Crystallization heat balances

In the special case of adiabatic vacuum cooling, the quantity of solvent evaporated is fixed by the crystallizer heat balance. Thas. ft, is a fixed ratio—referred to as which can be determined from the following... 

The heat balance follows a similar relationship with the rate of latent heat release in proportion with the amount of element crystallized... 

Combination of Equations 1 and 2 allows calculation of the rate of heat transfer from the growing crystal surface to the bulk solution. Under heat balance conditions, this rate of heat generation must be balanced by the amount of heat removed from the crystallizer by convection and conduction. This will be determined by the overall heat transfer coefficient, U, between the bulk solution and the refrigerant including convective resistances between the fluid and both sides of the crystallizer wall (refrigerant side and product side) as well as the conductive resistance across the crystallizer wall. 

Ice Crystal Growth. In order to quantify these results for the production of large disc and spherical crystals, seversd batch experiments on 6% lactose solutions were undertaken. The experimental conditions and results are shown in Table II. In these experiments, nuclei were generated at -2.5 C (except for Run Sa at -4.0°C) and input to the batch crystallizer controlled at various refirigerant temperatures. As these crystals grew, the total crystal surface area was controlled manually in order to maintain a heat balance for a constant value of the refrigerant temperature. Slurry removal rate for these experiments... 

Figure 3. Changes in size distribution with time during growth of ice crystal seeds in 6% lactose under batch or semi-batch growth conditions, concentration processes based on suspension growth. In addition, the relation of this observed widening to the heat balance conditions needs to be further explored.

The earliest employ s supported silver crystals. It leads to a heat balance equalized between the % apon2er and the exchanger/reaaor stage. It avoids methanol distillation and recyclings and achieves sufficient once-through conversion to leave the residual alcohol in the fonnaldehyde solunon. The total yield is 87.5 molar per cent based on the methanol introduced, and 91 per cent in relation to the metlianol cooverted The formaldehyde concentration of the final product ranges from 40 to 44 per cent weight... 

TGA curve, an abrupt weight loss occurs a little above 320 °C where the sample apparently becomes liquid and a significant amount of monomer crystals is detected in the quartz tube of the heating balance. This indicates sublimation of monomer formed through depolymerization. The DTA curve of the monomer (DSP) shows a melting point peak at 230 °C. Above 360 °C, the DTA curve of DSP coincides with that of poly-DSP since poly-DSP depolymerizes nearly quantitatively to DSP at high tempertures. On the other hand, the DTA curve of amorphous poly-DSP shows only a single sharp endothermic peak at 325 °C in helium. 

The specific models will be further subdivided into isothermal and non-isothermal models. This distinction is justified because mathematical modeling of a nonisothermal system involves a heat balance in addition to coverage equations (or reactor mass balances), and therefore introduces strong Arrhenius-type nonlinearities into the coverage equations. Nonisothermal processes are much more dependent on the reactor type and the form of the catalyst (supported, wire, foil, or single crystal). Thus these heat balance equations that describe them must take into account the type of catalyst and... 

Although the thermal demands of crystallization processes are small compared with those of possibly competitive separation processes such as distillation or adsorption nevertheless, they must be known. For some important systems, enthalpy-composition diagrams have been prepared, like those of Figure 16.4, for instance. Calculations also may be performed with the more widely available data of heat capacities and heats of solution. The latter are most often recorded for infinite dilution, so that their utilization will result in a conservative heat balance. For the case of Example 16.3, calculations with the enthalpy-concentration diagram and with heat of solution and heat capacity data are not far apart. 

Smith, A.L., Shirazi, H.M., and Mulligan, S.R. Water sorption isotherms and enthalpies of water sorption by lysozyme using the quartz crystal micro-balance/Heat-conduction calorimeter, Biochim. Biophys. Acta — Protein Struct. Mol. Enzymol., 1594,150, 2002. 

A heat balance can be made wherein the individual heat effects, such as the sensible heat required for heating or cooling the solution, the heat of crystallization of the product formed, and the latent heat of vaporization for liquid vaporized can be combined into an equation for the total heat effects. 

To supply the heat necessary sensible, latent, heat of solution, and heat of crystallization. (The last two are sometimes improperly omitted in heat-balance calculations.)... 

To determine the crystal yield from a vacuum crystallizer (section 7.5.3) it is necessary to estimate the amount of solvent evaporated, V. This depends on the heat made available during the operation of the crystallizer, i.e. the sum of the sensible heat drop of the solution, which cools from the feed temperature to the equilibrium temperature in the vessel, and the heat of crystallization Kber-ated. The heat balance, therefore, will be... 

The heat effects accompanying a crystallization operation may be determined by making heat balances over the system, although many calculations may be necessary, involving knowledge of specific heat capacities, heats of crystallization, heats of dilution, heats of vaporization, and so on. Much of the calculation burden can be eased, however, by the use of a graphical technique in which enthalpy data, solubilities and phase equilibria are represented on an enthalpy-composition H x) diagram, sometimes known as a Merkel chart. 

---