Model dispersion

The RTD as described by the dispersion model can be derived from the mass balance of a nonreacting species (tracer) over a volume element, AV = A Az, where A(,5 is the cross sectional area of the tube and z the axial coordinate. For constant fluid density and superficial velocity u, we obtain  

The total amount of a nonreactive tracer injected as a Dirac pulse at the reactor entrance is given by q. The Bodenstein number, Ho, is defined as the ratio between the axial dispersion time, = L /D, and the mean residence time, t = r = L ju, which is identical to the space time for reaction mixtures with constant density. For Bo - 0 the axial dispersion time is short compared to the mean residence time resulting in complete backmixing in the reactor. For Ho oo no dispersion occurs. In practice, axial dispersion can be neglected for Ho 100. 

Only for an open/open system, an analytical expression exists to describe the experimental response on a tracer pulse at the reactor inlet. The C-curve (see Equation 3.27) is given in Equation 3.45 as function of the dimensionless time. 

The relation between the mean value of the measured distribution curve compared to the mean of the -curve, respectively, the space time for constant density is given in Equation 3.46  

Replacing f by the mean value from the experimental curve leads to (Example 3.2)  

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Two alternative approaches are used ia axial mixing calculations. For differential contactors, the axial dispersion model is used, based on an equation analogous to equation 13 ... 

The next part of the procedure involves risk assessment. This includes a deterrnination of the accident probabiUty and the consequence of the accident and is done for each of the scenarios identified in the previous step. The probabiUty is deterrnined using a number of statistical models generally used to represent failures. The consequence is deterrnined using mostiy fundamentally based models, called source models, to describe how material is ejected from process equipment. These source models are coupled with a suitable dispersion model and/or an explosion model to estimate the area affected and predict the damage. The consequence is thus determined. 

Once the source modeling is complete, the quantitative result is used in a consequence analysis to determine the impact of the release. This typically includes dispersion modeling to describe the movement of materials through the air, or a fire and explosion model to describe the consequences of a fire or explosion. Other consequence models are available to describe the spread of material through rivers and lakes, groundwater, and other media. 

The dispersion model is typically used to determine the downwind concentrations of released materials and the total area affected. Two models are available the plume and the puff. The plume describes continuous releases the puff describes instantaneous releases. 

S. R. Hanna and P. J. Drivas, Guidelines for Use ofUapor Cloud Dispersion Models American Institute of Chemical Engineers, Center for Chemical Process Safety, New York, 1987. 

This recommended practice is intended to apply to faciUties that (/) handle or store flammable or explosive substances in such a manner that a release of ca 5 t of gas or vapor could occur in a few minutes and (2) handle toxic substances. The threshold quantity for the toxic materials would be determined using engineering judgment and dispersion modeling, based on a potential for serious danger as a result of exposures of <1 h. 

Vapor Cloud Source Dispersion Models (Workbook of Test Cases)... 

The NAAQS are expressed ia the form of ground level concentrations (GLC), which are the concentrations of pollutant ia the ambient air as measured at ground level, ia units of either micrograms per cubic meter or ppm. In order to convert a source s emission ia kilograms per hour to a GLC, dispersion modeling must be used. 

Costing investment analysis Data acquisition Database management Data conversion Development tools Dispersion models Distillation Drafting... 

Dispersion In tubes, and particiilarly in packed beds, the flow pattern is disturbed by eddies diose effect is taken into account by a dispersion coefficient in Fick s diffusion law. A PFR has a dispersion coefficient of 0 and a CSTR of oo. Some rough correlations of the Peclet number uL/D in terms of Reynolds and Schmidt numbers are Eqs. (23-47) to (23-49). There is also a relation between the Peclet number and the value of n of the RTD equation, Eq. (7-111). The dispersion model is sometimes said to be an adequate representation of a reaclor with a small deviation from phig ffow, without specifying the magnitude ol small. As a point of superiority to the RTD model, the dispersion model does have the empirical correlations that have been cited and can therefore be used for design purposes within the limits of those correlations. 

A dense-bed center-fed column (Fig. 22-li) having provision for internal crystal formation and variable reflux was tested by Moyers et al. (op. cit.). In the theoretical development (ibid.) a nonadiabatic, plug-flow axial-dispersion model was employed to describe the performance of the entire column. Terms describing interphase transport of impurity between adhering and free liquid are not considered. 

