Summary
Mixing of miscible gas with oil in a reservoir decreases the effective
strength of the gas, which can adversely affect miscibility and recovery
efficiency. The level of true mixing that occurs in a reservoir, however, is
widely debated and often ignored in reservoir simulation in which very large
grid blocks are used. Large grid blocks create artificially large mixing that
can cause errors in predicted oil recovery.
This paper examines mixing that occurs in porous media by solving for
single-phase flow in a connected network of pores. We differentiate between
true mixing that can reduce the effective strength of a miscible gas or
surfactant from apparent mixing caused by convective spreading. This work
differs from network models in that we directly solve the Navier-Stokes
equation and the convection-diffusion equation to determine the velocities and
concentrations at any location within the pores. Flow in series and layered
heterogeneous porous media are modeled through use of many grains in different
arrangements. We consider slug, continuous, and partial injection as well as
echo tests (single-well tracer tests) and transmission tests (interwell tracer
tests). We match the concentrations from the pore-scale simulations to the
analytical convection-dispersion solution that includes both transverse- and
longitudinal-dispersion coefficients.
The results show that for flow in series and in layers, echo- and
transmission-longitudinal dispersivities become equal and reach an asymptotic
value if complete mixing over a cross section perpendicular to flow has
occurred. In practice, the asymptotic value of dispersivity may never be
reached, depending on pattern-scale heterogeneity and well spacing.
Transverse-dispersion coefficients also are scale dependent, but they decrease
with traveled distance. We further demonstrate that the classical
Perkins-Johnston relationship between longitudinal-dispersion coefficient and
fluid velocity is obtained. We conclude that echo dispersivities are reliable
indicators of true mixing in porous media.
© 2009. Society of Petroleum Engineers
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History
- Original manuscript received:
3 August 2007
- Meeting paper published:
11 November 2007
- Revised manuscript received:
18 November 2008
- Manuscript approved:
22 November 2008
- Published online:
19 February 2009
- Version of record:
22 December 2009
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