# Configuration of Non-Pumping Reactive Wells Considering Minimum Well Spacing
## 3 Results and Discussion
### Practical Configuration of NPRW
#### 3.1.3 Process to Design NPRW Considering Field Constraints  
An efficient NPRW satisfying the minimum well spacing constraint can be designed by the following processes.  
1. Determine the well diameter (d\({}_{1}\)) that can be applied to the well construction site.
2. Determine an imaginary pollution barrier line perpendicular to the direction of groundwater flow and longer than the width of the contaminant plume, S\({}_{w}\).
3. Predict the capture width (d\({}_{2}\)) of a single well by considering the well diameter (d\({}_{1}\)) and the hydraulic conductivity of the reactive media and the geologic media. Previous studies reported that a highly permeable single well could capture contaminated groundwater flowing through a width 1.8-2.0 times greater than the well diameter [28,30]. The plume width captured by a single well (d\({}_{2}\)) is: \[\mathrm{d}_{2}=\alpha\cdot\mathrm{d}_{1}\] (5) where \(\alpha\) is the groundwater capture efficiency of a well, which is defined as the ratio of the capture width to the diameter of a single well, d\({}_{1}\).
4. Place the reactive wells along the contamination blocking line, spaced at a distance of d\({}_{2}\).
5. In the case where d\({}_{2}\) is closer than the minimum well space d\({}_{m}\), the unit well segment (for example, the red lines in Figure 3b) is defined so that the width of the unit segment, S\({}_{i}\), is greater than d\({}_{m}\). \[\mathrm{S}_{i}=\mathrm{d}_{2}\cdot\mathrm{N}\;\mathrm{and}\;\mathrm{S}_{i} \geq\mathrm{d}_{m}\] (6) where N is the number of wells in the unit segment (integer).
6. Optimize the configuration of the unit segment considering the site conditions, including the minimum well spacing. For example, some of the wells included in the unit segment may be moved in the downstream direction, thereby satisfying the limiting condition for minimum well spacing. Then, if a new well is installed in a place separated from the wells in the preceding transect by distance d\({}_{2}\) and d\({}_{3}\), in the transverse and longitudinal directions, respectively, the limiting condition of  
Figure 3: Well spacing in NPRWs: (**a**) zigzag array and (**b**) sawtooth array. Here, d\({}_{1}\) is well diameter; d\({}_{2}\) is the plume width captured by a single well; d\({}_{3}\) is the minimum distance between the transects; d\({}_{m}\) is minimum well spacing; the red line means unit segment; the green dashed circle means locations d\({}_{m}\) away from the center of a well located in the middle of well arrays. These configurations were constructed by assuming d\({}_{1}\) = 0.25 m, d\({}_{m}\) = 1.5 m, S\({}_{i}\) = d\({}_{m}\), and the hydraulic conductivity of the reactive media in the well is sufficiently higher than that of aquifer.  
minimum well spacing can be satisfied. Here, \(\mathrm{d}_{3}\) is the minimum distance between the transects, and it can be calculated by \[\mathrm{d}_{3}=\sqrt{\mathrm{d}_{m}^{2}-\mathrm{d}_{2}^{2}}\] (7) The number of segments is determined as \(\mathrm{N}_{\mathrm{s}}\) (integer), using the ratio of the width of the contaminant plume, \(\mathrm{S}_{\mathrm{w}}\), to the width of the unit segment, \(\mathrm{S}_{\mathrm{i}}\). The arrangement of NPRW should be wider than the width of the contaminant plume (\(\mathrm{S}_{\mathrm{w}}\)) to prevent contaminants from spreading downgradient. To prevent the spread of contaminants completely, the following condition should be satisfied: \[\mathrm{N}_{\mathrm{s}}\geq\mathrm{S}_{\mathrm{w}}/\mathrm{S}_{\mathrm{i}}\] (8) The designed PRB system can be completed by arranging \(\mathrm{N}_{\mathrm{s}}\) unit segments along the pollution barrier line.