A reduced order rate based model for distillation in packed columns: Dynamic simulation and the differentiation index problem

Abstract

This paper presents a rigorous dynamic rate based model suitable for simulation of distillation of mixtures in packed columns. The model equations are described in detail considering structure exploitation at simulation level in order to alleviate the large number of states involved in the model description. Moreover, this kind of model leads to differential-algebraic equations with a differentiation index higher than one. Here this issue is analyzed and a differentiation-index reduction procedure based on the incidence of model states in the Jacobian and the properties of the model dynamics is proposed. This procedure allows for a simplified index-1 model with a reduced stiffness so that dynamic simulation can be performed with off-the-shelf solvers.

Energy-Efficient Diabatic Distillation Using a Horizontal Distillation Column

“…Likewise in liquid phase, normald ( L x ) normald z = J normalL + Q normalΔ H v x and J normalL = k normalL a A c normalt normalL ( x e − x ) From the total material balance normald G normald z = prefix− normald L normald z and from the component material balance normald ( G y ) normald z = prefix− normald ( L x ) normald z The equilibrium relation at the interface is , y normale = K x normale The equilibrium constant was calculated from the average relative volatility.…”

“…Therefore, the rate-based model used in the simulation of the vertical distillation column was utilized in the computation of the horizontal distillation. The rate-based model used in this study employs the assumption of the perfect mixing in the bulk phases . For the examination of axial dispersion of mass and heat transfer in the diabatic horizontal column, the Peclet numbers were calculated in the phases of vapor and liquid, and the results are listed in Table S3 in the Supporting Information.…”

“…The rate-based model used in this study employs the assumption of the perfect mixing in the bulk phases. 26 For the examination of axial dispersion of mass and heat transfer in the diabatic horizontal column, the Peclet numbers were calculated in the phases of vapor and liquid, and the results are listed in Table S3 in the Supporting Information. The numbers are large enough to ignore the effect of the axial dispersion in the column.…”

A simultaneous approach for calibrating Rate Based Models of packed distillation columns based on multiple experiments

“…Although its structure is obtained directly from the formulation of balances and equilibrium relations separately, the variables and equations can be grouped per stage in order to exploit sparsity. This leads to a sparse and reduced band pattern in the model Jacobian (see Bonilla et al (2012) for the actual re-arranged banded structure). This banded structure is known in distillation models and equation-tearing methods have been proposed to solve the nonlinear system of equations (Seader and Henley, 2006;Taylor and Krishna, 6 Postprint version of paper published in Chemical Engineering Science 2013, vol.…”

“…The content is identical to the published paper, but without the final typesetting by the publisher. (Bonilla, 2011;Bonilla et al, 2012). This means a reduction of 6N − 5 equations, or approximately 30%.…”