Stoichiometry flow systems

There are two uses for Equation (2.36). The first is to calculate the concentration of components at the end of a batch reaction cycle or at the outlet of a flow reactor. These equations are used for components that do not affect the reaction rate. They are valid for batch and flow systems of arbitrary complexity if the circumflexes in Equation (2.36) are retained. Whether or not there are spatial variations within the reactor makes no difference when d and b are averages over the entire reactor or over the exiting flow stream. All reactors satisfy global stoichiometry. 

Attempts to define operationally the rate of reaction in terms of certain derivatives with respect to time (r) are generally unnecessarily restrictive, since they relate primarily to closed static systems, and some relate to reacting systems for which the stoichiometry must be explicitly known in the form of one chemical equation in each case. For example, a IUPAC Commission (Mils, 1988) recommends that a species-independent rate of reaction be defined by r = (l/v,V)(dn,/dO, where vt and nf are, respectively, the stoichiometric coefficient in the chemical equation corresponding to the reaction, and the number of moles of species i in volume V. However, for a flow system at steady-state, this definition is inappropriate, and a corresponding expression requires a particular application of the mass-balance equation (see Chapter 2). Similar points of view about rate have been expressed by Dixon (1970) and by Cassano (1980). 

This simple treatment of the data with a static ammonia system is not adequate for a flow system. In a rapidly flowing mixture the concentrations of all radicals and atoms will be low and hence (40) will predominate over (39). Hydrazine once formed will be swept rapidly into a zone in which the hydrogen atom concentration is low and it will be thus free from attack by these atoms. The results of Gunning and his coworkers indicate that the reaction for ammonia disappearance approaches the stoichiometry... 

Note that rB and v can also be defined on the basis of partial pressure, number concentration, surface concentration, etc., with analogous definitions. If necessary differently defined rates of reaction can be distinguished by a subscript, e.g. vp = vB 1dpB/dt, etc. Note that the rate of reaction can only be defined for a reaction of known and time-independent stoichiometry, in terms of a specified reaction equation also the second equation for the rate of reaction follows from the first only if the volume V is constant. The derivatives must be those due to the chemical reaction considered in open systems, such as flow systems, effects due to input and output processes must also be taken into account. 

The formation of ketene was first observed, in the temperature range 605-675 °C, using a flow system The amount of ketene found experimentally was, however, less than had been expected on the basis of the suggested stoichiometry... 

Provided that there is a change in the number of moles upon reaction, an obvious measure of the extent of a reaction is given by the change in pressure. The latter has to be related to the stoichiometry of the reaction by quantitative analysis of the products and reactant or reactants and by material balance. Abnormal pressure effects sometimes occur due to adiabatic reactions, unimolecular reactions which are in their pressure-dependent regions (particularly in flow systems)... 

The methods listed above all enable relative concentrations of atoms or radicals to be measured. It is a much more difficult problem to measure absolute magnitudes of atoms and radicals in discharge-flow systems, or indeed in any other systems such as flash photolysis experiments. Two principal methods are used for the derivation of absolute concentrations (a) the combination of spectrometric measurements with calculated transition probabilities or (b) the use of the stoichiometry of rapid titration reactions. Of these methods, (b) is probably the most frequently used at the present time. Emphasis will be given to the possibilities of absolute concentration measurements in the discussion of the methods which follows. 

Consider an elementary transfer reaction of an atom with a stable molecule, of simple stoichiometry, and sufficiently rapid for at least 99% extent of reaction to occur within the time resolution of a discharge-flow system (1 to 100 ms). Such a reaction constitutes a possible titration reaction for the measurement of atom concentrations if some means of detecting atoms in the system is also available. An atom indicator is sometimes provided conveniently by a chemiluminescent emission associated with the titration reaction. 

Several workers have considered the implications of the decay scheme for OH discussed above for the stoichiometry of the H + NOg reac-tion. The latter reaction constitutes one of the main methods for the measurement of [H] in discharge-flow systems. However, a limitation is that in the presence of appreciable amounts of Hg, a secondary reaction occurs leading to regeneration of H and consequent overestimation of initial [H] from the NOg titre ... 

Catalytic experiments were carried out using a flow system at atmospheric pressure. The procedure was the same as that described earlier [5]. The gas mixture used [0.75% CO + 0.1% NO 4- 0.35% O2 + N2 (diluent)] was almost stoichiometric, since the stoichiometry number was s = (2O2 + NO)/CO = 1.07. Activation of the catalyst consisted in a treatment at 500 C in the flowing reaction mixture (20L/h) for 3h. The conversions of CO and NO were measured at increasing temperatures in the range 150-500 0 at a programmed rate of 2 C/min. 

Titration reactions based on simple stoichiometry, and proceeding extremely rapidly, have been developed for the measurement of absolute concentrations of ground state atoms in flow systems. Well-known examples for N, O and H atoms include the reactions,... 

First, the preparations of powder and sintered specimens are mentioned. Polycrystalline boron phosphide powder (27) material was prepared by the reduction of a boron tribromide-phosphorus trichloride mixture with hydrogen in a gas flow system in a fused silica tube furnace at about 1100°C. An excess of phosphorus trichloride was used to maintain the stoichiometry of the deposit. The deposition rate was approximately 2 g/h. 

