Summary
We propose a two-step approach to permeability prediction from well logs that uses nonparametric regression in conjunction with multivariate statistical analysis. First, we classify the well-log data into electrofacies types. This classification does not require any artificial subdivision of the data population; it follows naturally based on the unique characteristics of well-log measurements reflecting minerals and lithofacies within the logged interval. A combination of principal components analysis (PCA), model-based cluster analysis (MCA), and discriminant analysis is used to characterize and identify electrofacies types. Second, we apply nonparametric regression techniques to predict permeability using well logs within each electrofacies. Three nonparametric approaches are examined - alternating conditional expectations (ACE), generalized additive model (GAM), and neural networks (NNET) - and the relative advantages and disadvantages are explored.
We have applied the proposed technique to the Salt Creek Field Unit (SCFU), a highly heterogeneous carbonate reservoir in the Permian Basin, west Texas. The results are compared with three other approaches to permeability predictions that use data partitioning based on reservoir layering, lithofacies information, and hydraulic flow units (HFUs). An examination of the error rates associated with discriminant analysis for uncored wells indicates that data classification based on electrofacies characterization is more robust compared to other approaches. For permeability predictions, the ACE model appears to outperform the other nonparametric approaches.
Introduction
Estimating rock permeability from well logs in uncored wells is an important yet difficult task in reservoir characterization. Most commonly, permeability is estimated from various well logs using either an empirical relationship or some form of statistical regression (parametric or nonparametric). The empirical models may not be applicable in regions with different depositional environments without making adjustments to constants or exponents in the model. Also, significant uncertainty exists in the determination of irreducible water saturation and cementation factor in these models. Statistical regression has been proposed as a more versatile solution to the problem of permeability estimation. Conventional statistical regression has generally been done parametrically using multiple linear or nonlinear models that require a priori assumptions regarding functional forms.1,2
In recent years, nonparametric regression techniques such as ACE and NNET have been introduced to overcome the limitations of conventional multiple-regression methods.3–6 Applications to complex carbonate reservoirs have shown great promise in handling many forms of heterogeneity in rock properties. However, significant difficulties remain in the identification of sharp local variations in reservoir properties caused by abrupt changes in the depositional environment. Another distinctive feature in carbonate reservoirs is the porosity/permeability mismatch (i.e., low permeability in regions exhibiting high porosity and vice versa). All these features are extremely important from the viewpoint of fluid flow predictions, particularly early-breakthrough response along high-permeability streaks.
Several approaches have been proposed to partition well-log responses into distinct classes to improve permeability predictions. The simplest approach uses flow zones or reservoir layering.4 Other approaches have used lithofacies information identified from cores, as well as the concept of HFUs.7–11 However, because of extreme petrophysical variations rooted in diagenesis and complex pore geometry, even within a single zone or class, a reliable correlation of permeability and logs frequently cannot be developed. A major difficulty in this regard has been the classification of well logs in uncored wells.12
Generally, a suite of logs can provide valuable but indirect information about the mineralogy, texture, sedimentary structure, fluid content, and hydraulic properties of a reservoir. The distinct log responses in the formation represent electrofacies13 that very often can be correlated with actual lithofacies identified from cores, based on depositional and diagenetic characteristics. The importance of electrofacies characterizations in reservoir description and management has been widely recognized.8,9,12–16
The objective of this paper is to further improve permeability predictions in heterogeneous carbonate reservoirs through a combination of electrofacies characterization and nonparametric regression techniques. We have applied the proposed technique to a highly heterogeneous carbonate reservoir in the Permian Basin, west Texas: Salt Creek Field Unit (SCFU). The results are compared with three other commonly used techniques for permeability predictions that use data partitioning based on reservoir layering, lithofacies information, and HFUs.
Methodology
Our proposed method is a statistical regression approach to permeability prediction from well logs based on data partitioning and correlation. Broadly, the method consists of two major parts:data classification through electrofacies determination, andpermeability correlation with nonparametric regression techniques.
To characterize and identify electrofacies groups, we perform a multivariate analysis of the well-log data using PCA, MCA, and discriminant analysis.8,9,12–16 Such electrofacies classification does not require any artificial subdivision of the data population: it follows naturally based on the unique characteristics of welllog measurements reflecting minerals and lithofacies within the logged interval. For permeability correlation, three different nonparametric regression techniques are considered - ACE, GAM, and NNET - and the relative advantages and disadvantages are explored.3-6,21–26
Electrofacies Determination
The method used to perform the electrofacies classification is based on attempts to identify clusters of well-log responses with similar characteristics. This three-step procedure is discussed next.
Numerical Simulation Modeling of Carbonate Reservoir Based on Rock Type