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Instability and Feedback Stabilisation of Desired Pipeline Flow Regimes. Truls Larsson Trondheim 25.08.2000 Trial lecture for the Doktor ingeniør degree. Outline . Stability Classical stability analysis Exemplified by stability of laminar flow Classification of two phase flow regimes

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Instability and Feedback Stabilisation of Desired Pipeline Flow Regimes

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Instability and Feedback Stabilisation of Desired Pipeline Flow Regimes

Truls Larsson

Trondheim 25.08.2000

Trial lecture for the

Doktor ingeniør degree

Trial lecture


  • 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

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

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

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

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

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

    Separated flow



    Distributed flow


    Slug flow

    Flow Regimes - Gas/liquid Flow







    Trial lecture

    Flow Maps

    Flow maps: the stability of flow regimes for a particular fluid and geometry

    Usually obtained by experiments

    Too simple!



    Liquid velocity



    Gas velocity

    Trial lecture

    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



    Trial lecture

    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 (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

    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

    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 1994) and (de Henau and Raithby 1995)

      • Other: start up, transients

    • Not a rigid classification:

      • Growth of normal slugs in long pipelines

    Trial lecture

    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

    Dynamic InstabilitySevere Slugging in Pipeline Riser

    Step 2: slug generation

    Liquid accumulates

    Gas pressure increases in the pipe

    Trial lecture

    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

    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

    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

    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 1985, Taitel 1985, Pots 1987, Taitel 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

    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

    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

    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 (1985). Choking and terrain slugging?

      • Hedne and Linga 1990: “success of manual choking depends also on the upstream pipeline topology”

    • Tighter separator control (Xu 1997)

    • Feedback control of pipeline

  • Trial lecture

    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

    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

    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

    Feedback Stabilisation of Severe Slugging

    Terrain slugging stabilisation:

    • Havre 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

    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


    • 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

    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


    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

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