A synthetic case study of measuring the misfit between 4D seismic data and numerical reservoir simulation models through the Momenta Tree

Data assimilation is an important and time-consuming process in petroleum reservoir numerical simulation. It produces a set of calibrated models used to forecast and optimize oil and gas production. The process focuses on reducing uncertainties related to reservoir properties, yielding numerical reservoir models that plausibly reproduce measured data from the field, such as well rates and pressure. Besides the traditional well-production data, 4D seismic data are increasingly being used to reduce the uncertainty of numerical reservoir models, by providing dynamic spatial data to be matched. Although 4D seismic data reveal essential information about the dynamic behavior of the reservoir, its integration in data assimilation procedures is challenging, especially in a quantitative way, because of their noisy and uncertain nature and their larger resolution when compared to the resolution of simulated data from numerical reservoir models. The development of metrics able to efficiently estimate the discrepancies between 4D seismic data and numerical reservoir model outputs is a current research interest for data assimilation, given the challenges of integrating these different types of data. We introduce the Momenta Tree. It uses orthogonal moments supporting a multi-level data representation, where features are organized in nodes related to different levels of region detail. It supports the comparison of simulated data from numerical reservoir models and observed 4D images of seismic data, images, using different resolutions and considering various domains. The similarity between data is calculated with the extended Jaccard distance and is represented by a phylogenetic tree; the simulated models are represented as circles in branches, and their similarity is captured by connections. We apply the Momenta Tree to a controlled case, introduced in this paper, to validate and compare the new metric with traditional metrics, and a more complex representative case based on real oil industry data. Our results show that the Momenta Tree metric retains the same sequential similarity in environments affected by noise. The highest-ranked models using the Momenta Tree relate to forecast behavior closer to the reference data than the highest-ranked models obtained with traditional methods. An additional advantage of the Momenta Tree is its ability to enable data comparison in various domains (P-impedance and Water Saturation) at different resolutions of seismic and simulation data.