Optimal Control of Periodic Adsorption Processes

周期性吸附过程在生产气体、精细化学品或药品的过程工程中广泛建立，并且涉及吸附和反应过程相结合的新用途。所有这些过程的特点是在固体固定床中不同物种的浓度前沿移动，并且在不同类型的操作之间进行周期性切换。每个相位的动力学可以用一维或二维的安装偏微分代数方程（PDAE）来建模，从而用周期性切换的PDAE来描述整个系统。启动后，最终达到周期吸引子或循环稳态（CSS）并用于生产。这种CSS在操作成本和产品规格方面应该是理想的，并且近年来已经看到了各种新型流程操作变体的发展，以提高效率。其中两种工艺将在多特蒙德进行研究：Engell教授小组研究的具有可变入口浓度的模拟移动床（SMB） （ModiCon-SMB）和Agar教授小组研究的具有解吸冷却（以下称为解吸冷却(DC)-工艺）的全新固定床催化反应器。由于过程模型的大规模和周期性，只有少数基于模型的优化方法存在，并且它们在大规模应用中的使用受到令人禁止的计算时间的限制。该项目的目的是开发有效的数值方法来优化周期性开关大型装置PDAE所描述的周期性吸附过程。这些方法应结合新颖的简化牛顿型优化方法和皮卡德迭代，以有效地处理周期性约束。我们的新方法具有以下特征：选择一个同步优化框架，其中离散模型方程作为非线性约束进入优化问题；只模拟和优化一个周期；采用时域分解来处理中间切换和大量数据，采用一种新颖的简化SQP框架来处理模型方程和控制离散化后的非线性规划问题，采用混合牛顿-皮卡德格式来有效地处理周期性约束在多特蒙德有两场比赛。该项目的最终应用目标是优化和实验验证新型解吸冷却（DC）过程的运行机制。

Periodic adsorption processes are widely established in process engineering for the production of gases, fine chemicals or Pharmaceuticals, and novel uses involve the combination of adsorption and reaction processes. Characteristic for all these processes are traveling concentration fronts of different species in a solid fixed bed, and periodic switching between different types of operation. The dynamics of each phase can be modelled by instationary partial differential algebraic equations (PDAE) in one or two spatial dimensions, so that the overall system is described by periodically switched PDAE. Following start-up, a periodic attractor, or Cyclic Steady State (CSS), is finally reached and used for production. This CSS should ideally be optimal with respect to operational costs and product specifications, and recent years have seen the development of a variety of novel process operation variants to improve efficiency. Two of these are the processes to be investigated in Dortmund: the simulated moving bed (SMB) with variable inlet concentrations (ModiCon-SMB) studied in the group of Prof. Engell and the entirely novel fixed bed catalytic reactor with desorptive cooling (in the following called Desorptive cooling (DC)-Process ) in the group of Prof. Agar.Due to the large scale of the process models and due to their periodic nature, only few model based optimisation approaches exist and their use for large scale applications is limited by prohibitive computation times. Aim of the project is to develop efficient numerical methods for optimisation of periodic adsorption processes described by periodically switched large scale instationary PDAE. These methods shall combine novel reduced Newton type optimisation methods with a type of Picard iteration to cope efficiently with the periodicity constraints. The following features shall characterise our new methods:¿ a simultaneous optimisation framework is chosen in which the discretised model equations enter the optimisation problem as nonlinear constraints¿ only one cycle is simulated and optimised, and periodicity is imposed in form of additional constraints¿ a time-domain decomposition is used to handle the intermediate switching and the enormous amount of data¿ a novel reduced SQP framework being able to cope with inexact Jacobians is used to solve the nonlinear programming problem resulting after discretisation of model equations and controls¿ a mixed Newton-Picard scheme is used to treat the periodicity constraints efficientlyThe method development is driven by the requirements of the two processes in Dortmund. Final application aim of the project is the optimisation and experimental validation of the operating regime of the novel desorptive cooling (DC) process.