Water storage tanks: the science of mixing and improving water quality

Water storage tanks and reservoirs are a critical component of distribution systems, yet they can pose a significant challenge for water utilities as they often have a negative impact on water quality, due to low turnover or inadequate mixing resulting in short-circuiting.

In water distribution networks, reservoirs are required for flow equalisation, to sustain pressure, to hold several days of storage for redundancy, and provide fire and emergency storage. In order to achieve these goals, reservoirs need to have adequate storage volume based on worst-case hydraulic scenarios and also must be designed to supply the system allowing for future community growth. Some of these design goals are contrasted by what is generally required to maintain safe drinking water.

Common problems in storage tanks and reservoirs are the loss of disinfectant residual, bacteria regrowth, spikes in disinfection by-products (DBPs) and nitrification (chloramines), resulting from hydraulic short-circuiting, poor mixing and circulation, poor turnover and excessive retention time. Many of these water quality problems can be specifically attributed to the location and orientation of the inlet and outlet piping.

In order to minimise water age, tanks must be turned over — that is, water volume must be exchanged to and from the tank by fluctuating tank levels. The required amount of turnover varies depending on the system, but a fairly common turnover goal is 3–5 days, or 20–33% daily fluctuation. However, tanks can have a significant localised increase in water age when they short-circuit and are not completely mixed, even if they are fluctuated 20–33%. Often the increased water age and all associated water quality problems are specifically attributed to the inlet and outlet pipes.

There are three primary design goals to preserve storage tank water quality:

1. Design the piping or mixing system to separate the inlet and outlet to eliminate short-circuiting.
2. Design the mixing system to achieve complete mixing during fill cycles.
3. Fluctuate tank levels to exchange water volume, or turnover the tank, to minimise water age.

The first two are the responsibility of the mixing system designer but they are hydraulically linked with the third. So, the designer must not only understand circulation patterns and mixing characteristics, but must also know how to design based on the tank turnover.

Short-circuiting

The simplistic description of short-circuiting is the last water that entered the tank is the first water drawn from the tank (last in, first out). Water quality problems develop for two reasons:

1. The entire tank volume is not completely mixed.
2. The oldest water cannot be drawn from the tank due to the location of the outlet pipe.

Short-circuiting is often not problematic over one or several days, but it is the consecutive daily fill and draw cycles with persistent short-circuiting that result in a localised increase in water age — resulting in the development of water quality problems such as loss of residual, bacterial regrowth, spikes in DBPs, elevated heterotrophic plate count (HPC) bacteria, nitrification and variance in dissolved oxygen and pH.

In some cases, short-circuiting can be mitigated by separating inlet and outlet pipes, but a solid understanding of the mixing and circulation patterns within the tank is required in order to know where to locate the outlet pipe. It is often incorrect to assume the best place for the outlet pipe is as far apart from the inlet pipe as possible. For example, Figure 1 is a CFD model of a circular reservoir with a horizontal inlet pipe through the wall of the tank, discharging horizontally towards the centre of the tank. Conventional wisdom would say to locate the outlet pipe on the opposite side of the tank, diametrically opposed to the inlet pipe, to get them as far apart as possible. However, new water would reach this location shortly after the fill cycle starts. There are actually two areas in the tank that mix last — the dark blue zones on each side of the centreline of the tank, in the centre of the semicircular circulation patterns. These areas can get mixed provided the fill cycles are long enough, but if they are not, the proper outlet design would be to locate an outlet pipe in each of those two locations, not a single outlet pipe on the opposite side of the tank from the inlet pipe. What complicates matters is that once there are temperature differences between the inlet water and tank water, the circulation patterns can be completely different and the dead zones are often in different locations.

Figure 1: CFD model of circular reservoir showing velocity magnitude and vectors. For a larger image click here.

In the past, much of the focus has been on separating the inlet and outlet pipes, which is a very good design goal. However, the focus needs to be on making sure the tank is completely mixed.

Mixing

Mixing in a water tank is a function of momentum of the inlet flow during the fill cycles. The turbulent jet of the inlet flow creates a velocity discontinuity with the water already in the tank. This creates turbulence and rapid mixing as the jet moves away from the port. Figure 2 shows a 3D laser-induced fluorescence (3DLIF) image of a submerged jet¹. Due to conservation of momentum from the enclosed water volume, circulation patterns develop through the entire tank volume. The circulation patterns are three-dimensional and quite complex. In the circular reservoir of Figure 1 the circulation patterns persist after the fill cycle has ended, often for many hours. During the fill cycle, new water is dispersed through the entire water volume via the circulation patterns provided that the fill cycle is long enough and temperature differences between inlet water and tank water do not produce circulation patterns that inhibit mixing.

Figure 2: 3DLIF image of jet mixing.

Scale model experiments on various styles of storage tanks have been conducted that yielded a theoretical mixing time equation^2,3. The degree of mixing is defined by the ratio of the standard deviation of the tracer concentrations to their mean value. This ratio, the coefficient of variation (COV), should approach zero as the tank becomes fully mixed. Full mixing is defined as the time for the COV to fall to 0.05 (5%) or 0.10 (10%) depending on which experiments are referenced. The empirical equation for mixing time, τ_m, is defined as:

where:

K′ is an experimental constant ≈ 10.2 for a single inlet with no temperature difference between inlet and tank water
V is the volume of the tank equal to (π/4)D²H where D is the tank diameter, and H is the water depth
M is the momentum flux of the inflowing jet equal to u_jQ where u_j is the inflow velocity and Q = (π/4)Du_j is the inflow rate

Designers can calculate how long the fill cycle needs to be to achieve complete mixing. In addition, the amount of drawdown can be calculated that will allow sufficient fill time on subsequent fill cycles to achieve complete mixing. This is what links the mixing system design with the operation and fluctuation of the tank. Achieving complete mixing yields a homogenous solution throughout the tank water volume and this eliminates any thermal, chemical and microbiological stratification, thereby preserving water quality. However, the above analysis is only one step in a proper design. The effect of potential temperature differences between inlet water and tank water needs to be addressed.

