A New Innovating Scheme to Model Hydrocarbon Migration at Basin Scale: A Pressure-Saturation Splitting

Sylvie Wolf, Isabelle Faille, Sylvie Pegaz-Fiornet, and Françoise Willien
IFP 1&4 Av. De Bois-Préau 92852 Rueil-Malmaison Cedex France

The modeling of multiphase flow in sedimentary basin integrates a lot of complex physics. First, the evolution of basin through geologic times must be calculated. Sediments are deposited and then compacted under given rheological laws. The expulsion of water through impermeable shaly sediments can lead to overpressures. On contrary, sandy sediments are most usually hydrostatic. Secondly, high temperature yield hydrocarbon generation in deep source rock. And finally, hydrocarbons migrate towards reservoirs. This migration is classically modelled by Darcy's law. It can be very rapid along sandy path-ways and is essentially due to gravity. Major controlling factors of oil migration are oil mobility and oil density. During this displacement, pressure and temperature do not change a lot. So, we attempted to decouple the calculation of pressure and porosity from the calculation of oil saturation.

For that purpose, we rewrote the Darcy velocity with the total velocity. We show that for incompressible fluid, the oil conservation equation depends only on that total velocity and saturation. We developed a new numerical upwind scheme to discretize this equation, which is better appropriate to split pressure from saturation.

Very often, classical numerical schemes based on Darcy law need to reduce time steps to avoid computing of unrealistic saturations until they interrupt. This occurs on cells located on sandy layers where oil just passes through at rapid velocity. The main consequence is to slow down the simulation because full matrix inversion on saturation-pressure becomes CPU-consuming. The previous splitting can allow us to use local time steps for solving saturation only and keep larger time steps for solving pressure and temperature computations. So, we can drastically speed up the computation.

This new approach has been implemented in the TEMIS software with local grid refinement capability which better captures processes at trap scale. It has been parallelised and extended to compressible fluid. We have performed several computations on 2D sections and 3D blocks provided from real case studies. We have noticed similar results from classical fully implicit scheme, but with a CPU time five times quicker.

The next step is to generalise this decoupling to compositional hydrocarbon flow. This approach could also help to the integration and understanding of new physical concepts such as diagenesis, fluid fracturing or oil biodegradation.

AAPG Search and Discovery Article #90091©2009 AAPG Hedberg Research Conference, May 3-7, 2009 - Napa, California, U.S.A.