A new process transforms properties measured at a fine scale to equivalent effective properties at a coarser scale.

Because accurately predicting permeability is one of the many challenges facing the log analyst, several methods have been developed to improve predictions. Most stem from the well-known porosity-permeability empirical relationship often implemented with a link to geological facies. Exploring this relationship, one can use a model built in a well with sufficient core coverage to extrapolate the permeability to other wells drilled in a comparable formation. This new method improves upon its predecessors.
The First Nearest Neighbor (FNN) method is used for modeling permeability coupled with multiresolution graph-based clustering (MRGC) electrofacies analysis. This combination helps identify what causes the poor performance of the standard permeability-estimating methods. The methodology benefits from the capability of MRGC to process array data and single-value data. This capability allows characterization of highly bimodal facies without the need for degrading the information through averaging.
Objectives
The geologist in charge of a reservoir description faces the complex challenge of populating the 3-D grid of a reservoir model with permeability values. No borehole measurement can provide a complete record of the permeability throughout the volume of the reservoir. Worse, permeability is controlled by the interaction of such geologic factors as sedimentation, diagenesis and tectonism, which are not directly addressed by any single log or combination of logs.
The new methodology can be used in operating conditions to model permeability, and it also provides insights for problems associated with:
• quality of the log dataset;
• difference in the scale of investigation between logs and plugs; and
• suitability of different mathematical methods to extrapolate core measurements.
The new method focuses on recognizing highly heterogeneous formations and correctly predicting permeability in these zones by using:
• a new technique of upscaling high-resolution (HR) core measurements; and
• MRGC electrofacies-clustering obtained from various logs.
Permeability prediction
Permeability is related to the distribution of the pore throat diameter, length and tortuosity. Two methods commonly are used to propagate permeability values over a reservoir model.
Permeability vs. facies. Empirical relationships tying permeability to facies are established from core measurements, then upscaled and compared to test results. Facies maps then are used to populate the reservoir model cells with permeability values. The method requires that facies profiles be inferred from logs and cores and that sedimentary models be proposed before any facies maps can be drafted.
Permeability vs. logs. Several methods proposed for evaluating permeability profiles attempt to reduce dependence on high-level expertise and the risks associated with the sequential process needed to derive permeability. These methods include deterministic estimation from logs and, more recently, "descriptive" or statistic approaches using logs as extrapolators for core measurements.
Permeability prediction from core measurement to uncored, but logged, zones can be described as follows:
• use available log data and associated core measurements to train a neural network or calculate a statistical model; and
• extrapolate the core measurements to the uncored, logged zones.
The new methodology uses a descriptive approach that allows:
• linking permeability prediction to electrofacies analysis for cross-checking the two datasets; and
• predicting data in highly heterogeneous formations.
Method description
Two methods used for permeability prediction are Operfimage and FNN. The new method is histogram upscaling (HU).
Operfimage was developed at Elf through dynamic clustering and has been used for operational purposes since 1994. Operfimage smooth-averages core measurements around the log data point in the log space. Surveys were conducted to compare different statistical methods (including Operfimage) and neural network methods for permeability prediction. Developers concluded from the surveys that, with an initialization, the results of these methods are significantly comparable. Fundamentally, they perform a kind of averaging in the log space. Because of this kind of averaging, these methods underestimate the maximum permeability values while overestimating the minimum values.
Used for permeability prediction, FNN differs fundamentally from previous methods because no smoothing is applied to the results. The permeability value of each log data point is directly obtained by copying the permeability value of its nearest point with a core measurement in the log space.
The FNN method requires the user to refer to the real object with no loss of original information, generating a spiky permeability curve over specific intervals. However, such apparent shortcomings can be turned into an advantage.
HU is a process for transforming properties measured at a fine scale to equivalent effective properties at a coarser scale. Electrofacies calibration and permeability prediction are two examples in which upscaling is critically important. In most cases, averaging the fine-scale measurements over predefined intervals or over a sliding window performs upscaling. Typically, for permeability prediction, the length of the sliding window is comparable to the size of the logging tool resolution.
