Navier-Stokes Equation on the Rectangle: Controllability by Means of Low Mode Forcing

We study controllability issues for the Navier-Stokes equation on a two-dimensional rectangle under so-called Lions boundary conditions. The Navier-Stokes equation is controlled by forcing applied to a small number of harmonic modes. Methods of Geometric/Lie Algebraic Control Theory are used to prove controllability by means of low mode forcing of finite-dimensional Galerkin approximations of this system. Proving the continuity of the “control ↦ solution” mapping in the so-called relaxation metric we use it to prove both solid controllability on the observed component and L ²-approximate controllability of the Navier-Stokes equation (full system) by low mode forcing. 2000 Mathematics Subject Classification. 35Q30, 93C20, 93B05, 93B29. Supported by FCT (Portuguese Foundation for Science and Technology).     

Reconstruction of a heat exchanger network under industrial constraints — the case of a crude distillation unit

Heat exchanger network retrofit using a pinch based approach is presented. In this approach, the criterion of minimum sensitivity of heat exchanger to fouling effects is accounted for. The present paper introduces this criterion without explaining its details that are described in the literature. A summary is given of HEN reconstruction in a crude distillation unit processing 4.2 million ton crude oil per year. While the total heat quantity of hot streams is 110 MW, the heat recovery in the existing HEN is 60 MW. Using Pinch Analysis, the target value of heat recovery at ΔT_min=10 K was determined at 91 MW. Measurements were carried out on the existing HEN with the aim to determine the influence of fouling effects on the heat transfer in the exchangers. Taking local constraints including fouling into account, HEN reconstruction was proposed. The heat savings in the reconstructed HEN was estimated at 75 MW.     

Optimal synthesis of a heat-exchanger network

Thermodynamic, heat transfer and economic concepts influencing the synthesis of a heat-exchanger network (HEN) coupled to a crude fractionation unit are examined. The impact of the variation of the minimum temperature approach (Δt_min) on energy and capital targets is studied using recent developments in pinch technology. The optimal pinch approach temperature has been determined using the ‘supertargeting’ concept where proper trade-off between energy and capital targets is observed prior to design. A heuristic evolutionary approach has then been used for the generation of the optimal HEN.     

Pinch locations at heat capacity flow-rate disturbances of streams for minimum utility cost heat exchanger networks

The work deals with heat exchanger network (HEN) targeting under heat capacity flow-rates of streams disturbances. In particular, the aim is to calculate all pinches that can exist in a HEN with utilities of minimum cost when stream heat capacity flow-rates (CPs) are allowed to change within given ranges. It is assumed that the disturbances are stochastic. The knowledge of pinches at certain as well uncertain data is of great importance in designing HENs. For instance, Pinch Technology is based on pinch phenomenon and its influence on HEN operation and design. In case of parameter disturbances, this is even more important since additional application in HEN’s control (see e.g. [1], [2]). It is worthnoting that in case of disturbances, pinches behave in very complex manner as it was shown in [1], [2], [3], [4], [5]. A rigorous approach has been developed for calculating all feasible locations of pinches that can occur in minimum utility cost of HENs operating at varying heat capacity flow-rates of process streams. The method is based on recursive solution of mixed-integer linear programming (MILP) optimisation model that requires quite moderate number of binary variables. Examples of method application and analysis of results are presented in the work.     

Paths combination for HENs retrofit

With the significant increase in fuel price, energy conservation projects should be reviewed and analyzed properly. Retrofit of heat exchanger networks (HENs) is among the common projects to reduce the plant operational cost. This paper introduced a new procedure using the path analysis approach for HEN retrofit. The developed procedure attempts at generating options for retrofit solution. These options are created by combining the available utility paths in HEN systematically. Instead of relying on a single path, the heat load could be shifted from HEN utilities using a set of paths simultaneously. To ensure feasible heat transfer between the hot and cold streams throughout, Exchanger Minimum Approach Temperature (EMAT) is maintained while shifting the heat load. The available exchangers’ pressure drop is considered in calculating the heat transfer coefficients. HEN devices are subjected to some additional area without any topological modification. In addition, the investment of such area could be recovered in a short span of time. The calculation of this approach encountered some iteration which has been overcome by mathematical programming. Demonstration example showed some options to be reasonable retrofit solutions. Energy savings ranged between $150 K and $450 K per year with payback time of less than 2 years were possible.     

Reflux Condensation under Vacuum of a Methanol/Water Mixture with Plain Tube and Tube Inserts

This paper presents preliminary observations and calculations obtained for the reflux condensation of a water–methanol vapor mixture in a plain tube and a tube fitted with inserts. It is an attempt to present findings that resolve the reflux condenser controllability and operability, which has always been a major issue in the industry.

A modification to the experimental apparatus has improved pressure measurement and aided in determining mass and heat balance information, thus giving greater confidence in the operation of the reflux condenser. Tube inserts are installed in the condenser tube in two different arrangements. The tube inserts are called HiTRAN® and are manufactured by Cal Gavin Ltd. (UK). This work describes some of the behaviors observed in the reflux condenser both with and without tube inserts. The dynamic temperature and pressure trends are notable.

