Upscaling of geothermal properties is necessary given the computational cost of numerical simulations. Nevertheless, accurate upscaling of thermo-physical properties of layers combined in simulation grid blocks has been a long-standing challenge. In stratified porous media, non-uniform velocity between layers combined with transverse thermal conduction across layers causes spreading of the thermal front: thermal Taylor dispersion. Neither effect of heterogeneity is accounted for in conventional upscaling. Based on thermal Taylor dispersion, we develop a new upscaling technique for simulation of geothermal processes in stratified formations. In particular, we derive a model for effective longitudinal thermal diffusivity in the direction of flow, α_eff, to represent this phenomenon in two-layer media. α_eff, accounting for differences in velocity and transverse thermal conduction, is much greater than the thermal diffusivity of the rock itself, leading to a remarkably larger effective dispersion. We define a dimensionless number, N_TC, a ratio of times for longitudinal convection to transverse conduction, as an indicator transverse thermal equilibration of the system during cold-water injection. Both N_TC and α_eff equations are verified by a match to numerical solutions for convection/conduction in two-layer systems. We find that for N_TC > 5, thermal dispersion in the system behaves as a single layer with α_eff This suggests a two-layer medium satisfying N_TC > 5 can be combined into a single layer with an effective longitudinal thermal diffusivity α_eff. Compared with conventional approaches by averaging, the α_eff model provides more accurate upscaling of thermal diffusivity and thus more-accurate prediction of cooling-front breakthrough. In stratified geothermal reservoirs with a sequence of layers, upscaling can be conducted in stages, e.g. combining two layers satisfying the N_TC criterion in each stage. The application of the new technique to upscaling geothermal well-log data will be presented in a companion paper.

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.

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.

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.

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.

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.

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.

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.

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.