Kinetic mass loss rate constants

Tables I, III, V, and VII give the kinetic mass loss rate constants. Tables II, IV, VI, and VIII present the activation parameters. In addition to the activation parameters, the rates were normalized to 300°C by the Arrhenius equation in order to eliminate any temperature effects. Table IX shows the char/residue (Mr), as measured at 550°C under N2.

Thermogravimetric analysis (TGA) measures cellulose pyrolytic mass loss rates and activation parameters. The technique is relatively simple, straightforward and fast, but it does have disadvantages. One disadvantage is that determination of the kinetic rate constants from TGA data is dependent on the interpretation/analysis technique used. Another disadvantage of TGA is that the rate of mass loss is probably not equivalent to the cellulose pyrolysis rate. 

Both 1st- and 2nd-order rate expressions gave statistically good fits for the control samples, while the treated samples were statistically best analyzed by 2nd-order kinetics. The rate constants, lst-order activation parameters, and char/residue yields for the untreated samples were related to cellulose crystallinity. In addition, AS+ values for the control samples suggested that the pyrolytic reaction proceeds through an ordered transition state. The mass loss rates and activation parameters for the phosphoric acid-treated samples implied that the mass loss mechanism was different from that for the control untreated samples. The higher rates of mass loss and... 

A in the normal Arrhenius equation. Note that k is the rate constant at T. The algorithm was used to fit kinetic constants to the pyrolysis of wheat straw at 5,10 and 40°C/min (one data set per heating rate). The algorithm use the local temperature and does not rely on a constant heating rate. The data from an experiment were converted to dry ash free basis and the mass loss rate was normalized by the maximum mass loss rate. The data in the range where the normalized mass loss rate was above 0.1 was then used. This excludes the lignin tail from the data. The mass data were then converted to degree of conversion and normalized so the conversion of the final data point was 1.300 points were used per data set. Kinetic parameters were fitted to the individual data sets as well as to all three data sets simultaneously, The kinetic values are listed in Table 1. 

Constant rate thermo gravimetry has been described [134—137] for kinetic studies at low pressure. The furnace temperature, controlled by a sensor in the balance or a pressure gauge, is increased at such a rate as to maintain either a constant rate of mass loss or a constant low pressure of volatile products in the continuously evacuated reaction vessel. Such non-isothermal measurements have been used with success for decomposition processes the rates of which are sensitive to the prevailing pressure of products, e.g. of carbonates and hydrates. 

Researchers in previous studies generally used lst-order kinetics to describe cellulose pyrolysis, but rarely have they examined 2nd-order kinetics. Thus, discussion of our results for untreated samples will concentrate on lst-order rate constants so that our results can be directly compared with results from prior studies. A true reaction order of cellulose pyrolysis based on TGA data is essentially meaningless, however, since mass loss involves complex competing multiple reactions (2,4,8). In addition, reaction order was calculated on a dimensionless mass value rather than on the correct but uncalculable molar concentration term. 

Cellulose pyrolysis kinetics, as measured by isothermal TGA mass loss, were statistically best fit using 1st- or 2nd-order for the untreated (control) samples and 2nd-order for the cellulose samples treated with three additives. Activation parameters obtained from the TGA data of the untreated samples suggest that the reaction mechanism proceeded through an ordered transition state. Sample crystallinity affected the rate constants, activation parameters, and char yields of the untreated cellulose samples. Various additives had different effects on the mass loss. For example, phosphoric acid and aluminum chloride probably increased the rate of dehydration, while boric acid may have inhibited levoglucosan... 

Notes i) The isotope effects dealt with in mass spectrometry are usually intramolecular kinetic isotope ejfects, i.e., two competing fragmentations only differing in the isotopic composition of the products exhibit different rate constants k and k, . [69] ii) The kinetic isotope effect is called normal if k k, > 1 and inverse if k ko < 1. iii) Isotope effects can also be observed on KER, [52,70] e.g. the KER accompanying H2 loss from methylene immonium ion varies between 0.61 and 0.80 eV upon D labeling at various positions. [52]... 

In Figure 4, the calculated mass losses for cellulose at different constant heating rates and initial sample masses are compared to experimental TGA results. The TGA curves at heating rates of 0.14 K/min and O.S K/min had been used to evaluate the kinetic parameters for the one step first order reaction model which was incorporated into the model to calculate the sample temperature distribution. Since the temperature gradients in those samples are nearly zero, the results of the heat transport reaction model represent simultaneously the best fit for the assumed reaction model. At a heating rate of 108 K/min, the initial sample mass influences the temperature at which a given mass loss is attained. Cellulose samples with mo = I - 3 mg are affected only to a minor... 

