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真空制盐结晶过程影响因素分析摘要:本文针对真空制盐生产过程,就制盐界关心的增加产品粒度的问题,从结晶机理角度分析了各因素对产品粒度影响的,指出研究生产大颗粒产品盐的方向。关键词:真空制盐;结晶;粒度控制中图分类号:TS36 文献标识码:AThe analysis of the Crystallization process in Vacuum Salt productionSha Zuoliang1 Zhou Ling1 Xhang Guanglin2(1.College of Marine Science and Engineering, Tianjin University of Science & Technology, Tianjin, 300457;2.Hunan Xiangheng Salt mine,Hunan,Xiangheng,421006)Abstract: In this paper, the factors which affect the crystallization process were discussed in the vacuum salt production process. The direction of the study on increasing the crystal size was pointed out.Key words: Vacuum salt; Crystallization; particle size1 前 言近年来,在真空制盐生产中产品的粒度及其分布越来越受到各生产企业的重视。盐的粒度作为衡量盐的重要指标之一,其粒度的大小和均匀性,直接影响到产品的质量、性能和销售价格。平均粒度大且均匀的产品易过滤,干燥过程能耗低盐质较高。同时粒度大且均匀的产品在贮存或运输的过程中结块的倾向小,即使发生了结块现象,由于单位接触点少,结块也易破碎。然而,在我国制盐生产中所使用的流程和设备结构在很多情况下是以提高产品产量和降低能耗的角度而设计,而对怎样提供较好的结晶环境和如何控制产品的粒度考虑不多。尤其是在多效蒸发系统,如何控制产品的粒度报道更是少见。为改善真空制盐过程的产品粒度控制,怎样提供较好的结晶环境,本文从结晶过程的机理角度提出需要探讨的问题和途径,以期引起各生产单位的重视和研究,从而改善我国真空制盐过程中产品粒度控制方面的欠缺。 2 工业结晶过程的基本理论1溶液结晶是溶质从溶液中析出形成晶体的过程,结晶过程的产量取决于结晶物质的溶解度。溶液的浓度恰好等于溶质的溶解度时,称为饱和溶液,溶液含有超过溶解度的溶质含量时,则称为过饱和溶液。溶质含量超过饱和溶液的部分用过饱和度表示。过饱和度是结晶过程的主要推动力。在结晶过程中,溶液的过饱和程度对结晶过程有很大影响,它决定着结晶过程所发生的不同过程及其不同过程的速率,因而直接影响到产品的粒度与粒度分布.根据大量实验研究证实1,溶液的过饱和度与结晶的关系可用图1表示图1 溶液溶解度与过溶解度曲线图溶解度曲线和过溶解度曲线将浓度温度图分割为稳定区、介稳区和不稳定区三个区域。在稳定区内,溶液未达到饱和,因而没有结晶的可能。在介稳区内,不会自发的产生晶核,但若加入晶种,这些晶种就会长大。在不稳定区域内,溶液能自发的产生晶核,越深入不稳定区,自发产生的晶核也多。因此在工业结晶过程中,控制溶液的过饱和程度是控制结晶过程的关键参数。对于工业结晶过程中溶液的过饱和度与结晶的关系,丁绪淮1曾进行了开拓性的研究,他指出,一个特定的物系只有一根明确的溶解度曲线, 但过饱和度曲线的位置却受很多因素的影响。例如有无搅拌、搅拌的强弱、有无晶种等。工业结晶过程只有尽量控制在介稳区内,才能避免自发成核,得到平均粒度大的结晶产品。2.1结晶动力学 一般来讲,在结晶过程中主要发生的过程为晶体的成核和成长。而在工业结晶过程中,成核过程和成长过程是同时发生的,其发生的速率称为成核速率和成长速率。成核速率和成长速率统称为结晶动力学2.1.1 晶核动力学晶核是晶体进而生长的核心,没有晶核的存在,在一定溶液的过饱和度下,不能发生相变过程,即溶液会保持其过饱和状态。晶核的来源主要有三种形式。其一是人为的加入晶体,称为晶种的添加。即通过人为控制的方法,提供所需的晶体成长的表面,使溶液中过饱和的溶质成长于晶种表面,实现结晶过程。第二种晶核的来源是从过饱和溶液中形成晶核,对这种成核过程我们称之为初级成核。初级成核的形成都是从较高的过饱和溶液中新生成的微小晶体粒子,是一种突发过程,过程很难控制。第三种是晶核来源于已存在的晶体。由于不同的原因使晶体破碎而形成的细小晶体作为晶体成长的核心,我们称之为二次成核。二次成核过程比较负载,影响因素很多,主要包括晶体本身的性质和外界操作条件,例如搅拌强度、悬浮密度和过程的过饱和度的影响。其详细的变化规律将在以后的专题部分讨论。经大量的研究发现1.2.3,影响晶体二次成核速率成核的主要的操作条件为系统中的搅拌强度、悬浮液中的晶体含量(悬浮密度)和溶液的过饱和度。因此二次成核速率与这些因素的关系常常以指数形式关联,并表示为: B=KNWiMTj(C)n式中: B成核速率,No./m3sKN成核动力学常数W搅拌强度(rpm,搅拌搅边缘速率,能量输入速率) MT悬浮密度,Kg/m3C过饱和度i 、j、n为经验动力学参数,可用实验数据的回归分析确定。2.1.2 结晶的成长1 在过饱和溶液中已有晶核形成或加入晶种后,以饱和度为推动力,晶核或晶种将长大,这种现象称为晶体生长。按照扩散学说,晶体的生长过程是由三个步骤组成的:(1)待结晶的溶质借扩散穿过靠近晶体表面的一个静止液层,从溶质中转移到晶体的表面;(2)到达晶体表面的溶质长入晶面,使晶体继续增大。同时放出结晶热;(3)放出来的结晶热借传导回到溶液中。因此溶液的过饱和度为其整个晶体成长的传质推动力,而直接影响晶体的成长速率。通常结晶成长速率与溶液过饱和度的关系可表示为:G=KgCg式中: G成长速率,m/sKg 成长动力学常数(一般为温度的函数)C 过饱和度,g/L从成核速率和成长速率两个模型可以看出,无论是晶核的形成还是晶体的成长都必须有过饱和度作推动力。而且过饱和度越大,晶核的形成和晶体的成长速率都越大。因此要使产品保持一定的粒度和分布,则必须控制适当的过饱和度,从而避免过多的晶核形成,维持晶体的成长速率。据研究发现,不同的晶体粒径可能会有不同的成长速率。在大量晶体的存在下,同一成长条件,相同的晶体粒径也许会以不同的成长速率成长。这就是所谓的晶体尺寸依赖型晶体成长速率和晶体成长速率的不同一性。关于晶体成长速率的这些特征,以及其对结晶过程的影响和对产品粒度分布的影响将在相关专题讨论。2.2 NaCl结晶动力学12.2.1氯化钠晶体生长速率与溶液的过饱和度关系 图2 NaCl的生长速率由晶体生长的扩散学说1,同一物料的结晶过程可以属于扩散控制,也可以属于表面反应控制。