Abstract
A method is proposed for the laboratory determination of permeability; a water-saturated core is shaken and the electrokinetic electromotive forces (emf's) generated thereby are measured as an indication of water movement within the core. This method also can provide a determination of the zeta potential. It is of special interest because of its possible extension to use as a well logging measurement.
Introduction
Permeability commonly is determined by applying a constant pressure differential lengthwise across a core and measuring the resultant flow through it. Permeability measurements also can be made in situ in boreholes by monitoring transient pressure variations resulting from flow disturbances. In the latter method, fluid and pore compressibilities generally must be taken into account. This paper considers a new laboratory procedure for permeability measurement wherein fluid compressibility again plays a role. The core to be measured is saturated with water, and electrodes are attached to its end faces. It is sealed so that no water can enter or leave. The core then is shaken parallel to its axis with a sinusoidal acceleration. Because the water is compressible, the core acceleration (acting like a synthetic gravity field) will cause some motion of the water relative to the rock frame. The water movement results in the generation of electrokinetic emf's that are monitored in amplitude and phase along with the acceleration. The upper part of Fig. 1 schematically indicates the arrangement of the core. The lower part of Fig. 1 indicates the measurement and interpretation. It is possible to determine k (permeability) and (zeta potential) by measuring a* (complex acceleration). V* (complex electrokinetic emf), and theta (phase angle between V* and a*). Measurements of this kind are described. These measurements, and others not reported here, have met with good success. The technique is of interest because of its good simulation of in-situ measurements and its possible use as a well logging measurement. Also, it can yield gas a by-product. There is the further possibility that it can be extended to measurements of relative permeability by controlling and the conductivity of the fluid.
Theory
The equations used to described fluid flow, which are a slight generalization of those used in pressure-testing analysis, are
(1a)
and
(1b)
in these equations, v is the pore/fluid velocity relative to the rock frame; a is the acceleration of the rock frame; mu and p are the viscosity and the density of the saturating fluid, respectively: K is the bulk modulus of the fluid, which can be corrected for pore compressibility in the usual way; phi and k are the rock porosity and permeability, respectively; and p is the excess pressure resulting from fluid compression. In Eqs. 1a and 1b, it is assumed that the rock frame itself is accelerated as a unit. Thus, a will not depend on the coordinate x along the core. The two terms on the left side of Eq. 1a correspond to flow and compression of the fluid resulting from the driving body force produced by a.
SPEJ
P. 670^
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