The efficient operation and management of a geothermal project can be largely affected by geological, physical, operational and economic uncertainties. Systematic uncertainty quantification (UQ) involving these parameters helps to determine the probability of the focused outputs, e.g., energy production, Net Present Value (NPV), etc. However, how to efficiently assess the specific impacts of different uncertain parameters on the outputs of a geothermal project is still not clear. In this study, we performed a comprehensive UQ to a low-enthalpy geothermal reservoir using the GPU implementation of the Delft Advanced Research Terra Simulator (DARTS) framework with stochastic Monte Carlo samplings of uncertain parameters. With processing the simulation results, large uncertainties have been found in the production temperature, pressure drop, produced energy and NPV. It is also clear from the analysis that salinity influences the producing energy and NPV via changing the amount of energy carried in the fluid. Our work shows that the uncertainty in NPV is much larger than that in produced energy, as more uncertain factors were encompassed in NPV evaluation. An attempt to substitute original 3D models with upscaled 2D models in UQ demonstrates significant differences in the stochastic response of these two approaches in representation of realistic heterogeneity. The GPU version of DARTS significantly improved the simulation performance, which guarantees the full set (10,000 times) UQ with a large model (circa 3.2 million cells) finished within a day. With this study, the importance of UQ to geothermal field development is comprehensively addressed. This work provides a framework for assessing the impacts of uncertain parameters on the concerning system output of a geothermal project and will facilitate analyses with similar procedures.

@en

Simulation of heat production in high-enthalpy geothermal systems is associated with a complex physical process in which cold water invades steam-saturated control volumes. The fully implicit, fully coupled numerical strategy is commonly adopted to solve the governing system composed of mass and energy conservation equations. A conventional nonlinear solver is generally challenged by the strong nonlinearity present during phase transition because of a huge contrast of thermodynamics between hot steam and cool water. In the process of solution, due to the steam condensation, the reduction in fluid volume reduces the pressure in the control volume. This generates multiple local minima in the physical parameter space, which indicates the Newton initial guess should be carefully selected to guarantee the nonlinear convergence. Otherwise, the Newton iteration will approach a local minimum and the solution based on Newton’s update cannot converge and needs to be repeated for a smaller timestep. This problem brings simulation to the stalling behavior where a nonlinear solver wastes a lot of computations and performs at a very small timestep. To tackle this problem, we formulated continuous localization of Newton’s method based on an Operator-Based Linearization (OBL) approach. In OBL, the physical space can be parameterized in terms of operators with supporting points at different levels of resolution. During the simulation, the operator values at supporting points are obtained through reference physics and the remaining part of the space is interpolated. In this way, the nonlinear physical parameter space can be flexibly characterized with different degrees of accuracy. In our proposed approach, the nonlinear Newton iterations are performed in parameter space with different resolutions from coarse to fine. Specifically, the Newton solution under coarser resolution is taken as the initial guess for that under finer resolution. A coarser parameter space represents more linear physics, under which the nonlinear solver quickly converges to a localized solution near the true solution. With refinement in physics, the Newton iteration will approach the true solution and the stalling behaviour in the simulation is avoided. Therefore, a larger timestep can be utilized in the simulation compared with the conventional nonlinear solvers.@en

The lateral resistance of ballast bed is an important parameter to prevent track expansion and maintain track stability. The invasion of sand particles can cause the change of lateral resistance of ballast bed and affect the stability of track structure, but little attention has been paid to the change characteristics of nonlinear lateral resistance of sandy ballast bed. In this paper, the field tests on the lateral resistance of windblown sand ballast bed were carried out to establish a multiscale three-dimensional discrete element model of sleeper-ballast bed. A systematic analysis on the evolution of lateral resistance, resistance to lateral deformation, micro-contact characteristics and lateral stability of ballast bed is performed. The results show that sand intrusion can increase the lateral resistance of ballast bed, which is approximately 40 % higher than that of clean ballast bed. In nonlinear strengthening stage and yield stage, the enhancement effect of sand particles on the lateral resistance of ballast bed is relatively weaker in comparison with the linear growth stage. With the increase in sand intrusion depth, the lateral resistance and resistance work of ballast bed both gradually go up, and the contribution of ballast shoulder to lateral resistance tends to play a leading role. Sand intrusion can increase the lateral stiffness of ballast bed and reduce the elasticity of track structure. Therefore, the maintenance operation should be carried out in time for the section with severe sandstorm.

