Column Profile Maps: A Tool for the Design and Analysis of Complex Distillation Systems

Student Number : 9510423G PhD Thesis School of Chemical and Metallurgical Engineering Faculty of Engineering and the Built EnvironmentTechniques for the design and analysis of simple column separations are well established. Shortcut design techniques have been employed in the initial design of these “traditional” distillation systems for a number of years and these columns are well understood. However, few currently available techniques are useful in the design of novel or complex configurations. The techniques that are available tend to be configuration specific. An all inclusive or universal, design and analysis tool, that can be applied to any and all configurations, is required. Tapp et al (2004) introduced Column Profile Maps (CPMS) as a means of addressing this issue. These are maps of composition profiles for column sections with defined net-molar-flow and reflux ratio. It is suggested that by producing CPMs for a configuration a designer can essentially superimpose these, determine feasible operating profiles and hence column operating parameters. In this thesis we show that this technique can be used to, not only produce quick and easy complex column designs but gain a comprehensive understanding of the steady-state operation of these arrangements. We demonstrate this analytical potential first by application of the CPM technique to the two-product feed distribution problem. It is shown that feed distribution can lower the minimum required reflux ratio for non-sharp separations and in some cases produce feasible separations from previously infeasible product specifications. A composition region of operation for all distributed feed policies is also found. The potential for detailed analysis, design and optimisation of complex configurations is demonstrated via application of the CPM procedure to the fully thermally coupled (Petlyuk) distillation column at both sharp and non-sharp split conditions. A detailed design methodology for any configuration results from this. It is found that the Petlyuk column can operate under five possible bulk/net flow conditions and that very interesting and counter-intuitive net-molar-flows are possible. A feasible column parameter region equivalent to the optimality region (Halvorsen and Skogestad, 2001) is found for zeotropic systems. Importantly a minimum reflux condition for the Petlyuk column is found. This condition can be applied to all zeotropic systems for all product specifications. It is also demonstrated that the CPM technique can be used for design optimisation of separation systems

A study of vector formulations for distillation processes

In the last decade Process Synthesis has been an emerging active area of research. Since 1999 at COMPS, we have continuously applied this technique to many studies and recently have carefully started to consider the integration of this technique with others to simplify multilevel process design. In this regard the need for new tools that do not require very accurate data or experimental technique has become an imperative for the initial analysis of systems. This thesis presents some of these results.Process synthesis requires new rapid tools for the assessment and comparison of new technologies (possibilities) in the process development stage.This thesis examines and formulates process synthesis problems in the case of separation processes (separation with mixing , separation with reaction).Using simple generic vectorial tools, the thesis addresses the folowing issue: How the topology and mapping of the process vector field defines patterns that may be used for alternative process synthesis solution and design (structure selection ,stability analysis or controllability etc...) . The tools presented are intended for preliminary process design and feasibility studies and will allow for simple comparisons of various options.The key principle used in the study is the exploitation of the generic vectorial representation of fundamental physical phenomena (separation, mixing , reaction) in the process models as used for process synthesis and analysis.The demonstrated power of this approach is that it allows one to exploit the formal mathematical similarities between the different processing modes. Extensive topological Reactive Column Profile has been generated and analysed, offering new insights for manipulation of process behaviour in process synthesis and design. The significance of the contribution of this research is in offering extended fundamental insigths in creating process synthesis options for reactive-separations systems, creating the essential structural basis for subsequent mathematical optimisation of the performanceof process designs

