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.

.

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.