Effect of Viscous Instability on Unsteady-State Relative Permeability

Abstract

This paper presents the results of an experimental investigation into the relationship between the extent of viscous instability involved in a laboratory displacement and the relative permeability inferred from measured displacement data. Oil displacement experiments were conducted in a triaxially confined silica sand pack. The extent of viscous instability was varied by using mineral oils of different viscosities and by conducting the displacement runs at different flow rates. Relative permeabilities were calculated using both a history matching technique developed by R. M. Sigmund and F. G. McCaffery (8) and an explicit technique suggested by H. K. Sarma and R. G. Bentsen (14). Although, in principle, this explicit technique is similar to the JBN method (11), it is simpler to use in that, it does not require graphical or numerical differentiation of the experimental data. The technique uses two monotonic functional equations, which satisfy all physical conditions that can be imposed on the system, to smooth cumulative oil production and pressure drop histories. Furthermore, these functional equations can also be utilized to predict end-point displacement parameters, such as : Sor and kwor, for displacement experiments which are terminated before reaching the actual end-point. The results show that the two techniques for calculating relative permeabilities from unsteady-state displacement data provide essentially similar results, and that viscous instability significantly affects the relative permeability measurements. The breakthrough recovery, residual oil saturation and the end-point water permeability were all affected by the extent of viscous instability present during the displacement. It was found that these parameters show a systematic dependence on the extent of viscous instability as characterized by the instability number (Isr) of E. J. Peters and D. L. Flock (19). Also, the results suggest that the relative permeability curves approach a limiting value at high values of Isr. It is evident that the relative permeability inferred from unsteady-state core floods conducted under unfavourable mobility conditions is a lumped parameter which includes the effects of viscous instabilities. Therefore, unless the laboratory displacements happens to be a fully scaled model of the field-scale displacement, the relative permeability curves generated in the laboratory would not fully describe the field behaviour. Hence, it is essential to assess the extent of instability likely to be present in the field process. If the field process involves favourable mobility ratio, the expectation is that it would be free of viscous instability. Accordingly, the laboratory tests should also be conducted under favourable mobility ratio conditions. When the field process is known to involve unfavourable mobility ratio, it would be desirable to simulate the extent of instability in laboratory tests. Unfortunately, the scaling criteria for the growth and propagation of viscous fingers are not yet fully known. However, the relative permeability curves approach a limiting value at high values of instability number and the instability numbers encountered in the field are likely to be much higher because much larger geometric size is involved. Therefore, for unfavourable mobility ratio systems, it would be desirable to conduct the laboratory displacements in the pseudostable regime, i. e. at a high value of the instability number (> 900). This can be achieved simply by using high flow rates, provided the complications of fines migration can be avoided.