Contact time optimization of two-stage batch adsorber systems using the modified film-pore diffusion model

In this paper, a contact time optimization methodology of a two-stage batch adsorber system taking minimum contact time as the objective function has been developed. The initial concentration of the second stage unit and adsorbent weight have been designated as variables and these have been studied under two conditions of the equilibrium solid-phase concentration, q_e, namely, when q_e is a variable and when q_e is a constant. Contact time optimization of a two-stage batch adsorber system has been demonstrated at three different conditions/cases for the adsorption of phenol on activated carbon and the adsorption of Astrazone Blue dye (Basic Blue 69) onto silica. A new concept of “pinch point” for the optimum design of batch adsorber system has been proposed. The optimization solutions show that there is a significant difference for minimum contact time at different process conditions.The diffusion mass transport model used to predict the concentration-time decay curve is a film-pore diffusion model. An analytical solution has been used for simplicity which assumes a constant capacity pseudo-irreversible isotherm.     

High mass flux evaporation

Experimental data for the evaporation of water, ethyl ether, dichloromethane, carbon tetrachloride, acetone and n-octane into a stagnant atmosphere at different temperatures are reported. A model for the evaporation process is presented. The calculation of the wet bulb temperatures is strongly dependent on the Lewis number and on the high mass flux conditions present. The calculated and experimental high mass flux transfer coefficients differ by an average of ± 10.5% provided the dimensionless groups Sh, Nu, Pr, Sc, Le and Gr are evaluated at surface temperature conditions except for the density in the Grashof number which is evaluated at bulk conditions. The theory incorporates Hanna's density variation factor.     

A numerical method of calculating secondary current distributions in electrochemical cells

A numerical method is proposed based on the analogy between the potential distribution in an electrolytic solution and the temperature distribution in a heat-conducting medium. Thus the equation of non-steady-state heat conduction which contains a hypothetical temperaturev(x, y, t) is solved numerically with appropriate boundary conditions. In the steady state the distribution ofv(x, y, t) corresponds to the distribution of potentialφ _s (x,y) which satisfies Laplace's equation. The method is useful not only for conventional electrochemical cells but also for complicated systems such as a bipolar electrode for which boundary conditions provide neither the potential nor the current density at the electrode surface.     

Evaluation of membrane reactor with hydrogen-selective membrane in methane steam reforming

A comparative analysis of a conventional industrial process and a membrane reactor plant for hydrogen production via natural gas steam reforming is proposed by calculating two sustainability metrics: mass and energy intensities. The analysis takes into account membrane reactors equipped with hydrogen-selective membranes (Pd-based) which can operate at milder temperature (500 °C) and pressure (1.0 MPa) conditions and at higher CH₄ conversion levels (90–100%) than that achieved in conventional industrial systems.The use of the MR retentate stream to produce the steam required as feed for the reforming section is proposed and for this option a reduced mass intensity is calculated (reduced amount of fuel to the process) with respect to the conventional plant. The reduction is in the range 25–32% for the MRs operated at m=3 and 44–50% for the MRs operated at m=2. A more important saving concerns the energy use.     

Postponing sharkskin of metallocene polyethylenes at low temperatures: the effect of molecular parameters

The effect of temperature on extrusion rheometry of single site metallocene-catalyzed polyethylenes and polyethylene copolymers is investigated. Samples of molecular weight, M_w, ranging from 90,000 to 330,000 and short-chain branching degree (SCB) from 0 to 21.2 CH₃/1000C, as well as samples with a small amount of long-chain branching, are analyzed. It is observed that all the samples display a low temperature region, limited by induced crystallization and gross melt fracture, in which smooth extrudates are produced at shear rates similar to those of industrial extrusion. A characteristic temperature of this region, T_s, is defined as the highest temperature at which sharkskin disappears. Clear symptoms of non-slip conditions at the capillary wall, are detected in this low temperature region. We assume that the necessary slip-stick conditions to produce sharkskin, would only be produced at shear rates above those involved in gross melt fracture. The analysis of the effect of the molecular parameters, leads to the conclusion that only SCB has a direct effect on T_s. A linear correlation between T_s and SCB level is established, showing the decrease of the former as the latter is increased. Considering the wide spectrum of the molecular characteristics of our samples, we claim that decreasing temperature is a sound route to postpone sharkskin of any polyethylene.     

