Contaminant Mass Discharge Estimation in Groundwater Based on Multi-Level Well Data. Evaluation of Expected Errors. Markus Kübert, Michael Finkel

Transkript

1 Contaminant Mass Discharge Estimation in Groundwater Based on Multi-Level Well Data Evaluation of Expected Errors Markus Kübert, Michael Finkel Center for Applied Geoscience, University of Tübingen Decision-Support Systems Integrating Technology and Economics

2 Mass discharge quantification on control planes Assessing mass flow rates in a contaminant plume perpendicular to the ground water flow direction Source zone F F 2 Contaminant plume F 3 Flow direction Applications of the mass flux approach in literature: Estimating Natural attenuation rate constants (e.g. King et al., 999; Bockelmann et al., 23 Assessing the efficiency of source remediation techniques (e.g. Soga et al., 24 Evaluation and prioritization of site management alternatives (e.g. Rao et al., 22 Methods to determine the mass flow rates on a control plane: Integral groundwater investigation IPT approach Point Measurements - Multi-Level-Wells MLW approach

3 Mass flow rate quantification with MLWs Basic principles real parameter distribution on a control plane extrapolated parameter distribution on a control plane (Thiessen-Polygon multi-level wells sampling ports A F i,j, q i,j,k i,j, C i,j W = C Q = C q A = F A = C K i A W: mass discharge F: mass flux C: concentration Q: volume flow rate q: specific discharge direct methods indirect methods

4 Mass flow rate quantification with MLWs Methods direct method Method A (direct method using fluxmeters W n n ( Fn, m An, m = well ver n= m= F n,m multi-level well (Hatfield et al. 22 and 24 indirect methods Method B W W = i = Method C K n well n ver ( Cn, m Kn, m An, m n= m= (Newell et al., 23; Béland-Pelletier et al., 24 i n well n ver ( Cn, m An, m n= m= C n,m K n,m, C n,m K n = well K... K n K q n, m = Kn, m i : uniform hydraulic gradient q well = i K i (Borden et al., 997, King et al., 999; Kao and Wang, 2 i : uniform hydraulic gradient

5 Relevant features resulting in uncertain mass flow rates Heterogeneity of the spatial distribution of the parameters on the control plane: Heterogeneity of the flow field Fluctuations over time Spatial distribution of contaminants in the source zone uncertain parameter Stochastic approach Sampling grid resolution and extrapolation technique real parameter distribution on a control plane d well extrapolated parameter distribution on a control plane (Thiessen-Polygon d ver Measurement errors associated with procedure of sampling and laboratory analysis

6 Basic principle Model to quantify the measurement errors Generating aquifer Sequential Gauss Simulation realizations (n real = f ( σ 2, λ, λ y h v Flow and Transport Modeling MODFLOW and Particle- Tracking Model W real Sampling and Extrapolation Different sampling grid resolutions ( f d well, d ver W est W Measuring error error = n Real Cumulative frequency distributions 2 f ( σ y, λh / v real W, d W real well est, d ver Number of realizations [%] 9 5 η(9% η(5% η(% Relative errors

7 3D model domain Cross-sectional view source zone Plan view Cross-sectional view control plane No flow boundaries General flow direction 5 m Fixed head boundaries m Multi-level well 3. m Monitoring well Fixed head boundaries Contaminant source Plume fringes No flow boundaries 4 m 6 m x = y = z =.25 m, i =.7, k f = E-3 m s - multi-level sampling ports

8 Results Zentrum für Angewandte Geowissenschaften (ZAG Mean errors of individual methods as a function of σ y ², d well, d ver and λ h/v = const. Mean errors of individual methods as a function of λ h/v, d well, d ver and σ y ² = const. Comparison of mean errors of analysed methods as a function of σ y ², λ h/v and d well, d ver

9 Relevant features of the Figures d well d well Increasing mean errors d ver d ver a d ver =.25 m σ 2 =.25 σ 2 =. σ 2 = 2. σ 2 = b d ver =.25 m Increasing horizontal sampling resolution Increasing horizontal sampling resolution

10 Performance of method A relative mean errors f(σ y 2, n well, d ver λ h = 3. m and λ v =.3 m a d ver =.25 m σ 2 =.25 σ 2 =. σ 2 = 2. σ 2 = b d ver =.25 m Decreasing mean errors for increasing sampling grid resolutions (n well, d ver Increasing mean errors for increasing aquifer heterogeneity (variance σ y ²

