With the aid of machine learning method, namely artificial neural networks, we established data-driven proxy models that could be utilized to maximize the net present value of a waterflooding process by adjusting the well control injection rates over a production period. These data-driven proxies were maneuvered on two different case studies, which included a synthetic 2D reservoir model and a 3D reservoir model (the Egg Model). Regarding the algorithms, we applied two different nature-inspired metaheuristic algorithms, i.e., particle swarm optimization and grey wolf optimization, to perform the optimization task. Pertaining to the development of the proxy models, we demonstrated that the training and blind validation results were excellent (with coefficient of determination,R²being about 0.99). For both case studies and the optimization algorithms employed, the optimization results obtained using the proxy models were all within 5% error (satisfied level of accuracy) compared with reservoir simulator. These results confirm the usefulness of the methodology in developing the proxy models. Besides that, the computational cost of optimization was significantly reduced using the proxies. This further highlights the significant benefits of employing the proxy models for practical use despite being subject to a few constraints.

Numerical reservoir simulation has been recognized as one of the most frequently used aids in reservoir management. Despite having high calculability performance, it presents an acute shortcoming, namely the long computational time induced by the complexities of reservoir models. This situation applies aptly in the modeling of fractured reservoirs because these reservoirs are strongly heterogeneous. Therefore, the domains of artificial intelligence and machine learning (ML) were used to alleviate this computational challenge by creating a new class of reservoir modeling, namely smart proxy modeling (SPM). SPM is a ML approach that requires a spatio-temporal database extracted from the numerical simulation to be built. In this study, we demonstrate the procedures of SPM based on a synthetic fractured reservoir model, which is a representation of dual-porosity dual-permeability model. The applied ML technique for SPM is artificial neural network. We then present the application of the smart proxies in production optimization to illustrate its practicality. Apart from applying the backpropagation algorithms, we implemented particle swarm optimization (PSO), which is one of the metaheuristic algorithms, to build the SPM. We also propose an additional procedure in SPM by integrating the probabilistic application to examine the overall performance of the smart proxies. In this work, we inferred that the PSO had a higher chance to improve the reliability of smart proxies with excellent training results and predictive performance compared with the considered backpropagation approaches.

Optimization studies are an important task in reservoir engineering practices such as production optimization and EOR (Enhanced Oil Recovery) assessments. However, they are extensive studies with many simulations that require huge computational effort and resources. In terms of EOR, CO₂ injection is one of the most common methods employed due to a high recovery potential and environmental benefits. To assess the feasibility of CO₂-EOR projects, a reservoir design study must be conducted before optimization is performed. Some studies have demonstrated the advantages of employing proxy models to perform this task in terms of saving huge amounts of computer memory space and time. In this study, proxy models were developed to solve a multi-objective optimization problem using NSGA-II (Non-dominated Sorting Genetic Algorithm II) in two selected reservoir models. The study was performed for a CO₂-WAG (Water Alternating Gas) application, where gas and water injection rates and half-cycle lengths were assessed to maximize the oil recovery and CO₂ stored in the reservoir. One model represents a simple geological model (the Egg Model), while the other represents a complex model (the Gullfaks Model). In this study, the good performance of the proxy models generated accurate results that could be improved by increasing the amount of sampling and segmenting the behavior of the reservoir model (depending on the complexity of the reservoir model). The developed proxies have an average error of less than 2% (compared with simulation results) and are concluded to be robust based on the blind test results. It has also been found that to reach the maximum oil recovery using CO₂-WAG, the maximum gas injection rate with the minimum water injection rate is required. However, this configuration may result in a reduction in the total CO₂ stored in the reservoir.

Machine learning-based Surrogate Reservoir Models (SRMs) can replace/augment multi-physics numerical simulations by replicating the reservoir simulation results with reduced computational effort while maintaining accuracy compared with numerical simulations. This research will demonstrate SRMs’ potential in long-term simulations and optimization of geological carbon storage in a real-world geological setting and address challenges in big data curation and model training. The present study focuses on CO₂ storage in the Smeaheia saline aquifer. Two SRMs were created using Deep Neural Networks (DNNs) to predict CO₂ saturation and pressure over all grid blocks for 50 years. 18 million samples and 31 features, including reservoir static and dynamic properties, build the input data. Models comprise 3–5 hidden layers with 128–512 units apiece. SRMs showed a runtime improvement of 300 times and an accuracy of 99% compared to the 3D numerical simulator. The genetic algorithm was then employed to determine the optimal rate and duration of CO₂ injection, which maximizes the volume of injected CO₂ while ensuring storage operations’ safety through constraints. The optimization continued for the reproduction of 100 generations, each containing 100 individuals, without any hyperparameter tuning. Finally, the optimization results confirm the significant potential of Smeaheia for storing 170 Mt CO₂.

Waterflooding is one of the methods used for increased hydrocarbon production. Waterflooding optimization can be computationally prohibitive if the reservoir model or the optimization problem is complex. Hence, proxy modeling can yield a faster solution than numerical reservoir simulation. This fast solution provides insights to better formulate field development plans. Due to technological advancements, machine learning increasingly contributes to the designing and building of proxy models. Thus, in this work, we have proposed the application of the two-stage proxy modeling, namely global and local components, to generate useful insights. We have established global proxy models and coupled them with optimization algorithms to produce a new database. In this paper, the machine learning technique used is a multilayer perceptron. The optimization algorithms comprise the Genetic Algorithm and the Particle Swarm Optimization. We then implemented the newly generated database to build local proxy models to yield solutions that are close to the “ground truth”. The results obtained demonstrate that conducting global and local proxy modeling can produce results with acceptable accuracy. For the optimized rate profiles, the R² metric overall exceeds 0.96. The range of Absolute Percentage Error of the local proxy models generally reduces to 0–3% as compared to the global proxy models which has a 0–5% error range. We achieved a reduction in computational time by six times as compared with optimization by only using a numerical reservoir simulator.