Instantaneous Irreversible Reaction Research Articles

Upscaling Mixing-Controlled Reactions in Unsaturated Porous Media

We study mixing-controlled chemical reactions in unsaturated porous media from a pore-scale perspective. The spatial heterogeneity induced by the presence of two immiscible phases, here water and air, in the pore space generates complex flow patterns that dominate reactive mixing across scales. To assess the impact of different macroscopic saturation states (the fraction of pore volume occupied by water) on mixing-controlled chemical reactions, we consider a fast irreversible reaction between two initially segregated dissolved species that mix as one solution displaces the other in the heterogeneous flow field of the water phase. We use the pore-scale geometry and water distributions from the laboratory experiments reported by Jiménez-Martínez et al. (Geophys. Res. Lett. 42: 5316–5324, 2015). We analyze reactive mixing in three complementary ways. Firstly, we post-process experimentally observed spatially distributed concentration data; secondly, we perform numerical simulations of flow and reactive transport in the heterogeneous water phase, and thirdly, we use an upscaled mixing model. The first approach relies on an exact algebraic map between conservative and reactive species for an instantaneous irreversible bimolecular reaction that allows to estimate reactive mixing based on experimental conservative transport data. The second approach is based on reactive random walk particle tracking simulations in the numerically determined flow field in the water phase. The third approach uses a dispersive lamella approach that accounts for the impact of flow heterogeneity on mixing in terms of effective dispersion coefficients, which are estimated from both experimental data and numerical random walk particle tracking simulations. We observe a significant increase in reactive mixing for decreasing saturation, which is caused by the stronger heterogeneity of the water phase and thus of the flow field. This is consistently observed in the experimental data and the direct numerical simulations. The dispersive lamella model, parameterized by the effective interface width, provides robust estimates of the evolution of the product mass obtained from the experimental and numerical data.

Optimal fluid stretching for mixing-limited reactions in rough channel flows

We study the reactive displacement of two miscible fluids in channel flows and establish a quantitative link between fluid stretching and chemical reactivity. At the mixing interface, the two fluids react according to the instantaneous irreversible bimolecular reaction $A + B \rightarrow C$ . We simulate the advection–diffusion–reaction problem using a random walk based reactive particle method that is free of numerical dispersion. The relative contributions of stretching and diffusion to mixing-limited reaction is controlled by changing the Péclet number, and the channel roughness is also systematically varied. We observe optimal ranges of fluid stretching that maximize reactivity, which are captured by a Lagrangian stretching measure based on an effective time period that honours the stretching history. We show that the optimality originates from the competition between the enhanced mixing by fluid stretching and the mass depletion of the reactants. We analytically derive the spatial distribution of reaction products using a lamellar formulation and successfully predict the optimal ranges of fluid stretching, which are consistent across different levels of channel roughness. These findings provide a mechanistic understanding of how the interplay between fluid stretching, diffusion and channel roughness controls mixing-limited reactions in rough channel flows, and show how reaction hot spots can be predicted from the concept of optimal fluid stretching.

Modeling and numerical analysis of counter-current dialyzer with chemical reaction in stripping solution

In the present work, the effect of a second-order chemical reaction A+B⇌P (both irreversible and reversible) in the stripping solution on the performance of a counter-current dialyzer is analyzed. An instantaneous irreversible reaction with an excess of a reactive component in the stripping solution results in the maximum attainable enhancement in the extraction ratio of the transported solute. The actual enhancement can be limited by low values of the forward reaction rate constant and equilibrium constant. These effects can be compensated by an excess of the reactive component in the stripping solution. As an alternative to rigorous modeling of mass transfer in the liquid film accompanied by achemical reaction, the enhancement factor concept can be adopted. This approach has the advantage of the significant reduction of the overall complexity of the mathematical model without significant loss of its accuracy.

Dynamics of Mobile Concentration Fronts in Gas–Liquid Reaction Systems: Analysis and Numerical Experiment

A mathematical model has been developed for the process of chemosorption with the moving front of an instantaneous irreversible reaction at small Reynolds numbers in a gas–liquid system before and after the reaction front formation moment. An analytical solution of this model has been found for the time period to the formation of a mobile chemosorption front with consideration for the effect of a reaction product on the dynamics of chemosorption. In contrast to the earlier known results, the model takes into account the effect of the diffusion transfer of a reaction product on the kinetic characteristics of chemosorption and different stages of the formation and motion of the concentration front. Some results of the processing and analysis of numerical experiment data are presented. The characteristic depths and times of the penetration of a captured component are plotted as functions of all the process-control parameters. Sherwood numbers and absorption acceleration and mass transfer coefficients are calculated for the captured component in the liquid phase.

