Linear model predictive control for transport‐reaction processes

The article deals with systematic development of linear model predictive control algorithms for linear transport‐reaction models emerging from chemical engineering practice. The finite‐horizon constrained optimal control problems are addressed for the systems varying from the convection dominated models described by hyperbolic partial differential equations (PDEs) to the diffusion models described by parabolic PDEs. The novelty of the design procedure lies in the fact that spatial discretization and/or any other type of spatial approximation of the process model plant is not considered and the system is completely captured with the proposed Cayley‐Tustin transformation, which maps a plant model from a continuous to a discrete state space setting. The issues of optimality and constrained stabilization are addressed within the controller design setting leading to the finite constrained quadratic regulator problem, which is easily realized and is no more computationally intensive than the existing algorithms. The methodology is demonstrated for examples of hyperbolic/parabolic PDEs. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2644–2659, 2017     

Analysis of mass transfer in parallel-flow dialyzer with internal recycle for improved performance

The internal reflux effect on dialysis through the retentate phase of a parallel-flow rectangular module is investigated. Theoretical analysis of mass transfer in the membrane devices with or without recycling is analogous to heat transfer in heat exchangers. In contrast to a device without reflux, considerable mass transfer is achievable if parallel-flow dialyzers are operated with reflux, which provides an increase in fluid velocity, resulting in a reduction in mass-transfer resistance. It is concluded that reflux can enhance mass transfer, especially for large flow rate and feed-concentration operated under high reflux ratio.     

Optimal boundary control of a diffusion–convection-reaction PDE model with time-dependent spatial domain: Czochralski crystal growth process

In this paper the optimal boundary control problem for diffusion–convection-reaction processes modeled by partial differential equations (PDEs) defined on time-dependent spatial domains is considered. The model of the transport system with time-varying domain arises in the context of high energy consuming Czochralski crystal growth process in which the crystal temperature regulation must successfully account for the change in the crystal spatial domain due to the crystal growth process realized by the pulling crystal out of melt. Starting from the first principles of continuum mechanics and transport theorem the time-varying parabolic PDE describing temperature evolution is derived and represented as a nonautonomous parabolic evolution system on an appropriately defined function space which is exactly transformed in the infinite-dimensional boundary control problem for which a boundary linear quadratic regulator is proposed. Properties of the solution of the time-varying parabolic PDEs given by the two-parameter evolutionary system are utilized in the synthesis of the optimal boundary regulator, and the control law is applied to the model given by a two-dimensional partial differential equation in the cylindrical coordinates representing the Czochralski crystal growth process with one-dimensional growth direction. Finally, numerical results demonstrate optimal stabilization of the two-dimensional temperature distribution in the crystal.     

顺流与逆流板式换热器的性能分析

以顺流与逆流两种形型的板式换热器为研究对象,通过计算热通量,换热效率,换热温差,对这两种换热器的性能进行比较分析。     

An investigation in the effects of recycles on laminar heat transfer enhancement of parallel-flow heat exchangers

It was demonstrated that fluid recycling could effectively enhance heat transfer rates of heat exchangers, however, related investigations were limited. In the current work, parallel-flow heat exchangers with basic recycles or revised recycles are investigated in the laminar regime. Theoretical models of thermo-hydraulic performances are established. The effects of reflux ratio, capacitance rate ratio, heat transfer area, and recycle length are investigated. The results demonstrate that the dimensionless heat transfer rate rises with the increase of reflux ratio or capacitance rate ratio, or with the decrease of heat transfer area, and the maximum values reach up to 127% and 121% for basic internal and external recycles, respectively. Basic internal recycles generate larger dimensionless heat transfer rates under larger reflux ratios, while basic external recycles perform more reliably over the whole reflux ratio range. Compared with basic recycles, revised recycles (i.e., partial-length recycles) require smaller pumping powers. Thus, partial-length recycles can improve the dimensionless overall performance of full-length recycle heat exchangers, e.g., half-length recycles increase the dimensionless overall performance by 65%. Fluid recycling does not need to change geometrical structures and fluid flow rates, thus it is a competitive approach of thermal augmentation in heat exchangers.     

