Density and residence time

Figure 7. Representation of the parameter problem in plasma processes. The symbols n, /(e), TV, and r are electron density, electron energy distribution, gas density, and residence time for molecules in the plasma volume, respectively. (Reproduced with permission from Ref. 32.)...

Finally, track-etched MF membranes are made from polymers, such as polycarbonate and polyester, wherein electrons are bombarded onto the polymeric surface. This bombardment results in sensitized tracks, where chemical bonds in the polymeric backbone are broken. Subsequently, the irradiated film is placed in an etching bath (such as a basic solution), in which the damaged polymer in the tracks is preferentially etched from the film, thereby forming cylindrical pores. The residence time in the irradiator determines pore density, and residence time in the etching bath determines pore size. Membranes made by this process generally have cylindrical pores with very narrow pore-size distribution, albeit with low overall porosity. Furthermore, there always is the risk of a double hit, i.e., the etched pore becomes wider and could result in particulate penetration. Such filter membranes are often used in the electronic industry to filter high-purity water. 

The solution to this problem requires an analysis of multiple gas-phase reactions in a differential plug-flow tubular reactor. Two different solution strategies are described here. In both cases, it is important to write mass balances in terms of molar flow rates and reactor volume. Molar densities and residence time are not appropriate for the convective mass-transfer-rate process because one cannot assume that the total volumetric flow rate is constant in the gas phase, particularly when the total number of moles is not conserved. In each reaction, 2 mol of reactants generates 1 mol of product. Furthermore, an overall mass balance suggests that the volumetric flow rate is constant only when the overall mass density does not change. This is a reasonable assumption for liquid-phase reactors but not for gas-phase problems when the total volume is not restricted. The exception is a constant-volume batch reactor. 

With Avogadro s number and F the Faraday constant. The density of kink site positions at the equilibrium potential [ksp] is given by the product of exchange current density and residence time. This equation will be discussed in the next section. 

Another empirical rule based on considerable practical experience (Bennett, Fiedehnan and Randolph, 1973) suggests that for scale-up at constant magma density and residence time, the quantity R /T should be kept constant, R = agitator tip speed and T = turnover time, i.e. crystallizer volume/volumetric liquor circulation rate. 

The problems of monomer recovery, reaction medium viscosity, and control of reaction heat are effectively dealt with by the process design of Montedison Fibre (53). This process produces polymer of exceptionally high density, so although the polymer is stiU swollen with monomer, the medium viscosity remains low because the amount of monomer absorbed in the porous areas of the polymer particles is greatly reduced. The process is carried out in a CSTR with a residence time, such that the product k jd x. Q is greater than or equal to 1. is the initiator decomposition rate constant. This condition controls the autocatalytic nature of the reaction because the catalyst and residence time combination assures that the catalyst is almost totally expended in the reactor. 

For systems following invariant growth the crystal population density in each size range decays exponentially with the inverse of the product of growth rate and residence time. For a continuous distribution, the population densities of the classified fines and the product crystals must be the same at size Accordingly, the population density for a crystallizer operating with classified-fines removal is given by... 

Another experimental approach (93. 941 to CSD control involved the use of on line solution and slurry density measurements as measured variables with jacket temperature and residence time as manipulated variables. This was attempted in a 10 liter MSMPR crystallizer employing K-alum. Results showed that this scheme was able to retirin the crystallizer to a steady state after the introduction of an upset and that on-line density measurements of solution and slurry could be obtained and used. 

The freezing time must now be equal to the residence time in the bed (see Mixing, dispersion and residence time, below) a mean residence time can be assumed to be equal to the mass hold-up in the bed divided by the mass flow rate. If the mass hold-up is the product of bed volume and the bulk density of the bed, and the bed depth is H, then... 

The laboratory-scale experimental setups are designed typically to conduct chemical reaction studies under a range of pressures, temperatures, densities, oxidant and organic concentrations, and residence times in several reactor configurations. In general, model compounds for simulating common pollutants in industrial waste streams are used in laboratory-scale experiments. 

