Separation efficiency in the cyclic steady state for periodic countercurrent adsorption

Using an equilibrium dynamics model and one taking into account internal diffusion resistance, the separation efficiency is calculated for systems obeying the Langmuir isotherm in periodic countercurrent adsorption. The equilibrium and kinetic parameters, the cycle time and the number of columns are varied over ranges considered to be reasonable for technical applications. If other parameters are constant, there is an optimum cycle time yielding maximum separation efficiency in all cases. Maximum separation efficiency depends more strongly on the curvature of the isotherm than on the kinetic parameter or the number of columns in series. All results were evaluated in the cyclic steady state, taking into account the desorption levels achieved within the finite cycle times available to ensure continuous flow. In general, the benefits of periodic counter-current operation are less than calculated by previous authors, who assumed that a column of completely regenerated adsorbent is available whenever needed. Single-column reverse-flow desorption appears to be an adequate alternative to periodic counter-current operation under most conditions. Rough approximations indicate the advantages of thermal-swing or displacing-agent desorption and demonstrate that the desorption step is the decisive phase in modelling adsorber performance.     

Adsorption on activated carbon in countercurrent flow: An experimental study

The work describes adsorption experiments from aqueous solutions on activated carbon using a counter-current adsorber. Phenol and paranitrophenol were used for single component adsorption and molasses colour for multicomponent adsorption experiments. Isotherms were determined using simple equilibrium experiments. Three different techniques were used for determination of the kinetics. These were finite bath, infinite bath and fixed bed experiments. A mathematical model for countercurrent adsorption was tested. The model includes the effect of film diffusion and pore diffusion as well as surface diffusion, and can handle systems with a nonlinear isotherms. Kinetic data in the form of an average diffusivity in the carbon determined from the finite bath experiments and isotherm data did not predict the operation of the countercurrent column well. Data from the fixed bed experiments predicted countercurrent column operation much better. This is deemed to be due to inhomogeneities in the carbon used, resulting in a fairly quick initial uptake of the main part of the solute and a slower uptake of a minor amount.     

Multiple steady states in continuous distillation and realization of a selected steady state

A general strategy for a column startup is suggested which enables one to attain all the feasible steady states. By numerical calculations, the whole space of the starting concentrations was partitioned into regions corresponding to each of the steady states.     

Modeling and optimization of the cyclic steady state operation of adsorptive reactors

Adsorptive reactors(AR),in which an adsorptive functionality is incorporated into the catalytic reactors,offer enhanced performance over their conventional counterparts due to the effective manipulation of concentration and temperature profiles.The operation of these attractive reactors is,however,inherently unsteady state,complicating the design and operation of such sorption-enhanced processes.In order to capture,comprehend and capitalize upon the rich dynamic texture of adsorptive reactors,it is necessary to employ cyclic steady state algorithms describing the entire reaction-adsorption/desorption cycle.The stability of this cyclic steady state is of great importance for the design and operation of adsorptive reactors.In this paper,the cyclic steady state of previously proposed novel adsorptive reactor designs has been calculated and then optimized to give maximum space–time yields.The results obtained revealed unambiguously that an improvement potential of up to multifold level could be attained under the optimized cyclic steady state conditions.This additional improvement resulted from the reduction of the regeneration time well below the reaction-adsorption time,which means,in turn,more space–time yield.     

An experimental investigation on engine speed and cyclic dispersion in an HCCI engine

This work presents the results of the experimental study on engine speed and cyclic dispersion in a homogeneous charge compression ignition (HCCI) engine. An engine TD43 is used to carry out the research. The combustion parameters are deduced from heat release rate which obtained from the first principle of thermodynamics during a cycle. The experimental results show that the duration of low temperature reaction plays an important role on HCCI combustion, particularly at higher engine speeds. Furthermore, cyclic dispersion in an HCCI engine presents, under certain operates conditions, a periodic behavior corresponding to 2 or 3 cycles of the engine. It is concluded that the residual gas of a cycle modifies the three properties (temperature, dilution and composition) of gas in-cylinder at the following cycle. Therefore, gas residual directly affects the course of combustion in an HCCI engine. The knowledge of the duration of the different phases of combustion, as well as conditions in which the periodical appearance of misfire cycles occurs, is useful for the definition of regulation strategies.     

Breakthrough curves in the cyclic steady state for adsorption systems with concave isotherms

Using numerical procedures, breakthrough curves are calculated as a function of one diffusional and one equilibrium parameter for systems obeying equilibrium isotherms concave to the gas concentration axis. For purposes of demonstration the Langmuir isotherm is chosen. The unfavorable effects of an increasingly concave isotherm in the cyclic steady state are the opposite of the “favorable” effects found by authors who investigated the first adsorption period or who assumed that total desorption is possible in the regeneration phase. These conclusions apply within the range of kinetic parameters studied. The results of technological changes, such as using countercurrent desorption, varying total cycle time or increasing the ratio of desorption to adsorption time are shown.     

