Risk-mitigation strategies are most effective when the major sources of uncertainty are determined through dedicated and in-depth studies. In the context of reservoir characterization and modeling, petrophysical uncertainty plays a significant role in the risk assessment phase, for instance in the computation of volumetrics. The conventional workflow for the propagation of the petrophysical uncertainty consists of physics-based model embedded into a Monte Carlo (MC) template. In detail, open-hole logs and their inherent uncertainties are used to estimate the important petrophysical properties (e.g. shale volume, porosity, water saturation) with uncertainty through the mechanistic model and MC simulations. In turn, model parameter uncertainties can be also considered. This standard approach can be highly time-consuming in case the physics-based model is complex, unknown, difficult to reproduce (e.g. old/legacy wells) and/or the number of wells to be processed is very high. In this respect, the aim of this paper is to show how a data-driven methodology can be used to propagate the petrophysical uncertainty in a fast and efficient way, speeding-up the complete process but still remaining consistent with the main outcomes. In detail, a fit-for-purpose Random Forest (RF) algorithm learns through experience how log measurements are related to the important petrophysical parameters. Then, a MC framework is used to infer the petrophysical uncertainty starting from the uncertainty of the input logs, still with the RF model as a driver. The complete methodology, first validated with ad-hoc synthetic case studies, has been then applied to two real cases, where the petrophysical uncertainty has been required for reservoir modeling purposes. The first one includes legacy wells intercepting a very complex lithological environment. The second case comprises a sandstone reservoir with a very high number of wells, instead. For both scenarios, the standard approach would have taken too long (several months) to be completed, with no possibility to integrate the results into the reservoir models in time. Hence, for each well the RF regressor has been trained and tested on the whole dataset available, obtaining a valid data-driven analytics model for formation evaluation. Next, 1000 scenarios of input logs have been generated via MC simulations using multivariate normal distributions. Finally, the RF regressor predicts the associated 1000 petrophysical characterization scenarios. As final outcomes of the workflow, ad-hoc statistics (e.g. P10, P50, P90 quantiles) have been used to wrap up the main findings. The complete data-driven approach took few days for both scenarios with a critical impact on the subsequent reservoir modeling activities. This study opens the possibility to quickly process a high number of wells and, in particular, it can be also used to effectively propagate the petrophysical uncertainty to legacy well data for which conventional approaches are not an option, in terms of time-efficiency.
A mechanistic model for airborne and direct human-to-human transmission of COVID-19: effect of mitigation strategies and immigration of infectious persons