在较高温度下,表面反应速率有较大幅度的提高,而扩散速率的增大有限,过程往往属于扩散控制;反之,在较低温度下,则可能属于表面反应控制。如图2所示NaCl的生长速率与过饱和度的标绘,在50 以上,关系为直线,为扩散过程控制,生长速率与过饱和度属1阶关系。但是到了50 以下,则关系变为曲线,属于表面反应控制。表面反应的级数从1级到4级都曾有报道,我们一般将表面反应过程方程写成:GM=dm/Adt=kG(C-C*)=kGCl.因此提高温度对提高晶体的成长速率有着明显的效果。2.2.2 氯化钠结晶动力学研究氯化钠从理论上讲,其溶解度曲线比较平缓,且最大过饱和度较小,介稳区窄,属于容易发生成核的结晶体系。由于其在过程中可维持的过饱和度相对较低,从而晶体成长速率相对较小。实现较大晶体的生长必须提供充足的晶体成长时间,同时有效的控制晶体的成核过程的发生。张宏等5在流化床装置中进行了氯化钠结晶动力学实验研究,实验得到氯化钠晶体在流化床内的生长速度分别与晶体粒径、溶液流量和过饱和度之间的关系, 在颗粒尺寸0.3260.693mm 范围内晶体生长速度G与晶体粒径关系不大;在颗粒尺寸0.6931.768mm范围内晶体生长速度G与晶体粒径L的关系式为:G=0.2931L1.5967。周利民6等人在流化床测室腔内研究了不同添加剂对NaCl晶体生长的影响,结果表明在很低的添加剂浓度下, PbCl2和K3Fe(CN)6能有效抑制NaCl晶体生长。根据荷兰科学家Grootsholten7对氯化钠体系研究发现,在MSMPR结晶器(V=55-91L)中,其二次成核速率可表示为:B=1.0*1020(P0N3d5)2/3G2MT;在中式放大结晶器(V=1000-1800L)中,其二次成核速率可表示为:B=0.023KN0.6N1.2-1.6MT,其中KN=5*1015。3 蒸发制盐过程的晶体粒度的影响因素及其控制途径在现阶段4,大部分真空制盐都是在四效强制蒸发器中进行,在四效强制蒸发制盐过程中,可能影响晶体粒径的各种因素作如下分析,同时指出待探讨的问题,建议其改善的可能途径。3.1 料液过饱和度的影响及控制影响结晶的最主要的因素是溶液的过饱和度。对一定的结晶过程而言,过饱和度越大结晶的生长速率大,有利于生长。但若过饱和度过大,超越介稳区极限会导致晶核的生成量过多,产品粒度过小。有效的控制结晶器内的过饱和度是实现晶体粒度控制的关键。结晶器内的过饱和度取决于过饱和度的产生速率与消耗速率的平衡。在蒸发结晶过程中,过饱和度的产生速率取决于蒸发速率,即设备的蒸发强度。蒸发强度愈大,其产生过饱和度的速度愈快,越易形成过高的过饱和度。而过饱和度的消除主要依赖于晶体的自发成核和晶体的成长过程。如果在结晶器内,具有足够的晶体表面和较快的成长速率,由于蒸发所产生的过饱和度,能全部成长在晶体表面上,溶液的过饱和度不会因为超过溶液的最大过饱和度而使溶质以成核过程来消除过饱和度,从而不会产生大量的晶核。如果溶液中晶体表面不足,晶体的生长不足以消除由于蒸发所产生的过饱和度,使得溶液的过饱和度过高,而处于不稳定区域,溶液的过饱和度将以自发成核过程来消耗过饱和度,从而形成大量的细小颗粒。因此控制消耗速率与产生速率将成为真空制盐过程控制粒度的关键所在。怎样实现这个平衡过程,将是我们今后的研究重点之一。但过高的蒸发强度是造成颗粒尺寸过小的一个重要因素。3.2 温度的影响如图2所示NaCl的结晶过程中,温度越高,晶体的生长速率越快。在真空制盐过程中,各效蒸发罐的料液温度均在50以上,所以结晶的过程为扩散控制。温度越高,结晶的成长速率就越大,盐的粒度相对就大。3.3 料液固液比的影响增加料液的固液比,会增大结晶面积而增加过饱和度的消耗速率,能使结晶器内的过饱和度水平较低,有效的抑制局部初级成核的发生,减少细晶量。同时会增加蒸发罐内晶粒停留时间,使产品粒度增大。但固液比太高,造成晶粒与循环泵、加热管以及循环管壁的摩擦加剧,晶体间的碰撞机会也越多,从而产生较多的二次晶核,影响产品粒度。由于固液比过高或过低都不能得到较好的产品粒度,适当的固液比要针对不同的设计罐型及其它参数进行摸索。这也是真空盐生产中控制粒径的重要和优待探讨的因素之一。改变结晶器结构,在增加结晶器固液比的前提下,有效地控制二次成核量也将是今后结晶器设计要重点考虑的问题之一。3.4 循环速度的影响 在蒸发操作中,选择适宜的循环速度对晶体的粒度控制是很重要的,如果流速较低,会增大循环料液的过热度,从而增大溶液的过饱和度,导致晶核数增多,不利于晶粒的长大。但如果循环速度过大而增大了晶体相互碰撞、与器壁撞击以及被叶轮撞击的力度和几率,容易造成已生成的结晶破碎,产生大量二次晶核,使得产品颗粒过细,影响产品质量。循环速度的大小对盐结晶粒度影响很大。对于每一特定的蒸发罐均有其生产大粒盐所对应的适宜的循环速度。利用变频调速电机可以在一定范围内对循环速度进行调节,便于找出适宜的循环速度。3.5 停留时间晶体在生长区的停留时间越长,晶体生长的时间越长,晶体粒度越大。粗粒径盐的生成必须有足够的生长时间。据有关资料介绍8,平均粒径0.4mm以上的晶体,停留时间不应少于1小时。采取小加热室,大蒸发罐的配置,可以维持低的过饱和度和较长的停留时间。然而停留时间过长,也会增加晶体的二次成核的数量,而不能达到生产大颗粒晶体的目的,同时也会降低设备的生产效率。确定适宜的停留时间,要在准确的结晶动力学数据的基础上,根据晶体生长速率而确定。如果在一定的操作条件下,成核速率过高,可使用改变操作参数或其他手段消除过多的晶核,维持晶体生长所需要的时间,同时控制晶体个数不能过高。3.6流程的安排在真空制盐生产中,有不同的进料和排料方式。进料和排料方式一般可分为三种:顺流、逆流和平流。从晶体粒度控制的角度,对纯的氯化钠溶液的制盐过程,顺流于逆流没有什么不同。仅仅在不同的蒸发器内,其结晶的温度不同,从而起操作条件不同,不会影响晶体的粒度。然而不同的排盐流程可能对产品的粒度有较大的影响。虽然理论上可以采用逆流排盐的操作方式,但是由于高温排料的很多弊端使得逆流排盐很少在真空制盐中使用。这里仅对排盐流程中的顺流和平流两种方式进行比较分析。顺流排盐是把盐浆从I效依次转向II、III、IV效。有效的利用了设备空间,增加了晶体的停留时间,在相对较小的蒸发室内,可以使晶体有较长的生长时间而有可能得到较大的晶体,从而得到较大颗粒产品。然而,在这种操作条件下,由于蒸发操作过程受到悬浮密度的限制,只有在末效可以使用较高的悬浮密度,而前三效的悬浮密度不能过高。因此其蒸发强度受到悬浮密度的限制,如果蒸发强度过高,就会产生过高的过饱和度,从而产生较大的成核速率,因而产品的粒度较小。一般情况下,在I效蒸发罐中的蒸发强度较高,因此在I效的蒸发器中会有大量细小晶体。要想得到较大的晶体,其蒸发强度就应控制在适宜的水平。平流排盐过程,各效的蒸发器可认为是一个独立的结晶器,只要在操作上和结晶器的设计上适宜,可得到较好的晶体粒度,晶体的粒度容易控制。