Reservoir Permeability Upscaling Indicators From Welltest Analysis
Authors: Prasad R.S. Srini , Al-Attar E.H. , Al-Jasmi Ahmad K. 
Published: December 2007

Reservoir Permeability Upscaling Indicators From Welltest Analysis.

Abstract
A methodology has been developed, for a non-fractured reservoir, to:–Correlate effective permeability values from upscaled core data with those inferred from welltest analysis.–Estimate a potential well's initial productivity
It could be applied to screen and rank potential development well locations, by relative initial productivity, based on appraisal well data. The observations are based on the analysis of core and welltest data from a Middle East carbonate reservoir which has been on production for over 30 years.

Introduction
Correlating effective permeability values from upscaled core data with those inferred from welltest analysis has traditionally been an issue of concern for reservoir engineers. The effective single-phase permeability of a region, characterized by a fine-scale permeability distribution, is defined to be the permeability of an equivalent spatially homogeneous permeability region which would produce the same flow rate for a given pressure drop applied across the region in any given direction. The effective permeability depends on both the frequency and the spatial distribution of the fine-scale permeability values. Higher fine-scale permeability values will result in a higher effective permeability and vice versa. To understand the influence of the second factor, please refer to Figure 1. It shows a typical plot of the effect of anisotropy on a region's effective permeability. Anisotropy characterizes the degree of layering in the system. For a spatially isotropic system, which is characterized by an anisotropy value of 1, the effective permeability Ke will be the same in all directions and can be approximated by the geometric average of the fine-scale permeability values. The fluid flow characteristics will be 100% random in nature. The effective horizontal permeability Keh will be the same as the effective vertical permeability Kev. As the anisotropy increases, Keh will increase while Kev will decrease. In the limit, for a perfectly layered system, Keh is given by the arithmetic average of the fine-scale horizontal permeability values and Kev is given by the harmonic average of the fine-scale vertical permeability values. The fluid flow will essentially be 100% parallel. Table 1 lists the three traditionally used permeability averaging equations. Please note that both the geometric and the harmonic averaging equations are "biased" by zero fine-scale permeability values. Cut-offs need to be used to screen the fine-scale permeability values being input into either equation.
Noetinger and Jacquin developed a general and rigorous theoretical framework for upscaling single-phase fine-scale permeability values in a 3D control volume and proposed an equation for determining the effective permeability of a region. In this study, a method has been proposed to modify their equation and apply it to upscale fine-scale core-plug permeability data and correlate the core-based effective permeability with that inferred from welltest analysis in a non-fractured reservoir.
As mentioned before, the analyses are based on data from a Middle East carbonate reservoir. Most of the core data, from 17 wells, was obtained on non-preserved rock under ambient conditions. Detailed description of core from 5 wells indicated that the reservoir is not fractured. Analysis of the 87Sr/86Sr isotope ratio in the residual salt present in core samples was coupled with log, core and pressure data to determine the presence of vertical flow barriers. This was used to better define the effective flow intervals for welltest analysis. Several pressure build-up tests were available for each well. However, most tests were plagued by missing early time data and poor data quality. Special steps had to be taken to account for the geology, address the uncertainty in the computed parameters and extract meaningful information from old welltest data.
This paper discusses the steps taken to address the limitations and uncertainty associated with analyzing old core and welltest data, provides the details of the methodology for correlating core and welltest KH data in a non-fractured reservoir and highlights the procedure that could be used to estimate the relative initial productivity of potential well locations.
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