Effect of temperature differences on mixing

When inlet and tank water temperatures differ, buoyant jets are formed and the circulation patterns can be significantly altered. This effect can be observed year round, but is mostly problematic in summer when inlet water is colder than the stored water. Colder inlet water is denser, heavier and therefore is negatively buoyant — it sinks. Figure 3 shows a CFD model of the fill cycle of a standpipe with the inlet pipe through the floor⁴. The inlet water is colder and the jet does not have enough momentum to overcome the negative buoyancy so the jet stalls, reverses direction and falls back to the floor. There is no mixing above the height where the jet stalls and stratification develops. In this case, it is about 40% of the water depth. The water in the bottom 40% has good water quality because it is well mixed. However, the top 60% of the water volume is not mixed. With each consecutive fill and draw cycle, the localised water age in the top part of the tank continually increases and water quality problems develop. Note that sampling outside the tank will never indicate there is a water quality problem until, for example, there is a large drawdown, a fire or a line-break. Even autumn and winter turnover, where colder ambient temperatures cool the water in the top of the tank, have also been the cause of poor water quality in the distribution system as the cooler water in the top of the tank falls to the bottom and is drawn out into the distribution system.

Figure 3: CFD model of standpipe with colder inlet water (for a larger image click here).

Stratification can develop in all styles of storage tanks, not just standpipes. Once the jet hits the floor, all vertical momentum is lost and stratification develops. Note that the outlet pipe, regardless of its location along the bottom of a tank, would not prevent stratification from developing in this tank. Therefore, emphasis needs to be placed on designing the piping/mixing system to achieve complete mixing, not just a simple inlet and outlet separation.

Multiple inlet jets

The effect of multiple inlet ports on mixing has been studied in various tank geometries⁵. Experiments showed that distributing the inlet through multiple inlet ports results in significantly faster mixing — up to 50% faster compared to a single inlet pipe. It is analogous to large public swimming pools that have inlet ports spaced 3–6 m around the perimeter of the pool. The design intent of using multiple inlet ports in pools is for the rapid dispersion of rechlorinated water, and to eliminate dead zones.

In addition to faster mixing, experiments also showed that multiple ports were able to completely mix tanks when inlet water is colder than tank water, as compared with a single inlet that resulted in stratification and an unmixed tank. Critical steps in designing the inlet ports are:

1. Determine the size, spacing, elevation and discharge angles to develop sufficient jet velocity and momentum to mix the tank based on the tank turnover.
2. Calculate the jet rise height of the negatively buoyant jets to ensure that the jets hit the water surface as complete mixing can only be achieved if the jets hit the water surface.

Duckbill valve style mixing systems are often utilised in all styles of storage tanks. Duckbill valves are inherently a variable orifice — they progressively open and close with the increase and decrease in flow rate. This characteristic produces a non-linear jet velocity profile that yields higher jet velocity at lower flows, which results in faster mixing compared to fixed-diameter pipes.

Tank-specific design

Given the many different tank styles and geometries, the inlet/outlet piping or mixing system must be specifically modelled and designed for each tank style. A common design for a circular reservoir, for example, is almost always not a good design for a standpipe. The same design process holds for every tank style, which is to determine the size, spacing, elevation and discharge angles to develop sufficient velocity to mix the tank based on the tank turnover and to calculate the jet rise height of the negatively buoyant jets.

Active mixing

Properly designed passive mixing systems have been extensively CFD and scale modelled and utilised for many years and have been proven effective through owner-conducted field sampling to achieve complete mixing, eliminate stratification and maintain water quality.

There are some cases where tanks have minimal fluctuation or do not fluctuate at all. A passive mixing system can be turned into an active mixing system by using a recirculation pump, which pulls water out of the tank and discharges it back into the tank via the inlet pipe or mixing system. Note, however, that mixing is only one component of maintaining storage tank water quality — volume must be exchanged in order to minimise water age. Another role of the pump that can be considered is to induce a forced drawdown whereby the pump discharges tank water into the distribution system, rather than back into the tank. This accomplishes two things — the water volume is exchanged and water age is reduced, and the tank can be passively mixed when the recirculation pump is turned off and the tank refills. The applicability of these concepts would need to be evaluated on a tank-by-tank basis.

References

1. Roberts P J W and Tian X 2002, ‘Application of Three-Dimensional Laser-Induced Fluorescence to Stratified Turbulent Mixing Processes’, Hydraulic Measurements & Experimental Methods Conference 2002, Estes Park, Colorado.
2. Rossman, L A and Grayman W M 1999, ‘Scale-model studies of mixing in drinking water storage tanks’, Journal of Environmental Engineering, ASCE, 125(8), pp755-761.
3. Roberts P J W, Tian X, Sotiropoulos F and Duer M 2006, ‘Physical Modeling of Mixing in Water Storage Tanks Final Report’, School of Civil Engineering, Georgia Institute of Technology, Prepared for AWWA Research Foundation.
4. Duer M J 2003, ‘Use of CFD to Analyze the Effects of Buoyant Inlet Jets on Mixing in Standpipes’, Proc. 2003 AWWA Annual Conference, Anaheim, CA.
5. Roberts et. al. 2006, op. cit.

Image source: ©stock.adobe.com/Direk Takmatcha