Rubis Guided Session #7: Compositional Isothermal model

Ecrin v4.30 - Doc v4.30.01 - © KAPPA 1988-2013 Rubis Guided Session #7 • RubGS07 - 1/19

Rubis Guided Session #7:

Compositional Isothermal model

A01 • Introduction

The compositional isothermal model detailed here allows simulations with an arbitrary number

of components where the Peng-Robinson (with volume translation) equation of state is used

for the hydrocarbon phases. The water phase is then treated separately by mean of

correlations; it is considered immiscible, and no gas dissolution in it is allowed. The boundary

conditions must be limited to ‘no flow’ or ‘constant pressure’ kind. Note that this formulation is

not simply an extension / reduction of the compositional thermal model: beyond the obvious

fact that less variables are needed (there is no temperature equation anymore…), the problem

equations are now such that massive parallelization of the flash calculations can be achieved

when the simulation is performed, leading to a modeling much faster than thermal modeling

cases.

In this example we will set a producer to deplete a closed reservoir filled with gas condensate

and oil. Lean gas is being injected in the underlying oil zone leading to a large pressure

support preventing the gas gap to dive below the dew point. In a second run the injector is not

started and comparisons of the runs show that recycling of the lean gas allow for a much

larger oil recovery.

B01 • Document Creation, PVT Initialization

Create a new Rubis document by clicking and accept all defaults in the Reservoir – field infos

dialog:

Fig. B01.1 • ‘Field Infos’ dialog


Click ‘OK’ to validate.

Click on the PVT icon in the control panel simulation page to obtain the following display:

Fig. B01.2 • ‘PVT definition’ dialog

We will select ‘EOS (Peng-Robinson)’ and change the reservoir temperature to 350° F.

Click now on to access the compositional dialog:

Fig. B01.3 • ‘Compositional PVT definition’ dialog


We will consider in this example a mixture composed of C2 (ethane), C10 (N-decane), and C12

(N-dodecane). Start by selecting from the left pane these components and add them to the

current composition - The current composition pane will show four components. Select

‘Methane’ and click on ‘Delete’ to obtain the following composition:

Fig. B01.4 • ‘Compositional PVT definition’ dialog

In order to visualize the properties of the fluid sample, we need to set a reference mixture

composition. To achieve so, click on ‘Edit mixture composition’ and input the following molar

composition, then click ‘OK’ to validate:

Fig. B01.5 • Edition of reference mixture molar composition

From the compositional PVT definition dialog, click now on ‘Edit component properties’ to

access the pure component properties dialog:


Fig. B01.6 • Edition of component properties

We will keep here all parameters to their default values and just click on ‘OK’ to get back to

the compositional PVT definition dialog. We can navigate through the various tabs to edit the

corresponding evaluated properties. Click finally on the ‘P. bubble’ tab:

Fig. B01.7 • Reference composition phase envelope

The table on the right hand side displays the bubble point pressure as a function of

temperature for the reference composition while the plot shows the complete phase envelope

composed of the bubble points (yellow), direct due points (green) and retrograde due points

(red) for the reference composition. Note for later use that by looking up at the plot, we see

that for a temperature of 350° F this composition gives a bubble point pressure of

approximately 1310 psia.

Click on ‘OK’ to validate this PVT definition.


C01 • Reservoir Geometry

Let us proceed with the definition of the reservoir geometry by setting the reservoir shape, the

number of layers and their respective thicknesses. Start by double-clicking on the contour in

the 2DMap, set the reservoir as a rectangle and set it to the following dimensions:

Fig. C01.1 • ‘Field contour’ dialog

Click on ‘OK’ to validate and click next on the ‘Geometry’ button available in the simulation

control panel tab: In the ‘Reservoir-Geometry’ dialog, we will keep the number of layers to 1

and its default thickness of 30 ft, but we will slightly tilt the reservoir. To achieve so, change

the top layer 1 type to ‘Data Set’, and click on the button to define the top horizon as

follows:

Fig. C01.2 • Layer 1 top horizon definition

Click on ‘OK’ to validate the changes.


D01 • Reservoir Properties

Click on the ‘Properties’ button to access the reservoir properties dialog.

Fig. D01.1 • Reservoir Properties Dialog

For the sake of simplicity we are going to keep a uniform description of the rock petrophysical

properties, and only change the permeability to 100 md while we will keep default values for

all other data.

We need to change to KrPc curves by specifying a residual oil saturation equal to 0. To proceed

click on the KrPc definition button ; the following dialog will appear:

Fig. D01.2 • KrPc definition Dialog

Set the residual oil saturation (Sorg) to zero in the first tab, then move to the ‘Pc Data’ tab and

set as well the residual oil saturation and the ‘PcMax’ value to zero. Click ‘OK’ to validate.


