Numerical Formulations For Attainable Region Analysis

Student Number : 9611112G - PhD thesis - School of Chemical and Metallurgical Engineering - Faculty of Engineering and the Built EnvironmentAttainable Region analysis is a chemical process synthesis technique that enables a design engineer to find process unit configurations that can be used to identify all possible outputs, by considering only the given feed specifications and permitted fundamental processes. The mathematical complexity of the attainable regions theory has so far been a major drawback in the implementation of this powerful technique into standard process design tools. In the past five years researchers focused on developing systematic methods to automate the procedure of identifying the set of all possible outputs termed the Attainable Regions. This work contributes to the development of systematic numerical formulations for attainable region analysis. By considering combinations of fundamental processes of chemical reaction, bulk mixing and heat transfer, two numerical formulations are proposed as systematic techniques for automation of identifying optimal process units networks using the attainable region analysis. The first formulation named the recursive convex control policy (RCC) algorithm uses the necessary requirement for convexity to approximate optimal combinations of fundamental processes that outline the shape of the boundary of the attainable regions. The recursive convex control policy forms the major content of this work and several case studies including those of industrial significance are used to demonstrate the efficiency of this technique. The ease of application and fast computational run-time are shown by assembling the RCC into a user interfaced computer application contained in a compact disk accompanying this thesis. The RCC algorithm enables identifying solutions for higher dimensional and complex industrial case studies that were previously perceived impractical to solve. The second numerical formulation uses singular optimal control techniques to identify optimal combinations of fundamental processes. This formulation also serves as a guarantee that the attainable region analysis conforms to Pontryagin’s maximum principle. This was shown by the solutions obtained using the RCC algorithm being consistent with those obtained by singular optimal control techniques

Reactor Network Synthesis Using Coupled Genetic Algorithm with the Quasi-linear Programming Method

This research is an attempt to develop a new procedure for the synthesis of reactor networks (RNs) using a genetic algorithm (GA) coupled with the quasi-linear programming (LP) method. The GA is used to produce structural configuration, whereas continuous variables are handled using a quasi-LP formulation for finding the best objective function. Quasi-LP consists of LP together with a search loop to find the best reactor conversions (xi), as well as split and recycle ratios (yi). Quasi-LP replaces the nonlinear programming (NLP) problem, and is easier to solve. To prevent complexity and ensure an optimum solution, two types of ideal reactors, namely plug flow reactor (PFR) and continuous stirred tank reactor (CSTR), were considered in the network. Since PFRs require the introduction of differential equations into the problem formulation, a CSTR cascade was used instead in order to eliminate differential equations. To demonstrate the effectiveness of the proposed method, three reactor-network synthesis case studies are presented

Linear and Non-Linear Programming Techniques for System Identification and Green Engineering Applications

This work focuses on linear and non-linear programming techniques for feasibility assessment, synthesis, and optimization of process networks. Analytical techniques, dimensionality reduction, convexification strategies, and functional analysis are developed to identify global optima and to enhance the efficiency of their computation. Green engineering, especially the hydrogen economy, is the primary motivation of this work. To this end, these strategies are implemented in identification of the attainable region for separator networks, optimization of compressors and coolers in series delivering hydrogen at high pressure, and minimum utility cost of an energetically-enhanced steam methane reforming process in the presence of carbon tax legislation.Pursuant to feasibility assessment of systems with respect to delivery of pure compounds, the applicability of the Infinite DimEnsionAl State-space (IDEAS) framework is extended to attainable region (AR) identification for separator networks. The AR for a water/methanol/acetone mixture involving one network feed stream with known species molar fractions and three network outlet streams at 1 atm pressure. The binary methanol/acetone system exhibits a minimum-boiling azeotrope at 79.07% mole fraction of acetone at 328.5 K. The IDEAS-generated AR successfully identified that the binary methanol/acetone azeotrope was inside the AR, and thus demonstrated there exists a separator network that can bypass the azeotrope. In the exploration of hydrogen as an alternative energy source, the minimum operating cost and minimum capital cost problems for a system of compressors and coolers in series that bring a gas with constant compressibility factor from a specified initial state (T0, P0) to a specified final state (T0, Pn). Through mathematical proof, the dimensionality of the optimization problems is reduced and analytical properties of the compressor outlet temperatures, when either operating costs or capital costs dominate, are established. A case study involving hydrogen compression was done to illustrate the methods, and shows the global optimum achieves cost savings of up to 13% from conventional designs. Lastly, a novel method for solution of linear parametric programming problems is proposed based on the concept of dimensionality reduction – this allows the analytic quantification of the optimum objective function value and associated optimum variable vector. Regions in carbon/renewable utility cost coefficient ratio space are identified, in which one technology is superior over the other. EESMR is shown to be preferable in the presence of significant levels of taxation on the use of natural gas as fuel

