A Fully-Automated Relative Permeameter
Authors: Ruth D.W. , Adamson R.J. , De Freitas D.R.A. , Hriskevich B.R.J. , Kendall J. , Nikakhtar B. 
Published: March 2010

Abstract
This paper describes an automatic relative permeameter. Problems which are encountered in operating unsteady state relative permeameters are first identified. Solutions are then offered, by describing a fully-automated relative permeameter which employs a pseudo-constant pressure flow system, a unique production mandrel design, and an innovative fractionmeter / flowmeter system. The new apparatus offers a fast and accurate method of obtaining displacement data, with direct input into a computer for data analysis.

Introduction
The relative permeabilities of a porousmedia to simultaneous flow of two different fluids are fundamental parameters of major importance to the study of flow in petroleum reservoirs. They are also the most difficult properties to measure in the laboratory. Superficially, the determination of relative permeabilities is straightforward. With two phases flowing through a rock sample, the pressure drop and flow rates of each phase are measured. Darcy's law in the form
Equation (Available In Full Paper)
where Qa is the flow rate of the Han phase, k is the absolute permeability, kar, is the relative permeability, µa is the viscosity, A is the cross-sectional area, Pa is the pressure and x is the spatial coordinate, is then used to determine kar,. The relative permeability is a function of saturation; therefore, the saturations of both phases are required for each set of flow rates. The difficulty in experimentally determining relative permeabilities lies not in the basic concept, but in the simultaneous measurement of flow rate, pressure drop and saturation.
There are two methods of obtaining relative permeability data: steady state and unsteady state. Only the unsteady state method is considered in this paper.
The unsteady state method is based on interpreting an immiscible displacement process. The interpretation of this displacement process to obtain relative permeability data is performed by one of two analysis techniques: application of Buckley-Leverett frontal advance theory(l) or direct computer simulation. Application of Buckley-Leverett theory requires a number of experimental restrictions. For example, the pressure drop across the sample must be sufficiently large so that capillary effects, particularly at the outlet end of the core, are negligible. This method of calculation is based on estimating the saturation of the flooding phase, and measuring the fractional flow of this phase at the outlet face of the core. In this way the relative permeability can be related to the saturation. Because the experiment is performed rapidly, these measurements are not always easy to obtain. For this reason, actual reservoir fluids are not generally used; instead, fluids with viscosities which facilitate interpretation of the experiment are employed.
Direct computer simulation is a more sophisticated and more meaningful method of extracting relative permeability data from displacement experiments, particularly' for vuggy samples(2). The method is applied by assuming that relative permeability is related to saturation by means of the following expressions (for a two-phase system, a and b):
Equation (Available In Full Paper)
where kir is the relative permeability, kire is the end point relative permeability (kare at Sbr and kbre at Sar), Si is the saturation, Sir is the residual saturation and ni is the saturation exponent.