The effect of impeller-to-tank diameter ratio on draw down of solids

The effect of impeller-to-tank diameter ratio (D/T) on the draw down of solids was investigated using a mixed flow impeller (pitched blade turbine) and a narrow blade hydrofoil (LE-20) of D=T/2 and T/3. Operational conditions (impeller speed and power consumption) at which solids do not remain at the liquid surface for more than 2- were determined for a given solid type (polyethylene particles) at a given concentration (X=1%). Under selected conditions, liquid velocity values were obtained from LDA measurements and CFD simulations to better interpret the findings.Both upward and downward pumping modes were studied with the impeller mounted over a range of submergences, and different mechanisms of draw down were noted. For LDA measurements and CFD simulations, only the upward pumping PBT was considered. These were carried out under conditions where draw down did not occur through air ingesting vortices.When solids were drawn down without air being entrained from the surface, a smaller diameter impeller (D=T/3) was more energy efficient, although it required higher speeds to achieve draw down. Results from LDA measurements and CFD simulations showed that the discharge flow from a larger impeller has a stronger radial component of flow, and as a result the liquid is directed towards the vessel walls rather than the surface which supported this finding. The only exception to this was when solids were drawn down along with air through vortices. In this case, the power demand could be lower with a larger diameter impeller.     

The adsorption of strychnine at a mercury—solution interface

The adsorption of strychnine in an aqueous acetate buffer has been studied in order to explain the optimum conditions of an electrochemical asymmetric synthesis in which it is used as inductor. In dilute solutions (m < 10^?4) the adsorption is a slow kinetic process while at more concentrated values (m > 10^?4) it is affected by an association in solution. This explains the fact that the optimum conditions for the synthesis are known to correspond to a concentration 10^?4 M in strychnine.Further more while it is not adsorbed at very positive charges, this molecule saturates the surface of the electrode for negative charges between ?2 and ?7 μCcm^?2ie between ?500 and ?900 mV (Calomel electrode KCl 0.1 M). At still more negative charges (?1300 mV) hydrogen is catalytically discharged.     

Marangoni instability in non-isothermal first order gas—liquid reactions—evaluations of Cl2—toluene and CO2—sodium hydroxide systems

A necessary condition for surface tension driven interfacial convection in non-isothermal gas—liquid reaction processes is that the interface be at a higher temperature than the adjacent liquid. In many important practical applications the interface is, however, hotter than the liquid, unless the liquid looses heat to the gas. The magnitude of the dimensionless quantity Biot number, (Bi), is a measure of the rate of this heat transfer. Its critical value Bi_crit is defined as that value which makes the temperature gradient at the interface vanishes. Thus when Bi ? Bi_crit the temperature gradient at the interface is positive. It is assumed here that Bi_crit constitutes a lower bound of the Biot number below which Marangoni type instability is not possible. Bi_crit is evaluated here from the governing unperturbed state equations. This analysis is presented for liquids of both finite and infinite depths.For system conditions which result in a positive temperature gradient at the gas—liquid interface, the results for critical Marangoni number are obtained using small perturbation analysis. Stationary neutral stability curves for chlorine—toluene systems and the relation between independent system parameters and the critical Marangoni number are outlined. The critical Marangoni number shows a curious U-type relation with Biot number. Practical significance of the stability results to the chlorine—toluene system is discussed.     