All available publications on the kinetics of furfural formation are based on xylose in water. Thus, it is hardly surprising that these kinetics are found to be far from correct when they are applied to the pentose contained in sulfite liquor, the obvious reason being that this liquor contains substances known to react with furfural and with intermediates of the pentose-to-furfural conversion [19], with lignosulfonate being the main culprit, so that the quantity of furfural produced per unit mass of pentose is very much smaller than what kinetics in water predict. In other words, the kinetics of furfural formation in water must he supplemented by further loss terms. So far, none of the respective rate constants have been determined. Only an overall yield for special circumstances can he given in a later chapter. 

Analysts studying the behavior of band profiles at increasingly large sample sizes have often mistaken the band broadening due to the nonlinear behavior of the isotherm, which is of thermod5mamic origin, for a loss of column efficiency. The column efficiency results essentially from the effects of axial dispersion and the kinetics of mass transfers and is kinetic in nature. Based on the implicit and erroneous concept of a strong dependence of the rate constant of mass transfers on the solute concentration, this quest [22-26] was doomed to fail. 

Part of the misconception regarding the kinetics of the deaquation-anation reaction stems from the fact that only a Hmited analysis of the data was performed. To be complete, the data should be analyzed using all of the rate laws shown in Table 7.2. A more recent study of this process by Hamilton and House was completed in which the reaction was studied by means of mass loss as the H2O is driven off. Figure 7.4 shows typical rate plots that were obtained for the process when carried out at several constant temperatures. 

In many TG experiments, the temperature of the furnace is raised at a constant rate. This type of experiment is referred to as non-isothermal, scanning or rising temperature. An alternative experimental technique is available, and is often used in kinetic studies. Instead of raising the temperature at a constant rate, the temperature is held constant and the mass loss (or mass gain) observed at this fixed temperature. The results are then presented as mass loss against time, t. In practice the sample has to be placed on the thermobalance and the furnace at first left away from the sample. The furnace is then run up to the required temperature and left to stabilise. When the furnace temperature is constant at the required value, the furnace has to be moved quickly around the sample. There are a number of difficulties with this technique. The sample, crucible, thermocouple and cradle have to move rapidly from room temperature to the experimental temperature. They all have a finite thermal capacity, so cannot heat instantaneously. There is a thermal lag while the sample temperature rises. The first part of this rise does not matter, because the reaction being studied will not occur rapidly at lower temperatures. However, as the reaction temperature is approached, some reaction will... 

Temperature may not always be raised in a linear fashion. In the case of CRT A (Controlled Rate Thermal Analysis), the heating rate is varied in such a manner as to produce a constant rate of mass loss. Alternatively a sinusoidal temperature rise is superimposed on the linear rise this is known as Modulated TG and allows the continuous calculation of activation energy and pre-exponential factor during a run. Sometimes a Temperature Jump (or stepwise isothermal) " is used, where temperature is held constant for a time, then jumped rapidly to a higher constant temperature (usually quite close in temperature). All of these procedures are supposed to help in the determination of kinetics of reaction. Another system accelerates the temperature rise when no mass loss is experienced, i.e. between reactions. The rate is slowed to a low value during mass loss. Some manufacturers call this High Resolution TG and an example follows. 

Although the diffusion constant D does not appear in the steady-state diffusion equation, it does appear in kinetic factors such as the time it takes for a droplet of a given initial mass to evaporate. The solution to Equation (50.1) is a concentration c that decreases as from the droplet so that the total evaporation rate AttcP E from Equation (50.2) is proportional to the product aD. Thus, it is not the siuface area that controls the rate of mass loss, but the radius. 

The second method makes use of data on mass loss, collected in a series of different constant-heating-rate experiments as outlined in Fig. 4.198 for polystyrene. Isoconversion occurs at different temperatures for different heating rates. As one reaches the point of isoconversion, the integrated, mass-dependent functions f(p) must be identical. Thus, one has again achieved information about k(T) at different temperatures. Naturally this analysis is only valid if the kinetics has not changed over the range of temperature and conversion. 

Kinetic Modeis. Full kinetic models for a reformer require a tremendous commitment of time and resources. Rate equations for each reaction of all feed components, products, and intermediates must be taken into account. Individual single component experiments are performed to determine individual rate constants for each reaction if constants are not available in the literature (38). Often each reactor is divided into a number of discrete sections and each section is solved for and used as input into the calculation of the subsequent section of the reactor. Equations accounting for heat transfer and loss and for mass diffiision must be incorporated into the model. 

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