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:
el Analytical models of routine releases of liquid effluents along open coasts are usually based on Gaussian-like solutions to the steady-state diffusion equation. The form of each solution may differ in detail, depending on the number of dimensions retained, the loca tion of the bounding surfaces, and the discharge configuration. 1.113-11 A simple diffusion model for a steady point-source discharge into a lake having a known steady longshore current, u, may be formulated by neglecting the longitudinal diffusion and time dependence in the dissolved constituent transport equation as follows: aC a2C ax "- y az 77 c~- AC (14) where Cy and ez are the lateral and vertical turbulent diffusion coefficients, respectively. The remaining symbols are as defined in Section 2. The decay term may again be removed through the transformation - XX/U C(x,y,z) - x(x,y,z)e (15) resulting in the following equation for the nondecaying concentration x: U x 32 a2 ax CY Czy (16) It is assumed that the discharge Is located at the point (O,yszs), i.e., at the origin of the x-axis and a distance ys from the shoreline and zs beneath the water surface. For a large lake of constant depth d and straight shoreline the solution is x a f(az,zzs.d)f(oy.y,ys) (17) where f(azsz,z -,d) M + z - z-z) )2o f Syyy) uexp (ysy)2 + ex J L JJý This model may be used for curved shorelines by substituting, for y and yst the corresponding distances normal to the shoreline. In Equation (17), the condition that there be no flux of material through the bounding surfaces is ensured by placement of an image source of strength W (Ci/sec) at y - -y and an infinite series of image sources along the z-axis. Equation (17) is a basic expression that can be modified to yield solutions for a variety of discharge configurations into bounded water bodies. For the sake of simplicity, the present discussion is limited to point discharges. However, If W is interpreted as source strength per unit length, or per unit area, line and