**Team:
**

**Supervised by:**

__LEGENDRE Dominique__: Professor and Researcher at INP-ENSEEIHT & IMFT

__LINE Alain__: Professor and Researcher at INSA Toulouse & LISBP

Gas-liquid two-phase flow occurs in both onshore and offshore crude oil and natural gas production and transportation facilities. In an offshore oil and gas production facility, pipeline-riser systems are required to transport two-phase hydrocarbons from subsurface oil and gas wells to a central production platform. Severe slugging reaching several thousands pipe diameters may occur when transporting gas and liquid in these pipeline-riser systems.

Severe slugging creates potential problems in the platform facilities, e.g. separators, pumps and compressors. Severe slugging may cause overpressurization of the separator, rupture of the pipe, and an increased back pressure at the wellhead. All of these might lead to the complete shutdown of the production facility. Therefore, the accurate predictions of severe slugging characteristics, e.g. slug length, oscillatory period, are essential for the proper design and operation of two-phase flow in the pipeline-riser systems.

LedaFlow is a new dynamic multiphase flow simulator for wells and flowlines. Based on models that are closer to the actual physics of multiphase flow, LedaFlow provides a step change in fidelity, quality, accuracy and flexibility over current generation multiphase flow simulation technology. This increase in model definition provides the engineer with much greater understanding of the flow in wells and pipelines.

First of all, the experimental data acquired at IMFT published by **J.Fabre and L.L. Peresson** was used to validate Ledaflow 1.3 software. The same experimental results were obtained using the numerical simulation by Ledaflow.

A full updated tutorial (12/03/2013) of the new version 1.3 of Ledaflow has been created.

Then, the focus was on three points with small gas and liquid flow rates referring to **J.Fabre and L.L Peresson **article. Three Turndown curves were traced for each point with the same gas and liquid mass fraction but with different gas and liquid flow rate.

Using these curves and transient simulations by Ledaflow, a flow map was created to distinguish the stable zone, the transient zone and the unstable zone (severe slugging).

Studies were made to compare the geometry effect on the results already found, once by doubling the length of the pipe by two and another time by doubling the height of riser by two.

The next **Video** was filmed at LISBP, INSA Toulouse for an experimental installation to capture the severe slugging phenomena.

**Why Flow Assurance is needed**?

Flow assurance is an engineering analysis process that is used to ensure that hydrocarbon fluids are transmitted economically from the reservoir to the end user. Because of the high pressures and low temperature in deep water, flow assurance is the most critical task during the transport of hydrocarbon fluids. It focuses mainly on the prevention and the control of concern, such as hydrates, wax, and asphaltenes, sometimes scale and sand are also included. For a given hydrocarbon fluid, these solids appear at certain combinations of pressure and temperature and they deposit on the walls of the production equipment and flowlines.

Figure 1-1 shows the hydrate and wax depositions formed in hydrocarbons flowlines, which ultimately may cause plugging and flow stoppage.

Figure 1-1 Solid Depositions Formed in Hydrocarbon Flowline

The most familiar two-phase flows in petroleum production are gas-water flow and oil-water flow. In our study, we focus on the gas-water vertical flow patterns.

Two-phase flow in vertical pipelines may be categorized into five different flow patterns, as shown in figure 1-2 and listed here: Bubble flow, Slug flow, Churn flow, Froth flow and Annular flow.

This plot is helpful for understanding the phenomena, several flow regimes are identified on the map such as annular flow at very high gas rates and very low liquid rates & bubble flow at very low gas rates. Also note the large zone of intermittent/slug/churn flow in the center of the plot.

Figure 1-2 Flow regime transition criterion for upward two-phase flow in vertical tube

*Source : http://aghajar.okstate.edu/content/singletwo-phase-heat-transfer-laboratory*

Figure 1-3 Slug flow pattern in vertical pipes

In our study, we are interested in the slug flow pattern in vertical pipes and risers, figure 1-3. In vertical flow, the bubble is an axially symmetrical bullet shape that occupies almost the entire cross-sectional area of the tubing. The velocity of the gas bubbles is greater than that of the liquid slug, thereby resulting in a liquid holdup that not only affects well and riser friction losses but also flowing density.

At low gas and liquid flow rates, unsteady state flow may occur in such two-phase pipeline-riser systems. The cyclic unsteady state flow characterised by large-amplitude, relatively long-period pressure and flow rate fluctuations is know as severe slugging.

