In line with the objectives of this project, which is to study severe slugging con-trol in a plant-wide scale, the modeling of the major system units of the riser production system and their performances is discussed in this section. The severe slug predicting model, which contains the models of the major system units of the riser-pipeline production system is known as a plant-wide model.
To develop the plant-wide model, these major system units namely: the riser-pipeline, the topside separator and the pressure driven fluid source are mod-elled and linked together. Experimental studies have shown that the interaction between the process variables in these systems, such as pressure, affect the ability to control severe slugging [116].
4.2.1 The riser-pipeline model
The riser-pipeline model is a very important part of the plant-wide model. One major condition for the occurrence of severe slugging is the inclination of the pipeline, upstream of the riser inlet. A number of severe slug models have been developed using only the pipeline and the riser as a single unit [6, 67, 103]. The challenge with these models is their ability to accurately predict the nonlinear characteristics of severe slugging and the control performances of the system
without complex and unrealistic mathematical solutions. The suitability of some riser-pipeline models for severe slug control design will be briefly discussed.
4.2.1.1 Suitability of riser-pipeline models
A reliable slug controller is required for the study and the analysis of the control performance of the slug control system. In order to design a model based slug controller, a linearised model is normally desired. The linearisation of a nonlinear model requires that the internal equations of the nonlinear model should be readily accessible, and that the linearisation should be performed with the existing tools and methods. The two fluid model, the drift flux model and commercial multiphase flow simulators such as the OLGA models, are some of the exisiting models, which can predict severe slugging. However, there are some challenges with the application of these models in slug control design and performance analysis.
The two fluid model is based on mass and momentum balance for each phase while the drift flux model applies mass balance equation for each phase and a combined momentum balance for all the phases [46]. Both models are ex-pressed in partial differential equations (PDEs) [102]. To obtain a model in ordinary differential equations (ODEs) for control design, the PDE model has to be transformed by space discretisation. However, the order of the model obtained from this process can be very high such that the numerical optimisa-tion required for model based controller design gets complicated. This limits the application of both PDE models in model based design for severe slugging control. A model based on commercial simulators such as OLGA, cannot pro-vide readily accessible internal equations due to commercial reasons, making
it unsuitable for linearisation. With these challenges, the need for a simplified severe slug model arises.
4.2.1.2 Simplified riser model (SRM)
An attempt to develop a simplified riser model (SRM), which can predict se-vere slugging as well as estimate relevant control performance, was made by Storkaas et al in 2005 [102]. The conservation equations of the SRM are de-scribed in this section. The simplified representation of the riser-pipeline sys-tem used to develop the SRM is shown in Figure 4.1.
h1 θ
HR
mLin
mGin
H1
mG1,PRB, VG1
mG2,PRT, VG2, αLT
mL
u
mmix
Figure 4.1: Riser-pipeline schematic diagram for the SRM
Based on Figure 4.1, the SRM was developed with three dynamical states, which account for the:
1. mass of gas in the pipeline, mG1
2. mass of gas at the riser top, mG2
3. mass of liquid in the riser, mL
The corresponding conservation equations are given in (A.1), (A.2) and (A.3).
dmG1
dt = mGin− mG (4.1)
dmG2
dt = mG− mGout (4.2)
dmL
dt = mLin− mLout (4.3)
From Figure 4.1, it can be observed that severe slugging is initiated when h1 ≥ H1, such that the riser base is blocked by liquid, where h1 is the liquid height in the riser base and H1 is the critical liquid height. In this condition, the gas mass flow rate, mG, into the riser will be zero (mG = 0). If h1 < H1, then the riser base is not blocked by the liquid, such that there is continuous flow of gas into the riser. Under this condition, the gas mass flow rate into the riser is dependent on the gas flow area, A, and the pressure drop at the riser base.
The full description of the SRM, showing the state dependent equations, the flow equations and the entrainment model equations is given in Appendix A.
In order to design an efficient slug controller for the physical plant, a validation of the model’s predictions against experimental results is required. Experimen-tal result obtained from the riser systems in the Cranfield University multiphase flow lab showed that the capability of the SRM is limited due to some assump-tions [77]. These assumpassump-tions and limitaassump-tions are discussed below.
Limitations of the SRM
The assumptions that limit the performance of the SRM are highlighted below:
1. The riser outlet pressure (separator pressure), Ps, is assumed to be stant, which effectively means a separator with an infinite volume con-nected at the riser outlet. This does not represent any real system as the dynamics of the topside processing equipment (the separator) has a significant effect on the severe slugging behaviour as was demonstrated in previous work by Yeung et al [116].
2. The model does not account for the slug production stage, which occur in the severe slug cycle. The omission of this stage affects the prediction of liquid flow pattern out of the riser, and limits the application of the model in analysing the accumulated production over a production period, during severe slugging.
3. The assumption of constant pipeline gas volume (VG1) in the pipeline, which implies constant liquid hold up, limits the prediction of the slug am-plitude and frequency accurately simultaneously. According to Storkaas (2005, pp 47), “..the simplified three state model predicts a slug frequency that, compared to the OLGA simulations, is about 10-20% too high for low-to-medium range valve openings and up to about 50% too high for large valve openings. The higher frequency probably comes from neglecting the liquid dynamics in the feed section. ...and when the upstream gas volume is fixed, we cannot achieve both frequency and amplitude simul-taneously”. Consequently, the model only offers the choice of predicting accurate slug amplitude or frequency at a time, not both.
4. The model assumes fixed liquid and gas inlet flow rates. Any change to the inlet flow rates will require re-tuning the model parameters. Therefore,
the inlet flow rates cannot be altered during a simulation. This limits the application of the model in analysing the impact of severe slugging control on production, with a pressure dependent fluid source.
In view of these limitations, a further mechanistic modeling effort is required to improve the performance and reliability of the SRM. This has led to the devel-opment of the improved simplified riser model (ISRM).