Nonlinear Model Predictive Control of Managed Pressure Drilling Based on Hammerstein-Wiener piecewise linear models 2015 Fall AIChE Meeting by Junho Park
Outline Overview the Managed Pressure Drilling Process - Motivation and Challenges Downhole Pressure Control using Lower Order Model Downhole Pressure Control using Hammerstein-Wiener Model Conclusion and future work
Managed Pressure Drilling Surface Rotation Speed Weight on Bit Choke Valve Main Mud Pump Measurable variables: - Surface measurements - Downhole pressure (mud pulse / wired pipe) Unmeasurable variables in annulus: - Downhole pressure (non wired pipe) Drill String Annulus Back Pressure Pump Downhole Reservoir Gas Influx
Why Automate MPD? Average of 4 uncontrolled well situations in the Gulf of Mexico each year (Morris, 2014) MPD Automation Project objectives: Regulate downhole pressure with a controller that changes chokes and pumps Combine pressure control with ROP maximization with a controller that changes chokes, pumps, RPM, and WOB Identify and attenuate unexpected gas influx Detect and automate cleaning of cuttings buildup Deepwater Horizon 2010 [1] Morris, D., Analysis of Well Control Incidents 2007-2013, U.S. Dept. of the Interior, Presented by Dan Fraser at the 2014 SPE ATCE Meeting, Amsterdam, The Netherlands
Types of Models for MPC First Principles Model - High Fidelity Model (WeMod, SINTEF, OLGA) - Lower Order Model (Stames et al.) Empirical Model - Linear Empirical Model (e.g. Transfer function, State-space, ARX, OE etc) - Nonlinear Empirical Model (e.g. Nonlinear ARX, Hammerstein-Wiener Model etc)
Fitting data with Steady State Values Estimate the initial parameters in Lower Order Model p p = β d V d q pump q bit p c = β a V a q bit + q back q choke + q res ROP A a q bit = 1 M p p F d q bit q bit + ρ d gh bit p bit h = ROP p bit = p c + ρ a F a q bit + q res q bit + q res h + ρ a gh bit p i p i+1 = ρ a,i F a,i q bit + q res q bit + q res h i h i 1 + ρ a,i g h v,i h v,i 1 Not a good agreement at low pressure range It results a model mismatch when pipe connection takes place
For Non-wired drillpipe rigs Estimate the downhole pressure using surface measurements via MHE MHE employs the Lower Order Model Downhole pressure Mud pump pressure Choke valve pressure Choke valve flowrate
PID and Model Predictive Control Performance comparison for Downhole pressure control Conventional (PID) Downhole pressure Advanced (MPC) Downhole pressure Choke opening Choke opening Mud pump flowrate Mud pump flowrate
Applying Piecewise Linear to MPC Nonlinearity Piecewise Linear Nonlinear static element (Gain) and Linear dynamic element (Time Constant) Assume that the variation of the dynamics is negligible. Time constant of Downhole pressure response is ~50 second.
Structure of Hammerstein-Wiener Models input nonlinearity F linear dynamic model G output nonlinearity H u(t) w(t) x(t) y(t) Transform the input and output instead of changing Gain directly. Changing Gain will occur the prediction error. Most efficient way to apply piecewise linear concept to MPC algorithm
Nonlinearity in MPD Process Increasing q_p Increasing z_choke Operation Range
Model Identification Hammerstein Wiener Mud Pump flowrate Back pressure Pump flowrate Choke opening Random Signal step test - Cover the entire operation range of interest to get nonlinearity. - Implementing Multi Variable Identification 3 input nonlinearity blocks 3 Linear Model blocks 1 output nonlinearity blocks
Structure of Hammerstein-Wiener MPC
Model Validation - 1 Linear Model vs Hammerstein Wiener Model 45% 78%
Model Validation - 2 Linear Model vs Hammerstein Wiener Model 45% 78%
Conclusion Estimate the downhole pressure by using Lower Order Model Validate the control performance - Maintain pressure within 1 bar during Normal drilling - Improved Model accuracy up to 80% for Pipe connection
Future work Improve the Lower Order Model for downhole estimation Performance verification with high fidelity simulator for: Kick attenuation Cuttings build-up detection and removal MPD Rig Testing at NOV Navasota test facility
Acknowledgements We gratefully acknowledge the technical support provided by NOV and BYU students including significant contributions from: Reza Asgharzadeh Mostafa Safdarnejad Thomas Webber David Pixton Tony Pink Reza Rastegar Adrian Snell Andy Craig Shantur Tapar Alan Clarke
Questions?
