Deterministic and Stochastic Modeling in Prediction of Petrophysical Properties of an Albian Carbonate Reservoir in the Campos Basin (Southeastern Brazil)

Abstract

Abstract —Permeability is one of the most significant and challenging parameters to estimate when characterizing an oil reservoir. Several empirical methods with geophysical borehole logs have been employed to estimate it indirectly. They include the Timur model, which uses conventional logs, and the Timur–Coates model, which uses the nuclear magnetic resonance log. The first goal of this study was to evaluate porosity, because it directly impacts permeability estimates. Deterministic and stochastic inversions were then carried out, as the main objective of this work was to estimate the permeability in a carbonate reservoir of the Campos Basin, Southeastern Brazil. The ridge regression scheme was used to invert the Timur and Timur–Coates equations deterministically. The stochastic inversion was later solved using fuzzy logic as the forward problem, and the Monte Carlo method was utilized to assess uncertainty. The goodness of fit for the estimations was all checked with porosity and permeability laboratory data using the Pearson correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE), and Willmott’s agreement index (d). The results for the Timur model were R = 0.41; RMSE = 333.28; MAE = 95.56; and d = 0.55. These values were worse for the Timur–Coates model, with R = 0.39; RMSE = 355.28; MAE = 79.35; and d = 0.51. The Timur model with flow zones had R = 0.55; RMSE = 210.88; MAE = 116.66; and d = 0.84, which outperformed the other two models. The deterministic inversion showed, thus, little ability to adapt to the significant variations of the permeability values along the well, as can be seen from comparing these three approaches. However, the stochastic inversion using three bins had R = 0.35; RMSE = 320.27; MAE = 190.93; and d = 0.73, looking worse than the deterministic inversion. In the meantime, the stochastic inversion with six bins successfully adjusted the set of laboratory observations, because it provides R = 0.87; RMSE = 156.81; MAE = 74.60; and d = 0.92. This way, the last approach has proven it can produce a reliable solution with consistent parameters and an accurate permeability estimation.