Effective approach to cyclic steady state in the catalytic reverse-flow combustion of methane

Computer-based simulations of a reverse-flow reactor should be carried out till the attainment of the so-called cyclic steady state. Usually this state is achieved by the method of direct dynamic simulations. In the paper of Unger et al. (Comput. Chem. Eng. 21 (1997) 5167.) special approaches, making use of various minimization algorithms based most often on Newton algorithms, are proposed. In the present paper one deals with a comparison and an appraisal of these methods, applied to the reverse-flow catalytic combustion of methane that occurs in coal-mine ventilation air.     

A solution to the distributed parameter model of a continuous grinding mill at steady state

A distributed parameter model of an open-circuit size reduction device at steady state is considered. The model is applicable to tumbling or vibratory mills. Material transport is described in terms of a size-dependent axial convective velocity and a size-dependent axial dispersion coefficient. For n size fractions, the model consists of a set of n coupled ordinary differential equations of second order with two-point boundary conditions. An explicit solution to the model equations is derived for the case in which these equations are linear with constant coefficients. This corresponds to the circumstance in which the axial convective velocities, axial dispersion coefficients and the quantities used to describe the size reduction process are independent of the axial position or of the dependence of the material holdup or size distribution on axial position in the device. These assumptions are not too restrictive and the solution appears to be a useful approximation for a broad range of material-mill combinations. Applications to other process unit operations are suggested.     

Theoretical study of dynamic countercurrent cyclic extraction processes for the separation and concentration of components of a liquid mixture

Some results of theoretical studies on different dynamic countercurrent cyclic extraction variants and the effect of principal process parameters on the efficiency of separation for liquid mixture components have been given. The studies are based on a modified model of the equilibrium stages. It has been established that the proposed extraction mode enables the concentration of target mixture components with their simultaneous separation.

     

Pore diffusion and solid diffusion models: Application in countercurrent chromatographic separation process

Difference and equivalence of two approaches for countercurrent chromatographic separation process were discussed. Although the two approaches are different in the TCC process in terms of model equations and definition of phase concentrations and flow rate ratios as well as complete separation regions expressed by flow rate ratios etc., they are equivalent in the SMB process. Experimental and simulation results are consistent with theoretical analysis. In application of the SMB process, it is of crucial importance to use these two approaches consistently.     

Numerical methods of solution for continuous countercurrent processes in the nonsteady state part I: Model equations and development of numerical methods and algorithms

Simple, efficient and noniterative algorithms are developed for the calculation of the dynamics of continuous countercurrent processes described by hyperbolic differential equations. The algorithms are derived using the method of characteristics and are particularly useful for either general quadratic or hyperbolic isotherms such as the Langmuir isotherm. The use of characteristic coordinates for the numerical solution avoids accumulating errors that would arise from computations based on a rectangular grid of real time and space coordinates. The proposed methods can provide an efficient framework for extension to transport processes with general nonlinear rate expressions. The algorithms and methods initially derived for simple models can be extended to more complex systems such as countercurrent flow with accumulating stationary phases and response to distributed disturbances. The application of the algorithm and methods to a number of countercurrent mass and heat transfer processes will be illustrated in Part II, where the accuracy and efficiency of the proposed methods will also be demonstrated by comparison to available analytic solutions. An example demonstrating the extension of the method to a system with complex coupled boundary conditions will also be discussed.     

On the dynamics of distillation processes—IV Uniqueness and stability of the steady state in homogeneous continuous distillations

Recent numerical studies by Magnussen et al.[1] have shown that multiple steady state solutions can be exhibited by the constant molar overflow (CMO) model for ternary azeotropic distillation in a multistaged column. This has such important consequences for distillation control, design and startup that further experimental and analytical work is desirable.This paper addresses the problem of uniqueness and stability of the steady state in the continuous distillation of homogeneous mixtures. It is shown that multiple steady state solutions are not exhibited by either binary homogeneous distillations in a multistage CMO column or multicomponent homogeneous distillations in a single stage CMO column (flash distillation). Therefore, the multiplicity is a consequence of multicomponents and multiple stages.     

