Species concentration profile

Other measurements such as gas species and soot all have importance in fire plumes but will not be discussed here. As we have seen for simple diffusion flames, the mixture fraction plays a role in generalizing these spatial distributions. Thus, if the mixture fraction is determined for the flow field, the prospect of establishing the primary species concentration profiles is possible. 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

The liquid and solid phases are often supposed to be well-mixed, and a perfect mixing model can be applied to model the species-concentration profile. However, many expressions for the description of axial dispersion in the liquid phase in a BSCR are given in the literature [37,38]. 

Figure 2.21 Temperature and species concentration profiles in a reverse-flow reactor (a) flow direction is left to right (b) flow is reversed to be from right to left (c) periodic quasi-steady state [47] (by courtesy of ACS).

Species-concentration profiles, obtained by integrating Equation (13.20), are plotted in Figure 13.7 for the case of two reactions in series (A —> B —> C) occurring in a catalytic hollow-fiber membrane. The reactant A contained in the bulk phase on shell-side flow through the membrane where reacting produces the intermediate product B then, B is converted in the final product C. Variations on concentration profiles are present only inside the fiber, outside the fiber there is no variation due to the reaction. No diffusion limitation in the films were considered in the present model in order to focus on transformation inside the membrane. 

The measurements of temperature and species concentrations profiles in premixed, laminar flames play a key role in the development of detailed models of hydrocarbon combustion. Systematic comparisons are given here between a recent laminar methane-air flame model and laser measurements of temperature and species concentrations. These results are obtained by both laser Raman spectroscopy and laser fluorescence. These laser probes provide nonintrusive measurements of combustion species for combustion processes that require high spatial resolution. The measurements reported here demonstrate that the comparison between a model and the measured concentrations of CH, O2,... 

Single-shot integrated Q-branch intensity measurements were performed to obtain the N2 and O2 molecular number densities from the reaction products. These data were reduced with the averaged CARS temperatures to obtain the species-concentration profiles also shown in Figs. 3-5. 

Temperature measurements (corrected for radiation) were made with silica-coated Pt-Pt/10% Rh thermocouples, about 4 mils in diameter. The temperature and species concentration profile as a function of distance through the flame provided the basic data for the kinetic analyses. 

Figure 5 Schematic plot of cathodic specie concentration profile for a mass transport controlled cathodic reaction with the electrode-solution interface at the far left. The solid line represents the actual concentration profile. The dashed line from Cs to Cb represents an approximating linear concentration gradient. Its interception with the horizontal line representing Cb defines an approximation of the mass transport boundary layer.

We have developed several new measurement techniques ideally suited to such conditions. The first of these techniques is a High Pressure Sampling Mass Spectrometric method for the spatial and temporal analysis of flames containing inorganic additives (6, 7). The second method, known as Transpiration Mass Spectrometry (TMS) (8), allows for the analysis of bulk heterogeneous systems over a wide range of temperature, pressure and controlled gas composition. In addition, the now classical technique of Knudsen Effusion Mass Spectrometry (KMS) has been modified to allow external control of ambient gases in the reaction cell (9). Supplementary to these methods are the application, in our laboratory, of classical and novel optical spectroscopic methods for in situ measurement of temperature, flow and certain simple species concentration profiles (7). In combination, these measurement tools allow for a detailed fundamental examination of the vaporization and transport mechanisms of coal mineral components in a coal conversion or combustion environment. 

Fig. 9 (A) Major species concentration profiles and (B) Some of the polycyclic aromatic hydrocarbons (PAH) formed in a fuel-rich, premixed laminar methane flame the formation of a large number of intermediates and by-products are evident. Highly toxic benzo-fl-pyrene is the 3rd PAH from the bottom. (From Ref. " l)...

The nature of intermediates formed in diffusion flames is similar to the premixed ones, albeit differences in the contacting pattern. In Fig. 11, the species concentration profiles in a laminar ethylene diffusion flame front are presented. The fuel and oxygen diffuse toward each other undergoing virtual annihilation within the flame zone concomitant with the establishment of a peak temperature of about 1600°C. Because premixed systems provide a better control of combustor temperature, and many practical combustion devices operate under diffusion limited conditions, considerable effort has been expended to ensure the rapid mixing of fuel and oxygen in combustion chambers and approach premixed conditions. 

Fig. 11 Species concentration profiles vs. distance from fuel burner surface for (A) major species and (B) PAHs generated in an ethylene opposed flow diffusion flame. (From Ref.. )...

