The second law optimal state of a diabatic binary tray distillation column

A new numerical procedure to minimize the entropy production in diabatic tray distillation columns has been developed. The method was based on a least square regression of the entropy production at each tray. A diabatic column is a column with heat exchangers on all trays. The method was demonstrated on a distillation column separating propylene from propane. The entropy production included contributions from the heat transfer in the heat exchangers and the mass and heat transfer between liquid and vapor inside the distillation column. It was minimized for a number of binary tray distillation columns with fixed heat transfer area, number of trays, and feed stream temperature and composition. For the first time, the areas of heat exchange were used as variables in the optimization. An analytical result is that the entropy production due to heat transfer is proportional to the area of each heat exchanger in the optimal state. For many distillation columns, this is equivalent to a constant driving force for heat transfer. The entropy production was reduced with up to 30% in the cases with large heat transfer area and many trays. In large process facilities, this reduction would ideally lead to 1-2 GWh of saved exergy per year. The most important variable in obtaining these reductions is the total heat transfer area. The investigation was done with a perspective to later include the column as a part in an optimization of a larger process. We found that the entropy production of the column behaved almost as a quadratic function when the composition of the feed stream changed. This means that the feed composition is a natural, easy variable for a second law optimization when the distillation column is a part of a process. The entropy production was insensitive to variations in the feed temperature.     

From graphical to model-based distillation column design: A McCabe-Thiele-inspired mathematical programming approach

We propose a mixed-integer nonlinear programming (MINLP) model for simple and complex distillation column design and optimization. The model is based upon the concepts and equations underpinning the McCabe-Thiele method. Generalizing this method, we introduce material balances at various locations of the column and employ binary variables to determine the optimal number of trays and optimal feed locations. We model the vapor–liquid equilibrium using continuous piecewise linear approximating functions. The model is extended to account for multicomponent mixtures and non-constant-molar overflow. We also discuss how to estimate the minimum number of trays and the minimum reflux ratio.     

Product tri-section based crude distillation unit model for refinery production planning and refinery optimization

Accuracy of a crude distillation unit (CDU) model has a significant impact on refinery production planning. High accuracy is typically accomplished via nonlinear models which causes convergence difficulties when the entire refinery model is optimized. CDU model presented in this work is a mixed-integer linear model with a modest number of binary variables; its accuracy is on par with rigorous tray to tray CDU models. The model relies on the observation¹² that a line through the middle of the product true boiling point (TBP) curve depends on the crude feed properties and the yields of the adjacent products. Novelty of the product tri-section CDU model is that it does not require models of individual distillation towers comprising the CDU, thereby leading to a much simpler model structure. Significant reduction in the computational effort required for the optimization of nonlinear refinery models is illustrated by comparison with previous work.     

Three‐phase fluidized distillation

Separation efficiency in distillation operations can be improved by modifying the characteristics of the dispersions formed on the trays. The present work reports on the hydrodynamic and mass transfer characteristics of liquid‐solid‐vapour dispersions formed on sieve trays without downcomers of a distillation column operating under total reflux conditions. Murphree efficiency and the operating limits of distillation using the ethanol‐n‐butanol system are analyzed for a large range of vapour velocities and liquid mixture compositions, utilising wettable PVC particles and non‐wettable silicone, PE, and Teflonr? particles. It was verified that wettable particles show a drastic reduction in the upper operating limit of vapour velocity, but this does not occur for non‐wettable particles. Tray efficiency can be increased when non‐wettable particles are used, mainly for high vapour velocity operations.     