Improving batch reactors using attainable regions: Towards automated construction of the attainable region and its application to batch reactors

The Attainable Region is the set of all achievable states, for all possible reactor configurations, obtained by reaction and mixing alone. It is a geometric method that is effective in addressing problems found in reactor network synthesis. For this reason, Attainable Region theory assists towards a better understanding of systems of complex reaction networks and the issues encountered by these systems. This thesis aims to address two areas in Attainable Region theory: 1. To help improve the design and operation of batch reactors using Attainable Regions. 2. To further advance knowledge and understanding of efficient Attainable Region construction methods. Using fundamental concepts of mixing and attainability established by Attainable Region theory, a graphical method of identifying opportunities for improving the production rate from batch reactors is first presented. It is found that by modifying the initial concentration of the batch, overall production performance may be improved. This may be achieved in practice by retaining a fraction of the final product volume and mixing with fresh feed material for subsequent cycles. This result is counter-intuitive to the normal method of batch operation. Bypassing of feed may also be used to improve production rate for exit concentrations not associated with the optimal concentration. The graphical approach also allows optimisation of batches where only experimental data are given. An improved method of candidate Attainable Region construction, based on an existing bounding hyperplanes approach is then presented. The method uses a plane rotation about existing extreme points to eliminate unachievable regions from an initial bounding set. The algorithm is shown to be faster and has been extended to include construction of candidate Attainable Regions involving non-isothermal kinetics in concentration and concentration-time space. With the ideas obtained above, the application of Attainable Regions to batch reactor configurations is finally presented. It is shown that with the appropriate transformation, results developed from a continuous Attainable Region may be used to form a related batch structure. Thus, improvement of batch reactor structures is also possible using Attainable Regions. Validation of candidate Attainable Regions is carried out with the construction algorithm developed in this work

A systematic approach to plant-wide control based on thermodynamics

Abstract In this work, a systematic approach to plant-wide control design is proposed. The method combines ingredients from process networks, thermodynamics and systems theory to derive robust decentralized controllers that will ensure complete plant stability. As a first step, the considered process system is decomposed into abstract mass and energy inventory networks. In this framework, conceptual inventory control loops are then designed for the mass and energy layers to guarantee that the states of the plant, both in terms of extensive and intensive properties, will converge to a compact convex region defined by constant inventories. This result by itself does not ensure the convergence of intensive variables to a desired operation point as complex dynamic phenomena such as multiplicities may appear in the invariant set. In order to avoid these phenomena, thermodynamics naturally provides the designer, in these convex regions, with a legitimate storage or Lyapunov function candidate, the entropy, that can be employed to ensure global stability. Based on this, the control structure design procedure is completed with the realization of the conceptual inventory and intensive variable control loops over the available degrees of freedom in the system. To that purpose, both PI and feedback linearization control are employed. The different aspects of the proposed methodology will be illustrated on a non-isothermal chemical reaction network

The application of the attainable region concept to the oxidative dehyrogenation of N-butanes in inert porous membrane reactors

