Investigations on the relationship among the porosity, permeability and pore throat size of transition zone samples in carbonate reservoirs using multiple regression analysis, artificial neural network and adaptive neuro-fuzzy interface system

Finding an accurate method for estimating permeability aside from well logs has been a difficult task for many years. The most commonly used methods targeted towards regression technique to understand the correlation between pore throat radii, porosity and permeability are Winland and Pittman equation approaches. While these methods are very common among petrophysicists, they do not give a good prediction in certain cases. Consequently, this paper investigates the relationship among porosity, permeability, and pore throat radii using three methods such as multiple regression analysis, artificial neural network (ANN), and adaptive neuro-fuzzy inference system (ANFIS) for application in transition zone permeability modeling. Firstly, a comprehensive mercury injection capillary pressure (MICP) test was conducted using 228 transition zone carbonate core samples from a field located in the Middle-East region. Multiple regression analysis was later performed to estimate the permeability using pore throat and porosity measurement. For the ANN, a two-layer feed-forward neural network with sigmoid hidden neurons and a linear output neuron was used. The technique involves training, validation, and testing of input/output data. However, for the ANFIS method, a hybrid optimization consisting of least-square and backpropagation gradient descent methods with a subtractive clustering technique was used. The ANFIS combines both the artificial neural network and fuzzy logic inference system (FIS) for the training, validation, and testing of input/output data. The results show that the best correlation for the multiple regression technique is achieved for pore throat radii with 35% mercury saturation (R35). However, for both the ANN and ANFIS techniques, pore throat radii with 55% mercury saturation (R55) gives the best result. Both the ANN and ANFIS are later found to be more effective and efficient and thus recommended as compared with the multiple regression technique commonly used in the industry.