Lactic Acid Extraction and Mass Transfer Characteristics in Slug Flow Capillary Microreactors

Capillary microreactors operated under the slug flow regime were investigated for the separation of lactic acid from the aqueous phase using liquid–liquid reactive extraction. The experiments were performed at a 1:1 flow ratio of the aqueous to organic phases in a setup consisting of an inlet Y-type mixer connected with a poly(tetrafluoroethylene) capillary microreactor and subsequently an outlet Y-shape phase splitter. The extraction of lactic acid (intake: 0.11 and 0.055 M in water) using 15% (v/v) tri-n-octylamine in n-octanol under ambient conditions approached equilibrium after about 90 s in microreactors without noticeable emulsion formation. The measured reactive extraction performance in microreactors can be well described by a physical mass transfer model according to the penetration theory (developed from a model experimental study for the extraction of acetanilide from water to n-octanol) combined with an instantaneous irreversible reaction assumption.

Gas-liquid mass transfer with instantaneous chemical reaction in a slurry bubble column containing fine reactant particles

In this study, the mass transfer accompanied by an instantaneous irreversible chemical reaction in a slurry bubble column containing sparingly soluble fine reactant particles has been analyzed theoretically. Based on the penetration theory, combining the cell model, a one-dimensional mass transfer model was developed. In the model, the effects of the particle size and the particle dissolution near the gas-liquid interface on the mass transfer were taken into account. The mass transfer model was solved and an analytical expression of the time-mean mass transfer coefficient was attained. The reactive absorption of SO2from gas mixtures into Mg(OH)2/water slurry was investigated experimentally in a bubble column reactor to validate the mass transfer model. The results indicate that the present model has good predicting performance and could be used to predict mass transfer coefficient for the complicated gas-liquid-solid three-phase system with an instantaneous irreversible chemical reaction.

Mass transfer of SO2 absorption with an instantaneous chemical reaction in a bubble column

Gas absorption accompanied by an instantaneous irreversible chemical reaction in bubble columns has been analyzed theoretically. A mass transfer model based on the Dankwerts surface-renewal model as well as the penetration theory for surface stretch proposed by Angelo et al. was developed, in which the effects of bulk motion and turbulence on mass transfer were taken into account. The analytical expressions for the time-average mass transfer coefficient and the enhancement factor have been obtained. The fast reactive absorption of SO2 from gas mixtures into aqueous NH4HCO3 solution was investigated experimentally in a bubble column reactor to validate the mass transfer model, and the results calculated by the present model agree well with the experimental results.

Formation of Alumina Inclusions during Counter Diffusion of Aluminum and Oxygen Dissolved in Molten Iron

The formation of alumina (Al2O3) inclusions was experimentally investigated with the capillary-reservoir method. The inclusions were observed with a SEM (scanning electron microscope). The compositions of iron matrix and inclusion were measured with an EDX (energy dispersive X-ray analysis). The content profile of aluminum was discussed by the counter-diffusion model of aluminum and oxygen with an instantaneous irreversible reaction for alumina formation. The inclusions of spherical and polygonal alumina and spherical hercynite (FeOAl2O3) were observed in the vicinity of the diffusion front of aluminum. The hercynite was detected when the initial oxygen content was 0.075 mass% and higher. When the initial oxygen content was more than 0.045 mass% and higher, dendritic alumina formed at the position that was nearer to the interface than the position of spherical and polygonal inclusions. No inclusion was observed around the interface because of the re-dissolution of the inclusions. The initiating position of the inclusion formation was approximated by the reaction position, Zr, obtained from the model on the assumption that aluminum and oxygen contents at the reaction position were zero. Empirically, 0.9×Zr and 0.17×Zr expressed the initiating positions of formation and re-dissolution of inclusions respectively. The critical supersaturation ratio was estimated to be from 1 to 7.4×105, depending on the initial aluminum and oxygen contents.