The deposition of boron phosphide by CVD was carried out in a gas flow system by the thermal decomposition of diborane-phosphine mixtures in a hydrogen atmosphere and the thermal reduction of boron tribromide-phosphorus trichloride mixtures with hydrogen (37). The hydrides are thermodynamically unstable at room temperature and decompose rapidly at above 500°C, which tends to promote homogeneous nucleation by pyrolysis in the gas phase. The halides are thermally more stable than the hydrides, and higher substrate temperatures may be used in the thermal reduction process with essentially no gas-phase reactions. At high substrate temperatures, a phosphorus pressure equal to or greater than the vapor pressure of boron phosphide must be present over the substrate surface to maintain the stoichiometry of the deposit. 

Step 4 Define the System Boundaries. This depends on the nature of the unit process and individual unit operations. For example, some processes involve only mass flowthrough. An example is filtration. This unit operation involves only the physical separation of materials (e.g., particulates from air). Hence, we view the filtration equipment as a simple box on the process flow sheet, with one flow input (contaminated air) and two flow outputs (clean air and captured dust). This is an example of a system where no chemical reaction is involved. In contrast, if a chemical reaction is involved, then we must take into consideration the kinetics of the reaction, the stoichiometry of the reaction, and the by-products produced. An example is the combustion of coal in a boiler. On a process flow sheet, coal, water, and energy are the inputs to the box (the furnace), and the outputs are steam, ash, NOj, SOj, and CO2. 

Most thermochemical calculations are made for closed thermodynamic systems, and the stoichiometry is most conveniently represented in terms of the molar quantities as determined from statistical calculations. In dealing with compressible flow problems in which it is essential to work with open thermodynamic systems, it is best to employ mass quantities. Throughout this text uppercase symbols will be used for molar quantities and lowercase symbols for mass quantities. 

The objectives of this project are consistent with the objectives (1) and (4) above. The general objective of this project has been to verify a new measurement method to analyse the thermochemical conversion of biofuels in the context of PBC, which is based on the three-step model mentioned above. The sought quantities of the method are the mass flow and stoichiometry of conversion gas, as well as air factors of conversion and combustion system. One of the specific aims of this project is to find a physical explanation why it is more difficult to obtain acceptable emissions from combustion of fuel wood than from for example wood pellets for the same conditions in a given PBC system. This project includes the following stages ... 

This paper deduces and mathematically defines some new concepts (see Figure 11), such as the conversion system, the conversion gas, the off-gas, the mass flow of conversion gas, the stoichiometry of conversion gas, the conversion efficiency the air excess numbers for conversion and combustion system (// ), and the combustion efficiency... 

The mass flow and stoichiometry of conversion gas in a PBC system is analogue to the mass flow and stoichiometry of gas fuel into a gas fuel combustion system, see... 

Figure 12. In other words, the conversion gas of a PBC system is equivalent to the gas fuel of a gas-fired system. Consequently, the mass flow and stoichiometry of the conversion gas are key quantities in the calculation of the correct excess air number (see Paper I), the latent heat flow of combustion, and the conversion efficiency, and the combustion efficiency of a PBC system.

What the three-step model really points out is that it is theoretically correct to carry out basic combustion calculations for a PBC system based on the mass flow and stoichiometry of the conversion gas from the conversion system and not based on the mass flow of solid fuel entering the conversion system. The two-step model approach applied on a PBC system, which is equivalent to assuming that the conversion efficiency is 100 %, is a functional engineering approach, because the conversion efficiency is in many cases very close to unity. However, there are cases where the two-step model approach results in a physical conflict, for example the mass flows in PBC sysfem of batch type cannot be theoretically analysed with a two-step model. 

Equation (4) states that, to quantify the combustion efficiency, the volume fractions of carbon monoxide and the total hydrocarbon (methane equivalents), the mass flow and the stoichiometry of conversion gas, and the volume flows of primary and secondary air need to be measured. The concept of combustion efficiency is a function of emissions, air dilution, and type of fuel. This concept can be applied to any type of continuous combustion system and any type of fuel. 

Two new efficiencies are deduced in the context of the three-step model that is, conversion efficiency and combustion efficiency, which can be very useful in the optimization of existing PBC system and in the design of new advanced environmental-friendly PBC systems. However, to be able to quantify these new parameters, the mass flow and stoichiometry of the conversion gas need to be measured. 

Paper II presents a hypothetical method to indirectly measure the key quantities of a PBC, that is, the mass flow and the stoichiometry of the conversion gas, as well as the air excess numbers of the conversion and combustion system, defined in paper I. It also includes a measurement uncertainty analysis. 

The sought quantities of the method are (1) mass flow of conversion gas, (2) stoichiometry of the conversion gas, (3) air factor of the conversion system, and (3) air factor of the combustion system. Mass flow and stoichiometry of the conversion gas are illustrated in Figure 13 above. 

For the sake of brevity the reader is referred to Paper II for the details regarding the constitutive mathematical models of the method applied to measure the mass flow and stoichiometry of conversion gas as well as air factors for conversion and combustion system. Below is a condensed formulation of the mathematical models applied. Here a distinction is made between measurands and sought physical quantities of the method. 

Based on the three-step model, a hypothetical mathematical model has been formulated to measure the mass flow and stoichiometry of conversion gas as well as the air factors of conversion and combustion system. 

---