A Machine Learning Approach to Predict the Permeability from NMR T2 Relaxation Time Distribution for Various Reservoir Rock Types
Authors: Mohamed Emad , Elsayed Mahmoud , Hassan Amjed , Mahmoud Mohamed , El-Husseiny Ammar 
Published: October 2022

Abstract
Nuclear Magnetic Resonance (NMR) is a powerful tool used to measure the fundamental petrophysical properties such as porosity, permeability, pore size distribution, saturation, and wettability. T2 relaxation time is the NMR industry-standard measurement because it is fast and provides valuable information. For single-phase, saturated core plugs, the T2 relaxation time distribution reflects the pore size distribution which can provide insights into the permeability and rock types. Here, several machine learning (ML) models were employed in NMR T2 relaxation data to predict permeability.
Extensive laboratory measurements were performed to collect enough datasets to train machine learning models for different permeability and rock types. Several rock types such as sandstone (clean, and shaly), and carbonates (limestone, dolomite, and chalk) were used in this study, including outcrop and reservoir rocks. Furthermore, the core plugs cover a wide range of porosity and permeability to investigate their effect on the T2 relaxation time distribution for each rock type. The measurements were carried out utilizing a machine operating at Larmor frequency ∼ 2 MHz (i.e. same as the wireline logging tools). In addition to the T2 relaxation time measurements, gas porosity and permeability experiments were performed in all samples as conventional methods to validate the outputs. ML techniques include five different types of Artificial Neural Networks (ANN) such as feed-forward backpropagation (FFNN), cascade-forward (CFNN), Elman (ELMNN), pattern recognition (PRNN), and distributed delay (DISTDNN) were applied. Several input parameters were selected to train ML models such as T2 logarithmic mean (T2LM), T2 peak (T2p), T2 components range (T2R), and T2 components range index (T2RI). The results showed that the Elman-type neural network with the Bayesian regularization back-propagation technique could predict the permeability as a function of the inputs, as mentioned above. The developed model also proved to work better than the previous neural network models used in literature, regression models, and empirical correlations such as SDR and Timur-Coates models. Correlation coefficient (CC) and Coefficient of determination (R2) were used to measure the accuracy of the model and to benchmark versus other models.
The dataset which included 186 cores was divided into 80% for training and 20% for validation. Elman network model was used, and the developed model compared well with the permeability measured from the conventional methods. Specifically, the model predicted permeability with more than 0.91 CC and 0.88 R2. In this study, we built an automated and flexible machine learning code that predicts the permeability with high accuracy from T2 relaxation time measurements. The novel approach of this work emanates from that it can be used globally because it considers several T2 fundamental parameters used for the first time.