# HydroGeoSphere/Fluid Mass Balance

## Sample fluid balance output

By default, fluid mass balance information is computed at each time step and written to the prefixo.lst file. Figure 5.17 shows some sample output as it appears in the .lst file:

--------------------------------------------------------------------
FLUID BALANCE, TIME:   0.500000000000000
--------------------------------------------------------------------
RATE OF FLUID EXCHANGE               IN               OUT
TOTAL
Fixed flux                       0.0059395897     0.0000000000
Critical depth                                    0.0000000000
NET1 EXCHANGE RATE (IN-OUT)                                     0.0059395897

RATE OF FLUID ACCUMULATION [L**3/T]
Porous medium                    0.0003197172
Overland                         0.0057208226
NET2 ACCUMULATION RATE                                          0.0060405397

FLUID BALANCE ERROR
Absolute: (NET1-NET2)                                          -0.0001009500
Relative: (NET1-NET2)/(abs(NET1)+abs(NET2))/2.0                 0.0168529029
Percent: abs(NET1-NET2)/NET1(+ve)*100.0d0             1.6996119929

FLUID EXCHANGE BETWEEN SURFACE AND SUBSURFACE DOMAIN
Infiltration                    0.0003219343
Exfiltration                    0.0000000000

Figure 5.17: Sample Fluid Balance Information for Example Abdul

This detailed fluid balance information is also written to a TECPLOT formatted ascii output file called prefixo.water_balance.dat so that it can be easily visualized. For each timestep in the flow solution one line is written to the file. The number of columns in the file depends on the nature of the problem. For example, for problems with no overland flow component, no overland flow data will be written to the file.

## Rates of water entering and leaving the domain

The first section of the fluid balance information relates to the rate at which water is entering (IN) or leaving (OUT) the domain via the various types of sources and sinks. Column headings that could appear in this section are:

• 1st+ 1st- The rate at which water is entering or leaving the domain via porous media first-type nodes.
• 1stdual+ 1stdual- The rate at which water is entering or leaving the domain via dual continuum first-type nodes.
• 1stSurface+ 1stSurface- The rate at which water is entering or leaving the domain via overland flow first-type nodes.
• 2nd+ 2nd- The rate at which water is entering or leaving the domain via second-type nodes.
• EvapoTrans- The rate at which water is leaving the domain via evapotranspiration.
• Well+ Well- The rate at which water is being added to or removed from the domain via wells.
• Tile+ Tile- The rate at which water is being added to or removed from the domain via tile drains.
• River+ River- The rate at which water is entering or leaving the domain via river nodes, as defined in Section 2.3.2.4.
• Drain- The rate at which water is entering or leaving the domain via drain nodes, as defined in Section 2.3.2.3.
• Seep- The rate at which water is entering or leaving the domain via seepage faces.
• ZeroDepth- The rate at which water is leaving the domain via zero-depth gradient boundaries.
• CritDepth- The rate at which water is leaving the domain via critical depth boundaries.
• FreeDr- The rate at which water is leaving the domain via free drainage boundaries.
• FixedFlow+ FixedFlow- The rate at which water is added to or removed from the domain via specified flowrate boundaries, as defined in Section 5.7.2.6.
• NET1 Sources/Sinks The total rate of all water entering or leaving the domain through sources and sinks, ${\displaystyle {\pm }Q}$ .

## Changes in storage

The next section of the fluid balance information relates to the changes in storage that occurred in the various media. Column headings that could appear in this section are:

• PM Rate of accumulation in the porous medium.
• Overland Rate of accumulation in the overland flow domain.
• Dual Rate of accumulation in the dual continuum.
• Fracture Rate of accumulation in discrete fractures.
• Tiles Rate of accumulation in tile drains.
• Wells Rate of accumulation in wells.
• NET2 Accumulation The rate of change of storage for the entire domain, ${\displaystyle {\Delta }S}$ .

In a perfectly balanced system the rate at which water enters or leaves the domain ${\displaystyle {\pm }Q}$  and the rate of change in storage ${\displaystyle {\Delta }S}$  would be equal and the fluid balance error ${\displaystyle {\varepsilon }}$  would be:

${\displaystyle {\varepsilon }={\pm }Q-{\Delta }S=0}$                          (Equation 5.13)

## Fluid balance error

The next section of the fluid balance information relates to the fluid balance error, which can be expressed in various ways:

• ERROR (NET1-NET2) The absolute error ${\displaystyle {\varepsilon }}$ .
• Error rel The relative error ${\displaystyle {\varepsilon }_{R}}$ :
${\displaystyle {\varepsilon }_{R}={\frac {\varepsilon }{(\left\vert {\pm }Q\right\vert +\left\vert {\Delta }S\right\vert )/2}}}$                          (Equation 5.14)
• Error percent The percent error ${\displaystyle {\varepsilon }_{P}}$ :
${\displaystyle {\varepsilon }_{P}={\frac {\left\vert {\varepsilon }\right\vert }{Q^{positive}}}100}$                          (Equation 5.15)

## Amount of water that has moved between domains

The final section of the fluid balance output gives the amount of water that has moved between the overland flow domain and the subsurface domain:

• Infilt The amount of water that has infiltrated the subsurface (i.e. moved from overland flow domain to subsurface domain).
• Exfilt The amount of water that has discharged from the subsurface (i.e. moved from the subsurface domain to the overland flow domain).