Application of Data-Mining Algorithms to Parameterize Static and Dynamic Models

Abstract Many field development plans leverage integrated reservoir studies (IRS) involving static modeling, dynamic modeling, and forecasts. Porosity and permeability fields are distributed in static models using probabilistic approaches such as sequential Gaussian simulation. The static model also requires petrophysical rock types (PRTs) and saturation-height function (SHF), which are parameters derived from mercury-injection-capillary-pressure (MICP) data. This study presents the application of data mining algorithms for deriving useful parameters to constrain static and dynamic models and to derive PRT and SHF from non-MICP sources. The paper presents the application of multivariate Gaussian regression for anomaly detection and filtering of core, log, and pressure data to rapidly eliminate outliers or incorrect values within a modeling dataset. We used a fixed window statistics algorithm to detect the intra-reservoir architecture (IRA) from the core permeability. The k-means clustering algorithm determined the PRT and SHF from core permeability and water saturation logs. Finally, a pattern recognition algorithm clustered the observed datum pressures into homogeneous groups and created a reservoir heterogeneity map to use as an input in the 3D permeability modeling. This study used data extracted from a hypothetical 3D model that distributes porosity and permeability using a sequential Gaussian simulation. The study defined the PRTs as functions of porosity and permeability using Winland's R35 equation and defined the SHFs for various PRTs to populate the water saturation in the hypothetical model. It assumed the hypothetical model as the truth model and subsequently defined several wells randomly in the truth model to obtain the porosity, permeability, water saturation, and PRT logs. This study obtained the observed datum pressures using a dynamic simulation of the truth model over a few years. We presented a new diagnostic plot that works with the traditional semi-log plot of porosity and permeability. This new diagnostic plots the semi-log of the global set of core permeability versus depth. We used the plot to obtain IRA by calculating the arithmetic mean permeability over every 1ft thickness and defining its boundaries of stationarity. The PRT and SHF derived from the k-means clustering were sufficiently similar to the truth model results. Anomaly filtering of the global pressure set helped detect data outliers that may have gone unnoticed. The data mining algorithms presented in this study could help obtain the PRT and SHF to complement Winland's interpretation when mercury injection capillary pressure (MICP) experiments are limited or unavailable, saving time and cost. Using IRA and reservoir heterogeneity maps in the static modeling process could produce a statistically and phenomenologically representative model, requiring limited history-matching intervention. To our knowledge, this is the first study to map the IRA of a reservoir using core data.