This paper presents a closed-loop workflow for short-term optimization of reservoir management powered by offshore wind energy. Motivated by the need to reduce CO2 emissions in the Norwegian oil and gas sector, the workflow integrates wind power forecasts into optimization of daily well control while adhering to a long-term production strategy optimized for economic output. The workflow utilizes coarsened reservoir models calibrated through ensemble-based data assimilation to minimize computational costs. A realistic benchmark model, Drogon, is used to demonstrate the methodology. The workflow dynamically adjusts well rates to align power demand with wind availability, minimizing reliance on gas turbines and thereby reducing emissions. The numerical experiment demonstrates the potential of the workflow by significantly reducing short-term emissions without compromising the NPV.

This paper addresses the challenge of incorporating offshore wind power into reservoir management. Traditionally, oil and gas production is powered by gas turbines. While stable, gas turbines are a major source of CO2 emissions. In contrast, wind power produces power with minimal emissions. However, due to its high variability and uncertainty, including it in the optimization of operational strategies over extended periods can be challenging. In this paper, the optimization of production strategies over an ensemble of realistic wind power series is investigated. The ensemble is generated by a mathematical model consisting of an autoregressive model with a seasonal trend. The model is conditioned on relevant wind speed data from the North Sea with Bayesian inference. The wind speed data is selected from the open-access NORA10EI dataset. The methodology developed in this paper is applied to a multi-objective optimization problem, focusing on studying the tradeoff between profit and emissions. A benchmark test reservoir model and a detailed CO2 emissions calculator are employed. In this scenario, wind power is combined with traditional gas power, and all results are compared with a reference where only gas power is used. The experiment indicates that it is not possible to reduce emissions by 40% without the use of wind power.

Ensemble-based optimization (EnOpt), commonly used in reservoir management, can be seen as a special case of a natural evolution algorithm. Stein’s lemma gives a new interpretation of EnOpt. This interpretation enables us to study EnOpt in the context of general mutation distributions. In this paper, a non-Gaussian generalization of EnOpt (GenOpt) is proposed, where the control gradient is estimated using Stein’s lemma, and the mutation distribution is updated separately via natural evolution. For the multivariate case, a Gaussian copula is used to represent dependencies between the marginals. The correlation matrix is also iteratively optimized. It is shown that using beta distributions as marginals in the GenOpt algorithm addresses the truncation problem that sometimes arises when applying EnOpt on bounded optimization problems. The performance of the proposed optimization algorithm is evaluated on several test cases. The experiments indicate that GenOpt is less dependent on the chosen hyperparameters, and it is able to converge more quickly than EnOpt on a reservoir management test case.

The Edvard Grieg field is a highly complex and heterogeneous reservoir with an extensive fault structure and a mixture of sandstone, conglomerate, and shale. In this paper, we present a complete workflow for history matching the Edvard Grieg field using an ensemble smoother for Bayesian inference. An important aspect of the workflow is a methodology to check that the prior assumptions are suitable for assimilating the data, and procedures to verify that the posterior results are plausible and credible. We thoroughly describe several tools and visualization techniques for these purposes. Using these methods we show how to identify important parameters of the model. Furthermore, we utilize new compression methods for better handling large datasets. Simulating fluid flow and seismic response for reservoirs of this size and complexity requires high numerical resolution and accurate seismic models. We present a novel dual-model concept for a better representation of seismic data and attributes, that deploy different models for the underground depending on simulated properties. Results from history matching show that we can improve data matches for both production data and different seismic attributes. Updated parameters give new insight into the reservoir dynamics, and are calibrated to better represent water movement and pressure.

We investigate the use of various momentum methods in combination with an ensemble approximation of gradients, for accelerated optimization. Although momentum gradient descent methods are popular in machine learning, it is unclear how they perform when applied to time-consuming dynamic problems such as production optimization for petroleum reservoir management. Four different momentum methods are extensively tested on a reservoir test case in one deterministic and one robust setting. The numerical experiments show that momentum strategies yield, on average, a higher net present value with fewer simulations needed.

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.

