Dynamical Modelling of the Drill-string Torsional Vibrations Conference... · Dynamical Modelling of the Drill-string Torsional Vibrations ... Forward and backward Whirling, bending

Dynamical Modelling of the Drill-string Torsional

Vibrations

Centre for Applied Dynamics Research (CADR) Department of Engineering

University of Aberdeen

Mohammad Hossein Khodadadi Dehkordi

[email protected]

Supervisors:

Professor Marian Wiercigroch

mailto:[email protected]

ETP Annual Conference-10th October 2017

Drill-string Vibrations Vibration types Axial Vibration: Bit bounce Damage bit cutters and bearings

Torsional Vibration: Stick-Slip Fatigue drill collar connection, damage bits, unstable drilling, decrease ROP

Lateral Vibrations: (instability or unbalance) Forward and backward Whirling, bending connection fatigue, over-gage borehole, accelerates wear, PDC cutter to chip

From: Schlumberger (www.slb.com), drill-string vibration and vibration modeling

angular vibration of drill-string along its axis of rotation

Vibrations of drill-string

http://www.slb.com/


Tool consists of: Helical spline Axial spring continuously control the weight to maintain a steady load by converting excess torque on bit into axial displacement of the drill-bit and prevent the bit from stalling and manage depth of cut (DOC) in the drillbit

From: Tomax user manual

The way AST works


http://www.tomax.no/resources/animations-in-well/

Movie shows stick-slip and application of AST

http://www.tomax.no/resources/animations-in-well/


Field results provided by TOMAX Field Results AST and PDC

Application of the tool in industry


From: Tomax performance report available at www.Tomax.no

Effect of AST on downhole stick-slip

http://www.tomax.no/


proposed project is to develop a mathematical model for this tool 1- Model drill-string 2- Find stick-slip (by using parameters) 3- Model AST by doing experiment 4- Apply AST to the model with having Stick-slip and show the system response

Defined project

The project:


Drill-string The combination of the drillpipe, the bottomhole

assembly and any other tools used to make the drill bit turn at the bottom of the wellbore.

Normally consists of: Drill pipes BHA Bit (main point of friction and vibration creation) Drill-string model: How stick-slip occurs (Self excited vibration) Reduced to lumped model of 2 discs and one

spring (linear equations) Bik-Rock equation is nonlinear

From: Aberdeen university CADR group

Drillstring components and stick-slip


Dynamical model of drilling string based on torsional pendulum Equation of motion Rotary: Jrr=Tm-TFR-c(rb)-k(rb) Equation of motion BHA: Jbb=-TFB-c(br)-k(br)

Drill-string model including friction model

Drill-string model

Teb= c(rb) + k(rb)-cb.b fb(b)=Rb.WOB.[cb+(sb-cb)..b] Tsb=Rb.WOB.sbStatic friction Tcb=Rb.WOB.cbDynamic friction

TFB=dry friction (Tfb) + viscous friction (Tvb) at bit, (Tvb=cbb)

Torque vs bit velocity


Time history showing stick-slip starting from zero initial conditions Between the vertical lines, the bit reaches zero velocity, and as the relative displacement continues to increase, the torque profile (dark blue) shows a corresponding increase, until the bit breaks free.

Time histories showing stick-slip


Parameter sensitivity study for WOB 10N to 200N showing coexistence (With initial condition zero and close to stable drilling)

Analysis of system by changing WOB and initial conditions


Phase portrait by changing WOB

Effect of decreasing WOB for stick-slip (Shows the AST application)

1. Decreasing WOB=> decrease friction

2. less energy require to free the bit

3. Required relative displacement decrease

Eventually there would be stable solution

50N


Effect of variable WOB on friction

1. Decreasing WOB=> decrease friction

2. Maximum static fricytion will reduce (Tsb=Rb.WOB.sb), less torque requires to free the bit

Friction by changing WOB

Does this model capture the drill-string/borehole integration? Why it is important?


Drilling parameters for experiment


Experimental validation in lab

From: V Vaziri PhD thesis

Scaled model of drill-string to use for experiment: Shaft stiffness when its

scaled down? Drill-string behaviour

when bit sticks? Helical buckling

How stiffness will be

affected? Need to know to use correct shaft with equivalent stiffness and order the tool, model it, and test it


Numerical model of buckling of rod


Numerical model of buckling

Verification of numerical model? with a rod


Analytical Calculations Torsional Stiffness Calculations

k=

kis torsional stiffness (

),

Jis torsional constant (m4),

Gis the rigidity modulus (Pa),

L is length (m).

