Radial Concentration Gradients Research Articles

Enhancement of methanol production in a novel fluidized-bed hydrogen-permselective membrane reactor in the presence of catalyst deactivation

In this study, a dynamic model for a novel bubbling fluidized-bed membrane dual-type methanol reactor has been developed in the presence of long-term catalyst deactivation. The proposed model has been used to compare the performance of a novel fluidized-bed membrane dual-type methanol reactor (FMDMR) with membrane dual-type methanol reactor (MDMR) and conventional dual-type methanol reactor (CDMR). In this new concept, the feed synthesis gas is preheated in the tubes of the gas-cooled reactor and flowing in a counter-current mode with reacting gas mixture in the shell side. Due to the hydrogen partial pressure driving force, hydrogen can penetrate from feed synthesis gas into the reaction side through the membrane. The outlet synthesis gas from this reactor is fed to tubes of the water-cooled packed-bed reactor and the chemical reaction is initiated by the catalyst. The methanol-containing gas leaving this reactor is directed into the shell of the gas-cooled reactor and the reactions are completed in this fluidized-bed side. This reactor configuration solves some observed drawbacks of new conventional dual-type methanol reactor such as pressure drop, internal mass transfer limitations, radial gradient of concentration and temperature in gas-cooled reactor. The proposed dynamic model has been validated against measured daily process data of a methanol plant recorded for a period of four years and a good agreement has been achieved. The simulation results show there is a favorable profile of temperature and activity along the fluidized-bed membrane dual-type reactor relative to membrane and conventional dual-type reactor systems. Therefore, the performance of methanol reactor system improves when membrane assisted fluidized-bed concept is used for conventional dual-type reactor system.

Physical properties of wax deposits on the walls of crude pipelines

Wax deposits on the wall of a crude oil pipeline are a solid wax network of fine crystals, filled with oil, resin, asphaltene and other impurities. In this paper, a series of experiments on wax deposition in a laboratory flow loop were performed under different conditions (flow rate, temperature differential between crude oil and pipeline wall, and dissolved wax concentration gradient), and the wax deposits were analyzed, so quantitative relationships among wax content, wax appearance temperature (WAT), shear stress, and radial concentration gradient of dissolved wax at the solid/liquid interface were obtained. Finally, a model was established to predict WAT and the wax content of the deposit.

Enhancement of hydrogen production in a novel fluidized-bed membrane reactor for naphtha reforming

In this work, a novel fluidized-bed membrane reactor (FBMR) for naphtha reforming in the presence of catalyst deactivation has been proposed. In this reactor configuration, a fluidized-bed reactor with perm-selective Pd–Ag (23 wt% Ag) wall to hydrogen has been used. The reactants are flowing through the tube side which is a fluidized-bed membrane reactor while hydrogen is flowing through the shell side which contains carrier gas. Hydrogen penetrates from fluidized-bed side into the carrier gas due to the hydrogen partial pressure driving force. Hydrogen permeation through membrane leads to shift the reaction toward the product according to the thermodynamic equilibrium. This membrane-assisted fluidized-bed reactor configuration solves some drawbacks of conventional naphtha reforming reactors such as pressure drop, internal mass transfer limitations and radial gradient of concentration and temperature. In FBMR the hydrogen which is produced in shell side is a valuable gas and can be used for different purposes. The two-phase theory of fluidization is used to model and simulate the FBMR. Industrial packed bed reactor (PBR) for naphtha reforming is used as a basis for comparison. This comparison shows enhancement in the yield of aromatic production in FBMR for naphtha reforming. Although using FBMR reduces hydrogen mole fraction in reaction side and enhances catalyst deactivation due to coking, but this effect can be compensated using advantages of FBMR such as suitable hydrogen to hydrocarbon molar ratio, lowering deactivation rate due to lower temperature, control of permeation rate by adjusting shell side pressure and shifting the equilibrium reactions. The impacts of hydrogen to hydrocarbon molar ratio, pressure, membrane thickness, flow rate and temperature have been investigated in this work.

