Prediction of porosity in a carbonate reservoir using hybrid simulated annealing algorithm with artificial neural network -A case study

1-Introduction
In wells with limited log and core data, porosity, a fundamental and essential property to characterize reservoirs, is challenging to estimate by conventional statistical methods from offset well log and core data in heterogeneous formations. True measurement of this parameter, carried out by laboratory measurements, is very expensive. Therefore, many researchers have attempted to find rapid and accurate alternative ways to predict this parameter (Bhatt and Helle 2002, Rezaee, Jafari et al. 2006, Hamada and Elshafei 2009, Al-Anazi and Gates 2010, Bjørlykke and Jahren 2012, Wang, Wang et al. 2013, Zerrouki, Aifa et al. 2014). Intelligent methods such as artificial neural networks (ANN) and swarm intelligence (SI) are robust tools for estimation of this parameter. Review of the literature shows that many intelligent methods for prediction of porosity have been suggested by the past researchers. In the research documented here, ANN optimized by simulated annealing algorithm (SAA), is investigated for its capability to predict porosity from log data.
 
2-Methodology
Reservoir characterization involves describing different reservoir properties quantitatively using various techniques in spatial variability. Nevertheless, the entire reservoir cannot be examined directly and there still exist uncertainties associated with the nature of geological data. Such uncertainties can lead to errors in the estimation of the ultimate recoverable oil. To cope with uncertainties, intelligent mathematical techniques to predict the spatial distribution of reservoir properties appear as strong tools. The goal here is to construct a reservoir model with lower uncertainties and realistic assumptions. Porosity is a petrophysical property that relates the amount of fluids in place and their potential for displacement. This fundamental property is a key factor in selecting proper enhanced oil recovery schemes and reservoir management. In this paper, the application of soft computing methods for data analysis called ANN optimized by SAA to estimate porosity is demonstrated. The simulated annealing algorithm was used for initial weighting of the parameters in the artificial neural network. The developed methodology was examined using real field data (Marun reservoir, Iran).
 
3-Results and Discussion
In this paper, hybrid ANN was SAA utilized to build a prediction model for the estimation of the porosity from available data, using MATLAB environment. A dataset that includes 1356 data points was employed in current study, while 1085 data points (80%) were utilized for constructing the model and the remainder data points were utilized for assessment of degree of accuracy and robustness. The training and testing procedures of ANN-SAA model were conducted from scratch for the mentioned five datasets. The obtained mean squared error (MSE), root mean squared error (RMSE) and correlation coefficient (R) values for training datasets indicate the capability of learning the structure of data samples, whereas the results of testing dataset reveal the generalization potential and the robustness of the system modeling method. The correlations between measured and predicted values of porosity for training and testing phases are shown in Figs. 1 and 2. Also, a comparison between predicted values of porosity and measured values for data sets at training and testing phases is shown in Figs. 3 and 4.
 
Figure 1. Correlation between measured and predicted values of porosity for training data
 
Figure 2. Correlation between measured and predicted values of porosity for testing data
 
Figure 3. Comparison between measured and predicted values of porosity for training data
 
Figure 4. Comparison between measured and predicted values of porosity for testing data
 
As shown in Figs. 3 and 4, the results of the ANN optimized by SAA model in comparison with actual data show a good precision of the ANN optimized by SAA model.
 
4-Conclusions
A quantitative formulation between conventional well logs (available in all wells) and porosity eliminates the aforementioned problems and makes it possible to perform geophysical and geomechanical studies. Due to significance of calling for porosity knowledge, several researchers attempted to determine porosity through empirical correlations and/or traditional intelligent systems. Nonetheless, the quest for highest precision possible demands looking for high accuracy methods. In this study, hybrid ANN with SAA was employed in order to respond this demand. ANN-SAA model was used to formulate conventional well log data. The results indicated ANN optimized by SAA performed acceptably and it was capable of mining hidden knowledge about porosity from conventional well logs.