

)

1000 2000 3000 4000 50000Well depth (m)

0

5

10

15



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

14

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

BHA1BHA2



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN



5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3





















































PDM+bent sub

Derrick Ground


MWD

(a)

RSSMWD

(b)

CHSDSPDM+

bent subMWD

(c)





dMt

ds f1RoN + m0

dTt

ds+ kbEI

dkb


g middot e

t 0

minusd2Mb


g middot e

n 0


dsminus kn

dMb


g middot e

b 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

where

f1 ωRof

v2

+ ωRo( 11138572

1113969

f2 vf

v2

+ ωRo( 11138572

1113969

N

N2n + N

2b

1113969

C 2πμ

ln Dw2Ro

mo 2πωR3o

τ

v2

+ ωRo( 11138572

1113969 +2μ

Dw minus 2Ro

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦

B 2πRoτv

v2

+ ωRo( 11138572

1113969

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)



e

g middot e

t cos α

e

g middot e

n kα

kb

sin α

e

g middot e

b minuskφ

kb

(sin α)2

e

g minuscos α e

t +kα

kb

sin α e

n +kφ

kb

(sin α)2

e

b

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where e

t e

n and e





dMt

ds f1RoN + m0

dTt

ds+ kbEI

dkb


minusd2Mb


kα

kb

sin α 0

minuskb

dMt


kφ

kb

sin2 α 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





T s sN( 1113857 minusWOB1113896 (5)







T s sTU( 1113857 T s sTL( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)


MOil tank Motorand

pump

Reliefvalve

Checkvalve



Clutchsystem



system

Gear pairs meshing



IO


Power



detection

(a)

(b)

(c)







T s sTU( 1113857 T s sTL( 11138571113896 (7)





⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(8)
























Mt (s = sT) = MTU


Mt (s = sT) = MTL




















Vert

ical

dep

th (m

)


3500

3000

2500

2000

1500

1000

500

0

(a)

0

400

800

1200

1600

2000

Nor

th co

ordi

nate

s (m

)


(b)


Dra

g (k

N)

1000 2000 3000 4000 50000Well depth (m)

ndash400

ndash200

0

200

400

600

800

1000




Dra

g di

ffere

nce (

kN)

050

100150200250300350400450500550

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)


Torq

ue (k

Nmiddotm

)

1000 2000 3000 4000 50000Well depth (m)

0

5

10

15



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

14

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

BHA1BHA2



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN



5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3




































dMt

ds f1RoN + m0

dTt

ds+ kbEI

dkb


g middot e

t 0

minusd2Mb


g middot e

n 0


dsminus kn

dMb


g middot e

b 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

where

f1 ωRof

v2

+ ωRo( 11138572

1113969

f2 vf

v2

+ ωRo( 11138572

1113969

N

N2n + N

2b

1113969

C 2πμ

ln Dw2Ro

mo 2πωR3o

τ

v2

+ ωRo( 11138572

1113969 +2μ

Dw minus 2Ro

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦

B 2πRoτv

v2

+ ωRo( 11138572

1113969

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)



e

g middot e

t cos α

e

g middot e

n kα

kb

sin α

e

g middot e

b minuskφ

kb

(sin α)2

e

g minuscos α e

t +kα

kb

sin α e

n +kφ

kb

(sin α)2

e

b

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where e

t e

n and e





dMt

ds f1RoN + m0

dTt

ds+ kbEI

dkb


minusd2Mb


kα

kb

sin α 0

minuskb

dMt


kφ

kb

sin2 α 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





T s sN( 1113857 minusWOB1113896 (5)







T s sTU( 1113857 T s sTL( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)


MOil tank Motorand

pump

Reliefvalve

Checkvalve



Clutchsystem



system

Gear pairs meshing



IO


Power



detection

(a)

(b)

(c)







T s sTU( 1113857 T s sTL( 11138571113896 (7)





⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(8)
























Mt (s = sT) = MTU


Mt (s = sT) = MTL




















Vert

ical

dep

th (m

)


3500

3000

2500

2000

1500

1000

500

0

(a)

0

400

800

1200

1600

2000

Nor

th co

ordi

nate

s (m

)


(b)


Dra

g (k

N)

