# Modeling Fixed Inflow from a Marginal Source

 Product(s): WaterGEMS, WaterCAD Version(s): 10..XX.XX.XX, 08.11.XX.XX Area: Modeling

# Background

A situation that arises, especially in a developing nation, where the source flow is steady but is sometimes inadequate and there is limited storage capacity in the distribution system. The source can be a stream, a spring or a small treatment plant but for now, assume that the flow is steady over a day.

Even though on average, the source flow is adequate or close to adequate, there may be times when demand exceeds supply such that the system is in failure or times when available supply exceeds demand such that all tanks are full. This can result in cases where the model will give results which may look odd if a user isn’t ready for them.

Note: for help on modeling an intermittent water supply (a slightly different case), see this article: Modeling intermittent water supply

# Modeling a Limited Source or Storage

There are two ways of modeling a limited source or storage:

1. Source as negative demand or

2. Flow control valve to limit source flow. Each is explained below.

### Approach 1. Source as negative demand

Such a system is shown below:

In this case:

The source flow (node in lower-left corner) is 160 gpm modeled as a negative demand (a pattern could be assigned)
The average demand is 150 gpm but it varies widely over the day
The tank total volume is 24,000 gal, such that it may fill completely during off peak times and totally drains during peak time.

There are actually several cases that must be considered:

1. Tank is neither completely full nor empty

a. If demand exceeds supply (i.e. > 160), tank is draining
b. If supply exceeds demand (i.e. < 160), tank is filling

The results will be what one normally expects from WaterCAD/WaterGEMS and the tank levels will fluctuate within limits.

2. Tank is completely full which may occur at night. In this case inflow exceeds demand and there is no place for the water to go. In reality, water from the source would simply spill into the local drainageway. This is the purpose of pipe P-5 and reservoir DRAIN. P-4 has a check valve to prevent the stream water from coming back into the system.  The reservoir node is needed because when the tank is off line, the network needs a hydraulic grade value or it will not calculate. The HGL at the reservoir should correspond to the HGL at the source.

As soon as the demand exceeds the source flow, the tank will begin to drain and the system will be back in case 1.

3. Tank is completely empty which may occur during peak times.  As soon as the demand drops below the supply flow, the tank will begin to fill and the system will be back in case 1 again.

However, the problem occurs when the tank is empty and the demand exceeds inflow supply. What will happen in a real system is that the tank system will depressurize and the full demand will not be met.

Realize that during these times, pressures will be inadequate and the model will not converge. Any results during this time will be questionable. This is a situation that the engineer or operator wants to avoid. The graph below shows the tank in such a situation. During hours 22.5 to 24, the tank is empty (HGL = 90) and model results model may not be accurate. The user needs to realize that the system has failed and pipes may not be flowing full even though some water may be supplied.

Results at user/demand:

### Approach 2. Flow control valve (FCV) to simulate limited source

In this approach the HGL is set by a reservoir node upstream of a FCV which limits the flow (to 160 gpm in this example). The model looks like the figure below with the same demand pattern and tank properties.

There are three cases here:

1. Tank is neither completely full nor empty

a. If demand exceeds supply (i.e. > 160), tank is draining

b. If supply exceeds demand (i.e. < 160), tank is filling

2. Tank is completely full which may occur at night. The model accurately calculates flow and head but the user notifications contain a collection of warnings “FCV cannot deliver flow” which is not applicable in this case.

3. Tank is completely empty which may occur during peak times.  As soon as the demand drops below the supply flow, the tank will begin to fill and the system will be back in case 1 again.

However, the problem occurs when the tank is empty and the demand exceeds inflow supply. What will happen in a real system is that the tank system will depressurize and the full demand will not be met. To simulate that condition, the demand at the users much be modeled as a pressure dependent demand (PDD) and the PDD function. The key with this approach is that the PDD function coupled with demand must result in total demand less than the FCV setting whenever the tank is completely empty. In this example, the following PDD function is used.

Which results in only a slight reduction in demand during peak demand times for this model. This may not always be the case.

With PDD, the tank can still be modeled correctly.

# Summary

When tanks become completely full or empty, the model may not be correct. For systems when the tanks can frequently become completely full, approach 1 which uses the drain line is the best approach while for tanks that frequently become empty, the PDD approach is more appropriate.