Warren D. Seider

Homotopy-continuation method for stability analysis in the global minimization of the Gibbs free energy

Abstract A new algorithm to determine phase equilibria at the global minimum of the Gibbs free energy is presented. Using the Newton homotopy-continuation method, when checking for phase stability, multiple stationary points of the tangent-plane-distance function (TPDF) are determined. Subsets of these are selected as estimates for the minimization of the Gibbs free energy. The algorithm, implemented in the HOMPEQ computer program, was tested for nine non-ideal mixtures. The homotopy paths, when initialized with nearly pure species, reliably located all of the stationary points of the TPDF. This was accomplished for mixtures that exhibit multiple immiscibility gaps. The combined algorithm located the global minimum for all of the systems involving symmetric and asymmetric models, with a final stability analysis implemented to ensure global minimization. In comparison with Michelsens programs, HOMPEQ is slower and provides comparable reliability, but is initialized with nearly pure phases, a much less elaborate initialization strategy.

Equilibrium solubilities of β-carotene in supercritical carbon dioxide

Equilibrium solubilities of pure crystalline β-carotene in supercritical CO2 have been measured using an LDC Analytical SPA extractor1. The apparatus features a recirculating loop with an in-line UV detector. Quantitation by UV absorbance permits the detection of lower solubilities than can normally be obtained gravimetrically. The values reported were obtained at temperatures from 40 to 70°C and pressures from 200 to 500 bar. The measured mole fractions ranged from 9.0×10−9 at 40°C and 275 bar to 1.9x10−6 at 70°C and 400 bar. Solubilities are also reported for β-carotene in mixtures of CO2and 1 wt.% ethanol, 1 wt.% methanol and 1 wt.% methylene chloride, at 70°C and various pressures. Addition of the cosolvent increased the solubility in every case, with the largest increase occurring in a mixture of CO2 and 1 wt.% ethanol. Pure component properties for β-carotene were estimated, and the experimental data were correlated to a modified Peng-Robinson equation of state. The model predictions compare well with the experimental data.

Global Optimization of Chemical Processes using Stochastic Algorithms

Many systems in chemical engineering are difficult to optimize using gradient-based algorithms. These include process models with multimodal objective functions and discontinuities. Herein, a stochastic algorithm is applied for the optimal design of a fermentation process, to determine multiphase equilibria, for the optimal control of a penicillin reactor, for the optimal control of a non-differentiable system, and for the optimization of a catalyst blend in a tubular reactor. The advantages of the algorithm for the efficient and reliable location of global optima are examined. The properties of these algorithms, as applied to chemical processes, are considered, with emphasis on the ease of handling constraints and the ease of implementation and interpretation of results. For the five processes, the efficiency of computation is improved compared with selected stochastic and deterministic algorithms. Results closer to the global optimum are reported for the optimal control of the penicillin reactor and the non-differentiable system.

Coordinated design and control optimization of nonlinear processes

Abstract On a small time-scale, disturbances to a process can lead to off-spec production, decreased profitability and the violation of hard process constraints, creating unsafe conditions. A strategy is presented for the design of processes that are operationally optimal, as well as steady-state optimal, and that operate prudently far from hard constraints. In addition to the evaluation of an economic objective, each potential design is evaluated for its controllability, using the closed-loop response to several disturbances, simulated with model predictive control (MPC) algorithms. These algorithms provide excellent responses to unmeasured disturbances, allow for the inclusion of constraints and are fairly insensitive to the tuning parameters, allowing for an evaluation of the inherent controllability of a process. This strategy has been applied to a fermentation process with complex chemical and physical interactions and characterized by hysteresis and periodic behavior for some ranges of its design parameters. A simple optimization of venture profit leads to a design that is highly constrained and unstable. Using the above strategy, it is demonstrated that alternative designs exist with improved controllability, but without retreating from the design constraints. This is counterintuitive and contrary to the results of several case studies. Furthermore, the design remains unstable.