Steel Shear Modulus G (78GPa), L= 3

= 32

(4)=> = 32

(0.064)= 1.2710-6m4

k= 33

Analytical Calculations


Analytical Calculations Buckling Torque Calculations

2

2=

2

42+

2

2

B=E.I,

E is Young's modulus (Pa),

K is buckling torque (Nm),

K is Axial load

L is length (m),

I is area moment of inertia (m4)

L= 3m, R=0, r=0.03m young's modulus steel (E=210 Gpa)

l=4

(4)=4

(0.034)=6.3610-7

K= 280 kNm x

y

z

Rk

k

R

Analytical Calculations


Numerical analysis boundary conditions Sensitivity analysis on total

number of elements (Mesh):

T

Top: Fixed

Bottom: Free in ( ) directions x,y,z

MeshA 3248:

MeshB: 4920

MeshC: 11360

MeshD: 19800

k

Number of elements

Length= 3m

Sensitivity Analysis


Results for sensitivity analysis 1 Cases Number

of Elements

Length [m]

Diameter [m]

Analytical Buckling Torque [kNm]

Numerical Buckling Torque [kNm]

Analytical Torsional Stiffness

[kNm/rad]

Numerical Torsional Stiffness

[kNm/rad]

K1 K2 K3

Mesh A 3248 3 0.06 280 280 33 38 38 39

Mesh B 4920 3 0.06 280 280 33 38 38 39

Mesh C 11360 3 0.06 280 280 33 36 36 37

Mesh D 19800 3 0.06 280 280 33 35 35 36

Results 1


Sensitivity analysis on total number of seeds along the length: Decreasing the aspect ratio

T

Top: Fixed

Bottom: Free in ( ) directions x,y,z

Mesh 200C1:

MeshC2: 300

MeshC3: 400

MeshC4: 450

k

Number of seedsalong the length

Length= 3m

Sensitivity Analysis


Results for sensitivity analysis 2 Cases Number

of Seeds on

Length

Length [m]

Diameter [m]

Analytical Buckling Torque [kNm]

Numerical Buckling Torque [kNm]

Analytical Torsional Stiffness

[kNm/rad]

Numerical Torsional Stiffness

[kNm/rad]

Mesh C1 200 3 0.06 280 280 33 34

Mesh C2 300 3 0.06 280 280 33 34

Mesh C3 400 3 0.06 280 280 33 33.5

Mesh C4 450 3 0.06 280 280 33 33

Results 2

Mesh C4 shows matching of analytical and numerical solutions K after buckling?

34 kNm/rad


Completed tasks: 1- Modelling of drill-string based on torsional vibration 2 DOF 2- Modelling the bit-rock friction with Stribeck friction law also by inclusion of Karnopp switching model into it 3- Showing the different trajectories for the system for stick-slip, sensitivity analysis and bifurcation diagram, also showing the coexistence 4- Showing how the AST can minimise the stick-slip 5- Rod buckling analysis to capture drill-string and borehole interaction 6- Numerical and analytical match of a rod under torsional force

completed


Future plans: 1- Adding a wall to the rod (casing) and capture the response of the rod stiffness during the helical buckling 2- Inclusion of the scaled AST to the drill-string model and doing parameter variation on the tool and show its response 3- optimising the tool

Future Work


Thank you

Questions?


stick-slip: severe form of torsional vibration of the drill-string

Results in: Bit stall Decrease ROP (rate of penetration meter/hour) Decrease the integrity of the drilled hole Decrease the lifetime of downhole equipment In severe cases it can result in catastrophic damages

Impact of the stick-slip phenomenon


By having borehole and drill-string interaction and considering the friction, the pipe torsional stiffness will rise T-Tf-=K. T=(K+Tf). =>T=Keq. K : nonlinear Tf: nonlinear Solutions: K : the materials behaviour will be similar (nonlinear after buckling) Tf : a wall should be added to the experiment rig, get a numerical and analytical match


Using the MATLAB to solve the equations

The model parameters used in MATLAB are: Tm=8.3N.m, Jr =0.518kg.m2, Jb = 0.0318kg.m2, c =0.0001N.m.s/rad,, k = 0.073N.m/rad, cr = 0.18N.m.s/rad, cb = 0.03N.m.s/rad, cb=0.5, sb =0.8, WOB=60N, Rb=0.1m, =0.9, Dv =10-6

Initial condition zero top and bottom velocity, and zero relative displacement which means no initial top speed, relative displacement and bottom speed receptivity

Parameters used


BHA

Drill-string consisting of (from the bottom up in a vertical well) Bit Bit sub Mud motor (in certain cases) Stabilizers Drill collar Heavy-weight drillpipe (HWDP) Jarring devices ("jars") and crossovers for various thread form measurements-while-drilling (MWD), logging-while-drilling (LWD) other specialized devices

BHA components


Wall moving-Spring-Mass with friction Stick

FspringFfriction


Dynamical modeling of drill-string without AST Assumptions: Main point of friction is Bit, friction between drill-string components and bore

hole is negligible in compare with bit and well Vertical well (no lateral movement) Inertia of bottom and rotary table considered The drill-string considered as series springs with having one equivalent stiffness

and damping to show the response of the system (one spring and damper) (Continues system of pipes and BHA are considered as a torsional pendulum with 2 degrees of freedom) Increasing the length of drilling string is not considered (for now)

Dynamical approach


Stick-Slip Stick-slip is a severe form of torsional vibration of the drill-string

caused by an overtorque at the interface between the formation and the drill bit that creates numerous difficulties which can ultimately degrade the safety of the drilling operations

What does it mean?

