# InterPore2018 New Orleans

14-17 May 2018
New Orleans
US/Central timezone

## On the macroscopic momentum balance equation for the fluid-fluid interfaces in two-phase porous media flows

15 May 2018, 12:11
15m
New Orleans

#### New Orleans

Oral 20 Minutes MS 1.21: Hydraulics and mechanics of unsaturated porous media: current state of knowledge and practice

### Speaker

Michele Starnoni (University of Bergen)

### Description

Although two-phase flow in porous media is an established research field since decades, its theoretical background is still incomplete. In particular, while a universal definition of capillary pressure exists at the micro-scale, its upscaling to the macro-scale is still rather vague and a rigorous theory of capillarity at the macro-scale is missing. In this work, a new macroscopic theory of capillarity based on the volume averaging method is presented. The novel feature of the proposed averaging approach is the use of the superficial surface average for upscaling the relevant conservation equations for a surface. This allows for rigorous derivation of the macroscopic momentum balance equation for all the fluid-fluid interfaces contained within the Representative Elementary Volume (REV), thus resolving most of the shortcomings of previous studies, such as the averaging-scale inconsistency and the accounting for the different orientation of interfaces within the averaging volume. This latter aspect is described by an additional parameter arising in the proposed derivation, namely the intrinsic surface average of interface normal vectors $\langle \mathbf{n}_{nw}\rangle^{nw}$. Furthermore, defining the macroscopic capillary pressure as the difference between the intrinsic surface averages of the bulk pressures, it is shown how the capillary pressure-fluid phase saturation curve can be determined in a more consistent manner by upscaling results of pore-scale simulations as oppose to traditional coreflooding experiments. This sets new challenges and opportunities for modelling unsaturated porous materials.

### References

[1] Gray, W. G., & Hassanizadeh, S. M. (1989). Averaging theorems and averaged equations for transport of interface properties in multiphase systems. International Journal of Multiphase Flow, 15(1), 81-95.
[2] Hassanizadeh, S. M., & Gray, W. G. (1993). Thermodynamic basis of capillary pressure in porous media. Water resources research, 29(10), 3389-3405.