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:
cale longitudinal diffusion. The more elaborate "real-time" models consider the actual tidal flow to be advective, with longitudinal-diffusion occurring through motions having time scales considerably shorter thania tidal cycle; Each type of model is discussed below. (1) Analytical Model (Steady State) The least elaborate one-dimensional model assumes a constant cross-sectional area A, a constant (tidally and sectionally averaged) longitudinal dispersion coefficient EL, and a con stant fresh water velocity Uf. For this case Equation (23) reduces to d2C dC_• - (24 L dx--•'Uf 37 0 (24) where C is the time and sectionally averaged concentration. The solution (Ref. 46) to Equation (24) for a source at x - 0 and the boundary conditions C - 0 at x + * is (U C U f + (E L5 ME L ex p EL 14 (25 Uf The sign within the exponential is negative downstream from the source (x positive) and positive upstream from the source (x negative). In terms of dimensionless variables, Equation (25) reduces to r rmax exp (N 2,' 4 C) (26) 1.113-17 where N- Uf r " -- C \UfT+4XE1 / •• X Figure 4 Illustrates this dimensionless equation evaluated for C and N. Several features of Equation (26) are evident from Figure 4. The dimensionless source concentration rmax depends not only on the source strength and freshwater flow, but also on the diffusivity EL and the decay constant x. This dependency is explained by the fact that a steady concentration is maintained by a balance between the discharge source, the net advective-diffusive transport away from the source, and a local sink due to radioactive decay. The upstream and downstream curves have equal but opposite slopes for N - 0, since there is no nontidal advection where the net freshwater flow is zero. The curves become skewed in the downstream 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