Crystal product rate

The crystallization yield (crystal product rate) and supplied or removed heat flow due to crystal formation in the solution, result from mass and energy balances over the crystallizer, in single or multistage crystallization plants. 

The crystal product rate expected during the crystallization process may be calculated from a mass balance over the crystallizer with known feed and discharge flows and the substance properties of the dissolved substance in the solvent, such as solubility behavior, crystal load, etc. 

A concentrated solution of flow rate with a saturation load A l, at entry temperature dy, given in kg dissolved substance per kg solvent, is fed to the crystallizer (Fig. 7-23). Fy is identical to in Chapters 7.2.1.1 and 7.2.1.2, if the solution is preevaporated to the saturation point. A ] therefore can be found from w,  

Representation according to Schaefer [0.1, Vol. 2] and data of GEA-Wiegand, Ettlingen. 

V Forced circulation evaporator, horizontal position a Evaporation section 

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Several features of the hypothetical system in Eigure 2 can be used to illustrate proper selection of crystallizer operating conditions and limitations placed on the operation by system properties. Suppose a saturated solution at temperature is fed to a crystallizer operating at temperature T. Because the feed is saturated, the weight fraction of in the feed is given as shown in Eigure 2. The maximum crystal production rate from such a process depends on the value of and is given by... 

Mass and Energy Balances. The formulation of mass and energy balances follows procedures outlined ia many basic texts (2). The use of solubihties to calculate crystal production rates from a cooling crystallizer was demonstrated by the discussion of equations 1 and 2. Subsequent to determining the yield, the rate at which heat must be removed from such a crystallizer can be calculated from an energy balance ... 

The measurement of the width of the metastable zone is discussed in Section 15.2.4, and typical data are shown in Table 15.2. Provided the actual solution concentration and the corresponding equilibrium saturation concentration at a given temperature are known, the supersaturation may be calculated from equations 15.1-15.3. Data on the solubility for two- and three-component systems have been presented by Seidell and Linkiv22 , Stephen et alS23, > and Broul et a/. 24. Supersaturation concentrations may be determined by measuring a concentration-dependent property of the system such as density or refractive index, preferably in situ on the plant. On industrial plant, both temperature and feedstock concentration can fluctuate, making the assessment of supersaturation difficult. Under these conditions, the use of a mass balance based on feedstock and exit-liquor concentrations and crystal production rates, averaged over a period of time, is usually an adequate approach. 

Now suppose a saturated solution at temperature T is fed to a crystallizer operating at temperature Since it is saturated, the feed has a mole fraction of R equal to x . The maximum production rate of crystals occurs when the solution leaving the crystallizer is saturated, meaning that the crystal production rate, mprod, depends on the value of Ty... 

P Crystallizer production rate (weight/unit time) r Particle radius r Critical particle radius rg Over-all growth rate coefficient... 

K is a constant and Lr is the size of a crystal grown from a nucleus (zero size) in the draw-down time, t, i.e. the overall residence time, defined as the ratio of the mass of crystals in suspension to the crystal production rate, or the volume of suspension to the volumetric feed rate. Saeman also compared the cases of mixed-suspension, classified-product removal (MSCPR) with MSMPR operation and showed, for example, that the age of a product mean size crystal was... 

The required crystal production rate and supply of feed liquor to the plant will generally be among the deciding factors in the choice between a batch and continuous unit. For example, for crystal production rates > 100 kg h or feed liquor rates >1 m h, continuous operation might be considered, but there is no general rule. Sugar, for example, is commonly produced batchwise at equivalent rates up to 20 000 kg h per crystallizer. 

Amongst the first quantities that may have to be specified, or calculated, in a design procedure are the crystal production rate, a clearly defined mean product crystal size, the crystallizer working volume, liquor circulation rate, magma density, mass of crystals in the suspension and the residence times of both crystals and liquor. Several of these quantities are interrelated and will not need separate calculation. Some are directly linked to the effective overall crystal growth rate, a sensitive system-specific quantity. 

The over-all residenee (draw-down) time, T, in many classifying crystallizers is about 2h. Thus the mass of crystals in suspension, W, may be determined from the crystal production rate, P, by equation 9.91. After the appropriate value for the suspension density or bed voidage, e, has been chosen the suspension volume may be calculated from equation 9.90 or 9.92. 

To determine the crystal production rate S for solvated crystals the general case of combined cooling and evaporation crystallization is postulated. A solution cooled... 

Fig. 7-23, Crystal product rate and heat rate. CS Concentrated solution ML Mother liquor VA Vapor CR Crystal...

The yield // of the crystallization process is proportional to the crystal production rate and is given by... 

Rearranging Eq. (7-41) with respect to the crystal product rate, S gives... 

Additional considerations for the selection of a crystallizer are given in Fig. 7-26. Figure 7-27 shows the specific crystal product rate of CSCPR crystallizers, with fluid-bed suspension. Modeling of crystallizers is described in [7-66]. 

Fig. 7-27. Specific crystal product rate of CSCPR crystallizers as a function of the upward flow velocity and allowable oversaturation Ac. Representation according to W6hlk and Hofmann [7.51].

The above thermodynamic information gives an idea about the maximum amount of material that will crystallize as a solid however, to get an insight into the rate of the prodnction of crystals we need information about its kinetics. The crystallization kinetics provide design information like crystal production rate, size distribution, and its shape. 

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