3.7 蒸发器结构蒸发器的结构对结晶过程的影响主要是从以下几个方面考虑。其一,在结晶内晶体的悬浮状态要好,尤其是在液体的蒸发区域,要存有较多的晶体才能有效地消除过饱和度,避免局部过饱和度过高而产生过剩的晶核。其二,尽量避免晶体与循环泵的接触时间,以避免碰撞产生的二次成核过多。在可能的情况下,可设置细晶消除装置。同时循环量的设计要考虑避免溶液的过热度过高所造成的局部过饱和度高。4.总结在真空制盐生产中,氯化钠的结晶过程包括过饱和溶液的形成、晶核的生成、晶体的生长等阶段。通过分析,在制盐生产中影响结晶的主要因素有:料液过饱和度、蒸发罐温度、固液比、循环流速、停留时间、流程安排、蒸发器结构等。要提高盐的质量,生产粒度符合要求,且分布均匀的盐,设计时选择的工艺条件和设备结构以及各种改进措施都应该从影响结晶因素方面考虑。符号说明:B成核速率,#./m3sKN成核动力学常数Kg 成长动力学常数W搅拌强度(rpm,搅拌边缘速率,能量输入速率)MT悬浮密度,Kg/m3G成长速率,m/sC过饱和度,g/LP0能量输入速率N搅拌速率,rpsd搅拌桨叶直径,m停留时间,s参考文献:1 丁绪淮.工业结晶M.化学工业出版社,19852 Cayey, N.W.and J.Estrin.Secondary nucleation in agitated magnesium solutions (J).Ind.Eng.Chem.Fundam.1967 (1).3 Sung, C.Y.Secondary nucleation of magnesium sulfate by fluid shear (J).AIChE.1963 (19):9574 苏家庆.真空蒸发制盐工艺M.全国井矿盐工业科技情报站,1992,57-66.5 张宏.流化床中氯化钠结晶动力学实验研究J.青海大学学报,2006(5):8-9,136 周利民.氯化钠和硫酸钾晶体生长动力学研究J.东华理工学院学报,2005(3):266-2697 P.A.M.Grootscholten.Effect of Scale-up on Secondary Nucleation Kinetics for the Sodium Chloride-water System J.Institution of Chemical Engineers.1984 (62):179-1898 吴香琦.增大真空制盐生产中盐粒度的途径J.中国井矿盐,2002(13):12-14The analysis of the Crystallization process in Vacuum Salt productionSha Zuoliang1 Zhou Ling1 Zhang Guanglin2(1.Tanjin Key laboratory of Marine resources and technology, Tianjin University of Science & Technology, Tianjin, China 300457;2.Hunan Xiangheng Salt mine company ,Hunan, Xiangheng, 421006)Abstract: In this paper, the factors which affect the crystallization process were discussed in the vacuum salt production process. The direction of the study on increasing the crystal size was pointed out.Key words: Vacuum salt; Crystallization; particle size1. INTRODUCTION In recent years, the product size and size distribution of the salt produced by vacuum evaporation system was paid more and more attention by many production enterprises. As the important quality parameters of the salt product, the particle size and uniformity of particle size distribution directly influence product purity, properties and selling price. The product which has large size and narrow distribution is easy to be filtered. The energy consumption in drying process is low. Simultaneously,the tendency of caking becomes smaller with large size crystals during the storage and transport. Even if they were agglomerated, it is easy to be broken because the unit contact points are less. Even the salt product size is so important parameter, it was not paid enough attention in the process and equipment structure in the vacuum salt production. The most attention was focused on increasing the capacity of the process and on the reducing the energy consumption. The consideration on how to provide the well crystallization environment and how to control the size of product is not much done. Especially, the report on how to control the size of the product in the multiple-effect evaporation system is rare. The aim of this paper is to analysis the problems and to discuss the ways to improve the size of the product in vacuum