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Multivariate Nonlinear Model Predictive
Controller for Managed Drilling Processes
Reza Asgharzadeh
Hector Perez
John Hedengren
Brigham Young University
18 Nov 2014
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Introduction
Why drilling automation and control?
- Extracting oil is more challenging with tighter
formations and harsher environments
- Drilling is a very costly process, reduced drilling
time means significantly less cost
- Improve the safety, automatically attenuate
abnormal conditions with a preventative versus
reactive approach
- Improved sensors and data transfer rate, e.g.
wired pipe drilling
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Managed Pressure Drilling
Reservoir
Main Mud Pump
Choke
Valve
Back Pressure Pump
Weight on Bit
Rotation
Speed
Downhole
Surface
Gas Influx
Unknown variables in annulus:
- Density (annulus)
- Friction Factor (annulus)
- Gas influx flow rate
- Drilling fluid flow rate (downhole)
Drill String
Annulus
Known variables:
- Surface measurements
- Downhole RPM, WOB
- Annulus pressure (mud pulse / wired pipe)
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Literature
Previous Research
Innovation
• Pressure and ROP control and optimization as two separate applications
• Estimation of downhole pressure instead of direct measurements
• Interaction between drillstring and hydraulics
• Quantify benefit of direct downhole pressure measurements (wired drillpipe)
Drill String ROP
RPM
WOB
Drilling (Hydraulics) DHP
𝑍𝑐ℎ𝑜𝑘𝑒
𝑞𝑝𝑢𝑚𝑝
RPM
WOB
𝑍𝑐ℎ𝑜𝑘𝑒
𝑞𝑝𝑢𝑚𝑝
ROP
DHP
System
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Schematic of the MPD Controller
Main Mud Pump
Choke
Valve
Back Pressure Pump
Dow
nh
ole
RP
M
RPM MPC
WOB MPC
Do
wn
ho
leW
OB
Reservoir
Surface Measurements
ρ𝑎, 𝑓𝑎
EstimatorGas Influx
Downhole RPM SP
Downhole WOB SP
ROP
Optimizer
Downhole Pressure, WOB, RPM
Operator Input
Pressure
Controller
ROP and RPM set point
Pressure set point
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Model Components
• Pressure Hydraulics: Lower order model (Stames et al.)
• 4 state equations:
• Mud pump pressure (pp)
• Choke valve pressure (pc)
• Drill bit flow rate (qbit)
• Drilling height (h)
• ROP: Bourgoyne & Young model
• 8 functions:
• Formation strength
• Pressure differential of bottom hole
• Formation compaction
• Bit diameter and weight
• Rotary speed
• Tooth wear
• Hydraulics
𝑅𝑂𝑃 = 𝑒𝑥𝑝 𝑎1 +
𝑖=2
8
𝑎𝑖𝑥𝑖
SPE 170962 • Multivariate Control for Managed Pressure Drilling Systems Using High Speed Telemetry • John D. Hedengren
Slide 6
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Model Components (Cont.)
• Drill String Dynamics
• Multiple mass-spring-damper pendulums in
series
• Johannessen, M.K. and T. Myrvold
• WOB Dynamics
• First order plus dead time model
• Surface WOB -> Downhole WOB
• Rotation Speed (RPM) effect on Friction Factor
• Fluid and cuttings rotational movement
• Affect hydrostatic head downhole
• Ozbayoglu et al. model
0 2 4 6 8 10 12 14 16 18 20100
102
104
106
108
110
112
114
116
118
120
Time (sec)