@en

Numerical simulation plays an important role for the efficient development of geothermal resources, considering all the uncertain and sensitive parameters that exist within the subsurface and during the operations. This thesis describes the numerical modeling of geothermal developments of various types and in various situations using the newly developed open-source numerical simulator, called Delft Advanced Research Terra Simulator, shortly DARTS. The main objective of this thesis is to investigate the influence of heterogeneity to geothermal developments...@en

A realistic deep low-enthalpy geothermal reservoir based on real data with high detail and complicated sedimentary structure is utilized to perform sensitivity analyses of the geological features influencing reservoir properties. We perform simulations using the Delft Advanced Research Terra Simulator (DARTS). Compelling numerical performance of DARTS makes it suitable for handling a large ensemble of models including efficient sensitivity and uncertainty analyses. The major finding is that shale facies, generally ignored in hydrocarbon reservoir simulations, can significantly extend the predictive lifetime of geothermal reservoirs exploited by deep well doublets. It is important to accurately account for the shale facies in the simulation, though with an additional computational overhead. The overburden layers can improve doublet performance, but the impact depends on reservoir heterogeneity. In addition, heterogeneity will also divert the flow path with even a minor shift in the well placement. The discharge rate, an essential parameter of geothermal operation strategy, inversely corresponds to the doublet lifetime but positively correlates with the energy production for studied parameter ranges. Low sensitivity of doublet lifetime to vertical-horizontal permeability ratio and permeability-porosity correlation is observed. All these systematic findings for a realistic geothermal field with characterization at unprecedented level of detail can help to provide a general guideline for forward simulation and farther improve the profitability of geothermal energy production in realistic deep geothermal reservoirs through computer-assisted modeling and optimization.

@en

Alternative to CPU computing architectures, such as GPU, continue to evolve increasing the gap in peak memory bandwidth achievable on a conventional workstation or laptop. Such architectures are attractive for reservoir simulation, which performance is generally bounded by system memory bandwidth. However, to harvest the benefit of a new architecture, the source code must be inevitably rewritten, sometimes almost completely. One of the biggest challenges here is to refactor the Jacobian assembly which typically involves large volumes of code and complex data processing. We demonstrate an effective and general way to simplify the linearization stage extracting complex physics-related computations from the main simulation loop and leaving only an algebraic multi-linear interpolation kernel instead. In this work, we provide the detailed description of simulation performance benefits from execution of the entire nonlinear loop on the GPU platform. We evaluate the computational performance of Delft Advanced Research Terra Simulator (DARTS) for various energy transition subsurface applications of practical interest on both CPU and GPU platforms, comparing particular workflow phases including Jacobian assembly and linear system solution with both stages of the Constraint Pressure Residual preconditioner.

