Gijs van Essen

Hierarchical Long-Term and Short-Term Production Optimization

Model-based dynamic optimization of oil production has a significant potential to improve economic life-cycle performance, as has been shown in various studies. However, within these studies, short-term operational objectives are generally neglected. As a result, the optimized injection and production rates often result in a considerable decrease in short-term production performance. In reality, however, it is often these short-term objectives that dictate the course of the operational strategy. Incorporating short-term goals into the life-cycle optimization problem, therefore, is an essential step in model-based life-cycle optimization. We propose a hierarchical optimization structure with multiple objectives. Within this framework, the life-cycle performance in terms of net present value (NPV) serves as the primary objective and short-term operational performance is the secondary objective, such that optimality of the primary objective constrains the secondary optimization problem. This requires that optimality of the primary objective does not fix all degrees of freedom (DOF) of the decision variable space. Fortunately, the life-cycle optimization problem is generally ill-posed and contains many more decision variables than necessary. We present a method that identifies the redundant DOF in the life-cycle optimization problem, which can subsequently be used in the secondary optimization problem. In our study, we used a 3D reservoir in a fluvial depositional environment with a production life of 7 years. The primary objective is undiscounted NPV, while the secondary objective is aimed at maximizing short-term production. The optimal life-cycle waterflooding strategy that includes short-term performance is compared to the optimal strategy that disregards short-term performance. The experiment shows a very large increase in short-term production, boosting first-year production by a factor of 2, without significantly compromising optimality of the primary objective, showing a slight drop in NPV of only ?0.3%. Our method to determine the redundant DOF in the primary objective function relies on the computation of the Hessian matrix of the objective function with respect to the control variables. Although theoretically rigorous, this method is computationally infeasible for realistically sized problems. Therefore, we also developed a second, more pragmatic, method relying on an alternating sequence of optimizing the primary- and secondary-objective functions. Subsequently, we demonstrated that both methods lead to nearly identical results, which offers scope for application of hierarchical long-term and short-term production optimization to realistically sized flooding-optimization problems.

A Two-Level Strategy to Realize Life-Cycle Production Optimization in an Operational Setting

We present a two-level strategy to improve robustness against uncertainty and model errors in life-cycle flooding optimization. At the upper level, a physics-based large-scale reservoir model is used to determine optimal life-cycle injection and production profiles. At the lower level these profiles are considered as set points (reference values) for a tracking control algorithm, also known as a model predictive controller (MPC), to optimize the production variables over a short moving horizon based on a simple data-driven model. We used a conventional reservoir simulator with gradient-based optimization functionality to perform the life-cycle optimization. Next, we applied this optimal strategy to a set of reservoir models with markedly different geological characteristics. We compared the performance (oil recovery) of these models when applying the life-cycle strategy with and without the corrections provided by the data-driven algorithm and the tracking controller. In this theoretical study we observed that the use of the lower-level controller enabled successful tracking of the reference values provided by the upper-level optimizer. In our example, a performance drop of 6.4 % in net present value, caused by differences between the reservoir model used for life-cycle optimization and the (synthetic) true reservoir, was successfully reduced to only 0.5% when applying the two-level strategy. Several studies have demonstrated that model-based life-cycle production optimization has a large scope to improve long-term economic performance of water flooding projects. However, because of uncertainties in geology, economics and operational decisions, such life-cycle strategies cannot simply be applied in reality. Our two-level approach offers a solution to realize the theoretical potential of life-cycle optimization in a more operational setting. Introduction

Coupled Static / Dynamic Modeling For Improved Uncertainty Handling

In the petroleum industry history-matched reservoir models are used to aid the field development decision-making process. Traditionally, models have been history-matched by reservoir engineers in the dynamic domain only. Ideally, if any changes are required to static parameters as result of history matching the dynamic model, then these should be reflected directly in the static reservoir model. This permits consistency between the static and dynamic domain. In addition, static model uncertainties are often not evaluated in the dynamic domain, which could result in the detailed modeling of geological features that have no impact on the dynamic behavior and the resulting development decision. This paper demonstrates a workflow where the reservoir simulator and static modeling package are closely linked to promote a more integrated approach and to enhance the interaction between the subsurface disciplines. Using either the simulator or the static modeling package as the platform, the output of the workflow is a sensitivity analysis of the uncertainties related to structure, rock properties, fluids and rock-fluid interactions. Next, computer-assisted history matching methods (i.e. adjoint-based and Design of Experiments) are used to find the parameter values that result in a successful history match. The workflow will be demonstrated both on a synthetic model and on a reservoir model from a real field case. This methodology results in history-matched models and a better understanding of the static and dynamic subsurface uncertainties, leading to more informed decision-making. The method presented here can significantly enhance the awareness of the impact of both static and dynamic subsurface uncertainties on development decisions. In addition, it offers a platform where all subsurface professionals can more optimally combine their efforts to improve the integrated understanding of reservoirs.

