Crystallizers enthalpy balances

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. 

SUPERSATURATION. Mass and enthalpy balances shed no light on the CSD of the product from a crystallizer. Conservation laws are unchanged if the product is one huge crystal or a mush of small ones. 

Overall Material and Energy Balance. Assuming specific heats are constaid and identical for solid and liquid, the heat of crystallization is constant, and the reference states are solid napthalene and liquid benzene at Tb, the spent liquor discharge temperature. We can express the overall enthalpy balance as... 

This fundamental relationship points out that the temperature at which crystal and liquid are in equilibrium is determined by the balancing of entropy and enthalpy effects. Remember, it is the difference between the crystal and... 

The specific enthalpies ia equation 9 can be determined as described earUer, provided the temperatures of the product streams are known. Evaporative cooling crystallizers operate at reduced pressure and may be considered adiabatic (Q = 0). As with of many problems involving equiUbrium relationships and mass and energy balances, trial-and-error computations are often iavolved ia solving equations 7 through 9. 

In any state preceding the onset of crystallization at T < To we assume that bundle stability is favored by localized attractive interactions between contacting (short) stems, some enthalpy advantage being balanced by a corresponding entropy loss (see Fig. 3). Depending upon the core structure of the crystalline stems, various bundle models were examined [8,9]. In the present... 

The solution of mass and energy balances requires solubility and enthalpy data on the system of interest. Various methods of presenting solubility data were given earlier, and the use of solubilities to estimate crystal production rates from a cooling crystallizer was demonstrated by the discussion of Eq. (2). Subsequent to determining the yield, the rate at which heat must be removed from the crystallizer can be calculated from an energy balance ... 

Calculate the energy removal An energy balance around the crystallizer (see Fig. 10.5) gives Q = LHl + SHs — FHf, where Q is the heat added (or the heat removed, if the solved value proves to be negative) L, S, and F are the flow rates for mother liquor, solid product, and feed, respectively and Hl, Hs, and Hp are the enthalpies of those streams relative to some base temperature. Select a base temperature Tr of 70°C, so that Hp = 0. 

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. 

A convenient way to represent enthalpy data for binary solutions is via an enthalpy-concentration diagram. Enthalpy-concentration diagrams (H-x) are plots of specific enthalpy versus concentration (usually weight or mole fraction) with temperature as a parameter. Figure 4.21 illustrates one such plot. If available, such charts are useful in making combined material and energy balances calculations in distillation, crystallization, and all sorts of mixing and separation problems. You will find a few examples of enthalpy-concentration charts in Appendix I. 

Irrespective of whether the crystallization response should be taken as Parts n and III or just Part II for lactose (see Figure 8.4, and earlier discussion), it is clear that the crystallization response is reduced in size due to the endotherm for water desorption. Buckton and Darcy (27) have shown that the measured calorimetric crystallization peak, plus the enthalpy of vaporization for an estimate of the amount of water desorbed (i.e., the quantity of water needed to plasticize Tg below T minus the quantity of water that is retained as a hydrate) approximates to the combined endotherms for hydrate loss and melting, which are measured in a DSC for the crystallized lactose. This balance of heats would indicate that the contributions within the saturated salt solution are relatively small during the crystallization response. It... 

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