@en

Multiphase mass and heat transfer are ubiquitous in the subsurface within manifold applications. The presence of fractures over several scales and complex geometry magnifies the uncertainty of the heat transfer phenomena, which will significantly impact, or even dominate, the dynamic transport process. Capturing the details of fluid and heat transport within the fractured system is beneficial to the subsurface operations. However, accurate modeling methodologies for thermal high-enthalpy multiphase flow within fractured reservoirs are quite limited. In this work, multiphase flow in fractured geothermal reservoirs is numerically investigated. A discrete-fracture model is utilized to describe the fractured system. To characterize the thermal transport process accurately and efficiently, the resolution of discretization is necessarily optimized. A synthetic fracture model is firstly selected to run on different levels of discretization with different initial thermodynamic conditions. A comprehensive analysis is conducted to compare the convergence and computational efficiency of simulations. The numerical scheme is implemented within the Delft Advanced Research Terra Simulator (DARTS), which can provide fast and robust simulation to energy applications in the subsurface. Based on the converged numerical solutions, a thermal Péclet number is defined to characterize the interplay between thermal convection and conduction, which are the two governing mechanisms in geothermal development. Different heat transfer stages are recognized on the Péclet curve in conjunction with production regimes of the synthetic fractured reservoir. A fracture network, sketched and scaled up from a digital map of a realistic outcrop, is then utilized to perform a sensitivity analysis of the key parameters influencing the heat and mass transfer. Thermal propagation and Péclet number are found to be sensitive to flow rate and thermal parameters (e.g., rock heat conductivity and heat capacity). This paper presents a numerical simulation framework for fractured geothermal reservoirs, which provides the necessary procedures for practical investigations regarding geothermal developments with uncertainties.

@en

Accurate prediction of temperature and pressure distribution is essential for geothermal reservoir exploitation with cold water re-injection. Depending on our knowledge about the heterogeneous structure of the subsurface, the reservoir development scheme can be optimized and the overall lifetime of the geothermal field can be extended. In this study, we present Delft Advanced Research Terra Simulator (DARTS), which provides fast and accurate energy production evaluation for geothermal applications. This simulation framework is suitable for uncertainty analysis with a large ensemble of models. In DARTS, we select the molar formulation with pressure and enthalpy as primary variables. Besides, the fully-coupled fully-implicit two-point flux approximation on unstructured grids is implemented to solve the mass and energy conservation equations. For the nonlinear solution, we employ the recently developed Operator-Based Linearization (OBL) approach. In our work, DARTS is compared with the state-of-the-art simulation frameworks using a set of benchmark tests. We demonstrate that DARTS achieves a good match for both low- and high-enthalpy conditions in comparison to other simulators. At the same time, DARTS provides high performance and flexibility of the code due to the OBL approach, which makes it particularly useful for uncertainty quantification in processes involving complex physics.

@en

The efficient development of a geothermal field can be largely affected by the inherent geological and physical uncertainties. Besides, the uncertain operational and economic parameters can also impact the profit of a project. Systematic uncertainty quantification involving these parameters helps to determine the probability of concerning outputs. In this study, a low-enthalpy geothermal reservoir with strong heterogeneity, located in the West Netherlands Basin, is selected as the research area. Detailed geological model is constructed based on various static data including seismic and log interpretation. However, significant uncertainties still exist in definition of the model parameters, mainly reservoir permeability and porosity. Besides, the fluid properties have not been sampled in this field and can vary in the range between brackish to highly saline water. Also, the heat price and operational investment fluctuate with time and add up to uncertainty. Taking all interested parameters into consideration, the Monte Carlo method is utilized to select specific input data set. The forward simulations are powered by the GPU version of Delft Advance Research Terra Simulator (DARTS), which provides efficient simulation capabilities for geothermal applications. Through this investigation, a wide range of production temperature has been observed due to the uncertainty of the input parameters.@en

To assess the influences of various parameters in ultra deep (>4km), high temperature, fractured geothermal systems, the system's NPV was evaluated as these parameters were varied. The examined fracture network had multiple fractures leading between the wells in a single doublet. The tested input parameters concern rock matrix parameters (permeability, porosity, thermal conductivity and heat capacity), apertures in the fracture network and cold-water injection rates. After simulation of flow, the resulting data has been used for the calculation of NPV, which provided an indication for the performance. Larger values for matrix parameters and higher fracture apertures amplified each other's positive effect they had on the NPV of the system, as they both prevented bottlenecked flow of injected water from injector to producer wells and kept the system lifetime longer by allowing injected water more time to absorb heat before reaching the production well. An optimum exists when selecting injection rate with regards to system NPV. Lower injection rates lead to lower energy production, while higher injection rates lead to shorter lifetimes. A balanced injection rate lead to a maximum NPV. More investigation into optimization of injection rate over system lifetime will prove valuable for maximizing performance.@en