Evaristo C. Biscaia

Characterization of the residence time distribution in loop reactors

Abstract A mathematical model is developed to describe the residence time distribution (RTD) characteristics of the liquid-phase loop reactor, taking into account the capacitance of the recycling pump. Based on the transfer function of the reactor model, the dynamic behavior of the limiting cases is investigated in order to characterize the main modes of macromixing in the reactor vessel. The full mathematical model is then used to simulate the RTD of the loop reactor. The full model comprises a set of coupled parabolic partial and ordinary differential equations and is solved numerically. The numerical approach allows the implementation of a time domain-based parameter estimation procedure for evaluation of the RTD parameters of the reactor model. Tracer pulse experiments are then carried out in a lab-scale polymerization loop reactor in order to provide data for the parameter estimation procedure. It is shown that simulated reactor responses match quite well with experimental data. Besides, the estimation procedure employed is able to provide parameter estimates with high accuracy and low standard deviations. Therefore, the modeling approach presented here may be used for reliable estimation of the macromixing parameters and proper description of the RTD dynamics of loop reactors.

Determination of the external mass transfer coefficient and influence of mixing intensity in moving bed biofilm reactors for wastewater treatment.

In moving bed biofilm reactors (MBBR), the removal of pollutants from wastewater is due to the substrate consumption by bacteria attached on suspended carriers. As a biofilm process, the substrates are transported from the bulk phase to the biofilm passing through a mass transfer resistance layer. This study proposes a methodology to determine the external mass transfer coefficient and identify the influence of the mixing intensity on the conversion process in-situ in MBBR systems. The method allows the determination of the external mass transfer coefficient in the reactor, which is a major advantage when compared to the previous methods that require mimicking hydrodynamics of the reactor in a flow chamber or in a separate vessel. The proposed methodology was evaluated in an aerobic lab-scale system operating with COD removal and nitrification. The impact of the mixing intensity on the conversion rates for ammonium and COD was tested individually. When comparing the effect of mixing intensity on the removal rates of COD and ammonium, a higher apparent external mass transfer resistance was found for ammonium. For the used aeration intensities, the external mass transfer coefficient for ammonium oxidation was ranging from 0.68 to 13.50 m d(-1) and for COD removal 2.9 to 22.4 m d(-1). The lower coefficient range for ammonium oxidation is likely related to the location of nitrifiers deeper in the biofilm. The measurement of external mass transfer rates in MBBR will help in better design and evaluation of MBBR system-based technologies.

Using kriging models for real-time process optimisation

Abstract Kriging models have been used in a number of engineering applications, to approximate rigorous models when those computer codes become too time-consuming to be used directly. In this context, they are called surrogate models or metamodels. The use of kriging models as metamodels for process optimisation was addressed in a previous paper [1] where a methodology for metamodel-based process optimisation was proposed, focusing on real-time applications. In this work, new developments were achieved through the use of new examples, one of which the optimisation of a real crude distillation unit involving 19 decision variables. The performance of the metamodel-based optimisation is compared with results obtained with the optimisation based on a first-principles model, embedded in a sequential-modular process simulator. It is shown that metamodel-based optimisation with adaptation of the metamodels during the optimisation procedure provides results with good accuracy and significant reduction of computational effort. The performance comparison between neural networks and kriging models for chemical processes is another contribution of this work.

An Efficient Adjoint-Free Dynamic Optimization Methodology for Batch Processing using Pontryagin's Formulation

Abstract The proposed methodology developed in this contribution solves the dynamic optimization of batch processes eliminating adjoint variables related with PontryaginNs formulation based on an extension of the procedure proposed by Rahman & Palanki (1998) . The optimal input profiles are obtained directly through an optimization procedure able to find optimal initial values of the control variables and their time derivatives or their optimal switching times. Problems related with activation of inequality constraints of the control or state variables during the optimal trajectories provoking variations of the differential index of the system, floating index DAE systems, are also considered. Inequalities associated with these variables were converted to equalities using suitable regularization functions. Benchmark examples were considered to validate the methodology, and obtained results were successfully compared with reported results in the literature.

Fast Nonlinear Predictive Control and State Estimation of Distillation Columns Using First-Principles Reduced-order Model

Abstract In this work, the performance of two first-principles reduced-order models of distillation columns are evaluated for using in nonlinear model predictive control and state estimation. The results reveal that the reduced-order model based on moment technique have a superior performance in comparison with the classic orthogonal collocation method. The analysis of the linearized models in each sampling time shows that the reduced models have a full rank observability matrix while the full model is rank deficient. In addition, the moments technique does not present the oscillatory behaviour of the classical orthogonal collocation, producing a jacobian matrix without complex eigenvalues, similarly to the full model. The control action with the reduced-order model can be obtained in less than 50 % of the CPU time spent by the full model.