A Novel Fluidized‐Bed Membrane Dual‐Type Reactor Concept for Methanol Synthesis

AbstractA novel fluidized‐bed membrane dual‐type methanol reactor (FBMDMR) concept is proposed in this paper. In this proposed reactor, the cold feed synthesis gas is fed to the tubes of the gas‐cooled reactor and flows in counter‐current mode with a reacting gas mixture in the shell side of the reactor, which is a novel membrane‐assisted fluidized bed. In this way, the synthesis gas is heated by heat of reaction which is produced in the reaction side. Hydrogen can penetrate from the feed synthesis gas side into the reaction side as a result of a hydrogen partial pressure difference between both sides. The outlet synthesis gas from this reactor is fed to tubes of the water‐cooled packed bed reactor and the chemical reaction is initiated by the catalyst. The partially converted gas leaving this reactor is directed into the shell of the gas‐cooled reactor and the reactions are completed in this fluidized‐bed side. This reactor configuration solves some drawbacks observed from the new conventional dual‐type methanol reactor, such as pressure drop, internal mass transfer limitations, radial gradient of concentration, and temperature in the gas‐cooled reactor. The two‐phase theory of fluidization is used to model and simulate the proposed reactor. An industrial dual‐type methanol reactor (IDMR) and a fluidized‐bed dual‐type methanol reactor (FBDMR) are used as a basis for comparison. This comparison shows enhancement in the yield of methanol production in the fluidized‐bed membrane dual‐type methanol reactor (FBMDMR).

Fixed-bed adsorption with nonplug flow: Perturbation solution for constant pattern behavior

Adsorption of a dilute solute from a fluid in nonplug flow through a fixed bed is investigated via a perturbation approach. The continuity equation for fixed-bed adsorption with axial dispersion is solved for the constant pattern concentration profile with the axial velocity characterized by a general axisymmetric function and the system having no resistances to external or intraparticle mass transfer. The isotherm is slightly favorable (i.e., concave downward) in order to justify the assumption that axial gradients of concentration are independent of the radial coordinate in the bed, as in the classical problem of Taylor diffusion. A series expansion of a general isotherm is used to treat adsorption equilibrium. The solution reveals the formation of a radial gradient of fluid-phase concentration and breakthrough behavior at the bed outlet dependent on the nonlinearity of the isotherm and the magnitude of the nonplug-flow-velocity profile. The results can be used to predict the breadth of the breakthrough wave of many chromatographic-type processes for packed beds and slightly favorable isotherms.

Separation of azeotropic mixtures of alcohols and water with FricDiff

FricDiff is an energy efficient separation process based on a difference in transport velocities of the components of a gas or vapor mixture when they diffuse through a sweep gas (‘enhancer’). The separation process takes place inside the pores of a non-selective macro-porous barrier. In this paper the separation of a 2-propanol–water mixture with the FricDiff-principle is studied, using CO 2 as the enhancer. A detailed numerical model is developed that describes the separation process that takes place inside a cylindrical FricDiff-unit. In this unit the vapor mixture to be separated and the sweep gas flow at opposite sides of a porous barrier in a counter current mode. Through the porous barrier selective mass transport of components of the feed mixture through the sweep gas takes place resulting in a separation. The model takes into account axial velocity profiles as a result of laminar flow of the gas and vapor mixtures through the flow channels, radial concentration gradients and radial velocities. The transport through the porous barrier is described with the Binary Friction Model. The influences of process conditions and the characteristics of the porous barrier on the separation process are studied.

Experiments and modeling of transport in composite Pd and Pd/Ag coated alumina hollow fibers

The mass transport processes are analyzed for H 2 permeation through Pd and Pd/Ag hollow fiber composite membranes. Experimental measurements of pure gas and two-component feeds quantify the extent of retentate-side transport limitations (concentration polarization) in reducing the hydrogen flux. The effects of membrane thickness, feed composition and flow rate, temperature, and total pressure on the extent of concentration polarization are measured. The data reveal that concentration polarization increases with increasing temperature and total pressure and decreasing hydrogen feed concentration. A hierarchy of transport models of varying complexity is presented. The complex 2D models account for gas-phase axial and retentate-side radial concentration gradients, and both selective transport of hydrogen through the Pd membrane and non-selective transport through membrane defects. Satisfactory agreement between model predictions and experimental data is obtained using experimentally measured parameters. An analysis of the characteristic times of the pertinent transport processes identifies the rate limiting regimes and helps to determine the conditions when gas-phase transport limits the overall productivity. The findings underscore the utility of small diameter fiber supports in providing a high surface to volume ratio and reduced concentration polarization.