The inserts threshold length is the length where the reflux condensation process avoids flooding and has a recovery of heavier and lighter components.     

Effect of Flow Distribution in Parallel Heat Exchanger Networks: Use of Thermo-Hydraulic Channeling Model in Refinery Operation

Abstract

Parallel branches are commonly observed in industrial heat exchanger networks (HENs). Despite the important relationship between flow distribution and network efficiency, not all parallel branches comprise of flow controllers or not least, flow measurements. When the network is subject to fouling, uncontrolled flow branches can introduce undesired phenomenon such as thermo-hydraulic channeling (THC) [presented at the 2007 HEFC conference; Ishiyama et al., Effect of fouling on heat transfer, pressure drop and throughput in refinery preheat trains]. Recent analysis of crude preheat train heat exchangers has shown the need to use THC models, in particular, for situations where there is insufficient flow measurement data, especially in nonsymmetric branches. This paper revisits the THC model and highlight practical importance of the THC phenomenon through analysis of plant data. The hydraulic aspect of the analysis is strongly linked to the knowledge of deposit thermal conductivity. A case study of a section of a crude refinery HEN is used to illustrate the use of thermo-hydraulic models in data reconciliation to understand flow imbalances caused due to differences in operating conditions and fouling of heat exchangers in each branch of a parallel network.     

Optimizing heat exchanger networks with genetic algorithms for designing each heat exchanger including condensers

This paper presents a procedure for the design of the components of a heat exchanger network (HEN). The procedure first uses pinch analysis to maximize heat recovery for a given minimum temperature difference. Using a genetic algorithm (GA), each exchanger of the network is designed in order to minimize its total annual cost. Eleven design variables related to the exchanger geometry are considered. For exchanger involving hot or cold utilities, mass flow rate of the utility fluid is also considered as a design variable. Partial or complete condensation of hot utility fluid (i.e., water vapor) is allowed. Purchase cost and operational cost are considered in the optimization of each exchanger. Combining every exchanger minimized cost with the cost of hot utility and cold utility gives the total cost of the HEN for a particular ΔT_min. The minimum temperature difference yielding the more economical heat exchanger network is chosen as the optimal solution. Two test cases are studied, for which we show the minimized total cost as a function of the minimum temperature difference. A comparison is also made between the optimal solution with the cost of utilities and without it.     

Application of intensified heat transfer for the retrofit of heat exchanger network

A number of design methods have been proposed for the retrofit of heat exchanger networks (HEN) during the last three decades. Although considerable potential for energy savings can be identified from conventional retrofit approaches, the proposed solutions have rarely been adopted in practice, due to significant topology modifications required and resulting engineering complexities during implementation. The intensification of heat transfer for conventional shell-and-tube heat exchangers can eliminate the difficulties of implementing retrofit in HEN which are commonly restricted by topology, safety and maintenance constraints, and includes high capital costs for replacing equipment and pipelines. This paper presents a novel design approach to solve HEN retrofit problems based on heat transfer enhancement. A mathematical model has been developed to evaluate shell-and-tube heat exchanger performances, with which heat-transfer coefficients and pressure drops for both fluids in tube and shell sides are obtained. The developed models have been compared with the Bell-Delaware, simplified Tinker and Wills-Johnston methods and tested with the HTRI® and HEXTRAN® software packages. This demonstrates that the new model is much simpler but can give reliable results in most cases. For the debottlenecking of HEN, four heuristic rules are proposed to identify the most appropriate heat exchangers requiring heat transfer enhancements in the HEN. The application of this new design approach allows a significant improvement in energy recovery without fundamental structural modifications to the network.     

换热网络优化设计的研究进展

换热网络优化是化工生产中常遇到的一类问题,综述了换热网络优化设计的三种基本方法,分别指出了夹点技术、数学规划法和炯经济分析法的基本原理、应用领域、优缺点及其在国内外的发展状况,并对其作了展望,注重更接近于工程实际的考虑。     

Controllability of Right-Invariant Systems on Solvable Lie Groups

We study controllability of right-invariant control systems $\Gamma = A + \mathbb{R}B$ on Lie groups. Necessary and sufficient controllability conditions for Lie groups not coinciding with their derived subgroup are obtained in terms of the root decomposition corresponding to the adjoint operator ad B. As an application, right-invariant systems on metabelian groups and matrix groups, and bilinear systems are considered.     

较大规模换热器网络的一种综合优化方法

基于分级超结构换热器网络模型的特点，改进了计算温度分布的通用解方法，以遗传算法和模拟退火算法为主，以瞎子爬山优化算法以及一些特殊优化策略为辅，设计了相应的计算程序，它需要的计算机内存要比现有的其他方法小。实例证明，该方法可成功地应用于较大规模的换热器网络的优化，并得到比现有各种方法更优的结果。     

Output Controllability for Semi-Linear Distributed Parabolic Systems

The purpose of this paper is to explore regional controllability developed for linear system [5, 15] to the semi-linear case. Under the hypothesis that the approximate regional controllability holds, we find a control which steers a system to a desired state in a subregion of the system domain and the approach is based on an extension of the Hilbert uniqueness method and the Schauder fixed-point theorem. The analytical case is then discussed using generalized inverse techniques and successfully illustrated by simulations.      

