Water is scarce in many parts of the world, one way to reduce water usage is to collect the rain water runoff, typically from your roof. This rain water collecting is rain water harvesting and in this post a simple rain water harvesting model is created to estimate the financial and ecological benefits of installing one.
How is rain water harvesting done?
A large water tank is used to collect the water that comes out of the roof drains and then this water can be used in multiple ways. The water can be used for watering the garden and / or flushing toilets, or for all the water needs of the dwelling.
What is needed in this example?
In this example the harvested water is for watering the garden, so this system is simpler than systems that make use of the water in the house.
List of parts:
- large water tank
- water pump to get water pressure
- a solid base, if one does not exist then a concrete slab could be laid
- leaf capturing filter
- first flush water valve; this diverts the initial rain water that typically contains lots of sand down the drain
- plumbing fittings
- a tap
The model
The model is presented in Figure 1.
Figure 1. A rain watering harvesting model
The model in Figure 1 is a simple rain water harvesting system; more detail about each component follows.
The dailyRain component
The dailyRain component outputs the amount of rain per day. This data is stored in a table (the data for this was obtained from the climate research centre CSAG).
Modelling the rain water capture
The amount of rainfall is used to estimate the roof runoff as follows:
Qt = C·It·A
where:
Qt is the roof runoff at time t
It is the amount of rain fall at time t
A is the roof top area
C is the runoff coefficient which is typically around 0.82 for tiles; for more details see Simulation-based Spatial System for Rainwater Harvesting Systems In the Sustainable Campus Project. This is implemented in the roofCapture component.
The water usage
The main purpose of the water in this example is for watering grass. The weekly estimate for the water required is 25mm per week per 1m2 as taken from the UK lawn care association website. The amount of rain during the week is subtracted from the water usage for that week. This is implemented in the waterUsage component.
The waterSource component
The waterSource component models the tank usage and tap usage. The volume of water in the tank is calculated by integrating the water flow, that is the amount of rain collected off the roof less the amount of water used to water the garden. The tank limits are taken into account and when the tank is empty the water used to water the grass comes from the tap. The amount of water used from the tap, from the tank, and in total is calculated.
Water usage cost
The cost of the water is calculated using the Cape Town Municipalities water prices. This pricing works on a tiered pricing system where the first n kl is at the lowest price, then the next m kl is at a higher price and so on. The Cape Town Municipality guidelines for pricing are here; this is not exactly what was used in the model, this was estimated from my water utility bills. This is implemented in the waterUsageCost component.
The overall cost over time
The overall cost over time is estimated as the installation cost and the maintenance and running costs less the amount of money saved by using less tap water.
The installation costs include the price of the tank, which was taken from the hardware store Builders, an estimate of the concrete slab that may need to be installed is taken from the diameter of the tank being used. Then the costs of the first flush filter and the filter and the pump and fittings were also taken from Builders.
The installation costs include an estimate of the professional installation costs and the maintenance assumes that the pump will need to be replaced every 10 years and that the water tank will last 20 years.
Model setup
The model has been setup to correspond to a water harvesting system that could be installed in my house to be used to water the garden. The roof area is 32m2 and the area of the grass is 50m2 .
The detailed pricing of the different components is not included here however they can be found in the model that can be obtained at the end of this post.
The Results
Figure 2 presents the results of simulating the model with a 2.4 kl tank.
Figure 2. Results of simulating the rainwater harvesting model with a 2.4kl tank
In the results in Figure 2 it can be seen that the amount of water used from the tank and the amount of water used from the tap is approximately equal, this means that the tap water usage was halved by using rain water harvesting.
The pay back time was 12 years for a professional installation and around 6 years when installed as DIY.
The tank is often empty during the dry summer periods.
Running the simulation with different tank sizes
The model was also used to check the effect of different tank sizes. To make it easy to perform this parameter sweep the details of the tanks were stored in records and then a list of tanks was created in the model with an index which could be altered to change which tank is used as in Figure 3.
Figure 3. Modelica code used to select the tank
The Dymola Sweep Parameter feature (see Section 7.5 of the Dymola Full User Manual) was used to run the simulation with 6 different tank sizes by altering the indexToTank parameter (note that Advanced.Translation.SmartSimulateExtended=true had to be set to be able to modify indexToTank). The results of the simulation with different tank sizes can be seen in Figure 4.
Figure 4. Comparison of water saved and cost over time for a number of different tank sizes that were professionally installed
From the top plot in Figure 4 it can be seen that with larger tank sizes the amount of tap water saved increases as more tank water is being used.
The largest amount of savings over the 20 year lifespan can be expected with the largest tank size, and with the professional installation the shortest payback time is with the largest tank in around 11.5 years. With a DIY installation the payback time is shorter with the smaller tank sizes (these results are not shown).
Conclusions
It is estimated that installing a rain water harvesting system can reduce the amount of water used in the garden by over half in this example. The payback period for the system is long, over 10 years, however if the installation is done by yourself this time period can be significantly reduced. The total money saved on watering the garden over the lifetime of the system increases with the larger tank sizes.
Note that the model is simple; this is partially because the amount of time to work on this was limited and improving the accuracy is time consuming and is not expected to affect the overall trends seen from this simple test. Possibly this model will be improved in the future to see how the results of a more accurate model would differ.
This simple system has a number of features that could be improved:
- the water usage model is very basic and should include effects such as sun exposure, temperature, soil dampness and evaporation
- roof wetting and first flush effects are ignored
- the water usage costs is an estimate and does not take into account how the price of water will vary over time
- the installation costs are basic and a more thorough investigation would give more accurate results
- the maintenance and running costs are poorly estimated in this example
- calculate how high the tank would need to be mounted so that no pump is required
One point to mention is that it is cheaper to put in fake grass and water-wise plants.
The Modelica model can be obtained here.
Written by: Garron Fish – Chief Engineer
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