Toxic Release and Dispersion ModelsGausian Dispersion Models

Dispersion ModelsPractical and Potential ReleasesPasquil-Gifford ModelsStability classesDispersion coefficientsPlume ModelPuffIntegrated doseIsoplethsRelease MitigationExample

Practical and Potential ReleasesDuring an accident process equipment can release toxic materials very quickly.Explosive rupture of a process vessel due to excess pressureRupture of a pipeline with material under high pressureRupture of tank with material above boiling pointRupture of a train or truck following an accident.

Practical and Potential ReleasesIdentify the Design basisWhat process situations can lead to a release, and which are the worst situationsSource ModelWhat are the process conditions and hence what will the state of the release and rate of releaseDispersion ModelUsing prevailing conditions (or worst case) determine how far the materials could spread

Types of Dispersion ModelsPlume models were originally developed for dispersion from a smoke stack.In an emergency if there is a leak in a large tank then a plume can develop.

Types of Dispersion ModelsPuff models are used when you have essentially an instantaneous release and the cloud is swept downwind.No significant plume develops

Dispersion ModelsPractical and Potential ReleasesPasquil-Gifford ModelsStability classesDispersion coefficientsPlume ModelPuffIntegrated doseIsoplethsRelease MitigationExample

Pasquil-Gifford Dispersion ModelsBecause of fluctuations and turbulence the eddy diffusivity is constantly changing and traditional transport phenomena equations dont do a good job of predicting dispersion.

Solution is to assume that the materials spread out in a normal Gausian-type distribution.

Pasquil-Gifford Dispersion ModelsFor a plume the instantaneous value is different then the average.Develop correlations to predict the average concentration profile

Pasquil-Gifford Dispersion ModelsAs the plume is swept downwind, the concentration profile spreads out and decreases

Pasquil-Gifford Dispersion ModelsHave dispersion coefficients defined in the direction of the wind, in a cross wind direction and with elevation.These coefficients are correlated for six different stability classes.

Pasquil-Gifford Dispersion ModelsTable 5-2 gives the six stability classes to be used in the Pasquil-Gifford models. For a given set of conditions, you can determine which stability class to use.Figure 5-10 and Figure 5-11 give the dispersion coefficients for as a function of distance downwind from release for Plume Models

Plume Model Dispersion Coefficients

Puff Model Dispersion Coefficients

Dispersion ModelsPractical and Potential ReleasesPasquil-Gifford ModelsStability classesDispersion coefficientsPlume ModelPuffIntegrated doseIsoplethsRelease MitigationExample

Plume ModelAssumes plume has developed, hence it is continuous. Thus there is no dispersion coefficient, x, in the direction of flow (direction of the wind)

Plume Model

Equation 5-49 is complete plume modelCan simplify as needed

Plume ModelReason for last term in the expression is that as the gaseous plume is dispersed eventually you get reflection back off of the ground

Plume Model - SimplificationsIf you a particulate or something that will react with the ground, then you remove reflection term

Plume Model - SimplificationsIf your source is at ground level Hr is zero. Note the two terms add to two. Results in Eq. 5-46

Dispersion ModelsPractical and Potential ReleasesPasquil-Gifford ModelsStability classesDispersion coefficientsPlume ModelPuffIntegrated doseIsoplethsRelease MitigationExample

Puff ModelsOften in accidents, the releases are essentially instantaneous and no plume develops. Need to use a different dispersion model that is based on a puff.Now need to have dispersion coefficient in the wind direction. However, assume it is the same as in the cross wind (y) direction.Dispersion coefficients only defined for three stability classes (Unstable, Neutral, Stable). See bottom of Table 5-2.

Puff Model Puff at height HrEq. 5-58 describes dispersion

Puff Model - SimplificationGround level source. Eq. 5-38

Puff Model-SimplificationCoordinate system moves along with puff. Eq. 5-54

Dispersion ModelsPractical and Potential ReleasesPasquil-Gifford ModelsStability classesDispersion coefficientsPlume ModelPuffIntegrated doseIsoplethsRelease MitigationExample

Integrated DoseWhen a person is standing in a fixed location and a puff passes over, he/she receives a dose that is the time integral of the concentration.

Integrated DoseFor person on ground at distance y cross wind, Eq. 5-43

For person on ground at centerline of flow, Eq. 5-44

Dispersion ModelsPractical and Potential ReleasesPasquil-Gifford ModelsStability classesDispersion coefficientsPlume ModelPuffIntegrated doseIsoplethsRelease MitigationExample

IsoplethsAn isopleth is a three dimensional surface of constant concentration.Calculated bySpecify desired desired, u and tFind concentration along x axis at that t (x,0,0,t) to define boundaries and points along centerlineAt each point to be evaluated find y using equation 5-45.

IsoplethsEquation 5-45 makes more sense if you write it as follows

Isopleths

Comparison of Plume & Puff ModelsPuff model can used for continuous calculations by representing a plume as a succession of puffs.

Effective Release HeightBoth the Plume and Puff model utilizes an effective release height, Hr.This is caused the momentum and buoyancyFor release from a stack

Dispersion ModelsPractical and Potential ReleasesPasquil-Gifford ModelsStability classesDispersion coefficientsPlume ModelPuffIntegrated doseIsoplethsRelease MitigationExample

Release MitigationUtilize toxic release models as a tool for release mitigation.Make changes in process, operations or emergency response scenarios according to results.

Release MitigationInherent SafetyInventory reductionChemical substitutionProcess attentuationEngineering DesignPhysical integrity of seals and constructionProcess integrityEmergency controlSpill containmentManagementPolicies and proceduresTraining for vapor releaseAudits & inspectionsEquipment testingRoutine maintenanceManagement of changeSecurity

Release MitigationEarly Vapor DetectionSensorsPersonnelCountermeasuresWater sprays and curtainsSteam or air curtainsDeliberate ignitionFoams

Emergency ResponseOn-site communicationsEmergency shutdownSite evacuationSafe havensPPEMedical treatmentOn-site emergency plans, procedures, training & drills

Examples

SolutionAssume point source plum developsx = 3 kmOvercast nightu=7 m/sTable 5.2 -> Stability class D

SolutionGround level concentration, z=0Centerline, y=0

Solution