## Year

2000

## Degree Name

Doctor of Philosophy

## Department

Faculty of Engineering

## Recommended Citation

Gamage, Ranjith, Analytical and experimental modelling of coupled water and air flow through rock joints, Doctor of Philosophy thesis, Faculty of Engineering, University of Wollongong, 2000. https://ro.uow.edu.au/theses/1818

## Abstract

Two-phase flow is of considerable importance in many applications such as chemical engineering, petroleum recovery, underground storage plants and mining engineering. Most commonly encountered two-phase flows are gas-liquid, gas-solid, liquid-liquid and liquid-solid. Out of these, the most complex flow is the gas-liquid phase, because of the complex interaction between fluids including compressibility and solubility characteristics. In fields such as, chemical and biomedical engineering, a vast number of studies have been carried out in order to understand the complex nature of two-flows. However, no generalized solution method for water-gas has been formulated in the rock mechanics literature because of the large number of geo-hydraulies variables involved, including the deformation characteristics of each phase and their influence one another.

In this research study, the characterisation of two-phase flow in a fractured rock was investigated, in order to understand the coupled flow-deformation mechanisms under various stress conditions. A comprehensive mathematical model to predict the quantity of each flow component in a single joint was developed. A joint with two parallel walls filled with layers of water and air was analysed. Effects of mechanical deformation of the joint, compressibility of fluids, the solubility of air in water phase change between fluids have been taken into account to develop analytical expressions, which describe the behaviour of the air-water interface. A state-of-the-two-phase high pressure triaxial equipment was developed in order to calibrate the model. Prior to testing, all the fractured specimens were mapped using the digital profilometer to estimate the roughness of the fractured surface. Tests were conducted on fractured hard rock specimens for different boundary conditions including confining pressures with inlet water and air pressures.

Accurate determination of flow structures is very important in developing mathematical models for multiphase flow analysis. An indirect method based on fluid flow parameters was employed for identifying flow patterns within rock joints. Using the plot of liquid superficial velocity against gas superficial velocity, a clear margin to identify bubble flow pattern from annular flow was observed. For a water saturated specimen, at a relatively low inlet air pressure, the expected flow pattern within the joint is bubble flow. At intermediate air pressures, the flow regime is best described annular flow, whereas at elevated air pressures, a complex flow pattern may develop. Although these plots do not show the clear margins of all different flow regimes, they distinguish clearly, the bubble flow pattern from annular or complex flow regimes.

Findings of this study also show that two-phase flow rate follows a linear relationship against inlet fluid pressures when inlet air pressure (pa) = inlet water pressure (pw). relatively low inlet fluid pressures, flow rate linearly varies with the fluid pressures. However, the linear relationship between the flow rate and the fluid pressure vanishes once the inlet fluid pressure exceeds a certain value. The non-linearity may probably be due to the formation of non-parallel laminar or turbulent flow at rough joint surfaces. According to the analysis of flow type (i.e., turbulent or laminar flow), flow can be best described by laminar flow. Non-parallel laminar flow occurs at elevated fluid pressures, whereas the development of turbulent flow within rock fractures is very remote.

From the comparison of single-phase flow with two-phase flow, it is evident that the two-phase flow rate is much lower than that of single-phase flow. The significant reduction of two-phase flow rate is attributed to the influence of one phase on the other. As an example, at 0.2MPa inlet fluid pressure, the individual components of water and airflow rates of two-phase flow have decreased by 50 % and 95 % from the respective single-phase flow rates. These findings also confirm that two-phase flows follow Darcy's law for the considered range of confining pressure and inlet air and water pressures. Therefore, Darcy's law can be extended to model unsaturated flow through jointed rocks by introducing the factor, 'relative permeability' (Kr).

For fully saturated water flow through rock joints, various studies have shown that the flow rates decrease with the increase in confining pressure due to the closure of apertures. Similar to single-phase flow, two-phase flow is also influenced by the confining pressures in a similar way. However, beyond a confining pressure of 6MPa, the rate of change of flow becomes marginal. For example, the flow rates of both phases decrease by as much as 80% when the confining pressure exceeds 6MPa, which is mainly due to the reduction of effective aperture by joint deformation. Beyond this point, any change of flow rate is mainly due to interaction between the fluids including solubility, compressibility and change of fluid properties. Depending on the magnitude and orientation of the joint network relative to the direction of axial loading, two-phase flow rate may increase or decrease.

From the mathematical model, it is shown that the joint deformation contributes most to the change in phase levels of air and water layers, and the effects of air solubility and compressibility components are relatively small. Nevertheless, at significantly elevated confining pressures, where the joint apertures have reached their residual values, the effects of compressibility and solubility of air in water become increasingly more pronounced. The measured flow rate of the water phase was found to be almost equal to the calculated flow rate. However, for the flow rate of air, a slight deviation from theory was encountered, which was probably due to some discontinuous air pockets trapped within the rock matrix.

It is evident that the flow through a fractured sample is not always stratified. Nevertheless, the computed water and air phase heights, i.e. hw(t) and ha(t), introduced in the model give a realistic prediction of flow volumes, as verified by the laboratory measurements. The study confirms that the analytical model can accurately predict the flow rates of both air and water phases in a single joint, for given applied stress conditions. The developed theory can be employed to predict water and gas flows through fractured rock mass in underground works and in oil recovery process in petroleum engineering. Particularly in nuclear waste storage plants, the common unsaturated flow through fractured tight rocks can be simulated using the developed theory in order to estimate radioactive contamination with groundwater. The measured relative permeability values can be incorporated in numerical models to model actual flow behaviour in fractured rock mass.

**Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.**