Closed-loop Reservoir Management Research Articles

Life-cycle production optimization with nonlinear constraints using a least-squares support-vector regression proxy

When nonlinear constraints such as field liquid or water production rate, injection pressures, etc., as functions of time need to be honored in addition to linear ones, the life-cycle production optimization problem, a component of a closed loop reservoir management, becomes challenging and computationally expensive to perform using a high-fidelity reservoir simulator with the existing gradient-based methods using the adjoint or stochastic approximate gradient methods. Therefore, the objective of this study is to present computationally efficient methods for deterministic production optimization under nonlinear constraints using a kernel-based machine learning method where the cost function is the net present value (NPV). We use the least-squares support-vector regression (LSSVR) to approximate the NPV function. To achieve computational efficiency, we generate a set of output values of the NPV and nonlinear constraint functions, which are field liquid production rate (FLPR) and water production rate (FWPR) in this study, by running the high-fidelity simulator for a broad set of input design variables (well controls) and then using the collection of input/output data to train LSSVR proxy models to replace the high-fidelity simulator to compute NPV and nonlinear state constraint functions during iterations of sequential quadratic programming (SQP). To obtain improved (higher) estimated optimal NPV values, we use the existing so-called iterative sampling refinement (ISR) method to update the LSSVR proxy so that the updated proxy remains predictive toward promising regions of search space during the optimization. Direct and indirect ways of constructing LSSVR-based NPVs as well as different combinations of input data, including nonlinear state constraints and/or the bottomhole pressures (BHPs) and water injection rates, are tested as alternative feature spaces. The results obtained from our proposed LSSVR-based optimization methods are compared with those obtained from our in-house stochastic simplex approximate gradient (StoSAG)-based line-search SQP programming (LS-SQP-StoSAG) algorithm that uses directly a high-fidelity simulator to compute the gradients of the objective function and the nonlinear state functions with StoSAG for the Brugge reservoir model. The results show that nonlinear constrained optimization with the LSSVR ISR with SQP is computationally 3.25 fold more efficient than LS-SQP-StoSAG. In addition, the results show that constructing NPV indirectly using the field liquid and water rates for a waterflooding problem where inputs come from LSSVR proxies of the nonlinear state constraints requires significantly fewer training samples than the method constructing NPV directly from the NPVs computed from a high-fidelity simulator. LSSVR has advantages for its computational efficiency which is the main goal in our research, and robustness against overfitting especially for the cases where we have limited data. However, DNNs and random forest require large training size and require much more computational resources and longer training times. Also, Random Forests and Gradient Boosting Machines can be prone to overfitting and become computationally intensive.

Competitive Knowledge Transfer–Enhanced Surrogate-Assisted Search for Production Optimization

Summary Production optimization is a crucial component of closed-loop reservoir management, which typically aims to search for the best development scheme for maximum economic benefit. Over the decades, a large body of algorithms have been proposed to address production optimization problems, among which the surrogate-assisted evolutionary algorithm (SAEA) gained much research popularity due to its problem information-agnostic implementation and strong global search capability. However, existing production optimization methods often optimize individual tasks from scratch in an isolated manner, ignoring the available optimization experience hidden in previously optimized tasks. The incapability of transferring knowledge from possibly related tasks makes these algorithms always require a considerable number of simulation runs to obtain high-quality development schemes, which could be computationally prohibitive. To address this issue, this paper proposes a novel competitive knowledge transfer (CKT) method to leverage the knowledge from previously solved tasks toward enhanced production optimization performance. The proposed method consists of two parts: (1) similarity measurement that uses both reservoir features and optimization data for identifying the most promising previously solved task and (2) CKT that launches a competition between the development schemes of different tasks to decide whether to trigger the knowledge transfer. The efficacy of the proposed method is validated on a number of synthetic benchmark functions as well as two production optimization tasks. The experimental results demonstrate that the proposed method can significantly improve production optimization performance and achieve better optimization results when certain helpful previously optimized tasks are available.

