Wavelet Neural Network: A Hybrid Method in Modeling Heterogeneous Reservoirs

Abstract

Static modeling of heterogeneous reservoirs remains as an important challenge in petroleum engineering applications which requires more investigations. Ordinary Kriging (OK), sequential Gaussian simulation (SGS) or multilayer perceptron neural network (MLP) are the common methods which are utilized in modeling different type of reservoirs. However, it is well known that these methods are inapplicable for heterogeneous reservoirs. In this paper, wavelet neural network (WNN) is introduced for modeling heterogeneous reservoirs. In order to investigate the applicability of WNN, two exemplar heterogeneous reservoirs were generated. The first model, represents a heterogeneous reservoir being divided into three homogeneous subzones. The second model simulates a heterogeneous reservoir composed of randomly distributed data with wide range of variability. The applicability of methods for porosity modeling in a heterogeneous carbonated reservoir in south-west of Iran has also investigated. The OK, MLP and WNN methods were applied to model both synthetic reservoirs. The results showed that in the second model, all three methods presented biased solutions. However, in the case of first model, the MLP resulted in biased solution, whereas the OK and WNN models presented unbiased and acceptable solutions. The results also showed that the WNN was more accurate with lower range of error in comparison to the OK. In addition, it was noted that the CPU time of the WNN was approximately 15% of the CPU time of the OK, and 5% of the CPU time of the MLP. In the case of the real reservoir, all three methods resulted in unbiased solutions, because heterogeneity was less than both synthetic data. By the way, the error for WNN was less than OK and MLP, meanwhile, WNN resulted in a lower range of error in comparison to other methods. However, similar to synthetic data, the CPU time of WNN was approximately 20% of the CPU time of OK, and 7% of CPU time of the MLP. Considering the complexity associated with up-scaling in heterogeneous reservoirs and the difficulty of history matching in large blocks which introduces large uncertainty, the results of this study suggests that the WNN, with faster running time, can handle more blocks (finer grids) and offer advantages in modelling heterogeneous reservoirs.