Adjoint-based History-Matching of Production and Time-lapse Seismic Data

Time-lapse (4D) seismic attributes can provide valuable information on the fluid flow within subsurface reservoirs. This spatially-rich source of information complements the poor areal information obtainable from production well data. While fusion of information from the two sources holds great promise, in practice, this task is far from trivial. Joint Inversion is complex for many reasons, including different time and spatial scales, the fact that the coupling mechanisms between the various parameters are often not well established, the localized nature of the required model updates, and the necessity to integrate multiple data. These concerns limit the applicability of many data-assimilation techniques. Adjoint-based methods are free of these drawbacks but their implementation generally requires extensive programming effort. In this study we present a workflow that exploits the adjoint functionality that modern simulators offer for production data to consistently assimilate inverted 4D seismic attributes without the need for re-programming of the adjoint code. Here we discuss a novel workflow which we applied to assimilate production data and 4D seismic data from a synthetic reservoir model, which acts as the real yet unknown reservoir. Synthetic production data and 4D seismic data were created from this model to study the performance of the adjoint-based method. The seamless structure of the workflow allowed rapid setup of the data assimilation process, while execution of the process was reduced significantly. The resulting reservoir model updates displayed a considerable improvement in matching the saturation distribution in the field. This work was carried out as part of a joint Shell-IBM research project. Introduction In history matching, production measurements are assimilated to obtain a dynamical reservoir model that is consistent with historical data; see e.g. Oliver et al (2008). However, production measurements – although generally of a high temporal resolution – provide only very localized spatial information about the subsurface around the wells, especially in the early production phase when wateror gas-breakthrough has not yet occurred in the producers. After breakthrough, somewhat more insight can be gained into the reservoir model parameters that influence the mismatch between measured and simulated data. At that time however the benefits of using a pro-active reservoir management strategy have often diminished considerably. Interpreted time-lapse (4D) seismic data can provide information on the areal distribution of pressure and saturation changes due to fluid production or injection. The seismic data are generally more noisy and uncertain than production data, but due to the field-wide distribution of the data, very valuable additional information on the subsurface can be gathered; see e.g. Calvert (2005). In production data assimilation, the quality of the updated model is usually evaluated with a cost function defined as the summed squared error between the observations (measurements) and simulated production data, sometimes weighted by a measure of the accuracy of the observations. Ensemble Kalman filter (EnKF) methods (Naevdal et al. (2005); Evensen (2009); Aanonsen et al. (2009)), streamline-based methods (Vasco et al. (1999); Wang and Kovscek (2000).) and adjoint-based methods (Chen et al. (1974), Chavent et al. (1975); Li et al. (2003); Rodrigues (2006); Oliver et al. (2008)) are the most common data-assimilation techniques reported in literature to deal with the history matching problem. All these methods update the reservoir model using the sensitivities of a least-squares cost function with respect to model parameters, but differ in the considered measurement types, model parameters and derivation of the sensitivities. Of these three methods, the adjointbased method is the preferred method, because: