Pressure Related Demand

Hydraulic scenarios (e.g. PRV installation, Tank storage optimisation, pump optimisation) tested on calibrated networks often have a major impact on the pressure regimes and hence the demand. Therefore, simulations incorporating the InfoWorks WS pressure related demand (PRD) capability are used in order to take account of demand fluctuations and replace traditional network modelling techniques.

It is a known fact that local pressures have an influence on demands and losses in the network. Higher pressures lead to increased consumption (open tap use) and losses (bursts), and vice versa. This is particularly true for leakage losses, where a standard relationship has been established based on the measurements in several existing water supply systems.

The concepts of PRD means that modelled solutions are calculated in which local demands die away as local pressures tend towards zero. Often the pressure die-off effect above a user defined 'nominal' is ignored as the effect is felt to be negligible. Physically this model is much more representative of how water networks behave following changes to the networks controls.

• Reducing Leakage and Demand by pressure reduction
• Hydrant operation or exceptional flow effects on the water supply network
• Investigation of intermittent supplies and emergencies (e.g. pipe bursts)

Several equations have been derived within the industry to describe how pressure relates to leakage/consumption some of which are shown below based on a nominal pressure of 50m. Although InfoWorks doesn’t support the entry of equation you can calculate the curves externally and copy and paste the values into the user defined PRD curves.

InfoWorks has 6 inbuilt curves, 2 of which at anyone time can be applied to a network at any one time. A different curve may be assigned to those demand categories designated as leakage compared to those designated as consumption i.e. those that do not have the leakage check box ticked in the demand diagrams.

Figure 1 - Demand / Pressure factors

1. Run base network model normally your calibrated model. These results can be used for comparison with PRD runs and to update network’s nominal pressures.
2. On a checked out network define your consumption and leakage demand/pressure relationships. Selecting the PRD curve tab on the nodes grid view can do this.

Figure 2 -PRD Curves Tab on Nodes Grid

To create a new curve, type in the curve ID and then select the row and go to properties. This provides you with a dialogue box in which to enter your derived demand and pressure ratios. Ticking the power law check box and entering a value (research shows values are between 0.5 and 1.5) will produce a curve based on the power law.

Figure 3 - PRD Curve Properties

1. Now specify the value of nominal pressure for each node with a demand.
   • This can be done manually by entering a value for nominal pressure at each node.
   • Checking out the base network and updating nominal pressures from your base simulation, via Network > Update > Nominal pressures and selecting a simulation.

Figure 4 - Nominal pressure at nodes

1. Modify the checked out network and if required the control to represent the new system requirements e.g. new pump or valving.
2. Set up the demand diagram that will be used in the run so that the demand categories show the correct % to be applied as pressure related. It is suggested that all leakage be applied as 100% PRD.

Figure 5 - PRD and leakage at demand diagrams

1. Ensure that all demand categories that require the application of the leakage Q/P curve rather than consumption have the leakage check box ticked in the demand diagram.
2. Set up a simulation incorporating the network with nominal pressure assigned and demand diagram with leakage and % PRD set.
   • Ensure that the PRD check box is ticked.
   • Define which PRD curves you wish to be used for both consumption and leakage by selecting the Curves button.

Figure 6 - PRD Run dialogue

1. Select "simulation options" - set the required check boxes
   • Pressure related demand % - overrides any % PRD values set for demand diagrams categories.
   • Use iterative pressure related demand - overrides the convention of using the pressure from the previous time step to calculate the demand, instead it forces IWs to use pressures for the current time step via an iterative process.

See calculations section for further information

Figure 7 - PRD Simulation options

1. Select run - Run the simulation

The simulation options dialogue allows the selection of iterative PRD that will override the convention of using the pressure from the previous time step to calculate the demand.