At relatively low flow rates, liquid accumulates at the bottom of the riser, blocking the gas, until sufficient upstream pressure has been built up to surge the liquid slug out of the riser followed by gas surge. After fluid and gas surge, part of the liquid in the riser falls back to the riser base to create a new blockage and the cycle repeats. This transient cyclic phenomenon causes period of no liquid and gas production at the riser top followed by very high liquid and gas surges, and is called severe slugging.

Figure 1 shows the different stages of a cycle of severe slugging

Fig. 1 : Stages of Severe Slugging

To highlight the differences between all types of severe slugging, we can better describe a cycle of SS1 in five stages: (1) Blockage of the riser base ; (2) slug growth; (3) liquid production; (4) fast liquid production; (5) gas blowdown. In Fig. 2 these five stages are illustrated.

Fig. 2: Stages for severe slugging of type 1 (a) a graphical illustration (b) marked on a cycle of an experimental riser $\Delta\:P$ trace (U_{SL}=0.2 m/s & U_{SG0} =1 m/s)

The transitional severe slugging of type 2 is qualitatively similar to SS1, but the slug length is shorter than the height of the riser and it often has intermittent unstable oscillations. In Fig. 3 four stages of SS2 are illustrated.

Fig. 3: Stages for severe slugging of type 2 (a) a graphical illustration (b) marked on a cycle of an experimental riser $\Delta\; P$ trace (U_{SL}= 0.10 m/s & U_{SG}=2.00 m/s)

We describe a cycle of SS3 in four stages: (1) transient slugs; (2) aerated slug growth; (3) fast aerated liquid production; (4) gas blowdown. In Fig. 4 these four stages are illustrated.

Fig. 4: Stages for severe slugging of type 3 (a) a graphical illustration (b) marked on a cycle of an experimental riser $\Delta P$ trace (U_{SL}= 0.39 m/s & U_{SG}=2.33 m/s)

Severe slugging creates potential problems in the platform facilities downstream of the riser top which have been designed to operate under steady state conditions, e.g. separators, pumps and compressors. During the liquid and gas surges, the peak flow rates might cause overpressurization of the separator, which consequently might lead to the complete shutdown of a production facility. Moreover, an increased back pressure at the wellhead may lead to the end of the production and abandonment of the well. These repeating impacts provoke a faster mechanical fatigue and can eventually lead to a rupture.

Therefore, the accurate prediction of severe slugging characteristics is essential for the proper design and operation of two-phase flow in these systems

LedaFlow is a new dynamic multiphase flow simulator for wells and flowlines. Based on models that are closer to the actual physics of multiphase flow, LedaFlow provides a step change in fidelity, quality, accuracy and flexibility over current generation multiphase flow simulation technology. This increase in model definition provides the engineer with much greater understanding of the flow in wells and pipelines.

Ledaflow development started in 2001 in collaboration between Total, ConocoPhillips and SINTEF. In 2009, Kongsberg joined as the industrialization and commercialization partner. First commercial release was in June 2011 and in March 2013 the 4^{th} version, release 1.3 was issued.

- To meet the challenges with Oil and Gas fields found in deeper water, longer tie-backs, harsh and remote environments
- To improve accuracy in multiphase flow prediction
- To increase the detail of information available

http://www.kongsberg.com/en/kogt/offerings/software/ledaflow/

The flow regimes are model elements that describe the geometrical distribution of the various phases. In LedaFlow there are two sets of flow regimes: the gas-liquid flow regime and the oil-water flow regime.

The gas-liquid flow regime describes the geometrical configuration of the gas and liquid. Here the liquid is considered as a mixture of oil and water with its own internal structure represented by the oil-water flow regime. There are three basic gas-liquid flow regimes:

- Separated flow: the flow consists of a gas zone (possibly with liquid droplets) and a liquid zone (possibly with gas bubbles)
- Bubbly flow: the gas exists only as bubbles inside the liquid
- Slug flow: the flow is intermittent, consisting of liquid slugs and slug bubbles. The flow regime inside the slugs is assumed to be bubbly and the flow regime in the slug bubbles is assumed to be separated. As such, slug flow is a mixture of separated and bubbly flows.

In separated flow, the gas and liquid flow in different zones. The liquid may be a mixture of oil and water, which may be fully mixed, completely or partially separated. The gas zone may have droplets of oil and water and the liquid zone may have gas bubbles. Gas entrainment in the liquid film is only modelled in slug capturing.

The separated flow regime is sub-divided into two categories:

- Stratified flow(where the liquid is located at the bottom of the pipe)
- Annular flow (where the liquid is distributed symmetrically around the pipe periphery).

