Daniel O'Malley

Where Does Water Go During Hydraulic Fracturing

During hydraulic fracturing millions of gallons of water are typically injected at high pressure into deep shale formations. This water can be housed in fractures, within the shale matrix, and can potentially migrate beyond the shale formation via fractures and/or faults raising environmental concerns. We describe a generic framework for producing estimates of the volume available in fractures and undamaged shale matrix where water injected into a representative shale site could reside during hydraulic fracturing, and apply it to a representative site that incorporates available field data. The amount of water that can be stored in the fractures is estimated by calculating the volume of all the fractures associated with a discrete fracture network (DFN) based on real data and using probability theory to estimate the volume of smaller fractures that are below the lower cutoff for the fracture radius in the DFN. The amount of water stored in the matrix is estimated utilizing two distinct methods-one using a two-phase model at the pore-scale and the other using a single-phase model at the continuum scale. Based on these calculations, it appears that most of the water resides in the matrix with a lesser amount in the fractures.

Push-pull tracer tests: Their information content and use for characterizing non-Fickian, mobile-immobile behavior: INFORMATION CONTENT OF PUSH-PULL TESTS

Path reversibility and radial symmetry are often assumed in push-pull tracer test analysis. In reality, heterogeneous flow fields mean that both assumptions are idealizations. To understand their impact, we perform a parametric study which quantifies the scattering effects of ambient flow, local-scale dispersion and velocity field heterogeneity on push-pull breakthrough curves and compares them to the effects of mobile-immobile mass transfer (MIMT) processes including sorption and diffusion into secondary porosity. We identify specific circumstances in which MIMT overwhelmingly determines the breakthrough curve, which may then be considered uninformative about drift and local-scale dispersion. Assuming path reversibility, we develop a continuous time random walk-based interpretation framework which is flow-field agnostic and well suited to quantifying MIMT. Adopting this perspective, we show that the radial flow assumption is often harmless: to the extent that solute paths are reversible, the breakthrough curve is uninformative about velocity field heterogeneity. Our interpretation method determines a mapping function (i.e. subordinator) from travel time in the absence of MIMT to travel time in its presence. A mathematical theory allowing this function to be directly “plugged into” an existing Laplace-domain transport model to incorporate MIMT is presented and demonstrated. Algorithms implementing the calibration are presented and applied to interpretation of data from a push-pull test performed in a heterogeneous environment. A successful four-parameter fit is obtained, of comparable fidelity to one obtained using a million-node 3D numerical model. Finally, we demonstrate analytically and numerically how push-pull tests quantifying MIMT are sensitive to remobilization, but not immobilization, kinetics. This article is protected by copyright. All rights reserved.

Large‐scale inverse model analyses employing fast randomized data reduction

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally-efficient technique for solving inverse problems with a large number of observations (e.g. on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called “sketching” matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

ToQ.jl: A high-level programming language for D-Wave machines based on Julia

Quantum computers are becoming more widely available, so it is important to develop tools that enable people to easily program these computers to solve complex problems. To address this issue, we present the design and two applications of ToQ.jl, a high-level programming language for D-Wave quantum annealing machines. ToQ.jl leverages the metaprogramming facilities in Julia (a high-level, high-performance programming language for technical computing) and uses D-Waves ToQ programming language as an intermediate representation. This makes it possible for a programmer to leverage all the capabilities of Julia, and the D-Wave machine is used as a co-processor. We demonstrate ToQ.jl via two applications: (1) a pedagogical example based on a map-coloring problem and (2) a linear least squares problem. We also discuss our experience using ToQ.jl with a D-Wave 2X, particularly with respect to a linear least squares problem which is of broad interest to the scientific computing community.

Bayesian-information-gap decision theory with an application to CO2 sequestration

Decisions related to subsurface engineering problems such as groundwater management, fossil fuel production, and geologic carbon sequestration are frequently challenging because of an overabundance of uncertainties (related to conceptualizations, parameters, observations, etc.). Because of the importance of these problems to agriculture, energy, and the climate (respectively), good decisions that are scientifically defensible must be made despite the uncertainties. We describe a general approach to making decisions for challenging problems such as these in the presence of severe uncertainties that combines probabilistic and non-probabilistic methods. The approach uses Bayesian sampling to assess parametric uncertainty and Information-Gap Decision Theory (IGDT) to address model inadequacy. The combined approach also resolves an issue that frequently arises when applying Bayesian methods to real-world engineering problems related to the enumeration of possible outcomes. In the case of zero non-probabilistic uncertainty, the method reduces to a Bayesian method. Lastly, to illustrate the approach, we apply it to a site-selection decision for geologic CO2 sequestration.

Learning on Graphs for Predictions of Fracture Propagation, Flow and Transport

Microstructural information plays a key role in governing the dominant physics for various applications involving fracture networks. Resolving the interactions of thousands of interconnected sub-micron scale fractures is computationally intensive, and is intractable with current technologies. Coarsening of the domain and simplification of the physics are two commonly used workarounds, but these methods often eliminate features critical to accurately predicting macroscale behavior. Additionally, traditional Uncertainty Quantification (UQ) methods which account for parametric and model uncertainties have been shown to be inadequate in failure predictions that do not include these subgrid scale effects. We propose to overcome this hurdle by exploiting the fact that fracture networks have an underlying discrete structure that can be compactly represented and propagated via graphs. We have outlined two separate approaches for two separate applications -- prediction of flow in the subsurface and brittle failure at the macroscale. In the first approach, we expect to discover accurate graph representations of previously neglected microscale physics. An alternate approach would be using machine learning algorithms to mimic the detailed physics at the microscale. The resulting workflow using either approach will be memory/computationally efficient by at least one to two orders of magnitude over existing methods.

Robust decision analysis for environmental management of groundwater contamination sites

In contrast to many other engineering fields, the uncertainties in subsurface processes (e.g., fluid flow and contaminant transport in aquifers) and their parameters are notoriously difficult to observe, measure, and characterize. This causes severe uncertainties that need to be addressed in any decision analysis related to optimal management and remediation of groundwater contamination sites. Furthermore, decision analyses typically rely heavily on complex data analyses and/or model predictions, which are often poorly constrained as well. Recently, we have developed a model-driven decisionsupport framework (called MADS; http://mads.lanl.gov) for the management and remediation of subsurface contamination sites in which severe uncertainties and complex physics-based models are coupled to perform scientifically defensible decision analyses. The decision analyses are based on Information Gap Decision Theory (IGDT). We demonstrate the MADS capabilities by solving a decision problem related to optimal monitoring network design.