Effect of Mass-Transport Limitations on the Performance of a Packed Bed Membrane Reactor for Partial Oxidations. Intraparticle Mass Transport

For partial oxidation systems, where the reaction order in oxygen of the formation rate of the target product is smaller than the reaction order in oxygen of the consecutive reaction rate toward the waste product, a packed bed membrane reactor can be applied to distributively dose oxygen along the reactor in order to improve the selectivity toward the desired intermediate product. In this paper, how the performance of a PBMR for partial oxidations is influenced by the extent of intraparticle diffusion limitations has been investigated. First, the intrinsic effects for a single catalyst particle are discussed, and subsequently the integral effects over the entire reactor on the conversion and selectivity are studied with numerical models (considering different sets of reaction orders, different ratios of reaction rates of the primary and secondary reaction, and different stoichiometric coefficients). In Part 2, the effects of radial oxygen concentration gradients from the membrane wall to the center of the packed bed are investigated. The main objective of this work is to provide guidelines to assess whether mass-transfer limitations inside the particles (Part 1) and/or from the membrane wall to the center of the catalyst bed (Part 2) affect the reactor performance and to quantify these effects.

Consequences of the radial heterogeneity of the column temperature at high mobile phase velocity

When a high velocity stream of mobile phase percolates through a chromatographic column, the bed cannot remain isothermal. Due to the mobile phase decompression, heat is generated along the column. Longitudinal and radial temperature gradients take place along and across its bed. The various consequences of this thermal heterogeneity are calculated and their effects on the column efficiency investigated for a 0.46cm×25cm stainless steel column packed with 5μm particles. The maximum pressure drop applied was varied from 0.1 to 2kbar. The amplitude of the longitudinal temperature gradient can be estimated on the basis of the integral heat balance equation applied to the whole column and of measurements of the eluent temperature at the column exit. Assuming that the radial gradient is parabolic and the longitudinal gradient linear, the amplitude of the radial gradient can be determined on the basis of the energy balance across the column and of direct measurements of the radial gradient at high inlet pressures. A radial temperature gradient causes a radial distribution of the eluent viscosity, hence of its local velocity. The result is that bands move faster in their center than along the wall, become warped, hence a radial concentration gradient, similar in origin to the one observed in open cylindrical tubes. Diffusion relaxes this gradient. If there is only a longitudinal temperature gradient, the column efficiency would be 30% smaller for a 2kbar pressure drop than if there is no longitudinal temperature gradient. However, when both a longitudinal and a radial temperature gradient coexist, there is a large loss of efficiency. If the influence of the diffusive relaxation of the radial concentration gradient is neglected, the peak shape would be broad and exhibit a marked shoulder.

Coke formation possibility during production of reducing gas in large scale direct reduction plant

For the production of synthesis gas utilised in Midrex direct reduction plants, catalytic steam/CO2 hydrocarbon reforming in tubular reformer is the major process. Owing to the high heat input through the Midrex reformer tube wall, the endothermic nature of reforming reactions, low mass velocity of feed gas and large tube diameter, the catalyst bed is exposed to considerable axial and radial temperature gradients. These radial concentration and temperature gradients may create local areas with potential for carbon formation. To investigate this phenomenon, a rigorous two-dimensional model is developed for simulating the operation of a Midrex reformer which applies a dual catalyst loading profile. Both process side and furnace side have been included in this integrated model. Simulation results are in good agreement with available data from an actual plant. Using this model, a thermodynamic approach is applied to recognise zones in which the risk of carbon formation is high inside the reformer tubes. The results show that the first half of tubes, both in centre and near the wall, is critical from carbon forming point of view. Furthermore, the model shows that how a certain catalyst loading profile will affect the operation of the reformer.

Coated-Wall Reactor ModelingCriteria for Neglecting Radial Concentration Gradients. 1. Empty Reactor Tubes

The influence of radial mass transport on the conversion in a coated-wall reactor was investigated in a modeling study. Criteria based on the observed conversion are developed to allow for neglecting radial concentration gradients and to be able to use the simple plug-flow model to describe the reactor performance and to determine reaction kinetics. The simulations were carried out using Athena Visual Studio 10.0 and Comsol Multiphysics 3.2 for several reactor geometries (round, square, annular, rectangular, and triangular channels) and reaction orders. It was verified that the entrance effects, which enhance the radial mass transfer, can be neglected in most typical situations. The criterion for the maximum allowable conversion with a less than 5% deviation in the rate constant is a function of the modified Péclet number (Pe‘), the reaction order (n), and two constants a and b that depend on the reactor geometry: XCWR < b/(a + nPe‘). The criterion is valid for both gases and liquids.

