Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Comparing remote sensing and ground-based methods of quantifying cover type and carbon storage in an urban forest

Understanding the canopy cover of an urban environment leads to better estimates of carbon storage and more informed management decisions by urban foresters. The most commonly used method for assessing urban forest cover type extent is ground surveys, which can be both timeconsuming and expensive. The analysis of aerial photos is an alternative method that is faster, cheaper, and can cover a larger number of sites, but may be less accurate. The objectives of this paper were (1) to compare three methods of cover type assessment for Los Angeles, CA: handdelineation of aerial photos in ArcMap, supervised classification of aerial photos in ERDAS Imagine, and ground-collected data using the Urban Forest Effects (UFORE) model protocol; (2) to determine how well remote sensing methods estimate carbon storage as predicted by the UFORE model; and (3) to explore the influence of tree diameter and tree density on carbon storage estimates. Four major cover types (bare ground, fine vegetation, coarse vegetation, and impervious surfaces) were determined from 348 plots (0.039 ha each) randomly stratified according to land-use. Hand-delineation was better than supervised classification at predicting ground-based measurements of cover type and UFORE model-predicted carbon storage. Most error in supervised classification resulted from shadow, which was interpreted as unknown cover type. Neither tree diameter or tree density per plot significantly affected the relationship between carbon storage and canopy cover. The efficiency of remote sensing rather than in situ data collection allows urban forest managers the ability to quickly assess a city and plan accordingly while also preserving their often-limited budget.

Approach to carbon dioxide capture and storage at ambient conditions

Carbon dioxide (CO2) capture and storage experiments were conducted at ambient conditions in varying weight % sodium carbonate (Na2CO3) solutions. Experiments were conducted to determine the optimal amount of Na2CO3 in solution for CO2 absorption. It was concluded that a 2% Na2CO3 solution, by weight, was the most efficient solution. The 2% Na2CO3 solution is able to absorb 0.5 g CO2/g Na2CO3. These results led to studies to determine how the gas bubble size affected carbon dioxide absorption in the solution. Studies were conducted using ASTM porosity gas diffusers to vary the bubble size. Gas diffusers with porosities of fine, medium, and extra coarse were used. Results found that the medium porosity gas diffuser was the most efficient at absorbing CO2 at 50%. Variation in the bubble size concluded that absorption of carbon dioxide into the sodium carbonate solution does depend on the bubble size, thus is mass transfer limited. Once the capture stage was optimized (amount of Na2CO3 in solution and bubble size), the next step was to determine if carbon dioxide could be stored as a calcium carbonate mineral using calcium rich industrial waste and if the sodium carbonate solution could be simultaneously regenerated. Studies of CO2 sequestration at ambient conditions have shown that it is possible to permanently sequester CO2 in the form of calcium carbonate using a calcium rich industrial waste. Studies have also shown that it is possible to regenerate a fraction of the sodium carbonate solution.

Parameter identification of a copper-zeolite SCR catalyst model using reactor data

The selective catalytic reduction system is a well established technology for NOx emissions control in diesel engines. A one dimensional, single channel selective catalytic reduction (SCR) model was previously developed using Oak Ridge National Laboratory (ORNL) generated reactor data for an iron-zeolite catalyst system. Calibration of this model to fit the experimental reactor data collected at ORNL for a copper-zeolite SCR catalyst is presented. Initially a test protocol was developed in order to investigate the different phenomena responsible for the SCR system response. A SCR model with two distinct types of storage sites was used. The calibration process was started with storage capacity calculations for the catalyst sample. Then the chemical kinetics occurring at each segment of the protocol was investigated. The reactions included in this model were adsorption, desorption, standard SCR, fast SCR, slow SCR, NH3 Oxidation, NO oxidation and N2O formation. The reaction rates were identified for each temperature using a time domain optimization approach. Assuming an Arrhenius form of the reaction rates, activation energies and pre-exponential parameters were fit to the reaction rates. The results indicate that the Arrhenius form is appropriate and the reaction scheme used allows the model to fit to the experimental data and also for use in real world engine studies.

A Novel Approach to Carbon Dioxide Capture and Storage

The novel approach to carbon capture and storage (CCS) described in this dissertation is a significant departure from the conventional approach to CCS. The novel approach uses a sodium carbonate solution to first capture CO2 from post combustion flue gas streams. The captured CO2 is then reacted with an alkaline industrial waste material, at ambient conditions, to regenerate the carbonate solution and permanently store the CO2 in the form of an added value carbonate mineral. Conventional CCS makes use of a hazardous amine solution for CO2 capture, a costly thermal regeneration stage, and the underground storage of supercritical CO2. The objective of the present dissertation was to examine each individual stage (capture and storage) of the proposed approach to CCS. Study of the capture stage found that a 2% w/w sodium carbonate solution was optimal for CO2 absorption in the present system. The 2% solution yielded the best tradeoff between the CO2 absorption rate and the CO2 absorption capacity of the solutions tested. Examination of CO2 absorption in the presence of flue gas impurities (NOx and SOx) found that carbonate solutions possess a significant advantage over amine solutions, that they could be used for multi-pollutant capture. All the NOx and SOx fed to the carbonate solution was able to be captured. Optimization studies found that it was possible to increase the absorption rate of CO2 into the carbonate solution by adding a surfactant to the solution to chemically alter the gas bubble size. The absorption rate of CO2 was increased by as much as 14%. Three coal combustion fly ash materials were chosen as the alkaline industrial waste materials to study the storage CO2 and regeneration the absorbent. X-ray diffraction analysis on reacted fly ash samples confirmed that the captured CO2 reacts with the fly ash materials to form a carbonate mineral, specifically calcite. Studies found that after a five day reaction time, 75% utilization of the waste material for CO2 storage could be achieved, while regenerating the absorbent. The regenerated absorbent exhibited a nearly identical CO2 absorption capacity and CO2 absorption rate as a fresh Na2CO3 solution.