# Analyze of the results

In this part, results of the simulations carried out with Fluent and Jadim are analyzed and compared.

As explained previously, convergence issues make three-phase flow simulations on Jadim difficult to achieve. On another hand, if Fluent seems to avoid these problems, the fact that the access to the code is not possible leads us to be critical about the results.

Therefore, a comparison of similar simulations carried out with these two softwares is important to validate the results.

Two simulations with different velocities and physical properties are realized:

- In the first simulation, a velocity of 1 m/s is used , oil, gas and water viscosities are multiplied by 100 and the gas density is multiplied by 10.

- In the second simulation, real properties of oil, gas and water are used with a velocity of 0.1 m/s.

# Post-treatment

• Matlab Post-treatment

To visualize the geometry with matlab, the command  les2asc filename geom is used.
To visualize an animation of a serie of timesteps (for instance every 2 timestep from 4 to 10), the command les2asc filename range 4 2 10 is used.

Then, a matlab script file allows to load output jadim variables in matlab, using the function fscanf. Afterwards, values of variables such as volume fraction of oil and gas, velocity, position or pressure are saved into matrices which contain a value for each cell. The loop time gives access to every timestep.

The matlab script is used to plot macroscopic dimentionless data of interest:

- The repartition of oil/water/gas volume fraction in the domain in function of time, plotted in function of a time:

$$oil_{mean}=\frac {\sum \limits_{i=1}^m \sum \limits_{j=1}^l \tau_{oil,ij}}{m \times l}$$                    $$gas_{mean}=\frac {\sum \limits_{i=1}^m \sum \limits_{j=1}^l \tau_{gas,ij}}{m \times l}$$

$$gas_{mean}=1-oil_{mean}-gas_{mean}$$

With:

$m \times l$: numbers of cells of the domain

$\tau_{oil,i}$: Oil volume fraction of cell $i$

$\tau_{gas,i}$: Gas volume fraction of cell $i$

- The outlet oil flow rate in function of time, plotted in function of time:

$$Q_{outlet}=\frac{1}{n}\sum \limits_{i=1}^n \tau_{oil,i} v_i L_{outlet}$$

With

$n$: number of outlet cells
$v_i$: outlet velocity of cell $i$
$m \times l$: numbers of cells of the domain

- The ratio of remaining and the ratio of oil recovered:

$$ratio_{oil-remaining}=\frac{oil_{initial}-Q_{Outlet}t}{oil_{initial}}$$
$$ratio_{oil-recovery}=1-ratio_{oil-remaining}$$

With

$oil_{initial}=\sum \limits_{i=1}^m \sum \limits_{i=1}^l \tau_{oil,ij} S_{cell}$
and $S_{cell}$: area of a cell

• Paraview post-treatment

Thanks to the command les2par filename range 1st-timestep interval final-timestep, jadim data can be loaded on paraview and it is possible to vizualize the different variable in function of time. In our BEI, paraview was mainly used to create video and to observe the general flow behaviour.

• Dimentionless Values

As results of this project will be used by Schlumberger, it is important to work with dimentionless variables:

- the outlet oil flow rate is divided by the inlet gas flow rate

- the time is divided by Tref, the time needed to fill up the domain with gas:

$t= \frac{ physical-time}{T_{ref}}$

$T_{ref}=\frac{S}{V_{Inlet}\times D}$

With

$S$:  surface of the domain without the obstacle

$V_{inlet}$ : velocity of the gas injection

$D$:  lenght of the inlet

# Simulation 1 : High viscosities

In this first simulation, oil, gas and water viscosities are multiplied by 100. Indeed, increasing viscosity values should allows Jadim to avoid convergence issues and to reduced numerical diffusion.

The table below recaps the main caracteristics of the simulation:

 Physical properties Velocity inlet Time step Scheme Order Time simulated Quantity of N2 injected Fluent Viscosities x100 0.1 m/s 10-4 Second Order 2.5 sec 6.25.10-3 m² Jadim Viscosities x100 0.1 m/s max. 10-4 Second Order 2.5 sec 6.25.10-3 m²

This simulation is carried out for a velocity of 0.1 m/s, 1m/s and 10 m/s. In term of convergence, CPU time and accuracy of the results, the velocity of 1 m/s appeared to be the suitable velocity for this case, for bth Fluent and Jadim simulations. Therefore, the simulations presented in this page have been carried out with a velocity of 1 m/s.

The inlet is characterized by a gas Reynolds Number of 260 at the inlet. Therefore, the gas jet at the inlet is not turbulent.

If a flow Reynold Number in the domain  is complicated   to calculate, velocities in function of time can be  observed. In  both Jadim and Fluent  simulations,  flow  velocity  does  not exceed 7 m/s. The picture  on the   right shows the velocity field at 1.5 sec with Jadim.

Thus, it is relevant to conclude that the flow  is laminar and  that turbulence models are not needed.

The two videos below show the same case simulated with Fluent and Jadim. As explained previoulsy, gas is injected on the lower right side of the domain, and the outlet is situated on the middle left side. The physical time simulated is 2.5 seconds, which correpond to an injection of %47 of gas i the domain.