The availability of kinetic data for the oxidative dehydrogenation (ODH) of n-butane from Téllez et al. (1999a and 1999b) and Assabumrungrat et al. (2002) presented an opportunity to submit a chemical process of industrial significance to Attainable Region (AR) analysis. The process thermodynamics for the ODH of n-butane and 1-butene have been reviewed. The addition of oxygen in less than the stoichiometric ratios was found to be essential to prevent deep oxidation of hydrocarbon products {Milne et al. (2004 and 2006c)}. The AR concept has been used to determine the maximum product yields from the ODH of n-butane and 1-butene under two control régimes, one where the partial pressure of oxygen along the length of the reactor was maintained at a constant level and the second where the oxygen partial pressure was allowed to wane. Theoretical maxima under the first régime were associated with very large and impractical residence times. The Recursive Convex Control policy {Seodigeng (2006)} and the second régime were applied to confirm these maxima {Milne et al. (2008)}. Lower and more practical residence times ensued. A differential side-stream reactor was the preferred reactor configuration as was postulated by Feinberg (2000a). Abstract A.D. Milne Page 4 of 430 The maximum yield of hydrocarbon product, the associated residence time and the required reactor configuration as functions of oxygen partial pressure were investigated for the series combinations of an inert porous membrane reactor and a fixed-bed reactor. The range of oxygen partial pressures was from 85 kPa to 0.25 kPa. The geometric profile for hydrocarbon reactant and product influences the residence times for the series reactors. The concept of a residence time ratio is introduced to identify the operating circumstances under which it becomes advantageous to select an inert membrane reactor in preference to a continuously stirred tank reactor and vice versa from the perspective of minimising the overall residence time for a reaction {Milne et al. (2006b)}. A two-dimensional graphical analytical technique is advocated to examine and balance the interplay between feed conditions, required product yields and residence times in the design of a reactor {Milne et al. (2006a)}.. A simple graphical technique is demonstrated to identify the point in a reaction at which the selectivity of the feed relative to a product is a maximum {Milne et al. (2006a)}. Literature Cited Assabumrungrat, S. Rienchalanusarn, T. Praserthdam, P. and Goto, S. (2002) Theoretical study of the application of porous membrane reactor to Abstract A.D. Milne Page 5 of 430 oxidative dehydrogenation of n-butane, Chemical Engineering Journal, vol. 85, pp. 69-79. Feinberg, M. (2000a) Optimal reactor design from a geometric viewpoint – Part II. Critical side stream reactors, Chemical Engineering Science, vol. 55, pp. 2455-2479. Milne, D., Glasser, D., Hildebrandt, D., Hausberger, B., (2004), Application of the Attainable Region Concept to the Oxidative Dehydrogenation of 1- Butene in Inert Porous Membrane Reactors, Industrial and. Engineering Chemistry Research, vol. 43, pp. 1827-1831 with corrections subsequently published in Industrial and Engineering Chemistry Research, vol. 43, p. 7208. Milne, D., Glasser, D., Hildebrandt, D., Hausberger, B., (2006a), Graphical Technique for Assessing a Reactor’s Characteristics, Chemical Engineering Progress, vol. 102, no. 3, pp. 46-51. Milne, D., Glasser, D., Hildebrandt, D., Hausberger, B., (2006b), Reactor Selection : Plug Flow or Continuously Stirred Tank?, Chemical Engineering Progress. vol. 102, no. 4, pp. 34-37. Milne, D., Glasser, D., Hildebrandt, D., Hausberger, B., (2006c), The Oxidative Dehydrogenation of n-Butane in a Fixed Bed Reactor and in an Inert Porous Membrane Reactor - Maximising the Production of Butenes and Butadiene, Industrial and Engineering Chemistry Research vol. 45, pp. 2661-2671. Abstract A.D. Milne Page 6 of 430 Milne, D., Seodigeng, T., Glasser, D., Hildebrandt, D., Hausberger, B., (2008), The Application of the Recursive Convex Control (RCC) policy to the Oxidative Dehydrogenation of n-Butane and 1-Butene, Industrial and Engineering Chemistry Research, (submitted for publication). Seodigeng, T.G. (2006), Numerical Formulations for Attainable Region Analysis, Ph.D. thesis, University of the Witwatersrand, Johannesburg, South Africa. Téllez, C. Menéndez, M. Santamaría, J. (1999a) Kinetic study of the oxidative dehydrogenation of butane on V/MgO catalysts, Journal of Catalysis, vol. 183, pp. 210-221. Téllez, C. Menéndez, M. Santamaría, J. (1999b) Simulation of an inert membrane reactor for the oxidative dehydrogenation of butane, Chemical Engineering Science, vol. 54, pp. 2917-2925. _________________________________

The application of the attainable region analysis in comminution.

