Dynamic optimization for grade transition processes using orthogonal collocation on molecular weight distribution

Abstract

To meet the demands of a competitive market, an industrial plant often produces several grades of polymer product through the same process in an economical way. As molecular weight distribution (MWD) is a crucial quality index of polymers, dynamic optimization for grade transition based on MWD is highly important, but challenging. This study considers the development of optimization models for MWD‐based grade transition. An MWD reconstruction method using orthogonal collocation in two dimensions is developed to capture the dynamic feature of MWD in time and the distributive feature in chain length. The simultaneous collocation approach is adopted to discretize the model. Two optimization formulations are proposed to describe minimizing the transition time as well as off‐spec production. Both formulations inherit the advantages of the simultaneous collocation approach. The numerical results show that the proposed methods can efficiently solve the grade transition problem with MWD specification, and obtain high performance control profiles to reduce the production cost. © 2019 American Institute of Chemical Engineers AIChE J, 65: 1198–1210, 2019

Generalized initialization for the dynamic simulation and optimization of grade transition processes using two‐dimensional collocation

“…The difficulty of solving the dynamic model is related to the difference between the two transition grades. The easier grade transition from grade 2 to 3 is shown in Ma et al 15 ; the total CPU secs in IPOPT for this dynamic simulation based on Ma's initial values and our initialization methods are 14.586 and 10.157 s, respectively. Also, the total CPU secs in IPOPT for our initialization is 1.352 s. The simulation time based on initial values with Ma's tests takes longer.…”

“…In this work, a collocation model that describes dynamic grade transition of an industrial HPDE slurry process 15 is used to demonstrate the initialization. This flexible process can achieve several different grades by adjusting the operating conditions.…”

“…Grades 1 and 4 almost reach the lower and upper limits of the molecular weight of polyethylene chains and are used as challenging demonstrations for extremely wide ranges of transitions. Grades 2 and 3 are steady‐state grades with the normal transition range in Ma et al 15 Operating conditions of steady‐state simulation for four example grades are given in Table 1.…”

“…Recently, Ma et al 15 proposed a fully dynamic model for a HDPE slurry process and directly reconstructed the detailed MWD based on orthogonal collocation method in two dimensions. Different from orthogonal collocation methods in one dimension (e.g., time), 16 this method describes the complete grade transition process in terms of the MWD, using an EO model with dimensions of time and chain length.…”

Inferential Model Predictive Control of Continuous Pulping under Grade Transition

“…Although the previous modeling efforts made remarkable contributions on capturing macroscopic phenomena in the pulp digester, important microscopic properties are still partially described; recently developed multiscale models are able to capture the evolution of fiber morphology such as porosity, CWT, and fiber length, − but these models have focused on a batch pulping, which is not applicable to a large-scale commercial continuous pulp digester. Furthermore, even though optimal grade transition techniques have been developed for polymerization processes, ,, very limited efforts have been made to implement the strategies to Kraft pulping processes, despite the need for those techniques to handle the frequent grade changes and unexpected demand surges. Motivated by the limitation, we developed a multiscale model of continuous pulping and designed an inferential model-based feedback controller to regulate blow-line pulp properties and achieve optimal grade transition operations.…”