Material balance emulsion phase

Important aspects of all the models include limestone-S02 kinetics, combustion kinetics and other gas-solids reaction kinetics, gas phase material balances, solid phase material balances, gas exchange between the bubble and emulsion phases, heat transfer, and bubble hydrodynamics. 

As in the fluidized beds analysis (Section 3.8.3), a similar simplification has been made in Kunii-Levenspiel model for the material balances in the emulsion phase, where again the corresponding derivatives have been omitted (eqs. (3.529) and (3.530)). As in the case of liquid flow in trickle beds, the flow of the gas in the emulsion phase is considered too small and so the superficial velocities can be neglected. Thus, in trickle beds, from eq. (3.367),... 

Applying the appropriate material balances for the solids and the gas, the fraction of the bed occupied by the bubbles and wakes can be estimated using the Kunii-Levenspiel model. The fraction of the bed occupied by that part of the bubbles which does not include the wake, is represented by the parameter d, whereas the volume of the wake per volume of the bubble is represented by a. Consequently, the bed fraction in the wakes is a and the bed fraction in the emulsion phase (which includes the clouds) is 1 — <5 — ot<5. Then (Fogler, 1999)... 

Material balances can be written over a differential section of the bed (dz) for a reactant, in each of the three-phases (bubble, cloud, and emulsion). Then, the equations of the model are as follows ... 

Emulsion phase gas in plug flow Solutions for bubble phase free of solids In the following, a simplified solution is presented under the following assumptions first-order reactions, gas flow only through the bubble phase (fh = 1), and absence of solids in the bubble phase (yb = 0). Under these conditions, the material balances (3.519) and (3.520) become the following. 

Under this condition, the reactant A is unlikely to reach the emulsion phase. Integrating the material balance for the bubble phase, eq. (3.534) yields the desired performance expression in terms of conversion ... 

Using the usual assumptions, we obtain the following dimensionless unsteady-state material and energy balance equations for the dense (emulsion) phase of the bubbling fluidized bed ... 

After reaction, the acid-hydrocarbon emulsion passes from the reactor to a baffled settler where a phase separation takes place and settled acid is pumped back to the reactor. The settled hydrocarbon phase is caustic scrubbed to remove any entrained acid and sent either to a material balance accumulator or to a product accumulation system. 

Because bubble diameter is a function of the height from the distributor, and the height from the distributor is taken to the center of the bubble in question, an iterative procedure is used to determine D]. The initial guess is taken to be the bubble diameter computed for the previous compartment. For each compartment there are three material balance equations with three unknowns, the concentrations in each phase (bubble, cloud and emulsion). The total number of equations then is three times the total number of compartments. These may be solved by a matrix reduction scheme or a trial and error procedure. The average superficial gas velocities in each phase are first determined from Eqns. (4) - (6). The computational sequence for the remaining parameters in Eqn. (1) is given in Table 1. 

In more realistic situations there is a certain probability of the emulsion droplets coalescing with the bulk oil phase or a part of the bulk oil becoming emulsified. The physics of such complex fiow conditions is not well understood at present. The starting point of describing such a fiow would be to treat it as a normal two-phase flow and use the concept of relative permeability and a model for the rheological properties of the emulsion phase. To account for the material exchange between the bulk phase and the emulsion phase, some form of droplet population balance model will be needed. 

In order to develop a continuous separation process, Kataoka et al. [54] simulated permeation of metal ion in continuous countercurrent column. They developed the material balance equation considering back mixing only in the continuous phase and steady-state diffusion in the dispersed emulsion drops which is similar to the Hquid extraction situation. Bart et al. [55] also modeled the extraction of copper in a continuous countercurrent column. They considered only the continuous phase back mixing in the model and assumed that the reaction between copper ions and carrier is slow, so that the differential mass balance equation for external phase in their model is... 

