Liquid phase volume

The total pore volume can also be determined from adsorption measurements if one knows the volume of vapor adsorbed under saturation conditions. For high surface area catalysts the amount of material adsorbed on particle exteriors will be negligible compared to that condensed in the pores. Hence the liquid phase volume equivalent to the amount of gas adsorbed is equal to the pore volume. The liquid density is assumed to be that corresponding to the saturation conditions in question. This technique is less accurate than that described previously. 

The liquid phase volume can be considered as constant (except for the semibatch ), since the change in molar volume going from the reagent to product is minimal, especially in the case of the rather large molecules used in pharmaceutical applications and/or the reagent is diluted with a solvent. 

The principal difference between homogeneous and heterogeneous reaction rates is that the latter is based on mass, volume, or more rarely, on the area of the solid and not on the fluid-phase volume or reactor volume. The reactor volume or liquid-phase volume is of secondary significance in heterogeneous reactions since the reaction takes place on the solid rather than throughout the reactor volume. Moreover, the mass of the solid is usually used instead of the solid volume or surface, because it is the most easily measured property. 

Laboratory-scale bubble columns for ozonation preferably have a reactor liquid phase volume of VL = 2-10 L, with a height-to-diameter-ratio of hid = 5-10. The ozone/oxygen (ozone/air) gas mixture is supplied through a ceramic or stainless steel porous plate fine pore diffuser (porosity 3,10-40 pm hole diameter). PTFE-membranes are a comparatively new alternative for the ozone gas-to-water transfer (Gottschalk et al., 1998). 

Under reasonable assumptions about the structure of the film surface layer, the concentrations of different clusters in the pseudoliquid layer can be assessed based on the corresponding free energies. The computational results are shown in Figure 14.3. According to these data, under the typical experimental conditions of co-condensation (overall metal amount, lx 10-5 mol liquid phase volume, 0.1ml overall metal concentration [Mg]0, 0.1M), the concentration of Mg5 at 80 K should be six orders of magnitude lower than that of Mg4. At 120 K, this difference is four orders of magnitude. 

A similar dependence can be obtained by comparing the fluidity (l/rj) of a concentrated disperse system with the volume fraction of the liquid phase in it (e = 1 — filler content This dependence is shown on Fig. 5. As long as the liquid phase volume in a disperse system does not exceed Ecr, i.e. as long as the filler content in it does not drop below cpmax, there is no flow (1/r) = 0). Thus the dependence of fluidity on the liquid phase content in dispersion... 

Volume variations with conversion are large for constant-pressure gas-phase reactions with change in mole number. Here, as a rule, operation at constant volume poses no difficulties. Liquid-phase reactions may also entail volume contraction or expansion. However, these are not related to changes in mole number and can be predicted only if information on partial molar volumes is at hand. Because liquids are essentially incompressible, even at elevated temperature, it is unsafe to conduct liquid-phase reactions without a gas cap in a closed reactor. Some variation of liquid-phase volume with conversion therefore is apt to occur. Fortunately, the variation at constant temperature is usually so small that it can be neglected in the evaluation or accounted for by a minor correction. 

Based on the previous considerations, some authors proposed thermodynamic-based approaches to SAS. De la Fuente Badilla et al attempted to develop a thermodynamic-based criterion for optimum batch antisolvent precipitation (GAS) using a definition of the volume expansion that takes into account the molar volume of the system studied. They analyzed various binary and ternary systems and concluded that the pressure corresponding to a minimum value of the liquid-phase volume expansion coincides with the pressure at which the solute precipitates. In a subsequent work, Shariati and Peters further highlighted the role of SC-CO2 in GAS. It acts as a co-solvent (cosolvency effect) at lower concentrations, whereas at higher concentrations it acts as an antisolvent. 

In addition to these pressure drop models, models to represent spreading of liquid in packed beds because of spatial variation in flow resistance are needed. In a randomly packed bed, the void fraction is not uniform. This implies that some flow channels formed within a packed bed offer less resistance to flow than other channels of equal cross-sectional area. Liquid will tend to move toward channels of lower resistance, leading to higher liquid hold-up in such channels. Thus, even if the initial liquid distribution is uniform, inherent random spatial variation of the bed leads to non-uniform liquid flow. Yin et al. (2000) assumed that the dispersion coefficient for liquid phase volume fraction is linearly proportional to the adverse gradient of... 

The first major decision in the choice of a reactor for gas-liquid reactions taking place in the liquid phase is based on the optimal usage of the total reactor volume, i.e. the choice of the parameter P, which is the ratio of the liquid-phase volume to the volume of the diffusion layer (see Section 8.4.2). When reactions are slow compared to the mass transfer from the gas to the liquid, sparged stirred tanks and bubble columns are preferred, as these reactors have the largest bulk liquid volume. On the other hand, fast reactions for a large part take place in the diffusion layer, so in this case spray columns and packed columns are more suitable. 

Instead of the partial differential equation model presented above, the model is developed here in dynamic difference equation form, which is suitable for solution by dynamic simulation packages, such as Madonna. Analogous to the previous development for tubular reactors and extraction columns, the development of the dynamic dispersion model starts by considering an element of tube length AZ, with a cross-sectional area of Ac, a superficial flow velocity of V and an axial dispersion coefficient, or diffusivity D. Convective and diffusive flows of component A enter and leave the liquid phase volume of any element, n, as indicated in Fig. 4.24 below. Here j represents the diffusive flux, L the liquid flow rate and and Cla the concentration of any species A in both the solid and liquid phases, respectively. 

