A mathematical model for unsteady mixed flows in closed water pipes

We present the formal derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipe. In the case of free surface incompressible flows, the \FS-model is formally obtained, using formal asymptotic analysis, which is an extension to more classical shallow water models. In the same way, when the pipe is full, we propose the \Pres-model, which describes the evolution of a compressible inviscid flow, close to gas dynamics equations in a nozzle. In order to cope the transition between a free surface state and a pressured (i.e. compressible) state, we propose a mixed model, the \PFS-model, taking into account changes of section and slope variation

Thermal Decomposition Kinetics of Woods with an Emphasis on Torrefaction

The pyrolysis kinetics of Norwegian spruce and birch wood was studied to obtain information on the kinetics of torrefaction. Thermogravimetry (TGA) was employed with nine different heating programs, including linear, stepwise, modulated and constant reaction rate (CRR) experiments. The 18 experiments on the 2 feedstocks were evaluated simultaneously via the method of least-squares. Part of the kinetic parameters could be assumed common for both woods without a considerable worsening of the fit quality. This process results in better defined parameters and emphasizes the similarities between the woods. Three pseudo-components were assumed. Two of them were described by distributed activation energy models (DAEMs), while the decomposition of the cellulose pseudo-component was described by a self-accelerating kinetics. In another approach, the three pseudo-components were described by n-order reactions. Both approaches resulted in nearly the same fit quality, but the physical meaning of the model, based on three n-order reactions, was found to be problematic. The reliability of the models was tested by checking how well the experiments with higher heating rates can be described by the kinetic parameters obtained from the evaluation of a narrower subset of 10 experiments with slower heating. A table of data was calculated that may provide guidance about the extent of devolatilization at various temperature residence time values during wood torrefaction

Kinetic Behavior of Torrefied Biomass in an Oxidative Environment

The combustion of four torrefied wood samples and their feedstocks (birch and spruce) was studied at slow heating programs, under well-defined conditions by thermogravimetry (TGA). Particularly low sample masses were employed to avoid the self-heating of the samples due to the huge reaction heat of the combustion. Linear, modulated and constant-reaction rate (CRR) temperature programs were employed in the TGA experiments in gas flows of 5 and 20% O2. In this way the kinetics was based on a wide range of experimental conditions. The ratio of the highest and lowest peak maxima was around 50 in the experiments used for the kinetic evaluation. A recent kinetic model of Várhegyi et al. [Energy & Fuels 2012, 26, 1323-1335] was employed with modifications. This model consists of two devolatilization reactions and a successive char burn-off reaction. The cellulose decomposition in the presence of oxygen has a self-accelerating (autocatalytic) kinetics. The decomposition of the non-cellulosic parts of the biomass was described by a distributed activation model. The char burn-off was approximated by power-law (n-order) kinetics. Each of these reactions has its own dependence on the oxygen concentration that was expressed by power-law kinetics, too. The complexity of the applied model reflects the complexity of the studied materials. The model contained 15 unknown parameters for a given biomass. Part of these parameters could be assumed common for the six samples without a substantial worsening of the fit quality. This approach increased the average experimental information for an unknown parameter by a factor of 2 and revealed the similarities in the behavior of the different samples