Graphical techniques for analysing and synthesising separation processes

Recently, Column Profile Maps were developed as a generalized, graphically based distillation synthesis method. Unlike several other synthesis methods, it is not specific to any configuration and therefore allows the designer to devise almost any separation before being constrained by equipment. This thesis attempts to expand the theory of Column Profile Maps. Specifically, it is shown how new, and somewhat counter intuitive, column sections may be designed by merely imposing a sharp split constraint on a particular system. This special mathematical constraint makes it possible to maneuver topological characteristics of the system in almost any imaginable direction. This could lead to new designs being sought to exploit these profile behaviors, specifically in columns that require internal column sections (complex columns). Thermally coupled columns have received considerable attention for their ability to drastically reduce operating expenditures. Here, we have extended the Column Profile Map technique to encompass a systematic procedure for the design of single and multiple side rectifying and stripping units. It is shown how one may go about designing such columns rigorously without making simplifying assumptions with regard to the phase equilibrium behaviour and/or product specifications (as classical methods such as Underwood do), with the use of a Temperature Collocation method, as well as through a shortcut technique for rapid synthesis assuming ideal phase equilibrium behavior based on Column Profile Map eigenvectors. The efficacy of the shortcut technique is demonstrated with finding the best thermally coupled column comprising of a large main column and appending side-units. Naturally, the best structure is dependent on the objective function, and simple calculations presented here allow one to choose the best structure with regard to both heat quantity and quality. Furthermore, the eigenvector method allows one to construct an Attainable Region consisting of all potential designs for even the most complex column. The Column Profile Map technique is also extended to Reactive Distillation, which allows one to graphically assess the complex interaction of phenomena. Valuable conclusions can be gleaned from this method, specifically that improving a single piece of equipment’s performance may prove detrimental to the overall system’s operation. The methods developed here allow one to understand exactly why a complex process such as reactive distillation has some of the strange characteristics often reported in literature. Furthermore, it is shown how non-ideal phase equilibrium behavior may improve the column’s operability and in fact improve the overall feasibility of the unit. Using this method, one may quickly assess desirable process chemistry, feed compositions, desirable phase equilibrium and equipment sizes. Again, an Attainable Region is presented which shows all possible modes of operation that would give rise to a predefined product specification. Finally, computational techniques are presented which allows for swift calculation of stationary points in systems ranging from constant volatility to highly non-ideal, multi azeotropic systems. The importance of quickly and accurately knowing where pinch points are located, even in negative composition space, is demonstrated by critically looking at several design methods. Notably, it is shown that the Rectification Body Method is neither a necessary nor sufficient condition for design and cannot be safely extrapolated to complex column design. With knowledge of all pinch points and using the Column Profile Map technique it is shown how one may synthesise new and counter-intuitive column sections, so much so that azeotropes can be shifted outside the physically realizable space

Real-time fluid simulations under smoothed particle hydrodynamics for coupled kinematic modelling in robotic applications

Although solids and fluids can be conceived as continuum media, applications of solid and fluid dynamics differ greatly from each other in their theoretical models and their physical behavior. That is why the computer simulators of each turn to be very disparate and case-oriented. The aim of this research work, captured in this thesis book, is to find a fluid dynamics model that can be implemented in near real-time with GPU processing and that can be adapted to typically large scales found in robotic devices in action with fluid media. More specifically, the objective is to develop these fast fluid simulations, comprising different solid body dynamics, to find a viable time kinematic solution for robotics. The tested cases are: i) the case of a fluid in a closed channel flowing across a cylinder, ii) the case of a fluid flowing across a controlled profile, and iii), the case of a free surface fluid control during pouring. The implementation of the former cases settles the formulations and constraints to the latter applications. The results will allow the reader not only to sustain the implemented models but also to break down the software implementation concepts for better comprehension. A fast GPU-based fluid dynamics simulation is detailed in the main implementation. The results show that it can be used in real-time to allow robotics to perform a blind pouring task with a conventional controller and no special sensing systems nor knowledge-driven prediction models would be necessary.Aunque los sólidos y los fluidos pueden concebirse como medios continuos, las aplicaciones de la dinámica de sólidos y fluidos difieren mucho entre sí en sus modelos teóricos y su comportamiento físico. Es por eso que los simuladores por computadora de cada uno son muy dispares y están orientados al caso de su aplicación. El objetivo de este trabajo de investigación, capturado en este libro de tesis, es encontrar un modelo de dinámica de fluidos que se pueda implementar cercano al tiempo real con procesamiento GPU y que se pueda adaptar a escalas típicamente grandes que se encuentran en dispositivos robóticos en acción con medios fluidos. Específicamente, el propósito es desarrollar estas simulaciones de fluidos rápidos, que comprenden diferentes dinámicas de cuerpos sólidos, para encontrar una solución cinemática viable para robótica. Los casos probados son: i) el caso de un fluido en canal cerrado que fluye a través de un cilindro, ii) el caso de un fluido que fluye a través de un alabe controlado, y iii), el caso del control de un fluido de superficie libre durante el vertido. La implementación de estos primeros casos establece las formulaciones y limitaciones de aplicaciones futuras. Los resultados permitirán al lector no solo sostener los modelos implementados sino también desglosar los conceptos de la implementación en software para una mejor comprensión. En la implementación principal se consigue una simulación rápida de dinámica de fluidos basada en GPU. Los resultados muestran que esta implementación se puede utilizar en tiempo real para permitir que la robótica realice una tarea de vertido ciego con un controlador convencional sin que sea necesario algún sistema de sensado especial ni algún modelo predictivo basados en el conocimiento.Programa de Doctorado en Ingeniería Eléctrica, Electrónica y Automática por la Universidad Carlos III de MadridPresidente: Carmen Martínez Arévalo.- Secretario: Luis Santiago Garrido Bullón.- Vocal: Benjamín Hernández Arreguí

