Bayesian NMR petrophysical characterization

Identification of reservoir rock types is necessary for the exploration and recovery of oil and gas. It involves determining the petrophysical properties of rocks such as porosity and permeability which play a significant role in developing reservoir models, estimating the volumes of oil and gas reserves, and planning production methods. Nuclear magnetic resonance (NMR) technology is a fast and accurate tool for petrophysical rock characterization. The distributions of relaxation times ($T_2$ distributions) offer valuable insights into the distribution of pore sizes in rocks, and these distributions are closely linked to important petrophysical parameters like porosity, permeability, and bound fluid volume (BFV).

This work introduces a Bayesian estimation method for analyzing NMR data. The Bayesian approach uses prior knowledge of $T_2$ distributions in the form of the prior mean and covariance. The Bayesian approach combines prior knowledge with observed data to obtain improved estimation. We use the Bayesian estimation method where prior information regarding the rock sample type, for example shale, is available.

The estimators were evaluated on decay data simulated from synthesized distributions that replicate the features of experimental $T_2$ distributions of three types of reservoir rocks. We compared the performance of the Bayesian method with two existing methods using porosity, bound fluid volume (BFV) geometric mean (T2LM) and root mean square error (RMSE) of the estimated $T_2$ distribution as evaluation criteria. Additional experiments were carried out using experimental $T_2$ distributions to validate the results.

The performance of the Bayesian methods was also tested using mismatched priors.

The experimental results illustrate that the Bayesian estimator outperforms other estimators in estimating the $T_2$ distribution. The Bayesian method also outperforms the ILT method in estimating derived petrophysical properties except in cases where the noise level is below 0.1 and the $T_2$ distributions are associated with short relaxation times.