Heat Transfer Enhancement for Heat Exchanger Network Retrofit

Heat exchanger networks (HEN) play important roles in a chemical plant. In a plant lifetime, it may be required to retrofit a HEN several times in order to improve the energy efficiency or to accommodate the increase in throughput. The network pinch method developed by Asante and Zhu [1] can identify bottlenecks, which limit the increase in heat recovery for an existing HEN and also indicate promising structure changes to overcome the bottlenecks. As a result of HEN retrofit, additional surface area is required for some heat exchangers. There are a number of options to provide additional area, such as installing new shells or new units, adding new tubes to an existing bundle, etc. If heat transfer enhancement (HTE) is applied, additional area can be reduced significantly. This can result in a great reduction in capital cost and implementation time for modifications. However, in practice, heat transfer enhancement techniques have not been applied extensively, particularly in the petroleum refining industry. Several main aspects need to be addressed when HTE is taken into consideration for HEN retrofit. The first is how to determine which heat exchangers are suitable to apply HTE in the network and the second issue is to determine what level of augmentation of heat transfer performances is required. The last is about how to select a particular enhancement technique that can fulfil the enhancement requirement. A new strategy for applying HTE in HEN retrofit at the conceptual design stage has been developed. The above issues can be addressed properly by this new method. The new procedure is demonstrated using a case study.     

Heat integration retrofit analysis of a heat exchanger network of a fluid catalytic cracking plant

The impact of a process system on environmental pollution has both a local and global effect. The performance of the heat exchanger network (HEN) in a plant is an important aspect of energy conservation. Pinch technology and its recent extensions offer an effective and practical method for designing the HEN for new and retrofit projects.The fluid catalytic cracking (FCC) is a dominant process in oil refineries and there has been a sustained effort to improve the efficiency and yield of the unit over the years. Nevertheless, benefits and scope for improvement can still be found. The HEN of the FCC process considered here consists of a main column and a gas concentration section. Appropriate data were extracted from the existing network, using flowsheeting simulation. The stream data consists of 23 hot and 11 cold streams and cost and economic data required for the analysis were specified. The incremental area efficiency methodology was used for the targeting stage of the design and the design was carried out using the network pinch method consisting of both a diagnosis and optimisation stage. In the diagnosis stage promising designs were generated using UMIST developed sprint software. The generated design was then optimised to trade-off capital cost and energy savings. The design options were compared and evaluated and the retrofit design suggested.The existing hot utility consumption of the process was 46.055 MW with a ΔT_min of 24°C. The area efficiency of existing design was 0.805. The targeting stage using incremental area efficiency sets the minimum approach temperature at 11.5°C, thereby establishing the scope for potential energy savings. To achieve a practical project, the number of modifications is limited. The selected retrofit design has 8.955 MW saving – 74% of the whole scope. This corresponds to 27% utility cost savings with a payback period of 1.5 years. The modifications include addition of four heat exchanger units and repiping of one existing exchanger.     

Controllability of the Second-Order Nonlinear Differential Equations with Non-instantaneous Impulses

The objective of this paper is to establish the sufficient condition for the controllability of a control problem represented by second-order nonlinear differential equation with non-instantaneous impulses in a Hilbert space X. The results are obtained using the strongly continuous cosine family of linear operators and Banach fixed point method. Also, we study the controllability of the nonlocal as well as integro-differential systems. Finally, a few examples are provided to illustrate the applications of the obtained abstract results.     

Optimization of an industrial retrofitted heat exchanger network, using a stage-wise model

The heat exchanger network (HEN) can be optimized using the stage-wise model of superstructure representation, as proposed by Yee and Grossmann. This model can be easily solved regarding both trivial problems, and serious and complex new industrial design plants. In this paper, a stage-wise model for new designs is extended for retrofits by using a stage-wise model for a retrofitted HEN. This method using a stage-wise model is very general; it can be used in new designs as well as during existing process integration. The methodology of the stage-wise model for retrofitted HEN can be used to solve HENs easily and well enough, over a short time, and simultaneously. A mathematical model of stage-wise for retrofit HEN can include additional equations and limitations for retrofits. This model was tested by using a retrofitted methanol process generating an additional profit of 189,200 EUR/a.     

Approximate Controllability of Fractional Semilinear Stochastic System of Order <Emphasis Type="Italic">α</Emphasis>∈ (1,2]

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in L _p spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory.     

换热器网络优化研究进展

本文阐述了国内外换热器网络研究的最新进展,详细比较了研究换热器网络的两种不同的方法,还对换热器网络的动态特性研究做了简要介绍。作者认为：把窄点理论和混合整数非线性优化应用在其它动力系统如：制冷、空调、热泵、热电联产等,并对这些系统的节能也有一定的帮助。最后指出了换热器网络研究的发展方向。