control de vibraciones en sarta de perforaci´oncontrol de vibraciones en sarta de perforaci´on...

Control de Vibraciones en

Sarta de Perforacion

Miguel Angel Corchero, Francisco Rodrıguez RubioEn colaboracion con Carlos Canudas-de-Wit

Dpto. Ingenierıa de Sistemas y AutomaticaEscuela Superior de Ingenieros

Universidad de Sevilla

JIC’06 - Pamplona - Marzo - 2006

D-OSKIL: A New Me hanism for Suppressing Sti k-Slip

OUTLINE

� Introdu tion.� System Des ription.� System Model.� Velo ity Control.� Sti k-Slip Predi tion based on DF-Analysis.� Drilling Os illation Killer Me hanism.� Con lusions and Future Work.

CDC-ECC'05 - Sevilla - De ember 2005 2


INTRODUCTION� Ri h dynami al behavior.� Display sti k-slip self-ex itedos illations.� Redu ing os illations yield substantial ost savings.� Paper fo used in torsional sti k-slipos illations.Rotatory speed of utting devi e � [0; 6!d℄� Phenomenon mainly due to fri tion.



Contributions On Reje ting Os illations� Varying di�erent drilling parameters (rotary speed, WoB, mud, ...)[Sananikone 1992, Pavone 1994 ℄.{ Not formal analysis.{ Good performan e results.� New ontrols to ompensate sti k-slip.{ Soft Torque Rotatory System [Halsey 1988 ℄.{ Top vibration absorber [Jansen 1995 ℄.{ Linear H1 ontrol [Serrarens 1998 ℄.{ ...� Use WoB as a new ontrol variable.CDC-ECC'05 - Sevilla - De ember 2005 4


SYSTEM DESCRIPTION� Rotatory Table moved by DCmotor at onstant velo ity.� Bit oupled by a elasti shaft alledDrillstring.{ Upper part: Sequen e of tubes.{ Lower part: BHA.� Mud pumped to lubri atethe onta t.� Total normal for e alled WoB.� Fri tion torque at Bit alled ToB.

motor

rotatory table

drillstring

drillcollar

bit

mud

transmision



SYSTEM MODEL

� Lumped parameter model.� Torsional behavior model.� Two degrees of freedom.� Drilling Rig modelled by an elasti shaft.� ToB = normal for e � fri tion.

Jr �'r + ( _'r � _'b) + k('r � 'b) + dr _'r = vJb �'b + ( _'b � _'r) + k('b � 'r) + db _'b = ��(�)uCDC-ECC'05 - Sevilla - De ember 2005 6


Fri tion Torque and State-Spa e modelFri tion at the bit (LuGre Model)� u = ~u+ u0: Total WoB.� u0: Nominal WoB.� ~u: Control signal.� �( _'b; z): Normalized torque.ToB = �( _'b; z) � u�( _'b; z) = �0z + �1 _z_z = _'b � �0 j _'bjg( _'b)z;g( _'b) = �C + (�S � �C)e�( _'b=vs)2

State-Spa e Model

_x = Ax+Bv +H�(x; z)u_z = f(x; z)A = 0BB� 0 1 �1�kJr � (dr+ )Jr JrkJb Jb � ( +db)Jb

1CCA

B = h 0 1Jr 0 iTH = h 0 0 �1Jb iT



VELOCITY CONTROL� Rotary velo ity regulated todesired value ( _'r ! !d)� Standard ontrol form[Christoforou 2003 ℄� Gains designed using 2-time-s aleseparation method.� Equations in losed-loop:_x = A lx+B l!d +H l�(x; z)u_z = f(x; z)

Qualitative Behavior

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30Stick−Slip simulation

Time [s]

Rot

ator

y S

peed

[rad

/s]

surface

downhole



Di�erent Behaviors(lo al stability - lo al attra tive limit y le)

0 20 40 60 80 100 120 140 160 180 2000

5

10

15

Time [s]

Rot

ator

y S

peed

[rad

/s]

Unstable limit cycle produced by perturbation on WoB

0 20 40 60 80 100 120 140 160 180 2000

5

10

15

Time [s]

Rot

ator

y S

peed

[rad

/s]

