恒馏出液组成常规间歇精馏过程模拟的数值计算误差

Numerical Calculation Errors of Simulating Conventional Binary Batch Distillation Process with Constant Distillate Composition Operation

为了完善间歇精馏过程的模拟技术,研究了模拟间歇精馏过程的数值计算误差及其相对稳定定量方法。采用拟稳态法模拟理想条件下恒馏出液组成操作常规二元间歇精馏过程,总汽化量数值计算结果的误差是截断误差、舍入误差和传播误差的耦合。根据大数定律,提出了理论板有限时,总汽化量数值计算结果误差的近似计算方法,及提出了采用拟合法计算Richardson外推法的误差系数。拟合法通过拟合足够多组总汽化量的数值计算结果和相应的过程离散段数计算误差系数,有效降低了(或消除)随机误差(舍入误差和传播误差)对计算误差系数的影响,提高了Richardson外推法估计截断误差的准确(稳定)性。

To improve the simulation technology of batch distillation process,the numerical calculation errors of simulating batch distillation process and its relatively stable quantitative method were studied.The quasi steady-state method was used to simulate the process of conventional binary batch distillation with constant distillate composition operation under ideal conditions.The errors of the numerical calculation result of the total vaporization are the coupling of truncation errors,rounding errors and propagation errors.According to the law of large numbers,an approximate calculation method for the errors of the numerical calculation results of the total vaporization was proposed when the number of theoretical plates was limited,and a fitting method was proposed to calculate the error coefficient of Richardson's extrapolation method.The fitting method of calculating the error coefficients by fitting enough sets of the numerical calculation results of the total vaporization and the corresponding number of discrete segments of the process effectively reduces(or eliminates)the influence of random errors(rounding errors and propagation errors)on the calculation of the error coefficients,and improves the accuracy(stability)of Richardson's extrapolation method for estimating the truncation errors.