Accelerated computation of cyclic steady state for simulated-moving-bed processes

Industrial applications of the simulated-moving-bed (SMB) chromatographic technology have brought an emergent demand to improve the SMB process operation for higher efficiency and better robustness. Improved process modelling and more-efficient model computation will pave a path to meet this demand. However, the SMB unit operation exhibits complex dynamics, leading to challenges in SMB process modelling and model computation. One of the significant problems is how to quickly obtain the steady state of an SMB process model, as process metrics at the steady state are critical for process design and real-time control. The conventional computation method, which solves the process model cycle by cycle and takes the solution only when a cyclic steady state is reached after a certain number of switching, is computationally expensive. Adopting the concept of quasi-envelope (QE), this work treats the SMB operation as a pseudo-oscillatory process because of its large number of continuous switching. Then, an innovative QE computation scheme is developed to quickly obtain the steady state solution of an SMB model for any arbitrary initial condition. The QE computation scheme allows larger steps to be taken for predicting the slow change of the starting state within each switching. Incorporating with the wavelet-based technique, this scheme is demonstrated to be effective and efficient for an SMB sugar separation process. Moreover, investigations are also carried out on when the computation scheme should be activated and how the convergence of the scheme is affected by a variable stepsize.

How long does it take for aquifer recharge or aquifer discharge processes to reach steady state?

Groundwater flow models are usually characterized as being either transient flow models or steady state flow models. Given that steady state groundwater flow conditions arise as a long time asymptotic limit of a particular transient response, it is natural for us to seek a finite estimate of the amount of time required for a particular transient flow problem to effectively reach steady state. Here, we introduce the concept of mean action time (MAT) to address a fundamental question: How long does it take for a groundwater recharge process or discharge processes to effectively reach steady state? This concept relies on identifying a cumulative distribution function, $F(t;x)$, which varies from $F(0;x)=0$ to $F(t;x) \to \infty$ as $t\to \infty$, thereby providing us with a measurement of the progress of the system towards steady state. The MAT corresponds to the mean of the associated probability density function $f(t;x) = \dfrac{dF}{dt}$, and we demonstrate that this framework provides useful analytical insight by explicitly showing how the MAT depends on the parameters in the model and the geometry of the problem. Additional theoretical results relating to the variance of $f(t;x)$, known as the variance of action time (VAT), are also presented. To test our theoretical predictions we include measurements from a laboratory–scale experiment describing flow through a homogeneous porous medium. The laboratory data confirms that the theoretical MAT predictions are in good agreement with measurements from the physical model.

Mathematical model of COREX melter gasifier: Part I. Steady-state model

The COREX melter gasifier is a countercurrent reactor to produce liquid iron. Directly reduced iron (DRI), noncoking coal, and other additives are charged to the melter gasifier at their respective temperatures, and O-2 is blown through the tuyeres. Functionally, a melter gasifier is divided into three zones: a moving bed, fluidized bed, and free board. A model has been developed for the moving bed, where the tuyere region is two-dimensional (2-D) and the rest is one-dimensional (1-D). It is based on multiphase conservation of mass, momentum, and heat. The fluidized bed has been treated as 1-D. Partial equilibrium is calculated for the free board. The calculated temperature of the hot metal, the top gas, and the chemistry of the top gas agree with the reported plant data. The model has been used to study the effects of bed height, injection of impure O-2, coal chemistry, and reactivity on the process performance.

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.

THE APPLICATION OF AN ULTRAMICROELECTRODE IN HOMOGENEOUS CATALYTIC REACTION .1. GENERAL CHARACTERISTIC OF A HOMOGENEOUS CATALYTIC REACTION AT AN ULTRAMICROELECTRODE WITH ARBITRARY GEOMETRY UNDER STEADY-STATE

A general characteristic of the electrochemical process coupling with a homogeneous catalytic reaction at an ultramicroelectrode under steady state is described. It was found that the electrochemical process coupling with homogeneous catalytic reaction has a similar steady state voltammetric wave at an ultramicroelectrode with arbitrary geometry. A method of determination for the kinetic constant of homogeneous catalytic reaction at an ultramicroelectrode with arbitrary geometry is proposed.

On the complexity of the water-gas shift reaction mechanism over a Pt/CeO2 catalyst: Effect of the temperature on the reactivity of formate surface species studied by operando DRIFT during isotopic transient at chemical steady-state

The present report investigates the role of formate species as potential reaction intermediates for the WGS reaction (CO + H2O -> CO2 + H-2) over a Pt-CeO2 catalyst. A combination of operando techniques, i.e., in situ diffuse reflectance FT-IR (DRIFT) spectroscopy and mass spectrometry (MS) during steady-state isotopic transient kinetic analysis (SSITKA), was used to relate the exchange of the reaction product CO2 to that of surface formate species. The data presented here suggest that a switchover from a non-formate to a formate-based mechanism could take place over a very narrow temperature range (as low as 60 K) over our Pt-CeO2 catalyst. This observation clearly stresses the need to avoid extrapolating conclusions to the case of results obtained under even slightly different experimental conditions. The occurrence of a low-temperature mechanism, possibly redox or Mars van Krevelen-like, that deactivates above 473 K because of ceria over-reduction is suggested as a possible explanation for the switchover, similarly to the case of the CO-NO reaction over Cu, I'd and Rh-CeZrOx (see Kaspar and co-workers [1-3]). (c) 2006 Elsevier B.V. All rights reserved.