When planning wind farms it is important to optimize the layout to increase production and reduce costs. In this paper we minimize the levelized cost of energy (LCOE) fora floating wind farm using wind data in an area around Porto Santo in Portugal. We use ensemble based optimization (EnOpt), which is frequently applied in the geophysical community to find optimal controls of oil reservoirs. EnOpt is usually used for unconstrained optimization problems or for problems with simple constraints, for example upper and lower bounds on the optimization variables. Here we consider a layout problem with many constraints on the distances between turbines. To handle the constraints, we use an extension of EnOpt called EPF-EnOpt, in which the constrained problem is replaced by a series of unconstrained problems with increasing penalty terms. We compare the performance of this method with EnOpt with a fixed penalty term, and with a deterministic gradient method. All the tested methods reduce the LCOE, but EPF-EnOpt gives better results than both a single run of EnOpt with a fixed penalty term and the deterministic gradient method, and at a lower computational cost than using the gradient method. We also consider the problem of maximizing the annual energy production without taking into account any costs. EPF-EnOpt performs the best also for this problem.

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.

In robust optimisation problems the objective function consists of an average over (an ensemble of) uncertain parameters. Ensemble optimisation (EnOpt) implements steepest descent by estimating the gradient using linear regression on Monte-Carlo simulations of (an ensemble of) control parameters. Applying EnOpt for robust optimisation is costly unless the evaluations over the two ensembles are combined, i.e. 'paired'. Here, we provide a new and more rigorous perspective on the stochastic simplex approximate gradient (StoSAG) used in EnOpt, explaining how it addresses detrimental cross-correlations arising from pairing by only capturing the variability due to the control vector, and not the vector of uncertain parameters. A few minor variants are derived from a generalised derivation, as well as a new approach using decorrelation. These variants are tested on linear and non-linear toy gradient estimation problems, where they achieve highly similar accuracy, but require a very large ensemble size to outperform the non-robust approach when accounting for variance and not just bias. Other original contributions include a discussion of the particular robust control objectives for which EnOpt is suited, illustrations, a variance reduction perspective, and a discussion on the centring in covariance and gradient estimation.

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.

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.

In science and engineering, non-linear constrained optimization has been a useful mathematical technique for many practical applications. Of interest to us is its applicability in the modeling and prediction of hydrocarbon reservoir production. In this paper, a new efficient, robust, and accurate optimal solution strategy based on the exterior penalty function (EPF) method and the adaptive ensemble-based optimization (EnOpt) approach (with backtracking line-search technique) for non-linear constrained optimization problems is presented. The purpose of this work is to provide a better user-friendly strategy which mitigates the problem often faced with the current constraints handling technique utilized when using the EnOpt method to solve constrained problems of water or EOR flooding. This study notes that the problem contributes to uncertainties in the gradient computation of the objective function and hence leads to the poor convergence rate of the standard EnOpt method. In this work, we used the EPF method to transform a given constrained optimization problem to a sequence of unconstrained subproblems and then sequentially solve the subproblems by unconstrained EnOpt procedure until convergence to the solution of the original problem. To demonstrate the advantage of the proposed methodology, we used it to solve analytical 2D bound constrained Rosenbrock's problem and a practical high dimensional bound constrained water flooding optimization problem associated with a 2D 5Spot field and a 3D Reek reservoir field. The numerical results are compared with EnOpt using classical Lagrangian approach, as well as the traditional EnOpt. Our findings showed that the proposed solution method has a fast convergence rate and is more accurate and robust.

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.

In this document we present a workflow for ensemble-based 4D seismic history matching. Ensemble-based history matching has become standard for production data, but 4D seismic data poses a number of additional challenges. One issue is that the amount of data is considerably larger, but another, probably more complicating factor is that for utilizing the seismic data, either the seismic data must be inverted to properties that is included in the reservoir simulation model, or a seismic response must be modeled, given the current estimate of the reservoir properties. This leads to a number of choices on how to utilize the information of the 4D seismic data. We will discuss this, as well as point to approaches for handling large amounts of data in ensemble-based history matching. The developed approach has been applied on the Norne field and is currently being evaluated at the Ekofisk field. This document is primarily addressed to reservoir engineers and researchers that are working on history matching 4D seismic data, but it might also be of interest to those working with 4D seismic data from a geophysical perspective. After all, 4D seismic history matching should be viewed as an interdisciplinary subject. Although, our focus has been on ensemble-based history matching, some of the choices that have to be made in utilizing 4D seismic data is independent of the actual method used for history matching.