salt-making process based on the crystallization mechanism, so that the attention can be paid in particle size control from all companies. The technology in controlling the product size for the vacuum salt-making process can be established.2THE BASIC THEORY OF INDUSTRY CRYSTALLIZATION PROCESS The solution crystallization is the process in which solute in the solution becomes crystals. The amount of the production rate per unit solution in crystallization process is determined by the solubility of solute. The solution whose concentration is equal to solubility is called saturated solution. When the concentration is higher than solubility, the solution is called as supersaturated solution. The difference between the concentration of supersaturated solution and the saturated solution expresses by supersaturation. The supersaturation is driving force in the crystallization process. The supersaturation has tremendous influence in the crystallization process. The level of the supersaturation decides process which occurs in crystallization process and the rate of different processes, further it influences the product size and size distribution. According to many estudies1 the relation between statue of solution and crystallization can be expressed as Fig 1.Fig.1 the solubility curve and supersaturated solubility curveThe saturated and supersaturated curve divides concentration - temperature chart into the stable region, transition region and not stable region. In the stable region, the solution is not saturated, thus the crystallization will not occur. In the transition region, the spontaneous nucleation does not occur, but if crystal is existing, the crystals will grow. In the “not stable region”, nucleation will occur spontaneously. The less the stability is, the more the nuclei will be formed. Therefore in the industry crystallization process, the degree of supersaturation is the key parameter to be controlled. Regarding relations between degree of supersaturation and the crystallization process in the industry process, the result reported by Ding 2 pointed out that a specific system only have an explicit solubility curve, but the supersaturation curve was depended on many factors such as agitation speed, seed of crystal. In the industry crystallization process, solution should be controlled in transition region as far as possible for avoiding spontaneous nucleation and obtaining large size of product. 2.1 Crystallization Kinetics Generally speaking, the nucleation and growth are the main processes in the crystallization process. The nucleation and growth are simultaneous occurred in the industry crystallization process. The nucleation rate and growth rate are together called as the crystallization kinetics.2.1.1 Nucleation The nucleus is the core of crystal growth. If the nucleus is not existence, the phase will not change at certain degree of supersaturation, namely the solution can maintain