二元提馏式间歇精馏的优化操作与最小汽化总量

理想操作条件下二元提馏式间歇精馏优化操作的汽化总量与最小汽化总量的计算是约束函数优化问题。本文采用罚函数法,将此约束函数优化转变为无约束函数优化,并采用固定双步长因子梯度法数值求解该函数的极值。计算表明:固定双步长因子梯度法具有良好的收敛性,同时,降低分段数较多时,数值截断误差积累对计算结果的影响。二元提馏式间歇精馏优化操作较恒残液组成操作的能耗低的原因如下:在理论板数相对较少(接近二元提馏式间歇精馏恒残液组成操作所需的最少理论板)时,优化操作通过控制再沸比提高了能耗效率;在理论板数相对较多时,优化操作通过控制再沸比,在保证过程的能耗效率较高的同时,可尽可能快地将物料移出系统,减少了精馏过程中塔顶贮槽内液体的混合熵产。通过对计算结果的归纳与外推,得到了理想操作条件下理论板数为无穷多时二元提馏式间歇精馏优化操作再沸比的变化方式以及最小汽化总量的计算公式。     

Effect of two-pass trays on distillation efficiencies

Two important structural factors that affect distillation efficiencies, the outlet weir heigh and the liquid flowpath length, are investigated. Performance and efficiency data of an industrial scale i-butane/n-butane distillation column equipped with two-pass trays are used as a basis for the calculations. A mathematical development for a new method for predicting the numbers of vapor and liquid phase transfer units is given. This method together with some other NTU calculation methods is used to assess the effect of the outlet weir height on efficiencies. The effect of outlet weir height on the Murphree tray efficiencies is investigated using the observed point efficiencies and different point efficiency to the Murphree tray efficiency relation methods. The effect of varying liquid flowpath lengths on efficiencies is studied by calculating the Murphree tray efficiencies for one-pass and two-pass trays. The results obtained using the NTU calculation method presented in this study show that a certain outlet weir height point efficiency reaches its maximum. Most of the other methods give opposite results giving a minimum for point efficiency at a certain outlet weir length. The results also show that the Murphree tray efficiencies for one-pass trays are higher than for two-pass trays. Obviously, this is caused by the longer liquid flowpath length of one-pass trays. The Murphree tray efficiencies are also calculated for an industrial-scale MTBE purification column. The column is equipped with two-pass trays in the stripping section and with one-pass trays in the rectifying section. The Murphree tray efficiencies of one-pass trays are considerably higher than the two-pass tray Murphree tray efficiencies.     

Design method for multi-component distillation system based on quasi-binary method

A novel design method for a multi-component distillation system based on the quasi-binary model is presented. The quasi-binary method, which converts the multi-component system to a quasi-binary system, could simplify the design process of multi-component distillation. Subsequently the software integration method is introduced to the distillation design and an automatic calculation program is developed by using Visual C++ language. The design of multi-component distillation, in which the minimum reflux ratio R _min or liquid-vapor ratio (L/V) _min and the minimum numbers of stage N _min is determined easily and quickly, is automatically performed by the technology of software integration. Three examples are solved to demonstrate the feasibility and effectiveness of the presented method for the multi-component distillation. Supported by the National Nature Science Fund Program of China (No. 20376078).     

A disjunctive programming approach for the optimal design of reactive distillation columns

A generalized disjunctive programming formulation is presented for the optimal design of reactive distillation columns using tray-by-tray, phase equilibrium and kinetic based models. The proposed formulation uses disjunctions for conditional trays to apply the MESH and reaction kinetics equations for only the selected trays in order to reduce the size of the nonlinear programming subproblems. Solution of the model yields the optimal feed tray locations, number of trays, reaction zones, and operating and design parameters. The disjunctive program is solved using a logic-based outer-approximation algorithm where the MILP master problem is based on the big-M formulation of disjunctions, and where a special initialization scheme is used to reduce the number of initial NLP subproblems that need to be solved. Two examples are presented that include reactive distillation for the metathesis reaction of 2-pentene and for the production of ethylene glycol. The results show that the proposed method can effectively handle these difficult nonlinear optimization problems.     