Back up slides
Pressure Controller Results Normal Drilling: Estimator adapts within 1.5% error margin in 30 sec Drill bit pressure is controlled to set point Connection Procedure: The controller is able to control the drill bit pressure +/- 3 bar Kick Attenuation: Improved response to unexpected gas influx Immediate action avoids more intrusive well control efforts
ROP and Downhole Pressure Control Increased ROP due to the decreased downhole pressure Improved kick attenuation compared to single pressure controller ROP 20% higher Observe limits for RPM and WOB from drilling engineer
PID and Model Predictive Control Model Predictive Control sees into the future to make an optimal moves of MV Conventional (PID) Advanced (MPC) PAST FUTURE Input (eg. Flow rate) Output (eg. Valve) k
Models Adapt to Changes Moving Horizon Estimation Model Predictive Control Historical Data Measured Output Estimated Output Manipulated Variable Estimated Variable 24
PID and Model Predictive Control Multivariable control aspects Single-Input-Single-Output Multi-Input-Multi-Output SP Set point or Range CV PID MV CV 1 CV 2 CV n MPC MV 1 MV 2 MV 3 MV m
Control System Overview Inputs and Outputs (Downhole pressure control) Mud Pump Pressure Choke Valve Pressure Choke Valve Flowrate MHE MPC Downhole Pressure Choke Valve Opening Mud Pump flowrate
Controller: Normal Operation During normal operation, the optimum downhole pressure values are determined to give the highest possible ROP. Desired ROP Find the optimum WOB, RPM and BHP that lead to the desired ROP Manipulate topside WOB to regulate the downhole WOB Manipulate topside RPM to regulate the downhole RPM Manipulate choke valve and mud pump to regulate BHP
Previous Work in Pressure Control Using advanced technology which transmits pressure data to surface can improve pressure control Main Mud Pump Choke Valve Back Pressure Pump Surface measurements (without WDP) Delayed response to kick events Estimation of fluid properties difficult Reactive pressure control vs. proactive Most prior work with linear controllers Nonlinear viscoelastic mud properties Nonlinear ROP effects Decreased and more variable ROP Surface Measurements Reservoir Controller Estimated Downhole Pressure Estimator Indirectly Controlling the Downhole Pressure
Previous Work in ROP Control Ignore change of WOB and RPM along drill string Ignore effect of downhole pressure dynamics Potential for ROP improvement Weight on Bit Rotation Speed Multiple Linear Regression Real Time Optimization Cost Function Rate of Penetration Reservoir
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 a 1 + 8 i=2 a i x i
Single Pressure Controller MHE Within 30 seconds of operation, the estimator accurately determines the friction factor and the annulus density within 1.5% of the actual value.
Pressure Control with Normal Drilling Within 30 seconds, the drill bit pressure has been controlled within 0.72% of its set point of 345 bar
Kick Attenuation Improved Response to Unexpected Gas Influx. Immediate action avoids more intrusive well control efforts.
Connection Procedure The controller is able to control the drill bit pressure within 1% error margin.
