Machine learning accelerated approach to infer nuclear magnetic resonance porosity for a middle eastern carbonate reservoir

Abstract

Carbonate rocks present a complicated pore system owing to the existence of intra-particle and interparticle porosities. Therefore, characterization of carbonate rocks using petrophysical data is a challenging task. Conventional neutron, sonic, and neutron-density porosities are proven to be less accurate as compared to the NMR porosity. This study aims to predict the NMR porosity by implementing three different machine learning (ML) algorithms using conventional well logs including neutron-porosity, sonic, resistivity, gamma ray, and photoelectric factor. Data, comprising 3500 data points, was acquired from a vast carbonate petroleum reservoir in the Middle East. The input parameters were selected based on their relative importance with respect to output parameter. Three ML techniques such as adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), and functional network (FN) were implemented for the development of prediction models. The model’s accuracy was evaluated by correlation coefficient (R), root mean square error (RMSE), and average absolute percentage error (AAPE). The results demonstrated that all three prediction models are reliable and consistent exhibiting low errors and high ‘R’ values for both training and testing prediction when related to actual dataset. However, the performance of ANN model was better as compared to other two studied ML techniques based on minimum AAPE and RMSE errors (5.12 and 0.39) and highest R (0.95) for testing and validation outcome. The AAPE and RMSE for the testing and validation results were found to be 5.38 and 0.41 for ANFIS and 6.06 and 0.48 for FN model, respectively. The ANFIS and FN models exhibited ‘R’ 0.937 and 0.942, for testing and validation dataset, respectively. Based on testing and validation results, ANFIS and FN models have been ranked second and third after ANN. Further, optimized ANN and FN models were used to extract explicit correlations to compute the NMR porosity. Hence, this study reveals the successful applications of ML techniques for the accurate prediction of NMR porosity.

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“…ANFIS used fuzzy logic theory to formulate the mapping of the input and output layers. Neural networks are used to regulate the mapping parameters by leaning functions . A fuzzy set A in X which is referred to as the universe of discourse is defined as a set of ordered pairs: A = false{ ( x , μ A false( x false) ) | x ∈ X false} where μ A ( x ) is called membership function (MF) for the fuzzy set A which ranges between 0 and 1. .25ex2ex R j : if .25em x 1 .25em is .25em A j 1 .25em and .25em x 2 .25em is .25em A j 2 .25em and .25em x n .25em is .25em A j n .25em then y = f j ( x 1 , x 2 , ... , x n ) = f j ( X ) , .25em j = 1 , 2 , ... , N where R j is the rule label; A ji is the antecedent fuzzy set; y = f j ( X ) is a crisp function whic...…”

“…where 40 A fuzzy set A in X which is referred to as the universe of discourse is defined as a set of ordered pairs:…”

“…Neural networks are used to regulate the mapping parameters by leaning functions. 40 A fuzzy set A in X which is referred to as the universe of discourse is defined as a set of ordered pairs: where μ A ( x ) is called membership function (MF) for the fuzzy set A which ranges between 0 and 1. where R j is the rule label; A ji is the antecedent fuzzy set; y = f j ( X ) is a crisp function which is usually a polynomial function of input variables; and N is the total number of fuzzy if–then rules.…”

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