Fuel grade ethanol by diffusion distillation: an experimental study

BACKGROUND: Fuel grade ethanol (anhydrous ethanol) is considered to be an excellent alternative clean burning fuel to gasoline. It is now used as an additive to gasoline to enhance its octane number and combustibility. Owing to its high energy values, ethanol is the most promising future biofuel. Because of azeotrope formation, anhydrous ethanol cannot be achieved by conventional distillation. Diffusion distillation is one of the several processes that can be used to separate azeotropes. Diffusion distillation takes advantage of differences in relative rates of diffusion using inert gas as selective filter. RESULTS: Effect of vaporization temperature and feed composition on diffusion distillation of an ethanol–water mixture using air as the inert gas has been studied. A new quantity S_az(N₂/N₁) has been suggested to find the optimum vaporization temperature. In the present study this was found to be about 46 °C. The pseudo‐azeotrope has been observed at 0.697 mole fraction of ethanol at a vaporization temperature of 50 °C. Separation is effected by diffusion distillation even at the azeotropic ethanol mole fraction of 0.894. The experimental results were compared with a Stefan–Maxwell equations based mathematical model and found to be in good agreement with theoretical results. CONCLUSIONS: Experimental results demonstrate that fuel grade ethanol can be produced by diffusion distillation. The new quantity S_az(N₂/N₁) is a key variable for vaporization temperature optimization. Copyright © 2011 Society of Chemical Industry     

Generalized short-cut distillation column modeling for superstructure-based process synthesis

We introduce a generalized Underwood method to calculate the minimum vapor flowrate for distillation in superstructure-based process synthesis. Our method addresses two important limitations of current methods, namely, separation tasks where (1) the flow rates of some components may be zero, and (2) the key components may be unknown prior to optimization. This is achieved through the introduction of binary variables and mixed-integer constraints to implicitly determine the active roots and the root loci. In addition, we develop strategies tailored to improve the numerical stability and computational performance when using the proposed method.     

Comparative Study of the Model and Optimum Cascades for Multicomponent Isotope Separation

The possibility of estimating the minimum total flow in a cascade with concentrations of a target component given in the product and waste flows by means of a model match abundance ratio cascade (MARC) is studied. The parameters required to describe MARC characteristics are the total number of separation stages, the feed flow location, and the M* parameter, which is equal to a half-sum of mass numbers of the target and the supporting components. Specific research carried out independently in two scientific labs in China and Russia has demonstrated that the integral parameters of the MARC, optimized by the M* parameter, are very close to that of the optimum by the minimum total flow cascade found by means of numerical optimization. The calculation is performed for separation of krypton isotopes when the end component ⁷⁸Kr and the intermediate component ⁸³Kr are considered to be the targets. It paves the way to use the optimized MARC parameters for two purposes: first, for fast and easy evaluation of the real cascade parameters and second, as an initial guess in its further direct numerical optimization, thereby allowing significant savings in computation time.     

Global optimization of multicomponent distillation configurations: 2. Enumeration based global minimization algorithm

We present a general Global Minimization Algorithm (GMA) to identify basic or thermally coupled distillation configurations that require the least vapor duty under minimum reflux conditions for separating any ideal or near‐ideal multicomponent mixture into a desired number of product streams. In this algorithm, global optimality is guaranteed by modeling the system using Underwood equations and reformulating the resulting constraints to bilinear inequalities. The speed of convergence to the globally optimal solution is increased by using appropriate feasibility and optimality based variable‐range reduction techniques and by developing valid inequalities. The GMA can be coupled with already developed techniques that enumerate basic and thermally coupled distillation configurations, to provide for the first time, a global optimization based rank‐list of distillation configurations. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2071–2086, 2016     

Performance and applications of flow-guided sieve trays for distillation of highly viscous mixtures