Model-based control and optimization of large scale physical systems - Challenges in reservoir engineering

Due to urgent needs to increase efficiency in oil recovery from subsurface reservoirs new technology is developed that allows more detailed sensing and actuation of multiphase flow properties in oil reservoirs. One of the examples is the controlled injection of water through injection wells with the purpose to displace the oil in an appropriate direction. This technology enables the application of model-based optimization and control techniques to optimize production over the entire production period of a reservoir, which can be around 25 years. Large scale reservoir flow models are used for optimizing production settings, but suffer from high levels of uncertainty and limited validation options. One of the challenges is the development of reduced complexity models that deliver accurate long-term predictions, and at the same time are not more complex than can be warranted by the amount of data that is available. In this paper an overview will be given of the problems and opportunities for model-based control and optimization in this field aiming at the development of a closed-loop reservoir management system.

A Comprehensive Workflow for Assisted History Matching Applied to a Complex Mature Reservoir

Currently a multitude of techniques exist for (computer-) assisted history matching (AHM) of simulation models, each with their merits and limitations. In this paper, it is demonstrated how different AHM techniques can be combined to quickly reveal diagnostics of a subsurface model and to obtain a better model in less time, optimally using the strengths of each method. A completed field application of AHM will be presented, in which several AHM techniques are sequentially used to arrive at a history match on pressures and fluid rates and, equally important, an improved understanding of both the static and dynamic model. The water flooded field, located in the Middle East, has decades of historical production data from about 30 wells and is notoriously difficult to match. The first technique that has been applied involves Design of Experiments to generate proxies followed by Monte Carlo Markov Chain to find the ensemble of global parameters that give an improved match. Subsequently, adjoint-based history matching has been used to find the areas in the model that were under-modelled and needed additional attention of the subsurface team members. Based on the results in this step of the workflow the static model has been improved such that it is consistent with the information in the production measurements. For this field, the AHM workflow has achieved a considerable reduction of history matching time and improved quality of both the match and the model. For general simulation studies this workflow is estimated to result in a time saving of 40% with respect to manual history matching. In addition, it results in a better understanding of the static and dynamic subsurface uncertainties.

Integrated dynamic optimization and control in reservoir engineering using locally identified linear models

Studies on dynamic real-time optimization (D-RTO) of waterflooding strategies in petroleum reservoirs have demonstrated that there exists a large potential to improve economic performance in oil recovery. Unfortunately, the used large-scale, nonlinear, physics-based reservoir models suffer from vast parametric uncertainty and generally poor short-term predictions. This seriously limits the industrial and economic feasibility of a production strategy based at long-term economic objectives alone. In this work, a two level optimization and control strategy is investigated, consisting of a D-RTO and model predictive control (MPC) level. In this structure, long-term economic performance is addressed by the design of optimal reference trajectories, while reliability of reaching these long-term goals is managed through a short-term tracking control problem, based on locally identified linear models.

Hierarchical Long Term and Short Term Production Optimization

This paper (SPE 124332) was accepted for presentation at the SPE Annual Technical Conference and Exhibition, New Orleans, 4–7 October 2009, and revised for publication. Original manuscript received for review 2 November 2009. Revised manuscript received for review 11 March 2010. Paper peer approved 26 April 2010. Summary Model-based dynamic optimization of oil production has a significant potential to improve economic life-cycle performance, as has been shown in various studies. However, within these studies, short-term operational objectives are generally neglected. As a result, the optimized injection and production rates often result in a considerable decrease in short-term production performance. In reality, however, it is often these short-term objectives that dictate the course of the operational strategy. Incorporating short-term goals into the life-cycle optimization problem, therefore, is an essential step in model-based life-cycle optimization. We propose a hierarchical optimization structure with multiple objectives. Within this framework, the life-cycle performance in terms of net present value (NPV) serves as the primary objective and shortterm operational performance is the secondary objective, such that optimality of the primary objective constrains the secondary optimization problem. This requires that optimality of the primary objective does not fix all degrees of freedom (DOF) of the decision variable space. Fortunately, the life-cycle optimization problem is generally ill-posed and contains many more decision variables than necessary. We present a method that identifies the redundant DOF in the life-cycle optimization problem, which can subsequently be used in the secondary optimization problem. In our study, we used a 3D reservoir in a fluvial depositional environment with a production life of 7 years. The primary objective is undiscounted NPV, while the secondary objective is aimed at maximizing shortterm production. The optimal life-cycle waterflooding strategy that includes short-term performance is compared to the optimal strategy that disregards short-term performance. The experiment shows a very large increase in short-term production, boosting first-year production by a factor of 2, without significantly compromising optimality of the primary objective, showing a slight drop in NPV of only −0.3%. Our method to determine the redundant DOF in the primary objective function relies on the computation of the Hessian matrix of the objective function with respect to the control variables. Although theoretically rigorous, this method is computationally infeasible for realistically sized problems. Therefore, we also developed a second, more pragmatic, method relying on an alternating sequence of optimizing the primaryand secondary-objective functions. Subsequently, we demonstrated that both methods lead to nearly identical results, which offers scope for application of hierarchical long-term and short-term production optimization to realistically sized flooding-optimization problems.

