液相色谱填料粒内传质参数识别及简化General Rate模型的应用
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摘要
高效液相色谱技术作为一种有效的分离手段,已经在生化和医药等诸多领域得到广泛应用。在这些领域的分离问题中,粒内传质过程的影响已表现得比较突出,因此吸引了众多色谱研究者对这一问题的关注。目前,虽然有关色谱粒内传质过程的研究已经在各个层面展开,但仍然有一些与色谱的应用和研究实践密切相关的问题尚待解决。首先,表征粒内传质过程需要应用能全面反映各种扩散、传质阻力因素影响的GR(General Rate)模型,而GR模型中包含的粒内传质参数尚缺乏准确、有效的方法来确定。其次,GR模型求解难度较大,因而限制了GR模型的实际应用,尤其是在复杂色谱系统、如模拟移动床(SMB)中的应用。本文工作正是围绕这些问题而开展的。
探索有效易行的粒内传质参数识别方法。在文献调研基础上确立了以矩分析法为主的参数识别方法。本文首先对谱带三阶中心矩测量误差的影响因素进行了实验分析,在此基础上改进测量条件并获得了相对误差小于10%的三阶中心矩的测量结果,进一步分析表明,在本文所涉及的各反相液相色谱体系中都存在相同的谱带三阶中心矩与流动相流速的定量关系。综合分析该定量关系、GR模型矩方程及谱带二阶中心矩测量结果,得出外部传质系数正比于流动相流速的结论。在这一结论的基础上,只需利用二阶中心矩测量结果,就可以方便地计算出粒内传质参数的数值。
给出了GR模型的简化模型。在上面所推导的GR模型矩方程基础上,导出了与GR模型等效的MED(Modified Equilibrium-Dispersion)模型。由于MED模型仅能保证所计算出的谱带与GR模型计算结果有相同的一、二阶矩,所以两模型的等效性还需进一步验证。本文比较了两个模型的数值解分别对不同水平粒内传质参数、非线性效应及流动相流速的响应情况,结果表明两模型数值解在各种参数条件下都具有很好的一致性。这可极大地简化GR模型的求解过程。
讨论了粒内传质参数对模拟移动床(SMB)可分离区间及分离结果的影响。以上述MED模型替代GR模型,用数值算法分别计算了不同水平的粒内传质参数条件下SMB可分离区间及分离产品的纯度、回收率及富集率。结果表明粒内有效扩散系数对SMB分离过程的影响始终大于外部传质系数；粒内传质过程与非线性浓度效应共同影响SMB可分离区间,且随粒内传质参数值的减小,SMB可分离区间缩小,分离产品纯度下降,但产品回收率及富集率增加。
High Performance Liquid Chromatography is a highly effective separation method used widely in biochemical and Pharmaceutical fields. In practice, the remarkable effect of intraparticle mass transfer processes in column on separation result has been extensively studied by many chromatographic researchers. So far, there have been many reports focusing on the problem. However, some difficulties baffle the researchers and prevent them from understanding further the intraparticle mass transfer processes in chromatographic column. First, the General Rate (GR) model is necessary to describe detailedly the mass transfer processes in column, but the parameters involved in GR model are difficult to determine accurately. Second, the numerical calculation of GR model is complicated and time consuming. Thus, the practical application of GR model, especially the application in complicated chromatographic systems, is limited.
In this dissertation, the identification of intraparticle mass transfer parameters involved in GR model is discussed. And the moment analysis method is adopted in this work. Because the accurate measuring result of the third central moment is difficult to obtain, the factors which result in the error of measurement of the third central moment of eluted band profiles are investigated experimentally in this work. The experimental conditions for the measurement of the third central moment have been optimized. Under this improved condition, the third central moments of band profiles are measured with their relative standard deviations below than 10%. Further analysis about the measurement results of the third central moments indicates thatμ3u0 4(whereμ3 is the third central moment of band profile and u0 the surperficial velocity of mobile phase) is always proportional to u0 under all the experimental conditions in this work. And then it can be deduced that the external mass transfer coefficient is proportional to u0 according to the measurement results of the moments and the moment equations of GR model calculated in this work,. Consequently, the intraparticle mass transfer parameters can be determined from the measurement result of the second central moments of band profiles which can be measured accurately in practice.
Secondly, the Modified Equilibrium-Dispersion (MED) model equivalent to the GR model is developed based on the moment equations of GR model deduced in this work. Although the first and second moments of the band profiles calculated from MED model are same with those from GR model, the equivalence between the two models is investigated under the conditions of different levels of intraparticle mass transfer parameters, nonlinearity and velocity of mobile phase, respectively. And the results show that the band profiles calculated from the two models always match well with each other. Therefore, the numerical solution of the GR model can be substituted by that of the MED model to simplify the calculation of GR model greatly.
