SPE 124883

Slug Control With Large Valve Opening to Maximise Oil Production A.I. Ogazi, Y. Cao, H. Yeung, and L. Lao, Cranfield University

Copyright 2009, Society of Petroleum Engineers This paper was prepared for presentation at the 2009 SPE Offshore Europe Oil & Gas Conference & Exhibition held in Aberdeen, UK, 8–11 September 2009. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract Severe slugging in an offshore riser pipeline imposes a major challenge to production and flow assurance in the oil and gas industry. Riser top valve choking has shown effectiveness in eliminating severe slugging. However, most manual choking and active control techniques were tuned by trial and error resulting in operation at a smaller than required valve position. This imposes unnecessarily high back pressure on the riser-pipeline which leads to reduction in production. One way to overcome this problem is to design the active control system to operate at a large valve position. However, at such an operating point, the riser pipeline system is naturally open-loop unstable associated with severe slugging flows.

In this work, an approach to tune a robust PID slug controller at an open-loop unstable condition is proposed. Firstly, at an open-loop unstable operating condition, a reliable linear model is derived from the nonlinear simplified riser-separator model (SRSM) developed in previous work. Then, a robust stabilizing PID controller is designed based on the linearised model.

The controller was successfully applied to a 2” laboratory riser at Cranfield University and a 8” generic industrial riser system modeled in the commercial simulator, OLGA. OLGA simulation on the industrial riser system shows that the proposed approaches not only can eliminate severe slugging but can also increase oil production. It also shows that the percentage improvement in oil production compared with manual choking will increase as the well pressure declines. This means that even more can be gained by adopting active slug control for mature oil fields than for relatively new fields.

The result is very significant for mature fields which are susceptible to severe slugging and low oil production due to declining reservoir pressure. Keywords Severe slugging, Pipeline-riser, Unstable systems, Robust PID tuning, Oil production, Mature fields

1. Introduction Severe slugging in an offshore riser-pipeline system is one of the most undesired flow regimes due to its potential to initiate and sustain system instability. Due to huge variation in pressure and flow associated with it, its consequences in oil and gas production are of a very serious concern. Severe pressure and flow oscillations can cause depletion of reservoir performance and productivity, poor phase separation, compressor overloading, trips and production deferment. Conversely, a slug control system will eliminate or reduce the occurrence of these adverse conditions.

The primary objective of a slug control system is to stabilise the riser-pipeline system by suppressing severe slugging. Conventional solutions to address this severe slugging issue include design modification of upstream facilities (Fargharly, 1987, Makogan and Brook, 2007), riser base gas lift (Alvarez and Al-Malik, 2003, Cousin and Johal, 2000, Duret and Tran, 2002, Al-Kandari and Koleshwar, 1999, Jansen and Shoham, 1994, Meng and Zhang, 2001, Pots et al 1987), gas re-injection (Tengesdal et al, 2002), homogenising the multiphase flow (Hassanein and Fairhurst, 1998), installation of slug catchers and riser topside valve choking (Schmidt et al, 1980). Among these solutions, choking transforms the unstable flow in the riser to stable flow; however, it induces extra back pressure on the pipeline. Active feedback, feed forward and cascade control systems have been applied to dynamic choking for slug control (Henriot et al 1999, Drengstig and Magndal 2001, Jasen et al 1996, John-Morten et al, 2005, Molyneux and Kinvig, 2000, Storkaas et al, 2001, Storkaas and Skogestad, 2004).

However, these methods have focused primarily on system stability with little or no attention on their adverse impact on oil production. Due to the difficulty of control tuning for open-loop unstable systems, most slug controllers are designed to operate around an open-loop stable condition, i.e. the control valve operating around a position where a manual choking method is able to stabilize the system usually at a smaller than necessary valve position. This imposes unnecessarily high back pressure on the riser-pipeline system and leads to a production reduction. In this work, the application of an active feedback

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control tuned at wide valve opening positions, corresponding to an open-loop unstable operating point, is studied. This technique achieves system stability with minimum back pressure imposed on the riser-pipeline, thereby minimising impact of slug control on production.

In order to tune the controller at an open-loop unstable condition, a linear model is derived from a simplified riser model at the unstable condition. Since the multiphase riser-pipeline system is extremely nonlinear, to ensure the stability of the control system for a wide operating range, the PID controller is designed based on a number of robust performance criteria. As a result, the robustly designed PID controller is able to work at a much wider valve opening position, further reducing the controller’s impact and under the right conditions could even increase production.

