A Dynamic Method For Measuring Relative Permeability
Authors: Islam M. Rafiqul , Bentsen R.G. 
Published: March 2010

Abstract
Currently available techniques for estimating effective permeabilities are valid only if the displacement is stable and stabilized. That is, only effective permeabilities which are applicable to steady-slate situations can be measured. As many field displacements are thought to be unstable there is a need to develop techniques capable of measuring unstable (unsteady-stale) effective permeabilities. This paper describes the progress made in developing one such method.
The method uses the microwave attenuation technique to measure how saturation is distributed along the length of a core. This enables the estimation of the fraction of water flowing at any point along the core. Because a pressure profile is also available it is possible to relate the fraction flowing to the pressure gradient by means of the differential form of Darcy's law to obtain a dynamic estimate of the effective permeability at any given location (and saturation) along the length of the core. As data acquisition and storage is automated it is possible to obtain a complete set of relative permeability data in less than a day.
Experimental results suggest that effective permeability is a unique function of saturation only if the displacement is steady-state, or if the displacement is stable and stabilized. If the displacement is unstabilized or if it is unstable, different effective permeability curves are obtained.

Introduction
One of the most important properties needed to make a waterflood prediction is the water-oil relative permeability characteristics of the reservoir rock. Such information may be obtained by either the steady-state or the external-drive techniques for measuring relative permeability. Steady-state methods require approximately one day to acquire a complete set of relative permeability data. External drive methods, on the other hand can acquire the same information in a few hours. However, it should be noted that both these methods have severe limitations when it comes to determining water-oil flow properties(1–4).
Apart from being time-consuming, steady-state methods may not be applicable to systems where saturations change with time and show spatial gradients(1). Unfortunately, in most field situations the displacement is dynamic and thus the application of steady-state relative permeabilities to describe unsteady-state flow behaviour is questionable from a conceptual point of view. In this regard, it should be noted that many researchers have found disagreement between unsteady-state and steady-state relative permeabilities(3,5,6). Recently, Aleman-Gomez et al(7) concluded from their theoretical study of unsteady-state displacement that steady-state and unsteady-state relative permeabilities are similar only under certain limited conditions. They also commented that, if a discrepancy between steady-state and unsteady-state relative permeabilities was not observed, it was most probably because of the fact that the unsteady-state method was not capable of describing truly unsteady-state flow. In retrospect, the existence of this problem may have been deduced from the early work of Kimbler and Caudle(8) who concluded that the fluid distributions for steady-state flow differ significantly from those which pertain to unsteady-state flow.
It is well known that the external drive method is based on the assumption that Buckley-Leverett(9) theory is valid.