Numerical methods of solution for continuous countercurrent processes in the nonsteady state part I: Model equations and development of numerical methods and algorithms

Simple, efficient and noniterative algorithms are developed for the calculation of the dynamics of continuous countercurrent processes described by hyperbolic differential equations. The algorithms are derived using the method of characteristics and are particularly useful for either general quadratic or hyperbolic isotherms such as the Langmuir isotherm. The use of characteristic coordinates for the numerical solution avoids accumulating errors that would arise from computations based on a rectangular grid of real time and space coordinates. The proposed methods can provide an efficient framework for extension to transport processes with general nonlinear rate expressions. The algorithms and methods initially derived for simple models can be extended to more complex systems such as countercurrent flow with accumulating stationary phases and response to distributed disturbances. The application of the algorithm and methods to a number of countercurrent mass and heat transfer processes will be illustrated in Part II, where the accuracy and efficiency of the proposed methods will also be demonstrated by comparison to available analytic solutions. An example demonstrating the extension of the method to a system with complex coupled boundary conditions will also be discussed.     

Heat exchanger network synthesis with detailed exchanger designs: Part 1. A discretized differential algebraic equation model for shell and tube heat exchanger design

A new method for the detailed design of shell and tube heat exchangers is presented through the formulation of coupled differential heat equations, along with algebraic equations for design variables. Heat exchanger design components (tube passes, baffles, and shells) are used to discretize the differential equations and are solved simultaneously with the algebraic design equations. The coupled differential algebraic equation (DAE) system is suitable for numerical optimization as it replaces the nonsmooth log mean temperature difference (LMTD) term. Discrete decisions regarding the number of shells, fluid allocation, tube sizes, and number of baffles are determined by solving an LMTD-based method iteratively. The resulting heat exchanger topology is then used to discretize the detailed DAE model, which is solved as a nonlinear programming model to obtain the detailed exchanger design by minimizing an economic objective function through varying the tube length. The DAE model also provides the stream temperature profiles inside the exchanger simultaneously with the detailed design. It is observed that the DAE model results are almost equal to the LMTD-based design model for one-shell heat exchangers with constant stream properties but shows significant differences when streams properties are allowed to vary with temperature or the number of shells are increased. The accuracy of the solutions and the required computational costs show that the model is well suited for solving heat exchanger network synthesis problems combined with detailed exchanger designs, which is demonstrated in Part 2 of the paper.     

用动量方程进行平行流列管式固定床反应器的设计

采用动量方程建立了平行流列管式固定床反应器管外流动模型，计算出反应器管外压力分布和速度分布，并用６０°角度的片状平行流试验模型加以验证，试验结果和模型计算结果取得了良好的一致性。同时，研究了实现管外流动和传热均布的分布板环隙孔和小孔调节方法。     

Backstepping control of chemical tubular reactors

In this paper, a globally stabilizing boundary feedback control law for an arbitrarily fine discretization of a nonlinear PDE model of a chemical tubular reactor is presented. A model that assumes no radial velocity and concentration gradients in the reactor, the temperature gradient described by use of a proper value of the effective radial conductivity, a homogeneous reaction, the properties of the reaction mixture characterized by average values, the mechanism of axial mixing described by a single parameter model, and the kinetics of the first order is considered. Depending on the values of the nondimensional Peclet numbers, Damköhler number, the dimensionless adiabatic temperature rise, and the dimensionless activation energy, the coupled PDE equations for the temperature and concentration can have multiple equilibria that can be either stable or unstable. The objective is to stabilize an unstable steady state of the system using boundary control of temperature and concentration on the inlet side of the reactor. We discretize the original nonlinear PDE model in space using finite difference approximation and get a high order system of coupled nonlinear ODEs. Then, using backstepping design for parabolic PDEs we transform the original coupled system into two uncoupled target systems that are asymptotically stable in l²-norm with appropriate homogeneous boundary conditions. In the real system, the designed control laws would be implemented through small variations of the prescribed inlet temperature and prescribed inlet concentration. The control design is accompanied by a simulation study that shows the feedback control law designed with sensing only on a very coarse grid (using just a few measurements of the temperature and concentration fields) can successfully stabilize the actual system for a variety of different simulation settings (on a fine grid).     