In bubbly flow the gas is assumed to exist only in the form of bubbles entrained inside the liquid, so there is no gas zone. In three-phase flow with separated oil and water, we assume that the geometric distribution of oil and water is the same as in separated flow and that the gas bubbles are uniformly distributed across the pipe cross-section.

Hydrodynamic slug flow is an intermittent transient flow regime, where flow consists of liquid slugs with regions of separated flow in between. In the liquid slugs the local flow regime is assumed to be bubbly. Between the slugs the local flow regime is assumed to be separated. The models used in these two regions are consistent with the modelling used in the bubbly flow and separated flow.

In the standard LedaFlow model, hydrodynamic slug flow is modelled on a sub-grid level, i.e. the slugs are not resolved on the grid. Instead, the steady-state solution to the slug flow equations (called the Unit Cell Model, or UCM) is calculated, and the results are subsequently used to calculate the appropriate friction terms, etc. in the transient code.

The UCM consists of 34 equations and 34 unknowns in the case of three-phase flow. The unknown quantities are:

- 6 field fractions and 6 velocities inside the slug
- 9 field fractions and 9 velocities inside the slug bubble
- The pressure gradient in the slug
- The pressure gradient in the slug bubble
- The slug fraction
- The slug front pressure drop

The UCM equations for three-phase flow are:

- 2 steady state momentum equations in the slug
- 2 oil/water dispersion models in the slug
- 1 void-in-slug model
- 4 slip relations in the slug
- 1 volume constraint in the slug
- 3 steady-state momentum equations in the slug bubble
- 2 oil/water dispersion models in the film
- 1 droplet entrainment model in the slug bubble
- 1 oil/water split model for droplet entrainment
- 6 slip relations in the slug bubble
- 3 global mass conservation equations
- 1 slug bubble velocity correlation
- 1 volume constraint in the slug bubble
- 2 gas entrainment models for the oil/water film in the slug bubble
- 1 model for slug front pressure drop

Slug flow is selected if a physical solution to the UCM is found, that is a solution with a slug fraction between 0 and 1. If no such solution can be found the flow regime is deemed either bubbly flow or separated flow. The flow regime selection logic within LedaFlow is formulated so that the UCM equations are only solved if the flow regime is slug flow.

The logic can be summarised by:

- If the slug gas fraction is greater than the gas fraction in steady state bubbly flow the flow is regime is bubbly
- If the gas-liquid slip velocity in stratified flow is greater than in slug flow the regime is slug flow
- Otherwise the regime is stratified

In LedaFlow we have two basic oil-water flow regimes:

- Separated oil-water flow: the oil and water flow in separate zones, possibly with oil droplets in the water zone and water droplets in the oil zone
- Mixed oil-water flow: the oil and water are completely mixed in the form of oil droplets in the water (water-continuous) or water droplets in the oil (oil-continuous)

The oil-water regime is modelled as mixed if the absolute value of the pipe angle exceeds 9 degrees in separated flow or 15 degrees in slug/bubbly flow. In addition, if the no-slip phase fraction of either oil or water is less than 10^{-5} , the oil-water regime is also assumed to be mixed.

For the gas phase

\begin{equation}

\frac{\partial (V_{g}\rho _{g})}{\partial t}=-\frac{1}{A}\frac{\partial (AV_{g}\rho _{g}v_{g})}{\partial z}+\psi _{g}+G_{g}

\end{equation}

For the liquid droplets

\begin{equation}

\frac{\partial (V_{D}\rho _{L})}{\partial t}=-\frac{1}{A}\frac{\partial (AV_{D}\rho _{L}v_{D})}{\partial z}-\psi _{g}\frac{V_{D}}{V_{L}+V_{D}}+\psi _{e}-\psi _{d}+G _{D}

\end{equation}

For the liquid film

\begin{equation}

\frac{\partial (V_{L}\rho _{L})}{\partial t}=-\frac{1}{A}\frac{\partial (AV_{L}\rho _{L}v_{L})}{\partial z}-\psi _{g}\frac{V_{D}}{V_{L}+V_{D}}-\psi _{e}+\psi _{d}+G _{L}