The exterior phase was analyzed for phenylalanine concentration and pH. All sample volumes were recorded and used for mass balance determination. Phenylalanine was measured spectrophotometrically at lmax = 257.5 nm. Changes in interior phase volume were calculated using material balances. All material balances closed to within 2%. Interior phase concentrations were estimated by the use of material balances and exterior phase concentrations. The interior phase components of several representative emulsions were measured by analyzing the interior phase components after thermally demulsifying the emulsion samples. These measurements agreed with estimates to within 10%. 

The local bubble fraction can be determined by either an optical or a capacitance probe. Suppose that a probe output as shown in Fig. 47 is obtained. By introducing a threshold value, which has to be carefully determined by the real eye observation and/or material balance, the time can be divided into bubble passage periods ATb, (i=l,2,...) and emulsion phase passage periods AT i. The sum of bubble passage periods divided by the total observation period (AT),-t-ATg,) corresponds to the bubble fraction... 

In poly(vinyl acetate) copolymer emulsions, the properties are significantly affected by the composition of the aqueous phase and by the stabilizers and buffers used iu the preparation of these materials, along with the process conditions (eg, monomer concentrations, pH, agitation, and temperature). The emulsions are milk-white Hquids containing ca 55 wt % PVAc, the balance being water and small quantities of wetting agents or protective coUoids. 

The system utilized in Figure 3.13 for HIPS can also be used to produce a solution polymerization ABS. This type of ABS is used in non-glossy applications. The glossy ABS is usually produced in an emulsion process in which emulsified polybutadiene latex is grafted and agglomerated and blended with a continuous phase of SAN. This blended material is then dried and pelletized. This process is not cost competitive with the continuous solution polymerization, but it produces a product with a superior balance of properties that commands a premium price. 

From the above discussion, it should be apparent that for POE nonionics, there is a particular temperature where the hydrophilic and lipophilic characters of the surfactant balance each other and yow is at, or close to, its minimum value. It is usually defined operationally, for example, as the temperature where the surfactant phase solubilizes equal volumes of water and nonpolar material or the temperature at which an emulsion (Chapter 8) of the surfactant, water, and nonpolar material inverts. In the latter case, it is known as the phase-inversion temperature (PIT) (Chapter 8, Section IVB). Similarly, there is an electrolyte content at which the hydrophilic and lipophilic characters of ionic surfactants balance. The point at which equal volumes of water and nonpolar material are solubilized into the surfactant is known as the optimal salinity (Healy, 1974) and has been extensively investigated for enhanced oil recovery (Healy, 1977 Hedges, 1979 Nelson, 1980). The optimal salinity or PIT is at or close to the point where the parameter Vh/lcao (Chapter 3, Section II) equals 1 and lamellar normal and reverse micelles are readily interconvertable. 

In 1960, Blair [59] and Dodd [68] published key studies on water-in-crude oil emulsions and their films (see [1-6] for references). Using a Cenco surface film balance to study the water-oil interface, Blair showed that the principal source of stability arises from the formation of a condensed and viscous interfaciai film by adsorption of soluble material from the petroleum phase, such film presenting a barrier to coalescence of the dispersed droplets. This primary film may be augmented by secondary adsorption of large particles or micelles originally suspended in the petroleum. The classical picture of emulsion stabilization by an adsorbed monolayer yielding low interfaciai tension values does not seem to be an accurate one in this case. It appears that a primary adsorbed layer is initially formed, almost certainly comprised of asphaltenes, and a secondary layer superimposes on this primary layer and is likely comprised of asphaltenes, wax particles, and possibly... 

As described earlier in the section on bead or suspension polymers (Section 3.3.1.2), a solution of monomer(s) is prepared in water and then mixed into a low to medium viscosity non-volatile oil phase. In this process, which is often referred to as an inverse emulsion polymerisation technique, surfactants which promote the formation of water-in-oil emulsions are commonly used. These would usually be materials with an HLB (hydrophihc-lipophilic balance) value in the range 4—7, an example of which is sorbitan mono-oleate. In order to achieve the desired droplet particle size of a maximum around 1 pim prior to polymerisation, high shear homogenisers are used to assist the formation of such very small... 

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