Producing – Equipment, Methods and Materials - Field Evaluation of Cathodic Protection of Casing

The mechanism of two-phase flow in porous media has been a subject of wide controversy. One of the properties essential for understanding the dynamic behavior of two-phase flow is relalive permeability. Relative permeability to a certain phase is defined as the ratio of the effective permeability of that phase to its permeability when it is the only fluid present and powing. In this research, a theoretical analysis was made to determine the effect of viscosity ratio between the non-wetting and the wetting phase on relative permeability. Experimental work was conducted to test the validity of the derived equations. The experiment was conducted on four natural cores. Four oils were used as the non-wetting phases with a viscosity range of 0.42 to 71.30 cp and two wetting phases with a viscosity range of 0.86 to 0.96 cp. Oil and bring were made to flow simultaneously at various ratios, and relative permeability curves were constructed. A total of eight relative pertileability cycles representing eight viscosity ratios were run oil each sample. It was found that relative permeability to the non-~cletting phase varies with viscosity ratio. The relative effect of this variation on relative permeability values was a function of the sample's single-phase permeability, decreasing with its increase. It was concluded that, for .samples of single-phase permeability over I darcy. the effect of viscosity ratio could be disregarded, and relative permeability would be, in effect, a function of satrtration only. INTRODUCTION Two-phase as well as multiphase flow occurs in many fields of science. This type of flow is of particular interest in petroleum production. The knowledge of relative permeability, which describes the dynamic behavior of two-phasc as well as multiphase flow, is essential for solution of problems arising in that field. Thc relative permeability ot a porous medium to a given phase in multiphase flow. is generally considered to be only a function of the saturation of that phase, independent of the properties of fluids involved and ranging in value from zero to unity. Work by Leverett' and Leverett and Lewis' apparently supports this concept. In his experiments Leverett used a clean, packed unconsolidated sand of high permeability (3.2 to 6.2 darcies) with two phases (water and oil) flowing and a viscosity ratio range of 0.057 to 90.0. His results showed that the wide range of viscosity had practically no effect on relative permeability-saturation relationship. Recently accumulated evidence from work performed by several laboratories and a paper by Nowak and Krueger,2 in which relative permeability to oil of a few core samples in the presence of interstitial water was considerably greater than single-phase permeability to water, cast some doubt on the conclusions reached by Leverett' and subscribed to by a large number of individuals in the oil industry. One explanation advanced to explain this behavior states that it is caused by the variable extent of hydra-tion of clay minerals present in the sand. The greater the water saturation, the greater will be the area of contact between water and clay minerals; therefore, the greater will be the extent of swelling with corresponding reduction in permeability. Yuster4 presents another explanation for the recently accumulated evidence. Utilizing Poiseuille's law, he analyzed concentric flow in a single capillary where the non-wetting phase flows in a cylindrical portion of the capillary and concentric with it. The wetting phase flows in the annulus between the non-wetting phase and the capillary wall. The equations obtained indicate that relative permeability to the non-wetting phase is a function of saturation and viscosity ratio. Although Yuster's equations show that fractional rel-ative permeability to oil could be greater than unity, as was indicated by the data of Nowak and Krueger,1 they failed to present an explanation to the experimental data of early investigators such as Leverett.1 Due to the importance of relative permeability in understanding the flow behavior of petroleum reservoir fluids, this work—theoretical as well as experimental —was undertaken to determine whether relative permeability is a function of saturation only as was concluded by Leverett1 or a function of saturation and viscosity ratio as was theorized by Yuster.4 THEORETICAL ANALYSIS An equation will be derived for the rate of oil flow through a porous medium that is initially filled with water. Based on this equation, an analytic expression for relative permeability will be developed. The porous medium will be assumed to consist of .straight circular capillaries of different radii. It will also be assumed that there are no interconnections among the capillaries and no mass transfer across the oil-water interface. Consider a porous sample initially saturated with a wetting phase (water). As a non-wetting phase (oil) is