\end{equation}

$g= Gas$

$D=Droplets$

$L=liquid\;film$

$V=Volume\;fraction\;(-)$

$v=velocity\;m/s$

$\rho=density\;(kg/m^3)$

$A=cross-sectional\;area\;of\;the\;pipe\;(m^2)$

$\psi_g=mass\;transfer\;rate\;between\;phases\;(kg/m^3/s)$

$\psi_e=entrainment\;rate\;of\;liquid\;droplets\;(kg/m^3/s)$

$\psi_d=deposition\;rate\;of\;liquid\;droplets\;(kg/m^3/s)$

$G=possible\;mass\;source\;of\;a\;particular\;phase\;(kg/m^3/s)$

For the gas phase

\begin{equation}

\frac{\partial (V_{g}\rho _{g}v_{g})}{\partial t}=-V_{g}\left (\frac{\partial p}{\partial z} \right )-\frac{1}{A}\frac{\partial (AV_{g}\rho _{g}v_{g}^{2})}{\partial z}\\

-\lambda _{g}\frac{1}{2}\rho_{g} \left |v_{g} \right |v_{g}\frac{S_{g}}{4A}-\lambda _{i}\frac{1}{2}\rho_{r} \left |v_{r} \right |v_{r}\frac{S_{i}}{4A}+V_{g}\rho_{g}g\,cos\alpha+\psi_{g}v_{a}-F_D

\end{equation}

For the liquid droplets

\begin{equation}

\frac{\partial (V_{D}\rho _{L}v_{D})}{\partial t}=-V_{D}\left (\frac{\partial p}{\partial z} \right )-\frac{1}{A}\frac{\partial (AV_{D}\rho _{L}v_{D}^{2})}{\partial z}\\+V_{D}\rho_{L}g\,cos\alpha+\psi_g \frac{V_D}{V_L+V_D}v_a+\psi_{e}v_{i}-\psi_{d}v_{D}+F_D

\end{equation}

Eqs. (4) and (5) are combined to yield the following equation.

\begin{equation}

\frac{\partial }{\partial t}\left ( V_g \rho_g v_g+V_D\rho_L v_D \right )=-\left ( V_g+V_D \right )\left ( \frac{\partial p}{\partial z} \right )-\frac{1}{A}\frac{\partial }{\partial z}\left ( AV_g\rho_gv_g^{2} +AV_D\rho_L v_D^2\right )-\lambda_g\frac{1}{2}\rho_g\left | v_g \right |v_g\frac{S_g}{4A}\\-\lambda_i\frac{1}{2}\rho_g\left | v_r \right |v_r\frac{S_i}{4A}+\left ( V_g\rho_g+V_D\rho_L \right )\,g\,cos\alpha+\psi_g\frac{V_D}{V_L+V_D}\,v_a+\psi_e\,v_i-\psi_d\,v_D

\end{equation}

For the liquid film

\begin{equation}

\frac{\partial }{\partial t}\left ( V_L\rho_Lv_L \right )=-V_L\left ( \frac{\partial p}{\partial z} \right )-\frac{1}{A}\frac{\partial }{\partial z}\left ( AV_L\rho_Lv_L^2 \right )-\lambda_L\frac{1}{2}\rho_L\left | v_L \right |v_L\frac{S_L}{4A}+\lambda_i\frac{1}{2}\rho_g\left | v_r \right |v_r\frac{S_i}{4A}\\+V_L\rho_L\,g\,cos\alpha-\psi_g\frac{V_L}{V_L+V_D}v_a-\psi_ev_i+\psi_dv_D-V_Ld\left(\rho_L-\rho_g \right )\,g\,\frac{\partial V_L}{\partial z}\,sin\alpha

\end{equation}

where,

$v_a=v_L \;\;for\;\; \psi_g>0\;\; \left(and\; evaporation\; from\; the \;liquid \;film\right)$

$v_a=v_D \;\; for \;\; \psi_g>0\;\; \left(and\; evaporation \; from \; the \;liquid\;droplets\right)$

$v_a=v_g\;\; for \;\; \psi_g<0\;\;\left(condensation\right)$

$alpha\;=\;pipe\; inclination\;from\; the\;vertical\;\left(rad\right)$

$p\; = \; pressure\; \left(Nm^{-2}\right)$

$v_r\;= \;relative\; velocity\; \left(ms^{-1}\right)$

$G\;=\;internal\; mass\; source\; - assumed\; to\; enter\; perpendicular\; to\; the\; pipe\; wall\;, carrying\; no\; moment$

$ S_g\;=\;wetted\; perimeter\; of\; the\; gas\; \left(m\right)$

$S_L\;=\;wetted\; perimeter\; of\; the\; liquid \; \left(m\right)$

$S_i\;=\;wetted\; perimeter\; of\; the\; interface \; \left(m\right)$

The relative velocity is given by the following equation

\begin{equation}

v_g=R_D\left( v_L+v_r\right)

