Features of Convection and Diffusion in Porous Media for Binary Systems
Authors: Ghorayeb K. , Firoozabadi A. 
Published: March 2010

Abstract
Compositional variation in a vertical rectangular porous medium containing a two-component single phase fluid in the presence of a prescribed linear temperature field is considered. We investigate by using a finite volume method, the effects of convection, thermal diffusion, and pressure diffusion on the compositional variation. Calculations show that, for high permeabilities, convective mass transfer overrides both thermal and pressure diffusion; it is the main phenomenon affecting compositional variation within the porous medium. In this case, the permeability increase makes the composition variation less pronounced. For low permeabilities, compositional variation is mainly affected by the ratio (-CT Tz)/(CP PZ) where CP, CT, PZ, and TZ are the pressure and thermal diffusion coefficients and the vertical pressure and thermal gradients, respectively. When this ratio is &gt;1, thermal diffusion is the main phenomenon affecting compositional variation and the horizontal composition gradient reaches a maximum at some permeability. For (-CT Tz)/(CP PZ) &gt;1, compositional variation is mostly affected by pressure diffusion and the horizontal compositional gradient decreases monotonically with permeability increase.

Introduction
Composition variation in hydrocarbon reservoirs has been a mystery until very recently. Measured data indicate several trends of compositional variation.
There is mainly vertical compositional variation of the hydrocarbon components in some reservoirs(1). Some other reservoirs show pronounced horizontal compositional variation(2). In some other reservoirs there is very little compositional variation with depth(3).
There are four distinct mechanisms that affect the variation of composition in a single-phase hydrocarbon reservoir. These mechanisms are:molecular diffusion,pressure diffusion,thermal diffusion, andnatural convection. Molecular diffusion is the tendency to mix due to concentration gradient. Pressure diffusion (gravitational segregation) is the separation by pressure gradient; it is negligible in the horizontal direction even when there exists natural convection, but may be pronounced in the vertical direction due to high vertical pressure gradient. Because of the pressure diffusion, the bottom fluid is richer in heavy components than the top. Thermal diffusion is the tendency of a convection-free mixture to separate under a thermal gradient. Natural convection is the convective circulation due to density gradient. Density gradient is established due to temperature and concentration gradients. Steady state convection in hydrocarbon reservoirs is caused by horizontal temperature gradient.
A considerable number of investigations of compositional variation in hydrocarbon reservoirs exist in the literature(4-10).
Those studies consider mainly the gravitational effect in a 1D convection-free system(4-7), where it has been shown that the gravitational effect causes the heavier components to segregate towards the bottom of the reservoir. From References (8) to (10) one concludes that thermal diffusion may have the same order of magnitude and may have an opposite effect than pressure diffusion. However, the above studies(4-10) neglect the effect of convection on compositional variation and do not consider horizontal compositional variation.