Cyclic Steady State Behavior Research Articles

Anti-dumping duties on Indian imports of fumed silica

Biobutanol has received significant attention as a renewable gasoline substitute and as a chemical feedstock owing to its high energy content, low volatility, and low water solubility. Low volumetric productivity caused by the toxicity of butanol in batch fermentation stands as one of the major obstacles to the commercialization. In this paper, continuous biobutanol fermentation with ex-situ adsorption recovery of butanol is investigated as a way to overcome this limitation. In this integrated system, the spatial segregation of the adsorption system and the fermentation process enables continuous biobutanol production without the need to stop the fermentation. Since the adsorption column needs to be switched periodically owing to the limited capacity of the adsorbent, the overall operation follows a cyclic pattern and the fermentation process converges to a cyclic steady state (CSS). In this study, a dynamic model of the integrated process is constructed and used for dynamic simulation to determine the system. Major operating variables are optimized through grid search for given feed concentrations based on the predicted CSS behavior in order to design an operation strategy that satisfies given requirements.

A simple and practical process modeling methodology for pressure swing adsorption

Although many dynamic models exist for the design and simulation of pressure swing adsorption (PSA) processes, these models involve the solution of a complex system of coupled partial differential equations. Process engineers need a simple, practical, and yet robust short-cut model that helps decide whether to implement a PSA system in a process flowsheet. This work presents a “virtual” moving bed modeling methodology that considers only mass and energy balances and adsorption isotherms to describe the cyclic steady state behavior of PSA systems. Similar to tray efficiencies in distillation calculations, adsorption efficiencies are further introduced to account for system “non-ideality.” A lab-scale air separation system is used to illustrate the application of this modeling methodology. Topical Heading: Process Systems Engineering

Temperature Swing Adsorption for Postcombustion CO2 Capture: Single- and Multicolumn Experiments and Simulations

A mathematical model used to describe cyclic adsorption processes is calibrated and validated for the simulation of temperature swing adsorption (TSA) processes applied to the capture of CO2 from a model flue gas (CO2/N2) using zeolite 13X as sorbent material. Three types of experiments are reported in this work, all of them performed in jacketed columns packed with 13X. During these experiments, the temperature was measured at five positions along the central axis of the column, and the exit composition was measured on line by mass spectrometry. The first series of experiments were breakthrough experiments, used to characterize transport phenomena within the packed bed. The second series were heating and cooling experiments, which were used to study the heat transfer from the heating fluid in the column jacket to the bed. Lastly, cyclic TSA experiments were performed to test the model’s ability to predict the cyclic steady state behavior of the column as well as the separation performance of the process.

Effect of dead volumes on the performance of an industrial‐scale simulated moving‐bed Parex unit for p‐xylene purification

The cyclic steady state (CSS) of the industrial‐scale, seven‐zone, simulated moving‐bed (SMB) unit for p‐xylene (p‐x) purification (Parex unit) with three types of dead volumes—bed lines, push‐around and pump‐around circulation lines, and bed heads—is analyzed. In particular, the effects of the size and level of hydrodynamic dispersion of each dead volume on process performance and on its CSS are studied in detail. The circulation lines change the CSS behavior from ‐periodic to ‐periodic, where is the switching interval and is the number of columns in each adsorbent chamber. A high level of axial dispersion in the bed lines, characterized by Péclet numbers smaller than 100, affects the p‐x purity. Moreover, the bed lines lower the average p‐x concentration in the extract, which reduces the p‐x recovery. If the small time lags introduced by the circulation lines are neglected, it is possible to develop a detailed process model that considers the operation of the Parex unit over a single switching interval as opposed to a full cycle, and whose CSS solution can be efficiently computed using a full‐discretization approach. Finally, it is shown that the volume of the bed heads influences significantly the performance of the Parex unit, and that its impact on the location of the operating point with respect to the boundaries of the separation region can be approximately taken into account using the standard true moving‐bed‐SMB equivalence rules if they are corrected for the presence of extra interparticle fluid. © 2015 American Institute of Chemical Engineers AIChE J, 62: 241–255, 2016

Optimization of the Cyclic Operation of a Continuous Biobutanol Fermentation Process Integrated with Ex-Situ Adsorption Recovery

Abstract Biobutanol has received significant attention as a renewable gasoline substitute and as a chemical feedstock owing to its high energy content, low volatility, and low water solubility. Low volumetric productivity caused by the toxicity of butanol in batch fermentation stands as one of the major obstacles to the commercialization. In this paper, continuous biobutanol fermentation with ex-situ adsorption recovery of butanol is investigated as a way to overcome this limitation. In this integrated system, the spatial segregation of the adsorption system and the fermentation process enables continuous biobutanol production without the need to stop the fermentation. Since the adsorption column needs to be switched periodically owing to the limited capacity of the adsorbent, the overall operation follows a cyclic pattern and the fermentation process converges to a cyclic steady state (CSS). In this study, a dynamic model of the integrated process is constructed and used for dynamic simulation to determine the system. Major operating variables are optimized through grid search for given feed concentrations based on the predicted CSS behavior in order to design an operation strategy that satisfies given requirements.