\end{equation}

For the conservation of energy a single mixture energy balance equation is applied

\begin{equation}

\frac{\partial }{\partial t} \left [m_g\left( E_g+\frac{1}{2}v_g^{2}+gh \right)+m_L\,\left(E_L+\frac{1}{2}v_L^{2}+gh \right ) +m_D \left ( E_D+\frac{1}{2}v_D^{2}+gh \right )\right ]\\ =-\frac{\partial }{\partial z}\left [ m_gv_g\left ( H_g+\frac{1}{2}v_g^{2} +gh\right ) + m_Lv_L\left ( H_L+\frac{1}{2}v_L^{2} +gh\right )+ m_Dv_D\left ( H_D+\frac{1}{2}v_D^{2} +gh\right ) \right ]\\+H_S+U

\end{equation}

where,

$m_f=V_f\rho_f\; for \; the \; phase\; f$

$E=internal\; energy\; per \; unit\; mass\; \left( Jkg^{-1} \right)$

$U=heat\; transfer\; per\; unit\; volume\; from\; the \; pipe\; walls\; \left(Jm^{-3} \right)$

Work between the gas and liquid phases are usually negligible when compared to the heat transfer from the pipe walls.

All fluid properties, e.g. densities, compressibilities, viscosities, surface tension, enthalpies, heat capacities, and thermal conductivities, can be provided to LedaFlow by a file that contains a table in which these fluid properties of the phases are given for a number of thermodynamic conditions, i.e. pressure and temperature.

The fluid properties during a simulation are found by interpolating in this table.

The two-fluid model, as formulated above, provides a set of coupled first-order, nonlinear, one-dimensional partial differential equations. LedaFlow uses a finite difference scheme on a staggered grid for the spatial discretization. A semi-implicit time integration method used. The time step is limited by the average phase velocities based on the mass-transfer criterion

\begin{equation}

\Delta t \leq min_{j}\left( \frac{\Delta z_j}{\left | v_{fj} \right |}\right)

\end{equation}

where,

$\Delta z= \:length\: of\: a\: grid\: cell\: (m) $

$v_f = velocity\: of\: phases\:\: f$

$_j=index \: to \: identify\: a\: grid\: cell$

In this section it is compared the data obtained from the new version of Ledaflow 1.3 to the experimental data acquired at IMFT published by **J.Fabre and L.L. Peresson 1987. **The test loop consist of a 25 m horizontal pipe connected to a 13.5 m vertical riser as shown in figure 1. The diameter of the pipe is 0.053 m. Air and water are the fluid used, and the test loop operates under the atmospheric end pressure. The conditions and geometry data are given in Table 1.

Table 1

Figure 1

In order to download the full updated tutorial (12/03/2014) of the new version 1.3 of Ledaflow, click here.

Figure 2 shows the comparison between the predicted pressure tend at the bottom of the riser by the new version 1.3 of Ledaflow and the **J.Fabre and L.L. Peresson.**

Figure 2

From the previous figure, the pressure amplitude found by Ledaflow is approximately the same as the experimental result but the predicted period is just a little bit longer.

Therefore, we can validate the results found by the new version 1.3 of Ledaflow.

The turndown curve (TDC) is a graph that represents the pressure drop versus the mass flow rate in a flow line vulnerable to terrain slugging, It is represented by a convex curve.

The left zone to the inflection point in the TDC represents the zone where the **gravity forces are preponderant**. On the other hand, the right zone to the inflection point in the TDC represents a zone where the **friction forces** **are preponderant**.

The TDC is helpful for this project since it shall suggest the start point to simulate the transition between a stable flow (No severe slugging) and a no stable flow (severe slugging). This start point should be the lowest point of the TDC.

It is important to note that the lowest point of the TDC does not always represent the transition point between a stable and a no stable flow. It only indicates the starting point. This subject will be broaden in the next sections

- Liquid and gas mass fraction are fixed.
- A total mass flow rate is fixed.
- All the parameters and variables are introduced in LedaFlow.
- The simulations is run with the steady-state pre-processor.
- The pressure is measured.
- The differential pressure is calculated by subtracting the atmospheric or outlet pressure of the system.

These are the steps to calculate one point of the TDC. The same procedure is repeated (from #2 to #6) in order to calculate the rest of the points, just the liquid and gas mass fraction remains constant and fixed.

As its name indicates, the flow map is a map that shows at which conditions of superficial velocity of liquid, superficial velocity of gas, liquid mass fraction and gas mass fraction the flow is stable, where there is no severe slugging, and no stable, where there exist severe slugging.