Approximation of a PSA process based on an equivalent continuous countercurrent flow process: Blow-up and blow-down representation

To design cyclic separation processes by adsorption, such as pressure swing adsorption (PSA) processes, one has to simulate the start-up time in order to determine the cyclic steady state (CSS), which can be very time-consuming. A fast way to estimate the CSS reached by a PSA process is proposed by Suzuki (1985)—assuming equivalency between the PSA system and a continuous countercurrent flow system (CCF). The CCF model is improved in the present paper, taking into account the gaseous phase located in a column when the system switches from a constant pressure step to another step. By performing a parametric study, the limits of the CCF model are tested. It is shown that this model can quantitatively predict the purities and recoveries obtained at CSS for kinetically controlled separation by comparison with a detailed model of PSA. It is also shown that the CCF model can also give a good approximation of the dynamic behavior of the PSA process. Finally, the simulation of dry air separation is proposed.     

A method for computing the degree of mixing in steady continuous flow systems

The degree of mixing was first proposed by Danckwerts and further discussed by Zwietering more than 50 years ago to measure mixing performance of a continuous flow system. Although the measure has been widely discussed in mixing literature, there has never been a method to compute its value for a general continuous flow. In this paper, a method is developed to compute this measure for a general steady continuous flow system for the first time. The method is based on the recently developed mean age theory. The governing equations for the mean age and higher moments of age are also derived for different types of tracer introduction other than pulse input in the current mean age theory.     

A stochastic treatment of unimolecular reactions in an unsteady state continuous flow system

A stochastic approach, namely a continuous time Markov chain (Markov process), is employed to analyze and model, in a unified fashion, both the kinetics of unimolecular reactions and mixing accompanied by flow in a continuous flow reactor under an unsteady state operation; the results reduce to those under the corresponding steady state operation in the limit as t→∞. This approach can be applied to both the time homogeneous and heterogeneous processes. The transitional distributions of the number of molecules of each type inside the reactor as well as at the exit are formulated. The treatment leads to the general expressions for the transient internal and exit age distributions of molecules in the flow reactor. The life time distribution of molecules under steady state is also derived. The statistical basis of the residence time distribution theory for flow reactors is clarified. The approach is illustrated with two examples.     

Devolatilization rate of biomasses and coal-biomass blends: an experimental investigation

Devolatilization behavior of different coals and biomasses under heating conditions typical of conventional pyrolysis processes was investigated. Thermogravimetric analyses were performed on coals (with high and low volatile matter), biomasses (pine sawdust and dried sewage sludge) and coal-biomass blends with different weight ratios. The different behavior of coals and biomass fuels in the devolatilization process (different amount and nature of volatile species released, different rate of devolatilization and different reactivity of produced chars) was analyzed for abstracting kinetic data. In addition, analyses of coal-biomass blends revealed that in the operative conditions used (i.e. low heating rate 20 °C/min and high nitrogen flowrate), primary reactions of the thermal decomposition of biomass fuels are not significantly affected by the presence of coal, and also coal does not seem to be influenced by the release of volatile matter from biomass. This led to the first conclusion that the weight loss of a blend can be obtained from the weighted sum of reference materials.Further, a kinetic analysis was performed in order to fit the experimental results and verify simple sub-models (namely, distribution activation energy model and lumped model) to be used in comprehensive combustion codes (computational fluid dynamic) assuring a major accuracy compared with SFOR model, but maintaining both simplicity and computational velocity. A quite good fitting was obtained for all materials and blends studied.     

Multiplicity of the steady state in fluidised bed reactors — I.: Steady state considerations

Multiple steady states are known to be possible in many types of chemical reactor due to the non-linear dependence of reaction rate on either temperature or reactant concentration. It is reasoned in this study that multiple steady states can also exist in a gas-solid fluidised bed reactor. The calculations are based on the two-phase theory of fluidisation and on the important assumption that the interstitial phase gas in completely mixed. Both thermal and concentration multiplicites are shown to be possible.     

Mathematical modeling,steady state simulation,parametric analysis and optimization of SO2 capture in a countercurrent moving bed (CaO and C) reactor

The use of absorbents based on calcium for the reduction of SO₂ emissions from power plants has been studied for the last 30 years. The present work is part of a research project aimed at the development of a moving bed limestone filter. It is placed after burning in order to capture the SO₂ from the flue gases of pulverized lignite combustors. A heterogeneous mathematical model was developed for the steady‐state simulation of a gas–solid countercurrent moving bed reactor. The mathematical model was solved using the method of finite elements and gave results for the temperature and conversion profile along the reactor. Also, parametric analysis (for T_g,in, T_s,in, u_s, q_o, , , d_o, z_o) was performed and useful conclusions concerning the behavior of a moving bed reactor in different conditions were drawn. Finally, optimization of conditions was performed to give an SO₂ conversion higher than 0.95. The results are of important technological interest as a dry process in applications of SO₂ capture. © 2018 Society of Chemical Industry     

The dynamic behaviour of continuous polymerization reactors—III: An experimental study of multiple steady states in solution polymerization

A study involving small scale reactor experiments coupled with detailed non-isothermal reactor modelling has been carried out shows that ‘isoia” ty