Abstract

Accessing difficult to reach hydrocarbon reservoirs while simultaneously reducing risk and increasing efficiency demonstrates a need for improved autonomous directional control of rotary steerable systems (RSS). The inherently uncertain drilling environment presents a challenge for control algorithms and human operators alike, where model mismatch can be significant and the parameters are time varying. Parameter estimation can improve the performance of steering controllers through model adaptation as well as provide valuable information to human operators. This paper proposes the use of a Markov Chain Monte Carlo (MCMC) method to estimate time-varying model parameters in real-time using only measurements commonly obtained while drilling. The proposed method is evaluated on historical field data and its accuracy is quantified by prediction accuracy to achieve a mean absolute error of 0.68 deg over 30 m. Next, the proposed method is used to adapt the model of a model predictive controller (MPC) and its performance is compared with a static MPC in closed-loop simulation of a prototypical drilling scenario. The estimator reduces tracking error of the MPC by 93.36% and produces a higher quality borehole. Finally, the utility of estimation for human-in-the-loop operation is explored through the design of an early warning system (EWS). The posterior distribution produced by MCMC is utilized in the EWS to predict the probability of undesirable future trajectories. By providing automatic alerts, the EWS serves as a safety mechanism that enhances operators' proficiency when monitoring several autonomously drilled wells.

