第九章 结晶系统取样和分析
Chapter 9 Sampling and Analyzing Crystallizing Systems
取样技术应该满足下列要求The technique of sampling should satisfy the following requirements:
-取样区的体积最小，使得取出的样品代表结晶器内一个点的晶体尺寸和过饱和度，而不是从结晶器的一部分上取的样（在后一种情况下这些参数将是平均值）the sampling should be such as to minimize the volume from which a sample is taken so that, effectively, the sample provides representative crystal size and supersaturation parameters at a point within the crystallizer, rather than from a portion of the crystallizer(in which case these parameters will be averages);
-被取样溶液的温度必须足够精确地测出the temperature of solution being sampled must be measured with sufficient accuracy;
-取样器的结构和形状应该对流动方式，不管是晶体或者溶液，引入最小的流体力学扰动the construction and shape of sampler should be such as to introduce minimum hydrodynamic disturbance to the flow patterns, either of crystals or of solution;
-取样器最好应该能用于同时抽取晶体和溶液样品preferably, the sampler should be used for sampling both crystals and solution. 处理样品时必须保证样品的真实性。这条原则在结晶系统中往往难以达到。在取样、样品处理、液相和固相分析过程中可能的误差来源见图9.1。 non-representative Sampling withdrawal Liquid Solids non-representative withdrawal mechanical damage to solids Handling of a sample loss of solvent Liquid Solids loss in authenticity through through evaporation nucleation, growth, dissolution, gain of solute agglomeration, breakage, etc. through dissolution loss of solute through nucleation and growth Analysis systematic and non- Liquid Solids systematic and non- systematic errors systematic errors Figure 9.1 Illustration of sources of errors involved in sampling, sample handling and
analysis of liquid and solid phase in crystallization
§9.1液相样品的取样和分析 Sampling and analyzing liquid phase samples
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9.1.1 液相取样技术Sampling techniques for liquid phase 在大气压下运行的结晶器中液体的取样，可用图9.2所示的装置。 如果要同时取出悬浮液中的固体和液体样品，则可用图9.3所示的装置。 9.1.2过饱和度测定 Measurement of supersaturation 结晶推动力可以定义为浓度推动力或过饱和度。在这里，我们将浓度推动力表示成： Δc = c-c* ------------------------------------------------(9.1) 而将过饱和度表示成： ζ=(cˊ-c*ˊ)/ c*ˊ ---------------------------------------(9.2) 式中where c 溶液浓度solution concentration, kg/kg solution c* 溶液平衡浓度solution equilibrium concentration, kg/kg solution cˊ溶液浓度solution concentration, kg/m3 solution c*ˊ溶液平衡浓度solution equilibrium concentration, kg/m3 solution ζ过饱和度supersaturation 图9.4举例说明测量硫酸铝钾（即钾明矾）水溶液中过饱和度的方法。 Solution Sample Sampling Density measurement θ ρL Solubility Data Density-concentration c* =P(t) calibration curve c=P(ρL) c* c supersaturation Δc= c-c* ζ=( c-c*)×100/ c* Figure 9.4 Schematic representation of experimental and computational procedures involved in the technique for determination of supersaturation
过饱和度测量精度估算Expected accuracy of the supersaturation determination 过饱和度可以表示成浓度推动力c-c*, 或相对过饱和度，（cˊ- c*ˊ）/c*ˊ。 第一种情况下最大百分误差为 The maximum percentage error in the first of these cases is：
??c??c??c*c?c*?100???????(9.3)
式中where εc and εc* 分别是c and c* 的95％置信限 εc and εc* are 95% confidence limits on the values of c and c* respectively。 对于钾明矾体系：
εc＝±0.00014 kg hydrate/kg solution
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εc*＝±0.00016 kg hydrate/kg solution Equation (9.3) thus becomes: εΔc=0.0003×100/(c-c*) ------------------------------------------(9.4) 式9.4指出浓度差小于0.0003 kg hydrate/kg solution不太可能用这种方法测出。 按式9.2计算过饱和度时，会产生附加误差。If the supersaturation is to be calculated from equation(9.2),an additional error will be introduced by dividing the difference (cˊ- c*ˊ）by c*ˊ. 过饱和度测定中的最大百分误差成为The maximum percentage error involved in the determination of supersaturation now becomes:
102???[?c??(1??)?c*?]???c*???????9.5?
式中where ζ是待测的过饱和度ζis the supersaturation that has to be measured. 代入c*ˊ，εcˊ，εc*ˊ的值Taking the value of c*ˊat 30 ℃ and substituting forεcˊ andεc*ˊ， 式9.5变成equation(9.5) becomes:
???704.1[0.00014?0.00016(1??)]?1??????(9.6) 图9.5示出了最大百分误差与Δc和ζ之间的关系。 从图9.5就可以看得很清楚，浓度差小于0.0003 kg水合物/kg溶液或过饱和度小于0.002，是不太可能测出来的。因为此时误差已达100％。
9.1.3 密度的快速和准确测定Rapid and accurate density measurement
§9.2 固相样品的取样和分析 Sampling and analyzing solid phase samples
9.2.1 从悬浮液中取固体样Sampling of solids from suspensions 一般认为有二个因素决定从搅拌悬浮液中产品取出特征：
1．结晶器内悬浮液的均匀性 The homogeneity of suspension within the crystallizer.
