Evolution of strength and physical properties of ultramafic and carbonate rocks under hydrothermal conditions

Interaction of rocks with fluids can significantly change mineral assemblage and structure. This so-called hydrothermal alteration is ubiquitous in the Earth’s crust. Though the behavior of hydrothermally altered rocks can have planet-scale consequences, such as facilitating oceanic spreading along slow ridge segments and recycling volatiles into the mantle at subduction zones, the mechanisms involved in the hydrothermal alteration are often microscopic. Fluid-rock interactions take place where the fluid and rock meet. Fluid distribution, flux rate and reactive surface area control the efficiency and extent of hydrothermal alteration. Fluid-rock interactions, such as dissolution, precipitation and fluid mediated fracture and frictional sliding lead to changes in porosity and pore structure that feed back into the hydraulic and mechanical behavior of the bulk rock. Examining the nature of this highly coupled system involves coordinating observations of the mineralogy and structure of naturally altered rocks and laboratory investigation of the fine scale mechanisms of transformation under controlled conditions. In this study, I focus on fluid-rock interactions involving two common lithologies, carbonates and ultramafics, in order to elucidate the coupling between mechanical, hydraulic and chemical processes in these rocks. I perform constant strain-rate triaxial deformation and constant-stress creep tests on several suites of samples while monitoring the evolution of sample strain, permeability and physical properties. Subsequent microstructures are analyzed using optical and scanning electron microscopy. This work yields laboratory-based constraints on the extent and mechanisms of water weakening in carbonates and carbonation reactions in ultramafic rocks. I find that inundation with pore fluid thereby reducing permeability. This effect is sensitive to pore fluid saturation with respect to calcium carbonate. Fluid inundation weakens dunites as well. The addition of carbon dioxide to pore fluid enhances compaction and partial recovery of strength compared to pure water samples. Enhanced compaction in CO2-rich fluid samples is not accompanied by enhanced permeability reduction. Analysis of sample microstructures indicates that precipitation of carbonates along fracture surfaces is responsible for the partial restrengthening and channelized dissolution of olivine is responsible for permeability maintenance.

Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework.