Fate and Transport Model

The fate and transport model describes the contaminant transport from the point of release in the aquifer to the receptor. The model consists of three sub-models. The first sub-model follows the advective-dispersive flow and transport formulation. The second sub-model accounts for degradation and attenuation. The third sub-model accounts for the aggregation of all mass discharges of one contaminant typej.

Module 5: Transport Model

The transport model calculates the impact (=amount of mass discharge) to the drinking wa-ter well, depending on the massm₀ that has been released to the aquifer after an eventF

has occurred (see Fig. 7.1, module 1-4).

Practically, all methods solving the advection dispersion equation can be used to get the in-dividual mass discharges at the well. Nevertheless, methods that calculate mass discharge-based impact of multiple hazards within the drinking water catchment can easily lead to high computational demands, especially when multiple transport simulations with contam-inants injected at each possible spill locationx_h within the entire catchment have to be per-formed. To decrease computational costs, smart simulation concepts are needed. Here, I will use the tool set as already introduced for the VIP framework (see Section 4.3). In spe-cific, the application of STORM in Chapter 9 will use MODFLOW (e.g., Harbaugh et al., 2000) and PEST (e.g., Doherty and Hunt, 2010). The mathematical description for modeling and simulating flow and transport in a Bayesian geostatistical framework has been given in Chapter 5.

Following the same approach as Einarson and Mackay (2001), background concentration valuesc_h,j of contaminant jof hazardh in the well can be estimated for steady-state flow fields with a constant mass release (continuous plume) as

c_h,j = m˙_0,h,j

Q_P , (7.6)

with Q_P being the pumping rate, andm˙_0,h,j being the mass release rate for hazard hand contaminantj.

The effect of longitudinal dispersion is neglected in case of background concentration as transport in the aquifer is assumed to be at steady-state. Transverse dispersion only plays a role close the bounding streamlines. The background concentration, here simultaneously used for continuous sources, can be added to the overall breakthrough curvec_{T ot,j} of con-taminantj.

Module 6: Fate Model

It is possible to account for linear sorption and first-order degradation processes in a post-processing to module 5. A full mathematical description has been provided in Section 5.6.

Module 7: Space and Time Convolution

The drinking water well acts as an integral receptor for all contaminants that have been re-leased on the catchment level at different locations and time scales (see Fig. 7.5). All hazards h = 1, . . . , n_h are mapped to individual location x_h in the catchment. Mass release events (see Fig. 7.5, stronger coloring) are mapped over time, showing multiple failure events over simulation time (see Hazard 2 in Fig. 7.5). The uncertainty in risk source failure and thus mass release is resolved via Monte Carlo simulation of possible failure and release histories in the catchment.

Fig. 7.6 illustrates temporal, spatial and frequency aspects within a single random release history, leading to the cumulative concentration historyc_{T ot,j}in the well of the three hazards (green line). In the given example (taken from Chapter 10), these three hazardsh= 7, . . . , 9

Figure 7.5.: Conceptual visualization of mass-flux aggregation (module 6) due to event oc-currences (module 1) of spatially-distributed hazards within the whole catch-ment and temporal offsets, showing potential hazardous events by highlighted areas (stronger coloring).

are of the same contaminant typej = 3. Hazard 7 is an areal hazard source type, discretized inl= 1, . . . ,9point sources.

None of the individual hazards within the presented time period would exceed a critical concentration level withc_crit,1 > 3.5·10⁻⁶. However, there are two important aspects for aggregation. First, risk managers often deem the situation to be safe, when individual haz-ards are treated independently of each other. In fact, only considering the breakthrough curves of hazard 6, 7 and 8 in a cumulative setting leads to an overall failure. Second, con-sidering the frequency of hazard failure also adds to the cumulative contaminant impact (tsim >1400d). Aggregation of single events may not lead to critical threshold exceedance (tsim < 1400d). Only after a total of ≈ 72failures (hazard 7), the critical level c_crit,2 is ex-ceeded. A one-time failure of hazard 7 does not lead to contaminant well exposure with a critical value ofccrit,2 = 2·10⁻⁶. Please note that the initial buildup of the time-related aggregation in an initially clean aquifer leads to a statistically not representative time period within the simulation. This start-up will have to be discarded from statistical analysis.

The decisions and risk measures derived from the cumulative breakthrough curve strongly

0 500 1000 1500 2000 2500 3000 3500 0

0.5 1 1.5 2 2.5 3 3.5 4

x 10⁻⁶

Simulation Time [d]

Concentration [g/l]

Contam. Type 3 Hazard 6 Hazard 7(1) Hazard 7(2) Hazard 7(3) Hazard 7(4) Hazard 7(5) Hazard 7(6) Hazard 7(7) Hazard 7(8) Hazard 7(9) Hazard 8 Hazard 7(cum)

Figure 7.6.: Example to add mass-discharge for aggregating threshold-based values, due to a non-linear behavior in adding threshold-dependent damage values (module 6).

depend on regulatory levels or critical levels, which are denoted asc_crit. Please note, any changes in critical levels c_crit lead to a non-linear response in risk (see Fig. 7.6). For ex-ample,c_crit,1 only leads to a relevant impact, if the total concentration breakthrough curve is considered. Choosingc_crit,2 = 2.0·10⁻⁶ at a lower level already leads to relevant well contamination by hazard 7 alone, although it would have been no risk before. The total breakthrough curve (green) is continuously above the threshold level, leading to long-term well down-times. This might lead to unacceptable risk levels and such to well closure in the most unfavorable case (e.g., Fischhoff, 1990).

