* Corresponding author. E-mail address: tokhmechi@ut.ac.ir (B. Tokhmechi). Journal Homepage: ijmge.ut.ac.ir Estimation of heterogeneous reservoir parameters using Wavelet neural network: A comparative study Behzad Tokhmechi a, * , Jalal Nasiri a , Haleh Azizi b , Minou Rabiei b , Vamegh Rasouli b a Faculty of Mining, Petroleum and Geophysics Engineering, Shahrood University of Technology, Shahrood, Iran b Department of Petroleum Engineering, University of North Dakota, United States A B S T R A C T Static modeling of heterogeneous reservoirs remains an important challenge in petroleum engineering that requires more attentions. Ordinary Kriging (OK), sequential Gaussian simulation (SGS) or Multilayer Perceptron Neural Network (MLP) are the common methods that are utilized in modeling different type of reservoirs. However, it is well known that these methods are impractical on heterogeneous reservoirs. In this paper, Wavelet Neural Network (WNN) is introduced for modeling the heterogeneous reservoirs. In order to investigate the applicability of the 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 a wide range of variability. The applicability of such methods for porosity modeling in a heterogeneous carbonated reservoir in south- west of Iran has been 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 a lower range of error compared to the OK. In addition, it was noted that the CPU time of the WNN was approximately 15% of that 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 that of both synthetic datasets. Moreover, the error of the WNN was less than that of the OK and MLP approaches, meanwhile, the WNN resulted in a lower range of error compared to the other methods. However, same as the synthetic data, the CPU time of the WNN was approximately 20% of the CPU time of the OK, and 7% of the CPU time of the MLP. Considering the complexity associated to up-scaling the heterogeneous reservoirs and the difficulty of history matching in large blocks, which introduces large uncertainty as well, the results of this study suggests that the WNN, with a faster running time, can handle more blocks (finer grids) and offer advantages in modeling heterogeneous reservoirs. Keywords : Heterogeneous Reservoirs, Wavelet Neural Network, Upscaling, CPU processing time, Uncertainty, Asmari 1. Introduction Various modeling methods have been used in reservoir characterization in the literature. Geostatistical [1, 2], intelligent [3, 4, 5], fractal [6, 7, 8], and hybrid-based modeling methods [9, 10], are some examples of many available methods. Researchers have discussed the shortcomings of some of the widely used methods when used in the simulation of heterogeneous reservoirs [11, 12]. The past studies show that the followings are the two critical factors in developing a robust estimator for modeling heterogeneous reservoirs:  Localization property: Estimators with localization properties are less influenced by heterogeneity, as they use the neighboring data for the estimation. However, those estimators that use the whole dataset on a global basis, are not able to integrate the local variabilities into the model, therefore, in heterogeneous media, the details at local scales are discarded. This suggests that in heterogeneous media, it is advisable to use the estimators that have localization properties.  CPU time: This is an important parameter to generalize the applications of an estimator to the situation where the media is composed of large datasets. The CPU time is important because the static models should be coarse to yield reliable processing time during the history matching. In heterogeneous reservoirs, a large portion of the data variance is reduced due to the coarse block sizes used in the modeling. Although this suggests using finer size models, it introduces long processing times. Therefore, if a model offers a shorter processing time, it would be the preferred method for static modeling. The results of this work indicate that the wavelet neural network (WNN) requires less CPU time than the ordinary kriging (OK) and multilayer perceptron neural network (MLP) methods. The literature suggests that the geostatistical estimators/simulators yield more reasonable results in heterogeneous reservoirs than other methods [11]. The use of hybrid methods with their localization property lend some promises but they suffer from long CPU times to process the data [13]. In fractal-based simulators, the idea of the cost function is to keep the fractal dimension of the data constant to ensure that the original variability of the data is maintained [14].Compared to other modeling methods, these fine-based simulators properly show the data variability of heterogeneous media. In specific, the geostatistical-based models with their cost function being based on minimizing the error, smoothen the data variability. However, the long CPU time, lack of control over the Article History: Received: 03 June 2018, Revised: 26 August 2018 Accepted: 27 September 2018.