On the need to use steady-state or operando techniques to investigate reaction mechanisms: An in situ DRIFTS and SSITKA-based study example

The nature of the surface species formed at the surface of 2 wt.% Pt/CeO2 catalyst during the forward water-gas-shift (WGS, CO + H2O -> CO2 + H-2) and the reverse reaction (RWGS) were essentially identical. More, the surface concentration of formate, carbonate and carbonyl species was similar in each case. The presence of well-resolved IR bands allowed an unequivocal relative quantitative analysis of each species, avoiding the use of the carboxylate stretching region (1600-1200 cm(-1)). However, the quantitative analysis in the case of an isotopic study was complicated due to the overlapping of the various isotope bands, yet this problem could be overcome by integrating the high-wavenumber part of the bands. The reactivity of the surface species formed under RWGS conditions was followed under two different gaseous streams. Firstly, the reactivity of these intermediates were followed under an inert gas (i.e., At), in which case carbonates were essentially stable and less reactive than formates. Secondly, the reactivity of the same surface species was followed when switching to the corresponding C-13-labelled feed (i.e., (CO2)-C-13 + H-2), in which case carbonates were exchanged significantly faster than formates. While carbonates species have been reported as reaction intermediate under reaction conditions, the increased stability or surface poisoning by these carbonates in the absence of reaction mixture was highlighted. Ultimately, this work re-emphasises the need to use steady-state conditions if the true operando reactivity of the adsorbates and structure of the solid are to be determined. (c) 2005 Elsevier B.V. All rights reserved.

Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removal

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

Spectral solution for the air stripping pollutants removal dynamic model with non linear steady state conditions

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

Development and application of a novel algorithm for steady-state optimising control using dynamic information

A novel optimising controller is designed that leads a slow process from a sub-optimal operational condition to the steady-state optimum in a continuous way based on dynamic information. Using standard results from optimisation theory and discrete optimal control, the solution of a steady-state optimisation problem is achieved by solving a receding-horizon optimal control problem which uses derivative and state information from the plant via a shadow model and a state-space identifier. The paper analyzes the steady-state optimality of the procedure, develops algorithms with and without control rate constraints and applies the procedure to a high fidelity simulation study of a distillation column optimisation.

Steady state and dynamic modelling of nitrogen in the River Kennet: impacts of land use change since the 1930s

Steady state and dynamic models have been developed and applied to the River Kennet system. Annual nitrogen exports from the land surface to the river have been estimated based on land use from the 1930s and the 1990s. Long term modelled trends indicate that there has been a large increase in nitrogen transport into the river system driven by increased fertiliser application associated with increased cereal production, increased population and increased livestock levels. The dynamic model INCA Integrated Nitrogen in Catchments. has been applied to simulate the day-to-day transport of N from the terrestrial ecosystem to the riverine environment. This process-based model generates spatial and temporal data and reproduces the observed instream concentrations. Applying the model to current land use and 1930s land use indicates that there has been a major shift in the short term dynamics since the 1930s, with increased river and groundwater concentrations caused by both non-point source pollution from agriculture and point source discharges. �

Undersökning av steady state och utvärdering av valskraft och friktion vid kallvalsning av aluminium

The purpose with this thesis was to examine the cold rolling mill located at Högskolan Dalarna and to stabilize the rolling process, to achieve steady state. Experiments with cold rolling of an aluminium strip have given results for rolling force, friction, reduction, strip tension and strain hardening. Results show that steady state has been found for the experiments with roll force and strain hardening, and not been found for the experiments with friction and reduction. Results show that increased strip tension gives lower roll forces. The roll force equation of Stone shows comparable results with reality for dry contact with reductions up to 30 %, but starts being incomparable with higher reductions. The roll force equation of Stone shows a bit higher roll forces than reality gave, but was comparable within reductions from 13 to 50 %. Experiments have shown that the aluminium strip has gone through strain hardening. Experiments show how the set roll gap did not yield the desired thickness reduction, there for the elastic spring constant for the rolling mill was examined and determined to be 417 N / mm for the specific alloy band. The influence of tension strip for roll force was examined and Results confirm the theory about how the roll force is decreased by increasing tension strip. The work rolls started to slip against the alumina strip as high tension strip; 70 N/mm2, gave low roll force; < 15kN.

Setting the preheating and steady-state operation of electronic ballasts, considering electrodes of hot-cathode fluorescent lamps

This paper presents a new methodology for the adjustment of the preheating process and steady-state operation of electronic ballasts intended for hot-cathode fluorescent lamps. The classical series-resonant parallel-loaded half-bridge inverter is the power stage analyzed in this paper. In addition, the preheating process is based on the imposition of a constant rms current through the electrodes, in order to provide a proper value of the R-h/R-c ratio before the lamp start. According to the proposed methodology, it is possible to set suitable operating points for, the electronic ballast, considering optimal conditions for the lamps electrodes. Therefore, the proposed methodology for setting the preheating and steady-state operation is a complete platform to the design of electronic ballasts for hot-cathode fluorescent lamps.

Efficiency of extrinsic and intrinsic charge-carrier photogeneration processes obtained from the steady-state photocurrent action spectra of poly(p-phenylene vinylene) derivatives

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The steady-state behavior of the synthetic and side-sensitive synthetic double sampling (X)over-bar charts

The steady-state average run length is used to measure the performance of the recently proposed synthetic double sampling (X) over bar chart (synthetic DS chart). The overall performance of the DS X chart in signaling process mean shifts of different magnitudes does not improve when it is integrated with the conforming run length chart, except when the integrated charts are designed to offer very high protection against false alarms, and the use of large samples is prohibitive. The synthetic chart signals when a second point falls beyond the control limits, no matter whether one of them falls above the centerline and the other falls below it; with the side-sensitive feature, the synthetic chart does not signal when they fall on opposite sides of the centerline. We also investigated the steady-state average run length of the side-sensitive synthetic DS X chart. With the side-sensitive feature, the overall performance of the synthetic DS X chart improves, but not enough to outperform the non-synthetic DS X chart. Copyright (C) 2014 John Wiley &Sons, Ltd.