Stochastic optimization for optimal and model-predictive control

Abstract The integrated-controlled-random-search for dynamic systems (ICRS/DS) method is improved to include a moving-grid strategy and is applied to more challenging problems including: (1) the optimal control of a fed-batch bioreactor, a plug-flow reactor exhibiting a singular arc, the van der Pol oscillator; and (2) the model-predictive control (MPC) of the Czochralski (CZ) crystallization process. This technique has several advantages over the gradient-based optimization methods with respect to convergence to the global optimum and the handling of singular arcs and non-differentiable expressions. Furthermore, its implementation is very simple and avoids tedious transformations that may be required by other methods. In MPC, a nonlinear program is solved to adjust the manipulated variables so as to minimize a control objective. The major difficulty in MPC implementation is in the handling of the dynamic constraints. The ICRS/DS method is applied for the control of the CZ crystallization process and is shown to be an attractive alternative to: (1) sequential integration and optimization, (2) the use of finite element/orthogonal collocation to convert the ODEs to algebraic constraints, and (3) successive linearization of the ODEs.

Multiphase equilibria of reactive systems

Abstract This paper reviews recent developments in the analysis and calculation of multiphase equilibria involving chemical reactions. Emphasis is placed on the reaction tangent plane and its importance for stability analysis. Calculation methods to locate the global minimum of the Gibbs free energy are reviewed with emphasis on the GOP method that achieves ϵ-global convergence. Methods for the simulation and design of reactive-distillation columns are considered with emphasis on reactive azeotropes and reactive residue curves for chemical reactions at equilibrium or kinetically controlled.

Real-time risk analysis of safety systems

Methods for plant-specific, real-time, risk assessment are presented using Bayesian analysis with copulas. These are used to develop: (i) a forecasting analyzer that predicts the frequencies of occurrence of abnormal events, (ii) a reliability analyzer that predicts the failure probabilities of safety systems involving equipment and human actions, and (iii) an accident closeness analyzer that predicts the fuzzy memberships to various critical zones, indicating the proximity of a current plant state to a failure or disaster, through the use of accident precursor data. These methods, which involve repetitive risk analysis after abnormal events occur, are especially beneficial for operations involving complex nonlinearities and multi-component interactions, helping to achieve inherently safer operations. Furthermore, these methods demonstrate the importance of using plant-specific estimates of failure probabilities rather than generic values in the risk assessment of chemical plants. In this analysis, the propagations of abnormal events through the safety systems are modeled in real-time using SIMULINK and ASPEN DYNAMICS. The analysis methods are illustrated for a continuous ethyl benzene process.

ASPEN: An Advanced System for Process Engineering

Abstract The paper presents an overview of ASPEN (Advanced System for Process Engineering) which is a next-generation process simulator and economic evaluation system. The system is presently under development for use in engineering of fossil energy conversion processes.

Model-predictive control of the Czochralski crystallization process. Part I. Conduction-dominated melt

Two model-predictive controllers (MPCs), operating on different time and length scales, coupled through constraints, are introduced for the Czochralski crystallization process. The first, a capillary controller, controls the radius of the crystal by manipulating the pulling velocity. The second, a bulk controller, manipulates the power inputs to the heaters (and heat pipes) to control the pulling velocity, the thermal stresses, and the oxygen and dopant distributions under the crystal. The latter employs a distributed-parameter, conduction-dominated model for heat transfer in the melt and crystal, discretized using the boundary-element method to reduce the order of the system. A model for the melt/crystal interface is developed to represent the radius dynamics as a function of the pulling velocity for the capillary controller. The main advantage of the coupled MPCs, compared with conventional, proportional-integral-derivative (PID) control, is that the microscopic properties in the crystal, such as the distributions of oxygen, dopant, and dislocations, are controlled indirectly by the addition of constraints to their nonlinear programs (NLPs).

Semicontinuous, middle-vessel, extractive distillation

Abstract A decentralized control configuration is proposed for the semicontinuous, extractive distillation of a low-boiling azeotropic mixture of acetone and methanol. The separation is performed in a middle-vessel column (MVC), having a large external middle vessel, from which the column is fed, and to which a full-liquid sidedraw from the stage above the feed tray is sent. The extractive agent, water, feeds the column on a scheduled basis of facilitate the separation. Based upon the simplicity of a decentralized configuraiton and the desire to avoid controller overrides, a DB-control configuration is selected. This configuration, in which the distillate flow rate is manipulated to control the composition of the distillate, and the bottoms flow rate is manipulated to control the composition of the bottoms product, has been widely labeled as inoperable. Herein, the configuration is shown to perform satisfactorily when a middle vessel with a full-liquid sidedraw is utilized. A cyclic campaign is simulated showing the satisfactory performance of the DB-MVC control configuration. The advantages of the control configuration are discussed and design specifics are provided. An analysis of the campaign, highlighting the problems overcome, is given.