J.M. Le Lann

Optimal selection of sensor location on a complex plant, using a graph oriented approach

Abstract This paper deals with the improvement of process instrumentation design. We suggest a flow sensor arrangement method based on an accurate analysis of the graph representing the process. Our algorithm leads to a sensor arrangement (with a minimum sensor number) which satires either a total or a partial observability of the process and takes into account the unmeasurability of some streams. A Brandi and Bound type optimization method which enables to find an optimal arrangement of those sensors has been adapted. The optimality of the solution is considered from a cost point of view. These technics are applied to opaned literature examples and their efficiency is enlighted.

A general strategy for parameter estimation in differential-algebraic systems

Abstract In this paper, a general method is presented for parameter estimation in differential and algebraic equation systems (DAE systems). It is more specifically developed for the kinetic parameter estimation of an isothermal batch reactor kinetic model. How to improve the Gauss-Newton method used for parameter estimation in the context of dynamic simulation involving DAE systems is shown. Emphasis is put on the calculation and conditioning of the Gauss-Newton operator. At the minimum, the joint linearized confidence region is evaluated and used to discriminate among rival models. The given methodology has been applied to determine a suitable Langmuir—Hinshelwood model for multiple catalytic hydrogenations.

Steady-state and dynamic simulation of plate fin heat exchangers

Abstract This study deals with the steady-state and dynamic simulation of the plate fin heat exchanger. It inlights some aspects of the modelling of such a complex system in transient and, especially the impact on the numerical treatment. Illustrative applications sketch the importance of dynamic studies in complement with steady-state ones.

Accuracy, temporal performance and stability comparisons of discretization methods for the numerical solution of Partial Differential Equations (PDEs) in the presence of steep moving fronts

Abstract In this paper, several competitive spatial discretization methods recently developed for the convection term are reviewed and analyzed in terms of accuracy, temporal performance, and stability. This analysis was performed using a prediction–correction DAE integrator within the framework of the MOL (Method Of Lines). The discretization methods are classified by Fixed Stencil (FS), Adaptive Stencil (AS) and Weighted Stencil (WS) approaches and their main characteristics are demonstrated via a number of bench marking tests. Of the 14 discretization methods tested, four have been shown to be the most reliable, when we consider the accuracy of the calculation and the computational time required. Application of commonly-used FS methods to convection-dominated problems containing a moving shock results in a relatively short calculation time. However, almost of the FS methods, except for the first-order upwind FS method, are unstable, providing spurious oscillatory profiles (termed the Gibbs phenomena) near the shock. Employing AS methods such as ENO (Essentially Non-Oscillatory) schemes, this Gibbs phenomena disappears. Therefore, AS methods enhance stability and accuracy but are somewhat prohibitive. WS methods (i.e. Weighted ENO schemes), which use a convex combination of candidate stencils weighted by the ENO idea, can reduce the calculation time, and are inheriting of the non-oscillation nature inherent in the AS methods. The ENO and WENO methods are efficient to track a shock and steep moving front and these methods are essential for numerical schemes which use relatively small number of mesh points.

Dynamic models for start-up operations of batch distillation columns with experimental validation

The simulation of batch distillation columns during start-up operations is a very challenging modelling problem because of the complex dynamic behaviour. Only few rigorous models for distillation columns start-up are available in literature and generally required a lot of parameters related to tray or pack geometry. On an industrial viewpoint, such a complexity penalizes the achievement of a fast and reliable estimate of start-up periods. In this paper, two “simple” mathematical models are proposed for the simulation of the dynamic behaviour during start-up operations from an empty cold state. These mathematical models are based on a rigorous tray-by-tray description of the column described by conservation laws, liquid–vapour equilibrium relationships and equations representative of hydrodynamics. The models calibration and validation are studied through experiments carried out on a batch distillation pilot plant, with perforated trays, supplied by a water methanol mixture. The proposed models are shown by comparison between simulation and experimental studies to provide accurate and reliable representations of the dynamic behaviour of batch distillation column start-ups, in spite of the few parameters entailed.