Developed versions of the gradient and Boussinesq hypotheses were employed to model the second-order covariance terms. The liquid phase volume fraction-velocity covariance and the Re3molds stresses, for example, were approximated by ... 

By use of (8.11), the gas-volume fractions has been substituted with the liquid volume fraction. The gradient of the gas phase volume fraction is thus related to the liquid phase volume fraction in accordance with ... 

Liquid-phase hydrogenation (H2 4.0, Linde-Technoplyn) experiments were carried out in a 300 ml batch reactor in kinetic regime under 7 MPa of total pressure at 433 K. Typically 3.0 g of cinnamaldehyde (98%, Aldrich) and 0.5 g of catalysts were stirred in 2-propanol (p.a.). Total liquid phase volume in autoclave was 200 ml. The products were identified with GC-MS and analyzed by gas chromatography. 

Fir,. 16. Three fundamental procedures for contacting gases and liquids. /3 is the ratio of the liquid phase volume to the volume of the diffusion layer within the liquid phase. 

Citral (Alfa Aesar, 97%) hydrogenation was carried out in a pressurized reactor working in a special mode, in which small amounts of the liquid phase initially introduced in the reactor were constantly pumped out from the reactor, whereas the supported Pd-ionic liquid catalyst remained in the reactor. The initial liquid phase volume was 325 ml. The catalyst bulk density was changed during the reaction via pumping out the liquid phase from the reactor with a rate of 1 g/min. Such procedure allows efficient investigation of consecutive reactions... 

One method of quantifying phase behavior is to mix two polymers in a common solvent and observe the two liquid phase volumes (2, 3). The theoretical basis for the incompatibility of polymer solutions was discussed by Scott (4) however, complete phase relationships are rarely measured. The poly-(methyl methacrylate)/benzene/rubber system was described by Bristow (5), but even he did not calculate solubility parameters from the data. Thus, measurement and data interpretation techniques need to be defined. 

Excess enthalpy for each species is obtained from (5-16). For propane, the liquid-phase volume fraction is computed from (5-7) as in Example 5.1. 

Vi = total liquid-phase volume within the CSTR (mL)... 

It is a common practice for qualitative analysis to be based on measurements of tr, this is especially true in those laboratories that run standards with each analysis. Nevertheless, is not the ideal parameter for identification purposes because it is a function of temperature, flow rate, and liquid-phase volume. (Indeed, the liquid-phase volume is continuously changing with time because of evaporation even its chemical composition can vary under the conditions of the experiment.) What is needed, then, is a parameter that is independent of all these factors. A very successful, but not perfect, solution is the Kovats index system, which relates the retention volume (or the retention time t ) of the unknown compound with that of M-hydrocarbons eluting before and after it. To each of a series of paraffins is attached an index I, given by... 

Therefore, important parameters such as phase transfer phenomena (i.e. solubility of the reactants in the ionic liquid phase), volume ratio of the different phases, efficiency of mixing so as to provide maximum liquid-liquid interfacial area, are key factors in determining and controlling reaction rates and kinetics. Kinetic models have been developed for aqueous biphasic systems and are continuously refined to improve agreement with experimental results. These models might be transferable to biphasic catalysis with ionic liquids, but more data concerning the solubility ofliq-uids (and gas) in these new solvents and the existence of phase equilibria in the presence of organic upper phases have still to be accumulated (see Sections 3.3 and 3.4). 

A comparison of equations (18.31) and (18.42) for the rninimum drop radius in horizontal and vertical separators shows that if the equality U /Uj(. = D/,/D holds (here the bottom indexes v and h correspond to the parameters of horizontal and vertical separators), then, all other things being equal, the minimum radii of drops in both separators coincide. But this certainly does not mean that their CE s should be the same, because the ratio of liquid phase volume concentrations at the exit of the two separators is... 

The estimation of Rav for characteristic parameter values shows that Rav where Aq = d/Re /" is the internal scale of turbulence. In a turbulent flow, both heat and mass exchange of drops with the gas are intensified, as compared to a quiescent medium. The delivery of substance and heat to or from the drop surface occurs via the mechanisms of turbulent diffusion and heat conductivity. The estimation of characteristic times of both processes, with the use of expressions for transport factors in a turbulent flow, has shown that in our case of small liquid phase volume concentrations, the heat equilibrium is established faster then the concentration equilibrium. In this context, it is possible to neglect the difference of gas and liquid temperatures, and to consider the temperatures of the drops and the gas to be equal. Let us keep all previously made assumptions, and in addition to these, assume that initially all drops have the same radius (21.24). Then the mass-exchange process for the considered drop is described by the same equations as before, in which the molar fluxes of components at the drop surface will be given by the appropriate expressions for diffusion fluxes as applied to particles suspended in a turbulent flow (see Section 16.2). In dimensionless variables (the bottom index 0" denotes a paramenter value at the initial conditions). 

Droplet deformation and collision are also important features in the intermediate regime. In addition, in the intermediate region, the droplet loading could be severe. The variations in the local liquid-phase volume fraction also become important and should be considered in order to capture the droplet dynamics correctly. A robust algorithm capable of addressing all numerical issues related to spray modeling is necessary. 

---