No abstract

No abstract

No abstract

This paper briefly introduces the current state in computer modelling of geothermal reservoir system and then focuses on our research efforts in high performance simulation of enhanced geothermal reservoir system. A novel supercomputer simulation tool has been developing towards simulating the highly non-linear coupled geomechanical-fluid flow-thermal systems involving heterogeneously fractured geomaterials at different spatial and temporal scales. It is applied here to simulate and visualise the enhanced geothermal system (EGS), such as (1) visualisation of the microseismic events to monitor and determine where/how the underground rupture proceeds during a hydraulic stimulation, to generate the mesh using the recorded data for determining the domain of the ruptured zone and to evaluate the material parameters (i.e., the permeability) for the further numerical analysis and evaluation of the enhanced geothermal reservoir; (2) converting the available fractured rock image/fracture data as well as the reservoir geological geometry to suitable meshes/grids and further simulating the fluid flow in the complicated fractures involving the detailed description of fracture dimension and geometry by the lattice Boltzmann method and/or finite element method; (3) interacting fault system simulation to determine the relevant complicated rupture process for evaluating the geological setting and the in-situ reservoir properties; (4) coupled thermo-fluid flow analysis of a geothermal reservoir system for an optimised geothermal reservoir design and management. A few of application examples are presented to show its usefulness in simulating the enhanced geothermal reservoir system. KEY WORDS: numerical simulation, geothermal, EGS, microseismicity, finite element method, lattice Boltzmann method. INTRODUCTIONOver the past 30 years, a large amount of research and field testing on engineered geothermal system (EGS), also known as hot dry rock (HDR) and hot fractured rock (HFR) geothermal reservoirs, have been accomplished worldwide which include the reservoir construction, fluid circulation and heat extraction (e.g., Tester et al., 2006). A successful EGS reservoir depends on thermal-fluid flow at any given time which primarily determined by its mean temperature and pressure, the nature of the interconnected network of hydraulic stimulated joints and open fractures (including both stimulated and natural), the cumulative amount of fluid circulation (reservoir cooling) that has occurred and water loss (Rybach, 2010; Brown et al., 1999). The reservoir characteristics are complicated and functions of the applied reservoir pressure/stress that are controlling the nature and degree of interconnection within the network of fractures, therefore it is crucial to have good measures and understanding of such reservoir characteristics (i.e., permeability)

For the optimal design of electromagnetic components, surrogate model methods can usually be used, but obtaining labeled training samples from full-wave electromagnetic simulation software is most time-consuming. How to use relatively few labeled samples to obtain a relatively high-precision surrogate model is the current electromagnetic research hotspot. This paper proposes a semi-supervised co-training algorithm based on Gaussian process (GP) and support vector machine (SVM). By using a small number of initial training samples, the initial GP model and initial SVM model can be trained by some basic parameter settings. Moreover, the accuracy of these two models can be improved by using the differences between these two models and combining with unlabeled samples for jointly training. In the co-training process, to ensure the performance of the proposed algorithm, a stop criterion set in advance to control the number of unlabeled samples introduced. Therefore, the accuracy of the model can be prevented from being reduced by introducing too much unlabeled samples, which can find the best solution in the limited time. The proposed co-training algorithm is evaluated by benchmark functions, optimal design of Yagi microstrip antenna (MSA) and GPS Beidou dual-mode MSA. The results show that the proposed algorithm fits the benchmark functions well. For the problem of resonant frequency modeling of the above two different MSAs, under the condition of using the same labeled samples, the predictive ability of the proposed algorithm is improved compared with the traditional supervised learning method. Moreover, for the groups of antenna sizes that meet the design requirements, the fitting effects of their return loss curve (S 11) are well. The effectiveness of the proposed co-training algorithm has been well verified, which can be used to replace the time-consuming electromagnetic simulation software for prediction. INDEX TERMS Semi-supervised learning (SSL), Gaussian process (GP), support vector machine (SVM), co-training, antenna optimization.

For the optimal design of electromagnetic devices, it is the most time consuming to obtain the training samples from full wave electromagnetic simulation software, including HFSS, CST, and IE3D. Traditional machine learning methods usually use only labeled samples or unlabeled samples, but in practical problems, labeled samples and unlabeled samples coexist, and the acquisition cost of labeled samples is relatively high. This paper proposes a semisupervised learning Gaussian Process (GP), which combines unlabeled samples to improve the accuracy of the GP model and reduce the number of labeled training samples required. The proposed GP model consists two parts: initial training and self-training. In the process of initial training, a small number of labeled samples obtained by full wave electromagnetic simulation are used for training the initial GP model. Afterwards, the trained GP model is copied to another GP model in the process of self-training, and then the two GP models will update after crosstraining with different unlabeled samples. Using the same test samples for testing and updating, a model with a smaller error will replace another. Repeat the self-training process until a predefined stopping criterion is met. Four different benchmark functions and resonant frequency modeling problems of three different microstrip antennas are used to evaluate the effectiveness of the GP model. The results show that the proposed GP model has a good fitting effectiveness on benchmark functions. For microstrip antennas resonant frequency modeling problems, in the case of using the same labeled samples, its predictive ability is better than that of the traditional supervised GP model.

Gaussian process (GP) is a rapidly developing supervised machine learning (ML) method in recent years, which has been widely used in the establishment of surrogate models in the field of electromagnetics. However, it has the problems of large sample demand, high computational complexity and low accuracy when processing high dimensional data. To solve this problem, a manifold Gaussian process (MGP) ML method based on differential evolution (DE) algorithm is proposed in this study. For the proposed method, the DE algorithm is used to get dimension reduction parameters, and the method can work very well with the optimized parameters. Compared with the traditional GP model, the dimensionality reduction method based on Isomap is adopted to simplify the mapping relationship between data pairs. Therefore, the model is more suitable for the problem of insufficient samples and high data dimension. In this study, the proposed DE-based MGP (DE-MGP) is applied to the extraction of coupling coefficients of the fourth-order and sixth-order coupling filters, in which the test error of the fourth-order coupling filter surrogate model can be reduced to 0.84%, and the test error of the sixth-order coupling filter is expected to be reduced to 1.53%, which proves that the proposed method is very effective.

No abstract