Capillary Number Correlations for Gas-Liquid Systems
Authors: Ding M. , Kantzas A. 
Published: March 2010

Abstract
Conventional capillary number theory predicts that residual oil will not be mobilized until a critical capillary number (2E - 5) is exceeded. This theory was tested to determine residual oil saturation mobilization after forced water imbibition. In the literature, high residual oil saturation was established from waterflooding at a certain pressure. Then gradually increasing pressure was applied for water injection until residual oil production was observed. It was confirmed that this critical capillary number is applicable when the initial residual oil saturation was estimated from spontaneous water imbibition tests. The same types of experiments were repeated for gas-liquid systems by creating the initial residual gas saturation through spontaneous oil or water imbibition tests on the same samples. The procedures, which included spontaneous imbibition tests followed by forced imbibition tests, were monitored by an on-line NMR system. Analysis of the experimental results produced an estimate of the critical capillary number for mobilizing residual gas from water imbibition or oil imbibition tests. In this research, we broadened the term of "imbibition" for both water and oil terms since, compared to gas, both water and oil are in the wetting phase. It was found that the critical capillary number for a gas-liquid system is very different from that of an oil-water system in the same type of rock.
Berea sandstone plugs were used in all the experiments. The reason for using Berea sandstone plugs is due to their relatively homogeneous pore structure. Additional Western Canadian sandstone plugs were used for testing gas-water systems to confirm the results obtained from the Berea sandstone plugs. Understanding the different mechanisms to produce discontinuous residual oil or residual gas is important for enhanced oil and gas recovery operations. Hopefully, this research can provide new insights into recovering additional gas from gas reservoirs with active aquifers.

Introduction
Increasing the capillary number has long been investigated as a strategy for improving oil recovery. Many methodologies around increasing the capillary number have been either tested in the laboratory or applied in the field. Capillary number is defined as the ratio of viscous forces to capillary forces. Evaluation of the capillary number can be used to describe the relative importance of viscous forces to capillary forces during immiscible displacements. There are various forms of the capillary number. The most common versions of capillary number are those by Saffman and Taylor(1):
Equation (1) (Available in full paper)
and Melrose and Brandner(2):
Equation (2) (Available in full paper)
When non-wetting phase oil is trapped in porous media, the pressure gradient required to move it through a capillary tube is much higher than what would be predicted by the pipe flow equation, due to the pressure discontinuity at the wetting/non-wetting interface. Because of the contact angle hysteresis, this discontinuity is not of the same magnitude on both sides of the discontinuous non-wetting phase. For example, in a water-wet medium, an oil droplet represents the discontinuous non-wetting phase. As the oil droplet is pushed through a pore throat, its downstream end gets squeezed into a much narrower segment making its radius of curvature much smaller than the upstream part.