Extrusion drawn amorphous poly(ethylene terephthalate): 4. Irreversible spontaneous elongation

Uniaxially-oriented poly(ethylene terephthalate) (PET) films prepared by solid-state co-extrusion exhibit irreversible spontaneous elongation (rather than shrinkage) under specific conditions. Results for these conditions show that marked elongation (up to 20%) can occur during annealing of unconstrained samples. This phenomenon, which is not commonly observed for polymers, depends strongly on the prior conditions of extrusion draw. There is significant increase in length for films prepared with extrusion draw ratio (EDR) at 2.0 in the extrusion draw temperature (T_ext) range 80–100°C. The extrusion rate is also significant. Lower extrusion rates favour spontaneous elongation on subsequent heating. In addition, the annealing temperature (T_a) also affects elongation. Samples extruded at T_ext=80°C to EDR of 2.0 show maximum elongation at T_a=180–190°C. However at higher temperatures, e.g. at 10°C below the melting temperature and higher, shrinkage occurs instead. Moreover, annealing at T_a=90°C for different periods of time (t_a) shows that prior to the elongation a moderate amount of shrinkage occurs (t_a ? 30 s). The results suggest a correlation between spontaneous elongation and crystallization during anealing.     

Predicting precipitate particle breakage in a pipeline: Effect of agitation intensity during precipitate formation

This paper describes the breakage behaviour of whey protein aggregates formed under different agitation intensities when flowing turbulently through a pipe. The experimental results show that particles formed at lower agitation intensity remain larger along the pipeline even after long exposure time to turbulent conditions than those particles formed at higher agitation rates. This suggests that the agitation rate during the formative stages of precipitates has important effect on the size and perhaps on the structure of aggregates which in turn determine their flow behaviour under turbulent conditions. It is postulated that larger aggregate cores were formed at low agitation which were hardly broken during precipitate transportation.A predictive model that relates particle breakage with the local dissipation rate (ε_i) in the pipe, the maximum or threshold dissipation rate (ε_th) that a particle with a given size can withstand before any disruption occurs and the residence time of the particle in the pipeline (t) was used to model the break-up of the precipitates. The profile of the turbulent eddy dissipation rate (ε_i) along the experimental flow geometry was described using the results of CFD simulations which in turn were run using the standard κ-ε turbulent model. The breakage model was improved by introducing a new term which accounts for the restructuring process during the aggregate formation stage. The predicted results agree well with the experimental data allowing one to conclude that the particle size reduction was well coupled with the variation of ε along the turbulent flow path.     

Solids flow pattern in gas-flowing solids-fixed bed contactors. Part II: Mathematical modeling

In this paper a mathematical model for solids flow in gas-flowing solids-fixed bed contactors is developed. The presented four-parameter model assumes plug flow with axial dispersion in the dynamic, fast moving solids zone and the exchange of particles from this zone with the static zones. The complex dynamic behavior of the ‘static’ particles is described with a model of exchange between the dynamic and three static zones: (a) the ‘fast’ exchanging, (b) the ‘slow’ exchanging and (c) the ‘dead’ zone.The model parameters are optimized on the basis of two different tracer experiments: the step change response at the outlet—x_dyn, and the static holdup response—x_st. The model was tested for seven experimental series which correspond to different operating conditions (e.g., different superficial gas velocity and solids mass flux).The influence of the operating conditions on the model parameters is presented and discussed. Model reduction was also implemented in order to analyze the model simplifications and alternatives. Model sensitivity analysis was performed as well.     