Torsional vibration


Initiates when frictional forces preventing the drill bit from rotating for a moment

Now, bit is in stick phase, while rotary table continues

spinning, applying torque continuously (energy stores and twists the drill-string) until static friction (transient)

Apply torque becomes more than static friction bit breaks

free and overshoots (slip phase) Because it overshoots it slow down and stick again Repeat again!

Why bit stops and initiates this cycle?

Stick-slip stages


Going to stick phase: Drilling normal

Encountering hard rock Increases dynamic friction while drive torque is constant

Bit slows down and stops from rotation (Sticks) Friction coefficient switches to from dynamic to static

Static friction> dynamic friction More energy requires to rotate the bit

When Torque (or energy stored at the bottom of drill pipe)> static friction, Bit overshoots (higher speed than the rotary table)

Friction coefficient switches from static to dynamic

Stick-slip stages


How to identify stick-slip? Inertia rotary table is high=> absorbs vibrations and reflect it back down MWD and LWD

Torque and Rotation (RPM) fluctuations Better to be prevented Fish? (severe forms which spins out or breaks a joint of drill-string)

Identification of stick-slip


Dynamical model of drilling string based on torsional pendulum Tk= k(r b) Spring torque Tc= c(rb) Damping torque Newton law of motion for torsional pendulum: Jii=Ti TFB is dissipative energy =dry friction (Tfb) + viscous friction (Tvb) at bit, (Tvb=cbb) TFRis dissipative energy =dry friction (Tfr) + viscous friction (Tvr) at rotary, (Tvr=crr) Tm is the drive torque by rotary table or top drive Tr= (Tm-TFR) Tb= (-TFB)

Equation of motion Rotary: Jrr=Tm-TFR-c(rb)-k(rb)

Equation of motion BHA: Jbb=-TFB-c(br)-k(br)

Drill-string model

Drill-string model


Friction model bottom Tfb (bit-rock) The bitrock contact is proposed as a variation of the Stribeck friction together with the dry friction model. (As b Increases friction bottom decays exponentially from static friction to coulomb friction) The dry friction model when b=0, is approximated by a combination of the switch model proposed and the model in which a zero velocity band is introduced (Karnopp) which almost matches the real interaction of bit-rock:

Tfb(b)

b bl0 ,WOB is weight on bit, 0< cb< sb


Hysteresis between the two responses of stable drilling and stick-slip Choosing different initial conditions for WOB of 80N, can have both stable drilling and stick-slip. The green point in the middle is the stable drilling since there are not any zero velocities and high oscillations, and the red line is the stick-slip line. Choosing different initial conditions can lead the system into stick-slip or stable drilling

Phase portrait by changing initial conditions


Time history shows stick-slip with initial conditions, zero top and bottom velocity, and zero relative displacement. The bit has zero velocities periodically with high oscillations (stick-slip)

Phase portrait with stick-slip for initial conditions, zero top and bottom velocity, and zero relative displacement. It can be identified by having zero velocity while the relative displacement is increasing

Torque on bit which is the total friction at bit at different velocities. To breakfree the bit and initiate the motion, the drive toque (Teb) must exceed the static friction torque (Tsb). After that the friction declines exponentially by increasing the bit velocity but rises again due to viscous friction at higher speeds

Stick-slip results


Scaling down table


G: In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or , is defined as the ratio of shear stress to the shear strain pas=N.m-2=kg.m-1.s-2

Rigidity modulus


The torsion constant is a geometrical property of a bar's cross-section which is involved in the relationship between angle of twist and applied torque along the axis of the bar

Torsion constant


Flexural regidity

B=E.I B: Flexural rigidity is defined as the force couple required to bend a non-rigid structure in one unit of curvature or it can be defined as the resistance offered by a structure while undergoing bending

Dynamical Modelling of the Drill-string Torsional VibrationsCentre for Applied Dynamics Research (CADR)Department of EngineeringUniversity of Aberdeen Drill-string VibrationsSlide Number 3http://www.tomax.no/resources/animations-in-well/Slide Number 5Slide Number 6Slide Number 7Slide Number 8Dynamical model of drilling string based on torsional pendulum Slide Number 10Parameter sensitivity study for WOB 10N to 200N showing coexistence (With initial condition zero and close to stable drilling) Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Thank youSlide Number 27Slide Number 28Using the MATLAB to solve the equationsBHAWall moving-Spring-Mass with frictionDynamical modeling of drill-string without ASTStick-SlipSlide Number 34Going to stick phase:How to identify stick-slip? Dynamical model of drilling string based on torsional pendulum Friction model bottom Tfb (bit-rock)Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44

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Dynamical Modelling of the Drill-string Torsional Vibrations Conference... · Dynamical Modelling of the Drill-string Torsional Vibrations ... Forward and backward Whirling, bending