A flow reac tor with some deviation from plug flow, a quasi-PFR, may be modeled as a CSTR battery with a characteristic number n of stages, or as a dispersion model with a characteristic value of the dispersion coefficient or Peclet number. These models are described later. 

Dispersion model is based on Fick s diffusion law with an empirical dispersion coefficient substituted for the diffusion coefficient. The material balance is... 

Dispersion Model An impulse input to a stream flowing through a vessel may spread axially because of a combination of molecular diffusion and eddy currents that together are called dispersion. Mathematically, the process can be represented by Fick s equation with a dispersion coefficient replacing the diffusion coefficient. The dispersion coefficient is associated with a linear dimension L and a linear velocity in the Peclet number, Pe = uL/D. In plug flow, = 0 and Pe oq and in a CSTR, oa and Pe = 0. 

The Erlang (or gamma) and dispersion models can be related by equating the variances of their respective E(E) functions. The result for the closed-ends condition is... 

FIG. 23-15 Chemical conversion by the dispersion model, (a) First-order reaction, volume relative to plug flow against residual concentration ratio, (h) Second-order reaction, residual concentration ratio against kC t. 

CTDMPFUS Complex terrain dispersion model plus algorithms for unstable situations SARA Superfund Amendments and Reauthorization Act... 

EPA, Guidance on the Application of Refined Dispersion Models for Air Toxins Releases, EPA-450/4-91-007. 

Dispersion Models, CCPS-AIChE, New York, 1987. TNO, Methods for the Calculation of the Physical Effects of the Escape of Dangerous Materials Liquids and Gases ( The Yellow Book ), Apeldoorn, The Netherlands, 1979. 

FIG. 26-51 The procedure for using a gas dispersion model to estimate the release impact. 

TABLE 26-28 Atmospheric Stability Classes for Use with the Pasquill-Gifford Dispersion Model... 

A complete analysis of dense gas dispersion is much beyond the scope of this treatise. More detailed references are available (Britter and McQuaid, Workbook on the Dispersion of Dense Gases, Health and Safety Executive Report No. 17/1988, England, 1988 Lees, 1986, pp. 455 61 Hanna and Drivas, 1987 Workbook of Test Cases for Vapor Cloud Source Dispersion Models, AlChE, 1989 Guidelines for Chemical Process Quantitative Risk Analysis, 1989, pp. 96-103). 

Dispersion modeling of credible worse case scenarios indicates the one-hour exposure to nearest human receptor exceeds ERPG-2 level or equivalent. 

Steven R. Elanna and Peter j. Privos, Guidelines for Use of Vapor Cloud Dispersion Models, Second Edition, American Institute of Chemical Engineers, New York, NY, 1996. 

Hanna, S. R., and Dtivas, P. J., "Guidelines for Use of Vapor Cloud Dispersion Models."... 

Perrv, S. G., Bums, D. J., Adams, L. A., Paine, R. J., Dennis, M. G., Mills, M. T., Strimaitis, D. G., Yamartino, R. J., and Insley, E. M., "User s Guide to the Complex Terrain Dispersion Model plus Algorithms for Unstable Conditions (CTDMPLUS)," Vol. I "Model Description and User Instructions," EPA/600/8-89/041, U.S. Environmental Protection Agency, Research Triangle Park, NC, 1989. 

Perry, S. G., Paumier, J. O., and Burns, D. J., Evaluation of the EPA Complex Terrain Dispersion Model (CTDMPLUS) with the Lovett Power Plant Data Base, pp 189-192 in "Preprints of Seventh Joint Conference on Application of Air Pollution Meteorology with AWMA," Jan. 14-18,1991, New Orleans, American Meteorological Society, Boston, 1991. Bums, D. ]., Perry, S. G., and Cimorelli, A. ]., An advanced screening model for complex terrain applications, pp. 97-100 in "Preprints of Seventh Joint Conference on Application of Air Pollution Meteorology with AWMA," Jan. 14-18, 1991, New Orleans, American Meteorological Society, Boston, 1991. 

Turner, D. B, Zimmerman, J. R., and Busse, A. D., An evaluation of some climatological dispersion models, in "Proceedings of the Third Meeting of the Expert Panel on Air Pollution Modeling." North Atlantic Treaty Organization Committee on the Challenges of Modem Society Pub. No. 14. Brussels, 1972. (National Technical Information Service PB 240-574.)... 

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