With a particular focus on the distillation of highly viscous or self-polymerized mixtures, this study reports the hydrodynamic and mass transfer performance of two flow-guided sieve trays, including their pressure drop, entrainment, weeping and tray efficiency, obtained experimentally with an air-water/oxygen system in a Φ600 mm plexiglass column. The results show that the 8 mm hole flow-guided sieve tray tested shows better characteristics than the 7 mm flow-guided hole tray in terms of pressure drop and mass transfer. Then we present practical industrial examples of applications of the flow guided trays for distillation of viscous mixtures, i.e., the separation of vinyl acetate (VAC) from a polyvinyl acetate (PVAC) polymer solution with dynamic viscosity μ=50,000 mPas, the separation of highly unsaturated C5 mixtures by extractive distillation, and the distillation of thick, condensed and highly viscous fermentation mixtures made from fermented mash. It is demonstrated that flow-guided sieve trays with relatively large holes are an excellent candidate for distillation of mixtures with suspended solids, or concentrated/self-polymerized polymer solutions.     

A framework for efficient large scale equation-oriented flowsheet optimization

Despite the economic benefits of flowsheet optimization, many commercial tools suffer from long computational times, limited problem formulation flexibility and numerical instabilities. In this study, we address these challenges and present a framework for efficient large scale flowsheet optimization. This framework couples advanced process optimization formulations with state-of-the-art algorithms, and includes several notable features such as (1) an optimization-friendly formulation of cubic equation of state thermodynamic models; (2) a new model for distillation column optimization based on rigorous mass, equilibrium, summation and heat (MESH) equations with a variable number of trays that avoids integer variables; (3) improvements on the Duran–Grossmann formulation for simultaneous heat integration and flowsheet optimization; and (4) a systematic initialization procedure based on model refinements and a tailored multi-start algorithm to improve feasibility and identify high quality local solutions.Capabilities of the framework are demonstrated on a cryogenic air separation unit synthesis study, including two thermally coupled distillation columns and accompanying multistream heat exchangers. A superstructure is formulated that includes several common ASU configurations in literature. As part of the optimization problem the solver selects the best topology in addition to operating conditions (temperatures, flowrates, etc.) for coal oxycombustion applications. The optimization problem includes up to 16,000 variables and 500 degrees of freedom, and predicts specific energy requirement of 0.18 to 0.25 kWh/kg of O₂ depending on design assumptions. These results are compared to literature and plans to extend the framework to an entire coal oxycombustion power plant optimization study are discussed.     

乙醇脱水塔内两相和三相共沸精馏

研究了乙醇脱水塔内的两相共沸精馏和汽液液三相共沸精馏过程。利用Aspen plus模拟软件对乙醇脱水塔内4种工况的精馏曲线、共沸剂浓度分布、回流量和再沸器能耗进行了分析比较。结果表明,苯做共沸剂时,脱水塔内两相共沸精馏和汽液液三相共沸精馏的精馏曲线、共沸剂浓度分布、回流量和再沸器能耗相近,脱水塔精馏曲线都跨越了精馏边界,并且共沸剂在塔内大多数板上都有较高浓度分布。而环己烷做共沸剂时,两相共沸精馏工况和汽液液三相共沸精馏工况条件下的脱水塔内精馏曲线、共沸剂浓度分布、回流量和再沸器能耗有较大差别。汽液液三相共沸精馏工况条件下,环己烷在塔内大多数板上有较高浓度分布,起到较好的脱水作用,而两相共沸精馏工况条件下脱水塔内共沸剂仅分布在塔顶几块塔板上,塔内多数板上没有起到共沸剂作用。     

Stepwise periodic distillation—I: Total reflux operation

The theoretical predictions of doubled overall efficiency for plate distillation columns operated in the controlled cycling mode have not been confirmed by pilot scale experiments. In an attempt to circumvent the hydrodynamic problems causing this failure, we have found a new periodic operating mode where the liquid flow is manipulated directly, and not indirectly through pulsations of the vapour flow rate (as in controlled cycling).In this paper we present the theory of stepwise periodic distillation, under assumptions allowing a comparison with known results for controlled cycling. We show that the two processes have the same asymptotic efficiencies for large values of the number of trays while periodic stepwise distillation is slightly more efficient than controlled cycling for a finite number of trays     