Experimental simulation of distillation column profile maps

ABSTRACT One of the most important tasks in the chemical industry is the separation of multicomponent liquid mixtures into one or more high-purity products. Several technologies are feasible for this task, either alone or in combination, such as distillation, extraction, crystallization, ect. Among these, distillation is by far the most widely spread and has a long history in chemical technology. However, until recently, there has been no systematic approach for understanding the separation of complex mixtures where azeotropes and multiple liquid phases may occur. There has been a growing interest in the use of residue curve and column profiles for the preliminary design of distillation columns. Residue curves and column profile are not only used to predict the composition changes in the distillation column but also to determine the feasibility of the proposed separation. Recently, theory underlying column profile maps has been developed by Tapp, Holland and co-workers. However there has been no direct experimental validation of the predictions of the column profile map theory. The main aim of this thesis is to experimentally verify some of the predictions of column profile map theory. A simple experimental batch apparatus has been developed to measure residue curve maps (RCMs) by Tapp and co-workers, the apparatus was modified so that it could be used to measure column profile maps (CPMs) in this thesis. CPM theory has shown that CPMs are linear transforms of the residues curve maps (RCMs). A stable node which was the apex of a mass balance triangle (MBT) was introduced inside the MBT, this was done by transforming the RCMs to CPMs using the appropriate distillate composition xd and reflux ratio R. It was also shown that the saddle point which was on the boundary of the triangle of the RCM can be shifted inside the MBT by transforming the RCM to CPM. This is again in accordance with theoretical predictions of CPM theory. iv Residue curves (RCs) and pinch point curves (PPCs) are used to determine the operation leaves and hence the feasible region for distillation columns operating at a specific distillate and bottoms composition for all fixed reflux ratio. The operating leaves were expanded beyond the pinch point curve by varying the reflux ratio from a higher reflux to a lower reflux ratio. This showed that one can effectively cross the pinch point curve hence expanding the operating leave. Finally the importance of experimentally measuring CPMs is demonstrated. Two thermodynamic models were used to predict the profiles of a complex system. The binary vapor-liquid equilibrium (VLE) diagrams and the residue curves produced from using these two thermodynamic models did not predict the same topology. The composition of the profiles were not the same because there were multiple liquid phases involved in this system, which made it difficult for the researchers to measure the correct profiles. Column profile maps were simulated using the different thermodynamic models, they also showed that there is some discrepancy between the predictions of the two models

Production of TAME and n-Propyl propionate by reactive distillation

Tese de doutoramento. Engenharia Química. 2006. Faculdade de Engenharia. Universidade do Port

Developing a novel theory for the synthesis and design of membrane-based separations

A novel approach for the design and synthesis of membrane separation systems has been developed. The theory is shown to be applicable to both batch and continuous membrane operations, and has been formulated in such a way that it is valid for any type of membrane. In this thesis, however, only vapour permeation and pervaporation membranes are incorporated for illustration purposes. The method, which employs a graphical technique, allows one to calculate and visualise the change in composition of the retentate. An integral part of the approach was the derivation of the Membrane Residue Curve Map (M-RCM), and the related differential material balance which describes it. By definition, this plot shows the change, in time, of the retentate composition in a batch still. However, it has been shown that the M-RCM is applicable to conventional continuously-operated membrane units, as well as infinite reflux membrane columns. Finite reflux columns and cascades have been examined by using column sections (CS): any column, or arrangement, no matter how complex, can be broken down into smaller units, namely CS. The development of the Difference Point Equation (DPE) for non-constant flow allowed one to generate, and interpret, profiles for individual CS’s, which can ultimately be connected to form a membrane column arrangement. The profiles, which are more complex than those obtained in the M-RCM, exhibit a unique behavior. Since there is varying flow, the reflux is continually changing, orientating the profile so as to seek a stable node that is “mobile”. Thus, the movement of CS profile is dictated by the location and direction of the pinch point locus. Finally, having membrane permeators examined in an analogous manner to other separation methods, allows for easy synthesis and design of combinations of different processes. Hybrid distillation-membrane systems are analyzed by incorporating CS’s and the appropriate DPE’s which describe each. Investigating the arrangement as a thermally-coupled column introduces a novel way of synthesizing hybrids. Regions of feasibility, which are dictated by the relevant pinch point loci of each separation method, are ultimately sought

