Geostatistical data integration in complex reservoirs

One of the most challenging issues in reservoir modeling is to integrate information coming from different sources at disparate scales and precision. The primary data are borehole measurements, but in most cases, these are too sparse to construct accurate reservoir models. Therefore, in most cases, the information from borehole measurements has to be supplemented with other secondary data. The secondary data for reservoir modeling could be static data such as seismic data or dynamic data such as production history, well test data or time-lapse seismic data. Several algorithms for integrating different types of data have been developed. A novel method for data integration based on the permanence of ratio hypothesis was proposed by Journel in 2002. The premise of the permanence of ratio hypothesis is to assess the information from each data source separately and then merge the information accounting for the redundancy between the information sources. The redundancy between the information from different sources is accounted for using parameters (tau or nu parameters, Krishnan, 2004). The primary goal of this thesis is to derive a practical expression for the tau parameters and demonstrate the procedure for calibrating these parameters using the available data. This thesis presents two new algorithms for data integration in reservoir modeling. The algorithms proposed in this thesis overcome some of the limitations of the current methods for data integration. We present an extension to the direct sampling based multiple-point statistics method. We present a methodology for integrating secondary soft data in that framwork. The algorithm is based on direct pattern search through an ensemble of realizations. We show that the proposed methodology is sutiable for modeling complex channelized reservoirs and reduces the uncertainty associated with production performance due to integration of secondary data. We subsequently present the permanence of ratio hypothesis for data integration in great detail. We present analytical equations for calculating the redundancy factor for discrete or continuous variable modeling. Then, we show how this factor can be infered using available data for different scenarios. We implement the method to model a carbonate reservoir in the Gulf of Mexico. We show that the method has a better performance than when primary hard and secondary soft data are used within the traditional geostatistical framework.