Rota
tional R
ate
(R
PM
)
Top Drive
Mid-Point in Drill String
Bottom Hole Assembly
𝑅𝑒𝑎 =757 𝜌 𝑣𝑎 𝐷𝑜 − 𝐷𝑖
𝜇𝑎Velocity in Axial Direction
𝑓𝑎 = 𝑎 𝑅𝑒𝑎𝑥𝑖𝑎𝑙𝑏 + 𝑐 𝑅𝑒𝑎𝑛𝑔𝑢𝑙𝑎𝑟
𝑅𝑒𝜔 =2.025 𝜌 𝑅𝑃𝑀 𝐷𝑜 − 𝐷𝑖 𝐷𝑖
𝜇𝜔Rotation Speed of Drill String
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Kick Attenuation Mode
Normal Drilling Operation
𝑃𝑏𝑖𝑡 > 𝑆𝑎𝑓𝑒𝑡𝑦 𝑀𝑎𝑟𝑔𝑖𝑛 + 𝑃𝑠𝑝 and
𝑞𝑖𝑛𝑓𝑙𝑢𝑥 > 0
Switch the controlled variable from
downhole pressure into choke valve
pressure and set the set point as
𝑃𝐶𝑆𝑃 = 𝑃𝐶
𝑏𝑒𝑓𝑜𝑟𝑒 𝑘𝑖𝑐𝑘+ 𝑘𝑝𝐸 + 𝑘𝐼 𝐸 + 𝑘𝑑
𝑑𝐸
𝑑𝑡
𝐸 = 𝑃𝑏𝑜𝑡𝑡𝑜𝑚𝑐𝑢𝑟𝑟𝑒𝑛𝑡 − 𝑃𝑏𝑜𝑡𝑡𝑜𝑚
𝑠𝑝
Change choke valve opening, surface
RPM and pump flow rate
Hold until
𝑞𝑏𝑖𝑡 < specified limit Reservoir
Gas Influx
Downhole Pressure
Set Point
Choke Pressure
Set Point
Pump flow Rate
Choke Valve
Surface RPM
Calculate
the new
reservoir
pore
pressure
(Pres)
Switch the controlled variable from choke
valve pressure to downhole pressure
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Control and Estimation
Nonlinear Model predictive controller and Moving Horizon Estimator- Objective function: ℓ1-norm
𝑥,𝑦𝑚,𝑢𝑚𝑖𝑛Φ = 𝑤ℎ𝑖
𝑇 𝑒ℎ𝑖 + 𝑤ℎ𝑜𝑇 𝑒𝑙𝑜 + 𝑦𝑚
𝑇 𝑐𝑦 + 𝑢𝑇𝑐𝑢 + 𝛥𝑢𝑇
𝑠. 𝑡. 0 = 𝑓 𝑥, 𝑥, 𝑢, 𝑑0 = 𝑔 𝑦𝑥, 𝑥, 𝑢, 𝑑𝑎 ≥ ℎ 𝑥, 𝑢, 𝑑 ≥ 𝑏
𝜏𝑐𝛿𝑦𝑡,ℎ𝑖𝛿𝑡
+ 𝑦𝑡,ℎ𝑖 = 𝑠𝑝ℎ𝑖
𝜏𝑐𝛿𝑦𝑡,𝑙𝑜𝛿𝑡
+ 𝑦𝑡,𝑙𝑜 = 𝑠𝑝𝑙𝑜
𝑒ℎ𝑖 ≥ 𝑦𝑚 − 𝑦𝑡,ℎ𝑖𝑒𝑙𝑜 ≥ 𝑦𝑡,𝑙𝑜 − 𝑦𝑚
- Orthogonal collocation on finite elements for DAE to NLP conversion
- Active set Method or Interior Point Optimization Method
Moving Horizon Estimator- Estimates the values of densities in the annulus
Extended Kalman Filter- Estimates the gas influx flow rate
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
L1 norm vs. Squared Error
20 40 60 80 100 120 140 1600
0.005
0.01
0.015
0.02
0.025
0.03
Time, s
Annulu
s M
ud D
ensi
ty,
10
-5 k
g/m
3
Cle
an
Data
20 40 60 80 100 120 140 1600
0.005
0.01
0.015
0.02
0.025
0.03
Time, s
Annulu
s M
ud D
ensi
ty,
10
-5 k
g/m
3
20 40 60 80 100 120 140 160 1800
0.005
0.01
0.015
0.02
0.025
0.03
Time, s
Annulu
s M
ud D
ensi
ty,
10
-5 k
g/m
3
20 40 60 80 100 120 140 160 1800
0.005
0.01
0.015
0.02
0.025
0.03
Time, s
Annulu
s M
ud D
ensi
ty,
10
-5 k
g/m
3
OutlierNoise OutlierNoise
Co
rru
pte
dD
ata
5.93% dev. 0.82% dev. 1.67% dev. 0.41% dev.
Squared Error ℓ1-norm
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
15 20 25 30 35 40 45 50 55 60 65 701200
1250
1300
1350
1400
1450
1500
1550
1600
1650
Time, s
Density,
kg/m
3
2
3
4
5
6
7
8
9
10
Results - Normal Drilling
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Results – Kick Attenuation
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Conclusion
Multivariate Nonlinear Controller
- Estimation (MHE and EKF) and optimizing control (NMPC)
- Regulating pressure and ROP simultaneously
Enhanced Economics
- Higher ROP
- Less ROP fluctuations
Enhanced Safety
- Improved gas influx attenuation
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Acknowledgements
We appreciate the support of National Oilwell Varco
Multivariate nonlinear model predictive controller for managed drilling processesNov 18, 2014
Thank You For Your Attention
Questions ?
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