Permeability Distributions in Reservoirs
Authors: Richardson J.G. , Sangree J.B. , Sneider R.M. 
Published: December 2007

Technology Today Series articles provide useful summary informationon both classic and emerging concepts in petroleum engineering. Purpose: To provide the general reader with a basic understanding of a significantconcept, technique, or development within a specific area of technology.

Introduction
Determining permeability distributions in reservoirs from data measured atwells requires conceptual models of how the rock properties vary between wells. Many formations or zones have been laid down in strata that are laterallycontinuous over large areas. Geologists can correlate zones or layers ofsimilar rock properties from well to well using core descriptions, porositiesand permeabilities measured on cores, and logs. It is usually observed thatarithmetic averages of foot-by-foot horizontal permeabilities measured parallelto the bedding planes permeabilities measured parallel to the bedding planes inthe cores agree with permeabilities calculated from well tests. This is logicalbecause, as shown in Fig. 1, arithmetic averaging assumes that flow occursthrough the various strata parallel to the bedding planes. In this conceptualmodel, a consistent planes. In this conceptual model, a consistent assumptionis that vertical permeabilities measured perpendicular to the bedding planesshould be perpendicular to the bedding planes should be averaged harmonically(in series) to reflect flow in the vertical direction (see Fig. 1) in a zonebetween two continous shales.

The Model
Two tacit assumptions are made in using harmonic averages of verticalpermeabilities measured on cores in this simplified model. The first assumptionis that there are no zero or near-zero values resulting from small, localizedclay plugs or shale laminae that extend only across the width of the verticalcore sample. Inclusion of a zero value in the harmonic averaging will result ina zero average for the entire zone. Thus, selection of a permeability cutoff isrequired to exclude low values so that more plausible estimates can beobtained. The second tacit assumption is that there be no small, discontinuous, isolated shale barriers within the zone of interest. A classic paper by Pratsshowed that the presence of isolated shales can drastically reduce the verticalpermeability to a single phase. For example, results of Prats' model(illustrated in Fig.2) show that the effective vertical permeability is only 5%of the matrix value if the zone contained an array of shales 150 Ft [45.7m]wide spaced every 10ft [3 m]; 2 b/h=30ft [9.1m], the shales just overlap, and=0.5. The cause of this drastic reduction in vertical permeability is that mostof the flow path for a single permeability is that most of the flow path for asingle phase is in the horizontal direction. phase is in the horizontaldirection. The effect of discontinuous shales on reducing the gravity drainageof oil from a region invaded by gas or water can be less severe than thatpredicted by the single-phase model. For example, oil that drains from agas-invaded region will collect in thin layers above the shales and drainrapidly off the edges if the shales are small in areal extent (see Fig. 3). This process can make the effective vertical permeability process can make theeffective vertical permeability to gravity drainage several-fold higher thanfor single phase flow for shales of the order of 100 ft [30 m] phase flow forshales of the order of 100 ft [30 m] wide. The benefits of this two-phase flowmechanism decrease rapidly as the shale widths increase because the rate ofdrainage is inversely proportional to the width squared.
JPT
p. 1197