InfoWorks WS has two default built-in functions (un-dimensional), one for leakage and the other for consumption that take into account the effects of service pressure in the following way:

Actual Consumption i.e. the consumption that will be applied to the node during the simulation:

Actual losses i.e. the leakage losses that will be applied to the node during the simulation:

Here Q_C and Q_Ldenote the consumption and losses respectively, while F_Cand F_L are the corresponding built-in functions that apply the factoring to the nominal demand. %_Drepresents the percentage of nominal demand that will be applied as pressure related. The pressure, P, is taken from the previous time step unless the iterative option is selected.

PRD factor is applied to % of nodal Consumption/Leakage flow e.g. assume nodal demand 100 l/s, PRD dependant is 60% (40% non PRD)

Q_PRD = 100 * 0.6 * PRD_Factor

Therefore resulting nodal demand is

Q_C = (100*0.4) + Q_PRD

Figure 2 shows the effect of having the % set to 100 and 50 percent for a consumption category in the demand diagrams.

Figure 8 - % PRD

Figure 9 - Network

Figure 9 shows a simple network with a fixed head source with a head of 100m AOD supplying two nodes one with leakage applied and the other with consumption.

Figure 10 shows predicted results for a simple case using conventional modelling techniques without using pressure related demand. The available pressure was fixed at 100m at a source node “FH100” and demand was increased from 1L/s at time 00:00 to 100L/s at time 24:00 at downstream nodes "Leakage" and "Consumption". The interconnecting links were 1000m in length with internal diameter 150mm and a low hydraulic roughness.

The model can meet the steadily increasing demand but only by simulating an unrealistic circumstance where available pressure at demand node “Consumption” and leakage drops to –43.25m below atmospheric pressure. Physically pressure cannot drop below absolute vacuum, but by ignoring this, the modeller is provided with very useful results to see where model data is flawed, and/or unrealistic operating conditions are being applied to the model.

Figure 10 - conventional modelling negative pressures

For pressure dependent demand analysis, a nominal pressure is required above which demand can be set to be independent of pressure, this is usually set for every node independently, as each node in the network has a different nominal pressure. At present the pressure dependent demand follows this equation:

Where:

Q_actual = demand with PRD applied

Q_nominal = normal demand

F is a user definable P-Q curve

The pressure, P, is taken by default taken from the previous time step. InfoWorks allows for the % of PRD to be varied by demand category via the demand diagrams, in this instance a value of 100% was used.

Figure 11 shows an example where the nominal pressure has been set to 50m, from this we can see that at first the rise in demand and fall in pressure follows the same trend as that for the traditional non-pressure dependent demand as shown in figure 10.

Figure 11 – Progressive increase in downstream demand from fixed head

However when the predicted pressure drops below 50m, the pressure-dependent demand functionality comes into effect. Growth in demand is subsequently impeded and the drop in pressure also slows down. If the analysis was extended it would be found that the demand wound tend towards a maximum as the predicted pressure tends to zero.

InfoWorks supplies 2 options that allow you to influence the way pressure related demand is calculated based on the ratio between simulated and nominal; pressure, these are:

• Increase pressure related demand on increase pressure
• Increase pressure related leakage on increase pressure
• Decrease pressure related demand on decreased pressure
• Decrease pressure related leakage on decreased pressure

Figure 12 demonstrates the application of these options on a consumption category.

The yellow line represents the effects when both Increase pressure related demand on increase pressure and Decrease pressure related demand on decreased pressure are checked.

The green line demonstrates the effect of when only Increase pressure related demand on increase pressure is switched on.

The blue line demonstrates the effect of when only Decrease pressure related demand on decreased pressure is switched on.

Figure 12 - PRD Application

Figure 13 demonstrates the effects of the 2 different PRD curves applied to nodes that are fed from the same source and co-located. Note the differences in the 2 curves with demand applied as leakage being influenced differently to that applied as consumption. NB 2 different factors are applied depending on whether the demand category is designated as leakage or not.

Figure 13 - Leakage and consumption application

1. Leakage Control Policy and Practice (Report 26), Standing Technical Committee reports Number 26, DWI0190. Department of the Environment / National Water Council, July 1980.
2. UK Water Industry: Managing Leakage, National Leakage Initiative, October 1994.

Article © Wallingford Software 2005