Theoretical and Experimental Study of the Absorption rate of H 2S in CuSO 4 Solutions : The Effect of Enhancement of Mass Transfer by a Precipitation Reaction

In this paper the desulphurization of gas streams using aqueous copper sulphate (CuSO 4) solutions as washing liquor is studied theoretically and experimentally. The desulphurization is accomplished by a precipitation reaction that occurs when sulphide ions and metal ions are brought into contact with each other. Absorption experiments of H 2S in aqueous CuSO 4 solutions were carried out in a Mechanically Agitated Gas Liquid Reactor. The experiments were conducted at a temperature of 293 K and CuSO 4 concentrations between 0.01 and 0.1 M. These experiments showed that the process efficiently removes H 2S. Furthermore, the experiments indicate that the absorption of H 2S in a CuSO 4 solution may typically be considered a mass transfer limited process at, for this type of industrial process, relevant conditions. The extended model developed by Al-Tarazi et al. (2004) has been used to predict the rate of H 2S absorption. This model describes the absorption and accompanying precipitation process in terms of, among others, elementary reaction steps, particle nucleation and growth. The results from this extended model and results obtained with a much simpler model, regarding the absorption of H 2S in CuSO 4 containing aqueous solutions as absorption of a gas accompanied by an instantaneous irreversible reaction were compared with experimental results. From this comparison it appeared that the absorption rate of H 2S in a CuSO 4 solution can, under certain conditions, be considered as a mass transfer rate controlled process. Under a much wider range of conditions the error that is made by assuming that the absorption process is a mass transfer controlled process, is still within engineering accuracy. Application of the simple model allows for a considerable reduction of the theoretical effort needed for the design of a gas–liquid contacting device, thereby still assuring that the desired gas specification can be met under a wide range of operating conditions. A comparison of the experimental results and the simulated results showed that the extended model gives an under prediction of the H 2S absorption rate for the experimental conditions applied.

Methods for Calculating the Process of Chemisorption in Systems with a Moving Front of an Instantaneous Irreversible Reaction

Methods for Calculating the Process of Chemisorption in Systems with a Moving Front of an Instantaneous Irreversible Reaction

Mass transfer enhancement in the membrane aromatic recovery system (MARS): experimental results and comparison with theory

This paper describes an experimental investigation into mass transfer enhancement by chemical reaction in the membrane aromatic recovery system (MARS). The MARS process has recently been commercialised for recovery of cresols from aqueous process streams. In this paper, mass transfer enhancement as a function of the pH and organic concentration of the stripping solution is examined for constant bulk solution conditions. The application of two models of mass transfer enhancement (the Olander and Hatta models) is evaluated by determining the model parameters through independent experiments, limiting cases, and from literature. Model predictions are then compared to experimental data. Three organic compounds are used in this work: phenol, 4-chlorophenol (4CP), and triethylamine (TEA), which span a range of properties of typical molecules recovered by the MARS process. It is concluded that for compounds such as phenol, for which membrane mass transfer resistance dominates the system, there is no reaction enhancement. For compounds such as 4CP and TEA, enhancement effects are important. These were found to be best described through application of the Olander model, which allows for a second-order instantaneous reversible reaction, although the Hatta model, allowing for a second-order instantaneous irreversible reaction, was found to give a good description in some cases as well.

Modeling flue gas desulfurization by spray-dry absorption

Abstract A detailed model for flue gas desulfurization by spray-dry absorption with a lime slurry is presented. The model combines a steady state one-dimensional spray-dryer model with a single-drop model for SO2 absorption with instantaneous irreversible reaction in a rigid droplet containing uniformly dispersed fine lime particles. The fate of the droplets is followed from atomization until formation of a porous coherent shell around the drying droplets. The model results were validated against available experimental spray-dry FGD results, showing excellent agreement at low to medium Ca/S feed ratios. The model was then used to study the relevance of the different resistances to SO2 absorption and to predict the influence of the main operating variables on the spray-dryer desulfurization performance. Analysis of variables profiles along the spray-dry column showed that the initial droplet velocity has no influence on model results and that the initial droplets decelerating phase always accounts for negligible SO2 capture. Results further showed that the controlling resistance to SO2 absorption shifts from a liquid-phase one near the atomizer to a gas-phase one at the column exit. The operating variables that exert the largest influence on the overall desulfurization efficiency are the Ca/S molar feed ratio, the mean initial droplet size and the mean lime particle size. In particular, careful control of the last two variables is critical in order to obtain a good spray-dryer performance.

Gas Absorption with Instantaneous Irreversible Chemical Reaction in a Slurry Containing Sparingly Soluble Fine Reactant Particles

The problem of gas absorption followed by instantaneous irreversible chemical reaction in a slurry containing sparingly soluble fine reactant particles is considered. Models are developed for an infinitely deep quiescent liquid and, using the film theory, for an agitated liquid when the reactant particle dissolution in the liquid film next to the gas−liquid interface is nonnegligible. Simple analytical expressions for the rate of gas absorption are derived under the assumption of slow particle dissolution, and conditions are given for applicability of the models. A numerical example for the system SO2−Ca(OH)2 in water is discussed.