Coated-Wall Reactor ModelingCriteria for Neglecting Radial Concentration Gradients. 2. Reactor Tubes Filled with Inert Particles

The influence of radial mass transport limitation on the conversion in a coated-wall reactor filled with inert particles was investigated in a modeling study. Criteria are developed to allow for neglecting the radial concentration gradients and to use the simple plug-flow model for performance testing and kinetic studies using the measured conversion. The simulations were carried out using Athena Visual Studio 10.0 for several reaction orders in a tubular reactor filled with inert particles of different sizes. It was verified that the entrance effects, which enhance the radial mass transfer, can be neglected in most typical situations. The criterion for the conversion is a function of the modified Péclet number (Pe‘), the reaction order (n), and a constant a that depends on the reactor geometry and the internal tube radius/particle size ratio: XCWR < 1.42a/(a + nPe‘). The criterion is valid for both gases and liquids as long as the viscous contribution to the pressure drop is much larger than the turbulent contribution. This applies for most gas-phase applications and some liquid-phase applications. At conditions where the turbulent contribution becomes comparable or larger than the viscous contribution, the criterion for the modified Péclet number becomes stricter. In that case, the criterion with assumed dp = 0 can be used as a conservative estimate. The most relaxed criterion is obtained for relatively large particles, up to dp/dt = 0.4.

Characterization of Microbial Transport in Cylindrical Pores

The mathematical model to characterize the transport of microorganisms in a finite-length cylindrical pore with the inside surface rich in microbial nutrients is developed, and the transport behavior of microorganisms in such a pore is discussed. Incorporated with key parameters such as microbial chemotaxis, diffusion, in-situ propagation and water flooding, this model is focused on the concentration profile of microorganisms in both radial and axial directions in the cylindrical pore during microbial transport under these parameters. Prediction by simulation based on the model shows that higher concentration of microorganism at and near the pore inside surface occurred during water flooding, and the radial concentration gradient in the cylindrical pore was consequently formed mainly due to microbial chemotaxis. Prediction also provides better understanding on the transport mechanism of microorganism in cylindrical pores, which is believed to be significant in the process of microbial enhanced oil recovery.

Wall-flow filters with wall-integrated oxidation catalyst: A simulation study

Diesel soot abatement via diesel particulate filters composed of so-called wall-flow monoliths is well established. Today, due to recent improvements in the production technology full-featured catalyst functionality can be implemented in the filter walls.This work focuses on a comparison of the reactor performance of the wall-flow filter and the conventional flow-through monolith. To this end a two-dimensional numerical model is set up for each of the two reactor configurations.Concentration profiles in the wall-flow filter systematically change as a function of flow velocity.At high flow velocities transport from the inlet channel into the porous wall is nearly entirely dominated by convection. This leads to uniform axial concentration profiles in the inlet and outlet channel and a steep gradient in the porous wall.At low velocities radial transport into the porous wall is dominated by diffusive transport. This leads to a negligible radial concentration gradient between the inlet and the outlet channel.Under most operating conditions relevant for an automotive exhaust catalyst the flow velocity is in an intermediate range with contributions of diffusive and convective transport.The transition from entirely convection dominated transport at high space velocities to increasingly diffusion dominated transport at lower flow velocities is similarly found for first order kinetics and a generalized Langmuir–Hinshelwood–Hougen–Watson (LHHW) rate law.Wall-flow filters show systematic conversion advantages over the conventional monolith for a first order reaction. For a reaction with LHHW-type kinetics this effect is not generally observed. It is one major result of this work that the relative performance of the two reactor configurations depends on the kinetics of the catalyzed reaction.

No Correlation between Latewood Formation and Leader Growth in Douglas-Fir Saplings

The width of earlywood and latewood in conifer xylem may have a profound effect on water transport and storage, vulnerability to embolism, and wood strength, yet the controls over the timing of latewood formation are unclear. Tracheids differentiating in the cambial zone are influenced by IAA, indole-3 acetic acid, the radial concentration gradient of which appears to either increase cell expansion (earlywood) or increase cell wall deposition (latewood). There are suggestive data that latewood begins to form when the growth of the leader stops, but definitive results are lacking. Height growth was measured in 14 Douglas-fir (Pseudotsuga menziesii) saplings at 10 dates between May and August, from the beginning of the growing season until after height growth had ceased. The cambium was also pinned six times between June and July, to induce xylem scarring at known dates. After height growth ceased, saplings were harvested and transverse sections of the wood were made at the pin insertion points. The date at which 95% of the height growth had occurred and the date at which latewood formation had begun were estimated. Analysis showed no correlation of these data, suggesting that the two phenomena may occur around the same time, but that one is not causal of the other.

