**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 dom

$\tau_{oil,i}$: 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

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

$$ratio_{oil-recovery}=1-ratio_{oil-remaining}$$

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