PEC
Predict concentration in an ideal constant-volume mixed receiving reservoir with fixed input, outflow and first-order degradation; not a site-specific fate assessment.
Description
Predict a completely mixed reservoir concentration trajectory under constant loading and first-order loss.
A predicted environmental concentration, or PEC, is a model estimate for a defined scenario. A completely mixed reservoir model assumes that concentration is uniform throughout the volume, so outflow carries material at the same concentration as the reservoir.1
This tool balances a constant mass loading against outflow and first-order degradation in a fixed volume. It returns concentrations in mg/L at requested times in days and the steady-state concentration reached under unchanged inputs.
Loading is mg/day, reservoir volume is L, outflow is L/day, and degradation is a rate in 1/day. The fixed-volume assumption requires a water balance; any contaminant carried by replacement inflow must be accounted for in the supplied mass loading.
When to use PEC
Use it for a transparent one-reservoir scenario or to compare how loading, turnover, and degradation affect approach to steady state.
How to use PEC and interpret its calculation
- Enter nonnegative initialConcentrationMgPerLiter and inputMassRateMgPerDay, and positive reservoirVolumeLiters.
- Enter nonnegative outflowLitersPerDay and degradationPerDay, with at least one producing a positive total loss rate.
- Enter a nonempty timesDays list of nonnegative times and run the model. Read predictedConcentrationsMgPerLiter in the same order and compare with steadyStateConcentrationMgPerLiter.
k = Q/V + kd; Css = loading/(k × V); C(t) = Css + [C(0) − Css] × exp(−k × t) Q is outflow, V volume, and kd degradation rate. The analytical trajectory solves V × dC/dt = loading − (Q + kd × V) × C.
Each requested time is evaluated independently, so unsorted and repeated times are allowed. The implementation requires positive total loss and does not implement the no-loss accumulation case.
{
"input": {
"initialConcentrationMgPerLiter": 0,
"inputMassRateMgPerDay": 10,
"reservoirVolumeLiters": 100,
"outflowLitersPerDay": 10,
"degradationPerDay": 0.1,
"timesDays": [
0,
1,
2
]
},
"output": {
"predictedConcentrationsMgPerLiter": [
0,
0.09063462346100909,
0.16483997698218034
],
"steadyStateConcentrationMgPerLiter": 0.5
}
}If initial concentration equals steady state, the trajectory stays constant. Zero loading gives decay toward zero. Either outflow or degradation can be zero; both zero are rejected, even for a no-loading scenario.
Limitations and assumptions
The model does not account for incomplete mixing, changing volume, variable loading, sediment exchange, sorption, multiple compartments, or changing degradation. No measured environmental data are fitted.
The steady state is a conditional limit under constant inputs, not a concentration standard or proof of ecological acceptability. Exposure and effect comparisons require compatible scenarios and endpoints.
Alternative or Complementary methods
Use more detailed fate modeling when spatial variation or changing water balance matters. An SSD quantile can provide a separately derived effect-concentration summary; an ingestion-dose calculation converts a suitable exposure concentration into an assumed absorbed daily dose.
References
-
Mechanistic Modeling — U.S. Environmental Protection Agency
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