Vertical Permeability From In Situ Horizontal Measurements in Shaly-Sand Reservoirs
Authors: Zahaf K. , Tiab D. 
Published: March 2010

Abstract
The oil industry has become increasingly aware that reservoirs exhibit complex variations of reservoir continuity; in particular, of pore space-related properties such as porosity, permeability, and capillary pressure. These variations reflect the original depositional process, and subsequent diagenetic and tectonic changes. Simple models are often inadequate for predicting reservoir performance and designing a field production management program that optimizes recovery. It is evident to reservoir engineers that optimization depends on the quality of the reservoir undergoing water injection, where the recovery factor is very sensitive to reservoir heterogeneity. Therefore, an accurate knowledge of vertical and lateral permeability distribution is essential.
This paper represents results of a research project aimed at determining vertical permeability from in situ horizontal permeability in shaly reservoirs. This is accomplished by considering the microscopic and macroscopic features, such as the type of shale (Kaolinite, Chlorite, and Illite) and grain size. In situ vertical permeability correlations are derived by using various water saturation correlations for Shaly-Sand formations.
Several vertical permeability relationships were obtained as a function of horizontal permeability, hydraulic mean radius grain size, and the amount and/or type of shale. Generalized models were developed, and were applied to real oilfield data for calculating vertical and horizontal permeabilities.

Introduction
Permeability is one of the most important of all formation parameters used by petroleum engineers to determine whether a well should be completed and brought online or abandoned. Vertical permeability is also essential in developing a reservoir management and development program, including determining the optimal drainage points and production rate, optimization completion and perforation design, and planning EOR patterns and injection conditions.
Extensive research on permeability has been conducted on clean formations for decades. Vertical permeability in Shaly-Sand formations has long been viewed as problematic. Formations with shale and/or different pore geometries constitute the majority of heterogeneous reservoirs. In this case, reservoir heterogeneity is no longer viewed as a problem, but rather as an opportunity for recovering more oil.
In early studies of reservoir engineering, reservoirs were assumed to be homogeneous and isotropic, but also non-uniform. In recent studies, however, the porosity-permeability transform has been used for a better description of a reservoir having some complex geological continuity. Clark(1) showed that, if the rock grains are large, flat, and uniformly oriented along the longest dimension, then the horizontal permeability (Kh) would be higher than the vertical one. Clark(1) also showed that, if the rock was composed mostly of large and uniformly rounded grains, its permeability would be considerably higher and almost equal in both the horizontal and vertical directions. Generally, vertical permeability is lower than horizontal permeability, especially if the sand grains are small and have irregular shape. Most petroleum reservoirs fall in this category.
Neasham(2) studied the effect of clay on permeability. He showed that the morphology of clay with the highest air permeability is predominantly the discrete particle. The morphology of dispersed clay in samples falling within an intermediate air permeability range is predominantly of a pore-lining variety.