# Configuration of Non-Pumping Reactive Wells Considering Minimum Well Spacing
## 3 Results and Discussion
### Prediction of the Contaminant Removal Using Multiple Transect NPRW
#### 3.3.2 Effect of Minimum Well Spacing and Well Configurations on PRB Performance  
Numerical simulations of contaminant transport were conducted for various multiple transect configurations considering minimum well spacing to validate the performance curve. Figure 6 shows the effect of the minimum well spacing (d\({}_{\rm m}\)) and number of wells (N) in multiple transect configurations on the removal ratio (R\({}_{\rm e}\)). Here, the well diameter (d\({}_{1}\)) was assumed to be 0.25 m, and the width of the interval was set equal to the minimum well spacing. The smaller the N and larger the S\({}_{\rm i}\) (=d\({}_{\rm m}\)), the greater the contaminant plume that flowed downstream untreated. The contaminant removal ratios for each simulation were calculated and are presented in Table 1. For a given configuration with the same number of transects, the removal ratio decreased with increasing minimum well spacing (or width of unit segment). A single transect had low removal efficiency even at the smallest minimum well spacing (1.0 m), confirming that additional downgradient transects need to be installed, such as those in double transect or sawtooth configurations. For a given well spacing, the removal efficiency increased in the order of single, double, and triple (sawtooth arrays) configurations. For instance, at d\({}_{\rm m}\) = 1.5 m, the removal efficiency was only 31% for a single transect, but 63% and 95% for double transect and the sawtooth array, respectively. A contaminant plume passing between the upgradient transect of NPRW was trapped in the downgradient transects, resulting in increased removal efficiency. Here, we found that the sawtooth configurations of NPRWs could be a practical configuration that could achieve high removal efficiency with a small number of wells while satisfying the minimum well spacing considering the construction constraints. Figure 6: Simulation of steady-state solute transport through single transect (N = 1), double transect (N = 2), and sawtooth configurations (N = 3) of NPRW under various minimum well spacings, d\({}_{\rm m}\). Here, the well diameter (d\({}_{1}\)) was assumed as 0.25 m, and the width of interval was set equal to the minimum well spacing. After a minimum well spacing has been proposed in the field, it is necessary to determine the well diameter. The well diameter should be proportional to the capture width of each well, because fewer wells are required when well diameters are larger. However, as the well diameter increases, the well boring cost and the required mass of reactive material also increase. Therefore, additional factors such as availability of equipment and cost of well construction should be considered in determining the well diameter. The relationship between the diameter and the contamination removal performance was confirmed. This was done through a simulation of contaminant spread through a NPRW in sawtooth array configuration (N = 3), according to the well diameter and minimum well spacing (or width of unit segment) (Figure 7). When d1 was smaller and S1 (d2m) was larger, a greater proportion of the contaminant plume flowed downstream untreated. The contaminant removal efficiencies for the simulated PRB configurations were calculated and are presented in Table 2.  
The simulated contaminant removal was plotted as a function of minimum well spacing (\(\mathrm{d_{m}}\)) and the number of wells (Figure 8a). The simulated contaminant removal of triple transect PRB was also plotted as a function of well diameter (\(\mathrm{d_{1}}\)) and minimum well spacing (Figure 8b). The contaminant removal efficiencies by NPRWs were calculated numerically and compared with those expected using Equation (13). Using the trial and error method, the curves expected by Equation (13) were well-fitted to the simulated contaminant removal efficiency, when \(\alpha=1.85\). This value is similar to the maximum value reported in previous research [28; 30].