supersaturation. The origin of nucleus mainly has three forms. First, adds the crystal factitiously, it is called adding seed crystal. The crystallization process was carried out by growing the solute on the surface of seed. The second kind of nuclei are formed from the supersaturated solution, this kind of nucleation process was called as primary nucleation. The primary nucleation is a kind of sudden process which forms small size of crystals when solution is highly supersaturated and difficult to be controlled. The third kind of nuclei is from the existed crystal. The tiny crystals which was broken down from the existed crystal, this kind of nuclei was called as secondary nucleation. Secondary nucleation process is complex and influenced by many factors which mainly include properties of crystal and operation conditions, such as mixing intensity, suspension density and degree of supersaturation. It was found that the main factors which affect secondary rate are mixing intensity, suspension density and degree of supersaturation of the solution 1.2.3. The relationship between secondary nucleation rate and the factors are mostly expressed by the following equation.B = KNNiMTj(C)n Where, B is the nucleation rate No. /m3s, KN is the coefficient of nucleation rate, N is mixing intensity, MT is suspension density, Kg/m3 , C is the degree of supersaturation, i, j, n are the power of the relative parameters in the nucleation equation, which can be obtained by experimental data. 2.1.2 Crystal growth If the crystals which no matter come from the seed or secondary or primary nucleation were being in the supersaturated solution, they will grow. This kind of process is called as crystal growth. According to the diffusion theory, the crystal growth process have three steps: (1) the crystallized solute passes through the solution layer beside the crystal surface to crystal surface by diffusion; (2) the solute arrived at the crystal surface enters the crystal face, causes the crystal size to be continuously increased and release the heat of crystallization simultaneously; (3) the heat of crystallization returns to the solution by conduction. Therefore the degree of supersaturation is the driving force of crystal growth, and directly influences the rate of the crystal growth. Usually the relationship of crystallization growth rate and the degree of supersaturation solution is represented as: G = KgCgWhere G is the crystal growth rate, m/s, Kg is the coefficient of growth rate, C is the supersaturation solution , kg/m3.Because the supersaturation is the driving force for the nucleation and growth rate, the degree of supersaturation is the key factor in crystallization process. The higher the supersaturation is, the higher the nucleation and crystal growth rate are. Therefore, the degree of supersaturation has to be controlled in a proper level so that the excessive nucleation can be avoid and existing crystal