**Table 2.**

*Break-down of total outfall cost.*


*a Only for the design with a unidirectional diffuser.*

*b Only for a single port design.*

*c Assuming riser diameter equal to the nozzle diameter.*

*d From Davis [33].*

*e Ken* <sup>≈</sup> <sup>0</sup>*:*<sup>2</sup> <sup>þ</sup> ð Þ *Vd=Vr* <sup>2</sup> *from Fischer et al. [31]. Vd is the velocity inside the manifold and Vr is the velocity in the riser. With the constraint on u*<sup>0</sup> *for uniform flow (discussed later), Ken has a maximum value of 0.3 which is used here. <sup>f</sup> Assumed to vary linearly with the ratio of cross-sectional areas of the two pipes from 0.45 to 0.16 for area ratio (ratio of smaller cross-sectional area to larger cross-sectional area) from 0.04 to 0.64.*

#### **Table 3.**

*Components of total head loss.*

resulting in a range of values of the desired dilution. For simplicity, salinity is assumed to be the most constraining contaminant. The threshold concentration of salt is assumed to be 2 ppt in excess of ambient salinity [36] and outfall designs which dilute salinity to an excess of 2 ppt at impact point are discussed.

Effective dilution for a contaminant is defined as the ratio of its excess concentration in the source stream (e.g., brine for salinity) to its excess concentration at a given location. Thus, if the excess salinity of the diluted effluent at the impact point is equal to 4 ppt (in excess of ambient salinity), then the effective dilution of salinity at impact point is equal to 36*=*4 ¼ 9, where 36 ppt is the excess salinity of reject brine (**Table 1**). Similarly, the desired effective dilution for any contaminant is the ratio of its concentration in the source stream to the threshold concentration (both in excess of ambient concentration). Thus, the desired effective dilution of salinity is equal to 18.

Unlike the desired effective dilution, the desired physical dilution at the impact point also depends on the amount of pre-dilution or pre-concentration (the value of *RB* or *RC*), in addition to the source streams and threshold concentrations. For example, if brine is pre-diluted with TWE with *RB* ¼ 1*:*5, then the discharge excess salinity is 12 ppt and the desired physical dilution is equal to 12*=*2 ¼ 6, which is different than the desired effective dilution which is equal to 18. The outfall design in this case needs to provide an impact point dilution of 6.

#### **5.3 Design alternatives**

Brine can be discharged through an outfall in two ways – the discharge can be such that the plume stays below the water surface or it can be allowed to hit the surface. The former design would be implemented if the regulations require the plume to not be visible at the surface. However, the latter design usually costs less and should be preferred when there are no restrictions on plume visibility.

For a jet inclined at 30o, the depth below which the impact point dilution is affected by the water surface is more than the depth at which the jet hits the water surface [11]. Thus, for a submerged plume (which is not allowed to hit the surface), the maximum dilution (with minimum total cost) is achieved when the terminal rise height of the jet is just high enough that the ambient depth affects the dilution, i.e., at the transition point between deep and shallow conditions (*D*0*F*0*=H* ¼ 0*:*72). To dilute a contaminant to a threshold concentration, the design variables for this design can be determined by ensuring that the physical dilution is just enough to get the desired concentration and the discharge plume rises to just below the water surface (*D*0*F*0*=<sup>H</sup>* <sup>¼</sup> <sup>0</sup>*:*72 for an inclination of 30o). The design variables for this design are denoted using the subscript 'd', for deep.

These design parameters do not minimize the total cost as they require a large capital cost. Specifically, in locations with very small bottom slope, such as the Arabian Gulf [2], the capital cost can be several orders of magnitude larger than the pumping cost and the total cost can be very high. To reduce the capital cost, it is beneficial to achieve the desired dilution with smaller ambient depth by reducing the port diameter or to employ a multi-port diffuser. Using a single, smaller diameter port will result in an increase in discharge velocity, and thus the pumping cost.

**Figure 2.** *Schematic showing the plan view (top) and elevation view (bottom) of the four designs considered.*

The optimum design will be the one that minimizes the total cost (capital cost + pumping cost). The design variables for this design are denoted using the subscript 'sh', for shallow. Similarly, for a multiport diffuser, optimum design variables can be computed for the two designs, one with the diffuser plume submerged and the other with surfacing plume. A schematic of the four designs is shown in **Figure 2**.
