Instability and Feedback Stabilisation of Desired Pipeline Flow Regimes

1. Instability and Feedback Stabilisation of Desired Pipeline Flow Regimes Truls Larsson Trondheim 25.08.2000 Trial lecture for the Doktor ingeniør degree Trial lecture

2. Outline • Stability • Classical stability analysis • Exemplified by stability of laminar flow • Classification of two phase flow regimes • Stability of slug flow • Unstable flow: • Severe slug flow • Feedback stabilisation of severe slugging Trial lecture

3. Flow Regime in Pipeline Flow regime: velocity profile distribution of phases • One phase flow: • Laminar and turbulent • Two phase flow: • Spatial distribution of the phases Trial lecture

4. Classification of Flow Instabilities Bergles (1981): • Steady flow: The variables are a function of time only, except for rapid variations (turbulence, slug flow) • Static instability: if small changes leads to a new and different steady state • Dynamic instability: The system behaves in a “dynamic manner” Trial lecture

5. Classical Stability Analysis: Is laminar flow stable? (White 1974) • Solution to Navier-Stokes • Add a small disturbance to the solution • Insert into Navier-Stokes, and remove the solution and ignore square terms Trial lecture

6. Classical Stability Analysis: Is laminar flow stable? (White 1974) • The result: A set of linear partial equations with variable coefficient • The Orr-Sommerfield equations • Difficult to solve numerically • Still they show that laminar flow is unstable at high Reynolds numbers • Turbulent flow is stable in “our” timeframe Trial lecture

7. Multiphase Flow - Two Phase Flow • Gas, liquid and/or solid flows in the same pipe • Gas/solid flow • Gas/liquid flow • Offshore pipelines • Liquid/solid flow • Liquid/liquid flow • Gas/liquid/liquid flow • How are the phases distributed in the pipe? Trial lecture

8. Separated flow Annular Stratified Distributed flow Bubbly Slug flow Flow Regimes - Gas/liquid Flow Gas Liquid Gas Gas Liquid Liquid Trial lecture

9. Flow Maps Flow maps: the stability of flow regimes for a particular fluid and geometry Usually obtained by experiments Too simple! Bubbly Slug Liquid velocity Annular Stratified Gas velocity Trial lecture

10. Kelvin-Helmholtz Stability Criteria • Pressure drop due to smaller gas area • Gravity force on the perturbation • Conditions for stability of stratified flow: • Taitel and Duckler (1976) • Lin and Hanratty (1986) • And others Gas Liquid Trial lecture

11. Stability of Slugs • Is slug flow stable? • The front velocity of the slug has to be larger than the tail velocity (Bendiksen and Espedal 1992) • Equivalent to the minimum slip criteria • Ruder et.al (1989) gives two conditions for the stability of the slug • Low pressure: both stratified and slug flow is stablestable slug flow may be generated with a disturbed inlet Trial lecture

12. Stability of Slug FlowModelling and Control • Can it be stabilised? How? • Proper modelling of “dynamic” slug flow? • Is “normal” slug flow an instability? • A limit cycle? • Are new models needed? • Present models: mainly concerned with either slug or stratified flow. Slug initiation quasi stationary • Model need: A complete model which describes the whole cycle Trial lecture

13. Severe Slugging • Normal slug: High gas and liquid flow rates • Severe slug: Longer period • Generated at the base of a riser (Schmidt 1980) • Generated at low elbows (Zheng et.al 1994) and (de Henau and Raithby 1995) • Other: start up, transients • Not a rigid classification: • Growth of normal slugs in long pipelines Trial lecture

14. Simplified explanation ofSevere Slugging in Pipeline Riser Step 1: Initiation Gas velocity is not large enough to sustain the liquid film in the riser, which falls down and blocks the gas flow Trial lecture

15. Dynamic InstabilitySevere Slugging in Pipeline Riser Step 2: slug generation Liquid accumulates Gas pressure increases in the pipe Trial lecture

16. Dynamic InstabilitySevere Slugging in Pipeline Riser Step 3: slug production When the gas pressure equals the liquid head, the gas penetrates into the riser. As gas enters the liquid plug is accelerated Large peaks in the liquid flow rate Trial lecture

17. Dynamic InstabilitySevere Slugging in Pipeline Riser Step 4: gas blow-down The pressure drops as the expanding gas bubbles leaves the pipe The gas bubbles becomes continuos, leaving a liquid film at the wall The gas velocity becomes too small to ….. Trial lecture

18. Severe Slugging in Hilly Terrain Liquid blocks a low elbow, and gas pressure builds up. (Zheng et.Al. 1994) and (de Henau and Raithby 1995) Liquid is blocking the low elbow. Trial lecture

19. When to Expect Severe slugging • Assumed: the flow regime in the pipe before the riser should be stratified (Schmidt 1985) • Not consistent with experiments by Hedne and Linga 1990 • Condition for severe slugging in risers given in:Bøe 1981, Schmidt et.al. 1985, Taitel et.al. 1985, Pots et.al. 1987, Taitel et.al. 1990 and others • However: • Based on steady state analysis • Variables which are not readily available are needed • Not able to predict if the system will be stable Trial lecture

20. When to Expect Severe slugging • Dynamic model/simulation of the pipe is needed! • Slug initiation and growth • Still: (taken from the OLGA training course) • Pipeline with many dips and humps • High flow rates: steady flow • Low flow rates: dynamic flow • Low gas-oil ratio: dynamic flow • Gas-condensate lines: dynamic flow • Low liquid velocities, long transients in liquid • Decreasing pressure: dynamic flow Trial lecture

