Public PhD defence Control Solutions for Multiphase Flow Linear and nonlinear approaches to anti-slug control PhD candidate: Esmaeil Jahanshahi Supervisors: Professor Sigurd Skogestad Professor Ole Jørgen Nydal The thematic content of the series: 1 Facts Revenue from the last two years; Localization; History and surroundings 2 Research Six strategic areas; Three Centres of Excellence; Laboratories; Cooperation with SINTEF; 3 Education and student activities Study areas and programmes of study; Quality Reform; Further- and continuing education; Internationalization 4 Innovation and relationships with business and industry Innovative activities; Agreements with the public and private sectors 5 Dissemination Publications, events and the mass media Museum of Natural History and Archaeology, NTNU Library 6 Organization and strategy Board and organization; Vision, goal and strategies; For more on terminology, see www.uhr.no/informasjon/index.htm (“terminologiliste”) See also www.ntnu.no/intersek/english_matters/ (”Selected administrative terms with translations”) PhD Defence – October 18th 2013, NTNU, Trondheim

Outline Modeling Control structure design Linear control solutions Controlled variable selection Manipulated variable selection Linear control solutions H∞ mixed-sensitivity design H∞ loop-shaping design IMC control (PIDF) based on identified model PI Control Nonlinear control solutions State estimation & state feedback Feedback linearization Adaptive PI tuning Gain-scheduling IMC

Introduction * figure from Statoil

Slug cycle (stable limit cycle) Experiments performed by the Multiphase Laboratory, NTNU

Introduction Anti-slug solutions Conventional Solutions: Choking (reduces the production) Design change (costly) : Full separation, Slug catcher Automatic control: The aim is non-oscillatory flow regime together with the maximum possible choke opening to have the maximum production

Modeling

Modeling: Pipeline-riser case study OLGA sample case: 4300 m pipeline 300 m riser 100 m horizontal pipe 9 kg/s inflow rate

Modeling: Simplified 4-state model θ h L2 hc wmix,out x1, P1,VG1, ρG1, HL1 x3, P2,VG2, ρG2 , HLT P0 Choke valve with opening Z x4 h>hc wG,lp=0 wL,lp L3 wL,in wG,in w x2 L1 State equations (mass conservations law):

Simple model compared to OLGA

Experimental rig 3m

Simple model compared to experiments Top pressure Subsea pressure

Modeling: Well-pipeline-riser system OLGA sample case: 3000 m vertical well 320 bar reservoir pressure 4300 m pipeline 300 m riser 100 m horizontal pipe

Modeling: 6-state simplified model Two new states: mGw: mass of gas in well mLw: mass of liquid in well Pwh Pbh Pin Prt , m,rt , L,rt win wout Qout Prb Z1 Z2

Model fitting using bifurcation diagrams simplified model olga simulations

Control Structure Design

Control Structure What to control? using which valve? Candidate Manipulated Variables (MV): Z1 : Wellhead choke valve Z2 : Riser-base choke valve Z3 : Topside choke valve Candidate Controlled Variables (CVs): Pbh: Pressure at bottom-hole Pwh: Pressure at well-head Win: Inlet flow rate to pipeline Pin: Pressure at inlet of the pipeline Pt: Pressure at top of the riser Prb: Pressure at base of the riser Pr: Pressure drop over the riser Q: Outlet Volumetric flow rate W: Outlet mass flow rate m: Density of two-phase mixture L: Liquid volume fraction Disturbances (DVs): WGin: Inlet gas flow (10% around nominal) WLin: Inlet liquid flow (10% around nominal) L P2 m Q W Win Pwh Pin Prb Pbh

Control Structure Design: Method Input-output pairs Experiment or detailed model bad Simulations with Linearized Model Model fitting good Simplified Model Comparing Results bad Simulations with Nonlinear Model good Controllability Analysis Comparing Results bad Experiment good Robust input-output pairing

Controllability Analysis The state controllability is not considered in this work. We use the input-output controllability concept as explained by Skogestad and Postlethwaite (2005) Chapter 5, Chapter 6

Minimum achievable peaks of S and T Top pressure: Fundamentally difficult to control With large valve opening

Control Structure: Suitable CVs Good CVs Bottom-hole pressure or subsea pressures Outlet flow rate Top-side pressure combined with flow-rate or density (Cascade) Bad CVs Top-side pressure Liquid volume fraction

Control Structure: Suitable MVs Experiment Control Structure: Suitable MVs Using riser-base valve Using top-side valve Wellhead valve cannot stabilize the system

Nonlinearity of system Experiment Nonlinearity of system Process gain = slope

Linear Control Solutions

Solution 1: H∞ control based on mechanistic model mixed-sensitivity design WP: Performance WT: Robustness Wu: Input usage Small γ means a better controller, but it depends on design specifications Wu, WT and WP

Solution 1: H∞ control based on mechanistic model mixed-sensitivity design Controller:

