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Large-scale discrete fracture network (DFN) simulators are standard fare for studies involving the sub-surface transport of particles since direct observation of real world underground fracture networks is generally infeasible. While these simulators have seen numerous successes over several engineering applications, estimations on quantities of interest (QoI) - such as breakthrough time of particles reaching the edge of the system - suffer from a two distinct types of uncertainty. A run of a DFN simulator requires several parameter values to be set that dictate the placement and size of fractures, the density of fractures, and the overall permeability of the system; uncertainty on the proper parameter choices will lead to some amount of uncertainty in the QoI, called epistemic uncertainty. Furthermore, since DFN simulators rely on stochastic processes to place fractures and govern flow, understanding how this randomness affects the QoI requires several runs of the simulator at distinct random seeds. The uncertainty in the QoI attributed to different realizations (i.e. different seeds) of the same random process leads to a second type of uncertainty, called aleatoric uncertainty. In this paper, we perform a Sensitivity Analysis, which directly attributes the uncertainty observed in the QoI to the epistemic uncertainty from each input parameter and to the aleatoric uncertainty. We make several design choices to handle an observed heteroskedasticity in DFN simulators, where the aleatoric uncertainty changes for different inputs, since the quality makes several standard statistical methods inadmissible. Beyond the specific takeaways on which input variables affect uncertainty the most for DFN simulators, a major contribution of this paper is the introduction of a statistically rigorous workflow for characterizing the uncertainty in DFN flow simulations that exhibit heteroskedasticity., Comment: 23 pages, 6 figures, journal article

Modeling gas flow through fractures of subsurface rock is a particularly challenging problem because of the heterogeneous nature of the material. High-fidelity simulations using discrete fracture network (DFN) models are one methodology for predicting gas particle breakthrough times at the surface, but are computationally demanding. We propose a Bayesian machine learning method that serves as an efficient surrogate model, or emulator, for these three-dimensional DFN simulations. Our model trains on a small quantity of simulation data and, using a graph/path-based decomposition of the fracture network, rapidly predicts quantiles of the breakthrough time distribution. The approach, based on Gaussian Process Regression (GPR), outputs predictions that are within 20-30% of high-fidelity DFN simulation results. Unlike previously proposed methods, it also provides uncertainty quantification, outputting confidence intervals that are essential given the uncertainty inherent in subsurface modeling. Our trained model runs within a fraction of a second, which is considerably faster than other methods with comparable accuracy and multiple orders of magnitude faster than high-fidelity simulations.

We model flow and transport in three-dimensional fracture networks with varying degrees of fracture-to-fracture aperture/permeability heterogeneity and network density to show how changes in these properties can cause the emergence of anomalous flow and transport behavior. If fracture-to-fracture aperture heterogeneity is increased in sparse networks, velocity fluctuations can inhibit high flow rates and solute transport can be delayed, even in cases where hydraulic aperture is monotonically increased. As the density of the networks is increased, more connected pathways allow for particles to bypass these effects. We discover transition behavior where with relatively few connected pathways in a network from inflow to outflow boundaries, the first arrival times of particles are not heavily affected by fracture-to-fracture aperture heterogeneity, but the scaling behavior of the tails is strongly influenced due to the particles being forced to sample some of the heterogeneity in the velocity field caused by aperture differences. These results reinforce the importance of considering multi-scale effects in fractured systems and can inform flow and transport processes in both natural and engineered fracture systems, especially the latter where high aperture fractures are often stimulated and connect to existing fracture networks with smaller apertures.

Successful deployment of geological carbon storage (GCS) requires an extensive use of reservoir simulators for screening, ranking and optimization of storage sites. However, the time scales of GCS are such that no sufficient long-term data is available yet to validate the simulators against. As a consequence, there is currently no solid basis for assessing the quality with which the dynamics of large-scale GCS operations can be forecasted. To meet this knowledge gap, we have conducted a major GCS validation benchmark study. To achieve reasonable time scales, a laboratory-size geological storage formation was constructed (the "FluidFlower"), forming the basis for both the experimental and computational work. A validation experiment consisting of repeated GCS operations was conducted in the FluidFlower, providing what we define as the true physical dynamics for this system. Nine different research groups from around the world provided forecasts, both individually and collaboratively, based on a detailed physical and petrophysical characterization of the FluidFlower sands. The major contribution of this paper is a report and discussion of the results of the validation benchmark study, complemented by a description of the benchmarking process and the participating computational models. The forecasts from the participating groups are compared to each other and to the experimental data by means of various indicative qualitative and quantitative measures. By this, we provide a detailed assessment of the capabilities of reservoir simulators and their users to capture both the injection and post-injection dynamics of the GCS operations.

CO2 capture and storage (CCS) technology is likely to be widely deployed in coming decades in response to major climate and economics drivers: CCS is part of every clean energy pathway that limits global warming to 2C or less and receives significant CO2 tax credits in the United States. These drivers are likely to stimulate capture, transport, and storage of hundreds of millions or billions of tonnes of CO2 annually. A key part of the CCS puzzle will be identifying and characterizing suitable storage sites for vast amounts of CO2. We introduce a new software tool called SCO2T (Sequestration of CO2 Tool, pronounced "Scott") to rapidly characterizing saline storage reservoirs. The tool is designed to rapidly screen hundreds of thousands of reservoirs, perform sensitivity and uncertainty analyses, and link sequestration engineering (injection rates, reservoir capacities, plume dimensions) to sequestration economics (costs constructed from around 70 separate economic inputs). We describe the novel science developments supporting SCO2T including a new approach to estimating CO2 injection rates and CO2 plume dimensions as well as key advances linking sequestration engineering with economics. Next, we perform a sensitivity and uncertainty analysis of geology combinations (including formation depth, thickness, permeability, porosity, and temperature) to understand the impact on carbon sequestration. Through the sensitivity analysis we show that increasing depth and permeability both can lead to increased CO2 injection rates, increased storage potential, and reduced costs, while increasing porosity reduces costs without impacting the injection rate (CO2 is injected at a constant pressure in all cases) by increasing the reservoir capacity., Comment: CO2 capture and storage; carbon sequestration; reduced-order modeling; climate change; economics