Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

Mathematical Geosciences - We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic...     

Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics

We propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a pruned DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. The method allows for the level of accuracy to be a user-controlled parameter.     

Convolution-based particle tracking method for transient flow

A convolution-based particle tracking (CBPT) method was recently developed for calculating solute concentrations (Robinson et al., Comput Geosci 14(4): 779–792, 2010). This method is highly efficient but limited to steady-state flow conditions. Here, we present an extension of this method to transient flow conditions. This extension requires a single-particle tracking process model run, with a pulse of particles introduced at a sequence of times for each source location. The number and interval of particle releases depends upon the transients in the flow. Numerical convolution of particle paths obtained at each release time and location with a time-varying source term is performed to yield the shape of the plume. Many factors controlling transport such as variation in source terms, radioactive decay, and in some cases linear processes such as sorption and diffusion into dead-end pores can be simulated in the convolution step for Monte Carlo-based analysis of transport uncertainty. We demonstrate the efficiency of the transient CBPT method, by showing that it requires fewer particles than traditional random walk particle tracking methods to achieve the same levels of accuracy, especially as the source term increases in duration or is uncertain. Since flow calculations under transient conditions are often very expensive, this is a computationally efficient yet accurate method.     

Fourier amplitude sensitivity test applied to dynamic combined finite-discrete element methods–based simulations

Fracture propagation plays a key role for a number of applications of interest to the scientific community, from dynamic fracture processes like spallation and fragmentation in metals to failure of ceramics, airplane wings, etc. Simulations of material deformation and fracture propagation rely on accurate knowledge of material characteristics such as material strength and the amount of energy being dissipated during the fracture process. Within the combined finite-discrete element method (FDEM) framework material fracture behavior is typically described through a parametrized softening curve, which defines a stress-strain relationship unique to each material. We apply the Fourier amplitude sensitivity test to explore how each of these parameters influences the simulated damage processes and to determine the key input parameters that have the most impact on the model response. We present several sensitivity numerical experiments for the simulation of a split Hopkinson pressure bar (SHPB) test for weathered granite samples using different combinations of model parameters. We validate the obtained results against SHPB experimental data. The experiments show that the model is mostly sensitive to parameters related to tensile and shear strengths, even in the presence of other parameter perturbations. The results suggest that the specification of tensile and shear strengths at the interfaces dominate the stress-time history of the FDEM simulation of SHPB test.     

A particle tracking transport method for the simulation of resident and flux-averaged concentration of solute plumes in groundwater models

A new numerical technique called the convolution-based particle tracking (CBPT) method is developed to simulate resident or flux-averaged solute concentrations in groundwater models. The method is valid for steady-state flow and linear transport processes such as sorption with a linear sorption isotherm and first-order decay. The CBPT method uses particle tracking to take advantage of the ability of particle-based approaches to maintain sharp fronts for advection-dominated transport problems common in groundwater modeling and because of the flexibility of the random walk method to simulate a wide range of possible forms of the dispersion tensor. Furthermore, the algorithm for carrying out the convolution and superposition calculation from particle tracking results is very efficient. We show that from a single particle tracking run, source term variability, sorption, and decay can all be simulated rapidly without rerunning the underlying transport model unless the flow field or dispersion parameters are changed. A series of verification simulations are presented to demonstrate the accuracy and efficiency of the CBPT method compared to more conventional particle tracking approaches.     

Correction to: Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

Mathematical Geosciences - The publication of this article unfortunately contained a mistake. The assignment to the affiliations of author Satish Karra was not correct     

Machine learning for graph-based representations of three-dimensional discrete fracture networks

Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks (Hyman et al. Comput. Geosci. 84, 10–19 2015) are designed to simulate flow and transport in such porous media. Flow and transport calculations reveal that a small backbone of fractures exists, where most flow and transport occurs. Restricting the flowing fracture network to this backbone provides a significant reduction in the network’s effective size. However, the particle-tracking simulations needed to determine this reduction are computationally intensive. Such methods may be impractical for large systems or for robust uncertainty quantification of fracture networks, where thousands of forward simulations are needed to bound system behavior. In this paper, we develop an alternative network reduction approach to characterizing transport in DFNs, by combining graph theoretical and machine learning methods. We consider a graph representation where nodes signify fractures and edges denote their intersections. Using random forest and support vector machines, we rapidly identify a subnetwork that captures the flow patterns of the full DFN, based primarily on node centrality features in the graph. Our supervised learning techniques train on particle-tracking backbone paths found by dfnWorks, but run in negligible time compared to those simulations. We find that our predictions can reduce the network to approximately 20% of its original size, while still generating breakthrough curves consistent with those of the original network.     

Coherent rainfall zones: Case study for Karnataka

Generally average rainfall over meteorological subdivisions is used for assessment of the variability of monsoon rainfall. It is shown here that variations of seasonal rainfall over the meteorological subdivisions of interior Karnataka are not coherent. A methodology for delineating coherent rainfall zones is developed in this paper and applied to derive such zones for the State of Karnataka.