Summary
An improved technique based on the concept of hydraulic flow units or hydraulic units (HU's) is presented to calculate permeability distribution in uncored wells. Graphical probability methods, nonlinear regression, and the Ward's analytical algorithm are presented to perform cluster analysis on core data and identify prevailing HU's in a formation. A Bayesian-based probabilistic approach is discussed next to estimate HU's and permeability distributions in logged wells. This is an inverse problem that requires constructing an a priori training database to capture implicit relationships between core-derived HU's and various well log measurements. Information from the database is drawn statistically to infer HU distributions at target logged wells. The method is applied to two heterogeneous reservoirs, a carbonate formation, and a laminated sandstone formation. Comparisons of permeabilities calculated by the HU approach and other conventional techniques are provided that demonstrate the usefulness of the HU method.
Introduction
Estimation of permeability in uncored but logged wells is a generic problem common to all reservoirs. Any field-scale reservoir characterization study inevitably requires knowledge of petrophysical properties at drilled wells for its starting point. Therefore, scientifically sound and geologically compatible procedures must be sought to allow for reliable calculation of permeability distributions in wells.
Traditional approaches for estimation of permeability are based either on simple linear regressions or empirical inferences that use correlations among various well log responses. Usually, these empirically inferred models apply locally because there may be large differences in depositional characteristics at other locations. The regression method assumes that a linear relationship exists between core porosity and the logarithm of core permeability. Another linear regression establishes dependency between measured core porosity and well log-derived porosity. These two regression models, when combined, allow calculation of permeability at logged wells. The method explicitly ignores the scatter of data about the regression lines and implicitly attributes any scatter to measurement errors or second-order fluctuations in reservoir characteristics.
A partial improvement to this method is achieved by first identifying lithological categories of the formation1–3 and then calculating linear regression lines for petrophysical core measurements that belong to each lithology class. Because the regression methods smooth data, the predicted permeability values from these regression models lack the variability seen on actual core data. For this reason, probability field simulations may be applied to add stochastic fine-scale variations to the predicted permeability values.4,5
A more reasonable approach for prediction of permeability is to address the development of permeability in reservoir rocks from fundamentals of geology and physics of flow at pore network scale. This is best achieved by attributing the nature of interdependency between permeability and porosity to geological variations in reservoir rock and by seeking functional relationships for permeability that capture geological controls on flow properties. This will require establishing causal relationships between core-derived pore-throat parameters and log-derived macroscopic petrophysical attributes.6 Such relationships are achieved best if rocks of similar fluid conductivity are identified and grouped together. Each grouping is referred to as an HU. The HU's do not necessarily correspond to lithofacies, which have been referred to as geological flow units.4
Petrophysical properties are controlled by both depositional characteristics, such as grain-size and sorting, and by diagenetic features, such as the amount and type of cement or clay minerals. Thus, an HU involves more than a genetic facies of a depositional system. Generally, the variability of petrophysical properties is large among the HU's and low within them. Permeability calculation by HU's offers an improved estimation over traditional regression-based averaged relationships by incorporating geology and fluid-flow principles. The extent of improvement depends mainly on the geological characteristics of the formation, where larger enhancements are usually achieved in more heterogeneous deposits. In any case, the method can describe permeability variations in a reservoir more comprehensively and realistically because it integrates geology, petrophysics, and engineering.
This paper presents an improved technique for permeability estimation using HU's. The basic concept of HU's is first reviewed, and the theoretical basis for their classification in cored wells is provided. Next, a statistically based inference method is presented to identify HU's in uncored but logged wells and thereafter to calculate permeability distributions. Lastly, the applicability of the improved permeability estimation technique to a carbonate and a sandstone reservoirs is illustrated.
Method
Concept of HU's.
An HU is defined as the representative volume of total reservoir rock within which geological properties that control fluid flow are internally consistent and predictably different from properties of other rocks. Thus, a flow unit is a reservoir zone that is continuous laterally and vertically and has similar flow and bedding characteristics.7 HU's are related to geological facies distributions but do not necessarily coincide with facies boundaries. The parameters that influence fluid flow are mainly pore-throat geometrical attributes. The pore geometry is in turn controlled by mineralogy (type, abundance, location) and texture (grain size, grain shape, sorting, packing). Various combinations of these geological properties can lead to distinct rock flow units that have similar fluid transport properties. Therefore, an HU can include several rock facies types, depending on their depositional texture and mineralogical content. The grouping of rocks based on their fundamental geological flow attributes is the basis of HU classification.
If a porous medium is simulated as a bundle of straight capillary tubes, the following expression for rock permeability is obtained by combining Darcy's law for flow in porous media and Poiseuille's law for flow in tubes8:Equation 1
Concept of HU's.
An HU is defined as the representative volume of total reservoir rock within which geological properties that control fluid flow are internally consistent and predictably different from properties of other rocks. Thus, a flow unit is a reservoir zone that is continuous laterally and vertically and has similar flow and bedding characteristics.7 HU's are related to geological facies distributions but do not necessarily coincide with facies boundaries. The parameters that influence fluid flow are mainly pore-throat geometrical attributes. The pore geometry is in turn controlled by mineralogy (type, abundance, location) and texture (grain size, grain shape, sorting, packing). Various combinations of these geological properties can lead to distinct rock flow units that have similar fluid transport properties. Therefore, an HU can include several rock facies types, depending on their depositional texture and mineralogical content. The grouping of rocks based on their fundamental geological flow attributes is the basis of HU classification.
If a porous medium is simulated as a bundle of straight capillary tubes, the following expression for rock permeability is obtained by combining Darcy's law for flow in porous media and Poiseuille's law for flow in tubes8:Equation 1
