High performance computing for Darcy compositional single phase fluid flow simulations L.Agélas,...
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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. 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. Difficulty : solve a large non linear system of size, number of cells multiplied by (2 + number of mobile components) Lithology distribution Tranformation ratio (layers = 3, 7, 9, 12, 20) Oil saturation (layers = 11, 13, 15, 21) Mass conservation of the water phase Mass conservation of each component Generalised Darcy law, α = (w,o) w w w w w w q V S div t S ) ( ) ( j o o o j j o o q V S Z div t Z S ) ( ) ( ) )( ( g P K V S proc 3 proc 2 proc 1 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. Improvements and results
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Transcript of High performance computing for Darcy compositional single phase fluid flow simulations L.Agélas,...
High performance computing for Darcy compositional single phase fluid flow
simulations L.Agélas, I.Faille, S.Wolf, S.Réquena
Institut Français du Pétrole
AbstractThe 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.
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.
Difficulty : solve a large non linear system of size, number of cells multiplied by (2 + number of mobile components)
Lithology distributionTranformation ratio (layers = 3, 7, 9, 12, 20)
Oil saturation (layers = 11, 13, 15, 21)
Mass conservation of the water phase Mass conservation of each component Generalised Darcy law, α = (w,o)
wwwwww qVSdiv
t
S )(
)(
joooj
joo qVSZdivt
ZS )(
)(
))(( gPKVS
proc 3proc 2
proc 1
monoprocessorTo 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.
Improvements and results
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])
Some compositions (c2,c14+Csat,c14+aroU,NSO)at layer 21
Fluid properties
Api gravity Gor solution
Pressure Temperature
very heavy oil
Condensate gas
10°
API22,3° 31,1° 45
°
heavy oil medium oil
light oilGas volume liberated at Surf Cond.
GOR ------------------------------------------Oil Volume Surf Cond.
Huile
Gaz
case size of gridblock
number of unknowns
Long time period
Cpu time previous version Cpu time current version
Berkine section SWNE 149 x 39 81354 510 My 6h43mn 2h12mn
Berkine section NS 160 x 50 112000 510 My 23h17mn (until the event 48) 10h37mn
Some cpu time performances obtained on real cases 2D with 1 proc (16 components)
Conclusion
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
1 for only the water phase2 for two phases water and oil3 for three phases water/oil/gas4 for two phases water and gas
