Document: NRC Regulatory Guide
Document ID: c9ebcbb0-96c4-4d29-be51-5acae9cc858a
Document Type: regulatory_guide
Title: Estimating Aquatic Dispersion of Effluents from Accidental and Routine Reactor Releases for the Purpose of Implementing Appendix I (Rev. 1)
Source: NRC Regulatory Guide Division 1
Source URL: https://www.nrc.gov/docs/ML0037/ML003740390.pdf
Revision Date: 2023-06
Chapter: 
Section ID: RG-1.113
CFR Part: 
CFR Title: 

Content:
, a simple transient model can be formulated: c. exp +,, \ , x + ex~p ,st /- (19) where d is the depth; M is the amount of activity released (in curies); t is the time after the release; and the other terms are as previously defined. The case of a more general time-dependent release may be obtained by integrating Equation (19) with respect to time: 1.113-13 #1L-CLL* L RADIONUCLIDE CONCENTRATION I ,( in seconds per cubic metr) PER UNIT RELEASE RATE w C * * C - C al I F I" m "m 2 m n 0 zr •m> r 0lM Z 0 c t Wf(T) ri u~ - )2 2 C a Y, dx (t - T))) lexp /(y-YS fo ~ ~ ex~ 4 K- ) 4x~ )VYt-T -(y + Y) exP(4KY(t - TT dr . •)•(20) where the release rate is Wf(T) curies/sec. In general, Equation (20) must be solved using numerical quadrature. Equations (19) and (20) are also useful for releases into rivers in the region near the source, where the effects of the far shore are unimportant. (3) Numerical Models Analytical solutions to the diffusion equation are strictly applicable only to cases of steady uniform flow. In coastal regions having complex geometry and time-dependent nonuniform flow, analytical models might not be adequate for predicting realistic concentration values. In such cases multi-dimensional numerical models are more suitable. The use of such models is becoming increasingly common in water-quality simulation. Typical acceptable numerical models are the two-dimensional, vertically integrated models developed by Leendertse and co-workers (Refs. 29-34), Codell (Ref. 35), Loziuk et al. (Ref. 36), and Eraslan (Ref. 37). These and other numerical models fall into two broad categories, depending on the method in which the advective velocity field is obtained. The Leendertse, Codell, and Loziuk models, for example, compute the velocity field from the following vertically integrated two-dimensional equations of mass and momentum conservation: aU aU aU•S g(2 + V 2 ) S+ U -- + V -8 -f g 1 1 + x -9 Ch2H .av +3V + VA+ fu --gi+ -j- MAV+ (21) 7Fa y + Ch• 2H1 at ax