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:
m direction for increasing values of Uf because of the nontidal advection downstream. (2) Releases of Short Duration For releases of short duration, the preceding steady-state model does not apply. In the case of a time-dependent source term, the transport equation is given by 3C + C E 3'C - XC (27) iE+Ufaxu ax The solution to Equation (27) for a time-dependent release may be obtained from the solution corresponding to the instantaneous release of a finite quantity of effluent uniformly over the flow cross-section (unit impulse function) (Ref.47 ). The unit impulse solution is given by C N ex( (x - uft)2 A (28) C"AVG e xpt 4ELt -X(8 where N is the amount of activity introduced (Ci). For a more general time-dependent release, results may be obtained by time integration of Equation (28). Assume that, instead of the Instantaneous introduction of a finite quantity d .s at x a 0 and t a 0, effluent is continuously discharged at the rate if Wft Cl/sec. The concentration distribution resulting from a continuous discharge In the time interval O<T<t is given by 1.113-18 -0- Upstream Downstream - - N-2 N -1 kN-0.6 N-0.1 N-0 at -0. rMax 4 uf + 4XE L Uf In2 t% -1.5 -1 -0.5 0 0.5 1.0 DIMENSIONLESS DISTANCE FROM SOURCE, ! OIGURE 4. DIMENSIONLESS PLOT OF CONTAMINANT CONCENTRATION VS DISTANCE FROM SOURCE ('FROM O'CONNER ET AL. REF. 46) 1.113-19 0.5 0.4 0.3 0.2 0.05 0.04 0.03 0 CD 2 0 us 0.02 0.01 _____.x - Uf(t - 029 - a f(T)-exp 4EL(t r) 2 A(t - T dr From Equation (29) the concentration distribution corresponding to a square pulse release of amplitude W and duration'tD is a[ 2 c= - AD---exp -Uf -T )dr (30) -4wLf 4EL(t -r ~ Equation (30) may be integrated to give the following solution in terms of exponentials and error functions: W Ux C= exp (-)g(x~t) for 0 <t < to L . (31) C - exp (U1) [g(xt) - g(x,t - to)] for t t where eg(xt) " erfX +LIl t J+ 1 exp(L-) [erf tf L 1 exp - ) 7 • U2+4EL The function g(x,t - tO) has the same form as g(x,t), with (t - tD) replacing t. The sign