Clean Data Corrupted Data Estimator Performance Squared Error l1-norm Annulus Mud Density, 10-5 kg/m 3 0.03 0.025 0.02 0.015 0.01 0.005 0 20 40 60 80 100 120 140 160 Time, s Annulus Mud Density, 10-5 kg/m 3 0.03 0.025 0.02 0.015 0.01 0.005 0 20 40 60 80 100 120 140 160 Time, s 0.03 0.03 Annulus Mud Density, 10-5 kg/m 3 0.025 0.02 0.015 0.01 0.005 Drift Outlier Annulus Mud Density, 10-5 kg/m 3 5.93% dev. 0.82% dev. 0.01 1.67% dev. 0.41% dev. 0.025 0.02 0.015 0.005 Drift Outlier 0 20 40 60 80 100 120 140 160 180 Time, s 0 20 40 60 80 100 120 140 160 180 Time, s
MPD Controller Performance Squared Error l1-norm 400 60 370 60 360 55 Drill Bit Pressure, bar 350 300 40 20 Choke Valve Pressure, bar Drill Bit Pressure, bar 350 340 330 320 310 50 45 40 35 30 Choke Valve Pressure, bar Drill Bit Pressure Choke Valve Pressure 250 0 20 40 60 80 100 120 140 160 0 Time, s 300 Drill Bit Pressure 25 Choke Valve Pressure 290 0 20 40 60 80 100 120 140 160 20 Time, s
MPD Manipulated Variables Squared Error l1-norm Choke Valve Opening 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0 20 40 60 80 100 120 140 160 Time, s Choke Valve Opening 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% 0 20 40 60 80 100 120 140 160 Time, s Pump Flow Rate, L/min 6000 4000 2000 0 0 20 40 60 80 100 120 140 160 Time, s Pump Flow Rate, L/min 3000 2000 1000 0 0 50 100 150 200 Time, s
ROP Benefit Increased ROP due to the decreased downhole pressure. ROP 20% higher
Kick Attenuation Comprehensive controller is able to attenuate kick more effectively and faster compared with single pressure controller.
Kick Attenuation Drilling continues with consistent ROP during kick. Avoids cutting loading issues due to ROP fluctuations.
Surge/Swab Induced Kick 1500 1000 No communication loss Interrupt 20 sec Interrupt 60 sec Interrupt 100 sec Gas Influx (L/min) 500 0-500 0 50 100 150 200 250 Time (sec) Clear benefit in reducing the time that communication is lost with downhole pressure measurements. Automatic model-based controller is able to reject significant events of unexpected gas influx.
Cuttings Buildup Protection 1650 1600 1550 2 3 Density, kg/m 3 1500 1450 1400 1350 Density Difference at Location 5 4 5 6 7 8 9 10 1300 1250 1200 15 20 25 30 35 40 45 50 55 60 65 70 Time, s Early detection of cuttings buildup can improve the operational strategy for cuttings removal. The higher density estimate from location 5 (middle point in the axial direction of the annulus) is an indication of cuttings buildup.
Cuttings Buildup Protection Slight increase in pressure at location 5 relative to the other pressure sensors would be difficult for an operator to identify. Annular Pressures, bar 300 250 200 150 100 P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 P 10 Choke Valve Opening Pump Flow Rate, L/min 100 50 2000 1500 1000 Choke Valve Opening 0 0 10 20 30 40 50 60 70 Time, s Pump Flow Rate 500 0 10 20 30 40 50 60 70 Time, s 50 0 10 20 30 40 50 60 70 Time, s The density estimates are fed to the predictive controller to update the underlying model used in the forward looking optimization
Distributed Pressure Measurements 100 90 Single Sensor Multiple Sensors 80 70 Influx Rate, L/min 60 50 40 30 20 10 0 0 5 10 15 20 25 30 35 40 Time, s The pressure sensor closer to the kick location is able to sense the change earlier and with a higher degree of accuracy. The comprehensive controller manipulates the RPM, pump flow, and choke valve opening simultaneously to attenuate the kick.
Managed Pressure Drilling Surface Rotation Speed Drill String Annulus Weight on Bit Choke Valve Main Mud Pump Back Pressure Pump Known variables: - Surface measurements - Downhole RPM, WOB - Annulus pressure (mud pulse / wired pipe) Unknown variables in annulus: - Density (annulus) - Friction Factor (annulus) - Downhole drilling fluid and gas influx flow rate Downhole Reservoir Gas Influx
Previous Work in MPD Improve Economics Improve Safety Two Controllers Optimization: Maximize ROP Automation: BHP Regulation RPM WOB System f(rpm,wob,bhp) ROP Z choke q pump System f(z choke,q pump,friction) BHP Ignore change of WOB and RPM along drill string Surface measurements (without WDP) Ignore effect of downhole pressure dynamics Delayed response to kick events Potential for ROP improvement Estimation of fluid properties difficult Reactive pressure control vs. proactive Most prior work with linear controllers Decreased and more variable ROP Is it possible to design a comprehensive controller which considers both tasks simultaneously?