References

1.
Lohrenz
,
J.
,
1991
, “
Horizontal Oil and Gas Wells: The Engineering and Economic Nexus
,”
Energy J.
,
12
(
3
), pp. 35–54.10.5547/ISSN0195-6574-EJ-Vol12-No3-4
2.
Perneder
,
L.
,
2013
,
A Three-Dimensional Mathematical Model of Directional Drilling
,
University of Minnesota
,
Minneapolis, MN
.
3.
Panchal
,
N.
,
Bayliss
,
M. T.
, and
Whidborne
,
J. F.
,
2010
, “
Robust Linear Feedback Control of Attitude for Directional Drilling Tools (13th IFAC Symposium on Automation in Mining, Mineral and Metal Processing)
,”
IFAC Proc. Vol.
,
43
(
9
), pp.
92
97
.10.3182/20100802-3-ZA-2014.00022
4.
Bayliss
,
M. T.
, and
Whidborne
,
J. F.
,
2015
, “
Mixed Uncertainty Analysis of Pole Placement and H∞ Controllers for Directional Drilling Attitude Tracking
,”
ASME J. Dyn. Syst., Meas., Control
,
137
(
12
), p.
121008
.10.1115/1.4031576
5.
Bayliss
,
M. T.
,
Bogath
,
C.
, and
Whidborne
,
J. F.
,
2015
, “
MPC-Based Feedback Delay Compensation Scheme for Directional Drilling Attitude Control
,” SPE/IADC Drilling Conference and Exhibition,
OnePetro
,
London, UK
, Mar., Paper No.
SPE-173009-MS
.10.2118/173009-MS
6.
Inyang
,
I. J.
,
Whidborne
,
J. F.
, and
Bayliss
,
M. T.
,
2016
, “
Bilinear Modelling and Bilinear PI Control of Directional Drilling
,” UKACC 11th International Conference on Control (
CONTROL
),
IEEE
,
Belfast, UK
, Aug. 31–Sept. 2, pp.
1
6
.10.1109/CONT ROL.2016.7737607
7.
Demirer
,
N.
,
Zalluhoglu
,
U.
,
Marck
,
J.
,
Darbe
,
R.
, and
Morari
,
M.
,
2019
, “
Autonomous Directional Drilling With Rotary Steerable Systems
,” American Control Conference (
ACC
),
IEEE
,
Philadelphia, PA
, July 10–12, pp.
5203
5208
.10.23919/ACC.2019.8814644
8.
Sun
,
H.
,
Li
,
Z.
,
Hovakimyan
,
N.
,
Başsar
,
T.
, and
Downton
,
G.
,
2012
, “
L1 Adaptive Control for Directional Drilling Systems
,”
IFAC Proc. Vol.
,
45
(
8
), pp.
72
77
.10.3182/20120531-2-NO-4020.00035
9.
Koesdwiady
,
A. B.
,
Elferik
,
S.
, and
Karray
,
F.
,
2017
, “
Adaptive Control for Directional Drilling Systems With Delay and Parameter Uncertainty
,”
Robot Intelligence Technology and Applications
, Vol.
4
,
Springer
,
Cham
, pp.
123
140
.
10.
Pirovolou
,
D.
,
Chapman
,
C. D.
,
Chau
,
M.
,
Arismendi
,
H.
,
Ahorukomeye
,
M.
, and
Penaranda
,
J.
,
2011
, “
Drilling Automation: An Automatic Trajectory Control System
,” SPE Digital Energy Conference and Exhibition,
OnePetro
,
The Woodlands, TX
, Apr., Paper No.
SPE-143899-MS
.10.2118/1211-0084-JPT
11.
Villarreal Magaña
,
O. A.
,
Monsieurs
,
F. H. A.
,
Detournay
,
E.
, and
van de Wouw
,
N.
,
2018
, “
Robust Output-Feedback Control of 3D Directional Drilling Systems
,”
Int. J. Robust Nonlinear Control
,
28
(
18
), pp.
5915
5942
.10.1002/rnc.4362
12.
Kremers
,
N. A. H.
,
Detournay
,
E.
, and
Van De Wouw
,
N.
,
2016
, “
Model-Based Robust Control of Directional Drilling Systems
,”
IEEE Trans. Control Syst. Technol.
,
24
(
1
), pp.
226
239
.10.1109/TCST.2015.2427255
13.
Menegaz
,
H. M.
,
Ishihara
,
J. Y.
,
Borges
,
G. A.
, and
Vargas
,
A. N.
,
2015
, “
A Systematization of the Unscented Kalman Filter Theory
,”
IEEE Trans. Autom. Control
,
60
(
10
), pp.
2583
2598
.10.1109/TAC.2015.2404511
14.
Athans
,
M.
,
Wishner
,
R.
, and
Bertolini
,
A.
,
1968
, “
Suboptimal State Estimation for Continuous-Time Nonlinear Systems From Discrete Noisy Measurements
,”
IEEE Trans. Autom. Control
,
13
(
5
), pp.
504
514
.10.1109/TAC.1968.1098986
15.
Julier
,
S. J.
, and
Uhlmann
,
J. K.
,
1997
, “
New Extension of the Kalman Filter to Nonlinear Systems
,”
Signal Processing, Sensor Fusion, and Target Recognition VI
,
International Society for Optics and Photonics
, Vol.
3068
, pp.
182
193
.10.1117/12.280797
16.
Spall
,
J. C.
,
2003
, “
Estimation Via Markov Chain Monte Carlo
,”
IEEE Control Syst. Mag.
,
23
(
2
), pp.
34
45
.
17.
Ljung
,
L.
,
2012
,
System Identification: Theory for the User
,
Prentice Hall PTR
,
Upper Saddle River, NJ
.
18.
Tikhonov
,
A. N.
,
Goncharsky
,
A. V.
,
Stepanov
,
V. V.
, and
Yagola
,
A. G.
,
1995
,
Numerical Methods for the Solution of Ill-Posed Problems
, Vol.
328
,
Springer Science & Business Media
,
Dordrecht, The Netherlands
.
19.
Lange
,
K.
,
Chambers
,
J.
, and
Eddy
,
W.
,
2010
,
Numerical Analysis for Statisticians
, Vol.
1
,
Springer
,
New York
.
20.
Tierney
,
L.
,
1994
, “
Markov Chains for Exploring Posterior Distributions
,”
The Ann. Stat.
, 22(4), pp.
1701
1728
.
21.
Haario
,
H.
,
Laine
,
M.
,
Mira
,
A.
, and
Saksman
,
E.
,
2006
, “
DRAM: Efficient Adaptive MCMC
,”
Stat. Comput.
,
16
(
4
), pp.
339
354
.10.1007/s11222-006-9438-0
22.
Lofberg
,
J.
,
2004
, “
YALMIP: A Toolbox for Modeling and Optimization in MATLAB
,”
IEEE International Conference on Robotics and Automation (IEEE Catalogue No. 04CH37508)
, Taipei, Taiwan, Sept. 2–4, pp.
284
289
.10.1109/CACSD.2004.1393890
23.
Save
,
L.
,
Feuerberg
,
B.
, and
Avia
,
E.
,
2012
, “
Designing Human-Automation Interaction: A New Level of Automation Taxonomy
,”
Proceedings of Human Factors of Systems and Technology
, Toulouse, France, Oct., pp.
43
55
.
24.
de Wardt
,
J. P.
,
Macpherson
,
J. D.
,
Zamora
,
M.
,
Dow
,
B.
,
Hbaieb
,
S.
,
Macmillan
,
R. A.
,
Laing
,
M. L.
,
DiFiore
,
A. M.
,
Inabinett
,
C. E.
, and
Anderson
,
M. W.
,
2015
, “
Drilling Systems Automation Roadmap-The Means to Accelerate Adoption
,” SPE/IADC Drilling Conference and Exhibition,
OnePetro
,
London, UK
, Mar., Paper No.
SPE-173010-MS
.10.2118/173010-MS
You do not currently have access to this content.