Liquid film effect on dynamics of optical oxygen probe. Comparison with polarographic oxygen probes. Diffusion coefficients measuring technique

The dynamic behaviour of the optical oxygen probe at the presence of the liquid film is well described by unsteady one-directional oxygen diffusion into the probe membrane through liquid film. It is shown that the asymmetry caused by hyperbolic form of the Stern-Volmer relation between the probe signal and oxygen concentration is strongly suppressed in the presence of liquid film for the optical probes used in this work. In such case, the response calculated with respect to the mean oxygen concentration in the membrane describes well the optical oxygen probe dynamics.Liquid film effects on the signal of the optical and the polarographic oxygen probes are compared. Special attention is paid to find properties of membranes minimizing the liquid film effect on the rate of its response. From this point of view, the most suitable material for the optical probe membrane is one with high diffusivity but low solubility. Thus, silicone (used by optical probe manufacturers in these days) is the least suitable material. When both probes are covered with the same membrane, the response of polarographic probe is faster and less influenced by the liquid film compared with optical one. From this point of view, the polarographic probe is more suitable for monitoring of fast changing oxygen concentration in bulk liquid as it occurs, e.g. measurement of k_La in gas-liquid dispersions, usually with the need to know the L_L parameter characterizing the liquid film diffusion resistance. In addition, only the polarographic probe allows determination of a local value of the parameter L_L (under the given hydrodynamic conditions where the probe is situated) which is not possible with an optical probe. The optical probe is more suitable for measurements under steady-state conditions and for slower oxygen changes, even under the conditions, when the liquid film resistance is high in comparison with the membrane resistance as it occurs for diffusivity measurements in liquids. A modified method for evaluation of the oxygen diffusion coefficient in liquids from the dynamic probe response is presented.     

Evaluation of pseudohomogeneous models for heat transfer in packed beds with gas flow and gas-liquid cocurrent downflow and upflow

Several pseudohomogeneous models are used by researchers in the study of heat transfer in packed beds. In this work, five of the most used pseudohomogeneous models (to one, two and three parameters) are analyzed, for gas and gas-liquid flow configurations. The models were evaluated concerning the following aspects: (a) the fitting between calculated and measured temperatures, (b) the values of thermal parameters, (c) their confidence intervals, (d) the quality of the estimation of the thermal parameters by analysis of their Box biases, and (e) the nonlinear dependence of the calculated temperatures on the thermal parameters (using the curvature measures of Bates and Watts). It was observed, particularly in gas-liquid flow, that the fittings between calculated and measured temperature profiles are better for models in which a wall heat transfer coefficient is incorporated to consider the convective resistance at the bed wall. It was also noted that the values of the thermal parameters fitted from the pseudohomogeneous models may be very different at identical operational conditions. The effective axial thermal conductivity may be neglected in the modeling because its estimation does not affect the residual functions. Besides, the estimation of k_a is tricky because it depends on the initial guess and also because the parameter is extremely sensitive to changes in the operational conditions. The confidence intervals for the parameters depend on the model and are also affected by the experimental conditions. The estimation of the parameters was adequate for the k_r-h_W and k_r-k_a models and the curvatures measures were satisfactory only for models in which h_W was not incorporated.     

Chemical expansion of nonstoichiometric Pr0.1Ce0.9O2−δ: Correlation with defect equilibrium model

Undoped and acceptor doped cerium dioxide is known to exhibit non-stoichiometry induced chemical expansion at elevated temperatures and reducing environments with impact on the mechanical integrity of solid oxide fuel cells and permeation membranes. In this paper, the chemical expansion of Pr_0.1Ce_0.9O_2−δ is measured and analyzed with respect to its defect equilibria and the chemical coefficient of expansion, analogous to thermal coefficient of expansion, is extracted. The addition of Pr to CeO₂ leads to major deviations from stoichiometry, and correspondingly to large chemical expansions, under readily accessible experimental conditions (e.g. in air at elevated temperatures). Pr_0.1Ce_0.9O_2−δ, therefore, serves as a model system for studying chemical expansion in ceria-based solid solutions in order to predict the conditions in which they exhibit suppressed chemical expansion.     

