Efficient big data assimilation through sparse representation: A 3D benchmark case study in petroleum engineering

Abstract

Data assimilation is an important discipline in geosciences that aims to combine the information contents from both prior geophysical models and observational data (observations) to obtain improved model estimates. Ensemble-based methods are among the state-of-the-art assimilation algorithms in the data assimilation community. When applying ensemble-based methods to assimilate big geophysical data, substantial computational resources are needed in order to compute and/or store certain quantities (e.g., the Kalman-gain-type matrix), given both big model and data sizes. In addition, uncertainty quantification of observational data, e.g., in terms of estimating the observation error covariance matrix, also becomes computationally challenging, if not infeasible. To tackle the aforementioned challenges in the presence of big data, in a previous study, the authors proposed a wavelet-based sparse representation procedure for 2D seismic data assimilation problems (also known as history matching problems in petroleum engineering). In the current study, we extend the sparse representation procedure to 3D problems, as this is an important step towards real field case studies. To demonstrate the efficiency of the extended sparse representation procedure, we apply an ensemble-based seismic history matching framework with the extended sparse representation procedure to a 3D benchmark case, the Brugge field. In this benchmark case study, the total number of seismic data is in the order of . We show that the wavelet-based sparse representation procedure is extremely efficient in reducing the size of seismic data, while preserving the salient features of seismic data. Moreover, even with a substantial data-size reduction through sparse representation, the ensemble-based seismic history matching framework can still achieve good estimation accuracy.

4D Seismic History Matching Incorporating Unsupervised Learning

“…It also considers that the initial framework of the un-cemented sand rock is a densely random pack of spherically shaped grains having the porosity around 36%, which is the maximum porosity value that the rock could have before the suspension. I denote this parameter as the critical porosity (Luo et al, 2018). The shear modulus and dry bulk modulus ( ) at critical porosity is then calculated using the Hertz-Mindlin model as denoted in (Mindlin, 1949, Luo et al, 2018 = √ 2 (1 − ) 2 2 18Π 2 (1 − ) 2…”

“…I denote this parameter as the critical porosity (Luo et al, 2018). The shear modulus and dry bulk modulus ( ) at critical porosity is then calculated using the Hertz-Mindlin model as denoted in (Mindlin, 1949, Luo et al, 2018 = √ 2 (1 − ) 2 2 18Π 2 (1 − ) 2…”

“…Some numerical issues may arise for ensemble-based history matching algorithms when assimilating big data, e.g., ensemble collapse of the ensemble when tracking the true signal and large costs in storing and computing the Kalman gain matrices (Luo et al, 2018, Skjervheim 2007. Also, the history matching may become over-determined with big data (such that there is no solution that could match the observational data exactly) as opposed to the under-determined nature required for most successful implementation of history matching which may affect accuracy of the algorithm results (Luo et al 2018, Tarantola 2005, Skjervheim 2007). Therefore, data reduction is a necessary approach in big data analytics, as seen in geosciences (Luo et al, 2018).…”

Divergence of the Ensemble Transform Kalman Filter (LETKF) by Nonlocal Observations

“…Data assimilation (DA) merges models and observations to gain optimal model state estimates. It is well-established in meteorology [1], geophysics [2], and attracts attention in life sciences [3]. Typical applications of DA serve to estimate model parameters [4] or provide initial conditions for forecasts [5].…”

Sequential estimation of the generated curing heat of composite materials by data assimilation: A numerical study

“…[ 21 ] used data assimilation methods to improve the accuracy of predicting the remaining useful life of a turbine blade affected by creep. Thus, the application of data assimilation methods has expanded to include a variety of fields such as meteorology, fluid mechanics [ 22 ], petroleum engineering [ 23 ], biomechanics, marine engineering, and materials science.…”