An Ensemble 4D-Seismic History-Matching Framework With Sparse Representation Based On Wavelet Multiresolution Analysis

Abstract

In this work we propose an ensemble 4D seismic history matching framework for reservoir characterization. Compared to similar existing frameworks in reservoir engineering community, the proposed one consists of some relatively new ingredients, in terms of the type of seismic data in choice, wavelet multiresolution analysis for the chosen seismic data and related data noise estimation, and the use of recently developed iterative ensemble history matching algorithms.Typical seismic data used for history matching, such as acoustic impedance, are inverted quantities, whereas extra uncertainties may arise during the inversion processes. In the proposed framework we avoid such intermediate inversion processes. In addition, we also adopt wavelet-based sparse representation to reduce data size. Concretely, we use intercept and gradient attributes derived from amplitude versus angle (AVA) data, apply multilevel discrete wavelet transforms (DWT) to attribute data, and estimate noise level of resulting wavelet coefficients. We then select the wavelet coefficients above a certain threshold value, and history-match these leading wavelet coefficients using an iterative ensemble smoother.As a proof-of-concept study, we apply the proposed framework to a 2D synthetic case originated from a 3D Norne field model. The reservoir model variables to be estimated are permeability (PERMX) and porosity (PORO) at each active gridblock. A rock physics model is used to calculate seismic parameters (velocity and density) from reservoir properties (porosity, fluid saturation and pressure), then reflection coefficients are generated using a linearized AVA equation that involves velocity and density. AVA data are obtained by computing the convolution between reflection coefficients and a Ricker wavelet function. The multiresolution analysis applied to the AVA attributes helps to obtain a good estimation of 1 noise level and substantially reduce the data size. We compare history matching performance in three scenarios: (S1) with production data only, (S2) with seismic data only, and (S3) with both production and seismic data. In either scenario S2 or S3, we also inspect two sets of experiments, one using the original seismic data (full-data experiment) and the other adopting sparse representations (sparse-data experiment). Our numerical results suggest that, in this particular case study, using production data largely improves the estimation of permeability, but has little effect on the estimation of porosity. Using seismic data only improves the estimation of porosity, but not that of permeability. In contrast, using both production and 4D seismic data improves the estimation accuracies of both porosity and permeability. Moreover, in either scenario S2 or S3, provided that a certain stopping criterion is equipped in the iterative ensemble smoother, adopting sparse representations results in better history matching performance than using the original data set.

Ensemble-based kernel learning for a class of data assimilation problems with imperfect forward simulators

“…When no MEC is introduced, the RMSEs tend to decrease at the first five iteration steps, and then bounce back to somewhat higher values at the last two iteration steps. This kind of “U-turn” behavior was also found in the earlier work of [6], and can be mitigated or avoided by introducing a procedure of sparse data representation [6], or localization [7, 9], to the iES (an investigation on this issue, however, is beyond the scope of the current work). In contrast, with MEC introduced to the iES, the “U-turn” behavior seems vanished.…”

“…We then use the last analysis ensemble obtained from the trial process as the background at the next outer iteration step. Apart from the maximum number of (outer) iteration steps, we also adopt another two stopping criteria, which become effective if (1) the change of average data mismatch values in two consecutive iterations are less than 1% (for runtime control); or if (2) the average data mismatch is lower than four times the number of observations for the first time (to avoid over-fitting observations, see [6]). For ease of comparison, localization [7, 9, 42, 43] is not adopted in the iES.…”

“…To this end, instead of solving Eq (9) to obtain a single set of estimated parameters, we aim to estimate an ensemble of such parameters. By doing so, we will obtain all the intrinsic benefits in using ensemble-based methods, which includes, for instance [6],…”

“…In our investigations, we encountered a few major challenges, namely, big data , uncertainty quantification and imperfection in forward seismic simulators [12]. Driven by the needs to address these identified challenges in our studies, certain (multidisciplinary) methods, such as image processing [4, 10], sparse data representation [2, 4, 6], adaptive localization [7–9], have been exploited or developed, and integrated into an ensemble-based SHM workflow, whose efficacy is now demonstrated in a full Norne field case study using real production and seismic data [5].…”

Managing Uncertainty in Geological Scenarios Using Machine Learning-Based Classification Model on Production Data

“…The SVM was coupled with a discrete wavelet transform (DWT), which is a widely used method for feature extraction via the selection of principal features from among input data [55][56][57]. The DWT uses the superposition of a group of wavelets to construct a basis function for wavelet transform.…”