WATER AGE IN CS MODELS
Summary
Water Age in MIKE+ Collection System models is treated as a water quality component that increases with time and behaves like a conservative tracer affected by hydraulic conditions and flow dynamics. The model calculates water age based on transport processes such as advection and dispersion, reflecting the travel time of water through the network under both steady and dynamic flow conditions. In this article this Water Age Calculation Method is explained together with a simple example in which a one directional pipeline discharges a constant outflow demonstrating that water reaches 7 hours matching the travel time of water from the source to the demand point. The model's water age result furthers confirms physical consistency with analytical expectations.
Description:
In MIKE+ CS, Water Age [T] is modelled as a water quality component subject to transport processes in the network - advection and dispersion. At any location in the network, water age is calculated by incrementally increasing its current value by the elapsed time, i.e., by the actual simulation time step. Effectively, the network, water age behaves as a conservative tracer with a constant source term in every computational point and it changes dynamically based on system hydraulics, storage, flow reversals and mixing processes. Water Age is then a very dynamic result of the simulated flow conditions through the network and its initial values at the inflow boundaries. Under steady conditions, calculation results in steady water age values. This allows for a simple verification against hand water age calculation. For a single pipe, the computation of water age should be:
Ageout = Agein + L/v Where L is the pipe length and v is the mean velocity in the pipe.
Example
The best way to explain this computation is through a simple example. Consider a simple pipeline of 20000 feet long with a diameter of 4 feet, carrying water from external source (outlet node) up to the demand point, where 10 cubic feet per second are taken out constantly, see Figure 1. Water Age is defined as a WQ component “Age”. There are no user-specified initial conditions for this component thus the initial value of “Age” is set to zero throughout the models.
Fig. 1. Simple model setup of a long pipe, single outlet.
The model is run for 24 hours and the time series of “Age” in the model three nodes is presented, see Figure 2 below. The results show that a steady-state condition is reached after approximately 7 hours, at which point the water age at Node 1 stabilizes at about 25,177 s (≈ 7 h). From this moment onward, the longitudinal profile of Water Age exhibits a linear increase, starting from 0 s at the outlet node (the source) and reaching approximately 7 hours at the downstream demand node. This represents the travel time of a water parcel from the source to the point of withdrawal.
Fig. 2. Water age time series at the model nodes.
A hand calculation aids confirming this result. First calculate the pipe volume:
In terms of calculated time there is a slight discrepancy in the simulated results and the manual calculation expected. This difference can be attributed to the Preissmann slot applied during pressurized flowing conditions in 1D pipes which increased the numerical volume interpreted by MIKE 1D.
Conclusion
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