Experiment Solution 1: H∞ control based on mechanistic model Experiment, mixed-sensitivity design

Solution 2: H∞ control based on mechanistic model loop-shaping design Controller:

Experiment Solution 2: H∞ control based on mechanistic model Experiment - loop-shaping design

Solution 3: IMC based on identified model Model identification First-order unstable with time delay: Closed-loop stability: Steady-state gain: First-order model is not a good choice

Solution 3: IMC based on identified model Model identification Fourth-order mechanistic model: Hankel Singular Values: Model reduction: 4 parameters need to be estimated

Solution 3: IMC based on identified model IMC design Bock diagram for Internal Model Control system IMC for unstable systems: Model: y u e r + _ Plant IMC controller:

Solution 3: IMC based on identified model PID and PI tuning based on IMC IMC controller can be implemented as a PID-F controller ---- IMC/PID-F ---- PI PI tuning from asymptotes of IMC controller

Solution 3: IMC based on identified model Experiment Closed-loop stable: Open-loop unstable: IMC controller:

Solution 3: IMC based on identified model Experiment PID-F controller: PI controller:

Comparing linear controllers IMC controller does not need any mechanistic model IMC controller is easier to tune using the filter time constant H ∞ loop-shaping controller results in a faster controller that stabilizes the system up to a larger valve opening

Experiments on medium-scale S-riser Open-loop unstable: IMC controller:

Experiments on medium-scale S-riser PID-F controller: PI controller:

Nonlinear Control Solutions

Solution 1: observer & state feedback PT Nonlinear observer K State variables uc Pt

High-Gain Observer

State Feedback Kc : a linear optimal controller calculated by solving Riccati equation Ki : a small integral gain (e.g. Ki = 10−3)

Nonlinear observer and state feedback OLGA Simulation Control signal

High-gain observer – top pressure Experiment High-gain observer – top pressure measurement: topside pressure valve opening: 20 %

Fundamental limitation – top pressure Measuring topside pressure we can stabilize the system only in a limited range RHP-zero dynamics of top pressure Z = 20% Z = 40% Ms,min 2.1 7.0

High-gain observer – subsea pressure Experiment High-gain observer – subsea pressure measurement: subsea pressure valve opening: 20 % Not working ??!

Chain of Integrators Fast nonlinear observer using subsea pressure: Not Working??! Fast nonlinear observer (High-gain) acts like a differentiator Pipeline-riser system is a chain of integrator Measuring top pressure and estimating subsea pressure is differentiating Measuring subsea pressure and estimating top pressure is integrating

Nonlinear observer and state feedback Summary Anti-slug control with top-pressure is possible using fast nonlinear observers The operating range of top pressure is still less than subsea pressure Surprisingly, nonlinear observer is not working with subsea pressure, but a (simpler) linear observer works very fine. Method \ CV Subsea pressure Top Pressure Nonlinear Observer Not Working !? Working Linear Observer Not Working PI Control Max. Valve 60% 20%

Solution 2: feedback linearization PT Nonlinear controller uc Prt

Solution 2: feedback linearization Cascade system

Output-linearizing controller Stabilizing controller for riser subsystem System in normal form: : riser-base pressure : top pressure Linearizing controller: dynamics bounded Control signal to valve:

CV: riser-base pressure (y1), Z=60% Experiment CV: riser-base pressure (y1), Z=60% Gain:

CV: topside pressure (y2), Z=20% Experiment CV: topside pressure (y2), Z=20% y2 is non-minimum phase

Solution 3: Adaptive PI Tuning Static gain: slope = gain Linear valve: PI Tuning:

Solution 3: Adaptive PI Tuning Experiment

Solution 4: Gain-Scheduling IMC Three identified model from step tests: Z=20%: Z=30%: Z=40%: Three IMC controllers:

Solution 4: Gain-Scheduling IMC Experiment

Comparison of Nonlinear Controllers Gain-scheduling IMC is the most robust solution Gain-scheduling IMC does not need any mechanistic model Adaptive PI controller is the second controller, and it is based on a simple model for static gain Controllability remarks: Fundamental limitation control: gain of the system goes to zero for fully open valve Additional limitation top-side pressure: Inverse response (non-minimum-phase)

Conclusions A new simplified model verified by OLGA simulations and experiments Suitable CVs and MVs for stabilizing control were identified Anti-slug control using a subsea valve close to riser-base Online PID and PI tuning rules for anti-slug control New linear and nonlinear control solutions were developed and tested experimentally We showed that … Simple methods work better for process control Fundamental controllability limitations are idependant from control design

Thank you! Acknowledgements SIEMENS: Funding of the project Master students: Anette Helgesen, Knut Åge Meland, Mats Lieungh, Henrik Hansen, Terese Syre, Mahnaz Esmaeilpour and Anne Sofie Nilsen. Thank you!