Solid particle distribution of moderately concentrated suspensions in a pilot plant stirred vessel

Detailed particle distribution of a solid–liquid suspension in the just suspended state was measured by means of a conductivity probe. A total of eight experimental settings were investigated, involving two particle diameters (0.14 and 0.35 mm), two average particle concentrations (5 and 10 vol.%) and two impeller off-bottom clearances (H2/d = 1 and 0.5). A pilot plant stirred vessel of 1 m in diameter stirred with flat six pitched-blade turbine was used. A particle-filled layer of suspension was observed in all these experiments, and was particularly pronounced at the solid concentration of 10 vol.% and impeller off-bottom clearance H2/d = 0.5. The local solid concentration profiles within this layer were investigated. The axial and radial concentration gradients and their standard deviations were determined. The results indicate the presence of a concentration gradient in the radial direction within the particle layer, and of significant concentration fluctuations at the interface between the particle layer and the clear liquid layer in the upper part of the stirred vessel.

Chemotaxis of Caenorhabditis elegans during simultaneous presentation of two water-soluble attractants, l-lysine and chloride ions

Lysine and chloride ions are water-soluble attractants for Caenorhabditis elegans. When chemotaxis behavior to either of these attractants was assayed separately, the radial concentration gradients of 3 M lysine and 0.1 M ammonium chloride had similar potencies for attracting worms. However, when the concentration gradients of lysine and ammonium chloride at these concentrations were presented simultaneously, worms preferred lysine to ammonium chloride more than expected from the results obtained in separate experiments, suggesting the presence of an interaction between these two sensory information pathways within the nervous system. Chemotaxis behavior toward the radial concentration gradient of one of these attractants superimposed on a uniform concentration of the other attractant showed that the chemotaxis was augmented or attenuated by the ammonium chloride background depending on the background concentration, and attenuated by the lysine background, further supporting the interaction between the two sensory information pathways.

CFD simulation of UV photocatalytic reactors for air treatment

AbstractA photocatalytic reactor was simulated through computational fluid dynamics (CFD) with surface reaction for trichloroethylene (TCE) oxidation at various pollutant concentrations, flow rates, and reactor lengths. The results were compared with those from experiments. The experimental work involved using a differential photoreactor for kinetics studies and an annular flow photoreactor for overall removal investigations under various conditions. The modeling predictions agreed closely with the experimental data within the range in which results were examined. The modeling results indicated significant radial TCE concentration gradient and nonuniform flow distributions in the annular photoreactor. CFD was applied to predict the performance of a number of UV photocatalytic reactor design concepts, to study the impacts of some design parameters on the reactor efficiency. The modeling results demonstrated that under similar flow rate conditions, the thickness of the contaminated air layer flowing over the photocatalyst surface could substantially influence the reactor performance. Thinner contaminated air layers provided more uniform radial concentration distribution of TCE and improved the reactor performance. © 2005 American Institute of Chemical Engineers AIChE J, 2005

Modeling of Particle Separation in Bends of Rectangular Cross-section

A new theoretical model for predicting particle separation efficiency in bends is developed based on the investigation of flow pattern, the critical particle size separation theory and the boundary layer separation theory. The radial particle concentration gradient, instead of the usually assumed uniform radial particle concentration within the bends, is considered in this mathematical model. The local particle concentration and the separation efficiency can be calculated on the base of a time-of-flight model in terms of the particle size distribution of the feed. The effects of curvature ratio and bend angle on the separation efficiency in bends are also evaluated by the model.

Determination of Microvessel Permeability and Tissue Diffusion Coefficient of Solutes by Laser Scanning Confocal Microscopy

Interstitium contains a matrix of fibrous molecules that creates considerable resistance to water and solutes in series with the microvessel wall. On the basis of our preliminary studies, by using laser-scanning confocal microscopy and a theoretical model for interstitial transport, we determined both microvessel solute permeability (P) and solute tissue diffusion coefficient (D) of alpha-lactalbumin (Stokes radius 2.01 nm) from the rate of tissue solute accumulation and the radial concentration gradient around individually perfused microvessel in frog mesentery. P(alpha-lactalbumin) is 1.7 +/- 0.7(SD) x 10(-6) cm/s (n = 6). D(t)/D(free) for alpha-lactalbumin is 27% +/- 5% (SD) (n = 6). This value of D(t)/D(free) is comparable to that for small solute sodium fluorescein (Stokes radius 0.45 nm), while p(alpha-lactalbumin) is only 3.4% of p(sodium fluorescein). Our results suggest that frog mesenteric tissue is much less selective to solutes than the microvessel wall.