The potential benefits of feed distribution when applied to atmospheric crude distillation units

Distributed feed was applied on an Atmospheric Crude Distillation Unit (ACDU) to establish the energy and capital expenditure saving potential of the distributed feed policy, with the aid of (Column Profile Maps) CPMs and Aspen Plus as analysis tools. As shown by Holland (2005), the advantages of using distributed feed over single feed are seen in separations with non-sharp split product specifications, thus making ACDU an ideal candidate for feed distribution. For multicomponent mixtures with more than 3 components, compositional plot visualisation is more difficult, thus most graphical methods fail and as a result a representative three component constant volatility mixture of pentane, heptane and hexane was selected on the assumption that it would fairly mimic the paraffinic synthetic crude oil behaviour. After analysis of the three component distributed feed schemes, the ideas were then extended to a synthetic crude oil system in Aspen Plus. The results showed that there was potential to reduce equipment size, such as the condenser and furnace, plus there is a real opportunity to possibly do away with at least one or two pump-around circuits. Energy savings of above 30% were realized

Robotic manipulation of cloth: mechanical modeling and perception

(Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.(Esp) En este trabajo estudiamos varios problemas matemáticos relacionados con la manipulación robótica de textiles. En primer lugar, desarrollamos un modelo continuo libre de 'locking' para la simulación física de textiles inextensibles. Presentamos una novedosa discretización usando 'elementos finitos' de nuestras restricciones de inextensibilidad resultando en un tratamiento unificado de mallados triangulares y cuadrangulares de la tela. A continuación, explicamos cómo incorporar contactos, autocolisiones y fricción en las ecuaciones de movimiento, de modo que las fuerzas de fricción y las restricciones de inextensibilidad y colisiones puedan integrarse implícitamente y sin ningún desacoplamiento. Desarrollamos un 'solver' de tipo 'conjunto-activo' adaptado a nuestro problema no lineal que tiene en cuenta las restricciones activas pasadas para acelerar la resolución de los contactos no resueltos y, además, puede inicializarse desde cualquier punto no necesariamente factible. Posteriormente, nos embarcamos en la validación empírica del modelo desarrollado. Grabamos en un entorno de laboratorio -con cámaras de profundidad y sistemas de captura de movimiento- los movimientos de siete tipos de textiles (entre los que se incluyen, por ejemplo, algodón, tela vaquera y poliéster) de varios tamaños y a diferentes velocidades, terminando con más de 80 grabaciones. Los escenarios considerados son todos dinámicos e implican sacudidas y torsiones rápidas de los textiles, colisiones con obstáculos e incluso golpes con una varilla cilíndrica. Finalmente, comparamos las grabaciones con las simulaciones dadas por nuestro modelo inextensible, y encontramos que, de media, el error es del orden de 1 cm incluso para las telas más grandes (DIN A2) y los escenarios más complicados. Además, también abordamos otros problemas relevantes para la manipulación robótica de telas, como son la percepción y la clasificación de sus estados. Presentamos un algoritmo de reconstrucción basado en la teoría de Morse que procede directamente de una nube de puntos para obtener una descomposición celular de una superficie con o sin borde: los resultados son una parametrización a trozos de la superficie de la tela como una unión de celdas de Morse. A partir de la descomposición celular puede deducirse inmediatamente la topología de la superficie. Por último, estudiamos el espacio de configuración de un trozo de tela: dado que el estado original de la tela es plano, el conjunto de estados posibles bajo la hipótesis de inextensibilidad es el conjunto de superficies desarrollables isométricas a una fija. Demostramos que una curva genérica simple, cerrada y regular a trozos en el espacio puede ser el borde de un número finito de superficies desarrollables con curvatura media no nula. Inspirándonos en este resultado, introducimos las coordenadas dGLI, una representación de dimensión baja del estado de un pedazo de tela basada en una derivada direccional de la integral de enlazamiento de Gauss. Estas coordenadas -calculadas a partir de la posición del borde de la tela- permiten distinguir cambios cualitativos clave en distintas secuencias de plegado.Postprint (published version