Proposed Comprehensive Controller Expected Advantages Higher ROP and less fluctuations in that. q pump Single Controller Considers Multivariate Effects Improved Kick attenuation with adding extra manipulated variable. Z choke RPM WOB Comprehensive Controller: Maximize ROP + Regulate BHP Earlier detection of cuttings loadings during drilling. Improved safety and reduced drilling cost. BHP System ROP Features of Comprehensive Controller Comprehensive controller which controls ROP and BHP simultaneously. Considers the interaction between drill string and hydraulics. Kick attenuation methodology based on the direct BHP measurements using wired pipe telemetry. Designing multivariate controller using multiple sensor measurement along annulus.
Model Components Pressure Hydraulics Lower order model (Stames et. al) Interaction Between Drill String and Hydraulics ROP also depends on the downhole pressure ROP, Bourgoyne & Young Model Friction factor in the annulus depends both on axial and rotational flow of the mud Rotation Speed (RPM) effect on Friction Factor b f a = a Re axial + c Re angular Drill String Dynamics 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 http://wwtinternational.com/index.php/torque_reduction
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 Re a = 757 ρ v a D o D i μ a Velocity in Axial Direction Rotational Rate (RPM) 120 118 116 114 112 110 108 106 104 102 Top Drive Mid-Point in Drill String Bottom Hole Assembly 100 0 2 4 6 8 10 12 14 16 18 20 Time (sec) b f a = a Re axial + c Re angular D i Re ω = 2.025 ρ RPM D o D i μ ω Rotation Speed of Drill String
Downhole WOB Downhole RPM Control System Scheme WOB MPC Downhole RPM SP Downhole WOB SP Main Mud Pump Operator Input RPM MPC Choke Valve Back Pressure Pump Estimator Surface Measurements ρ a, f a Gas Influx Downhole Pressure, WOB, RPM ROP and RPM set point Pressure Controller Pressure set point ROP Optimizer Reservoir
Kick Attenuation Mode Normal Drilling Operation Kick attenuation has higher priority than achieving higher ROP P bit > Safety Margin + P sp and q influx > 0 Surface RPM Pump flow Rate Set Point Calculate the new reservoir pore pressure (P res ) Switch the controlled variable from downhole pressure into choke valve pressure and set the set point as P C SP = P C before kick + k p E + k I E + k d de dt E = P current sp bottom P bottom Change choke valve opening, surface RPM and pump flow rate Hold until q influx < specified limit Switch the controlled variable from choke valve pressure to downhole pressure Reservoir Choke Pressure Choke Valve Set Point Downhole Pressure Gas Influx
Clean Data Corrupted Data Less Sensitive to Bad Data Squared Error l1-norm Annulus Mud Density, 10-5 kg/m 3 0.03 0.025 0.02 0.015 0.01 0.005 0 20 40 60 80 100 120 140 160 Time, s Annulus Mud Density, 10-5 kg/m 3 0.03 0.025 0.02 0.015 0.01 0.005 0 20 40 60 80 100 120 140 160 Time, s 0.03 0.03 Annulus Mud Density, 10-5 kg/m 3 0.025 0.02 0.015 0.01 0.005 Drift Outlier Annulus Mud Density, 10-5 kg/m 3 5.93% dev. 0.82% dev. 0.01 1.67% dev. 0.41% dev. 0.025 0.02 0.015 0.005 Drift Outlier 0 20 40 60 80 100 120 140 160 180 Time, s 0 20 40 60 80 100 120 140 160 180 Time, s
Controller Results Drilling continues with consistent ROP during kick. Avoids cutting build up issues due to ROP fluctuations.