Reduced Rigorous Models for Efficient Dynamic Simulation and Optimization of Distillation Columns

Abstract In this work, we compare the technique of model order reduction based on weighted residuals in discrete domain with the aggregated modelling method for efficient dynamic simulation and optimization of distillation columns. To compute the weighted residuals, a discrete form of Lobatto-Gauss quadrature was developed in a previous work Ribeiro et al. (2010) , allowing a high degree of accuracy on the calculations of the weighted sums of heat and mass balances residuals on real stages. Balances related with upstream and downstream stages are considered as boundary conditions of corresponding difference-differential equations system. The aggregated modelling method is based on the two-step procedure of Linhart & Skogestad (2010) . In the first step, aggregation stages are selected to compose the reduced dynamics with the corresponding holdup factors, and in the second step the resulting algebraic equations after applying the quasi-steady-state assumption to the remaining stages are replaced by pre-computed functions. Optimization of start-up policies, Wozny & Li (2004) , optimal feed tray location, Kamath et al. (2010) , and dynamic simulation of binary and multicomponent distillation columns were solved to compare the performance of both model reduction techniques.

A Continuous Implementation of the Ideal Time Delay in EMSO

Abstract The concept of time delay arises in many practical chemical engineering applications. Ideal time delay appears every time an advective transport is the solely transport mechanism present in part of the process. Due the distributed nature of pure time delay, this phenomena cannot be directly simulated by a finite dimension lumped system. The main objective of this contribution is the automatic development of rational approximations of ideal time delay transfer functions resulting in lumped systems of specified finite dimension. Different approximations were generated and their dynamic behaviors were analyzed and compared, where stability properties are the main focus of the analysis. Oscillations and inverse response appear in various time delay approximations, therefore these undesirable behaviors were minimized through the inclusion of adjustable m-order filters in the approximations. Data buffering is the common strategy considered in many dynamic process simulators to include pure time delays. However, this strategy is not compatible with numerical time integration that uses variable time steps in order to meet specified accuracy, because the delayed data must be interpolated compromising the accuracy of the numerical integration. Different continuous approximations were included in EMSO – Environment for Modeling Simulation and Optimization – and their performances were compared through some practical examples. The orthogonal collocation approach presented better stability properties for high-order approximations and the undesirable oscillations were well-controlled with low-order filters.

Strategies for numerical integration of discontinuous DAE models

Abstract In this work, it is presented a novel strategy to solve discontinuous DAEs of floating index type. The switching between DAE models of different indexes and the reinitialization of the system are performed automatically by the code. The direct integration of the high index DAE model is aided by the software. The equation actually fed to the numerical integrator is a weighted sum of the different model equations. The weights are either 0 or 1 inside integration intervals, depending on whether the corresponding equation is active or not during the time interval in consideration. Across model discontinuities, the numerical values of the weights are taken from 0 to 1 (or vice-versa) via a smooth regularization function, which is a continuous representation of a step function. Several functions are suitable to perform such task, and the authors suggest a family of functions which are simple and differentiable up to the order needed. As an example, the optimal control of a fedbatch fermentation (production of ethanol by S. cerevisiae ) is presented.

Multi-Objective parameter estimation problems: an improved strategy

A multi-objective optimization approach has been applied to solve parameter estimation problems. An improved algorithm, based on evolutionary strategies, has been proposed to optimize mathematical model parameters. The algorithm makes use of a new concept of fitness function, which determines the reproduction ratio as a function of the population density, and a new class of operators, which enhance the algorithm performance. Two processes have been analyzed: a grain cooling process and a grain drying process. In order to estimate the coefficient of heat transfer and the drying rate parameters of these models, minimization of the sum of the least squares of temperature and equilibrium moisture content have been conducted. Experimental data obtained from the soybean cooling in a continuous cross-flow moving bed heat exchanger and the corn drying in a fixed bed dryer have been used to evaluate the estimated parameters. The simulated results demonstrated the algorithm efficiency to perform parameter estimation. The validated model consistently fits the experimental data.

Differential-Algebraic Approach to Solve Steady-State Two-Phase Flow Drift-Flux Model with Phase Change

Abstract Two-phase flow in pipes occurs frequently in petroleum refineries. Simulation and design calculations for their processing units require methods for predicting void fractions and axial pressure drops, thus making it essential that precise models of the relevant thermo-fluid dynamics be combined with efficient numerical techniques. In this work, the two-phase flow with phase change problem of a refinery multicomponent naphtha (C5-C8) was modeled through the steady-state one-dimensional mixture model, which comprises continuity, momentum and energy differential equations for the mixture, in addition to an extra continuity equation for the vapor phase. Relative motions between the phases are accounted for by a constitutive expression for the one-dimensional drift velocity. Evaporation and condensation are considered via vapor-liquid equilibrium calculations, and suitable thermodynamic methods are also applied in the evaluation of physical properties. It is proposed in this work that this rigorous formulation fits in the scope of Differential-Algebraic Equations (DAE) systems and is preferably solved by proper established numerical methods rather than the customary iterative segregated semi-implicit algorithms based on finite volume approaches. Efficiency and accuracy gains are demonstrated as a result of the proposed numerical strategy, which yields higher-order numerical solutions in much less CPU time. Specific regularization functions were also developed in order to eliminate expected numerical issues of convergence failure due to discontinuities in the drift-flux parameters at flow-regime transitions.