Nonstationary Simulation Model of Absorber with Falling Film of Suspension

A nonstationary model of SO₂ absorption from a gas phase to a countercurrent falling film of absorbing slurry was developed. Laminar, wavy and turbulent film structures were considered based on published information. Resistances to the mass transfer on the gas and the liquid sides of the interphase were considered, together with chemical reactions in the liquid phase. Relevant chemical equilibria in the liquid phase were modeled. Original experimental data on the neutralization reagent dissolution rate presented as a polydispersed two‐phase system of solids and on the rate of dissolved sulfite oxidation were used. The model was verified with experimental data from a laboratory‐scale falling‐film absorber using a single vertical tube under various geometrical and operating conditions, and a very good agreement was found with the experiment. Parametric sensitivity analysis showed the critical parts of the model.     

喷雾冲击条件下液膜流动与传热模型

针对现有喷雾冷却计算模型的不足,以质量、动量、能量守恒方程为基础,建立喷雾冷却非沸腾区的液膜流动与传热方程,并采用数量级分析的方法对方程简化,最后运用数值方法对模型进行求解。给定液滴速度及液体温度,由模型计算液膜厚度、平均热通量与液体流出温度,与实验测试结果对照。结果显示,液膜厚度的计算结果与实验结果相差6%以内;平均热通量和液体离开待冷却表面的最终温度计算结果与实验结果相差10%以内,且超过60%的计算结果偏差小于5%。计算结果与实验结果的高度匹配证明该模型可较好地反映喷雾冷却过程的流动与换热。由模型可以获取不同位置处液膜厚度与温度,从而加深对喷雾冷却传热机理的理解。     

Etude numérique de l'évaporation dans un courant d'air humide laminaire et turbulent d'un film d'eau ruisselant sur une plaque inclinée

The authors have proposed an appropriate model based on the liquid film transfer equations which are one‐dimensional, partially two‐dimensional and two‐dimensional. They have compared their results with those of other works and studied the influence of the liquid mass flow rate and the inclined angle. They have shown that the interracial heat transfer is dominated by the latent heat transfer; the contribution of the sensible heat is only important in the turbulent region where the interfacial temperature and the evaporating mass flux are practically constant and the thickness of the liquid film is uniform. For the adiabatic plate, the liquid mass flow rate and the inclined angle have no influence on the transfers. For the isothermal or the heated plate, the liquid mass flow rate essentially influences the turbulent region by reducing the interrfacial temperature and the heat and mass transfer coefficients. However, the inclination angle affects mainly the laminar region by increasing the interfacial velocity, reducing the film thickness and has little effects on the transfer coefficients.     

ENHANCEMENT FACTOR OF GAS ABSORPTION ACCOMPANIED BY REVERSIBLE CYCLIC CHEMICAL REACTIONS

Theoretical effect of mass transfer by reversible cyclic chemical reactions is studied in this paper. On the basis of the film theory, an analytical equation has been derived to express the enhancement factor of gas absorption with first-order reversible cyclic chemical reactions. The finite difference method has been used to study the enhancement of gas absorption with second-order reversible cyclic reactions. The results indicate that the gas absorption rate is enhanced by the forward reaction rate, while is suppressed by the backward reaction. Although the diffusivity has some effects on enhancement factor, the influence is not as much as that of reaction rate. The theoretical equations are used to predict the enhancement factors for absorptions of carbon dioxide in acidic solution and l-butene in liquid phosphoric acid.     

ENHANCEMENT FACTOR OF GAS ABSORPTION ACCOMPANIED BY REVERSIBLE CYCLIC CHEMICAL REACTIONS

Theoretical effect of mass transfer by reversible cyclic chemical reactions is studied in this paper. On the basis of the film theory, an analytical equation has been derived to express the enhancement factor of gas absorption with first-order reversible cyclic chemical reactions. The finite difference method has been used to study the enhancement of gas absorption with second-order reversible cyclic reactions. The results indicate that the gas absorption rate is enhanced by the forward reaction rate, while is suppressed by the backward reaction. Although the diffusivity has some effects on enhancement factor, the influence is not as much as that of reaction rate. The theoretical equations are used to predict the enhancement factors for absorptions of carbon dioxide in acidic solution and l-butene in liquid phosphoric acid.     

An analysis of complex gas-liquid reactions in an isothermal CSTR

A mathematical model was developed for complex gas-liquid reactions with general-order kinetics in a continuously stirred tank reactor. The model equations were solved by the method of orthogonal collocation from which component concentration profiles in both the bulk and film liquid were computed. A parametric study revealed several interesting relationships between the chemical and physical parameters describing the reaction system. Specifically, the effects of mass transfer on the formation of reaction intermediates were analyzed for the case of two consecutive gas-liquid reactions over a wide range of reactor conditions.     