This flow map is a result of the transient simulation of each point of the different Turndown Curves.

In this section it will be carried out several transient simulations with a geometry shown in the following table.

Pipeline (m) | 25 |

Riser (m) | 13,5 |

Radius bend (cm) | 50 |

The several transient simulations are three (3) to four (4) different total mass flow rates from each Turndown Curve (TDC). Bear in mind that each TDC has a specific quality, e.i. same liquid and gas mass fraction.

Turndown Curve 1

Liquid mass fraction = 0,9981

Gas mass fraction = 0,0019

Turndown Curve 2

Liquid mass fraction = 0,9947

Gas mass fraction = 0,0043

Turndown Curve 3

Liquid mass fraction = 0,9905

Gas mass fraction = 0,0095

The following table show the specifications of the turndown 1.

Pipeline (m) | 25 |

Riser (m) | 13,5 |

Radius bend (cm) | 50 |

Liquid mass fraction (-) | 0,9981 |

Gas mass fraction (-) | 0,0019 |

Four different total mass flow rate were simulated in this case. These simulations represent the four points to the left from the lowest point. It will be paid specific attention to the relation between the turndown point (lowest point of the turndown curve) and the existence of severe slugging.

For the following set of figures, the graph to the left indicates the point that is going to be simulated in a transient fashion. The graph to the right, shows in this order: the pressure at the pipeline bending, the volume fraction at the pipeline bending, the volume fraction at the pipeline outlet, the mass flow rate of the liquid at the pipeline outlet and the mass flow rate of the gas at the pipeline outlet.

- Point 1, Total mass flow rate $ Ft\;=\;0,2807\;kg/s$

- Point 2, Total mass flow rate $Ft\;=\;0,5614\;kg/s$

- Point 3, Total mass flow rate $Ft\;=\;0,8421\;kg/s$

- Point 4, Total mass flow rate $ Ft\;=\;1,26314\;kg/s$

From the observation of this set of figures, It can be said that there is an absence of the severe slugging phenomenon as the studied point moves toward the Turndown point (lowest point of the Turndown Curve).

Yet , it cannot be conclude that this type of behaviour appears for all geometry configuration. This subject will be broaden in the further sections.

The following table show the specifications of the turndown 2.

Pipeline (m) | 25 |

Riser (m) | 13,5 |

Radius bend (cm) | 50 |

Liquid mass fraction (-) | 0,9957 |

Gas mass fraction (-) | 0,0043 |

Four different total mass flow rate were simulated in this case. These simulations represent the four points to the left from the lowest point. It will be pay specific attention to the relation between the turndown point (lowest point of the turndown curve) and the existence of severe slugging.

For the following set of figures, the graph to the left indicates the point that is going to be simulated in a transient fashion. The graph to the right, shows in this order: the pressure at the pipeline bending, the volume fraction at the pipeline bending, the volume fraction at the pipeline outlet, the mass flow rate of the liquid at the pipeline outlet and the mass flow rate of the gas at the pipeline outlet.

- Point 1, Total mass flow rate $ Ft\;=\;0,2878\;kg/s$

- Point 2, Total mass flow rate $ Ft\;=\;0,5756\;kg/s$

- Point 3, Total mass flow rate $ Ft\;=\;0,8634\;kg/s$

- Point 4, Total mass flow rate $ Ft\;=\;1,1512\;kg/s$

The following table show the specifications of the turndown 3.

Pipeline (m) | 25 |

Riser (m) | 13,5 |

Radius bend (cm) | 50 |

Liquid mass fraction (-) | 0,9905 |

Gas mass fraction (-) | 0,0095 |

Three different total mass flow rate were simulated in this case. These simulations represent the three points to the left from the lowest point. It will be pay specific attention to the relation between the turndown point (lowest point of the turndown curve) and the existence of severe slugging.

For the following set of figures, the graph to the left indicates the point that is going to be simulated in a transient fashion. The graph to the right, shows in this order: the pressure at the pipeline bending, the volume fraction at the pipeline bending, the volume fraction at the pipeline outlet, the mass flow rate of the liquid at the pipeline outlet and the mass flow rate of the gas at the pipeline outlet.

- Point 1, Total mass flow rate $ Ft\;=\;0.2896\;Kg/s$

- Point 2, Total mass flow rate $ Ft\;=\;0.4344\;Kg/s$

- Point 3, Total mass flow rate $ Ft\;=\;0.5792\;Kg/s$

The most important objective in our study is to find the transition point in each turndown curve,. Therefore in this section it will be specified how to determine the border between the steady and unsteady flow.