The paper begins with a description of the severe slugging phenomenon, methodology and system description. Analysis of the open loop control of the laboratory 2” riser system and the generic (industrial) riser system using bifurcation maps is then presented. This is followed by a description of the open loop unstable PID tuning method, implementation and impact on production. Finally, analysis of stability and production in declining reservoir pressure condition based on the manual choking and active control method is presented before concluding the work.

Background Severe Slugging

Severe slugging is a four stage cyclic flow phenomenon. One major condition for severe slugging to occur is the presence of a low point (dip) in the pipeline upstream of the riser. This causes liquid to accumulate at the riser base due to the balance of pressure by the opposing gravitational force; causing the liquid to block the pipeline. With the pipeline blocked, gas flow into the riser is stopped and further inlet gas is compressed in the pipeline, resulting in pipeline pressure building up with a continuous liquid accumulation in the riser. This continues until the pipeline pressure overcomes the hydrostatic head in the riser such that the liquid slug is pushed out of the riser. This results in a pressure reduction in the pipeline, which allows the gas to expand, penetrates the liquid and increase the flow velocity. With the gas front entering the riser, the liquid is blown out with a drop in velocity and pressure. This causes the liquid to fall back and block the riser base again causing a repeat of the cycle. A detailed description of the severe slugging phenomenon was given by Taitel (1986).

Simplified Riser and Separator Model (SRSM)

To design a stabilizing controller for an open-loop unstable system, it is necessary to have a reliable model of the system. Extended from the simplified riser model (SRM) developed by Storkaas et al (2005), an improved simplified riser separator model (SRSM) has been developed in the previous work (Ogazi et al, 2009). Simulation results obtained by using the improved SRSM closely match the experimental results much better than those obtained by using the original SRM. A detailed comparison between the SRM and the SRSM is reported by Ogazi et al (2009). Basic equations of the SRSM are provided in appendix B.

Experimental and Simulation Systems

In this study, experimental and simulation studies have been carried for two riser-pipeline systems. The first system is a 2'' riser-pipeline system in the multiphase flow laboratory at Cranfield University. The configuration and operating conditions of the system are described in Appendix A. The second system is a generic (industrial) riser system modeled using the commercial simulator, OLGA, developed by the SPT Group. The generic model is an 8'' riser-pipeline system consisting of a 5000m long pipeline, a 120m high riser and a pressure driven well of 69 barg. An additional gas lift source with a constant mass flowrate of 0.525 kg/s is applied at the well-head.

Both systems are modeled using the SRSM in Matlab software. Then linear models required for controller design are obtained at open-loop unstable points using the SRSM of both systems. The controller designed for the 2'' riser pipeline system is implemented in the physical plant and tested through simulation using the SRSM as well; while the controller designed for the 8'' generic riser system is examined through OLGA simulation. The impact on oil production is evaluated though OLGA simulation using the generic model with a pressure dependent well source. The flow-rate and pressure conditions of both systems are summarised in Table 1 below.

Table 1. Flowrate and operating pressure conditions of riser systems

Choking and Bifurcation Maps To demonstrate the suitability of the SRSM for control design, a series of manual choking positions are tested on both riser systems. The results predicted by the SRSM models are compared by those obtained from experiment on the 2” riser system

System Top separator operating pressure (barg)

Fluid source type Flowrate condition Liquid (kg/s) Gas (kg/s)

2” riser system (experiment) 1 Constant flow rate 0.75 0.0033 8” generic system (simulation) 30 Constant reservoir pressure @69 barg Pressure dependent 0.525

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and from OLGA simulation on the 8” generic model respectively. These results are presented in riser-base pressure bifurcation maps shown in Figures 1 and 2 for the 2” and 8” riser systems respectively.

Bifurcation Map of the 2” System

Results from open-loop simulation of the 2'' riser-pipeline system using the SRSM (solid line) and those through experiments (dashed line) are presented in the bifurcation map shown in Figure 1. The PRB oscillates between a minimum and a maximum pressure points for large z (>30%). Both SRSM and the experimental results show that at a critical z of 25% the desired stable non-oscillatory flow regime is obtained. The corresponding PRB from simulation and from experiment are 2.25 barg and 2.27 barg respectively.