Stick−Slip cycle produced by perturbation on WoB

surfacedownhole

surfacedownhole

Change on WoB

Change on WoB

Equilibrium Domain

Stable Orbit CDC-ECC'05 - Sevilla - De ember 2005 9


STICK-SLIP PREDICTION BASED ON DF-ANALYSIS� Use of SBDF to predi t limit y le.� Steady-state hara teristi of LuGre fri tion model.Harmoni balan e:G(j!0) = �1N1(A0; !0; y0)y0 [1 +G(0)N0(A0; y0)℄ = W (0)!dy0 = W (0)[1 +G(0)N0(A0; y0)℄!d = !dIm fG(j!0)g = 0Re fG(j!0)g = � 1N1(A;!d)CDC-ECC'05 - Sevilla - De ember 2005 10


Des ribing Fun tion Analysis� Points jp0j; jp1j � 1WoB� Two sets of limit y les predi ted.� Control by modifying !n:{ !n upper bounded by noise and power onstraints.{ !n lower by poor performan e.� Control by keeping WoB small:{ High-performan e drilling requires WoBlarge.{ Knowledge of map [!n;WoB℄.CDC-ECC'05 - Sevilla - De ember 2005 11


The Sti k-Slip Os illations� High-performan e drilling intoos illation zone.� System traje tories at equilibrium.� Perturbations may ause limit y les.� Os illation eliminated by de reasingWoB.� Lo al attra tion domain is enlarged.� WoB returns slowly to nominal valueagain. 0 10 20 30 40 50 60 700

1

2

3

4

5

6

7x 10

4 Stable WoB − wn domain

wn [rad/s]

WoB

[N]

Oscillations zone

prediction

simulation



Possible System Traje tories



DRILLING OSCILLATION KILLER MECHANISM� Output re e ting the sti k-slip.� Filter F (s) extra ts bias and mainos illatory omponent.� Compute RMS value.� Control law for es u(t) 2 [0; u0℄.� Os illation frequen y estimator.

Oil Well

Drillstring

RMS

value

External

disturbances

yu0

Band-pass

filter

~

Drilling Oscillator Killer

D-OSKIL

Frequency

Estimator

u

u

Adaptation

with

saturation

yf = F (s) � Cx = F (s) � _'b 1� _~u = �~u� satu00 (KI�); ~u(0) = 0� = Z t+Tt y2f (�)d� u = u0 + ~u



DOSKIL Typi al Operation (Simulation)

0 20 40 60 80 100 120 140 160 180 200−20

0

20

40

y(t)

Operation under OSKIL

0 20 40 60 80 100 120 140 160 180 200−40

−20

0

20

40

y f and

ζ

0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

4

u 0 − u

Time (sec)

Activation of theOSKIL mechanism

Os illation vanishes. WoB re overs nominal value.



CONCLUSIONS AND FUTURE WORK

� WoB as additional ontrol variable.� Sti k-slip behavior insight using SBDF.� Simulations show os illations eliminated.� Redesign of velo ity ontrol notne essary.� Stability analysis under investigation.� S aled Drillstring platform is being built. ��M1

M2 �CDC-ECC'05 - Sevilla - De ember 2005 16

Os ila iones en una sarta de perfora i�onEstabilidadModelo de error: _e = A le+H l [�(e3)~u+ ~�(e3)u0℄_~u = ��~u+�(�) on ~�(e3) = �(e3)� ��.

G : � = �~u1 � ~u2 7! y = e3

A : y 7! ~u1 = �(e3)~u

� : y 7! ~u2 = ~�(e3)u020 de Enero 2005 13

Os ila iones en una sarta de perfora i�on

Sistema Lineal Perturbado� De�ni i�on: _e = A le+ g(t; e)g(t; e) = H l(~u1 + ~u2)� Perturba i�on a otada: jj~u1jj1 = supt�0 j~u1j = supt�0 j�(�)j � j~uj � u0 <1jj~u2jj1 = supt�0 j~u2j = supt�0 j~�(�)j � ju0j � 2 � u0 <1jjg(t; e)jj � jjH ljj � [jj~u1jj+ jj~u2jj � 3jjH ljju0℄� Los estados est�an a otados: jje(t)jj � Æ Æ > 0; 8t > 0

20 de Enero 2005 14


Fun i�on de Transferen ia G(s)

� De�ni i�on: G(s) = �C(sI �A l)�1H l� Expresi�on: G(s) = s(a2s2+a1s+a0)b4s4+b3s3+b2s2+b1s+b0� Cara ter��sti a: Fun i�on SPR.{ 9P; Q > 0 s:t AT lP + PA l = �Q{ PH l = �C{ G : �! y es pasivo onV (e) = eTPe{ G : �! y tiene ganan iaL2 finita 2(G) = supt�0 jG(j!)j−120

−110

−100

−90

−80

−70

−60

−50

−40

−30

−20

Mag

nitu

de (

dB)