Adjoint-based History-Matching of Production and Time-lapse Seismic Data

Time-lapse (4D) seismic attributes can provide valuable information on the fluid flow within subsurface reservoirs. This spatially-rich source of information complements the poor areal information obtainable from production well data. While fusion of information from the two sources holds great promise, in practice, this task is far from trivial. Joint Inversion is complex for many reasons, including different time and spatial scales, the fact that the coupling mechanisms between the various parameters are often not well established, the localized nature of the required model updates, and the necessity to integrate multiple data. These concerns limit the applicability of many data-assimilation techniques. Adjoint-based methods are free of these drawbacks but their implementation generally requires extensive programming effort. In this study we present a workflow that exploits the adjoint functionality that modern simulators offer for production data to consistently assimilate inverted 4D seismic attributes without the need for re-programming of the adjoint code. Here we discuss a novel workflow which we applied to assimilate production data and 4D seismic data from a synthetic reservoir model, which acts as the real yet unknown reservoir. Synthetic production data and 4D seismic data were created from this model to study the performance of the adjoint-based method. The seamless structure of the workflow allowed rapid setup of the data assimilation process, while execution of the process was reduced significantly. The resulting reservoir model updates displayed a considerable improvement in matching the saturation distribution in the field. This work was carried out as part of a joint Shell-IBM research project. Introduction In history matching, production measurements are assimilated to obtain a dynamical reservoir model that is consistent with historical data; see e.g. Oliver et al (2008). However, production measurements – although generally of a high temporal resolution – provide only very localized spatial information about the subsurface around the wells, especially in the early production phase when wateror gas-breakthrough has not yet occurred in the producers. After breakthrough, somewhat more insight can be gained into the reservoir model parameters that influence the mismatch between measured and simulated data. At that time however the benefits of using a pro-active reservoir management strategy have often diminished considerably. Interpreted time-lapse (4D) seismic data can provide information on the areal distribution of pressure and saturation changes due to fluid production or injection. The seismic data are generally more noisy and uncertain than production data, but due to the field-wide distribution of the data, very valuable additional information on the subsurface can be gathered; see e.g. Calvert (2005). In production data assimilation, the quality of the updated model is usually evaluated with a cost function defined as the summed squared error between the observations (measurements) and simulated production data, sometimes weighted by a measure of the accuracy of the observations. Ensemble Kalman filter (EnKF) methods (Naevdal et al. (2005); Evensen (2009); Aanonsen et al. (2009)), streamline-based methods (Vasco et al. (1999); Wang and Kovscek (2000).) and adjoint-based methods (Chen et al. (1974), Chavent et al. (1975); Li et al. (2003); Rodrigues (2006); Oliver et al. (2008)) are the most common data-assimilation techniques reported in literature to deal with the history matching problem. All these methods update the reservoir model using the sensitivities of a least-squares cost function with respect to model parameters, but differ in the considered measurement types, model parameters and derivation of the sensitivities. Of these three methods, the adjointbased method is the preferred method, because:

Lexicographic optimization of multiple economic objectives in oil production from petroleum reservoirs

In oil production waterflooding is a popular recovery technology, which involves the injection of water into an oil reservoir. Studies on model-based dynamic optimization of waterflooding strategies have demonstrated that there is a significant potential to increase life-cycle performance, determined using an economic objective function. However, in these studies the additional desire of many oil companies to maximize daily production is generally neglected. To resolve this, a lexicographic optimization structure is proposed that regards economic life-cycle performance as primary objective and daily production as secondary objective. The existence of redundant degrees of freedom allows for the optimization of the secondary objective without compromising optimality of the primary objective.

Reduced Space Dynamics-Based Geo-Statistical Prior Sampling for Uncertainty Quantification of End Goal Decisions

The inversion of large-scale ill-posed problems introduces multiple challenges. These include, identifying appropriate noise model, prescription of suitable prior information, design of an informative experiment, uncertainty quantification, incorporation of heterogeneous sources of data, and definition of an appropriate optimization scheme. In the context of flow in porous media, subsurface parameters are inferred through the inversion of oil production data (a process called history matching). In this study, the inherent uncertainty of the problem is mitigated by devising efficient and comprehensive approaches for prior sampling. Despite meticulous efforts to minimize the variability of the solution space, the distribution of the posterior may remain intractable. In particular, geo-statisticians may often propose large sets of prior samples that regardless of their apparent geological distinction are almost entirely flow equivalent. As an antidote, a reduced space hierarchical clustering of flow relevant indicators is proposed for aggregation of these samples. The effectiveness of the method is demonstrated both with synthetic and field scale data. In addition, numerical linear algebra techniques that exploit the special structure of the underlying problems are elucidated.