Figure 1. Riser base pressure bifurcation map of the 2'' riser

Bifurcation Map of the 8” System

Results from open-loop simulation of the 8'' generic riser model using the SRSM with well source (dashed line) and OLGA (solid line) are presented in the bifurcation map shown in Figure 2. For z between 100% and 13%, the system is unstable and the PRB oscillates between a minimum and a maximum pressure points. The desired stable non-oscillatory flow regime is obtained at a critical z of 12% for both SRSM and the OLGA simulation results. The corresponding PRB from the SRSM and from OLGA simulation are 41.2 barg and 41.05 barg respectively.

Figure 2. Riser base pressure bifurcation map of the 8'' generic system

These critical values indicated by the above bifurcation maps give the minimum PRB and maximum z of the system to be

stabilised by manual choking. Our interest is to stabilise these systems on unstable operating points, where the values of z are larger than these critical values such that the total pressure drop across the riser and the valve is reduced; thus, the overall production is increased.

Robust PID Tuning Using Linear Models Linear models of both systems are obtained using the SRSM at open-loop unstable operating points. These linear models are then used to obtain appropriate parameters for PID controller tuning. The PID controller parameters are obtained to satisfy a number of robust stability criteria. These robust stability criteria are described in the next section with a brief introduction of the control system structure.

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Control System Structure and Sensitivity Functions Figure 3 shows the basic control structure applied to both riser-pipeline systems for severe slugging control as a feedback

control system. The manipulated variable u (controller output) is the valve opening, z, and the controlled variable is the riser base pressure, PRB.

Figure 3. Feedback control loop diagram for severe slug control

In Figure 3, G is the transfer function of the riser-pipeline system obtained through linearization of the SRSM, K is the PID

controller transfer function given as:

⎟⎟⎠

⎞⎜⎜⎝

⎛++= s

sKK D

ic τ

τ11 (1)

where Kc is the controller gain, τi is the controller integral time and Dτ is the controller derivative time. n represents uncertainties due to measurement noise and modeling errors. Gd is the transfer function from disturbances to PRB, where disturbances, d, include the liquid and gas flowrate variations, well pressure and downstream (topside separator) pressure fluctuations.

According to Figure 3, the riser base pressure of the riser-pipeline control system can be represented as: dGGuP dactualRB +=_ (2)

where u, the controller output (valve opening, z) can be written as:

( )nPPKu actualRBsetpoRB −−= _int_ (3)

Substituting u in (2) with (3), we have:

( ) dGnPPGKP dactualRBsetpoRBactualRB +−−= _int__ (4) Thus, we can obtain the closed-loop response of actualRBP _ as:

( ) ( ) ( ) TndSGTPGKnGKdGGKGKPGKP dsetpoRBdsetpoRBactualRB −+=+−+++= −−−int_

11int_

1_ 111 (5)

In equation (5), ( ) 11 −+= GKS is know as the sensitivity function and ( ) GKGKT 11 −+= is known as the complementary sensitivity function because 1=+ TS . These sensitivity functions are used to define the criteria for robust PID controller design shown as follows.

Control Design Criteria

The criteria used in determining suitable PID parameters are the lower and upper bound on the loop gain, GK, the upper bound on sensitivity function, ||S||∞ and the lower bound on bandwidth, ωb

*. 1. Upper bound on sensitivity function peak, ||S||∞:

Good disturbance rejection, set point tracking, and minimal noise transmission are performance requirements which the controller aims to achieve to ensure robust stability. Considering the basic control objective which is to manipulate the controller output, u, so that actualRBP _ is as close to int_ setpoRBP as possible, a set of requirements are imposed on equation (5). From the equation (5), the first requirement is rejection of disturbance effect, d. These disturbances could be due to liquid and gas flowrate variations, well pressure and downstream (topside

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separator) pressure fluctuations. The second requirement is the tracking of the PRB set point change. These two requirements are ideally achieved with 0≈S or 1≈T which requires GK to be large. In reality, the sensitivity function peak, ||S||∞, is typically required to be less than 2 (6dB) at all frequencies where control is required. Larger values of ||S||∞, indicates poor performance and poor robustness.