Multi-asset closed-loop reservoir management using deep reinforcement learning

Multi-asset closed-loop reservoir management using deep reinforcement learning

Reservoir Modeling, History Matching, and Characterization with a Reservoir Graph Network Model

Summary Efficient reservoir models are more desirable for fast-paced reservoir management. Moreover, due to the complexity of flow underground, it is also essential to capture the fundamental physics for model reliability. Although they are fast, pure data-driven models frequently have issues associated with interpretability, physical consistency, and ability to forecast. On the other hand, we have used full-physics simulation models to mimic and investigate hydrocarbon systems for over several decades. However, considering its infrequent model updates related to high model complexity, it is a big challenge to manage reservoirs using full-physics models in short cycles. The objective here is to propose an approach that blends reservoir physics with data-driven models to fit in the framework of dynamic reservoir management. We propose to use a reservoir graph network (RGNet) modeling approach based on a diffusive time-of-flight (DTOF) concept to simulate reservoir behaviors. By assimilating field observation data (such as pressure and rates), an RGNet model can be used for future predictions, scenario studies, and well-control optimizations. By discretizing DTOF of a 3D system with multiple wells, RGNet simplifies the system into a graph network represented by a set of 1D grid blocks that significantly reduces the system complexity and run time. RGNet can also handle multiple flow problems with various types of physics. In this work, we propose to use two methods to develop reliable and parsimonious models scalable to large-scale systems. In addition, we propose a more robust method to assimilate pressure data. We applied the proposed approach to a synthetic and a field example. Two different history-matching algorithms, the ensemble smoother with multiple data assimilation (ES-MDA) and an adjoint-based method, are compared. While ES-MDA provides the capability for uncertainty analysis, an adjoint-based method generally requires fewer simulation runs to generate a posterior model. With the proposed methods for generating interwell connections, RGNet model calibration can be achieved without system redundancy and spurious long-distance well connectivity. Also, by using a more stable pressure-matching technique, we show that pressure data are better matched and reservoir volume is accurately characterized. RGNet provides a novel hybrid physics and data-driven reservoir modeling method to fit in closed-loop reservoir management (CLRM). As RGNet models are combined with fundamental flowing physics, the calibrated model parameters are easy to interpret and understand. An RGNet model runs with far less computational cost than required by a full-physics model, which allows it to be a more practical solution to history match, predict, and optimize real assets.

Convolutional – recurrent neural network proxy for robust optimization and closed-loop reservoir management

Production optimization under geological uncertainty is computationally expensive, as a large number of well control schedules must be evaluated over multiple geological realizations. In this work, a convolutional-recurrent neural network (CNN-RNN) proxy model is developed to predict well-by-well oil and water rates, for given time-varying well bottom-hole pressure (BHP) schedules, for each realization in an ensemble. This capability enables the estimation of the objective function and nonlinear constraint values required for robust optimization. The proxy model represents an extension of a recently developed long short-term memory (LSTM) RNN proxy designed to predict well rates for a single geomodel. A CNN is introduced here to processes permeability realizations, and this provides the initial states for the RNN. The CNN-RNN proxy is trained using simulation results for 300 different sets of BHP schedules and permeability realizations. We demonstrate proxy accuracy for oil-water flow through multiple realizations of 3D multi-Gaussian permeability models. The proxy is then incorporated into a closed-loop reservoir management (CLRM) workflow, where it is used with particle swarm optimization and a filter-based method for nonlinear constraint satisfaction. History matching is achieved using an adjoint-gradient-based procedure. The proxy model is shown to perform well in this setting for five different (synthetic) ‘true’ models. Improved net present value along with constraint satisfaction and uncertainty reduction are observed with CLRM. For the robust production optimization steps, the proxy provides O(100) runtime speedup over simulation-based optimization.

