DMSTA Hydraulics, Bypass, & Seepage Computations

The treatment train consists of a user-defined series of cells, each with separate phosphorus cycling & hydraulic properties.

Up to 6 cells can be simulated at once. Cells can be configured in series and/or parallel (I.e. 1-dimensional branched network)

Each cell is assumed to have a flat bottom. Conservative (low) estimates for cell area should be used in hilly terrain.

To reflect transport properties, each cell is divided into a series of "tanks" (CSTR's) for computing mass balances.

Hydraulic properties vary across cells, but not across tanks.

Each cell is assumed to be hydraulically independent (I.e. backwater effects are not simulated).

Hydraulic gradient (inflow - outflow depth) within each cell is ignored (assumed small in relation to temporal variations in depth).

Computations of outflow from cell & bypass are described below.

Factor

Parameters

hydraulic resistance of vegetation as a function of depth

a,b

empirically calibrated (see below)

outlet control depth

Z_C

outflow pump capacity (forces water level backup)

QO_MAX

= 0 assumes infinite capacity

maximum water depth (forces bypass)

Z_MAX

= 0 assumes infinite depth

inflow capacity (forces bypass)

QIN_MAX

= 0 assumes infinite capacity

Vegetation

Qo = W a Z ^b

Outlet Control

If Z <= Z_C Then Qo = 0

Z_C = Z_CO + Z_C(t)

If a=0, Qo computed from the water budget & depth set equal to control depth ( Z = Z_C)

Outflow Capacity

Qo <= QO_MAX

If specified QO_MAX = 0, this constraint is ignored.

Maximum Depth & Inflow Capacity (Bypass Criteria for First Cell in Treatment Train):

If Z >= Z_MAX and Z_MAX > 0 then

Q_BYP = Q₁

bypass

else if QIN_MAX = 0 then

Q_BYP = 0

QIN_MAX = 0 assumed infinite inflow capacity

else

Q_BYP = Max ( 0 , Q₁ - QIN_MA

bypass

endif

Outflow from Tank J within a given cell is computed by linear interpolation based upon cumulative cell area

Variables:

outflow from cell (last tank)

hm³/d

computed from above equation

cell mean width

area / length

mean depth

computed from water budget

Z_C

control depth

computed from above equation

Z_CO

base control depth

input constant (parameter sheet)

Z_C(t)

control depth on day t

input time series

QOUT_MAX

maximum outflow rate (outflow pump capaci

hm³/d

input

QIN_MAX

maximum inflow rate

hm³/d

input

Z_MAX

max depth (levee constraint)

input

Calibration of Hydraulic Resistance Factors

Calibration Algorithm:

Set b = 3.5, seems to work for most systems; range 3-4.

Adjust control depth based upon observed flow vs. depth relationship

Adjust a to match observed mean depth over entire time series

If necessary, adjust b to match observed outflow vs. depth relationship

repeat 3, if necessary

Obs Mn

Pred Mn

Mean

Mean P

Calibration

Length

L/W

Depth

Veloc.

Storage

R-Squared

System

cm/sec

mg/m²

Depth

Outflow

Veget.

STA-6

1.200

3.500

1.876

1.00

0.151

873

0.843

0.915

Mixed

Cell-1_Z

0.400

3.500

3.560

2.71

0.189

1325

0.390

0.851

Mixed

Cell-2_Z

0.500

3.500

4.138

4.14

0.307

1970

0.587

0.836

Mixed

Cell-4_Z

0.700

3.500

1.723

2.02

0.334

1019

0.394

0.914

SAV

Cell-3_Z

1.200

3.500

2.583

1.92

0.279

822

0.395

#N/A

Mixed

WCA2A

1.000

3.500

12.000

1.14

0.287

418

0.524

#N/A

Mixed

Notes:

The calibrated "a" factor would reflect the combined effects of the following factors:

hydraulic resistance due to vegetation & associated litter layer

deviations from rectangular shape (assumed in computing width) ; likely to decrease "a" for a given vegetation type (e.g. Cell 4)

channelization (shortcircuiting around vegetation) due to remnant longitudinal farm canals or large open water areas

The user can estimate a & b independently based upon hydraulic equations (e.g, weir flow or mannings equation)

The hydraulic equation can be used to generate a theoretical Q/W vs. Z curve.

Parameters a & b can be fit to the theoretical curve.

Seepage Model

Average inflow & outflow seepage rates are computed for each cell based upon user-specified hydraulic properties.

Inflow Seepage Rate:

Seepin =

Max [ 0, E_I ( Z_I - Z ) ]

Seepin =

Inflow Seepage Rate (m/yr)

Z =

Mean Depth (m)

Computed

Z_I =

Inflow seepage control elev.

Input, reflects adjacent canal & gw elevations

E_I =

Inflow Seepage Coef (m/yr/m)

Input, reflects hydraulic conductivity

Outflow Seepage Rate:

Seepout =

Max [ 0, E_O ( Z - Z_O ) ]

Seepout =

Outflow Seepage Rate (m/yr)

Z_O =

Outflow seepage control elev.

Input, reflects adjacent canal & gw elevations

E_O =

Outflow Seepage Coef (m/yr/m)

Input, reflects hydraulic conductivity

Outflow seepage is collected across cells and routed to inflow, outflow, or to groundwater based upon user-specified parameters.

Inflow seepage has a user-specified concentration.

Outflow seepage concentration is constrained so that it does not exceed the average water-column concentration:

Cs = Min ( Csmax , Cavg ) , = Co if Csmax = 0

Csmax =

User-Specified Maximum Seepage Concentration (ppb)

Cavg =

Average concentration across all tanks (ppb)

This constraint is applied to each stirred tank in the treatment cell.

When Csmax < Cavg, there is a net uptake of phosphorus as the seepage moves through the soil.

Csmax can be set to reflect adsorption characteristics of soil.

This algorithm does not allow the soil to function as a net source of phosphorus.

06/08/02