2. Upper and Lower bound on the loop gain, GK: From equation (5), the requirement for minimal noise transmission is achieved with 0≈T or 1≈S , which requires GK being small. This places an upper bound on GK required to satisfy 1≈T and a lower bound on GK required to satisfy 0≈T . Thus, there is a need for tread off in the magnitude of GK to meet both requirements. This tread off is provided in different frequency ranges in which these performance requirements are most needed (Skogestad and Posthwaite, 2005). Since, noise is mainly of high-frequency, thus, most of these performance requirements can be achieved by designing the controller, K, such that |GK| is large, that is |GK|>1 at lower frequencies below the cross over frequency (ωc) , and that |GK| is small, that is |GK|<1 at higher frequencies above the cross over frequencies. The cross over frequency is the frequency where |GK| first crosses 1 from above, (Skogestad and Posthwaite, 2005).

3. Lower bound on bandwidth, ωB*:

Giving that the riser-pipeline system has a pair of complex-conjugate unstable poles expressed as yjxp += , at the open loop unstable operating point, the lower bound on bandwidth given as:

( )22* 3467.0 yxxB ++>ω (6)

is require for effective control, (Skogestad and Postlethwaite, 2005). *Bω is the frequency at which |S| first

crosses 0.707 (-3dB) from below. After G is obtained through linearization of the SRSM, the controller parameters, DicK ττ ,, are designed to satisfy these

criteria given as above.

Robust PID Tuning for the 2” System According to Figure 1, the 2'' riser system is open loop stable at z=25% and unstable at z>25% with manual choking. Consequently, we aim to stabilise the system at the open loop unstable operating of z=30%, using a PID controller. The transfer function of the linear model obtained at z=30% valve opening with z as input and PRB as output is given as

162345

1223

%30 10979.717.313.24515.175.63210641.3287103427011.54

−

−

×+++−+×−++=

ssssssssG (7)

Table 2. PID tuning parameters obtained at z=30% for the 2'' riser

Controller parameters Stability parameters Kc(barg-1) τi τD ||S||∞ ωc ωB

* |GK|ω< ωc ω > ωc

-0.001 800 0.005 5.6 0.0015 0.0014 158 2e-8 -0.05 800 0.005 1 14.06 2.19 6606 1.26e-6 -1.2 800 0.005 0.96 50.4 10.6 141253 2.37e-5

According to equation (7),we obtain a pair of complex conjugate poles, 0.0746 ± 0.633i. From equation (6), the lower

bound of ωB* is obtain as 0.791 rad/s. ||S||∞, and |GK| and the system ωB

* are evaluated by analysing the bode plot of |S| and |GK| at various controller parameters, DicK ττ ,, . Table 2 shows the PID controller design parameters and corresponding ||S||∞, ωB

* and |GK| obtained from the bode plot. From Table 2, parameters with Kc= -1.2 are the best satisfying the stability criteria. With this set of PID controller

parameters, the effectiveness of the controller is tested by implementing it on the SRSM and on the flow laboratory 2” riser system. The experimental result obtained from the physical plant as shown in Figure 4 indicates that the system is unstable (severe slugging) at 30% valve opening. However, when the controller is switched on after 900s, severe slugging is suppressed with PRB at 1.9barg corresponding to about 30% valve opening.

In simulation with the SRSM, similar result is obtained showing that when the controller is switched on, severe slugging is suppressed with PRB at 1.95 barg corresponding to z at 27%.

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Figure 4. Slug control experimental results on the 2" system.

Robust PID Tuning for the 8” System From Figure 2, the 8” generic riser system is open loop stable at z=12% and open loop unstable at z>13% (that is with manual choking). Consequently, we aim to stabilise the system at the open loop unstable operating of z=20%, using a PID controller tuned at this point. The transfer function of the linear model obtained at z=20% valve opening with z as input and PRB as output is given as:

00001282.0001128.0275.50002236.01037.0

23%20 +−+−−=

ssssG (8)

From equation (8) above, we obtain a pair of complex conjugate poles, 0.0001 ± 0.0016i. From equation (6), the lower

bound of ωB* is obtain as 0.00296rad/s. ||S||∞, and |GK| and the actual ωB

* are evaluated by analysing the bode plot of |S| and |GK| at various controller parameters, DicK ττ ,, . Table 3 shows the PID controller design parameters and corresponding ||S||∞, ωB

* and |GK| obtained from the bode diagram.