The contribution of homogeneous and non-oxidative side reactions in the performance of vanadyl pyrophosphate,catalyst for the oxidation of n-butane to maleic anhydride,under hydrocarbon-rich conditions

The reactivity of vanadyl pyrophosphate, catalyst for the selective oxidation of n-butane to maleic anhydride, was examined under n-butane-rich conditions, simulating a feed in which oxygen is the limiting reactant, and a process in which the unconverted n-butane is recycled. A lower selectivity to maleic anhydride was found with respect to the hydrocarbon-lean conditions, due to the higher selectivity to carbon oxides and to the formation of C₈ by-products: tetrahydrophthalic and phthalic anhydrides. The latter compounds formed by a consecutive reaction of maleic anhydride with the unsaturated C₄ intermediates. This occurred under conditions of total oxygen conversion, due to the decreased catalyst oxidizing property. A relevant contribution of radicalic, homogeneous reactions was also observed, which mainly led to the formation of carbon oxides and olefins. This contribution decreased in the presence of the catalyst, which acted as a radical scavenger, but nevertheless remained important at temperatures higher than 400 °C. When conditions were used under which the conversion of oxygen was not total, olefins generated in the gas phase reacted at the catalyst surface yielding maleic anhydride. This homogeneously initiated heterogeneous process led to an unusual effect, of a relevant increase of maleic anhydride yield over 400 °C.     

Flooding and drop size in a pulsed disc and doughnut extraction column

The hydrodynamic behavior of a pulsed disc and doughnut column has been investigated using three different systems in the absence of mass transfer. Sauter-mean drop diameter (d₃₂), flooding velocity and holdup at flooding have been measured at different operating conditions. The following operating variables have been studied: pulsation intensity and flow rate of both liquid phases. As expected, smaller mean drop sizes are obtained with the increase of pulsation intensity. The results also show no significant effect of continuous phase flow rate on mean drop size, which increases with increase of dispersed phase flow rate for the operating conditions investigated. A single correlation for the prediction of d₃₂ in the mixer-settler, transition and emulsion regimes of operation is proposed with a mean deviation of 7.32%. The maximum throughput is influenced mainly by pulsation intensity and interfacial tension. Two precise correlations are proposed for predicting flooding velocities in this column. The first is based on operating variables, column geometry, and system physical properties. The second one considers the same variables, except column geometry. Good agreement between prediction and experiments is found for all operating conditions investigated.     

New criteria for application of the well-mixed model to gas-liquid mass transfer studies

The well-mixed model presents several advantages for the evaluation of interphase mass transfer rates in gas-liquid contactors: it simplifies the mathematical analysis and eliminates the need for measuring numerous mixing parameters. Although the well-mixed model corresponds to a theoretical concept, it is shown in this paper that, under certain conditions, it can be safely applied to the liquid phase of contactors for the purpose of determining the overall volumetric mass transfer coefficient K_La_L. Based on a computer simulation of absorption and mixing processes, simple criteria were developed that specify the conditions for which the well-mixed model is applicable in practice, for either a semi-batch gas-liquid contactor or a continuous flow absorber at steady-state. The dimensionless group K_La_Lτ_c, where τ_c is the average circulation time in the liquid phase of the contactor, was found to be a key parameter in establishing the validity of the well-mixed model.     

Dynamic effects in capillary pressure-saturations relationships for two-phase flow in 3D porous media: Implications of micro-heterogeneities

