Premises Plumbing
We have developed a simulator for accounting age of exposure of water (or solutes) to either individual pipe sections or entire networks in premises plumbing. The schematic in Figure 1 shows the as-builts for the PACCAR building on the WSU campus. The kitchen faucets subnetwork is shown with color. This subnetwork was selected for testing in the demo, described below.
The simulator is a particle-tracking code written in Python that is given the as-built plumbing data for a given building, and a sequence of flows from various outlets over a given time interval.
The program can simulate ages given either a specified deterministic series of flows-at-taps over time or a statistical description of mean and variance of flow events. The code handles flows that overlap in time, by identifying the subnetwork of pipes involved in any combination of active outlets and solving the transport problem for each time step (down to one second). Reverse or circular flows are not accommodated. Transport may be purely advective, advective-diffusive, or advective-dispersive, including pre-asymptotic (make this yellow thing clickable to open the Pre-asymptotic dispersion page). dispersion. Age may be used to estimate relative residual free chloring disinfectant (relative to the chlorine concentration of the water entering the building), or the user can also simulate free chlorine reactive transport explicitly.
Demo Application
Here is a demonstration application of the model to free chlorine (disinfectant) test data from June of 2020 at WSU’s PACCAR building. In that experiment we sequentially measured free chlorine from the 4th floor kitchen sink faucet while flushing 1, 2, 4, 8,…, 256 liters of water. Then we repeated the procedure on the 3rd floor, and again 4 days later on the 2nd floor. The chlorine data for all three floors are shown as a function of flushed water volume in Figure 2. The concentrations all reach the same plateau values consistent with the chlorine concentration in the building main source water; thus the differences in time to reach that plateau are hypothesized as due to reaction with pipe wall biofilm, which increases with floor. As such these data can be used to test the hypothesis that the decay of free chlorine is proportional to solute exposure time to pipe specific surface area.
To use the model-calculated relative ages to reflect chlorine decay extent we adopted a hypothetical normalized-exponential decay model. If we assume the chlorine decay occurs uniformly within the pipe network then chlorine concentration at any given kitchen sink at any given age should be proportional to the age of the water at the time of effluence. This suggests a decay model of the form c(a) = co exp(-k a) where c is the chlorine concentration in the effluent at age a, co is the chlorine concentration just upstream of the root (blue, in Figure 2) pipe, and k is an effective decay rate. Knowing neither the upstream chlorine concentration nor the absolute ages in the pipes, we assign co to be the maximum value of chlorine concentration, 0.12mg/L as an estimate of that chlorine value present upstream of the root pipe, and we replace a in the argument of the exponential to be the normalized relative age, (a – amin)/amin. This qualitative model leads to a range in chlorine concentration between near zero, when the age is much larger than the minimum age amin, and unity, when the age is equal to the minimum age observed. This ignores decay during flowing intervals and ascribes decay as proportional to ages greater than the minimum age. The resulting prediction of chlorine from this model together with the measured data are shown in Figure 10, that includes a blow-up of the kitchen subnetwork with color-coding for convenience. Also overlain are the color codes for the pipes from which the flushed water originated, calculated from the known volumes of each pipe segment.
Comparison between the measured and age-simulated chlorine values shows the failure of the age model adopted. In particular the pipe network delivers waters from intermediate ages, originating from intermediate pipe segments within the network, which have appreciable chlorine concentrations. This suggests 1. that whatever the age of water in the pipe network prior to the experiment, it was insufficient to remove all or most of the chlorine in the water, and 2. that chlorine decay is not uniform in the pipe network. If chlorine decay were uniform in the pipe network then the chlorine values for effluent prior to the young water breakthrough would be more or less constant. One exception to this would occur in the case where the water was actually being used at frequencies on par with the characteristic decay time in the network, so that initial ages could be nonuniform and increasing along the pipe flow path; however, given the pandemic conditions (in June 2020 the building was visited only by “essential staff” who mainly reside on the 1st floor), this is unlikely. Furthermore the chlorine increase with distance upstream was observed to have similar trends on all three floors.
The implications of these results reinforce the hypotheses that a significant fraction of disinfectant decay in potable water distribution systems occurs within premises plumbing and that the decay rate is nonuniform and increasing with proximity to outlets. This is supported even in the context of a young building such as the PACCAR building that is ~ 7 years old. Note that the chlorine values in Figure 10 increase from low values in the appurtenance plumbing near the faucet (gray) building entry line close to the water main (to blue) pipe segments. All of the pipe segments in this color range are 2” diameter PEX pipes except for the gray-coded pipes that have smaller diameters and are of copper. Complicating this picture is the fact that the average flow rate floor-to-floor is not constant and the lower floor sections experience more frequent flows than higher floors. A more rigorous flush test with a certain pre-flush stagnation period and multiple sampling frequencies with incremental flushes corresponding to volumes of upstream pipe segments will help unravel the nature of the reactive transport in premises plumbing.
