A Deep Autoregressive Model for Multiple Petrophysical Evaluations

Abstract Deterministic methods of petrophysical evaluation is made complicated by petrophysical and geological heterogeneity within the formation even though Petrophysical logs provide most of the subsurface data to an exploration geologist. Biases between the calculated values of different petrophysical properties namely, final-porosity, horizontal-permeability, shale-volume and water-saturation, results from the use of multiple empirical formulae, assumptions and correction factors. The existing deterministic petrophysical models evaluate each petrophysical properties separately and then use empirical values to account for dependence between different properties. These models have limited flexibility to account for the existing high-dimensional non-linear dependencies between these parameters. In this paper, we propose a fully probabilistic and autoregressive deep learning model, which calculates values of final-porosity, horizontal-permeability, shale-volume and water-saturation with high accuracy in one single model instead of multiple empirical formulae. In this model, each petrophysical property is conditioned on the cumulative outcomes of the previous ones, thus evaluating all of the aforementioned petrophysical properties together. Herein, we have used raw log data from Volve, a field on the Norwegian continental shelf, which has been collected at every 0.1 m across 18 different producing and non-producing wells. The Dataset consists of raw input and corresponding multiple outputs, calculated using existing empirical equations by noted geologists. The model architecture used in this study is similar to WaveNet and consists of stack of dilated causal convolutions along with gated activations, residual connections and skip connections. Validation set, used for hyperparameter tuning and selection of best model out of all possible models, contains the properties of the entire training set. Encoders and decoders used in our model do not share parameters, allowing them to handle accumulated noise while training. When evaluated using symmetric mean absolute percentage error (SMAPE), a single deep learning model performs at par with the expert geologists. Multiple petrophysical values are calculated and were found to be remarkably accurate. Performance of the single model remains consistent across Hugin and Sleipner formation. The proposed probabilistic model models high-dimensional dependencies. It represents the information available in raw input as well as multiple calculated petrophysical values. It makes no assumption about the complex physical system, making it robust to the existing uncertainties. Proposed deep-learning model can ease the burden of repetitive and quality controlled petrophysical evaluation.