Heat exchanger network synthesis with detailed exchanger designs—2. Hybrid optimization strategy for synthesis of heat exchanger networks

We propose a new strategy to synthesize heat exchanger networks with detailed designs of individual heat exchangers. The proposed strategy uses a multistep approach by first obtaining a heat exchanger network topology through solving a modified version of the mixed integer nonlinear programming (MINLP) stage-wise superstructure of Yee and Grossmann, which includes a smoothed LMTD approximation and pressure drops. In a second nonlinear programming (NLP) suboptimization step, we allow for nonisothermal mixing to solve problems with or without exchanger bypasses. The selected heat exchangers along with the mass and energy balances obtained are then used to design the network with detailed exchanger designs through solving a sequence of NLPs for individual heat exchanger designs. The NLPs are based on the detailed discretized optimization models of Kazi et al., which solve quickly and reliably to obtain heat exchangers based on rigorous, first-principles derived coupled differential equations. These models solve a differential algebraic equation system and do not rely on usual assumptions associated with other heuristic-based exchanger design methods, such as log mean temperature difference and F_T correction factors. These detailed exchanger designs are then used to update the network optimization model through sets of correction factors on heat exchanger area, number of shells, heat transfer coefficients, and pressure drops of each exchanger design, in a method based on that of Short et al. The method solves reliably, guaranteeing feasible exchangers for every potential network generated by the shortcut models, through validation with rigorous heat exchanger models at every iteration. In addition, the method does not increase the nonlinearity of the MINLP model, nor does it require any manual intervention or initialization from the user. Three examples are solved and the results are compared to those obtained in the literature.     

Feedback control of hyperbolic distributed parameter systems

Hyperbolic distributed parameter systems (DPS) represent a large number of industrial processes with spatially nonuniform operating variable profiles. Research has been conducted to develop high-performance control strategies for these systems by exploiting their high-fidelity models. In this paper, a feedback control method that yields improved performance is proposed for DPS modelled by first-order hyperbolic partial differential equations (PDEs) using the method of characteristics. Simulation results show that this method can provide effective control for the systems modelled by a scalar PDE as well as a system of PDEs. Further, it can efficiently compensate the effect of model-plant mismatch and effectively reject the disturbances.     

Optimal operation of heat exchanger networks through energy flow redistribution

This article presents a novel energy flow redistribution methodology to achieve optimal operation of heat exchanger networks. The proposed method aims to manipulate the propagation path of a disturbance through the network to reduce its impact on utility consumption. Specifically, an optimization problem is formulated to generate new duty targets for heat exchangers of the network when a disturbance is encountered. Subsequently, a feedback control system is designed to track these targets by manipulating bypasses around the process heat exchangers. The effectiveness of the proposed framework is illustrated with the help of three benchmark examples. The proposed approach can handle disturbances in inlet as well as target temperature, inlet flow and heat transfer coefficient of individual heat exchangers.     

ACHEMA 2022 – Heat Exchanger

ACHEMA is an international exhibition for innovation and development in the process industry. Heat exchangers are necessary parts of many process engineering plants. This report intends to highlight the presented novelties in relation to heat exchangers at ACHEMA 2022. The trends and challenges of heat exchangers were explored in discussions with exhibitors and through presentations at the congress. The field of application for heat exchangers broadens as well as their performance increases. Existing designs are enhanced, traditional types of heat exchangers are combined, and software is developed based on both traditional models and artificial intelligence. An overview of relevant innovations and developments in heat exchangers is given.     

