Permeability Prediction for Carbonates: Still a Challenge?
Authors: Altunbay M. , Georgi D. , Takezaki H.M. 
Published: December 2007

Abstract
Permeability estimation for a well and mapping it for a field are extremely critical and difficult tasks in hydrocarbon exploration and production. Different statistical relationships between permeability, porosity, and wireline logs have been studied and presented in the literature. Some of these relations are useful for homogeneous clastic rocks, but they fail with increasing heterogeneity and non-uniformity that characterize carbonate rocks.
This study applies an extended form of the hydraulic unitization method to a Middle East carbonate reservoir. Wireline log data are used to predict permeability in an uncored well in the same geological strata. The extended hydraulic unitization method allows permeability transform equations to be derived as a function of core and conventional log data when a relationship is apparent between permeability, porosity, and the wireline logs. The technique also overcomes the limitation of 0.01-md permeability cutoff in the determination of permeability due to laboratory equipment limitations. This may be important for gas reservoir description.

Introduction
Hydrocarbon reservoir quality is mainly controlled by two properties - storage capacity (porosity) and flow capacity (permeability). Permeability is a key descriptor needed for reservoir development and management because it controls production rate. Among other factors, the spatial variation of permeability controls recovery efficiency; therefore, the prediction of permeability is vital to a field's economics analysis.
Carbonate rocks pose an extreme challenge for mapping rock properties, especially porosity and permeability, due to their complex and variable pore structure. Pore connectivity, pore throat structures, and shapes are products of the depositional environment and the diagenetic history. These micro-structures vary from random to self-repeating patterns. Therefore, the extrapolation of permeability, based on simple relationships derived from limited permeability and porosity data, is futile. Formation heterogeneity must be evaluated with a statistically sound and theoretically correct averaging technique. We propose and illustrate with data from the West Mubarras field an extended hydraulic unitization methodology for carbonate petrophysical characterization. The West Mubarras field data illustrate another common problem encountered when dealing with carbonate reservoir description. Often, the core data are not representative of the entire formation and the reported data are not accurate. This is especially problematic in low-porosity, low-permeability intervals. It is both technically challenging and time consuming to carry out accurate analysis in tight rocks. Thus, core analysts often will identity tight samples and merely assign a low permeability (e.g., 0.01 md) without actually measuring the permeability. This is not a problem from a reservoir description point of view as tight rocks generally do not contribute to reservoir capacity and productivity. However, this common practice significantly detracts from the core data value when deriving permeability transforms from wireline logs.

Background.
Fundamentally, we expect porosity and permeability to be correlated. Obviously, when there is no porosity (= 0), then the permeability is zero; when the there is no matrix (= 1), the permeability is infinite. Unfortunately, these two end points are not sufficient to derive a generalized porosity-permeability relationship. The earliest workers plotted permeability versus porosity, seeking general and reservoir-specific relationships between porosity and permeability. Generally, no simple linear relationships were apparent, but it was evident that scatter on the permeability-porosity crossplot could be reduced by plotting the permeability on a logarithmic scale. Sometimes the permeability-porosity crossplots can be rationalized by grouping the data according to depositional environment and/or rock type (see Fig. 1).
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