Estimation of the flammability zone boundaries with thermodynamic and empirical equations

The flammability zone boundaries are very important properties to prevent explosions in the process industries. Within the boundaries, a flame or explosion can occur so it is important to understand these boundaries to prevent fires and explosions. Very little work has been reported in the literature to model the flammability zone boundaries. Two boundaries are defined and studied: the upper flammability zone boundary and the lower flammability zone boundary. Three methods are presented to predict the upper and lower flammability zone boundaries: The linear model The extended linear model, and An empirical model The linear model is a thermodynamic model that uses the upper flammability limit (UFL) and lower flammability limit (LFL) to calculate two adiabatic flame temperatures. When the proper assumptions are applied, the linear model can be reduced to the well-known equation yLOC = zyLFL for estimation of the limiting oxygen concentration. The extended linear model attempts to account for the changes in the reactions along the UFL boundary. Finally, the empirical method fits the boundaries with linear equations between the UFL or LFL and the intercept with the oxygen axis. xx Comparison of the models to experimental data of the flammability zone shows that the best model for estimating the flammability zone boundaries is the empirical method. It is shown that is fits the limiting oxygen concentration (LOC), upper oxygen limit (UOL), and the lower oxygen limit (LOL) quite well. The regression coefficient values for the fits to the LOC, UOL, and LOL are 0.672, 0.968, and 0.959, respectively. This is better than the fit of the "zyLFL" method for the LOC in which the regression coefficient’s value is 0.416.

Critical evaluation of diameter increment modelling in the Great Lakes region

Simulations of forest stand dynamics in a modelling framework including Forest Vegetation Simulator (FVS) are diameter driven, thus the diameter or basal area increment model needs a special attention. This dissertation critically evaluates diameter or basal area increment models and modelling approaches in the context of the Great Lakes region of the United States and Canada. A set of related studies are presented that critically evaluate the sub-model for change in individual tree basal diameter used in the Forest Vegetation Simulator (FVS), a dominant forestry model in the Great Lakes region. Various historical implementations of the STEMS (Stand and Tree Evaluation and Modeling System) family of diameter increment models, including the current public release of the Lake States variant of FVS (LS-FVS), were tested for the 30 most common tree species using data from the Michigan Forest Inventory and Analysis (FIA) program. The results showed that current public release of the LS-FVS diameter increment model over-predicts 10-year diameter increment by 17% on average. Also the study affirms that a simple adjustment factor as a function of a single predictor, dbh (diameter at breast height) used in the past versions, provides an inadequate correction of model prediction bias. In order to re-engineer the basal diameter increment model, the historical, conceptual and philosophical differences among the individual tree increment model families and their modelling approaches were analyzed and discussed. Two underlying conceptual approaches toward diameter or basal area increment modelling have been often used: the potential-modifier (POTMOD) and composite (COMP) approaches, which are exemplified by the STEMS/TWIGS and Prognosis models, respectively. It is argued that both approaches essentially use a similar base function and neither is conceptually different from a biological perspective, even though they look different in their model forms. No matter what modelling approach is used, the base function is the foundation of an increment model. Two base functions – gamma and Box-Lucas – were identified as candidate base functions for forestry applications. The results of a comparative analysis of empirical fits showed that quality of fit is essentially similar, and both are sufficiently detailed and flexible for forestry applications. The choice of either base function in order to model diameter or basal area increment is dependent upon personal preference; however, the gamma base function may be preferred over the Box-Lucas, as it fits the periodic increment data in both a linear and nonlinear composite model form. Finally, the utility of site index as a predictor variable has been criticized, as it has been widely used in models for complex, mixed species forest stands though not well suited for this purpose. An alternative to site index in an increment model was explored, using site index and a combination of climate variables and Forest Ecosystem Classification (FEC) ecosites and data from the Province of Ontario, Canada. The results showed that a combination of climate and FEC ecosites variables can replace site index in the diameter increment model.