## DEVELOPMENT AND MATHEMATICAL ANALYSIS OF HIGH PERFORMANCE RESERVOIR SIMULATORS BASED ON ADVANCED MODELS

**De** 1987-03-01
**à** 1989-12-31

## Détails concernant le projet

### Coût total:

EUR 749 808
### Contribution de l'UE:

EUR 262 433
### Coordonné à/au(x)/en:

Spain
### Régime de financement:

DEM - Demonstration contracts
## Objectif

The main objective of this project is to improve the present technology in oil reservoirs numerical simulation, measured in terms of computer efficiency, investigating the behaviour of various numerical models for multicomponent flow equations in porous media.

As a result of this work we are able to draw a number of useful conclusions. These are given in what follows :

1. The standard finite element method preserves the essential features of a compositional system when applied to the simulation of retrograde gas condensate systems.

2. Although the finite element method provides an alternative approach for simulating compositional phenomena, it is more difficult to implement than the finite difference method.

3. The arithmetic operations required to achieve a solution in a finite element simulator typically exceed those required in a finite difference simulator. A a consequence of this, finite element simulators consume more computer time.

4. Numerical dispersion effects in both a finite element and finite difference simulator, for practical element or grid block sizes, dominate and mask the effect of molecular diffusion and hydrodynamic dispersion.

5. The adaptive implicit method provides the stability characteistics of a fully implicitcalculation for substantially less computer time.

6. By employing some of the novel mathematical approaches presented here for a finite difference simulator the cost of compositional simulation can be substantially reduced.

7. The finite difference formulation developed here, coupled with component pseudoisation, should bring the cost of compositional simulation close to that experienced for black-oil simulation.

8. The adaptive implicit implementation successfully reproduces the results obtained by nine different companies on a retrograde gas condensate test problem.

9. The particle characteristic method encounters a decoupling phenomenon when phase transfers occur. This leads to physicaly unrealistic results.

10. The particle characteristic method degenerates into a non-conservative approach when applied to coupled systems subject to phase transfers.

11. The introduction of artificial coupling does not improve the non-conservative nature of the particle-characteristic approach.

12. The particle-characteristic approach is not an appropriate method for simulation of compositional phenomena.

The project will develop advanced numerical simulation prototypes based on a compositional model of the state equation (Peng-Robinson ).

These prototypes will include the numerical models developed as follows :

- Investigation of time approximation methods, improving the adaptative implicit type.

- Investigation of space approximation methods. Three methods will be investigated :. Standard finite element method.. Mixed finite element method with method of characteristics.. Particle method.

Three main phases can be differenciated during the project development :

Phase 1. Numerical models development.

1. 1 Analysis and development of numerical models which will be further implemented.

1. 2 Models behaviour analysis using mathematical tools.

Phase 2. Software development.

2. 1 Algorithm design.

2. 2 Software design.

2. 3 Software implementation.

2. 4 Software tests and validation.

Phase 3. Models tests.

3. 1 Time approximation.

3. 2 Space approximation.

## Coordinateur

REPSOL EXPLORACION SA

Spain

PEZ VOLADOR 2

28007 Madrid

Spain

See on map**Contact administratif: ** PEREZ MANZANERA L

Tél.: +34-91-5747200