The HR measurements can be upscaled over a depth interval by binning them to produce a distribution (or histogram or frequency plot) that corresponds to the low-resolution measurements. The upscaled HR measurement distributions then are processed using the MRGC clustering method to reduce this large amount of information to a single log. The resulting permeability-facies log represents the clusters of permeability distributions.
FNN vs. Operfimage
Blind tests of both methods were performed under operational conditions on the same logs and core data sets. The upscaled core permeability logs for permeability prediction on the learning dataset and for performance evaluation on the application datasets were computed with the volumetric weighted-average upscaling (VWAU) method.
According to tests on the application wells, FNN had smaller average error on predicted permeability and a larger error dispersion. Operfimage had a larger average error and a smaller error dispersion. Smaller error dispersion can be explained by the averaging effect of Operfimage, which makes predicting extreme values impossible. A depth display of the Operfimage indicator points to zones of thin beds or transitional facies where depth-matching core is particularly difficult.
HU vs. MRGC
The differences between the predicted permeability logs and the core measurements cannot be solely explained by the difference in the prediction methods. These differences can originate from formation heterogeneity at a scale finer than log resolution. Furthermore, the way traditional core measurements were upscaled often was thought inappropriate. To detect intervals where the VWAU method is inappropriate, geologists performed the permeability prediction and then clustered it with conventional logs to produce electrofacies using MRGC. Electrofacies in the inner part of the cloud of logs exhibited a large dispersion of permeability values that corresponded to the values of facies with likely strong heterogeneity.
HR resistivity measurement and electrical borehole imaging are other means to confirm such diagnostics. Geologists analyzed the formation heterogeneity using the following HR resistivity techniques:
• performed a HU of the HR resistivity;
• used a sliding window with a length equal to the NMR T2 resolution;
• applied MRGC to cluster the upscaled HR resistivity distribution; and
• employed core data to calibrate the clusters.
Additionally, this method of upscaling and clustering simplified the facies analysis. Figure 1 shows frequency crossplots of two clustering results. Analysis showed:
• sedimentological facies cannot be used to discriminate the permeability values in certain facies;
• HU-HR resistivity proves to be a convenient way to extract heterogeneity from logs at fine scale;
• a strong relationship exists between grain-size distribution and sedimentological facies;
• a good relationship exists between the HU-HR resistivity and NMR T2 distribution;
• sand laminae are favored more than shale laminae as sampling sites; and
• NMR T2 distribution and HU-HR resistivity are the best log combination to separate sedimentary facies, identify the heterogeneity of facies and predict petrophysical characteristics.
Final comparison
Of the several methods developed to improve permeability prediction, geologists chose to investigate FNN first. The comparison between permeability logs predicted from FNN and from Operfimage led them to address the problems of upscaling conventional core measurements. These methods are inappropriate for retaining the original information from heterogeneous formations.
After using a method with MRGC electrofacies to detect intervals with heterogeneous facies, geologists proposed the HU method for keeping all information for multimodal permeability distributions in heterogeneous formations. They then could use upscaled permeability distributions clustered by MRGC to simplify the information and bring out its organization.
In tests, the combined use of HU and MRGC on various core measurements and logging data resulted in:
• a better understanding of the relationship among core data (porosity, permeability, grain-size distribution and sedimentary facies);
• positive evidence that the electrofacies obtained from NMR T2 distribution and HU-HR resistivity gave the best resolution of sedimentary facies.
The analysis of each NMR and HR resistivity dataset allowed posting of a permeability distribution on a geologic cross-section while considering formation heterogeneity.
While HU and MRGC are services of the Halliburton Energy Services Applied Formation Evaluation Centers, Landmark Graphics Corp. will offer the MRGC software commercially in late 2002.

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