21. Operational Problems Caused by Slugging • Operational problems on the platform • Separators • Compressors • Mechanical stresses • Reservoir • Pressure fluctuations are bad for the reservoir • Pipeline • The average flow is reduced? Trial lecture

22. Reducing the Effect of Severe Slugging • Design changes • Pipeline and separator • Extra/New equipment: slug catchers, venturi and gas lift • Operation • Increasing the separator pressure, may reduce production • Choking: changes the flow-pressure drop profile of the riser Schmidt et.al. (1985). Choking and terrain slugging? • Hedne and Linga 1990: “success of manual choking depends also on the upstream pipeline topology” • Tighter separator control (Xu et.al. 1997) • Feedback control of pipeline Trial lecture

23. Feedback Stabilisation of Severe Slugging • From control theory • Only feedback control moves the poles! • Requirement for feedback stabilisation: • Measurement: see the instability • Actuator: react faster than the instability • Not as sometimes suggested: • To deduce that the pipeline is slugging form measurements. (See Mcnulty et.Al 1999 for an example) Trial lecture

24. Riser induced slug stabilisation: Hedne and Linga 1990: Experimental work on the SINTEF two phase flow loop Downward sloping pipeline ca. 950 m. Long and 60 m high riser Experiments with different pressures and velocities Manual choking: 80% valve closure to suppress all the terrain slugging Automatic choking: completely removed terrain slugging PI control of the pressure drop in the riser using the choke valve Feedback Stabilisation of Severe Slugging Trial lecture

25. Feedback Stabilisation of Severe Slugging Riser induced slug stabilisation: • Courbot (1996): • The Dunbar pipeline was expected to show severe slugging in the riser. • Tests showed that: “It would be difficult, if not impossible, to operate the pipeline … without any slug control device” • Pressure in the bottom of the riser is controlled with the choke valve • Plus switches and overrides • Severe slugging was removed Trial lecture

26. Feedback Stabilisation of Severe Slugging Terrain slugging stabilisation: • Havre et.al. 2000: • Severe slugging at the Hod-Valhall pipeline caused large operational problems, and caused platform shutdown • A simulation in OLGA reproduced the severe slugging behaviour • It was due to the hilly terrain • The slug controller uses: • The pressure and temperature on both Valhall and Hod • The choke valve Trial lecture

27. Summary of feedback control • All of them used the choke valve • Both used a pressure upstream of the instability • The pressure build-up is upstream the liquid blocking. • A linear analysis/controllability analysis • to see where the instability is and where it could be observed • What is the flow regime after stabilisation? Trial lecture

28. Summary • Stability of flow regimes in pipelines • Stability of stratified and slug flow • Dynamic instability: severe slugging • Industrial stabilisation severe slugging • Pointed to some open issues. Trial lecture

29. Acknowledgements and Literature • Inputs and assistance from: • K. Havre • K. Falk • J. Morud • Hugo • T. Ytrehus • O.J. Nydal • M.S. Govatsmark • V. Olaissen Trial lecture

30. Literature Bendiksen, K. and M. Espedal (1991): onset of slugging in horizontal gas-liquid pipe flow. Int. J. Multiphase flow vol. 18 no 2, pp 237-242 Bergles, A.E. (1981): instabilities in two phase systems. Courbot, A. (1996): prevention of sever slugging in the dunbar 16” multiphase pipeline. Offshore technology conference, pp 1- 8 De henau, V. and G.D. Raithby. (1995): A study of terrain induced slugging in two phase flow pipelines. Int. J. Multiphase flow, vol. 21, no 3, pp 365-379. Falk, K. (2000): personal communications Havre, K., H. Stray and K.O. Stornes. (2000): stabilisation of terrain induced slug flow in multiphase pipelines. Submitted to ABB review. Hedne, P. and H. Linga (1990): suppression of terrain slugging with an automatic and manual riser choking. Advances in gas-liquid flow, pp 453-460 Lin, P.Y. and T.J. Hanratty (1986): A model for prediction flow regime transition Mcnulty, G., C. Wordsworth and I. Dis (1999): predicting, detecting, and controlling slugs in pipeline-riser systems. BHR group multiphase 1999, pp 105-118 Pots, B.F.M., I.G. Bromilow and M.J.W.F. Konijn. (1987): severe slugging Schmidt, Z., Brill, J.P. And beggs, H.D. (1979): choking can eliminate severe pipeline slugging. Oil & gas journal -pp 230-238. Schmidt, Z., Brill, J.P. And beggs, H.D. (1980): experimental study of severe slugging in a two phase flow pipeline riser system. Soc. Pet. Eng. J. Pp 407-414. Schmidt, Z., D.R. Doty, K. Dutta-roy. (1985): severe slugging in offshore pipeline riser-pipe systems. SPE J, pp 27-38. Taitel, T. and A.E. Dukler. (1975): A model for flow regime transition in horizontal and near horizontal gas-liquid flows. Aiche J. Vol. 19 no3, pp 47-55. Taitel, T. (1986): stability of severe slugging. Int. J. Multiphase flow, vol 12, no 2, pp 203-217 White F.M. (1974): viscous fluid flow. Mcgraw-hill. Xu, Z.G., P. Gayton, A. Hall and J. Rambeak (1997): simulation study and field measurement for mitigation of slugging problem in The hudson transportation lines. BHR group multiphase 1997, pp 497-507 Yocum, B.T. (1973): offshore riser slug avoidance: models for design and optimisation. SPE European meeting. Zheng, G., J.P. Brill and Y. Taitel (1994): slug flow behaviour in a hilly terrain pipeline. Int. J. Multiphase flow, vol. 20, no 1, pp 63-79 Trial lecture