The capillary pressure-saturation (P^c-S) relationships are essential in characterising two-phase flow behaviour in porous media. However, these relationships are not unique and depend on the flow dynamics, i.e., steady state or dynamic, among other factors. It has been shown that empirical models describing two-phase flow processes in porous media may be inadequate to account fully for the physics of flow in dynamic conditions. New capillary pressure relationships have been proposed which include an additional term to account for the dependence of capillary pressure on saturation and time derivative of saturation (∂S/∂t). This parameter is a capillary damping coefficient, also known as dynamic coefficient (τ), which establishes the speed at which flow equilibrium is reached. The dependence of P^c-S relationships on ∂S/∂t is called dynamic effects.In most laboratory experiments for measuring two-phase flow properties, it is implicitly assumed that the sample is homogeneous. However, this is not the case and micro-heterogeneities with their distinct multiphase flow properties may exist within the domain. They affect the dynamics of the multiple fluid phases and saturation distributions in the domain. These issues have been studied individually but the combination of dynamic effects and micro-scale heterogeneities on the P^c-S relationships has not been quantified accurately, particularly in 3D domains. Consequently, there are significant uncertainties on the reported values of τ in the literature.In this work, we have carried out a numerical study to investigate how the presence of micro-scale heterogeneities affects the dynamics of dense non-aqueous phase liquid (DNAPL) and water flow in porous domain. The relative significance of the variations in nature, intensity and distribution of micro-scale heterogeneities on dynamic flow conditions are manifested on P^c-S curves which are quantified in terms of the dynamic coefficient, τ. There is a complex interplay of various factors (e.g., dynamic flow conditions, distribution and intensity of micro-heterogeneity, pore size distribution, domain size and geometry and media anisotropy) which affects P^c-S curves. However, our results show that as the intensity of heterogeneity increases the dynamic coefficient at a given saturation increases, provided all other factors remain the same. The effects of domain shapes (cylindrical vs. rectangle), aspect ratios, dimensionality (2D vs. 3D), permeability anisotropy on τ are also analysed in order to generalise their effects as far as possible. We envisage that our simulations will minimise some of the inconsistencies on the reported data on τ in the literature.     

Development of an Efficient Electroporation Method for Iturin A-Producing Bacillus subtilis ZK

In order to efficiently introduce DNA into B. subtilis ZK, which produces iturin A at a high level, we optimized seven electroporation conditions and explored an efficient electroporation method. Using the optimal conditions, the electroporation efficiency was improved to 1.03 × 10⁷ transformants/μg of DNA, an approximately 10,000-fold increase in electroporation efficiency. This efficiency is the highest electroporation efficiency for B. subtilis and enables the construction of a directed evolution library or the knockout of a gene in B. subtilis ZK for molecular genetics studies. In the optimization process, the combined effects of three types of wall-weakening agents were evaluated using a response surface methodology (RSM) design, which led to a two orders of magnitude increase in electroporation efficiency. To the best of our limited knowledge, this study provides the first demonstration of using an RSM design for optimization of the electroporation conditions for B. subtilis. To validate the electroporation efficiency, a case study was performed and a gene (rapC) was inactivated in B. subtilis ZK using a suicide plasmid pMUTIN4. Moreover, we found that the rapC mutants exhibited a marked decrease in iturin A production, suggesting that the rapC gene was closely related to the iturin A production.     

Boundary value problems in transport with mixed or oblique derivative boundary conditions—I: Formulation of equivalent integral equations

When an internally heated body is cooled along its boundary by a peripherally flowing fluid that is continually replenished from an external source, a differential energy balance on the boundary leads to unfamiliar boundary conditions. Such boundary conditions involve mixed second derivatives with respect to spatial variables, which under additional assumptions (such as an infinite heat transfer coefficient) lead to oblique derivative boundary conditions; i.e. at the boundary an oblique derivative of the temperature is specified. Classical attempts at solution of elliptic partial differential equations with oblique derivative boundary conditions have been through the establishment of equivalent singular integral equations, using complex analytic continuation. The theory of singular integral equations is complicated, however.Using appropriate Green's functions, the boundary value problems of interest have been reduced to equivalent integral equations in this work. While oblique derivative boundary value problems are shown to lead to singular integral equations, the mixed derivative boundary value problem is shown to yield Fredholm integral equations directly. This surprising finding is mathematically significant, because Fredholm integral equations are solved more easily, and physically significant because the mixed derivative boundary condition is the more realistic condition in the present context. A method of solution of Fredholm integral equations is discussed.More complicated boundary conditions in which axial conduction in the coolant fluid is important have also been shown to lead to Fredholm integral equations. Finally a transient problem has been formulated.