First, all the data from the transient simulation in LedaFlow is exported to Matlab.

We introduce the $\Delta P$, which is defined as the difference between the pressure at the riser base, $\Delta P$ = $P_{max}$ - $P_{min}$

Fig. 1 is a dimensionless number ($\frac{\Delta P}{\rho gh}$) versus the total mass flow rate, each line represent a constant gas mass fraction.

In this project, it is defined a threshold of $\frac{\Delta P}{\rho gh}$ in order to determine the border between stable (no severe slugging) and no stable (severe slugging). If $\frac{\Delta P}{\rho gh}$ >0.3, it could considered severe slugging, otherwise, it is not. In addition, this data should read along with the graph $\frac{T_{QL}}{T_{total}}$ versus the mass flow rate to determine finally if it is severe slugging or not.

Fig.1

From Fig.1, it can be observed that as the total mass flow rate increases the $\frac{\Delta P}{\rho gh}$ decreases. This is due to the fact that the greater the mass flow rate, the higher the superficial velocity of each phase and therefore the more energy the fluid has in order to travel easily along the pipeline.

In addition, it can be observed three points, one from each series of data, are near to the transition line. It is a must to read these values along with the following graph in order to determine if they are severe slugging.

As mentioned before, it is not convenient to determine the severe slugging phenomenon with only one variable. Therefore the dimensionless number ($\frac{T_{QL}}{T_{total}}$) is computed. T_{QL} number represents the mean liquid production period in a complete cycle, and T_{total} exhibits the mean complete period. It could be considered as severe slugging if $\frac{T_{QL}}{T_{total}}$ < 0.5.

It is worth to mention that the hypothesis of the threshold value of 0.5, is that if the liquid production period is greater than the no liquid production period, then is not considered severe slugging.

Fig. 2 shows the dimensionless number ($\frac{T_{QL}}{T_{total}}$) versus the mass flow rate.

Fig. 2

From Fig. 2 it can be observed that one out of four points that were in the no severe slugging zone in the dimensionless differential pressure graph changed into the severe slugging zone. However, in this graph the first point of the series of data x=0,0095 (magenta colour) is severe slugging, while in the first graph it was not. This fact might be because the transition border is not a specific line and is rather a zone. Nevertheless, this point must be considered as severe slugging since one of the consequences of this phenomenon is the absence of production, which jeopardise the integrity of the pieces of equipment and process downstream.

Fig. 3 relates the dimensionless pressure differential presented in Fig.1 and the dimensionless liquid production period presented in Fig. 2, by dividing $\frac{\Delta P} {\rho gh}$ over $\frac{T_{QL}}{T_{total}}$.

Fig. 3

Fig.3 is created to show that even with a great value of dimensionless pressure differential (big amplitude), no severe slugging will be considered, because the non liquid production period is very small (neglected).

This figure exhibits the dimensionless total frequency $\frac{t_{QL}}{T_{total}}$. The numerator $t_{QL}$ means the time needed for the liquid to pass through the riser $t_{QL}=\frac{H}{U_{sl}}$ and the denominator is the aforementioned mean total frequency.

Fig.4 represents the relationship between the dimensionless number $\frac{t_{QL}}{T_{total}}$ an the total mass flow rate.

Fig. 4

Theoretically, if $\frac{t_{QL}}{T_{total}}$ <1, a severe slugging of type 1 will be found.

Please refer to the lowest point in the red line (Q=0.2807 Kg/s and x=0.0019), which has clearly a value lower than 1.

The pressure profile of this point is shown in figure 5, where a type of severe slugging 1 is clearly found.

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Fig.5 : represents Q=0.2807kg/s and x=0.0019

For more information about Severe Slugging of type 1, go to this page

If $\frac{t_{QL}}{T_{total}}$ =1, it corresponds to severe slugging of type 2, which is proved in Fig. 6 with which represents

Please refer to the second point from the left of the red line in Fig. 4 (Q=0.5614 and x=0.0019), which has clearly a value equal to 1.

The pressure profile of this point is shown in figure 6, where a type of severe slugging 2 is clearly found.

Fig. 6 represents Q=0.5614 and x=0.0019

For more information about Severe Slugging of type 2, go to this page

By combining all the figures above and with a global analysis, the transition points for each constant gas mass flow rate line can be defined, therefore a flow map can be traced in Fig.7

Fig. 7

Fig. 7 shows the flow map of the downward inclined pipeline-riser system based on the result of the simulations.