Simulation carried out with Fluent

In the videos, if befferent local flow features can be observed, the global flow in the domain has the same behaviour with Fluent and Jadim. Moreover, the phenomenon of numerical diffusion is not too important and the position of the norrow gas interface is accurate. From the observation of these videos, Jadim seems to handle the three-phase flow simulation and the results seem accurate and relevant.

In order to confirm these observations, macroscopic data of interest are analyzed with the matlab post-treatment. The figure below represents the evolution of oil, water and gas volume fraction in the domain in function of a dimentionless time. Results of Fluent and Jadim simulations are compared.

The first observation is that for both simulations, oil and water volume fraction decrease as gas volume fraction increase, which corresponds to the injection of gas and the disparition of oil and water into the outlet.

Secondly, it shows that no gas injected have left the domain after an injection of 74% of nitrogen. Indeed, the evolution of the gas volume fraction is a  linear curve with represents a constant evolution in the domain.

Finally, oil, pushed by water, starts to leave the domain after an injection of 14% of gas and at the end of the simulation, after an injection of 47% of gas, 52.7% of oil wedged remains in the domain.

The results obtained with Jadim and Fluent are similar: the same amount of oil has left the domain at the end and the evolution of phases repartition is similar during this period of time. These results confirm that  Jadim predicts well flow features in a case of   high viscosities.

Then, the evolution of the outlet oil flow rate is plotted in function of a dimentionless time.

When oil starts to leave the domain after 14% of nitrogen injected, the dimentionless oil flow rate reach a maximum of 1. The previous videos show that at the time, only oil goes out of the domain. Theses observations lead to the conclution that flow conservation between the inlet and the outlet is respected.

Moreover, like the evolution of the volume fraction, the comparison of the outlet oil flow rate shows that Jadim and Fluent produce similar results in this case.

Conclusion: If local flow features observed on the videos  have differences in function of the CFD software, the study of macroscopic values of interest shows that in this case, Jadim and Fluent give similar results. Jadim seems to gives more accurate results when it does not have to deal with the small viscosity of nitrogen.

# Simulation 2: Real properties of oil, gas and water

A second simulation is carried out with real properties of gas. In order to avoid convergence issues, the timestep is reduced to $10^{-5}$ and a small velocity inlet of 0.1 m/s is used. Because of this small velocities, the computational time of the simulation is really high. Therefore, only 5% of nitrogen is injected in the domain before convergence issues appear in the Jadim simulation.

The table below recaps the main caracteristics of the simulation:

 Physical properties Velocity inlet Time step Scheme Order Time simulated Nitrogen Injected (% of the domain) Fluent Real properties 0.1 m/s $10^{-5}$ Second Order 2.8 sec 5% Jadim Real properties 0.1 m/s max. $10^{-5}$ Second Order 2.8 sec 5%

The gas injection is characterized by a Gas Reynolds Number of 26. Moreover, as for the simulation 1, the velocity field in the domain observed on paraview shows that the velocity remains small in the domain in function of time.

Thus, it is relevant to conclude that the flow  can be consider as laminar and that turbulence models are not needed.

The two videos below show the same case simulated with Fluent and Jadim. As explained previoulsy, gas is injected on the lower right side of the domain, and the outlet is situated on the middle left side. The physical time simulated is 2.8 seconds, which correponds to a dimentionless time of 0.4

Simulation carried out with Fluent

On videos, differencies between local flow features can be observed with the Fluent and Jadim simulations.

In the Jadim simulation, the gas interface is not accurate and it seems that Jadim has difficulties to handle flow features. While bubble of gas should be expected, the gas is diffused and seems to mix with oil and water.

In the Fluent simulation, the interface is more accurate but the gas seems to "desappear", probably because of numerical diffusion.

If  numerical diffusion can explained the diffusion of the gas observed with Jadim, another explanation can be found in the scale of the mesh. Indeed, the size of cells is close to 1 mm. Therefore, if the gas forms bubbles smaller than 1 mm, Jadim is not able to represent the topology changes properly. If Fluent seems to provide a accurate interface, it is important to note that it is a really strong commercial software design to always give a result.

The graph below represents the repartition of  phases in function of time. The comparison between Jadim and Fluent shows that after an injection of 5% of nitrogen, the repartition of gas and water in the domains already starts to be different.  If the simulation has been run longer, the repartirion of phases obtained with Fluent and Jadim would have probably been even more different.

If we plot the outlet oil flow rate in function of time, results obtained with Jadim and Fluent are also different. When only oil goes out of the domain, which corresponds to a maximum oil flow rate, the flow rate ratio of the Fluent simulation as a value of 0.9, which represents an error of 10%.

Due to the small velocity, only 5% of nitrogen is injected in the domain and only 4% of oil is recovered.

To conclude, the results obtained by Fluent and Jadim does not seem as accurate as in the Simulation 1. As the viscosity of the gas is small, bubbles of gas are difficult to represent and the interface between gas and other phases is hard to predict.

However, the computational time of Fluent is smaller than the one with Jadim and Fluent is a strong software which had a good capability to handle topology changes. Therefore, the parametric study will only be simulated with Fluent.