The Dynamic Character of Porosity by Nuclear Magnetic Resonance and Production Logging for a Comprehensive Permeability Prediction in Carbonate Reservoirs

Permeability estimation in carbonate reservoirs is challenging and it generally consists of core-calibrated algorithms applied on open-hole logs. Moreover, due to inherent multi-scale heterogeneities, apparent permeability from production logging tool (PLT) is usually necessary to let the static log-based prediction honor dynamic data. The correspondence between dynamic corrections and carbonate rock types is a long-standing problem and an elegant solution is presented by integrating advanced nuclear magnetic resonance (NMR) log modeling with multi-rate PLT interpretation. The methodology, discussed on an oil-bearing carbonate reservoir, starts with a rigorous mapping between NMR responses and pore-size distribution, mainly determined by special core analyses (SCAL). Hence, a robust porosity partition template and a physically-based permeability formula are established downhole relying on the quantitative integration of SCAL and advanced NMR modeling. Multi-rate PLT and well test data are then analyzed to evaluate the boost needed for log permeability to match the dynamic behavior of the wells. Finally, porosity partition outcomes are used as pointwise predictors of dynamic permeability enhancement by means of a probabilistic approach. In details, a system built upon mercury injection capillary pressure measurements, representative of the entire reservoir, shows a well-defined pore structure consisting of micropores, mesopores and macropores. At the same time, a quantitative link is established between NMR transverse relaxation time and pore-size distributions through an effective surface relaxivity parameter, both at laboratory and reservoir conditions. This allows discriminating micro, meso and macro-porosity downhole. Effective surface relaxivity also plays a critical role in the subsequent NMR permeability estimation based on a capillary tube model of the porous media and exploiting the full NMR/pore-size distributions. Although the match with core data proves the reliability of the comprehensive rock characterization, log permeability values underestimate the actual dynamic performances from well test. Therefore, the standard apparent permeability method from multi-rate PLT interpretation provides the necessary correction from the dynamic standpoint. Macro-porosity content is demonstrated to be the driver for a quantitative estimation of the excess in matrix permeability and an additional term complements the original NMR permeability predictor in order to honor the dynamic evidences. The approach makes use of a probabilistic framework aimed at considering the uncertainties in the a-priori simultaneous static and dynamic characterization. The presented innovative methodology addresses the well-known issue of quantitatively incorporating dynamic log modeling into a purely static workflow, thus leading to a more accurate permeability estimation. This is fundamental for production optimization and reservoir modeling purposes in highly heterogeneous carbonate environments.