Absorption with instantaneous reaction in a droplet with sparingly soluble fines

AbstractThe problem of gas absorption followed by an instantaneous irreversible chemical reaction in a rigid droplet containing sparingly soluble fine reactant particles is discussed. A model was developed for the general case when the reactant particle dissolution near the gas–liquid interface is nonnegligible. Solids dissolution is treated taking into account the average spacing between the suspended particles. A simple analytical expression for the rate of gas absorption is derived under the assumption of slow particle dissolution, and conditions are given for applicability of the model. A numerical example, relevant for the spray‐dry desulfurization process, for the system SO2‐Ca(OH)2 in water is discussed.

Mass transfer with instantaneous chemical reaction in finite gas–liquid systems

The moving-boundary problem of gas absorption accompanied by an instantaneous irreversible chemical reaction in a limited gas–liquid system has been analyzed. Analytical solutions have been derived, under the restrictions of equal diffusivities of the two reacting species and stoichiometric factor of unity, for the cases of significant or negligible gas-film and surfactant-film resistances. A numerical scheme has been developed for the general case of unequal diffusivities and/or stoichiometric factor differing from unity. The effects of various parameters like film thickness, gas-bubble volume, stoichiometric factor, initial concentration in the liquid phase, etc., have been illustrated. Furthermore, the importance of the surfactant-film and gas-film resistances has also been demonstrated. The analytical solution has been found to be in agreement with the numerical solution, thus demonstrating the efficacy of the concept of negative concentration in solving such problems.

Interfacial resistance in exothermic gas absorption with an instantaneous irreversible reaction

Abstract Exothermic gas absorption accompanied by an instantaneous irreversible reaction is theoretically studied to take into account the effect of the interfacial resistance. The film theory model has been applied to yield a closed‐form solution of the diffusion/conduction equations. The behavior of the enhancement factor is complex due to the variation of the interfacial temperature with the surface resistance, which then affects the solubility. The analysis could be of particular importance for a rational design of the nonisothermal wet scrubbing systems for the gaseous pollutant removal with the impurities contaminating the gas‐liquid interface.

A criterion for gas supersaturation in simultaneous absorption and desorption with an instantaneous irreversible reaction

Le critere est etabli theoriquement a l'aide de la theorie des penetrations pour une reaction generale du type A (g) +ν B B→ν c C (g) B (reactif non volatil)

Mass transfer in a liquid-liquid jet with cocurrent laminar flow

The mass transfer coefficients in the dispersed (jet) and continuous phases of a laminar liquid-liquid jet apparatus were individually measured under the conditions of cocurrent down flow. For the dispersed phase mass transfer, experiments were performed on the dissolution of MIBK, n-butanol and cyclohexanol into a water jet. For the continuous phase mass transfer, experiments were carried out on the dissolution of water into a continuous phase of n-butanol and extraction of I 2 from cyclohexane and toluene into an aqueous Na 2S 2O 3 solution jet with an instantaneous irreversible reaction at the interface. These systems were chosen so that the physical properties varied in a large enough range to examine the effects of the jet shape and the velocity gradients at the interface on the mass transfer coefficients. When the median diameter of the jet was used as a representative diameter for any calculation and the interfacial velocity was evaluated as 1.2 times the value predicted from the expression for a fully developed relaxed jet, all the observed mass transfer coefficients were shown to agree with the penetration theory with an average error of 7.3%.

The effects of micromixing and the manner of reactor feeding on precipitation in stirred tank reactors

The effect of micromixing on the course of a precipitation process involving instantaneous irreversible chemical reaction (of the type: A + B → C) between two ionic solutions snd subsequent crystallization of the product is considered. It is demonstrated that the micromixing intensity and the manner of reactor feeding (batch or continuous, premixed or unpremixed feed system) are major factors affecting the precipitation process and the resulting size distribution of precipitated particles. The method of prediction of these effects is based on a micromixing model, which is related to the theory of turbulent mixing in an isotropic, homogeneous turbulent field.

Absorption of carbon dioxide into laminar falling films of aqueous kaolin slurries containing sodium hydroxide

AbstractTo confirm the theory for gas absorption accompanied by an instantaneous irreversible reaction in laminar falling films of power‐law liquids which was presented in a previous paper, experiments were carried out on the absorption of pure carbon dioxide into aqueous kaolin slurries containing sodium hydroxide by using a long wetted‐wall column. The experimental data were in fairly good agreement with the theoretical predictions, the average deviation being 3.0%. The discussion on the effect of the power‐law index of the liquid upon the reaction factor suggested an approximate method of estimating the reaction factors for power‐law liquids.