STA & Reservoir Performance Measures for the Everglades Restudy

Equations Used for Predicting Phosphorus Retention in Stormwater Treatment Areas & Storage Reservoirs

03/30/02

Variables |  Water Balance  | STA Equations |  Reservoir Equations |  Discussion | Index

Variable Definitions:

C   =    Water Column Phosphorus Concentration (ppb)

Q   =    Flow (hm³/yr)

P   =    Rainfall (m/yr)

E   =    Evapotranspiration Rate (m/yr)

C_p =    Rainfall Phosphorus Concentration, Bulk, Reflects Wet + Dry Deposition (ppb)

K_e =    Effective Settling Rate (m/yr)

F_w  =   Fraction of Days with Water Elevation Above Ground Surface

U_o  =   Infiltration Rate (Seepage Out of  STA) (m/yr)

U_s  =   Exfiltration Rate (Seepage Into STA) (m/yr)

C_s  =  Inflow Seepage Concentration (ppb)

A  =    Wetland Surface Area (km²⁾

Z  =    Mean Water Depth  (m)

C_b  =  Background Concentration (ppb)

i   =    Subscript Indicating Inlet Conditions

o  =   Subscript Denoting Outlet Conditions

Water Balances for STA's or Reservoirs:

Differential Equation:

d Q / d A    =    b    =    P -  E  +  U_s  -  U_o

Boundary Condition:

Q    =    Q_i   @    A  =  0 (inflow to wetland)

Solution for Outflow Volume:

Q_o  =  Q_i   +  b A

Phosphorus Balance for Stormwater Treatment Areas:

Reference:

Walker, W.W., "Design Basis for Everglades Stormwater Treatment Areas", Water Resources Bulletin, Vol. 31, No. 4, pp. 671-685, August 1995, Download stadesign.pdf (1.1 mb)

Differential Equation:

d ( QC ) / dA    =   P C_p +  U_s C_s  -  K_e  F_w  C   -    U_o C

Boundary Condition:

QC   =    Q_i C_i    @ A   =   0

Solution for Outlet Concentration (Plug Flow Conditions)::

C_o  =   C_b  +  ( C_i - C_b ) ( Q_o / Q_i ) ^{( -r / b )}

r    =    P  -  E  +  U_s   +   F_w K_e

b    =    P  -  E  +  U_s   - U_o

C_b   =    (  P C_p   +   U_s C_s  )  /  r

Phosphorus Balance for Storage Reservoirs:

References:

Walker, W.W., "Phosphorus Removal by Urban Runoff Detention Basins", Lake and Reservoir Management, Volume 3, North American Lake Management Society, pp. 314-238, 1987, Download dbasins.pdf (0.8 mb)

Walker, W.W., "Empirical Methods for Predicting Eutrophication in Impoundments, Report 3, Phase II, Model Refinements", prepared for U.S. Army Corps of Engineers, Waterways Experiment Station, Report E-81-9, March 1985.

Differential Equation:

d ( QC ) / dA    =    P C_p  +   U_s C_s  -  K₂ F_w  C ²   -  U_o C

Boundary Condition:

Q C   =   Q_i  C_i    @  A  =  0

Solution for Outlet Concentration (Completely Mixed Conditions):

q_o  =  Q_o / A + U_o

K₂  =  0.17  F_w q_o / ( q_o + 13.3)

P_i  =  ( Q_i C_i / A  +   P C_p  +  U_s C_s  )  /  q_o

N   =   K₂ P_i    Z  /  q_o

C_o =  P_i   ( -1  +  4   N  ) ^0.5   /  ( 2  N )

STA & Reservoir Performance Measures - Introduction & Methods

STA & Reservoir Performance Measures - Index

http://www.wwwalker.net/restudy/equations.htm      Updated:  03/30/02