Dynamic Effects in Two-Phase Flow in Porous Media: Inclusion of 3D and Microscale Heterogeneity Effects
Creators: name: Mirzaei, Mahsanam
name: Das, Diganta Bhusan
name: Mirzaei, Mahsanam
Publisher: name: XVI International Conference on Computational Methods in Water Resources
Year: 2006

description: To quantify nonaqueous phase liquids (NAPLs) transport in the subsurface, one 
requires a correct description of multiphase flow behaviour. This involves the 
determination of various fluid and porous media parameters and, the constitutive 
relationships among capillary pressure (Pc), fluid phase saturation (S) and 
relative permeability (Kr). The determination of Pc-S-Kr relationships is 
particularly difficult because of two effects: (i) presence of heterogeneities in 
the flow domain and (ii) dynamic effects in Pc-S-Kr relationships (see below for 
definition). While the significance of individual factor has been studied at 
various scales using different approaches, the combination of the two effects on Pc-
S-Kr relationships are not well characterised at any scale of observation.

Micro-scale heterogeneities in porous media occur at length scales below those of 
typical laboratory measurement devices (core scale). These micro-heterogeneities 
play a significant role in laboratory determination of Pc-S-Kr relationships. The 
dependence of the Pc-S-Kr relationships on the rate of change of saturation is 
known as the dynamic effect. Obviously, the dynamic effect stems from the fact that 
the time duration necessary for obtaining equilibrium flow conditions may be long 
(e.g., many days to weeks at laboratory conditions) depending on soil and fluid 
properties, scale of observation, degree of saturation, boundary conditions, types 
of media heterogeneity, if any, etc. One may also argue that since fluids do not 
necessarily flow under static conditions at shorter time periods, the empirical 
multiphase models, which assume that Pc is a unique function of fluid saturation, 
are not sufficient to account for the physics of the flow. Hence, there is an 
increasing interest in characterising the significance of dynamic effects for multi-
phase flow in porous media. Most previous work on this area has assumed simple 
scenarios ranging from pore scale and bundle of capillary tube model to 2D domain, 
which may or may not include media heterogeneities. It seems that there is little 
information on dynamic effects for two-phase flow in 3D domains which include both 
heterogeneity and gravity effects.

In this study, we carry out a systematic analysis of the effects of various flow 
and media properties on dynamic two-phase flow in 3D core scale domain, which 
include micro-heterogeneities. A number of factors are considered, e.g., boundary 
conditions; pore size distribution; permeability anisotropy, variations in nature, 
amount and distribution of the micro-scale heterogeneity, etc. Their effects on 
dynamic two-phase flow behaviour are quantified in terms of a capillary damping 
coefficient, which establishes the speed at which flow equilibrium is reached. 
Binary combinations of fine sand imbedded in coarse sand are used. Drainage dynamic 
and static curves for various 3D homogeneous and heterogeneous models have been 
obtained and compared to determine the relative significance of the heterogeneity 
patterns and intensity. Values of dynamic coefficient obtained in this work are 
higher than most previously reported values, but this is plausible considering the 
fact that we consider both 3D and micro-heterogeneity effects. Simulations have 
also been conducted to compare dynamic effects in domains of various shapes but of 
equal volume, namely, cylindrical, 3D rectangle (brick shape) and 2D rectangle. Our 
results suggest that similar  curves may be obtained; however, the dynamic 
coefficient may be very different from one domain to another. This implies that the 
dynamics of the flow depend on the shape of domain and Pc-S-Kr relationships 
obtained for one domain shape may not be used directly for domain of another shape 
at dynamic conditions.

All in all, the results obtained in our study give further evidence that the non-
uniqueness in  curves are caused by different factors: dynamic effects, applied 
boundary condition, micro-heterogeneities, pore size distribution, media 
anisotropy, domain shape and size, to mention just a few. For micro-heterogeneities 
of the type used in our study, we find that, in general, with the increase in the 
degree of heterogeneity, dynamic coefficient increases. However, this dependence is 
not a linear function and depends on a complex interplay of various factors, as 
mentioned above.