Using petro-elastic proxy model to integrate 4D seismic in ensemble based data assimilation

4D seismic data provide valuable information for petroleum engineers to update simulation models using different data assimilation algorithms. To assimilate 4D seismic data, the conventional approach is to use a petro-elastic model (PEM) to bring simulation models to the same domain as the 4D seismic data, or vice-versa. PEMs are constructed using rock and fluid models with uncertainty in both input parameters and models. Apart from their uncertainty, PEMs' inclusion in data assimilation algorithms requires an interdisciplinary team of rock physicists and petroleum engineers to develop and implement them. A method was developed in this research to replace the PEM with petro-elastic proxy model (PEM-Proxy) for 4D seismic data assimilation in ensemble based algorithms. PEM-Proxy used here was a linear equation with two coefficients linking water saturation and pore pressure changes to the 4D signal, in our case 4D acoustic impedance (4DAI). Two versions of the PEM-Proxy were developed namely PFC and PUC with fixed and uncertain coefficients, respectively. Eventually, PEM was replaced by the PEM-Proxies in Ensemble Smoother with Multiple Data Assimilation (ES-MDA) algorithm to integrate 4D seismic data. Our method was applied to a benchmark case study, using various data assimilation cases to compare the PEM-Proxies application with the PEM. Results showed that the implementation of the PEM-Proxies did not change the behavior of well and 4D seismic objective functions through data assimilation iterations. Interestingly the PUC implementation was satisfactory in terms of well objective functions and even provided better data assimilation cases for 4D seismic objective function. Production forecast reliability for various cases were analyzed and wells forecast showed similar behavior comparing PEM and PEM-Proxies cases. Our method helps petroleum engineers avoid demanding rock and fluid physics equations and replace them with a straightforward and computationally less expensive model for 4D seismic data assimilation.