1000 2000 3000 4000 50000Well depth (m)

ndash400

ndash200

0

200

400

600

800

1000




Dra

g di

ffere

nce (

kN)

050

100150200250300350400450500550

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)


Torq

ue (k

Nmiddotm

)

1000 2000 3000 4000 50000Well depth (m)

0

5

10

15



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

14

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

BHA1BHA2



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN



5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3



































T s sN( 1113857 minusWOB1113896 (5)







T s sTU( 1113857 T s sTL( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)


MOil tank Motorand

pump

Reliefvalve

Checkvalve



Clutchsystem



system

Gear pairs meshing



IO


Power



detection

(a)

(b)

(c)







T s sTU( 1113857 T s sTL( 11138571113896 (7)





⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(8)
























Mt (s = sT) = MTU


Mt (s = sT) = MTL




















Vert

ical

dep

th (m

)


3500

3000

2500

2000

1500

1000

500

0

(a)

0

400

800

1200

1600

2000

Nor

th co

ordi

nate

s (m

)


(b)


Dra

g (k

N)

1000 2000 3000 4000 50000Well depth (m)

ndash400

ndash200

0

200

400

600

800

1000




Dra

g di

ffere

nce (

kN)

050

100150200250300350400450500550

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)


Torq

ue (k

Nmiddotm

)

1000 2000 3000 4000 50000Well depth (m)

0

5

10

15



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

14

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

BHA1BHA2



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN



5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3





































T s sTU( 1113857 T s sTL( 11138571113896 (7)





⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(8)
























Mt (s = sT) = MTU


Mt (s = sT) = MTL




















Vert

ical

dep

th (m

)


3500

3000

2500

2000

1500

1000

500

0

(a)

0

400

800

1200

1600

2000

Nor

th co

ordi

nate

s (m

)


(b)


Dra

g (k

N)

1000 2000 3000 4000 50000Well depth (m)

ndash400

ndash200

0

200

400

600

800

1000




Dra

g di

ffere

nce (

kN)

050

100150200250300350400450500550

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)


Torq

ue (k

Nmiddotm

)

1000 2000 3000 4000 50000Well depth (m)

0

5

10

15



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

14

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

BHA1BHA2



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN



5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3













































Mt (s = sT) = MTU


Mt (s = sT) = MTL




















Vert

ical

dep

th (m

)


3500

3000

2500

2000

1500

1000

500

0

(a)

0

400

800

1200

1600

2000

Nor

th co

ordi

nate

s (m

)


(b)


Dra

g (k

N)

1000 2000 3000 4000 50000Well depth (m)

ndash400

ndash200

0

200

400

600

800

1000




Dra

g di

ffere

nce (

kN)

050

100150200250300350400450500550

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)


Torq

ue (k

Nmiddotm

)

1000 2000 3000 4000 50000Well depth (m)

0

5

10

15



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

14

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

BHA1BHA2



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN



5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3


















































Vert

ical

dep

th (m

)


3500

3000

2500

2000

1500

1000

500

0

(a)

0

400

800

1200

1600

2000

Nor

th co

ordi

nate

s (m

)


(b)


Dra

g (k

N)

1000 2000 3000 4000 50000Well depth (m)

ndash400

ndash200

0

200

400

600

800

1000




Dra

g di

ffere

nce (

kN)

050

100150200250300350400450500550

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)


Torq

ue (k

Nmiddotm

)

1000 2000 3000 4000 50000Well depth (m)

0

5

10

15



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

14

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

BHA1BHA2



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN



5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3


































Dra

g di

ffere

nce (

kN)

050

100150200250300350400450500550

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)


Torq

ue (k

Nmiddotm

)

1000 2000 3000 4000 50000Well depth (m)

0

5

10

15



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

14

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

BHA1BHA2



Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN



5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3


































Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

200 m250 m300 m


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

60 rpm30 rpm10 rpm


Dist

ribut

ed fr

ictio

n (k

Nm

)

00

02

04

06

08

10

12

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

120 kN80 kN20 kN



5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3


































5 Conclusion






Data Availability




Acknowledgments


References








500 1000 1500 2000 2500 3000 3500 4000 4500 50000Well depth (m)

00

02

04

06

08

10

12

14

Dist

ribut

ed fr

ictio

n (k

Nm

)

2200 kgm3

1800 kgm3

1200 kgm3


































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