Summary
We present formulation and numerical solution of two-phase multicomponent
diffusion and natural convection in porous media. Thermal diffusion, pressure
diffusion, and molecular diffusion are included in the diffusion expression
from thermodynamics of irreversible processes.
The formulation and the numerical solution are used to perform
initialization in a 2D cross section. We use both homogeneous and layered media
without and with anisotropy in our calculations. Numerical examples for a
binary mixture of C1/C3 and a multicomponent reservoir
fluid are presented. Results show a strong effect of natural convection in
species distribution. Results also show that there are at least two main
rotating cells at steady state: one in the gas cap, and one in the oil
column.
Introduction
Proper initialization is an important aspect of reliable reservoir
simulations. The use of the Gibbs segregation condition generally cannot
provide reliable initialization in hydrocarbon reservoirs. This is caused, in
part, by the effect of thermal diffusion (caused by the geothermal temperature
gradient), which cannot be neglected in some cases; thermal diffusion might be
the main phenomenon affecting compositional variation in hydrocarbon
reservoirs, especially for near-critical gas/condensate reservoirs (Ghorayeb et
al. 2003).
Generally, temperature increases with increasing burial depth because heat
flows from the Earth’s interior toward the surface. The temperature profile, or
geothermal gradient, is related to the thermal conductivity of a body of rock
and the heat flux.
Thermal conductivity is not necessarily uniform because it depends on the
mineralogical composition of the rock, the porosity, and the presence of water
or gas. Therefore, differences in thermal conductivity between adjacent
lithologies can result in a horizontal temperature gradient. Horizontal
temperature gradients in some offshore fields can be observed because of a
constant water temperature (approximately 4°C) in different depths in the
seabed floor.
The horizontal temperature gradient causes natural convection that might
have a significant effect on species distribution (Firoozabadi 1999). The
combined effects of diffusion (pressure, thermal, and molecular) and natural
convection on compositional variation in multicomponent mixtures in porous
media have been investigated for single-phase systems (Riley and Firoozabadi
1998; Ghorayeb and Firoozabadi 2000a).The results from these references show
the importance of natural convection, which, in some cases, overrides diffusion
and results in a uniform composition. Natural convection also can result in
increased horizontal compositional variation, an effect similar to that in a
thermogravitational column (Ghorayeb and Firoozabadi 2001; Nasrabadi et al.
2006).
The combined effect of convection and diffusion on species separation has
been the subject of many experimental studies. Separation in a
thermogravitational column with both effects has been measured widely (Schott
1973; Costeseque 1982; El Mataaoui 1986). The thermogravitational column
consists of two isothermal vertical plates with different temperatures
separated by a narrow space. The space can be either without a porous medium or
filled with a porous medium. The thermal diffusion, in a binary mixture, causes
one component to segregate to the hot plate and the other to the cold plate.
Because of the density gradient caused by temperature and concentration
gradients, convection flow occurs and creates a concentration difference
between the top and bottom of the column. Analytical and numerical models have
been presented to analyze the experimental results (Lorenz and Emery 1959;
Jamet et al. 1992; Nasrabadi et al. 2006). The experimental and theoretical
studies show that the composition difference between the top and bottom of the
column increases with permeability until an optimum permeability is reached.
Then, the composition difference declines as permeability increases. The
process in a thermogravitational column shows the significance of the
convection from a horizontal temperature gradient.
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
6 October 2004
- Revised manuscript received:
18 April 2006
- Manuscript approved:
31 July 2006
- Version of record:
20 October 2006
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