Iterative ensemble smoothers (IES) are among the popular reservoir data assimilation (RDA) algorithms for reservoir characterization. The actual deployment of an IES algorithm requires implementing certain stopping criteria, normally adopted for runtime control (e.g., by stopping the IES when it reaches the maximum number of iterations) and/or safeguarding the RDA performance (e.g., by preventing the simulated data from overfitting the actual observations). In practice, for various reasons, it is often challenging for existing stopping criteria to simultaneously achieve both purposes. One noticeable issue, as illustrated in this work, is that in many situations, the qualities of the estimated reservoir models may already start to deteriorate before a conventional stopping criterion activates to terminate the iteration process. Following this observation, one practically important question arises: Is it possible to further improve the efficacy of the IES algorithm by designing a different stopping criterion so that the IES can stop earlier, saving computational costs while achieving better RDA performance?
As one of the rare attempts in the community, this work aims to investigate the use of a new IES stopping criterion that has the potential to provide an affirmative answer to the above question. In this regard, our main idea is based on the concept of cross validation (CV), routinely adopted in supervised machine learning (SML) problems for early stopping to prevent SML models from overfitting the training data. Despite the noticed similarities between RDA and SML problems, some fundamental differences exist, making it fail to work well if one directly extends a vanilla CV procedure from SML to RDA. To tackle this identified challenge, we design an efficient CV procedure tailored for RDA problems, and inspect the performance of an IES algorithm equipped with this CV procedure (IES-CV) in both synthetic and real field case studies. Our numerical investigation indicates that the IES-CV algorithm achieves promising RDA performance in all case studies, confirming the possibility that with the aid of a proper stopping criterion, an IES algorithm can terminate at an appropriate iteration step with near-optimal RDA performance. Beyond these numerical findings, it is also our hope that the current work may help improve the best practices of applying IES to RDA problems, taking advantage of the effective, CV-based stopping criterion.
Tag: Iterative ensemble smoother
Improving pseudo-optimal Kalman-gain localization using the random shuflle method
In present days, Iterative ensemble smoothers (IES) are among the main methods to perform ensemble-based history matching in petroleum reservoirs. Generally, some localization technique is applied to the IES to pre- vent ensemble collapse, which is the consequence of an excessive reduction of the posterior ensemble variance. When the standard distance-based localization is applied, the assimilation of non-local parameters is difficult, and besides that, this kind of methodology has also several intrinsic parameters that need to be defined before the assimilation. In contrast, adaptive localization methods aim to overcome the noticed problems of distance-based localization, by using some statistical method to define the localization. This article proposes a novel adaptive localization scheme, on top of two preexisting techniques: pseudo-optimal and correlation-based localizations. The motivation here is to further improve the adaptive localization scheme, by combining the strengths of these two preexisting techniques. The efficacy of the proposed localization scheme is tested in one 2D and one 3D case studies, whereas the latter case study involves a field-scale reservoir model with both local and non-local pa- rameters, which often impose challenges on the conventional localization schemes. In comparison to other evaluated localization schemes, our results indicate that the proposed adaptive localization scheme achieves improved history matching performance.