Deep reinforcement learning for optimal well control in subsurface systems with uncertain geology

A general control policy framework based on deep reinforcement learning (DRL) is introduced for closed-loop decision making in subsurface flow settings. Traditional closed-loop modeling workflows in this context involve the repeated application of data assimilation/history matching and robust optimization steps. Data assimilation can be particularly challenging in cases where both the geological style (scenario) and individual model realizations are uncertain. The closed-loop reservoir management (CLRM) problem is formulated here as a partially observable Markov decision process (POMDP), with the associated optimization problem solved using a proximal policy optimization algorithm. This provides a control policy that instantaneously maps flow data observed at wells (as are available in practice) to optimal well pressure settings. The policy is represented by a temporal convolution and gated transformer blocks. Training is performed in a preprocessing step with an ensemble of prior geological models, which can be drawn from multiple geological scenarios. Example cases involving the production of oil via water injection, with both 2D and 3D geological models, are presented. The DRL-based methodology is shown to result in an increase in NPV of 15% (for the 2D cases) and 33% (3D cases) relative to robust optimization over prior models, and to an improvement of 2 - 7% in NPV relative to traditional CLRM. The solutions from the control policy are found to be comparable to those from deterministic optimization, in which the geological model is assumed to be known, even when multiple geological scenarios are considered. The control policy approach results in a 76% decrease in computational cost relative to traditional CLRM with the algorithms and parameter settings considered in this work.

Practical Closed-Loop Reservoir Management Using Deep Reinforcement Learning

Summary Traditional closed-loop reservoir management (CLRM) entails the repeated application of history matching (based on newly observed data) followed by optimization of well settings. Existing treatments can provide well settings that fluctuate substantially between control steps, which may not be acceptable in practice. Another concern is that the project life (i.e., the time frame for the optimization) is often specified somewhat arbitrarily. In this work, we incorporate treatments for these important issues into a recently developed control-policy-based CLRM framework. This framework uses deep reinforcement learning (DRL) to train control policies that directly map observed well data to optimal well settings. Here, we introduce a procedure in which we train control policies, using DRL, to find optimal well bottomhole pressures (BHPs) for prescribed relative changes between control steps, with the project life also treated as an optimization variable. The goal of the optimizations is to maximize net present value (NPV), with project life determined such that a minimum acceptable rate of return (MARR) is achieved. We apply the framework to waterflooding cases involving 2D and 3D geological models. In the 3D case, realizations are drawn from multiple geological scenarios. Solutions from the control-policy approach are shown to be comparable, in terms of NPV, to those from deterministic realization-by-realization optimization and clearly superior to results from robust optimization over prior models. These observations hold for a range of specified MARR and relative-change values. The optimal well settings provided by the control policy display gradual ramping, consistent with operational requirements.

An ensemble-based decision workflow for reservoir management

It is challenging to make optimal field development and reservoir management decisions with diminishing resources and low-emission requirements. For an optimal exploitation of the reservoir fluids, it is necessary to introduce advanced digital tools and account for geological uncertainty when making decisions. This paper discusses an ensemble-based probabilistic decision-making workflow for closed-loop reservoir management. The reservoir model is a synthetic but realistic model with oil, gas, and water. We show how to use ensemble methods in a workflow for integrated uncertainty prediction, history matching, and robust optimization. The workflow uses advanced ensemble-based history-matching techniques to update a reservoir model in the annual maturation process. After the history-matching update, an optimization process decides the best wells to drill next to gain the highest net present value. An additional robust decision step evaluates the wells over the ensemble of reservoir models to ensure they lead to a positive ensemble-averaged net present value. The approach allows for up-to-date predictions, including uncertainty estimates, leading to improved decision support for field development, well-planning, production strategies, and reservoir management.

A divide-and-conquer optimization paradigm for waterflooding production optimization

