Some Problems in Applying the Hassler Relative Permeability Method
Authors: Rose W. 
Published: December 2007

In 1945 Hassler described a method for relative permeability measurement that was conceptually permeability measurement that was conceptually well founded but from the start has presented laboratory workers with various measurement problems. Recent as well as earlier analyses of problems. Recent as well as earlier analyses of the situation, for example, have been motivated by the need for an independent standard against which relative permeability data obtained by other (more convenient, less exacting) techniques can be calibrated. The latter is wanted as a hedge against the possibility that reservoir simulation predictions of possibility that reservoir simulation predictions of reserves and recovery will exhibit marked sensitivity to the input relative permeability data.The purpose of this paper is to call attention to a previously unmentioned type of measurement previously unmentioned type of measurement problem that appears to be inherent to the Hassler problem that appears to be inherent to the Hassler flow systems (Fig. 1). For simplicity, attention will be limited to two-phase colinear flow of a wetting and a nonwetting fluid. In such a case, the intention is that the pressure drop be identical in the contiguous immiscible fluids so that the capillary pressure gradient (and, hence, the saturation gradient) will be zero along the flow path when the relative permeability measurements are being made. permeability measurements are being made.For example, suppose that in a particular run a pressure, p1, is set where the wetting fluid enters the pressure, p1, is set where the wetting fluid enters the inflow capillary barrier, and a pressure, p4 less than p1, is set where the wetting fluid exits from the outflow capillary barrier. Then, as schematized in Fig. 2, the internal wetting-fluid pressures at the surfaces of discontinuity between the core sample and the capillary barriers, p2 and p3 less than p2, will assume values according to Darcy's law that depend on factors such as the ratio of the length of the core sample to that of an end barrier M and the ratio of the effective permeability of the core (to the flow of the wetting permeability of the core (to the flow of the wetting fluid) to the absolute permeability of the barrier material N. In fact, it is easy to show that the relationships under discussion are
(1a)
and
(1b)
The critically important things in Hassler work, of course, is to have the pressures p2 and p3 measured or otherwise immediately known just as soon as two-phase flow is being initiated at each step in the measurement of the relative permeability curves. This is because the relative permeability data are to be referred to particular values of saturation and types (e.g., drainage, imbibition) of saturation distribution and specifically to those that are prescribed by the particular values of capillary prescribed by the particular values of capillary pressure, Pc, that have been imposed before each pressure, Pc, that have been imposed before each two-phase flow episode. In other words, the inflow and outflow pressures in the nonwetting fluid, p5 and p6, respectively, must be set at precisely the same time p1 and p4 are set (i.e., as two-phase flow is initiated simultaneously in both fluids) in such a way that the following condition is met.
(2)
The dashed curves of Fig. 2, for example, depict how pressure would be distributed in the wetting fluid for a representative case where the constraint condition, Eq. 2, has not been met. The consequence of encountering such a situation in a Hassler-like relative permeability run is illustrated in Figs. 3 and 4. The dashed curves indicate that a positive capillary pressure gradient gives rise to a negative saturation pressure gradient gives rise to a negative saturation gradient in the direction of two-phase flow (and vice versa).
P. 1161