Empirical, statistical, and connectionist methods coupled with log variables ranking for the prediction of pore network permeability in a heterogeneous oil reservoir

Abstract

Permeability is the most important petrophysical attribute for analyzing fluid flow behavior. So far, no universal approach can provide an accurate and reliable estimation of permeability for an entire hydrocarbon reservoir. The present study utilizes five empirical, three statistical, and three connectionist methods to estimate the permeability of a heterogeneous oil reservoir. The empirical models include ‘Tixier’, ‘Morris and Biggs’, ‘Timur’, ‘Coates and Dumanoir’, and ‘Coates and Denoo’. The statistical methods incorporate ‘multiple variable regression (MVR)’, ‘gaussian process regression (GPR)’, and ‘bagged tree (BT)’. The connectionist techniques are ‘support vector machine (SVM)’, ‘convolutional neural network (CNN)’, and ‘feed-forward backpropagation artificial neural network (ANN) with training algorithms Levenberg–Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG)’. Prediction efficiency of study methods are compared using six statistical indexes, such as regression coefficient, mean squared error, root mean squared error, average absolute error percentage, minimum absolute error percentage, and maximum absolute error percentage. Ranking of the log variables based on their importance in permeability modeling has been performed. To achieve the objectives, 439 data points comprising of laboratory derived core permeability information and seven well log parameters, namely gamma ray ($GR$), bulk density ($RHOB$), sonic travel time ($DT$), true resistivity ($LLD$), neutron porosity ($\varphi_{N}$), NMR porosity, and bulk volume of irreducible fluid are selected from a Jeanne d’Arc Basin’s reservoir. All these methods are tested on different data sets of study wells to confirm the reproducibility of the results. The results of the statistical indexes analysis imply that the empirical relationships are inappropriate for a heterogeneous reservoir as they provide a poor match with real data. However, the ‘Coates and Dumanoir’ model provides a relatively better match with core permeability among all five empirical approaches. The MVR is less efficient among statistical models, BT is reasonably efficient, and GPR is highly efficient. Amidst soft computing techniques, SVM, ANN with LM, and ANN with BR show very high efficiency, whereas ANN with SCG is moderately acceptable, and CNN provides extremely poor efficiency. A comprehensive comparison among all studied models shows that the best predictor is ANN with BR as it provides an excellent match between predicted and real data, and it requires only 14.9 s to process the data. Both statistical and connectionist methods imply that the $GR$ and $\varphi_{N}$ are the most vital log parameters in permeability modeling, whereas $DT$, $RHOB$, and $LLD$ are the least important predictor variables. The outcomes of this study will help engineers and researchers to apply an accurate permeability prediction tool in petroleum industries during the exploration phase to obtain accurate reservoir permeability data, correct analysis of fluid flow behavior, accurate reservoir characterization, and reduced uncertainty associated with a reservoir evaluation.

Article highlights

• Empirical models are incapable of predicting permeability accurately.

• SVM, ANN with LM, and ANN with BR are the most efficient predictive methods.

• An accurate and cost-effective permeability prediction strategy is achieved.