Flow pattern has an important influence on the prediction of the multiphase flow parameters, therefore, such a flow pattern map can be used in design and operation phase in an offshore oil-production system.

Research into severe slugging is aimed at the reliable prediction of its occurrence and of the associated slug length, frequency, and arrival velocity, all these has been studied in our base case. And also, we know that the gas and liquid flow rate, flowline inclination, riser-foot geometry, and liquid viscosity have effect on the occurrence of severe slugging. So in this part, we focus on the influence of the pipeline length.

We keep all of the characteristics of the pipeline-riser system and just change the geometry of the pipeline with 2 times longer as shown in the figure below.

We continue to take the same manipulation as the base case:

1. Drawing 3 turndown curve

2. Estimate the transition point in each turndown curve

3. Drawing the flow map

We do the same simulation for drawing 3 turndown curve as we did in the base case, and compare the turndown point in these two different pipeline length geometry.

Here is the table of the position of turndown point between two different pipeline length geometry.

Base case (Pipeline L) | Pipeline 2L | |

Turndown point 1 | (1.26314, 0.77) | (1.2228, 0.777) |

Turndown point 2 | (0.8634, 0.517) | (0.8634, 0.522) |

Turndown point 3 | (0.5792, 0.332) | (0.5792, 0.341) |

By comparing the turndown points for these two different pipeline length, it is clear that these points are basically the same.

The following figure gives us a distinct seeing by joining two turndown curve (Turndown Curve 1) together.

Although the left part of the turndown curve including the turndown point is almost the same, the transition point always need to be checked ( Turndown point =? Transition point or Transition point moves to left or right ).

- Run simulation for each transition point, if it is not severe slugging, directly move to the left point, if it is not sure, run the simulation for the left point and right point.
- Export all the data in Ledaflow to Matlab and do the same comparison as the base case.
- Determine the transition point.

Here is comparison of the transition line for two different pipelines, it is clear that the transition line of pipeline 2L moves to the right, and when we check the transition points with the turndown points, almost all the turndown points are transition points.

Why the transition line moves to the right when compared with the base case (pipeline 1L)? Longer pipeline, which increase the gas buffer volume, and lower the gas/liquid ratio's, which reduce the pressure buildup rate in the pipeline, increase the possibility of severe slugging.

The simulation of 2 times longer of pipeline gives us an understanding of the influence of pipeline length on the appearance of severe slugging, so now we move to testing the effect of riser length.

We keep all of the characteristics of the pipeline-riser system and just change the geometry of the riser with 2 times longer as shown in the figure below.

We continue to take the same manipulation as the base case:

1. Drawing 3 turndown curve

2. Estimate the transition point in each turndown curve

3. Drawing the flow map

We do the same simulation for drawing 3 turndown curve as we did before, and compare the turndown point in these two different riser 2 times higher geometry.

Here is the table of the position (mass flow rate, pressure drop) of turndown point between two different riser length geometry.

Base case (Riser H) | Riser 2H | |

Turndown point 1 | (1.26314, 0.77) | (1.3474, 1.684) |

Turndown point 2 | (0.8634, 0.517) | (1.1512, 1.684) |

Turndown point 3 | (0.5792, 0.332) | (0.8688, 0.692) |

By comparing the turndown points for these two different riser length, it is clear that these points have a great difference. The pressure drop augments because of the riser length is higher.

The following figure gives us a distinct seeing by joining two turndown curve together.

These two turndown curves have the same tendency, but have a difference in the pressure drop. We continue to find the transition point by using the turndown curve.

- Run simulation for each transition point, however, neither of the turndown point in this riser 2H has the doubt to judge it is severe slugging or not, it is always sure that the turndown point is not severe slugging. So we directly move to the left point, and even find that the severe slugging appears at the point which is far from the turndown point.
- Export all the data in Ledaflow to Matlab and do the same comparison as the base case.
- Determine the transition point.

Here is comparison of the transition line for two different riser length, it is clear that the transition line of riser 2H moves to left, and when we check the position of transition points with the turndown points, it is obviously not, the transition point appears at the point which is far from the turndown point.

Why the transition line moves to left when compared with the base case (riser 1H)? When the riser is 2 times higher, the hydrostatic pressure of the liquid-filled riser is 2 times larger, so the pressure at the riser base needs to be augmented to break the block, which increase the gas/liquid ratio. In this way, the possibility of severe slugging reduced.