Production optimization technique, as a crucial step in the closed-loop reservoir management (CLRM), aims to achieve optimal development efficiency by adjusting development schemes (e.g., well-controls) with the aid of optimization methods. However, due to the unbearable computational burden brought by full-scale reservoir simulation, few optimizers can obtain satisfactory solution(s) within limited simulation calls, especially when the problem dimension is very high. This phenomenon is common in many real-world scenarios, which is also referred to as the “curse of dimensionality”. To address this issue, a novel divide-and-conquer (DAC) optimization paradigm is proposed for production optimization problems. Specifically, given a large-scale production optimization problem, it can be decomposed into a number of simpler subproblems with low dimensions. Then, to overcome the computationally expensive issue, multiple data-driven surrogates are built for the subproblems. Finally, all the subproblem surrogates are optimized cooperatively using a reuse strategy of subproblem samples. From the perspective of production optimization, the joint scheme optimization of the original problem is turned into cooperatively optimizing the schemes involved in multiple subproblems. Interestingly, the obtained subproblems always correspond to multiple flow units with weak flow interferences caused by some obstruction factors (e.g., low-permeability channel and vertical barrier layer). This indicates that the DAC method can not only serve as an optimization enhancement technique but also can be employed as an auxiliary means of connectivity analysis. In return, many connectivity analysis methods such as flow diagnostics that require fewer simulation calls can serve as the decomposition tool. More importantly, the superior flexibility of the proposed DAC-based expensive optimization framework allows it to incorporate a wide variety of state-of-the-art surrogate-assisted evolutionary solvers. In this paper, the differential evolution (DE) and two advanced surrogate-assisted evolutionary solvers are implemented under the proposed paradigm. The experimental results conducted on two 100-dimensional benchmark functions and two production optimization tasks verified the effectiveness of the proposed method.

Generative adversarial networks for modeling reservoirs with permeability anisotropy

The geological model is a main element in describing the characteristics of hydrocarbon reservoirs. These models are usually obtained using geostatistical modeling techniques. Recently, methods based on deep learning algorithms have begun to be applied as a generator of a geologic models. However, there are still problems with how to assimilate dynamic data to the model. The goal of this work was to develop a deep learning algorithm - generative adversarial network (GAN) and demonstrate the process of generating a synthetic geological model:• Without integrating permeability data into the model• With data assimilation of well permeability data into the modelThe authors also assessed the possibility of creating a pair of generative-adversarial network-ensemble smoother to improve the closed-loop reservoir management of oil field development.

Self-adaptive multifactorial evolutionary algorithm for multitasking production optimization

The economic and efficient development of petroleum resources can be realized by dynamically adjusting the reservoir development scheme for the sake of higher recovery efficiency with low development cost. As an important part of the closed-loop reservoir management (CLRM), production optimization has gained increasing research interests. A number of sophisticated production optimization techniques have been proposed in the recent years. It is noteworthy that almost all of these existing methods optimize multiple distinct problems independently and neglect the latent synergies among them. However, seldom real-world problems exist in isolation. A number of studies in the community of computational intelligence demonstrated that the latent similarities among multiple distinct optimization tasks can be utilized to achieve knowledge transfer and thus significantly improve the overall optimization performance. With this in mind, a novel multitasking optimization method named multifactorial evolutionary algorithm (MFEA) is introduced to solve production optimization problems in this study. Different production optimization problems are seen as multiple distinct tasks in a multi-tasking environment thus the given problems can be solved in a multi-tasking manner. To the best of our knowledge, this is the first inspirational application of knowledge transfer to reservoir production optimization. Unfortunately, without any prior knowledge about inter-task similarity, a prespecified transfer intensity parameter adopted by the MFEA can potentially lead to performance slowdowns on some unrelated problems. This phenomenon is also known as the negative transfer. To address this issue, a novel self-adaptive multifactorial evolutionary algorithm (SA-MFEA) is proposed in this study. The transfer intensity parameter is estimated online based on a novel inter-task similarity measurement mechanism. The positive transfer between the problems with high degree of relatedness can be greatly boosted by estimating a higher transfer intensity, while the negative transfer between the distinct problems with low similarity can be effectively curbed by adopting a low value of transfer intensity. At last, the efficacy of the proposed method is experimentally verified on a synthetic multitasking problem with three distinct benchmark functions and two multitasking production optimization problems with distinct component reservoir models.

Robust Multiobjective Nonlinear Constrained Optimization with Ensemble Stochastic Gradient Sequential Quadratic Programming-Filter Algorithm