Three column intermittent simulated moving bed chromatography: 1. Process description and comparative assessment

The three column intermittent simulated moving bed (3C-ISMB) process is a new type of multi-column chromatographic process for binary separations and can be regarded as a modification of the I-SMB process commercialized by Nippon Rensui Corporation. In contrast to conventional I-SMB, this enables the use of only three instead of four columns without compromising product purity and throughput. The novel mode of operation is characterized by intermittent feeding and product withdrawal as well as by partial recycling of the weakly retained component from section III to section I. Due to the smaller number of columns with respect to conventional I-SMB, higher internal flow rates can be applied without violating pressure drop constraints. Therefore, the application of 3C-ISMB allows for a higher throughput whilst using a smaller number of columns. As a result, we expect that the productivity given in terms of throughput per unit time and unit volume of stationary phase can be significantly increased. In this contribution, we describe the new process concept in detail and analyze its cyclic steady state behavior through an extensive simulation study. The latter shows that 3C-ISMB can be easily designed by Triangle Theory even under highly non-linear conditions. The simple process design is an important advantage to other advanced SMB-like processes. Moreover, the simulation study demonstrates the superior performance of 3C-ISMB, namely productivity increases by roughly 60% with respect to conventional I-SMB without significantly sacrificing solvent consumption.

Lyapunov stability of economically oriented NMPC for cyclic processes

Several applications in process industries, such as simulated moving bed (SMB) separation and pressure swing adsorption (PSA), exhibit cyclic steady state behavior. Moreover, it is of economic interest to require energy intensive applications to take advantage of the periodically varying electricity price by changing the operating point frequently. Because traditional two-layer optimization methods are difficult to apply to these systems, we consider instead an economically oriented nonlinear model predictive control (NMPC) that directly considers system’s economic performance subject to the dynamic model. On the other hand, the commonly used Lyapunov framework to analyze the stability for the economically oriented NMPC cannot be applied directly. This work proposes two economically oriented NMPC formulations and proves nominal stability for both. We introduce transformed systems by subtracting the optimal cyclic steady state from the original system, for which the Lyapunov function can easily be established. Moreover, we show that the asymptotical stability of the transformed system is equivalent to that of the original system. Hence, the original systems are also nominally stable at the cyclic optimal solution. Finally, an industrial size air separation unit case study with periodic electricity cost is presented.

Stability of Economically-Oriented NMPC with Periodic Constraint

In smart grid environment, it is economically attractive to manage the load with respect prices and demands that could change periodically. Thus it is desired to operate some plants and system applications in a cyclic fashion. Model predictive control (MPC) and nonlinear MPC (NMPC) are widely accepted advanced control tools in process industry, due to their advantages of easily handling constraints and multi-input-multi-output systems. Nevertheless, the objective of the majority of NMPC applications is to track a predefined set point. This work proposes an economically-oriented NMPC formulation with periodic constraints that directly deal with systems that exhibit cyclic steady state behavior. The periodic constraint ensures the system converges to a cyclic steady state. In addition, nominal stability of the proposed NMPC formulation is analyzed, where we introduce a transformed system with the origin as the steady state. Hence, a Lyapunov function can be established at the steady state for the transformed system that is asymptotically stable at the origin. Consequently, asymptotic stability of the original system at the cyclic steady state can be inferred from the stability of the transformed system.

Modeling, Simulation of a Simulated Moving Bed for Separation of Phosphatidylcholine from Soybean Phospholipids

Abstract A rate model, which considers axial dispersion, external mass transfer, intraparticle diffusion and nonlinear isotherms, and ports periodic switching is adopted to simulate the simulated moving bed (SMB) process. The effects of flow rate in Sections 2 and 3 and switching time on the operating performance parameters: purity, recovery, productivity and desorbent consumption are studied. A simulation approach is applied to simulate the operation and performance of the SMB. The model predicts the performance of the transient and cyclic steady state behavior to a reasonably good extent, and provides guidance operation condition of the SMB process.

Chiral separation and modeling of the three-chiral-center β-blocker drug nadolol by simulated moving bed chromatography

Nadolol, a beta-blocker used in the management of hypertension and angina pectoris, has three chiral centers and is currently marketed as an equal mixture of its four stereoisomers. Resolution of three of the four stereoisomers of nadolol was obtained previously by HPLC, with a complete separation of the most active enantiomer (RSR)-nadolol, on a column packed with perphenyl carbamoylated beta-cyclodextrin (beta-CD) immobilized onto silica gel. In this study, continuous separation of the target enantiomer of (RSR)-nadolol from its racemic mixture (which is a ternary mixture in the chromatographic system) was studied by non-linear SMB chromatography. Different regions of (2, 3) and (1, 2) complete separation regime were determined in the (m2, m3) region and the effect of non-linearity such as overall feed concentration and component composition on the separation performances was investigated. A direct simulation approach has been proposed to simulate the SMB separation performance for the pseudo-binary mixture of nadolol. The simulation was conducted on the basis of a shortcut method constituted only of the weak-key and strong-key components. The performance of the cyclic steady-state behavior of the SMB unit was predicted reasonably well. It was also discussed quantitatively that the complete separation region obtained from the shortcut method is a subset of the true complete separation region and the optimal separation conditions obtained differed slightly from the "true" separation.

Continuous Separation of Enantiomers by Simulated Moving Bed Chromatography: Effect of Operating Parameters on the System Performance

The separation of 1,1’-bi-2-naphthol racemic mixtures by the simulated moving bed (SMB) method with chiral columns of Pirkle D-Phenylglycine was investigated in this study. First, a steady-state true moving bed (TMB) model, considering non-linear equilibrium, lumped kinetic and axial dispersion effects, was developed for predicting the cyclic steady-state behavior of the SMB system. The “triangle theory” was used to provide guidelines for the selection of feasible operating parameters of the SMB system, including liquid flow rates, switch time, feed concentration and zone length. Then, the effect of various operating parameters on the SMB performance, characterized by product purity, recovery, solvent consumption, and productivity, and the exact good separation region were studied through simulation of the TMB model. The package is an important tool to select the optimal operating conditions for the SMB operation.