Table 3. PID tuning parameters obtained at z=20% for the 8'' riser Controller parameters Stability parameters

Kc(barg-1) τi τD ||S||∞ ωc ωB* |GK|

ω< ωc ω > ωc -0.05 500 0.005 14 0.0025 0.0020 158 5.7e-7 -0.1 500 0.005 2.6 0.0034 0.0241 316 1.1e-6 -2 500 0.005 1 0.0392 0.0353 6309 2.7e-5

From Table 3, parameters with Kc= -2 are the best satisfying the stability criteria. Using this set of PID controller

parameters, the effectiveness of the controller is tested by implementing it on the generic riser model in OLGA and in the SRSM with well source.

In the OLGA model, the simulation result shown in Figure 5, indicates that at fixed valve opening of 20% (open loop) the system is unstable; thus the riser base pressure, PRB, oscillates. When the controller is switched on after 5 hours, with PRB set point at 36.8 barg, severe slugging is suppressed (system stabilised) with z at 20%. By reducing the PRB set point further, the controller maintained system stability to a minimum riser base pressure of 34.4 barg with valve opening increasing to a maximum value of 57.6%. Beyond this point the controller is not able to stabilise the system. However, when the valve opening was returned to 20% fixed valve opening (open loop) after 15 hours, the system gradually returned to a totally unstable condition. These pressures and valve opening conditions are summarised in Table 4 below, in comparison with the bifurcation map results shown in Figure 2.

Table 4. 8” system stable operation comparison

Variable Manual choking Active control Valve opening, z, (%) 12 20 57.6

Riser base pressure, PRB, (barg) 41.05 36.8 34.4 Thus, the controller tuned at open loop unstable operating point of z = 20% stabilised the system at this same point and also

capable of stabilising the system at wider valve opening with the set point, PRB, further reduced. The significance of these results is obvious when the accumulated production at these pressure and valve opening conditions is analysed as shown in the next sections.

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Figure 5. Slugging control OLGA simulation results.

Impact on Production Production in a 24hr period simulation is analysed to assess the impact of open loop tuned controller and compared with that in fixed choking at the same valve positions. It must be mentioned that when the choke valve is fixed at these openings, the system is unstable with large fluctuations in flow and pressure

Figure 6. Production comparison I: with and without active slug control.

Figure 7. Production comparison II: different stable and unstable operation modes

Figure 6 shows that from the OLGA simulation, the production under severe slugging condition at the valve position of

z=20% is 303.4 m3/day. By stabilizing the system with the controller designed at z = 20% as shown in Figure 5, the production obtained is 324.6 m3/day. With manual choking control, the system is stabilized (severe slugging eliminated) at z =12% as shown in Figure 2, and the production is 280.25 m3/day, as shown in Figure 7.

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This implies that by implementing the robust PID controller at this operating point (z=20%), production is increased by 7% when compared to the production under severe slugging condition at the same fixed valve position and that production is increased by 15% when compared to manual choking control at z =12%.

By implementing the controller at the maximum possible operating point of z = 57.6%, the production obtained is 340 m3/day as shown in Figure 6 and Figure 7. This implies that by operating the controller at this point, (z=57.6%), production is increased by 7.1% when compared to the production under severe slugging condition by fixing the valve at the same position and that production is increased by 21.3% when compared to manual choking control at z =12%.

Analysis of the production with the valve fully open (z=100%) shows that the production with severe slugging occurring at this condition is 335m3/day. This indicates that the production achieved by the robust PID controller operating at z=57.6% is even 1.4% higher than that with the valve fully open. Similar results were obtained through the SRSM simulation, but are not presented here because of space limitation.

It can be observed that for the flow and operating conditions applied, higher percentage increase in production is obtained with comparison to manual choking, which reflects the high reduction in production from the unstable condition if manual choking control method is implemented. Thus, manual choking control will adversely reduce production. With these results, it is evident that with the robust PID tuning method, active slug control will meet two fundamental objectives which have previously been considered to be incompatible, namely, stabilising the system (at a larger valve position other than the manual choking stable operating point), and increasing oil production. Stability and Production in Declining Reservoir Pressure Condition As the well pressure declines (as fields ‘mature’), the differential pressure between the topside pressure set point and the well source decreases; thus the fluid flowrate is reduced. This would impose further disturbance (instability) on the riser system such that further action is required to stabilise the system. With topside valve choking control, this further action would imply reducing the valve opening further. Implementing manual choking or the robust PID controller in this condition could have serious impact on production.

