Estimation of transport parameters

The main transport parameters to be estimated are the mass transfer coefficients (gas-liquid (liquid side) fc , gas-liquid (gas side) kg, and liquid-solid fc )). Coupled to that is the estimation of the interfacial area per unit volume a, and often it is the combination (i.e., kia or kgO) that is estimated in a certain experimental procedure. Thermodynamic parameters, such as Henry s law constant (fZ) can be estimated in a simpler manner since their estimation on the flow or on any time-dependent phenomenon. Mass transfer coefticients may be evaluated in well-defined geometries with known flow fields using classical theories like film theory, penetration theory, surface renewal 

For measurement of kfi, typically pure gas is used so that gas-side resistance to mass transfer is eliminated. Limiting situations can be employed in experimentation by performing the mass transfer coupled with limiting types of reactions in the homogeneous phase, such as mass transfer with no reaction (in which case the estimate is actually affected by RTD of liquid), mass transfer with slow reaction (for low Hatta numbers, the estimated kia is independent of liquid RTD), mass transfer with instantaneous reaction (in which case also the kia estimate works out to be independent of liquid-phase mixing and can 

Lee et al. [71] ir/a=2.36x (bubble-disintegrating regime) ir/a=1.10x 10 (bubble-coalescing or slug flow regime) (6.26) 

In summary, there are many known techniques to estimate the transport parameters, but most of them are application or equipment specific. Most importantly, it is a challenge to estimate them on a flow pattern-free basis. Table 6.8 shows some typical mass transfer coefficient values encountered in gas-liquid systems. These numbers are for guidance only, and the engineer interested 

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The main goal of this chapter is to review the most widely used modeling techniques to analyze sorption/desorption data generated for environmental systems. Since the definition of sorption/desorption (i.e., a mass-transfer mechanism) process requires the determination of the rate at which equilibrium is approached, some important aspects of chemical kinetics and modeling of sorption/desorption mechanisms for solid phase systems are discussed. In addition, the background theory and experimental techniques for the different sorption/ desorption processes are considered. Estimations of transport parameters for organic pollutants from laboratory studies are also presented and evaluated. 

Table 2. Published estimates of transport parameters in metamorphic flow systems.

The role of radionuclides as tracer of the chemical transport in river is also reinforced by the fact that each of the U-Th-Ra elements has several isotopes of very different half-lives belonging to the U-Th radioactive series. Thus, these series permit comparison of the behavior of isotopes of the same element which are supposed to have the same chemical properties, but very different lifetimes. These comparisons should be very helpful in constraining time scales of transport in rivers. This was illustrated by Porcelli et al. (2001) who compared ( " Th/ U) and ( °Th/ U) ratios in Kalix river waters and estimated a transit time for Th of 15 10 days in this watershed. The development of such studies in the future should lead to an important progress in understanding and quantifying of transport parameters in surface waters. This information could be crucial for a correct use of U-series radioactive disequilibria measured in river waters to establish weathering budgets at the scale of a watershed. 

Shah et al. [51] demonstrated the use of a donor-receptor compartment apparatus separated by a cell monolayer to estimate membrane transport parameters. Permeability coefficients, P, were calculated as... 

One procedure is to assume a parametrized form of the particle distribution function n[z) and compare the predictions of Eq. (8) to the measured scattered intensity to estimate the values of the parameters. This procedure was used to characterize the interaction of the interface with particles in a flowing stream above an interface [I2. There was no adsorption of particles on the surface, and the particle distribution function was obtained from a solution of a mass transport equation with a term describing the interaction with the interface. The analysis yielded estimates of the parameters in the interaction potential [12. ... 

Flynn, K. J. (1998). Estimation of kinetic parameters for the transport of nitrate and ammonium into marine phytoplankton. Mar. Ecol. Prog. Ser. 169, 13—28. 

A major limitation of solute transport simulation (even when the model represents field processes well) is the difficulty of obtaining good estimates of key parameters. Some aspects of this problem will be considered in the Discussion section later. Fundamental parameters identified in Equations 1, 3, 4, and 6 which require specification are K, d, k, Dg r % and p. Most other parameters are derived from these, with the exception of the parameters required to define hydraulic conductivity and water content as functions of soil water pressure head, for the water flow equation in the... 

A substantial number of a priori criteria for the estimation of transport effects on catalytic reaction rates has been reported by a number of workers. These criteria are generally derived on the premise that one does not desire the net transport effect to alter the true rate by more than some arbitrarily specified amount, normally 5%. Because of the uncertainty involved in knowing some of the parameters, the philosophy in applying these criteria should be conservative one does not look to marginal satisfaction of their requirements, but perhaps to be an order of magnitude better. 

ABSTRACT Soil hydraulic properties parameters are the crucial input parameters in water and solute transport modeling in the vadose zone. Pedotransfer functions are an alternative to direct measurement for obtaining soil hydraulic properties. In this study, Pedotransfer functions were established from particle-size distribution, bulk density, and organic matter using linear regression method with bootstrap analysis, then its prediction performance were further compared to artificial neural network and Vereecken with the Mean Error (ME) and the Mean Absolute Errors (MAE). The developed models were ranked the best models for estimation of hydraulic parameters with ME and MAE were less than O.lOcm /cm whereas Vereecken performed the worse results for hydraulic parameters, especially ME and MAE for parameters of a reached 0.74 1/cm and 0.63 1/cm, respectively. Function uncertainty evaluation was performed in Hydrus-ID model to simulate soil water, the developed pedotransfer functions and artificial neural network provide similar higher level of accuracy and precision with ME. 

The detailed information on initial and boundary conditions can be found in Ref. 115 and references therein. Partial differential equations (PDEs) describing processes of diffusion transport, adsorption/desorption, and reaction in the TAP micro-reactor can be solved either analytically or numerically. " Although the analytical solution allows fast estimation of kinetic parameters, the... 

Fig. 11 The time scales of transport parameters in material systems of different regioregularity, estimated via the time autocorrelation function of transfer integrals (blue circles), site energies (red squares) and the tail distribution of escape times (black triangles). Adapted with permission from Poelking et al. [13]. Copyright (2013) American Chemical Society...

Rotated electrodes are used for studies of the character of electrode reactions and their kinetics and for the estimation of electroanalytical parameters. Convection provides a constant mass transport of the analyte to the electrode surface with changed diffusion characteristics compared to quiescent liquids. The effect is similar to a stirring of the solution, but the rotation of an electrode can be controlled much more precisely than of a solution. Rotating ring-disc electrodes are practically used only for elucidating electrochemical reaction mechanisms where oxidation or reduction on the disc creates (collection experiment) or consumes (shielding experiment) electroactive substances which are monitored with the ring electrode. 

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