We need now to initialize the fluid column: click on the initial state button , the initial state

definition dialog will appear:

Fig. D01.3 • Initial state definition dialog

In this multiphase context we will specify the depth of the Gas-Oil Contact (GOC) as well as a

‘Reference Initial Pressure’ at a ‘Reference Depth’ in the initial fluid column. In this case we

want to initialize the fluid as a saturated gas cap overlying a condensate zone: to achieve so,

specify a reference initial pressure of 1300 psia at a reference depth of 6100 ft, and set also

the GOC at the same 6100 ft depth. Click on ‘OK’ to validate the initial state setup.

A few more explanations may be useful at this stage to precise what we actually did in this

quick initialization input: if a GOC is defined with its reference pressure point, Rubis will derive

the mixture composition of the corresponding fluid such that the gas-cap and the underlying oil

are in equilibrium at the contact. From the GOC input, phase compositions are adjusted to

ensure thermodynamic equilibrium in the initial fluid column:

- If the saturation pressure is not specified in the ‘Saturation pressure’ tab the

saturation pressure is considered constant below the GOC while the fluid is

considered at saturation in the gas cap. This result in a constant composition in the

oil zone and in a varying one in the saturated gas cap. Figure D01.4 (left pane)

illustrates the corresponding pressure profiles in a column in a general three phase

context – this situation corresponds to the input we just made.

- If the saturation profile is defined in the ‘Saturation pressure’ tab, the compositions

are adjusted in consequence and the saturation pressure is ‘forced’ at the GOC. If

the prescribed saturation pressure is larger than the reference pressure at the GOC,

it is lowered to the reference pressure and recomputed downward by adjusting the

oil composition. The resulting oil zone will hence be saturated and its composition

computed with an iterative process in the column. Figure D01.4 (right pane)

illustrates the corresponding pressure profiles in that case.


Fig. D01.4 • Initial phases and saturation pressure profiles corresponding to

a typical under-saturated oil zone (left) and to a saturated oil zone (right).

In order for the equilibrium condition at the GOC to be possibly met, one must ensure that the

chosen ‘Reference Initial Pressure’ at the corresponding reservoir temperature lies within the

critical point loci of all possible mixture of the chosen components.

In the present example, it occurs that Rubis will internally compute the following molar

compositions at the GOC:

%mol C2 %mol C10 %mol C12

Oil 0.5962 0.3028 0.1010

Gas 0.9390 0.0507 0.0103

In order to illustrate the consistency of the compositions computed at the GOC, one could go

back to the compositional PVT definition dialog and set in turns these two compositions as the

reference composition. Plotting the phase envelopes for these two compositions on top of each

other would lead to the plot presented in Figure D01.5. We can see from there that the

envelopes intersect at the specified GOC conditions. Care must then be taken in setting the

‘Reference Initial Pressure’ so that this condition can be met – in practice, Rubis will refuse to

proceed with the simulation step and issue a warning when the prescribed equilibrium occurs

to be impossible.


Fig. D01.5 • Phase envelopes for the two compositions at the GOC

E01 • Well Definition

In our example we are going to define one vertical producer and one vertical gas injector. In

the 2D Map tab , click on the button to create a vertical well and interactively place a

well in the western part of the reservoir (the exact position of the well will be set in the

following), place a second well in the eastern part.

Click next on the ‘Wells’ button in the simulation control panel page to access the

‘Reservoir – Wells’ dialog:

Fig. E01.1 • Reservoir – Wells dialog


Rename first the wells to ‘Producer’ and ‘Injector’ as shown on figure 4.1. Then, change the

position of the producer to X=-1250 ft and Y=0 ft, and set the injector’s location to X=1000 ft

and Y = 0 ft as shown below - In each case, you will need to visit the ‘Cross-section view’ tab

and to click on the icon to adjust the trajectory to fully penetrating:

Fig. E01.2 • Well Geometry dialog

Check that the producer well is carrying a unique, fully penetrating perforation in the Producer

– Perforations dialog – the unique perforation should run from MD=6000 ft to MD=6030 ft. In

turn, we will also define a unique perforation for the injector, but this will be a limited entry

one as we want to restrain it in the [6218 ft – 6230 ft] range as shown below:

Fig. E01.3 • Well Perforations dialogs


Even though we will not spend time defining each model in details and keep all defaults

instead, we will set the wellbore model to ‘All trajectory’ for the producer well, and to ‘Only

hydrostatic gradient’ for the injector, as shown below:

