Heterogeneity Index From Acoustic Image Logs and Its Application in Core Samples Representativeness: A Case Study in the Brazilian Pre-Salt Carbonates
Authors:   Petrobras -Petróleo Brasileiro S.A., de Oliveira Lucas Abreu Blanes , Gonçalves Leonardo ,   Petrobras -Petróleo Brasileiro S.A.
Published: November 2024

Heterogeneous reservoirs are challenging for petrophysical models based on laboratory analyses. The low representativeness makes models calibrated at the core scale unsuitable for estimating petrophysical properties at the log scale, generating unsatisfactory results. In the case of Brazilian presalt carbonates, complex depositional and diagenetic processes generate a porous medium with vugs, fractures, and caves of various sizes that are rarely appropriately sampled. In intervals with large pores, samples collected will represent the rock matrix, underestimating laboratory measurements such as porosity and permeability. Although most petrophysicists understand the importance of the representativeness of rock samples in their models, techniques to quantify them and guide their use are scarce and usually subjective. Therefore, the present work proposes calculating a heterogeneity index from acoustic image logs to support the choice of representative rock samples based on a case study in the Brazilian presalt carbonates. First, an investigation depth window is defined, usually related to the vertical resolution of well logs. In this case study, a 1-m window was chosen and applied to the image log. The image window is then divided into two equal-sized parts, and the standard deviation of each part’s average image amplitudes is calculated and stored. This process is repeated several times with smaller equal-sized parts until reaching the minimum size, in this case study, defined as four image pixels. Finally, a relationship between the partitioned window’s size and the amplitude average’s standard deviation is obtained. As the image log is related to the borehole wall, it can approximate the well cylinder, and this partitioned window can be related to a specific sample volume. A function that relates the volume to the standard deviation is then fitted. In homogeneous intervals, the standard deviation of the amplitude averages should show little to no variation as the volume decreases. However, in heterogeneous intervals, the standard deviation would increase as the volume decreases, with a greater rate as heterogeneity increases. Therefore, the slope of the fitted function can be considered a heterogeneity index. Furthermore, it is possible to use the function to estimate a given standard deviation for a volume, indicating the representativeness of a given sample volume. The heterogeneity index was calculated for the case study well, with 414 1.5-in.-diameter core samples collected. It was used to select samples from homogeneous intervals suitable for calibrating permeability through the Timur-Coates equation. Based on the index, 315 samples were kept in the model, and 99 were considered unsuitable. The R2 coefficient between selected core samples and log porosities increased by 28% compared to the correlation with all samples. Likewise, the permeability R2 increased by 14% after removing unrepresentative samples from heterogeneous intervals. The standard deviation equation per volume in these regions indicated that representative models could only be created with whole core samples. The present work demonstrated the importance of quantitatively estimating the formation’s heterogeneity through image logs.