Pilot‐scale studies of process intensification by cyclic distillation

Process intensification in distillation systems receives much attention with the aim of increasing both energy and separation efficiency. Several technologies have been investigated and developed, as for example: dividing‐wall column, HiGee distillation, or internal heat‐integrated distillation. Cyclic distillation is a different method based on separate phase movement—achievable with specific internals and a periodic operation mode—that leads to key advantages: increased column throughput, reduced energy requirements, and better separation performance. This article is the first to report the performance of a pilot‐scale distillation column for ethanol‐water separation, operated in a cyclic mode. A comparative study is made between a pilot‐scale cyclic distillation column and an existing industrial beer column used to concentrate ethanol. Using specially designed trays that truly allow separate phase movement, the practical operation confirmed that 2.6 times fewer trays and energy savings of about 30% are possible as compared with classic distillation. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2581–2591, 2015     

Beitrag zur Bewertung von Stoffaustauschböden

Assessment of fractionation trays. To assess fractionation trays from a process engineering point of view, the following need to be defined: the loading dependent separation efficiency and pressure drop, together with the loading range and the highest possible loadings at which an acceptable efficiency is reached. As an example, one of the trays used successfully in industry for many years which represents the latest in tray technology was tested together with a new development, the Dualflex tray. The results of the comparison tests show that: Based on the process characteristics of the Dualflex tray, it can be classed as a high capacity tray for thermal fractionation processes. With high loadings it has a good efficiency and correspondingly low pressure drop. Because it uses the dualflow principle it is capable of bearing significantly higher loads than conventional cross-flow trays. For example, Dualflex trays can be installed in column revamps to give an advantageous increase in capacity, or in new plants where more than 30% of the column cross-section can be saved compared with conventional fractionation trays. The above constructive and technological advantages combined with the optimal design of the Dualflex tray lead to a considerable reduction in product hold-up time when compared with traditional crossflow trays with downcomers. For example, this new tray can be used advantageously with the fractionation of thermally sensitive material systems. It would also be possible to use the Dualflex tray for the vacuum distillation (approx. 10 mbar) of fatty acid alcohol and esters (up to C12) with low reflux ratios (3:5) in columns which are fitted out with thin-film evaporators.     

Optimal Algorithmic Cooling of Spins

Algorithmic cooling (AC) is a recent spin-cooling approach that employs entropy compression methods in open systems. AC reduces the entropy of spins on suitable molecules beyond Shannon's bound on the degree of entropy compression by reversible manipulations. Remarkably, AC makes use of thermalization, a generally destructive facet of spin systems, as an integral part of the cooling scheme. AC is capable of cooling spins to very low temperatures and provides significant cooling for molecules containing as few as 5–7 spins. Application of AC to slightly larger molecules could lead to breakthroughs in high-sensitivity NMR spectroscopy in the near future. Furthermore, AC may be germane to the development of scalable NMR quantum computers. We introduce here a new practicable algorithm, “PAC3”, and several new exhaustive cooling algorithms, such as the Tribonacci and k-bonacci algorithms. In particular, we present the “all-bonacci” algorithm, which appears to reach the maximal degree of cooling obtainable by the optimal AC approach. AC is potentially beneficial for NMR-derived biomedical applications, which involve bio-molecules with isotope enrichments, such as ¹³ C- and ¹⁵ N-labeled amino acids. We briefly survey AC experiments, including a recent 3-spin experiment in which Shannon's bound was bypassed. The difficulties associated with cooling molecules bearing a greater number of spins are explained. Finally, the potential of selected cooling algorithms (practicable, exhaustive, and optimal algorithms) is illustrated with regard to a highly relevant bio-medical target— ¹³ C-labeled glucose.