Petrophysical parameters prediction and uncertainty analysis in tight sandstone reservoirs using Bayesian inversion method

Petrophysical parameters are of great importance in the evaluation and characterization for reservoirs, especially for the unconventional reservoirs with complex properties. The geophysical inversion is an efficient and economic method to obtain the petrophysical parameters. In this paper, Bayesian inversion method is presented to predict petrophysical model with conventional well logs. Statistical analysis results of accepted Markov chain Monte Carlo (MCMC) samples are used to study the uncertainty of forecasted parameters, since the MCMC is a powerful approach to obtain adequate samples obeying the posterior distribution of Bayesian inversion. The proposed method is applied to reservoirs of the Xiashihezi Formation which are typical tight sandstone layers in the Ordos Basin. Model prediction and corresponding uncertainty analysis are presented in detail at a specific depth. The interactive effects of multiple petrophysical parameters are investigated by correlation coefficients. Then, the accuracy and reliability of predicted model is validated by both forward log responses and core data of the whole depth interval. According to the results and discussions, it can be concluded that: (1) a reasonable prior information of model parameters will simplify the inversion problem, which provides much conveniences of statistical analysis of the MCMC samples; (2) the weak correlation between each two petrophysical parameters indicates that it is reasonable and feasible to disregard dependence of parameters; (3) synthetic logs calculated by predicted model are in good agreement with observed well logs, which implies the precision and credibility of Bayesian inversion; (4) the predicted porosity, permeability and minerals content are consistent with core data, verifying the effectiveness and reliability of proposed method and inversion results; (5) it is an advantage of Bayesian inversion to locate the most probable reservoirs with the extreme value.