Publications Accepted Journal Articles Asgharzadeh Shishavan, R., Hubbell, C., Perez, H.D., Hedengren, J.D., and Pixton, D.S., Combined Rate of Penetration and Pressure Regulation for Drilling Optimization Using High Speed Telemetry, SPE Drilling and Completions Journal, accepted for publication / in press. Hedengren, J. D. and Asgharzadeh Shishavan, R., Powell, K.M., and Edgar, T.F., Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers and Chemical Engineering, Volume 70, pg. 133 148, 2014. Asgharzadeh Shishavan, R, Perez, H., Hedengren, J., Brigham Young University; Pixton, D.S., NOV IntelliServ; Pink, A.P., National Oilwell Varco, Multivariate Control for Managed Pressure Drilling Systems Using High Speed Telemetry, Submitted to SPE Journal, under review. Submitted Journal Articles Reza Asgharzadeh Shishavan, David S. Pixton, Ammon N. Eaton, Junho Park, Hector D. Perez, and John D. Hedengren and Andrew Craig, Addressing UBO and MPD Challenges with Wired Drillpipe, Submitted to SPE Journal, under review. 54
Publications Cont. Peer Review Conference Papers Asgharzadeh Shishavan, R., Perez, H., and Hedengren, J.D., Multivariate nonlinear model predictive controller for managed drilling processes, AIChE Annual Meeting, Atlanta, GA, Nov 2014. Asgharzadeh Shishavan, R., Hubbell, C., Perez, H.D., Hedengren, J.D., Pixton, D.S., and Pink, A.P., Multivariate Control for Managed Pressure Drilling Systems Using High Speed Telemetry, SPE Annual Technical Conference and Exhibition (ATCE), Amsterdam, The Netherlands: 27-29 Oct 2014. Asgharzadeh Shishavan, R., Hubbell, C., Perez, H.D., Hedengren, J.D., and Pixton, D.S., Combined Rate of Penetration and Pressure Regulation for Drilling Optimization Using High Speed Telemetry, SPE Deepwater Drilling and Completions Conference, Galveston, TX: 10-11 Sept 2014. Asgharzadeh Shishavan, R., Brower, D.V., Hedengren, J.D., Brower, A.D., New Advances in Post-Installed Subsea Monitoring Systems for Structural and Flow Assurance Evaluation, ASME 33rd International Conference on Ocean, Offshore and Arctic Engineering, OMAE2014/24300, San Francisco, CA, June 2014. Brower, D.V., Brower, A.D., Hedengren, J.D., Asgharzadeh Shishavan, R., A Post-Installed Subsea Monitoring System for Structural and Flow Assurance Evaluation, Offshore Technology Conference, OTC 25368, Houston, TX, May 2014. Pixton, D., Asgharzadeh Shishavan, R., Hedengren, J.D., and Craig, A., Addressing UBO and MPD Challenges with Wired Drillpipe, SPE/IADC MPD & UBO Conference & Exhibition, Madrid, Spain: 8-9 Apr 2014. Brower, D., Hedengren, J.D., Asgharzadeh Shishavan, R., and Brower, A., Advanced Deepwater Monitoring System, ASME 32st International Conference on Ocean, Offshore and Arctic Engineering, OMAE2013/10920, Nantes, France, June 2013, ISBN: 978-0-7918-5531-7. 55 55
Publications Cont. Conference Proceedings Asgharzadeh Shishavan, R., Memmott, J., Hedengren, J.D, and Pixton, D., Pressure Regulation and Kick Attenuation with Wired Pipe Technology in Managed Pressure Drilling. AIChE Spring Meeting, New Orleans, LA, April 2014. Asgharzadeh Shishavan, R. and Hedengren, J.D., Improved Estimator Insensitivity to Outliers, Measurement Drift, and Noise, AIChE Spring Meeting, New Orleans, LA, April 2014. Brower, D., Brower, A., Memmott, J.A., Hedengren, J.D., Mojica, J.L., Asgharzadeh Shishavan, R., Safdarnejad, S.M., Recent Advances in the Application of MIDAE Systems, AIChE National Meeting, San Francisco, CA, Nov 2013.