2．取出面附近的流体力学条件。取出面即晶体悬浮液通过该平面进入取样管线。The hydrodynamic conditions in the vicinity of the discharge plane, i.e. the plane through which the crystal suspension enters the discharge line. 9.2.2 颗粒粒度分析 Particle size analysis 颗粒粒度分析的粒度范围可达10cm以上，幅度大于7个数量级。用同一种方法分析这么大的粒度范围是不可能的。 工业实际中遇到的大多数晶体粒度分布在临界晶核尺寸到几毫米范围内。很明显，分布的下限已超出了目前的粒度分析方法的检测范围。在结晶过程研究和技术领域，一个可靠的方法是用筛分法测出100μm以上的晶体粒度，用其它合适的方法测出小晶体的粒度。 筛分是最简单、最普遍的粒度分析方法。但筛分法只限于测定75μm以上颗粒。测定小晶体尺寸的一种适宜技术是Coulter计数法。 9.2.3筛分 Sieving
9.2.4 考尔特计数器法The Coulter counter method
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第十章 结晶器设计中基本原理的应用
Chapter 10 The Use of Fundamental Principles in Crystallizer Design
图10.1示出了成功的结晶器设计需要确定结晶器的类型和体积以及操作条件，以满足 在规定的生产速率下的产品要求，如平均粒度和变异系数。成功的结晶器设计就意味着使结晶器类型和操作条件符合结晶系统的要求，使结晶动力学和粒数事件能相互起良好作用，最终达到产品设计要求。
MAIN TARGETS OF SUCCESSFUL CRYSTALLIZER DESIGN
production average coefficient rate size of variation slurry discharge average residence rate time
suspension density
yield per-pass crystallizer crystallizer volume type
crystallizer TECHNICAL operating ASPECTS conditions reducing incrustation reducing energy requirements pure crystallization kinetics population functions
Figure 10.1 Schematic representation of interrelationships between design targets in industrial crystallization and the corresponding design formulation
图10.1隐含了结晶器设计需遵循的原则。例如，生产速率和平均晶体粒径这二项要求
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通过物料衡算和粒数衡算来决定结晶器体积。所需的变异系数对结晶器型式的选择起决定作用。结晶器操作条件通常由技术因素决定，例如减少结疤、降低能耗。操作条件直接与结晶过程推动力的产生方式相关联，影响结晶器内的物料衡算和粒数衡算。
§10.1利用物料衡算确定结晶器体积 The use of mass balance to formulate crystallizer volume
对于等温结晶器中清液进料、溶剂蒸发的情况，总物料衡算为The overall mass balance for a situation where clear feed solution is evaporated in an isothermal crystallizer becomes: Qiρi = Qoρo + Qcρc + Qvρv -----(10.1) (clear feed) (product solution) (product crystals) (evaporated solvent) （清液进料） （产品溶液） （产品晶体） （蒸发出的溶剂） 结晶组分的物料衡算为and the mass balance for crystallizing components: QiρiCi = QoρoCo + Ms(Qo + Qc) -------------------------(10.2) 式中where
Ms 为悬浮密度，定义为单位体积晶浆的产品晶体质量is the suspension density defined as mass of product crystals per unit volume of slurry. 式10.2可以重排为Equation 10.2 may be rearranged to give: QiρiCi - QoρoCo = Ms(Qo + Qc) = Pc --------------(10.3) (per-pass yield) (slurry discharge rate) (production rate) （单程产率） （晶浆排出速率） （生产速率）
为了满足一定的生产速率，需要的结晶器体积为The crystallizer volume required to deliver certain production rate brcomes: V = ( Qo + Qc) η = Pcη/ Ms --(10.4) (slurry discharge rate) (residence time) 式10.4表明，结晶器体积可以由晶浆排出速率和停留时间算出。式10.4中，Pc是规定的生产速率，是已知值。η是停留时间，决定于产品的平均粒度，Ms决定于物料衡算，也可以依据粒数衡算概念预测。例如，对于全混釜，当晶体生长与粒径无关时，稳态下的悬浮密度是： Ms = 6kvρcn0[Gη]4 ------------------------------------------------------------------(5.13) (For an MSMPR crystallizer) §10.2 利用粒数衡算概念表征产品晶体粒度分布 The use of the population balance concept to characterize product crystal size distributions
10.2.1利用粒数衡算概念预测平均粒径 The use of the population balance concept to predict average sizes 第四章已经讲到，平均粒径可以用下面几个方程求出： 众数mode size, LM dW(L)/dL=3kvρcnL2 + kvρcL3 dn/dL=0 --------------------------------(4.25) 解得L即得by solving for L yields LM. 中值median size, Lm ?50??
Lm?00nL3dLnLdL3?100??????????(4.26)
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