A natural Hessian approximation for ensemble based optimization

A key challenge in reservoir management and other fields of engineering involves optimizing a nonlinear function iteratively. Due to the lack of available gradients in commercial reservoir simulators the attention over the last decades has been on gradient free methods or gradient approximations. In particular, the ensemble-based optimization has gained popularity over the last decade due to its simplicity and efficient implementation when considering an ensemble of reservoir models. Typically, a regression type gradient approximation is used in a backtracking or line search setting. This paper introduces an approximation of the Hessian utilizing a Monte Carlo approximation of the natural gradient with respect to the covariance matrix. This Hessian approximation can further be implemented in a trust region approach in order to improve the efficiency of the algorithm. The advantages of using such approximations are demonstrated by testing the proposed algorithm on the Rosenbrock function and on a synthetic reservoir field.publishedVersio

Marginalized iterative ensemble smoothers for data assimilation

Data assimilation is an important tool in many geophysical applications. One of many key elements of data assimilation algorithms is the measurement error that determines the weighting of the data in the cost function to be minimized. Although the algorithms used for data assimilation treat the measurement uncertainty as known, it is in many cases estimated or set based on some expert opinion. Here we treat the measurement uncertainty as a hyperparameter in a fully Bayesian hierarchical model and derive a new class of iterative ensemble methods for data assimilation where the measurement uncertainty is integrated out. The proposed algorithms are compared with the standard iterative ensemble smoother on a 2D synthetic reservoir model.publishedVersio

Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery

In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we particularly focus on polymer flooding. The computational approach is based on an adaptive training procedure of a neural network that directly approximates an input-output map of the underlying PDE-constrained optimization problem. The training process thereby focuses on the construction of an accurate surrogate model solely related to the optimization path of an outer iterative optimization loop. True evaluations of the objective function are used to finally obtain certified results. Numerical experiments are given to evaluate the accuracy and efficiency of the approach for a heterogeneous five-spot benchmark problem.publishedVersio

Accounting for model errors of rock physics models in 4D seismic history matching problems: A perspective of machine learning

Model errors are ubiquitous in practical history matching problems. A common approach in the literature to accounting for model errors is to treat them as random variables following certain presumed distributions. While such a treatment renders algorithmic convenience, its underpinning assumptions are often invalid. In this work, we adopt an alternative approach, and treat model-error characterization as a functional approximation problem, which can be solved using a generic machine learning method. We then integrate the proposed model-error characterization approach into an ensemble-based history matching framework, and show that, with very minor modifications, existing ensemble-based history matching algorithms can be readily deployed to solve the history matching problem in the presence of model errors. To demonstrate the efficacy of the integrated history matching framework, we apply it to account for potential model errors of a rock physics model in 4D seismic history matching applied to the full Norne benchmark case. The numerical results indicate that the proposed model-error characterization approach helps improve the qualities of estimated reservoir models, and leads to more accurate forecasts of production data. This suggests that accounting for model errors from a perspective of machine learning serves as a viable way to deal with model imperfection in practical history matching problems.publishedVersio

Accounting for model errors of rock physics models in 4D seismic history matching problems: A perspective of machine learning

Model errors are ubiquitous in practical history matching problems. A common approach in the literature to accounting for model errors is to treat them as random variables following certain presumed distributions. While such a treatment renders algorithmic convenience, its underpinning assumptions are often invalid. In this work, we adopt an alternative approach, and treat model-error characterization as a functional approximation problem, which can be solved using a generic machine learning method. We then integrate the proposed model-error characterization approach into an ensemble-based history matching framework, and show that, with very minor modifications, existing ensemble-based history matching algorithms can be readily deployed to solve the history matching problem in the presence of model errors. To demonstrate the efficacy of the integrated history matching framework, we apply it to account for potential model errors of a rock physics model in 4D seismic history matching applied to the full Norne benchmark case. The numerical results indicate that the proposed model-error characterization approach helps improve the qualities of estimated reservoir models, and leads to more accurate forecasts of production data. This suggests that accounting for model errors from a perspective of machine learning serves as a viable way to deal with model imperfection in practical history matching problems

