In order to maximize the profits from oil recovery, an optimal control approach for reservoir production working systems using gradient-based method is considered in the paper. It regards reservoir as a large-scale complex dynamic system. On the basis of flow dynamics, reservoir numerical simulation and optimal control theories, the optimization mathematical model of production working system is established. The optimal objective is to maximize net present value or accumulative oil production. Using the algorithm presented to solve the optimal control problem, gradients of real-time control parameters are obtained. And then optimal control settings of each control step can be determined. Finally, a simulation example is employed to verify the validity of the proposed control algorithm.
To assess whether a development strategy will be profitable enough, production forecasting is a crucial and difficult step in the process. The development history of other reservoirs in the same class tends to be studied to make predictions accurate. However, the permeability field, well patterns, and development regime must all be similar for two reservoirs to be considered in the same class. This results in very few available experiences from other reservoirs even though there is a lot of historical information on numerous reservoirs because it is difficult to find such similar reservoirs. This paper proposes a learn-to-learn method, which can better utilize a vast amount of historical data from various reservoirs. Intuitively, the proposed method first learns how to learn samples before directly learning rules in samples. Technically, by utilizing gradients from networks with independent parameters and copied structure in each class of reservoirs, the proposed network obtains the optimal shared initial parameters which are regarded as transferable information across different classes. Based on that, the network is able to predict future production indices for the target reservoir by only training with very limited samples collected from reservoirs in the same class. Two cases further demonstrate its superiority in accuracy to other widely-used network methods.
History matching, which aims to calibrate uncertain parameters of the reservoir model by matching the simulation with the observation, plays a key role in reservoir development and management. It needs to be repeated during the life of the reservoir to provide a real-time and reliable model. Traditional methods take it as independent problems and optimize parameters from scratch in each stage, without fully utilizing common knowledge or experience among stages. In this work, a surrogate-assisted reinforcement learning algorithm is proposed to learn a reusable policy for different stages in history matching. This kind of policy can retain useful knowledge of previous stages, provide better initial solutions for the new stage, and enhance the convergence of history matching. With the deep-learning-based surrogate model, the sample complexity of reinforcement learning can be alleviated efficiently and then the application to large-scale problems becomes possible. Specifically, Principle component analysis (PCA) is used to map uncertain parameters into low-dimensional latent variables. Then, the surrogate model, projecting latent variables to the simulated data of wells, replaces the time-consuming simulation. Finally, an entropy-based reinforcement learning algorithm, Soft Actor-Critic (SAC), is integrated with the surrogate model to automatically adjust uncertain parameters in history matching. The proposed approach is verified on a synthetic 2D reservoir model with 3600 uncertain parameters and a complex 3D reservoir model with 24000 uncertain parameters. The computational cost for the two cases is less than 1100 reservoir simulations. The results demonstrate that the proposed approach can be applied to the history matching of large-scale reservoirs and the obtained policy can be reused in different stages, which is helpful for the entire life-cycle of history matching.
In practical development of unconventional reservoirs, fracture networks are a highly conductive transport media for subsurface fluid flow. Therefore, it is crucial to clearly determine the fracture properties used in production forecast. However, it is different to calibrate the properties of fracture networks because it is an inverse problem with multi-patterns and high-complexity of fracture distribution and inherent defect of multiplicity of solution. In this paper, in order to solve the problem, the complex fracture model is divided into two sub-systems, namely "Pattern A" and "Pattern B." In addition, the generation method is grouped into two categories. Firstly, we construct each sub-system based on the probability density function of the fracture properties. Secondly, we recombine the sub-systems into an integral complex fracture system. Based on the generation mechanism, the estimation of the complex fracture from dynamic performance and observation data can be solved as an inverse problem. In this study, the Bayesian formulation is used to quantify the uncertainty of fracture properties. To minimize observation data misfit immediately as it occurs, we optimize the updated properties by a simultaneous perturbation stochastic algorithm which requires only two measurements of the loss function. In numerical experiments, we firstly visualize that small-scale fractures significantly contribute to the flow simulation. Then, we demonstrate the suitability and effectiveness of the Bayesian formulation for calibrating the complex fracture model in the following simulation.
The stimulated reservoir volume (SRV) technology extends conventional fracturing technology. Understanding how to effectively and accurately determine modified fracture shape and volume is the key point to evaluating the stimulation effect. Using electromagnetic detection technology can provide a new option for measuring these parameters. By the finite method, the rationality of electromagnetic detection technology to obtain the relevant parameters of reconstruction fracture is testified through forward simulation. This study compared the signals of fractures with different conductivity, volume, and shape collected by electromagnetic detection tool, and the results show that the signals have a specific correspondence with fracture geometric parameters. According to the electromagnetic signal curve of the forward model, the description of propped fractures, including positions and sizes, can be realized.
In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method), for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model's parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively 'important' elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient.
In the production of the sucker rod well, the dynamic liquid level is important for the production efficiency and safety in the lifting process. It is influenced by multi-source data which need to be combined for the dynamic liquid level real-time calculation. In this paper, the multi-source data are regarded as the different views including the load of the sucker rod and liquid in the wellbore, the image of the dynamometer card and production dynamics parameters. These views can be fused by the multi-branch neural network with special fusion layer. With this method, the features of different views can be extracted by considering the difference of the modality and physical meaning between them. Then, the extraction results which are selected by multinomial sampling can be the input of the fusion layer. During the fusion process, the availability under different views determines whether the views are fused in the fusion layer or not. In this way, not only the correlation between the views can be considered, but also the missing data can be processed automatically. The results have shown that the load and production features fusion (the method proposed in this paper) performs best with the lowest mean absolute error (MAE) 39.63 m, followed by the features concatenation with MAE 42.47 m. They both performed better than only a single view and the lower MAE of the features fusion indicates that its generalization ability is stronger. In contrast, the image feature as a single view contributes little to the accuracy improvement after fused with other views with the highest MAE. When there is data missing in some view, compared with the features concatenation, the multi-view features fusion will not result in the unavailability of a large number of samples. When the missing rate is 10%, 30%, 50% and 80%, the method proposed in this paper can reduce MAE by 5.8, 7, 9.3 and 20.3 m respectively. In general, the multi-view features fusion method proposed in this paper can improve the accuracy obviously and process the missing data effectively, which helps provide technical support for real-time monitoring of the dynamic liquid level in oil fields.
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