Summary
Simple methods, such as the use of density during compositional simulations,
often fail to identify the phases correctly, and this can cause discontinuities
in the computed relative permeability values. The results are then physically
incorrect. Furthermore, numerical simulators often slow down or even stop
because of discontinuities. There are many important applications in which the
phase behavior can be single phase, gas/liquid, liquid/liquid,
gas/liquid/liquid, or gas/liquid/solid at different times in different
gridblocks. Assigning physically correct phase identities during a
compositional simulation turns out to be a difficult problem that has resisted
a general solution for decades. We know that the intensive thermodynamic
properties, such as molar Gibbs free energy, must be continuous, assuming local
equilibrium, but this condition is difficult to impose in numerical simulators
because of the discrete nature of the calculations. An alternative approach is
to develop a relative permeability model that is continuous and independent of
the phase numbers assigned by the flash calculation. Relative permeability is a
function of saturation, but also composition, because composition affects the
phase distribution in the pores (i.e., the wettability). The equilibrium
distribution of fluids in pores corresponds to the minimum in the Gibbs free
energy for the entire fluid/rock system, including interfaces. In general,
however, this relationship is difficult to model from first principles. What we
can easily do is calculate the molar Gibbs free energy (G) of each phase at
reference compositions where the relative permeabilities are known or assumed
to be known and then interpolate between these values by use of the G
calculated during each timestep of the simulation. Relative permeability values
calculated this way are unconditionally continuous for all possible
phase-behavior changes, including even critical points. We tested the new
relative permeability model on a variety of extremely difficult simulation
problems with up to four phases, and it has not failed yet. We illustrate
several of these applications.
© 2012. Society of Petroleum Engineers
View full textPDF
(
595 KB
)
History
- Original manuscript received:
25 June 2011
- Meeting paper published:
22 February 2011
- Revised manuscript received:
8 May 2012
- Manuscript approved:
7 July 2012
- Published online:
23 October 2012
- Version of record:
6 December 2012
View Cart
