Reservoir permeability is one of the most important properties of oil and gas fields for reservoir characterization. In un-cored intervals or wells, reservoir description and evaluation methods using well log data represent a significant technical as well as economic advantage because well logs can provide a continuous record over the entire well where coring is impossible. Permeability determination from well logs in heterogeneous formation has a difficult and complex problem to solve by conventional statistical methods. Recently artificial neural networks (ANNs) have been successfully used to solve many of complex problems in reservoir permeability estimation. However, the applications of the neural network to mapping complex nonlinear relationship have revealed a number of unsolved technical limitations despite of the high versatility. This paper proposes a group method of data handling (GMDH) based on polynomial neural network (PNN) for permeability prediction from well logs to alleviate limitations of the conventional neural network approach. The PNN evolutionally synthesizes network size, connectivity, processing element types, and coefficients for globally optimized structure through training. This self-organizing approach automatically presents internal relationships among data in the polynomial forms, and enhances data approximation and explanation capabilities of resulting data-based learning models. This technique is demonstrated with an application to the well data in offshore Korea. The comparative study with conventional neural networks reveals that the proposed model gives a relatively positive performance although the prediction accuracy of the PNN model is affected by errors in measurement data. The PNN is a practical and powerful tool for predicting reservoir permeability of a heterogeneous formation utilizing well logs.
Introduction
Reservoir permeability is a fundamental rock property which relate to its ability to flow when subjected to applied pressure gradients. This property has a significant impact on petroleum fields operations and reservoir management. In un-cored intervals and well, the reservoir description and characterization methods utilizing well logs represent a significant technical as well as economic advantage because well logs can provide a continuous record over the entire well1.
Permeability estimation from conventional well logs in heterogeneous formation has a difficult and complex problem to solve by statistical methods. The parametric methods like statistical regression require the assumption for the satisfaction of multi-normal behavior and linearity. Therefore, an artificial neural network (ANN) as a non-linear and non-parametric tool is becoming increasingly popular in well log analysis2,3. ANN is a computer model that attempts to mimic simple biological learning processes and simulate specific functions of human nervous system. Recently ANN has been successfully utilized to reservoir permeability estimation using the transformation between well logs and core analysis data4.
However, neural network training with extensive data still remains to be time-consuming. The back-propagation algorithm with a gradient descent approach suffers from a local minimum problem, resulting in the production of unstable and non-convergent solutions. To overcome the limitation of the conventional ANN model, this paper proposes a hybrid method of polynomial network (PNN) and genetic algorithm (GA) as a new neural network approach to determine reservoir permeability from well logs.
Polynomial Neural Network (PNN)
Applications of ANN to mapping complex nonlinear relationship have shown a number of technical limitations despite of its high versatility5. One of the major limitations is the complexity of the design space. Determining network topology and design parameters is generally a trial-and error process with no theoretical a priori guideline. These approaches are sensitive to choice of the network architecture parameters including the size of hidden layers and the type of activation function for neurons in each layer. The learning algorithm parameters to be predetermined include initial weights, learning rate, momentum, and the number of training cycles. These considerable amounts of user interventions not only slow down the processing of the model but also have difficulty in exploring the optimal model.