10−1

100

101

102

103

−90

−45

0

45

90

Pha

se (

deg)

Bode Diagram

Frequency (rad/sec)

0 0.02 0.04 0.06 0.08 0.1

−0.06

−0.04

−0.02

0

0.02

0.04

System: untitled1Real: 0.00779Imag: 0.0235Frequency (rad/sec): 1.05

Nyquist Diagram

Real Axis

Imag

inar

y A

xis

20 de Enero 2005 15


Bloque Perturba i�on �(y)� La perturba i�on pertene e al intervalo[a; b℄:{ �(0) = 0{ ay2 � y�(y) � by2 , 8y 2 <{ a = ��S��C!d u0{ b = �S+�C!d u0� La perturba i�on tiene ganan ia L2 �nita:{ 2(�) � max[jaj; jbj℄� La perturba i�on modi� ada��(y) = �(y) + "y es pasiva:{ Si " � jaj ) R t0 y��(y) � 020 de Enero 2005 16


Bloque de Adapta i�on A(y). Op i�on 1� Se toma �(y) = �y � sign[�(y)℄:{ Se puede asumir sign[�(y)℄ � sign[ _'b℄� Proposi i�on 1: El mapa A�(y) : y 7! (�(y)~u� "y)es pasivo si se toma:�� "�C� Proposi i�on 2: El equilibrio (e�; ~u�) = (0; 0) esglobalmente asint�oti amente estable, on:V (e; ~u) = 12eTPe+ Z t0 y��(y) ++ �Z t0 y(�(�)~u� "y) + 2u0ymax� �20 de Enero 2005 17


Bloque de Adapta i�on A(y). Op i�on 2� Se toma �(y) = ��jyj:{ Para �� < u0�ymax la se~nal de ontrol se mantiene a otada ~u 2 [�u0; 0℄.� Proposi i�on 1: La siguiente expresi�on es ierta:Z t0 y�(y)~u+ Z t0 �� y2 + 2u0ymax� � 0� Proposi i�on 2: El equilibrio (e�; ~u�) = (0; 0) es globalmente asint�oti amente estable, on:V (t; e) = 12 eTPe+ Z t0 y("y +�(y)) ++ Z t0 y�(y)~u+ Z t0 �� y2 + 2u0ymax�si tomamos: �� 12#min(Q)� "

20 de Enero 2005 18


Respuestas Obtenidas� Diferentes velo idades de respuesta.� Posibles limita iones de poten ia.� Per�les m�as o menos suave.0 50 100 150

0

10

20

30

40

Time [s]

Rot

atio

n V

eloc

ity [r

ad/s

]

Operation under DOSKIL

surface downhole

0 50 100 1502.6

2.8

3

3.2

3.4

3.6

3.8

4

x 104

Time [s]

Wei

ght O

n B

it [N

]

� Disponibilidad de medidas.� Limita i�on de valores de ~u.� Cara ter��sti as adaptativas.

0 50 100 1503.3

3.4

3.5

3.6

3.7

3.8

3.9

4

4.1x 10

4

Time [s]W

eigh

t On

Bit

[N]

0 50 100 1500

10

20

30

40

Time [s]

Rot

atio

n V

eloc

ity [r

ad/s

]

Operation under DOSKIL

surface downhole

20 de Enero 2005 19


Algunos trabajos en urso y futuros

� Todas las pegas anteriores ......� Compila i�on de todo el trabajo en un solo do umento.� B�usqueda �nan ia i�on.� Amplia i�on del estudio de estabilidad a otras posibles estru turas de ontrol.� Estudio del a oplamiento de os ila iones laterales y torsionales.� Impli a iones de DOSKIL es este a oplamiento.� Futuras pruebas de laboratorio on equipo experimental.20 de Enero 2005 20


Encoder Incremental salida seno/coseno

Masa ~ 12 kg

Masa ~ 2 kg

Acoplamiento Elastico Constante de torsion

0,4<k<1 N.m/rad

Motor brushless o CC + encoder + reductora 1:10

0-100 tr/mn - par nominal entre 0,5 y 1 Nm ��Estructura

Pieza a taladrar

Útil de perforación

Masa adicional (hasta 15 Kg)

Captor de fuerza

Motor brushless o CC + Captor de posicion +

reductora 1:10 par nominal ~2 Nm

Desplazamiento max. 20 cm

Rail de guía

M1

M2

F = 300 N max �Placas de fijacion a las guías

Masa Total

ap. 30 Kg

20 de Enero 2005 21

control de vibraciones en sarta de perforaci´oncontrol de vibraciones en sarta de perforaci´on...

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