Oil Layer Flow Along the Corners of Non- Circular Capillaries by Gravity Drainage
Authors: Dong M. , Chatzis I. 
Published: July 2010

Abstract
The fundamentals of oil layer drainage along the corners of non-circular capillaries in two-phase (gas-oil) and three-phase (gas-oil-water) systems were studied. Experiments of oil layer flow along the corners of square capillaries were carried out to investigate the saturation dependency of oil phase relative permeability in single layer drainage. The quadratic behaviour of oil relative permeability in the gas injection process reported in the literature was explained. For double-layer flow (water layer and oil layer) in a three-phase system, numerical analysis showed that the lubricating effect of a water layer on the relative permeability of oil phase in layer drainage was significant. The dependency of oil layer flow by gravity drainage on oil saturation, water saturation, and oil-to-water viscosity ratio was investigated numerically. The experimental results confirmed the mathematical analysis.

Introduction
Both laboratory experimental results and oil field performance analysis have demonstrated that very high oil recoveries of residual oil can be achieved if gravity drainage is the dominant production mechanism(1–4). Because of the importance of the oil relative permeability in the process of gravity drainage, extensive studies have been conducted on the measurement and analysis of threephase relative permeability.
Numerous measurements have been carried out to determine the three-phase relative permeability during the gravity drainage process(4). It was found that a quadratic change of oil relative permeability with respect to the oil saturation is followed if:the porous medium is water-wet;oil flows in layers; andwater flow is negligible.
Oil layer drainage is an important recovery mechanism in a gravity assisted gas injection process and other enhanced oil recovery methods such as steam assisted gravity drainage (SAGD) and vapour extraction process (VAPEX). To develop physically sound modelling capabilities for these processes, a better understanding of the fundamentals of oil layer flow is necessary at both the microscopic level and the macroscopic level. The results of this study can help improve the understanding and modelling of the oil phase flow in porous media in SAGD, VAPEX, and other gravity assisted gas injection processes.

Single Layer Drainage
In this instance, the procedure to measure the accumulation of wetting liquid by gravity drainage was essentially that of Chatzis, et al.(3) The oils used were heptane and Soltrol 170. At experimental temperature (23 ° C), heptane had a viscosity of 1.0 mPa.s and a density of 0.69 g/cm3, whereas Soltrol 170 had a viscosity of 3.0 mPa.s and a density of 0.70 g/cm3.
The flow rate of liquid in single layer drainage along the four corners of a square capillary under steady-state condition is expressed as follows(5):
Equation 1 (available in full paper)
where S is the saturation of the liquid in the tube, D is the size of the square capillary, and β?is the dimensionless resistance coefficient. If the saturation of the wetting liquid in two square capillaries of different sizes is the same, the layer drainage rate is proportional to the tube size raised to the fourth power.