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error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement).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.

Life cycle assessment of biofuels produced by the new integrated hydropyrolysis-hydroconversion (IH2) process

Biofuels are alternative fuels that have the promise of reducing reliance on imported fossil fuels and decreasing emission of greenhouse gases from energy consumption. This thesis analyses the environmental impacts focusing on the greenhouse gas (GHG) emissions associated with the production and delivery of biofuel using the new Integrated Hydropyrolysis and Hydroconversion (IH2) process. The IH2 process is an innovative process for the conversion of woody biomass into hydrocarbon liquid transportation fuels in the range of gasoline and diesel. A cradle-to-grave life cycle assessment (LCA) was used to calculate the greenhouse gas emissions associated with diverse feedstocks production systems and delivery to the IH2 facility plus producing and using these new renewable liquid fuels. The biomass feedstocks analyzed include algae (microalgae), bagasse from a sugar cane-producing locations such as Brazil or extreme southern US, corn stover from Midwest US locations, and forest feedstocks from a northern Wisconsin location. The life cycle greenhouse gas (GHG) emissions savings of 58%–98% were calculated for IH2 gasoline and diesel production and combustion use in vehicles compared to fossil fuels. The range of savings is due to different biomass feedstocks and transportation modes and distances. Different scenarios were conducted to understand the uncertainties in certain input data to the LCA model, particularly in the feedstock production section, the IH2 biofuel production section, and transportation sections.