4D seismic history matching

Reservoir simulation models are used to forecast future reservoir behavior and to optimally manage reservoir production. These models require specification of hundreds of thousands of parameters, some of which may be determined from measurements along well paths, but the distance between wells can be large and the formations in which oil and gas are found are almost always heterogeneous with many geological complexities so many of the reservoir parameters are poorly constrained by well data. Additional constraints on the values of the parameters are provided by general geologic knowledge, and other constraints are provided by historical measurements of production and injection behavior. This type of information is often not sufficient to identify locations of either currently remaining oil, or to provide accurate forecasts where oil will remain at the end of project life. The repeated use of surface seismic surveys offers the promise of providing observations of locations of changes in physical properties between wells, thus reducing uncertainty in predictions of future reservoir behavior. Unfortunately, while methodologies for assimilation of 4D seismic data have demonstrated substantial value in synthetic model studies, the application to real fields has not been as successful. In this paper, we review the literature on 4D seismic history matching (SHM), focusing discussions on the aspects of the problem that make it more difficult than the more traditional production history matching. In particular, we discuss the possible choices for seismic attributes that can be used for comparison between observed or modeled attribute to determine the properties of the reservoir and the difficulty of estimating the magnitude of the noise or bias in the data. Depending on the level of matching, the bias may result from errors in the forward modeling, or errors in the inversion. Much of the practical literature has focused on methodologies for reducing the effect of bias or modeling error either through choice of attribute, or by appropriate weighting of data. Applications to field cases appear to have been at least partially successful, although quantitative assessment of the history matches and the improvements in forecast is difficult.publishedVersio

Perfusion estimation using synthetic MRI-based measurements and a porous media flow model.

The measurement of perfusion and filtration of blood in biological tissue give rise to important clinical parameters used in diagnosis, follow-up, and therapy. In this paper, we address techniques for perfusion analysis using processed contrast agent concentration data from dynamic MRI acquisitions. A new methodology for analysis is evaluated and verified using synthetic data generated on a tissue geometry

Mathematics and Medicine: How mathematics, modelling and simulations can lead to better diagnosis and treatments

Starting with the discovery of X-rays by Röntgen in 1895, the progress in medical imaging has been extraordinary and immensely beneficial to diagnosis and therapy. Parallel to the increase of imaging accuracy, there is the quest of moving from qualitative to quantitative analysis and patient-tailored therapy. Mathematics, modelling and simulations are increasing their importance as tools in this quest. In this paper we give an overview of relations between mathematical modelling and imaging and focus particularly on the estimation of perfusion in the brain. In the forward model, the brain is treated as a porous medium and a two compartment model (arterial/venous) is used. Motivated by the similarity with techniques in reservoir modelling, we propose an ensemble Kalman filter to perform the parameter estimation and apply the method to a simple example as an illustrative example

Efficacy and safety of baricitinib in hospitalized adults with severe or critical COVID-19 (Bari-SolidAct): a randomised, double-blind, placebo-controlled phase 3 trial

International audienceAbstract Background Baricitinib has shown efficacy in hospitalized patients with COVID-19, but no placebo-controlled trials have focused specifically on severe/critical COVID, including vaccinated participants. Methods Bari-SolidAct is a phase-3, multicentre, randomised, double-blind, placebo-controlled trial, enrolling participants from June 3, 2021 to March 7, 2022, stopped prematurely for external evidence. Patients with severe/critical COVID-19 were randomised to Baricitinib 4 mg once daily or placebo, added to standard of care. The primary endpoint was all-cause mortality within 60 days. Participants were remotely followed to day 90 for safety and patient related outcome measures. Results Two hundred ninety-nine patients were screened, 284 randomised, and 275 received study drug or placebo and were included in the modified intent-to-treat analyses (139 receiving baricitinib and 136 placebo). Median age was 60 (IQR 49–69) years, 77% were male and 35% had received at least one dose of SARS-CoV2 vaccine. There were 21 deaths at day 60 in each group, 15.1% in the baricitinib group and 15.4% in the placebo group (adjusted absolute difference and 95% CI − 0.1% [− 8·3 to 8·0]). In sensitivity analysis censoring observations after drug discontinuation or rescue therapy (tocilizumab/increased steroid dose), proportions of death were 5.8% versus 8.8% (− 3.2% [− 9.0 to 2.7]), respectively. There were 148 serious adverse events in 46 participants (33.1%) receiving baricitinib and 155 in 51 participants (37.5%) receiving placebo. In subgroup analyses, there was a potential interaction between vaccination status and treatment allocation on 60-day mortality. In a subsequent post hoc analysis there was a significant interaction between vaccination status and treatment allocation on the occurrence of serious adverse events, with more respiratory complications and severe infections in vaccinated participants treated with baricitinib. Vaccinated participants were on average 11 years older, with more comorbidities. Conclusion This clinical trial was prematurely stopped for external evidence and therefore underpowered to conclude on a potential survival benefit of baricitinib in severe/critical COVID-19. We observed a possible safety signal in vaccinated participants, who were older with more comorbidities. Although based on a post-hoc analysis, these findings warrant further investigation in other trials and real-world studies. Trial registration Bari-SolidAct is registered at NCT04891133 (registered May 18, 2021) and EUClinicalTrials.eu ( 2022-500385-99-00 )