Figure 8. System stability at declining well pressure

Figure 9. Percentage of production increase against well pressure

Figure 8 shows the minimum riser base pressure and the maximum valve opening required to stabilise the generic

(industrial) riser model at declining reservoir pressure (from 69 barg to 45.3 barg) by using manual choking and using the open

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loop unstable tuned controller. To stabilise the system with manual choking, the maximum valve opening is reduced from 12% at 69 barg to 7% at 45.3 barg. However, with the robust PID controller, the system is stabilised at a wider maximum valve opening of 57% at 69 barg and 42% at 45 barg.

This result shows that with the manual choking, the minimum pressure drop across the riser is much higher than the maximum pressure drop across the riser obtained with the controller implementation for the range of the well pressures. The impact of this on production is illustrated in Figure 9 below.

From Figure 9, it is observed that the percentage of increase in production due to the controller implementation increases with declining well pressure. This reflects the significant reduction in production incurred due to manual choking control method as the well pressure decreases. Thus, with the robust PID controller, significant proportional production increase is maintained while with manual choking, production is further reduced with declining well pressure. This result also shows the degree of robustness of the controller in tracking PRB set point and in stabilising the system with disturbances imposed by the declining reservoir pressure and varying fluid flowrate as required by the stability criteria. It should be pointed out that this result is based on a linear well model. If the reservoir model is nonlinear, the trend of the impact of slug control on production may behave differently.

Conclusions In view of the work reported in this paper which focused on multiphase severe slug control at open-loop unstable operating point using robust PID controllers in an active feedback control loop, the following conclusions can be drawn based on the results.

Active feedback control implemented at an open-loop unstable operating point is effective in suppressing slug formation and controlling severe slugging in multiphase flow pipelines. Active feedback control at open-loop unstable operating point can impose the minimum possible back pressure on the riser-pipeline system; lower than the high back pressure imposed by manual choking method and some existing active control solutions designed around manual choking operating point. Due to the significant reduction in backpressure achieved by implementing severe slug control at open-loop unstable operating point with active feedback control, oil production is increased from the system. With the robust PID controller, the percentage of increase in production will increase when compared to manual choking as the well pressure declines. The open loop unstable tuned control is robust in changing flow conditions and declining well pressure condition. The total possible oil recovery from an oil field will be increased by controlling severe slugging at open loop unstable operating point using active feedback control as shown by simulation on the generic (industrial) riser OLGA model and the SRSM with a well source. This result suggests that the operation life of a reservoir might be extended by adopting a well tuned slug controller. Acknowledgements This work has been undertaken within the Joint Project on Transient Multiphase Flows and Flow Assurance. The Authors wish to acknowledge the contributions made to this project by the UK Engineering and Physical Sciences Research Council (EPSRC) and the following: - Advantica; BP Exploration; CD-adapco; Chevron; ConocoPhillips; ENI; ExxonMobil; FEESA; IFP; Institutt for Energiteknikk; PDVSA (INTEVEP); Petrobras; PETRONAS; Scandpower PT; Shell; SINTEF; StatoilHydro and TOTAL. The Author(s) wish to express their sincere gratitude for this support.

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Hong Kong. Storkaas, E., Skogestad, S., and Godhavn, J., (2005), A low dimensional dynamic model of severe slugging for control design and analysis.

Statoil ASA, R&D, Process Control, Arkitekt Ebells vei 10, Rotvoll, N-7005, Trondheim, Norway Tengesdal, J, Ø., Sarica, C. and Thompson, L., (2002), Severe slugging attenuation for deepwater multiphase pipeline and riser systems.

Paper SPE 87089 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September – 2 October. Taitel, Y., (1986), Stability of severe slugging. Int. J. of Multiphase Flow, 12(2); 203-217. Taitel, Y., and Dukler A.E., (1977), A model for frequency during gas-liquid flow in horizontal and near horizontal pipes. Int. J. Multiphase

flow, 3(6): 585-596. Appendix A: Multiphase Facility at Cranfield University

Figure A-10. Multiphase facility at Cranfield University

The facility consists of a 2'' and a 4'' riser-pipeline system which can run alternatively. The 2'' riser is a vertical riser with

upstream pipeline length of 39m inclined downwardly at 2o and a riser height of 11m while the 4'' riser is catenary with upstream pipeline length of 55m also inclined downwardly at 2o and a riser height of 10.5m. Fluid of both systems is supplied from three independent single-phase sources for oil (dielectric 250), water and air. For each riser system, the supplied fluid mixes at a mixing point into the pipeline which connects to the riser. The top of both risers is equipped with topside processing facility which includes a control valve, a two phase vertical separator which separates the fluid into liquid and gas for measuring instruments. The two phase separator is about 1.2m high and 0.5m in diameter. It consists of the gas and liquid outlet control valves and pressure, flow, temperature and level transmitters. Pressure and flow measurements are obtained at riser inlet and outlet. The schematic diagram of this facility is shown in Figure A-1.