growth grow. According to the report, different sizes of crystals may have different growth rates. On the other hand, the same size of crystals may also have different growth rates. This is so-called crystal size dependent crystal growth rate and crystal growth rate disperse. About the characteristics of crystal growth rate, and the influences to crystallization process as well as product size distribution are more complicated and not discuss here.2.2 Crystallization Kinetics of NaCl 2.2.1 NaCl Crystal Growth Rate Fig.2 The growth rate of NaClBase on diffusion theory1 the crystal growth rate may be controlled by diffusion or by surface reaction. At the high temperature, the surface reaction rate can be greatly enhanced but the diffusion rate increases limitedly so that the crystal growth rate of NaCl belongs to the diffusion control. On the other hands, the process could belong to surface reaction control at low temperature. The growth rate of NaCl is given in Fig. 2. When temperature is higher than 50, the crystal growth rate is proportional to the degree of supersaturation as a straight line. It means that the crystal growth is controlled by diffusion. When the temperature is lower than 50, the relationship becomes a curve, it is a surface reaction control. 2.2.2 NaCl Crystallization Kinetics Theoretically speaking, the solubility curve of NaCl is quite flat, and the degree of supersaturation is also small, transition area is narrow and system is easy to have nucleation. If the degree of supersaturation is small the crystal growth rate is small relatively. In order to get large size of crystals, the sufficient time for crystal growth should be provided, and crystal nucleation process should be controlled effectively. Zhang et al.5 studied NaCl crystallization kinetics in the fluid bed crystallizer. The relationship between NaCl crystal growth rate and the crystal particle size, the liquid flow rate and the degree of supersaturation was experimently obtained. The dependence of crystal growth rate G on the crystal particle size were not evidence when the particle sizes are 0.326mm to 0.693mm; The dependent of crystal growth rate G on crystal particle size L can be expressed as G=0.2931L1.5967, when the particle size is in the range of 0.693mm to 1.768mm.Zhou et al6 studied the influences of different additive on NaCl crystal growth in the laboratory fluid bed crystallize. The results indicated that PbCl2 and K3Fe(CN)6 could suppress NaCl crystal growth effectively even concentration of additive was very low. According to the studies of Grootsholten7, the secondary nucleation rate in the MSMPR crystallizer (V=55-91L) can be expressed as: B = 1.0*1020(P0N3d5)2/3G2MTThe secondary nucleation rate in the crystallizer (V=1000-1800L) can be express as: B = 0.023KN0.6N1.2-1.6MT, KN=5*10153. THE FACTORS AFFECTING THE CRYSTAL SIZE AND CONTROLLING STR

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