High performance computing for Darcy
compositional single phase fluid flow
simulations
L.Agélas, I.Faille, S.Wolf, S.Réquena
Institut Français du Pétrole
Abstract
The compositional description of flow through heterogeneous porous media is of primary interest to many applications such
as basin modeling. The flow equations that we consider model a Darcy compositional single phase migration in a porous
media. Our interest is to predict the pressure, the saturation and the fluid composition. Darcy fluid flow simulations on
nowadays million-cells and highly heterogeneous basin models are tremendously CPU-time consuming. To make Darcy
flow simulation tractable, different numerical techniques have been studied to improve the solution of the non linear system
on parallel computers.
Improvements and results
Generalised Darcy law, α = (w,o)
Mass conservation of the water phase Mass conservation of each component


 (  oS o Z j )
 (  wS w )
 div (  wS wVw )  q w
 div ( Z j  oS oVo )  q j
t



SV   K ( )(P   g )
t
Difficulty : solve a large non linear system of size, number of cells multiplied by (2 + number of mobile components)
monoprocessor
To cope with simulations of millions cells :
The global domain is split among the y dimension.
Each processor owns a private subdomain.
All the inter-processors communications are handled by MPI calls.
To save cpu-time :
We use the under relaxation technique to maintain a good convergence of the Newton algorithm.
We combine two finite volume schemes : the one explicit in composition and the other one implicit in composition.
For null saturations, the compositions are undefined. A good initialization is important to keep a good convergence.
proc 1
proc 3
proc 2
Real case : the time period is 250 My, the size of the block is 101 km x 65 km x 8.7 km refined on a 180x180x29 grid
(0.94M cells). The simulation is a full darcy compositional single phase migration with twelve components run with a
thermal gradient. The number of unknowns is 11.3 M. The test was performed on a 64 AMD Opteron 2.2 Ghz Infiniband
cluster with 64 procs. The CPU time is 15h. Overnight runs can be expected with more processors.
Lithology distribution
Tranformation ratio
(layers = 3, 7, 9, 12, 20)
Oil saturation
(layers = 11, 13, 15, 21)
Fluid properties
Here are the results of Api gravity, Gor solution and Number of phases obtained with a PVT flash EOS calculation in
postprocessing for layers 3, 4, 5, 6, 13, 14
Number of phases
Api gravity
1 for only the water phase
2 for two phases water and oil
3 for three phases water/oil/gas
4 for two phases water and gas
very heavy
oil
heavy oil
Gor solution
medium
oil
light oil
Condensate
gas
API
10
°
Some compositions (c2,c14+Csat,c14+aroU,NSO)
at layer 21
22,3
°
31,1°
Gas volume liberated at Surf Cond.
GOR -----------------------------------------Oil Volume Surf Cond.
45
°
Gaz
Huile
Temperature
Pressure
Some cpu time performances obtained on real cases 2D with 1 proc (16 components)
case
size of
gridblock
Berkine section SWNE 149 x 39
Berkine section NS
160 x 50
number of
unknowns
81354
112000
Long time
period
510 My
510 My
Cpu time previous version
Cpu time
current version
6h43mn
2h12mn
23h17mn (until the event 48) 10h37mn
Conclusion
We considerably speed up the Darcy compositional single phase fluid flow simulations. The new numerical techniques
considerably improve the convergence of the Newton algorithm both in terms of robustness and CPU time enabling the
efficient simulations of millions cells models on parallel computers.
Contact name : Leo Agelas ([email protected])