Summary
To better design and manage miscible gas injection, a fast and accurate
coarse-scale miscible simulation capability is required. In this paper, we
present a new technique for the upscaling of first-contact miscible
displacements. The method comprises two components: effective flux boundary
conditions (EFBCs) and the extended Todd and Longstaff with upscaled relative
permeabilities (ETLU) formulation. The former accounts approximately for the
effects of the global flow field on the local upscaling problems, while the
latter modifies the way that effective fluid properties and upscaled relative
permeabilities are computed so that effectively residual oil is properly
represented.
For a sequence of partially layered, synthetic 2D permeability fields, the
technique is shown to be successful in reproducing reference fine-scale
solutions. The method is also shown to outperform other upscaling techniques
over a wide range of coarsening factors. The upscaling procedure is then
applied to a 3D simulation of a miscible gas-injection field study. A near-well
upscaling technique is also incorporated into the methodology. We show that the
new approach provides coarse-scale simulation results that match the reference
solutions closely. In addition, the technique is shown to be very efficient
computationally.
Introduction
In many oil fields with significant amounts of associated gas, miscible gas
injection is a potentially attractive recovery method because it can yield high
local displacement efficiencies and may also offer a solution for gas handling.
For an accurate estimation of the displacement efficiency, complex phenomena
like viscous fingering need to be modeled properly. There are two broad
categories of approaches to modeling miscible displacements: fully
compositional (FC) and limited compositional (LC).
For multicontact miscible processes, FC simulations are generally required.
However, fine-scale FC simulations of miscible processes are prohibitively
time-consuming. While compositional streamline techniques may eventually
address many of the computational difficulties, several issues (e.g., gravity,
compressibility, and streamline updating) have yet to be fully resolved. When
first-contact miscibility is applicable, the LC formulation may be preferable
because of its computational efficiency. The LC formulation allows the
simulator to model miscibility within a black-oil framework and empirically
accounts for viscous fingering by modifying the fluid properties of the
pseudophases. However, because fine-scale LC simulations are still
computationally demanding, there remains a clear need for a robust miscible
upscaling technique.
In this work, we present a novel upscaling technique for the fast and
accurate coarse-scale simulation of first-contact miscible displacements. Our
method is an LC approach that has two components: the use of EFBCs for the
calculation of upscaled (pseudo-) relative permeabilities and the ETLU
formulation. EFBCs incorporate some approximate global flow information into
the local upscaling calculations and appropriately suppress the flux through
high-permeability streaks that are not continuous throughout the domain. As a
result, EFBCs address the problem of premature breakthrough of injected fluid,
which can occur because of the overestimation of flux that results from the use
of standard boundary conditions. Our ETLU formulation extends the Todd and
Longstaff method by accounting for the fact that, within reservoir-simulation
length scales, there exists an amount of oil that is practically immobile and
not available for mixing (Sorb). The computation of effective fluid properties
and upscaled relative permeabilities, therefore, should not include this Sorb.
This concept in fact leads to the improved behavior of the upscaled relative
permeabilities. Previous miscible upscaling approaches entailing upscaled
relative permeabilities neither included the Sorb concept nor used any
specialized boundary conditions such as EFBCs.
© 2005. Society of Petroleum Engineers
View full textPDF
(
2,486 KB
)
History
- Original manuscript received:
12 January 2004
- Revised manuscript received:
23 March 2005
- Manuscript approved:
30 March 2005
- Version of record:
15 June 2005
View Cart
