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Introduction

Predicting and extrapolating the permeability between wells to obtain the 3D distribution for the geological model, is a crucial and challenging task in reservoir simulation. Permeability is influenced by both digenetic characteristics and depositional factors like sorting and grain size. Hence, a reliable model should consider these characteristics for prediction of permeability. Although there are different research works in the literature on application of different approaches for prediction of permeability, but few papers are available on prediction of permeability in tight carbonate gas condensate reservoirs, which are among the most challenging reservoirs to develop in the world. Since developing new methodologies to accurately predict permeability is important, further analysis and examination of machine learning and regression methods to find reliable, fast and accurate models are of great importance. 

Grouping the rocks into different hydraulic flow units (HFU) or discrete rock types (DRT), improves the identity of the reservoir characteristics and provide a more accurate permeability prediction. Multi variable regression models and Artificial Neural Networks (ANN) were applied in this study to correlate core permeability and porosity with well logs to predict permeability logs. It was observed that the accuracy of the models diminished when dealing with heterogeneous reservoirs, where there is a wide range of permeability distribution.

 In this study, we are presenting a novel approach based on the artificial neural networks (ANN) to predict permeability in heterogeneous oil and gas reservoirs using the petrophysical log data and FZI from core data. In this method the core permeability and porosity data are categorized using the concept of DRT and the probability density functions are used to investigate the relationships between the logs and DRT groups. The ANN model is applied to correlate the core derived flow zone indicator (FZI) with wire-line logging data with a single key well to predict K-logs. Contrary to the existing ANN models, the novel approach presented in this paper applies one single well, which contains all DRT groups to develop and train the ANN model. It was observed that ANN model exhibits better prediction performance in heterogeneous reservoirs when it is developed and trained on single well data containing all DRT groups.  This approach can capture heterogeneity in the reservoirs where it has been applied successfully to predict permeability in an actual heterogeneous carbonate gas reservoir. 

Summary

The X field is a natural gas field, which covers an area of 3700 square kilometers. The field consists of four main gas bearing reservoirs, namely L1, L2, L3 and L4 with similar rock properties. The wide range of permeability distribution of this field indicates that the understudy gas field is very heterogeneous and for an accurate permeability prediction, clustering the core data into appropriate DRT groups is essential. The core data of eighteen wells were used in this study for rock typing based on the FZI approach (Amaefule et al. (1993)). The calculated FZI is then used to group the rocks into discrete rock types (DRTs). By applying the FZI rock typing approach ten different rock types were identified in the X gas field. In this study we are aiming to correlate FZI from core data with wire-line logging data. The probability density function (PDF) was used in order to investigate the relationships between the log responses and DRT groups. Based on the results of probability density function analysis that we conducted, five logs were selected to develop the polynomial regression and ANN models, namely effective porosity (PHIE), effective water saturation (SWE), bulk density (RHOB), calcite volume (VCALC) and dolomite volume (VDOL) logs. The polynomial regression model was utilized for correlating the core derived FZI with the log responses to predict the FZI values for the uncored but logged intervals of the wells. The predicted FZI-logs are then converted to K-logs. The results showed that no good match is achieved and the regression model is unable to match most points of very low and high permeabilities.  The second approach in this study used artificial neural networks (ANN) to predict K-logs. ANN are one of the main tools used in machine learning. These methods have been used widely in the petroleum industry (Anemangely et al. (2019), Rashidi et al. (2021) and Matinkia et al. (2022). In this study, one-hidden layer feed forward ANN model was trained with 17 hidden neurons. The number of hidden layers and neurons were determined based on a trial and error approach. The mathematical models were created using MATLAB 8.4 (R2014b) programming language. Having trained the ANN model, it was used to predict the FZI-logs in the cored intervals of the test wells to quality control the trained model. The predicted FZI-logs were then converted to K-logs. It was observed that better results have been achieved by ANN model, but like regression model, it is also unable to capture the heterogeneity in the field. In the fields, where permeability has a wide range of distribution and multiple DRT groups (rock types) are available, ANN models are unable to capture heterogeneity. In this study, we are presenting a novel approach to predict permeability in the heterogeneous reservoirs. In this method the core permeability and porosity data are categorized using the concept of discrete rock types (DRT). The ANN method is then applied to correlate the core derived flow zone indicator (FZI) with wire-line logging data to predict permeability.

Opposite to the existing ANN models, the new approach presented in this paper applies one single well, which contains all DRT groups (rock types) to develop and train the ANN model.  It was observed that ANN model exhibits better prediction performance in the heterogeneous reservoirs when it is trained on the data of a single key well containing all DRT groups. This approach enables the ANN models to capture heterogeneity in the heterogeneous oil and gas reservoirs. In order to check the prediction performance and accuracy of the developed ANN model, it was used to predict K-logs in the cored intervals of the blind-test wells, and was observed that good matches were achieved for all these wells.

Conclusions

1. Empirical equations, regression models and machine learning methods have been used by different researchers to date, to predict permeability in oil and gas reservoirs. However, it was observed that their accuracy diminished in heterogeneous reservoirs.
2. In this study the polynomial regression models and artificial neural networks were used to correlate the core derived FZI with wire-line logging data to predict K-logs. It was observed that both models were unable to predict permeability satisfactorily in heterogeneous reservoirs, where there was a wide range of permeability distribution.
3. A novel approach is presented in this paper to predict permeability in heterogeneous oil and gas reservoirs. This methodology is applying ANN models to correlate the core derived FZI with well logs to predict permeability in the uncored but logged intervals of the wells. This approach is applicable in reservoirs, which are subdivided into different hydraulic flow units or discrete rock types.  In this approach, opposite to the existing ANN models, one single well, which contains all DRT groups is considered as a key well to develop the ANN model.
4. It was observed that ANN model exhibits better prediction performance in heterogeneous reservoirs when it is developed and trained on single well data containing all DRT groups. This data reduction strategy, which is the novelty of this paper, enables the ANN models to capture the heterogeneity in heterogeneous oil and gas reservoirs. 

References

• Amaefule, J.O., Altunbay, M., Tiab, D., Kersey, D.G. and Keelan, D.K., 1993. Enhanced reservoir description: using core and log data to identify hydraulic (flow) units and predict permeability in uncored intervals/wells, SPE annual technical conference and exhibition. Society of Petroleum Engineers, Houston, Texas.
• Anemangely, M., Ramezanzadeh, A., Amiri, H. and Hoseinpour, S. A., 2019. Machine learning technique for the prediction of shear wave velocity using petrophysical logs. Journal of Petroleum Science and Engineering, 174: 306-327.
• Matinkia, M., Amraeiniya, A., Behboud, M. M., Mehrad, M., Bajolvand, M., Gandomgoun, M. H. and Gandomgoun, M., 2022. A novel approach to pore pressure modeling based on conventional well logs using convolutional neural network. Journal of Petroleum Science and Engineering: 110156.
• Rashidi, S., Mehrad, M., Ghorbani, H., Wood, D. A., Mohamadian, N., Moghadasi, J. and Davoodi, S., 2021. Determination of bubble point pressure & oil formation volume factor of crude oils applying multiple hidden layers extreme learning machine algorithms. Journal of Petroleum Science and Engineering, 202: 108425.