At last, the effects of intraparticle mass transfer parameters on the separation region and performance parameters of SMB (Simulated Moving Bed) are discussed in this work. The MED model above is adopted to replace the GR model as the mathematical model for the single column of SMB, and the separation regions (99% purity) as well as the purities, recoveries and enrichments of separation products of SMB are calculated under different levels of intraparticle mass transfer parameters. The calculated results indicate the following conclusions. The effect of effective diffusivity on SMB process is always more remarkable than that of external mass transfer coefficient. Both nonliearity and intraparticle mass transfer process influence the separation region of SMB obviously. The separation region of SMB shrinks, while the recovery and enrichment of separation products increases with the decrease of intraparticle mass transfer parameters.
探索有效易行的粒内传质参数识别方法。在文献调研基础上确立了以矩分析法为主的参数识别方法。本文首先对谱带三阶中心矩测量误差的影响因素进行了实验分析,在此基础上改进测量条件并获得了相对误差小于10%的三阶中心矩的测量结果,进一步分析表明,在本文所涉及的各反相液相色谱体系中都存在相同的谱带三阶中心矩与流动相流速的定量关系。综合分析该定量关系、GR模型矩方程及谱带二阶中心矩测量结果,得出外部传质系数正比于流动相流速的结论。在这一结论的基础上,只需利用二阶中心矩测量结果,就可以方便地计算出粒内传质参数的数值。
给出了GR模型的简化模型。在上面所推导的GR模型矩方程基础上,导出了与GR模型等效的MED(Modified Equilibrium-Dispersion)模型。由于MED模型仅能保证所计算出的谱带与GR模型计算结果有相同的一、二阶矩,所以两模型的等效性还需进一步验证。本文比较了两个模型的数值解分别对不同水平粒内传质参数、非线性效应及流动相流速的响应情况,结果表明两模型数值解在各种参数条件下都具有很好的一致性。这可极大地简化GR模型的求解过程。
讨论了粒内传质参数对模拟移动床(SMB)可分离区间及分离结果的影响。以上述MED模型替代GR模型,用数值算法分别计算了不同水平的粒内传质参数条件下SMB可分离区间及分离产品的纯度、回收率及富集率。结果表明粒内有效扩散系数对SMB分离过程的影响始终大于外部传质系数；粒内传质过程与非线性浓度效应共同影响SMB可分离区间,且随粒内传质参数值的减小,SMB可分离区间缩小,分离产品纯度下降,但产品回收率及富集率增加。
High Performance Liquid Chromatography is a highly effective separation method used widely in biochemical and Pharmaceutical fields. In practice, the remarkable effect of intraparticle mass transfer processes in column on separation result has been extensively studied by many chromatographic researchers. So far, there have been many reports focusing on the problem. However, some difficulties baffle the researchers and prevent them from understanding further the intraparticle mass transfer processes in chromatographic column. First, the General Rate (GR) model is necessary to describe detailedly the mass transfer processes in column, but the parameters involved in GR model are difficult to determine accurately. Second, the numerical calculation of GR model is complicated and time consuming. Thus, the practical application of GR model, especially the application in complicated chromatographic systems, is limited.
In this dissertation, the identification of intraparticle mass transfer parameters involved in GR model is discussed. And the moment analysis method is adopted in this work. Because the accurate measuring result of the third central moment is difficult to obtain, the factors which result in the error of measurement of the third central moment of eluted band profiles are investigated experimentally in this work. The experimental conditions for the measurement of the third central moment have been optimized. Under this improved condition, the third central moments of band profiles are measured with their relative standard deviations below than 10%. Further analysis about the measurement results of the third central moments indicates thatμ3u0 4(whereμ3 is the third central moment of band profile and u0 the surperficial velocity of mobile phase) is always proportional to u0 under all the experimental conditions in this work. And then it can be deduced that the external mass transfer coefficient is proportional to u0 according to the measurement results of the moments and the moment equations of GR model calculated in this work,. Consequently, the intraparticle mass transfer parameters can be determined from the measurement result of the second central moments of band profiles which can be measured accurately in practice.
Secondly, the Modified Equilibrium-Dispersion (MED) model equivalent to the GR model is developed based on the moment equations of GR model deduced in this work. Although the first and second moments of the band profiles calculated from MED model are same with those from GR model, the equivalence between the two models is investigated under the conditions of different levels of intraparticle mass transfer parameters, nonlinearity and velocity of mobile phase, respectively. And the results show that the band profiles calculated from the two models always match well with each other. Therefore, the numerical solution of the GR model can be substituted by that of the MED model to simplify the calculation of GR model greatly.
At last, the effects of intraparticle mass transfer parameters on the separation region and performance parameters of SMB (Simulated Moving Bed) are discussed in this work. The MED model above is adopted to replace the GR model as the mathematical model for the single column of SMB, and the separation regions (99% purity) as well as the purities, recoveries and enrichments of separation products of SMB are calculated under different levels of intraparticle mass transfer parameters. The calculated results indicate the following conclusions. The effect of effective diffusivity on SMB process is always more remarkable than that of external mass transfer coefficient. Both nonliearity and intraparticle mass transfer process influence the separation region of SMB obviously. The separation region of SMB shrinks, while the recovery and enrichment of separation products increases with the decrease of intraparticle mass transfer parameters.
引文
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