SPE 124883 11

Appendix B: SRSM Equations The description of the symbols used in the model is given in Table B-1.

Table B-1. Model Notations

Symbol Description Unit A Separator cross sectional area m2

 Internal gas mass flow area m2

Ap Pipe cross sectional area m2

G Gravity m/s2

HR Riser height m Hs Separator height m H1 Critical liquid level m h1 Liquid level upstream the riser bend m hL Separator liquid height m K1 Valve coefficient K2 Gas flow coefficient L3 Length of horizontal riser top section m

1Gm Mass of gas in pipeline kg

2Gm Mass of gas in the riser kg

Lm Mass of liquid in the riser kg

mLin Separator liquid inlet mass flowrate kg/s mLout Separator liquid outlet mass flowrate kg/s

mixoutm Total fluid mass flowrate at riser top kg/s

GM Molecular weight of gas kg/K.mol

GinM Mass flowrate of gas into the system kg/s

LinM Mass flowrate of liquid into the system kg/s

LoutM Mass flowrate of liquid out of the riser kg/s

GoutM Mass flowrate of gas out of the riser kg/s

1GM Internal gas mass flowrate kg/s

Ps Separator top pressure barg PRB Riser base pressure barg PRT Riser top pressure barg Qin Separator gas volume inlet flowrate m3/s Qout Separator gas volume outlet flowrate m3/s R Gas constant 8.314 J/K/mol T System temperature K

1Gv Internal gas velocity m/s

VG1 Volume of gas in pipeline m3

VT Total riser volume m3

Z Riser top valve position

LTα Average liquid volume fraction at riser top

Gα Gas volume fraction in the pipeline

MLα Liquid mass fraction

ρG1 Pipeline gas density kg/m3

ρG2 Riser top gas density kg/m3

ρL Liquid density kg/m3

12 SPE 124883

Conservation equations The SRSM consists of five dynamical state equations which account for mass of gas in the pipeline, 1Gm , mass of gas in

the riser, 2Gm , mass of liquid in the riser, Lm , separator top pressure, sP , and separator liquid height, Lh , which are stated below:

11

GGinG MM

dtdm −= (B-1)

GoutGG MM

dtdm −= 1

2 (B-2)

LoutLinL MM

dtdm −= (B-3)

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+−

−=

dtdhAQQ

hHAP

dtdP l

outinls

ss (B-4)

L

Loutlinl

Amm

dtdh

ρ)( −= (B-5)

State dependent variables

The state dependent variables such as the riser base pressure, RBP , and riser top pressure, RTP , is calculated using the ideal gas law given as:

GG

GRB MV

RTmP1

1= (B-6)

GG

GRT MV

RTmP2

2= (B-7)

where the volume of gas in the pipeline, VG1, and in the riser, VG2, is calculated as:

LAV PGG α=1 (B-8)

LRTG VVV −=2 (B-9)

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

=

L

Lin

G

Gin

PG

Gin

G mm

m

RB

ρρ

ρα (B-10)

)( 3LHAV RPT += (B-11) The internal gas mass flowrate (riser base), 1GM is given as:

AvM GGGˆ

111 ρ= (B-12) where

1

11

G

GG V

m=ρ (B-13)

SPE 124883 13

11

112111 )(

G

RLLRTRBG

HgPPh

hHKHhvρ

αρ−−<= − (B-14)

Total fluid flow out of the riser, mmixout, is calculated using a simplified valve equation given as

( )g

PPzKm sRTTmixout

−= ρ1 (B-15)

2)1( GLTLLTT ραραρ ++= (B-16)

2

22

G

GG V

m=ρ (B-17)

The gas and liquid mass flowrate out of the riser is therefore calculated as

outmixmLGout mM ,)1( α−= (B-18)

outmixmLLout mM ,)(α= (B-19)