11 Performance of method A relative mean errors f(σ y 2,n well,d ver Influence of erroneous measurements F n = F m error n, m E,, n, m, meas F n,m,error : erroneous measured mass discharge F n,m : measured mass discharge E n,m,meas : random error factor (E n,m,meas =., Hatfield et al., 22 Frequency µ = meas σ =.5 µ meas - σ µ meas µ meas + σ Measurement error E meas a d ver =.25 m.7 b d ver =.25 m method A;σ 2 = 4.5 method A W,err ;σ 2 = method A W,err method A W,err

12 Performance of method A, B and C relative mean errors f(σ y 2 σ y2 = 2., λ h = 3. m, λ v =.3 m, d ver =.25 m and.25m a d ver =.25 m Method A Method B Method C.8.6 b d ver =.25 m Method B: high relative mean errors; does not show the typical decreasing shape Insufficient description of the groundwater flux on the control plane Method C: provides reasonable estimates that are largely independent of the number of sampling points Assuming a uniform groundwater flux on the control plane yields lower mean errrors

13 Results Zentrum für Angewandte Geowissenschaften (ZAG Mean errors of individual methods as a function of σ y ², d well, d ver and λ h/v = const. Mean errors of individual methods as a function of λ h/v, d well, d ver and σ y ² = const. Comparison of mean errors of analysed methods as a function of σ y ², λ h/v and d well, d ver

14 Performance of methods A, B and C relative mean errors f(λ h/v λ h/v = 3. m /.3 m Low spatial correlation of k f λ h/v =. m /. m High spatial correlation log(k f of k f log(k f

15 Performance of method A relative mean errors f(λ h/v, n well,d ver.5.4 σ y ² = 2.; λ h = 3. m and λ v =.3 m σ y ² = 2.; λ h =. m and λ v =. m.5.4 b d ver =.25 m.3 a d ver =.25 m Mass discharge distribution on the control plane Low spatial correlation of k f High spatial correlation of k f log(w log(w

16 Performance of method B and C relative mean errors f(λ h/v Method B: decreasing values.4 d.2 ver =.25 m Method C: increasing values.4 d.2 ver =.25 m σ y ² = 2.; λ h = 3. m and λ v =.3 m σ y ² = 2.; λ h =. m and λ v =. m.4.2 W = i n well n ver ( Cn, m Kn, m An, m n= m= W = K i n well n ver ( Cn, m An, m n= m= Hydraulic heads for one single aquifer realization a λ h = 3. m; σ y ² = 2. b λ h =. m; σ y ² = 2. i i flow direction flow direction

17 Results Zentrum für Angewandte Geowissenschaften (ZAG Mean errors of individual methods as a function of σ y ², d well, d ver and λ h/v = const. Mean errors of individual methods as a function of λ h/v, d well, d ver and σ y ² = const. Comparison of mean errors of analysed methods as a function of σ y ², λ h/v and d well, d ver

18 Comparing the methods a d ver =.25 m.6 b d ver =.5 m c d ver =.75 m.6 d d ver =.25 m

19 Comparing the methods Total number of measurement points: n tot = n well n ver d ver =.25 m d ver =.5 m d ver =.75 m d ver =.25 m (n tot n tot

20 Comparing the methods Total number of measurement points: n tot = n well n ver d ver =.25 m d ver =.5 m d ver =.75 m d ver =.25 m (n tot n tot

21 Comparing the methods - f(σ y2, n well, n ver λ h = 3. m and λ v =.3 m.8 a σ y 2 =.25.8 b σ y 2 =..6.4 Method A Method B Method C Total number of measurement points Total number of measurement points.8 c σ y 2 = 2..8 d σ y 2 = Total number of measurement points Total number of measurement points

22 Summary and conclusions The common opinion the closer the sampling mesh the better is the picture of the real world situation is not generally valid The relative erros increase with increasing variance σ y 2 Different behaviour of methods A, B and C for increasing the spatial correlation length scale λ Method A is preferable at fine sampling grid resolutions and high variances σ y 2 Method B is only feasible at low variances σ y 2, otherwise method C is preferable Low influence of measurement errors associated with procedure of sampling and laboratory analysis on method A

23 Thank you!