Fate of a sessile droplet absorbed into a porous surface experiencing chemical degradation

A general‐purpose multiphase and multicomponent computer model was developed for simulation of the spread, evaporation, and chemical reaction of sessile droplet(s) in porous substrates. In the model, chemical reactions were allowed in or between any of the liquid, gas, or solid phases present. The species mass and momentum conservation equations were solved on a finite difference mesh representing the domain. These equations were marched in time using the Runge–Kutta fourth‐order method. The model's function was studied via simulation of experiments, both those performed by the authors and found in the literature. These simulations demonstrated a quantitative match to the time history of product evolution and a similar spread of liquid reactants. The model may be particularly beneficial for predicting the extent of contamination and the possible threat outcomes of those chemical agents that are harmful when introduced into the environment. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2557–2565, 2014     

Computational Approach to Characterize the Mass Transfer between the Counter‐Current Gas‐Liquid Flow

Structured packed columns are widely used in the chemical industry for distillation and absorption. However, the understanding of the transfer mechanism behind the counter‐current gas‐liquid flow in structured packed columns is still limited. In this work, a three‐dimensional CFD model that considers the local absorption and the local momentum transfer mechanism is developed for a film flow on a small plate with a counter‐current gas flow. The model, based on the Volume of Fluid (VOF) method, is built up on the basis of a pressure drop model and the penetration theory to quantitatively investigate the instantaneous hydrodynamics and mass transfer characteristics of the liquid phase. Simulations and experiments are carried out for a system consisting of propane and toluene. A comparison of the simulation results with the experimental data for the outlet concentrations shows good agreement.     

Probability density function simulation of turbulent reactive gas‐solid flow in a FCC riser

A newly developed hybrid solution algorithm applicable on turbulent multiphase, gas‐solid, reactive flows is presented. A finite volume (FV) and a probability density function (PDF) method are combined. The FV technique is used to solve the total mass and momentum conservation equations together with the k‐ε turbulence equation for the gas phase and the granular temperature equation for the solid phase. The PDF method is applied to solve the species continuity equations and avoids the need to model the chemical source terms in the latter. Stochastic differential equations (SDEs) are introduced as replicas of the transported composition PDF equations. The notional‐particle‐based Monte‐Carlo technique is used to solve the PDF model equations. The hybrid FV/PDF solution algorithm is applied to simulate a fluid catalytic cracking (FCC) riser using a 12‐lump kinetic model. A good agreement between simulated results and available plant data is obtained. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

GAS-LIQUID REACTORS WITH VOLATILE LIQUID REACTANTS: APPROXIMATE SOLUTION FOR CONSECUTIVE BIMOLECULAR REACTIONS OF GENERAL ORDER

An approximate solution of the film model in presence of volatile liquid reactants is presented for the case of a general van de Vusse-like reaction scheme and general power-law reaction rates. The solution is obtained in a closed-form and simply requires the numerical solution of a system of nonlinear equations. The developed approximate solution is valid for any reaction regime and any number of reactions taking place within the liquid him. The application to a CSTR is discussed; this also serves as a test of the accuracy of the approximate solution carried out by comparison with the complete film model solved via the orthogonal collocation method. The numerical studies show that the approximate solution can be used with confidence for the usual encountered rate laws and that the volatility of the liquid reactants affects the performance of the CSTR mostly at the intermediate value of the Halt a number.     

In‐situ‐Stoffübergangsmessungen mit Computertomographie: Auswahl des Testsystems

For the in‐situ measurement of the mass transfer of a gas phase into a liquid film on a packing using X‐ray computed tomography, a substance combination is needed. The thickness of the liquid film was measured using computed tomography, to ensure that enough pixels in the film are available for the mass transfer experiments. In order to decide if the substance combination is distinguishable in the CT images, the X‐ray activity of gases and of dissolved gas in the liquid phase was investigated. For the determination of the maximum solubility the quantum chemical model COSMO‐RS was used to simulate the vapor‐liquid equilibria.     

Finite element solution for gas–solid reactions: Application to the moving boundary problems

Gas–solid reactions are very important in the chemical and metallurgical process industries. Several models described these reactions such as volume reaction model, grain model, and nucleation model. These models give two coupled partial differential equations (CPDEs). In this work an integral transformation and subsequent finite element method is used for solving the coupled partial differential equations of these reactions. In each mesh the Rayleigh–Ritz method is applied. Finally the results of this work are compared with the existing numerical solutions and experimental data successfully.     

Computational fluid dynamics studies of dry and wet pressure drops in structured packings

Computational fluid dynamics was used to study the hydrodynamic of structured packings. The results showed that the k–ω was a suitable turbulence model for analyzing the flows in structured packings. A simple method was proposed for evaluating the liquid holdup based on the Iliuta and Larachi (2001) model [25], the calculated liquid film thickness in 2D framework, and the empirical correlation of Brito et al. (1994) [26]. The presented method can be used for estimating the wet pressure drop in 3D structured packings for loading region with good accuracy as well as computational economy. The process of liquid film formation was also discussed.     