Summary As the crucial step in closed-loop reservoir management, robust life-cycle production optimization is defined as maximizing/minimizing the expected value of a predefined objective (cost) function over geological uncertainties (i.e., uncertainties in the reservoir permeability, porosity, endpoint relative permeability, etc.). However, with robust optimization, there is no control over downside risk defined as the minimum net present value (NPV) among the individual NPVs of the different reservoir models. Yet, field operators generally wish to keep this minimum NPV reasonably large to try to ensure that the reservoir is commercially viable. In addition, the field operator may desire to maximize the NPV of production over a much shorter time period than the life of the reservoir under the limitation of surface facilities (e.g., field liquid and water production rates). Thus, it is important to consider multiobjective robust production optimization with nonlinear constraints and when geological uncertainties are incorporated. The three objectives considered in this paper are; to maximize the average life-cycle NPV, to maximize the average short-term NPV, and to maximize the minimum NPV of the set of realizations. Generally, these objectives are in conflict; for example, the well controls that give a global maximum for robust life-cycle production optimization do not usually correspond to the controls that maximize the short-term average NPV of production. Moreover, handling the nonlinear state constraints (e.g., field liquid production rates and field water production rates for the bottom-hole pressure controlled producers in the robust production optimization) is also a challenge because those nonlinear constraints should be satisfied at each control steps for each geological realization. To provide potential solutions to the multiobjective robust optimization problem with state constraints, we developed a modified lexicographic method with a minimizing-maximum scheme to attempt to obtain a set of Pareto optimal solutions and to satisfy all nonlinear constraints. We apply the sequential quadratic programming filter with modified stochastic gradients to solve a sequence of optimization problems, where each solution is designed to generate a single point on the Pareto front. In the modified lexicographic method, the objective is always considered to be the primary objective, and the other objectives are considered by specifying bounds on them to convert them to state constraints. The temporal damping and truncation schemes are applied to improve the quality of the stochastic gradient on nonlinear constraints, and the minimizing–maximum procedure is applied to enforce constraints on the normal state constraints. The main advantage that the modified lexicographic method has over the standard lexicographic method is that it allows for the generation of potential Pareto optimal points, which are uniformly spaced in the values of the second and/or third objective that one wishes to improve by multiobjective optimization.

About Identifiability of Oil and Water Relative Permeability Curves and Reservoir Heterogeneity through Integrated Well Test Study

Relative permeabilities (RP) play an important role in reservoir engineering. RP functions together with the permeability anisotropy coefficient predetermine waterflooding efficiency and oil/water ratio in production forecast. Traditionally multiphase flow parameters are estimated from core analysis data. But such measurements suffer from small representative elementary volume (REV) and limited characterization of reservoir properties. Therefore using core data in 3D reservoir modelling could lead to distorted description of actual flow conditions. Despite those functions (RP) could be history matched with assimilated production data, such a procedure would require long history of waterflooding. So the authors’ idea is to apply integrated well test study to estimate the displacement efficiency and/or relative permeability functions at downhole conditions. Well testing is traditionally applied in reservoir engineering for single-phase reservoir parameters estimation. Our approach is extended to multi-phase flow and is based on data collection at well bottomholes and subsequent data assimilation in flow model.In this paper we summarize both features of mathematical problem statement and identifiability of multiphase parameters through inverse problem solution, but also discuss 10+ -year experience in interpretation of two-phase well testing using our technologies. To estimate multiphase parameters, we have to jointly consider complex data of well logging and dynamic data of well testing. Both data sets are used in the inverse problem quality criteria, where the least squares method has been applied. Forward problem corresponds to a 3D multiphase fluid flow model in porous media. The latter consists of continuity equation with multiphase Darcy equation instead of moment balances. For data assimilation modern methods of optimal control theory were successfully applied. For all synthetic test cases real reservoir parameters were accurately recovered through the use of forward simulation data.In order to estimate reservoir heterogeneity, we applied a single-phase model to get the ratio of vertical to horizontal permeability. Data of well self-interference testing were used for vertical permeability estimation. Depending on the depth of reservoir pressure perturbation, reservoir properties could be properly inferred from observations. Two other options of 3D interference testing using vertical and horizontal wells are also presented.In other words, all the problems considered are identifiable, and the level of their correctness is completely predetermined by the amount and quality of observed data. And transition to digital (intelligent) oil-and-gas production and closed-loop reservoir management [1] provides a possibility to remove discussed restrictions and all inverse problems considered should be accounted as fully identifiable.

