A Vertical Permeability Study
Authors: Hollabaugh G.R. , Slotboom R.A. 
Published: December 2007

Abstract
A vertical permeability study was performed on three Rainbow field cores to examine the effect of crossflow on vertical permeability and to determine the best method for averaging vertical permeabilities. The study consisted essentially of a series of permeability measurements that were made as whole cores were progressively cut into smaller pieces.
Results show that crossflow does contribute to vertical permeability. Further, the effect of crossflow varies inversely with the length-to-area ratio of the cores and is a very important factor to consider when determining a formation vertical permeability. Formation vertical permeabilities determined from the usual core analysis results are probably low because crossflow bas been minimized by using cores with a relatively high length-to-area ratio. For this reason, a more representative formation vertical permeability can be obtained by using a greater number of shorter permeability samples. As expected, the harmonic average of a series of core vertical permeabilities was found to best approximate the core permeability itself. The geometric average of the same permeabilities was found to be more representative of the formation where crossflow contributes to the vertical permeability.

Introduction
The Rainbow field was discovered in northwestern Alberta in 1965 and is presently comprised of some 50 separate reef reservoirs. Production is primarily from the Middle Devonian Keg River formation that lies at a depth of about 6,000 ft. Most of these reefs have high-vertical-relief (up to 600 ft) oil-bearing zones that usually are underlain by an aquifer and are sometimes capped by an initial gas cap. The production mechanism in these reservoirs, whether it be primary depletion or pressure maintenance by gas, solvent, or water injection, will therefore be gravity controlled and drainage will be predominantly in a vertical direction. Under these conditions, the vertical permeability of the reservoir will be a major factor in determining recovery efficiencies. Knowledge of the representative vertical permeability of the reservoir is therefore important to predict recovery efficiencies.
Like other limestone reef formations, the Keg River is very heterogeneous, containing vugs, caverns, stylolites, and fractures. Because of the heterogeneities, it is difficult to determine the representative formation vertical permeability value from core analysis data. This paper deals with an attempt to determine the degree of contribution of crossflow to vertical permeability and to determine the best method for averaging vertical permeabilities.
Some work in the same broad category has been done in the past. Cardwell and Parsons indicated that the effective permeability in a radial system of heterogeneous sands lies between an upper and lower limit approximated by the arithmetic and harmonic averages, respectively. Warren and Price concluded from computational experiments that the most probable effective permeability value of a heterogeneous system can be approximated by the geometric mean. More recently, Lishman arrived at several of our conclusions in his computer study simulating a three-dimensional random arrangement of isotropic permeability cells.