Fig. 17 Comparative species concentration profiles in the flames of CH3CI/CH4 and CH4 under similar equivalence ratio and carbon density. (A) Major species mole fraction profiles (B) single ring aromatic species mole fraction profiles (C) two ring aromatic species mole fraction profiles (D) three and four ring aromatic species mole fraction profiles. (From Ref. l)...

A radial temperature gradient with a maximum at the wall is observed at the reactor entrance. Further away from the reactor entrance, the radial profile is flat. The mole fraction profiles also contain marked radial gradients within the first 1.5 meters of the reactor. The radial gradients observed in the species concentration profiles are caused by the limited heat flux added to the reactor through the wall. The reactions are endothermic and the heat transferred through the wall and/or from the wall into the bed is not sufficient to smooth out the temperature profile, thus the chemical conversion becomes non-uniform. 

Fig. 14. Close-up view of temperature and species-concentration profiles in subsurface...

Figure 27 shows the temperature and species-concentration profiles in the gas phase during HMX/GAP pseudo-propellant combustion at a CO2 laser intensity of 100 W/cm under atmospheric pressure. The ratio of HMX to GAP mass fraction is 8 2. Reasonable agreement was achieved with the experimental data reported in Ref. 3. The temperature rises rapidly from 677 K at the surface. 

Fig.27 (a) Calculated and (b) measured [3] species-concentration profiles of gas-phase flame of HMX/GAP pseudo propellant (mass ratio 8 2) at I atm and laser intensity of 100 W/cm. ... 

While the analysis described above is useful to define the surface parameters cf, St, and, by inference, cm more detailed analysis is required to define the velocity, temperature, and species concentration profiles in the boundary layer (see Refs. [112] and [113]). 

In the previous examples, we have exploited the idea of an effectiveness factor to reduce fixed-bed reactor models to the same form as plug-flow reactor models. This approach is useful and solves several important cases, but this approach is also limited and can take us only So far. In the general case, we must contend with multiple reactions that are not first order, nonconstant thermochemical properties, and nonisothermal behavior in the pellet and the fluid. For these cases, we have no alternative but to solve numerically for the temperature and species concentrations profiles in both the pellet and the bed. As a final example, we compute the numerical solution to a problem of this type. 

The use and importance of aromatic compounds in fuels sharply contrasts the limited kinetic data available in the literature, regarding their combustion kinetics and reaction pathways. A number of experimental and modelling studies on benzene [153, 154, 155, 156, 157, 158], toluene [159, 160] and phenol [161] oxidation exist in the literature, but it would still be helpful to have more data on initial product and species concentration profiles to understand or evaluate important reaction paths and to validate detailed mechanisms. The above studies show that phenyl and phenoxy radicals are key intermediates in the gas phase thermal oxidation of aromatics. The formation of the phenyl radical usually involves abstraction of a strong (111 to 114 kcal mof ) aromatic—H bond by the radical pool. These abstraction reactions are often endothermic and usually involve a 6 - 8 kcal mol barrier above the endothermicity but they still occur readily under moderate or high temperature combustion or pyrolysis conditions. The phenoxy radical in aromatic oxidation can result from an exothermic process involving several steps, (i) formation of phenol by OH addition to the aromatic ring with subsequent H or R elimination from the addition site [162] (ii) the phenoxy radical is then easily formed via abstraction of the weak (ca. 86 kcal moT ) phenolic hydrogen atom. 

Since kinetics for the system has already been provided in Chapter 1, the species concentration profiles achieved in the beaker may be computed using the standard batch reactor equation. This is done by numerically integrating the rate expressions with the new initial condition given by concentration 82. The batch profile resulting from this integration is shown in Figure 3.2, given by the curve a20. The profiles have been overlaid with the previous experiment for comparison. 

We shall be interested in plotting a PFR trajectory from the feed conditions, specified in Chapter 1, in Cb-Ce-Ct space. This example also wishes to demonstrate how integration limits, for the PFR equation, may be estimated from graphical inspection of the species concentration profiles. 

Let us now investigate the scenario when ax > a2, in particular, when ax = 20 and a2 = 2. As in the previous sections, constmction of the AR is achieved by first generating PFR trajectories from the feed point. Figure 5.6(a) provides species concentration profiles for the specific values of the rate constants supplied in Table 5.3 the corresponding PFR trajectory in concentration space is shown in Figure 5.6(b). 

To determine what occurs if a CSTR is introduced into the analysis, the CSTR locus from the feed point is generated next. Species concentration profiles in the CSTR are displayed in Figure 5.7. 

Figure 4.19 shows the results of a chronopotentiometry experiment, that is to say with a constant current density fixed over time. This involves fixing the slope at the interface (ieft in this case) of the electroactive species concentration profile. The interfacial concentration then changes over time . 

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