An integrated closed-loop solution to assisted history matching and field optimization with machine learning techniques

The traditional petroleum reservoir modeling workflow for reservoir characterization, history matching, and field development optimization requires a significant amount of computation during reservoir simulation and post-processing. In this work, we focus on incorporating various optimization, machine learning, and model-order reduction techniques to reduce the computational cost and build an integrated closed-loop workflow, in which the history matching and optimization procedures are carried out sequentially. The uncertainty in the predictions of petroleum reservoir behavior is addressed through multiple realizations of the petroleum reservoir system under study. The initial reservoir characterization is performed with a full physics flow simulator. Bayesian optimization (BO) is introduced for assisted history matching to find a solution reasonably fast with a small number of reservoir simulation runs. To determine the optimal field development strategy, several optimization algorithms are compared, including particle swarm optimization (PSO), genetic algorithm (GA), and a hybrid approach of these two, called genetical swarm optimization (GSO). The implementation of a proxy model for flow to replace full physics simulation effectively reduces the CPU time for the optimization tasks in the workflow. The proxy is built using machine learning algorithms applied to a set of simulation runs. In this work, proxy models built using simple multivariate regression (MVR), artificial neural network (ANN), and a decision tree-based algorithm named extreme gradient boosting (XGB) are compared. As a preprocessing step to both history matching and optimization, the parameter space for the reservoir model is reduced with Karhunen–Loève expansion (KLE) to make the size of the problem more manageable. The proposed integrated closed-loop reservoir management approach is demonstrated on a dataset representing a South Cowden reservoir in which waterflooding has been implemented.

Machine-Learning-Assisted Closed-Loop Reservoir Management Using Echo State Network for Mature Fields under Waterflood

Summary Closed-loop reservoir management (CLRM) consists of continuous application of history matching and optimization of model-predictive control to maximize production or reservoir net present value (NPV) in any given period. Traditional field-scale implementation of CLRM by using a large number of reservoir models, in particular when uncertainty is accounted for, is computationally impractical. This presented machine-learning-assisted workflow uses the echo state network (ESN) coupled with an empirical water fractional flow relationship as a proxy to replace time-consuming simulations and improve the computational efficiency of the CLRM. The ESN, under the paradigm of reservoir computing, provides a specific architecture and supervised learning principle for recurrent neural networks (RNNs). ESNs, with randomly generated and invariant input weights and recurrent weights, greatly minimize the computational load and solve potential problems during typical backpropagation through time in traditional RNNs while it still obtains the benefits of RNNs to memorize temporal dependencies. Also, the linear readout layer makes the training much faster using analytical ridge regression. Field-level well control and production-response data are fed into the workflow to obtain a trained ESN and fitted fractional-flow relationship, which will represent/reproduce the dynamics of the reservoir under various well-control scenarios. Further production optimization is directly applied to the matched models to maximize reservoir NPV. The optimized well-control scenario is applied, and further observation is obtained to update the models. History matching and production optimization are performed again in a closed-loop fashion. The previously mentioned advantages make ESN a very powerful tool for CLRM, with both history matching and production optimization quickly accomplished, and make near-real-time CLRM possible. In this paper, two case studies will be presented to prove the effectiveness of the proposed workflow.

Rapid Forecast Calibration Using Nonlinear Simulation Regression With Localization