Producer Injector

Fig. E01.4 • Setting wellbore models for the different wells

We will now define a unique well control for each of these wells, and set that the producer is

following a surface gas rate target of 200 Mscf/D, whereas the injector is re-injecting the same

amount (we can keep the default constraint pressure values). In essence, you should end-up

with the display shown in Fig. E01.5 and E01.6:

Fig. E01.5 • Well control dialog for the producer

Fig. E01.6 • Well control dialog for the injector


Last but not least, we will now precise the composition of the gas phase being injected: to

achieve so, click on the ‘Injection Hydrocarbon Composition’ button in the Injector – controls

dialog and set the injected fluid molar composition as in Figure E01.7:

Fig. E01.7 • Injected fluid composition dialog

By doing so, we just specified that the injector well will actually not re-inject the same fluid as

the one produced, but only the light component…

Before to proceed with the simulation of the problem, create a cross-section going through

both wells in the reservoir, as shown below:

Fig. E01.8 • Cross-section path


F01 • Building the Grid

Click on the ‘Grid’ button in the Simulation tab to access the grid dialog:

Fig. F01.1 • Simulation-Grid dialog

Accept all defaults and click on OK to obtain the problem geometrical grid – which will contain

about 6150 cells:

Fig. F01.2 • Unstructured Voronoi Grid


G01 • Run Settings and Initialization Step

We now need to specify the run settings for the run as well as the results to be output. In

order to do so, click on the run settings icon to access the ‘Simulation-run settings’ dialog:

Fig. G01.1 • Simulation-run settings dialog

In the ‘Time settings’ tab, set the starting date to January 1st, 2013 and set the end date of

the simulation to December 31st, 2015.

Click next on the Results tab, and add results logs as additional output for the producer with a

time period of 2000 hr and a ‘MDmin’ of 0 - in practice, we will output production logs from

bottomhole to surface:

Fig. G01.2 • Result settings


We will not store restarts in our case: visit the Restart settings tab, and uncheck the ‘Store

restarts’ checkbox.

Exit the Simulation – run settings with OK, and click on ‘Initialize’ the problem to build the

simulation grid and the initial fluid distribution. Maximizing the cross-section and selecting the

saturations as the property being shown should lead you to the following display:

Fig. G01.3 • Initial fluid saturation profile along the West-East reservoir cross-section

H01 • Numerical Simulation

Click now on Simulate to start the numerical simulation of the defined problem – the

simulation should be completed in approximately 370 time steps. Once the simulation is

completed, maximize the 3D plot and animate the saturation fields with time to get the

following display:

Initial saturation field (t=0):


Saturation field after 3500 hr of

production:

Saturation field after 7000 hr of

production:

As can be seen, the pressure support from the gas injector allows maintaining the pressure

above the dew point in the gas cap, prohibiting any condensate to form in the upper region of

the reservoir. That being said, a (small) condensate dropout actually shows up along the

producer wellbore itself as pressure decreases with depth:

Fig. H01.1 • Oil and pressure logs output at the producer

This ‘temporary’ dropout is due to the fact that the pressure in the wellbore gets below the

mixture saturation pressure (more and more oil appears), crosses the two-phase P-T region

and becomes small enough to converge towards the dew point (the oil turns into gas again).


I01 • Alternate Simulation Without the Injector

We are now going to create a new run by copy in which we will delete the injector to show the

impact of the gas cycling on the total oil production. To achieve so, rename the present run to

‘with cycling’, and create a new run by copy called ‘no cycling’:

Fig. I01.1 • New run dialog

In this new run, click on the Wells option and delete the injector by clicking on the icon

after its selection:

Fig. I01.2 • Deleting the injector

Once the injector has been deleted, initialize and run the simulation.

Inspection of the final oil saturation result field in the cross section plot allows us to check that

in that case condensate is being formed in the gas cap as illustrated on Fig. I01.4, where the

color scale has been changed to a maximum of 5 percent, as shown in Fig. I01.3:


Fig. I01.3 • Changing the Min-Max of the oil saturation field

Fig. I01.4 • Final oil saturation field: oil has formed in the higher part of the reservoir

A closer look at the producer logs hints that the fluid composition being produced is now

changing with time: due to this condensate bank being formed in the reservoir, the produced

well stream is becoming leaner and leaner (Fig. I01.5). This can be compared directly to

Fig.7.1 where the composition of the produced fluid was kept almost constant by applying a

large pressure support.


Fig. I01.5 • Oil and pressure logs output at the producer (run without injector)

Finally, one can use the browser to compare the cumulative surface oil produced in each case

– with and without the presence of the injector. This comparison is displayed in the Fig. I01.6

below, hinting that the total oil production is increased by approximately 13% when the

injector is active:

Fig. I01.6 • Cumulative surface oil produced with and without lean gas cycling.

Documents

Rubis Guided Session #7: Compositional Isothermal model