Determination of Kinetic and Energetic Parameters of Chemical Reactions in a Heterogeneous Liquid/Liquid System

A global method is proposed for estimating the kinetic and energetic parameters of chemical reactions taking place in the continuous phase of a heterogeneous liquid/liquid system. This method, based on energy and mass balances, uses the thermal power freed or absorbed by the reaction mass. It is only applicable to systems with sufficient thermal effects. Knowledge of the mass flow exchanged between the dispersed and continuous phases is needed to establish the mass balance. It is determined thanks to a model based on the double film theory. The model was applied to the saponification of pure ethyl acetate in an aqueous reaction mass. It was possible to determine simultaneously the velocity constant and the reaction enthalpy, as well as the apparent overall mass transfer constant.     

规整填料表面液膜流动特性的数值模拟

精馏过程气液两相流运动分布特征对分离效率具有重要影响。为研究规整填料表面液膜流体动力学特性建立了基于VOF方法的CFD分析模型,并基于文献试验结果进行了验证。对液膜随时间和空间的演化分布特征、速度场分布和液相流量影响进行了模拟分析。液膜在波纹顶部下沿聚集形成凸起状波峰,在波纹底部波峰消失,而到达下节波纹上沿时,波峰重新形成;瞬态液膜厚度随时间波动,且沿填料表面液膜平均厚度先减小后保持稳定;发现液相聚集及形成液滴坠落容易导致出现干板区。不同位置液膜速度分布存在明显差异,沿填料表面液膜平均速度先增后减或保持稳定;液膜绕过波纹顶部时会加速,在波纹底部和上沿处会减速。液相流量增大,液膜平均厚度和速度均有所增大。     

Computational analysis of an instantaneous chemical reaction in a T‐microreactor

We extend and apply a method for the numerical computation of convective and diffusive mixing in liquid systems with very fast irreversible chemical reaction to the case of unequal diffusivities. This approach circumvents the solution of stiff differential equations and, hence, facilitates the direct numerical simulation of reactive flows with quasi‐instantaneous reactions. The method is validated by means of a neutralization reaction which is studied in a T‐shaped micromixer and compared with existing experimental LIF‐data. Because of their large are‐to‐volume ratio, microreactors are well suited for fast chemical reactions which are seriously affected by the slow diffusive transport in aqueous media. Numerical computations for different reactor dimensions reveal the fact that, in a dimensionless setting, the obtained conversion is independent of the reactor size, if the flow conditions are the same. This corresponds to an increase of space‐time‐yield proportional to the square of the inverse scale factor. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Thermodynamics of wax formation in the fischer-tropsch synthesis products

A new method is suggested for calculating the thermodynamic equilibrium in a multicomponent multiphase system without chemical reactions. This method is based on ideas of statistical physics and non-equilibrium thermodynamics and includes numerical minimization of the Gibbs energy of the complex system. Component concentrations and the physically realizable roots of the equation of state are calculated as the steady state solutions of the set of ordinary differential equations that is implied by the procedure of seeking the probability maximum for the realization of the equilibrium distribution. The approach developed here is used to calculate the equilibrium distribution of the concentrations of vaporous, liquid, and solid substances in the Fischer-Tropsch synthesis products. A thermodynamic model of the formation of solid paraffins from the synthesis products is presented. The calculation of the properties of pure substances and liquid and gaseous products is based on the Lee-Kesler equation of state. The wax formation thermodynamics is considered in the regular solid solution approximation (Hildebrand-Scott model) and in the solid solution approximation taking into account the nonideality of the system (NRTL model). The calculated mass fractions of vaporous, liquid, and solid synthesis products are presented as a function of temperature for different values of the chain propagation constant.     

Simulation and Prediction of Methyl‐mercaptan Removal by Chemical Scrubbing with Hydrogen Peroxide

A model has been developed in order to predict the behavior of methylmercaptan chemical scrubbing using hydrogen peroxide. New constants concerning reactions involving methylmercaptan have been proposed based on mass transfer and kinetic equations for the dissociation of methylmercaptan by the hydroxide and the reaction with perhydroxyl ions. Once this step has been achieved, the model is used to characterize the influences of the different chemical scrubbing operating parameters, i.e., the gas‐liquid contact time, the oxidant concentration, and the pH. As expected, an increase in the hydrogen peroxide concentration, the contact time, or the pH leads to an increase in the methylmercaptan removal level. However, the most interesting aspect of the model lies in the possibility of defining a new or limiting value for each parameter, below which the process is not efficient enough to be industrially implemented.