Functional Networks as a Novel Approach for Prediction of Permeability in a Carbonate Reservoir

Permeability is one of the most difficult properties to predict, especially in carbonate reservoirs. Permeability prediction is a challenge to reservoir engineers due to the lack of tools that measure them directly. The most reliable data of permeability, obtained from laboratory measurements on cores, do not provide a continuous profile along the depth of the formation. This paper presents functional networks as a novel approach for forecasting permeability using Well Logs in a Middle Eastern Carbonate reservoir. Unlike the standard artificial neural network, functional network is a problem driven, in these networks there are no weights associated with the links connecting neurons, and it uses unknown neuron functions, that are learned from given families of linearly independent functions during the training process. Appropriate families can be chosen for each specific problem, such as, polynomials, Fourier, exponential, and trigonometric functions. This new computational intelligence scheme will overcome the weakness of the common softcomputing techniques, such as, neural networks and decision trees limitations. Two types of functional network models, separable and associativity functional networks are used to predict the permeability. Functional networks permeability model is chosen based on the minimum description length criterion, which takes care of both overfitting and complexity problems. A comparative study is carried out to compare their performance with those of statistical techniques and conventional neural network models. Preliminary results show that the new framework is flexible, more accurate, and comparable in performance to those of artificial neural networks and statistical techniques. Results were obtained with only the simplest structures of functional networks. It is possible to use more complex non-linear forms that lead to better accuracy, efficient results, and outperform the most common statistics, data mining techniques.