Click to edit Master title style - Brigham Young University · • WOB Dynamics • First order...

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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


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)


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


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


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


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


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


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


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


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


Results – Kick Attenuation


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


Acknowledgements

We appreciate the support of National Oilwell Varco


Thank You For Your Attention

Questions ?

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