Module 8: Stakeholder-objective Risk Measures

The STORM concept is based on four well vulnerability criteria (see Section 4.2). Due to multiple interests and available risk measures (e.g., DALY, CML, Micro morts, etc.), I intro-duced in Section 7.1.2 the motivation to use well vulnerability criteria as intermediate risk levels. These intermediate risk levels are called stakeholder-objective risk measuresξ. Here, I define the stakeholder-objective risk measures listed in Tab. C.1 in more detail:

Maximum concentration ratio,M CR: The maximum concentration ratio, M CR, is the ratio between the maximum concentration c_peak to be expected at the well and the contaminant-specific critical concentration levelc_crit. The ratio is defined as

M CR_h,j = c_peak,h,j

c_crit,j . (7.7)

Maximum concentration ratioM CRis a dilution measure, showing two dilution as-pects. First, the degree of reduced contaminant concentration due to plume dispersion

within the catchment is considered (e.g., Cirpka and Kitanidis, 2000b) . Second, the di-lution of concentration due to pumped clean well water is included to the assessment (Einarson and Mackay, 2001). Third,c_crit can be adopted accordingly, if water treat-ment facilities are available. Due to the contaminant-specific normalizing factorc_crit,j, hazards can be prioritized across contaminant typesj.

Maximum concentration ratio forms the basis for all health-related and concentration-based risk measures, such as toxic units in ecological risk assessment (e.g., McKnight et al., 2012). Limitations occur for long-term contaminant release types, as long-term contaminant uptake leads to chronic rather than acute health effects.

Contaminant Load Exposure,CLE: Concentration profiles are continuous functions, which can be integrated over time in order to get the total mass of contaminant load that a consumer is exposed to over a given time period. This is under the assumption that contamination stays undetected. Contaminant load exposureCLE is most suit-able for chronic health-related risk measures. The total load takes short and long-term contamination effects into account. It is defined as the load above a given threshold level, e.g., drinking water standard or RfD (US EPA, 2012).

CLE_h,j = Z _∞

0

c_h,j(c_h,j(t)≥c_crit,j) dt, (7.8) wherec_crit = 0can be used to assess the total load, such as necessary in carcinogenic health-risk assessment (e.g., US EPA, 1989).

Well Exposure Time,W ET: Well exposure time,W ET, is the time that concentration lev-els in the well are above a given threshold levelc_critand is identical to the fourth well vulnerability criteriontexp. It can be used to assess exposure duration, i.e. for cancer risk assessment (e.g., US EPA, 1989) or the risk of well down-time due to qualitative water unavailability. The duration of well down-time enables stakeholders to evaluate the risk economically, as the total unavailable volume of drinking water for exposure duration can be priced. The measure is further discussed in Chapter 10.

Response Time,RT: The response time, RT, returns the available time between hazard failure and the point in time, where the concentration exceeds a given threshold level in the production water. It is identical to the third well vulnerability criteriatreact. The response time can be used to install a smart network of monitoring wells, with travel times long enough for detection and installing mitigation measures or installing control planes (e.g., Verreydt et al., 2012).

Prioritization of hazards by response time depends on the gradient of the following two aspects in a cumulative risk setting. First, the hazardous concentration levelc_h,j being present in the well that day of exceedance. And second, the temporal duration since the hazard has failed until the day of exceedance.

Required Blending Ratio,RBR: Risk of supply failure can be reduced as long as the water distributor has alternative water sources (e.g., river, lake, sea, ...) or technical storage capacities that can be used to dilute critical concentration in the well to non-critical val-ues. The compensation capacities are accounted for when working with the required

blending ratio:

RBR_j = m˙_tot,j QT ot · 1

ccrit,j

, (7.9)

with QT ot being the total amount of raw water and m˙tot,j being the total mass dis-charge of contaminantjin the well, where in all other water sources that contribute to Q_{T ot}the contaminantjis absent. In reality, this might not be true, such thatm˙_tot,j is the aggregated mass discharge of contaminantjover all water sources.

A similar concept is available with well down-time, as the time of water being un-available can be compensated by the time water is un-available through storage. The compensation time is dependent on the water demand and may vary over time. In both cases, the water constructor can pre-define a maximum possible blending ratio, such that risk is defined as the probability of exceeding the pre-defined maximum blending ratio given a fixed water demand.

These stakeholder-specific risk measures deliver additional and valuable information for catchment managers, such that the following questions can be answered:

”What is the risk ...“

1. ”... of water treatment failure due to high concentration loading? (M CR)“

2. ”... to encounter adverse health effects due to acute and chronic concentration loading?

(M CR, CLE)“

3. ”... of closing a well due to qualitative issues? (W ET)“

4. ”... of suffering quantitative supply failure due to well down-times? (W ET)“

5. ”... of the population to be exposed to contamination accumulated over time?

(CLE, M CR, W ET)“

6. ”... of detection failure due to the installed groundwater monitoring network? (RT)“

7. ”... that maximum blending capacities fail to guarantee concentration levels below drinking water standards? (RBR)“