However, if the reactor is filled, for example, with a catalyst, the situation becomes more complicated. The Vr would be the empty volume of the reactor, which is then difficult to determine, for instance, using settled apparent densities. The residence time can also be experimentally determined, usually resulting in a residence time distribution however, the experimental effort for such experiments is often large. Therefore, it is useful to apply a modified residence time, as shown in Equation (27), which defines the ratio of the mass of the catalyst and the gas flow, two easily measurable values ... 

In continuous mechanical emulsification systems based on turbulent flow, the power density Py viz. power dissipated per unit volume of the emulsion) and residence time, L, in the dispersing zone have been found to influence the result of emulsification as measured by the mean droplet size 0(3 2 which is called the Sauter diameter . This dependency is in most cases described by the following expression ... 

Milne et al. [42] used an internally circulating fluidized bed to study pyrolysis of low-density PE (LDPE) at temperatures ranging from 780 to 860° C and residence times of 400-600 ms. They achieved gas yields in excess of 90 wt% with total aUcene yields as high as 75 wt%, demonstrating a waste treatment potential for processes snch as flash pyrolysis, distinguished from classical pyrolysis by its high heating rates and low retention times, where these conditions can be maintained. 

Diffusive and convective transport processes introduce flexibility in the design of catalyst pellets and in the control of FT synthesis selectivity. Transport restrictions lead to the observed effects of pellet size, site density, bed residence time, and hydrocarbon chain size on chain growth probability and olefin content. The restricted removal of reactive olefins also allows the introduction of other intrapellet catalytic functions that convert olefins to other valuable products by exploiting high intrapellet olefin fugacities. Our proposed model also describes the catalytic behavior of more complex Fe-... 

Rate of growth (high deformability) Decrease binder viscosity. Increase agitation intensity. Increase particle density. Increase rate of nuclei formation, collision frequency, and residence time, as above for low-deformability systems. Decrease binder concentration or change binder. Decrease any diluents and polymers that act as thickeners. Decrease operating temperature for systems with simultaneous drying. (Otherwise increase temperature. Increase mixer impeller or drum rotation speed or fluid-bed gas velocity. 

However, it is clear that the probability density distributions of the classical and quantum oscillations are quite different, particularly for low values of v the quantum oscillation has the largest probability density near r = re the classical probability density (the residence time ) is greatest at the turning points. 

Classical methods are designed to obtain thermodynamic and transport information, for example molar volume, density, viscosity, and surface tension. The effects of pressure and temperature on these properties can also be evaluated, and thus phase transition information such as melting points and glass transition temperatures. If molecular dynamics (in contrast to Monte Carlo) is used, data relating to reorientation of molecules, self-diffusion and residence times are all available. Information can also be obtained from the simulation equations on the contribution made by kinetic, coulombic, intramolecular and dispersion energies to the total potential energy. However, because the charges are fixed and there is no explicit wavefunction included in the classical methods, no electronic information can be obtained. 

A special situation that can cause stationary conditions is at the electrochemical equilibrium potential (Nemst potential). The current density at the Nemst potential is the exchange current density The density of kink site positions [fopJo is therefore proportional to the product of exchange current density Iq and residence time, as was already shown in Eq. (7.34). 

The concentrations of reactant and products at the outlet of a packed bed reactor can be easily calculated with the mass balances for each compound supposing ideal plug flow behavior. For irreversible first-order consecutive reactions (Eq. (11.5)), the concentrations at the reactor outlet depend on the inlet concentration, Cj g, the rate constant, and the residence time, r. For reaction systems with constant fluid density, the residence time corresponds to the space-time defined as, r = V/Vg, with V the reactor volume and Vq the volumetric inlet flow. The space time... 

The combination of mixing and residence times also determines the response of the compatibilization reaction to variations in process parameters. Hettema (14) verified this by experiments for different systems consisting of polypropylene, high-density polyethylene, polystyrene, and PVC in corotating and counterrotating extruders, and he came to the following general conclusions ... 

Increase particle density Increase rate of nuclei formation, collision frequency and residence time, as above for low-deformability systems... 

---