Influence of solvent choice on the optimisation of a reaction–separation operation : application to a Beckmann rearrangement reaction

In pharmaceutical syntheses, the solvent choice generally represents a complex design step. Traditionally, this choice is operated according to criteria connected with the reaction step and without any consideration on the following separation steps. The purpose of this study is to highlight the benefits of a global approach of optimisation for the solvent determination. In this way, an optimisation framework dedicated to global synthesis is applied to a simple reaction–separation operation integrating a Beckmann rearrangement reaction, leading to interesting solvent choices.

Dynamic modeling of three-phase upflow fixed-bed reactor including pore diffusion

The dynamics of a three-phase upflow fixed-bed reactor are investigated using a non-isothermal heterogeneous model including gas–liquid and liquid–solid mass transfer and diffusion/reaction phenomena inside the catalyst. The partial differential and algebraic equations involving three integration variables (time and two space coordinates) are solved via discretization of the spatial coordinates coupled with the Gear method. For a multistep hydrogenation on a shell catalyst, the model exhibits significant effects of the external and above all internal resistance to hydrogen transfer but also non-trivial internal hydrocarbons concentration profiles. A simplified model is compared with the extended one and with experimental data in transient regime. In the investigated conditions—hydrocarbons in large excess—the diffusion of hydrocarbons appears to be actually not limiting, so that the simplest model predicts accurately the transient reactor behavior.

Maxwell-Stefan approach coupled drop population model for the dynamic simulation of liquid-liquid extraction pulsed column

Abstract Zimmermann and al. (1995) have proposed a model for the simulation of a multi-component extraction process based on Maxwell-Stefan approach and incorporating a drop population model. In the continuation of this work, this paper presents some recent developments, notably the extension to the dynamic and some improvements at the hydrodynamic level. The model is characterised by the coupling of two main aspects in separation processes: hydrodynamics and multi-component mass transfer. Hydrodynamics is described by a drop population model: fundamental mechanisms like transport, axial back-mixing and forward-mixing, drop breakage and interdrop coalescence, including Marangoni effect, are described in a detailed way. Multi-component mass transfer is computed using the Maxwell-Stefan approach. The proposed model is able to predict the component concentration profiles in the dispersed and continuous phases, hold-up and drop size distribution throughout the column and the interactions between mass transfer and hydrodynamics under operating conditions up to flooding.

Moving mesh generation for tracking a shock or steep moving front

Abstract For tracking a shock or steep moving front in the numerical solution of Partial Differential Algebraic Equations (PDAEs), an accurate spatial discretization method, Weighted Essentially Non-Oscillatory (WENO) scheme, is combined with moving grid techniques so that spacing of moving meshes is smoothed locally and globally. Several monitor functions, as metric criteria of node concentration, are examined. While the fixed grid method (uniform grid size) needs many mesh points to obtain enough solution accuracy, the moving grid method (non-uniform grid size) enhances accuracy even at small mesh numbers but it may be prohibitive owing to the addition of complex and non-linear mesh equations into physical PDAEs. The combination of the WENO scheme (based on an adaptive stencil idea) with the moving grid techniques improves stability and accuracy in the numerical solution over the commonly used moving grid method of central discretization. To locate adequate grid position in the moving mesh method, suitable monitor function according to problems must be selected.

Numerical problems encountered in the simulation of reactive absorption: DAE index reduction and consistent initialisation

A general simulation model able to represent mass transfer in the presence of chemical reactions is presented. The model developed describes the behaviour of an absorption column. This model needs to be able to access certain information such as kinetic constants, equilibrium constants, activity coefficients, etc. Among these auxilary models, is the need to be able to calculate the mass flux and compositions at the boundary of the diffusional film. A set of equations describing the film has therefore been developed, and its resolution has proved to be troublesome. Indeed we have run into two problems that have had to be tackled. The problems encountered are directly due to the nature of the equations to be solved, that is a system of differential algebraic equations (DAE). These problems arise from the approach desired to treat the equations, based on Gears algorithm. The first problem deals with the solution of high order index systems, and the second involves the necessity of having consistent initial conditions. A suitable procedure has been implemented for index reduction, and several techniques have been tested for the obtention of consistent initial conditions.