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 193845, “Rapid Forecast Calibration Using Nonlinear Simulation Regression With Localization,” by Jincong He, SPE, Wenyue Sun, and Xian-Huan Wen, SPE, Chevron, prepared for the 2019 SPE Reservoir Simulation Conference, Galveston, Texas, 10–11 April. The paper has not been peer reviewed. The industry increasingly relies on forecasts from reservoir models for reservoir management and decision making. However, because forecasts from reservoir models carry large uncertainties, calibrating them as soon as data come in is crucial. Traditional probabilistic history matching remains time-consuming because it needs to calibrate the models before using them to update probability distributions (S-curves) of quantities of interest (QOIs). This paper presents a direct forecast method called simulation regression with localization (SRL), which is able to calibrate the forecast with observed data without calibrating the model. Introduction Production forecasts from reservoir-simulation models can be affected by the various uncertainties present in the subsurface, such as those in the geological characterization and rock and fluid properties. Calibrating uncertain QOIs, such as production-forecast or key subsurface parameters, to observation data is a crucial element in the context of closed-loop reservoir management. Traditionally, this task is accomplished by a two-step approach, as depicted in Fig. 1a. First, a probabilistic history-matching process needs to be carried out to condition the simulation models to the data. Probabilistic history matching generates an ensemble of reservoir models that characterize the posterior uncertainty given the measurement data (e.g., historical well-test and production data), as opposed to deterministic history matching, in which only one model that best matches the measurement data is generated. In the second step, reservoir simulations, subject to a given reservoir operation plan, are performed on the generated posterior samples, or models, to estimate the posterior distribution of the QOIs. There is rich literature on various probabilistic history-matching methods, and the complete paper cites and assesses several examples. However, the authors state that, although much progress has been made in probabilistic history matching, the resulting procedures still are generally time-consuming for realistic systems, and may not provide accurate sampling of posterior distribution when strong nonlinearity and non-Gaussianity exist. Proposed Work Flow The complete paper explores an alternative forecasting framework, as shown in Fig. 1b. The authors propose using SRL for direct forecasting to derive the posterior distributions for QOIs given the measurement data. As with other direct forecasting methods, the first step of SRL is to perform an ensemble of simulation runs according to the previous distributions of the uncertainties and construct a training data set for the QOIs and measurement data. Then, in SRL, a regression model is built on this training data set to estimate the mean value of the posterior distribution. Depending on the case at hand, this regression model can be as simple as a linear regression model, or as complex as a deep-learning model. The authors found that the quadratic partial least square (QPLS) regression model offers flexibility to handle a wide range of problems. However, the posterior variances of the QOIs are estimated by a localization process wherein the mismatch of the regression model for samples closed to observed data is used to estimate the posterior variance. Finally, the entire posterior distribution (in terms of the cumulative distribution function; i.e., the S-curve) can be estimated by scaling the prior S-curve with the updated mean and variance.

Technology Focus: Field Development (September 2019)

Technology Focus Field developers are making bold step changes to form their optimization strategies on the crests of digital transformation, using massive data analytics, machine learning, cloud computing, and data-sharing strategies for oil and gas fields in all stages of development. This trend will only grow, following the imperative to ensure the sustainability of new assets and extend the life of brownfields of any size.• Current trends in field development are to study, model, and understand the time-lapse effects in those fields where optimization of costs, environmental challenges, and sustainability are key differentiators. In onshore or offshore heavy-oil developments, as well as in shale oil and gas, massive data analytics and optimization techniques revolutionize work flows in field development with great force and speed. Digital oilfield frameworks, fast-track modeling, genetic algorithms, particle-swarm optimization, ensemble-based optimization, and closed-loop reservoir management are the leading best-decision loops. Operating companies of all sizes and profiles—national oil companies, large international oil companies, and small private investments—are migrating from structured, linear, and conventional approaches in field development toward more-efficient and data-driven work flows, with activities executed in parallel to benefit all fronts, and fit-for-purpose and temporary working teams. The investments of time and effort are focused to better understand and predict how to reduce or avoid the interference among child and parent wells in shale oil or to ensure the sustainable production from offshore heavy-oil developments. Field development and field-operation optimization become joint efforts as the loops of production are shorter and the data are shared among several disciplines, interconnecting and integrating their goals. The three selected papers provide an opportunity to catch up with the thrilling step-change evolution in field development. The industry continues its digital transformation, and field development is leading the•wave. Recommended additional reading at OnePetro: www.onepetro.org. SPE 191799 Time-Dependent Depletion of Parent Well and Effect on Well Spacing in the Wolfcamp Delaware Basin by•Cyrille•Defeu, Schlumberger, et al. SPE 193914 A Comprehensive Adaptive Forecasting Framework for Optimum Field-Development Planning by Amir Salehi, Quantum Reservoir Impact International, et al. IPTC 19468 Modeling Interwell Interference Caused by Complex Fracture Hits in Eagle Ford Using an Embedded Discrete Fracture Model by Mauricio Xavier Fiallos, The University of Texas at Austin, et al.