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.

The Olympus field is an optimization case prepared by TNO to test different optimization methods and workflows for field development. The authors have joined the Olympus optimization challenges by solving various optimization problems for field development. Here, we consider the well control problem from a different perspective by using well economic limits as parameters to optimize the objective function - the Net Present Value (NPV). The Ensemble-based Optimization (EnOpt) method applied to this problem has been shown to be simple and efficient to handle geological uncertainty in many literatures. In this work, the performance of EnOpt is illustrated on the Olympus benchmark case. The economic limit determines when a well will be shutin with respect to the water-cut, which directly affects the calculation of NPV. After optimizing the economic limits, we see that the producers are not necessarily following the fixed value of economic limits to give the best production benefit in terms of NPV. Given a well control scheme in the field, the NPV can be further improved by optimizing the economic limits of each producer. Optimizing the economic limits is a novel aspect for Olympus case, as this was not within the original scope of the Olympus optimization challenge. This work also shows that the NPV is further improved compared to the values obtained by the authors during the Olympus optimization challenge by utilizing optimized well economic limits.

Automatic history matching using production and seismic data is still challenging due to the size of seismic datasets. The most severe problem, when applying ensemble-based methods for assimilating large datasets, is that the uncertainty is usually underestimated due to the limited number of models in the ensemble compared with the dimension of the data, which inevitably leads to an ensemble collapse. Localization and data reduction methods are promising approaches mitigating this problem. In this paper, we present a new robust and flexible workflow for assimilating seismic attributes and production data. The methodology is based on sparse representation of the seismic data, using methods developed for image denoising. We propose to assimilate production and seismic data simultaneously, and to ensure equal weight on these data types, we apply scaling based on the initial data match. Further, a newly developed flexible correlation-based localization technique is used for both data types. The workflow is successfully implemented for the released Norne benchmark dataset, and an iterative ensemble smoother is used for the simultaneous assimilation of production and seismic data. We show that the methodology is robust and ensemble collapse is avoided. Furthermore, the proposed workflow is flexible, as it can be applied to seismic data or inverted seismic properties, and the methodology requires only moderate computer memory. The results show that through this method, we can successfully reduce the data mismatch for both production data and seismic data.

Summary Over the last decades several EOR methods have emerged, and corresponding models have been developed and implemented in increasingly more complex simulation tools. In this paper we present methodology and mathematical tools for optimizing and quantifying the value of EOR strategies, such as polymer, smart water or CO2. The developed methodology is demonstrated for polymer injection on medium to highly heterogeneous synthetic reservoir models with different complexity. The purpose of the work is to improve the understanding of the actual benefit of EOR methods, and to provide methodology that quickly allows users to find optimal production strategies that maximize the net present value (NPV). In this work, the control variables for the optimization problem are polymer concentration and water injection rates for each injecting well, and oil production rates or bottom hole pressures for the producing wells, over the exploration period. Each control variable is constrained with given production limitations. To account for the uncertainty in the reservoir model, an ensemble of geological realizations is considered, and a robust ensemble-based approximate gradient method (EnOpt) is utilized. The gradient is approximated using a sample of control vectors, drawn from a Gaussian multivariate distribution with known mean and covariance. The covariance matrix is defined so that the control variables of the same well is correlated in time. The mean is updated using a preconditioned gradient ascent method with backtracking until an optimum is found. The presented method is tested on three different synthetic reservoirs: a 2D five-spot field pattern with grid dimension 50×50×1, a 3D field provided by Equinor (the Reek field with dimension 40×64×14), and a 3D field provided by TNO (the OLYMPUS field with dimension 118×118×16). The first two fields have three phases (water, gas, and oil) and the third field has two phases (water and oil). For each case we find the optimal well controls for polymer flooding and then compared with convectional optimized continuous water flooding. The reservoir fluid flow is simulated using the Open Porous Media (OPM) simulator. However, it is worth noting that the optimization method is independent of the reservoir simulator used. Important findings of this study are the feasible control strategies for polymer EOR methods leading to an increased NPV, and comparison of the economic values for optimized polymer and traditional water flooding for the examples considered.