Previous studies of higher order schemes for compositional reservoir simulation have mainly involved the use of spatially accurate methods. Our compositional computations in IMPES mode with spatially accurate TVD schemes show that for practical time step sizes the method can introduce significant oscillations.

In this paper, a novel scheme is introduced that is higher order in space and time. Higher order values of the variables of the system are derived at cell faces and are constrained to be monotonicity preserving. The compositional flux is then composed from the cell face variables to produce a locally conservative scheme that is Total Variation Diminishing (TVD) for linear advection and is a higher order Godunov scheme in the case of a non-linear conservation law.

Four component (CH4/C3/C6/C16) and six component (C02/CH4/C4/C10/C14/C20) examples are presented that demonstrate the behavior of the new scheme for complex compositional simulation. The new scheme produces high resolution results at a fraction of the cost of single point upstream (SPU) weighting. One-dimensional computations show that 1000 grid blocks are sufficient for the higher order scheme to approximate 20,000 single-point upstream (SPU) reference solutions leading to significant speed-ups. Our new method permits larger time steps than TVD schemes that are only spatially accurate and is consequently more robust and less CPU intensive than a spatially accurate scheme.

You can access this article if you purchase or spend a download.