A data-space inversion procedure for well control optimization and closed-loop reservoir management

Data-space inversion (DSI) methods provide posterior (history-matched) predictions for quantities of interest, along with uncertainty quantification, without constructing posterior models. Rather, predictions are generated directly from a large set of prior model simulations and observed data. In this work, we develop a data-space inversion with variable control (DSIVC) procedure that enables forecasting with user-specified well controls in the post-history-match prediction period. In DSIVC, flow simulations on all prior realizations, with randomly sampled well controls, are first performed. User-specified controls are treated as additional observations to be matched in posterior predictions. Posterior data samples are generated using a randomized maximum likelihood procedure with a gradient-based optimizer. For prescribed post-history-match well control settings, posterior predictions can be generated in seconds or minutes. Results are presented for a channelized system, and posterior predictions from DSIVC are compared with those from the standard DSI method. Standard DSI requires prior models to be re-simulated using the specified controls, while DSIVC requires only one set of prior simulations. Substantial uncertainty reduction is achieved through data-space inversion, and reasonable agreement between DSIVC and DSI results is generally observed. DSIVC is then applied for data assimilation combined with production optimization under uncertainty, as well as for closed-loop reservoir management, which entails a sequence of data assimilation and optimization steps. Clear improvement in the objective function is attained in these examples.

Informed production optimization in hydrocarbon reservoirs

The exploitation of subsurface hydrocarbon reservoirs is achieved through the control of production and injection wells (i.e., by prescribing time-varying pressures and flow rates) to create conditions that make the hydrocarbons trapped in the pores of the rock formation flow to the surface. The design of production strategies to exploit these reservoirs in the most efficient way requires an optimization framework that reflects the nature of the operational decisions and geological uncertainties involved. This paper introduces a new approach for production optimization in the context of closed-loop reservoir management (CLRM) by considering the impact of future measurements within the optimization framework. CLRM enables instrumented oil fields to be operated more efficiently through the systematic use of life-cycle production optimization and computer-assisted history matching. Recently, we have proposed a methodology to assess the value of information (VOI) of measurements in such a CLRM approach a-priori, i.e. during the field development planning phase, to improve the planned history matching component of CLRM. The reasoning behind the a-priori VOI analysis unveils an opportunity to also improve our approach to the production optimization problem by anticipating the fact that additional information (e.g., production measurements) will become available in the future. Here, we show how the more conventional optimization approach can be combined with VOI considerations to come up with a novel workflow, which we refer to as informed production optimization. We illustrate the concept with a simple water flooding problem in a two-dimensional five-spot reservoir and the results obtained confirm that this new approach can lead to significantly better decisions in some cases.

Model-based decision analysis applied to petroleum field development and management

This work describes a new methodology for integrated decision analysis in the development and management of petroleum fields considering reservoir simulation, risk analysis, history matching, uncertainty reduction, representative models, and production strategy selection under uncertainty. Based on the concept of closed-loop reservoir management, we establish 12 steps to assist engineers in model updating and production optimization under uncertainty. The methodology is applied to UNISIM-I-D, a benchmark case based on the Namorado field in the Campos Basin, Brazil. The results show that the method is suitable for use in practical applications of complex reservoirs in different field stages (development and management). First, uncertainty is characterized in detail and then scenarios are generated using an efficient sampling technique, which reduces the number of evaluations and is suitable for use with numerical reservoir simulation. We then perform multi-objective history-matching procedures, integrating static data (geostatistical realizations generated using reservoir information) and dynamic data (well production and pressure) to reduce uncertainty and thus provide a set of matched models for production forecasts. We select a small set of Representative Models (RMs) for decision risk analysis, integrating reservoir, economic and other uncertainties to base decisions on risk-return techniques. We optimize the production strategies for (1) each individual RM to obtain different specialized solutions for field development and (2) all RMs simultaneously in a probabilistic procedure to obtain a robust strategy. While the second approach ensures the best performance under uncertainty, the first provides valuable insights for the expected value of information and flexibility analyses. Finally, we integrate reservoir and production systems to ensure realistic production forecasts. This methodology uses reservoir simulations, not proxy models, to reliably predict field performance. The proposed methodology is efficient, easy-to-use and compatible with real-time operations, even in complex cases where the computational time is restrictive.