Long range pipeline leak detection and localization using discrete observer and support vector machine

A realistic pipeline modeled by a nonlinear coupled first-order hyperbolic partial differential equations (PDEs) system is studied for the long transportation pipeline leak detection and localization. Based on the so-called water hammer equation, a linear distributed parameter system is obtained by linearization. The structure and energy preserving time discretization scheme (Cayley–Tustin) is used to realize a discrete infinite-dimensional hyperbolic PDEs system without spatial approximation or model order reduction. In order to reconstruct pressure and mass flow velocity evolution with limited measurements, a discrete-time Luenberger observer is designed by solving the operator Riccati equation. Based on this distributed observer system, data on different normal and leakage conditions (various leak amounts and positions) are generated and fed to train a support vector machine model for leak detection, amount, and position estimation. Finally, the leak detection, amount estimation, and localization effectiveness of the developed method are proved by a set of simulations. © 2019 American Institute of Chemical Engineers AIChE J, 65: e16532 2019     

Change in internal energy of thermal diffusion stagnation point Maxwell nanofluid flow along with solar radiation and thermal conductivity

This paper concerns the characteristics of heat and mass transfer in upper convected Maxwell fluid flow over a linear stretching sheet with solar radiation, viscous desperation and temperature based viscosity. After boundary layer approximation, the governing equations are achieved (namely Maxwell, upper convected material derivative, thermal and concentration diffusions). By using the self-similarity transformations the governing PDEs are converted into nonlinear ODEs and solved by RK-4 method in combination with Newton Raphson (shooting technique). The effects of developed parameters on velocity, temperature, concentration, fraction factor, heat and mass diffusions are exemplified through graphs and tabular form and are deliberated in detail. Numerical values of fraction factor, heat and mass transfer rates with several parameters are computed and examined. It is noticed that the temperature is more impactable for higher values of radiative heat transport, thermal conductivity and viscous dissipation. The comparison data for some limiting case are acquired and are originated to be in good agreement with previously published articles.     

管壳式换热器的优化设计

管壳式换热器是广泛应用于各个领域的工业设备，在国民经济中具有非常重要的作用，管壳式换热器的效率问题是设计工作的核心。本文利用优化设计原理，建立了以管壳式换热器优化设计模型。分析了影响年总费用的因素．编制了管壳式换热器优化设计计算机程序。最后给出了一个计算实例说明优化设计程序的作用。     

一种扁管管翅式换热器的高效数值设计方法

传统的数值模拟方法计算量大,计算时间长,很难满足现代工业发展的需求。以扁管管翅式换热器为例,采用适体坐标与最佳正交分解（POD）相结合的方法构建了低阶模型,在等热流边界条件下对扁管管翅式换热器中流动与传热过程进行计算,并将POD计算结果与有限体积法（FVM）计算结果进行了对比。结果表明：POD方法能准确地捕捉到不同数量参数变化情况下的温度场及速度场信息。对于3变量工况重构速度场及温度场的相对偏差平均值的最大值分别为1.90%、0.308%。采用POD方法在保证计算精度的前提下将FVM计算速度最大能提高3093.4倍。研究对于提高扁管管翅式换热器数值设计效率、拓展POD方法的工程应用领域有一定的理论参考价值。     

基于知识工程的换热器结构合理选择

换热器是调节工艺介质温度以满足工艺要求以及回收余热以实现节能降耗的关键设备,在炼油、化工、冶金、食品等许多工业部门以及日常生活中有着极为广泛的应用.换热器是非标设备,又是特种设备,虽然其设计有相应的设计标准和规范,但在满足工艺要求的前提下可选择的结构较多,也有进行创新设计的余地和必要.应用知识工程理论和相关技术,根据换热器的特点,利用Excel建立数据库,采用Visual Studio 2010开发换热器选型软件,实现换热器结构的合理快速设计.