ABSTRACT This work applies the concepts of the attainable region for process synthesis in comminution. The attainable region analysis has been successfully applied for process synthesis of reactor networks. The Attainable Region is defined as the set of all possible output states for a constrained or unconstrained system of fundamental processes (Horn, 1964). A basic procedure for constructing the attainable region for the fundamental processes of reaction and mixing has been postulated in reaction engineering (Glasser et al., 1987). This procedure has been followed in this work to construct the candidate attainable region for size reduction processes as found in a size reduction environment. A population balance model has been used to characterise the evolution of particle size distributions from a comminution event. Herbst and Fuerstenau (1973) postulated the dependency of grinding on the specific energy. A specific energy dependent population balance model was used for the theoretical simulations and for the fitting of experimental data. A new method of presenting particle size distributions as points in the Euclidian space was postulated in place of the traditional cumulative distribution. This allows successive product particle size distributions to be connected forming a trajectory over which the objective function can be evaluated. The curve connects products from successive batch grinding stages forming a pseudo-continuous process. Breakage, mixing and classification were identified as the fundamental processes of interest for comminution. Agglomeration was not considered in any of the examples. Mathematical models were used to describe each fundamental process, i.e. breakage, mixing and classification, and an The application of the attainable region analysis in comminution Abstract algorithm developed that could calculate the evolution of product particle size distributions. A convex candidate attainable region was found from which process synthesis and optimisation solutions could be drawn in two dimensional Euclidian space. As required from Attainable Region Theory, the interior of the bounded region is filled by trajectories of higher energy requirements or mixing between two boundary optimal points. Experimental validation of the proposed application of the attainable region analysis results in comminution was performed. Mono-sized feed particles were broken in a laboratory ball mill and the products were successfully fitted using a population balance model. It was shown that the breakage process trajectories were convex and they follow first order grinding kinetics at long grind times. The candidate attainable region was determined for an objective function to maximise the mass fraction in the median size class 2. It was proved that the same specific energy input produces identical products. The kinematic and loading conditions are supposed to be chosen as a subsequent event after the required specific energy is identified. Finally the fundamental process of classification was added to the system of breakage and mixing. The attainable regions analysis affords the opportunity to quantify exactly the reduction in energy consumption due to classification in a comminution circuit, thus giving optimal targets. Classification showed the potential to extend the candidate attainable region for a fixed specific energy input. The boundary of the attainable region is interpreted as pieces of equipment and optimum process conditions. This solves both the original process synthesis and successive optimisation problems

Systematic methods to help the identification and evolution of chemical process designs

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Operability-Based Design of Energy Systems: Application to Natural Gas Utilization Processes

Process operability emerged in the last decades as a powerful tool for the design and control of complex chemical processes. The design of such processes is a challenging task as they are represented by nonlinear models with large numbers of differential and algebraic equations that demand high computational effort for their solution. In particular, process operability was proposed as a method for verifying the ability of a process design, defined by the available input set, to reach an achievable output set that considers production targets. However, existing operability methods for nonlinear systems are limited by the problem size that they can address.;In this thesis, a novel operability framework for process design and intensification of high-dimensional nonlinear chemical and energy processes is developed. This proposed framework bridges the gap in the literature by addressing the challenges of process nonlinearity and model size. This framework also broadens the scope of the traditional path of operability approaches for design and control, mainly oriented to obtain the achievable output set from the available input set, and compare the computed achievable output set to a desired output set. In particular, an optimization algorithm based on nonlinear programming tools is formulated for the high-dimensional calculations of the desired input set that is feasible considering process constraints, performance levels, and intensification targets. The high computational effort required for the high-dimensional calculations is addressed by the incorporation of bilevel and parallel programming approaches into the classical process operability concepts.;To illustrate the effectiveness of the developed methods, two natural gas utilization processes of different dimensionalities are addressed: i) a catalytic membrane reactor for the direct methane aromatization conversion to benzene and hydrogen, for which an intensified reactor design footprint reduction up to 90% when compared to the base case is obtained; and ii) a natural gas combined cycle system for power generation, for which a dramatic reduction in size, from 400 to 0.11 [MW], is produced by specifying conditions of the gas and steam turbine cycles, while still keeping the high net plant efficiency between 55 and 56.5 [%]. These results indicate that this novel operability framework can be a powerful tool for enabling process intensification and modularity. Moreover, results on the implementation of the bilevel and parallel computing methods show a reduction in computational time up to 2 orders of magnitude, when compared to the original results. The results in this thesis have culminated in four peer reviewed publications and four delivered presentations by the time of the defense