**3. Previous studies**

Several studies have examined outfall optimization for brine disposal. Jiang and Law [23] provided semi-analytical solutions for the combination of port diameter (*D*0) and number of ports (*N*) required to meet design objectives (dilution greater than a specified value and rise height of plume lower than a fraction of the water depth) for non-interfering multiport diffusers. They investigated *D*<sup>0</sup> � *N* combinations for full submergence and surface contact scenarios (analogous to deep and shallow conditions, respectively) for a given range of brine flow rate. They did not consider a cost function but asserted that the capital cost increases with the number of ports, and thus the optimum design is the one that satisfies design objectives with minimum number of ports. They assumed jets to be non-interfering, and thus did not account for the interaction between jets in shallow water depths.

Maalouf et al. [24] provided a simulation-optimization framework to optimize SWRO outfall design. They used a regression model, calibrated using results from an initial mixing model (CORMIX), to quantify the effects of various parameters on dilution. Using this regression model for dilution, they optimized the design variables to minimize the total cost. The total cost was assumed to be a linear function of outfall pipe length (*X*), internal port diameter (*D*0) and number of ports (*N*). Their analysis was based on a similar analysis done by Chang et al. [25] to evaluate optimal strategies for the expansion of a wastewater treatment plant in South Taiwan. Uncertainties in ambient parameters (e.g., ambient current speed) were also considered.

The above studies only considered linear cost functions and have not been compared to cost functions in the real world.

### **4. Brine management strategies**

Recently proposed brine management options [3, 4] include pre-dilution with a lighter effluent and pre-concentration, and can cause significant changes to contaminant concentrations and, in turn, the required dilution. Contaminants of concern for the discharge of pre-diluted brine can be categorized into three categories

*Desalination Brine Management: Effect on Outfall Design DOI: http://dx.doi.org/10.5772/intechopen.99180*

[26]. First, there are contaminants similar to salt which are present in ambient water but get concentrated due to the desalination process. Thus, the discharge concentrations are higher than ambient concentrations and these contaminants need to be diluted. Examples include salts and metals. Second, there are contaminants that are introduced by the desalination process, such as anti-scalants and cleaning chemicals [27]. Third, there are contaminants that are present in the predilution stream. Examples include biochemical oxygen demand (BOD), nutrients etc. present in TWE and excess temperature from CW. While some of the contaminants of concern degrade with time (e.g., ammonia), most of them are conservative and require mixing with ambient water to reduce their concentrations below harmful levels.

For the case of pre-dilution, reject brine from a typical reverse osmosis (RO) plant (having double the salinity as ambient seawater and with flow rate ¼ *Qb*, reduced gravity ¼ *gb* <sup>0</sup> and excess salinity above ambient water ¼ Δ*sb*) is considered to be blended with a pre-dilution stream (flow rate ¼ ð Þ *RB* � 1 *Qb*, reduced gravity ¼ *gp* 0 , excess salinity ¼ Δ*sp* and excess temperature ¼ Δ*Tp*), making a total flow rate of *Q*<sup>0</sup> ¼ *RBQb*. The blending ratio (*RB*) is, thus, the ratio of the blended effluent flow rate (*Q*0) to the brine flow rate (*Qb*). The blended effluent has a reduced gravity of *g*<sup>0</sup> <sup>0</sup> ffi *gb* <sup>0</sup> þ ð Þ *RB* � 1 *gp* 0 n o*=RB* and excess salinity of <sup>Δ</sup>*s*<sup>0</sup> <sup>¼</sup> Δ*sb* þ ð Þ *RB* � 1 Δ*sp* � �*=RB*. In addition to the use of TWE and CW as the pre-diluting stream, pre-dilution with ambient seawater (SW) is also considered. **Table 1** gives the properties of brine, seawater, TWE and CW used in this analysis.

Pre-dilution with TWE leads to a rapid reduction in discharge salinity as the salinity deficit of TWE (with respect to ambient water) cancels out some of the salinity excess of brine. Similarly, the reduced gravity of the effluent when brine is blended with TWE decreases rapidly. On the other hand, SW and CW do not have any salinity excess or deficit (with respect to ambient water), and thus the reduction in discharge salinity (and, in turn, reduced gravity) is less than that for the case of pre-dilution with TWE. As CW is positively buoyant with respect to ambient water, the decrease in *g*<sup>0</sup> <sup>0</sup> as a function of *RB* is faster for the case of blending with CW than for the case of blending with SW.

For the case of pre-concentration, it is assumed that brine (with initial flow rate ¼ *Qb*) is concentrated by removing fresh water (salinity = 0 or excess salinity ¼ �Δ*sb*) such that a more concentrated discharge stream is produced with flow rate of *Q*<sup>0</sup> ¼ *Qb=RC* (with *RC* >1). Thus, the discharge salinity is equal to Δ*s*<sup>0</sup> ¼ ð Þ 2*RC* � 1 Δ*sb*, where *RC* is the concentration ratio defined as the ratio of the brine flow rate (*Qb*) to the discharge flow rate (*Q*0).

Since the salinity of brine is double the salinity of seawater and the salinity of TWE is assumed to be zero, the blended effluent has the same salinity as ambient seawater when the flows (of brine and TWE) are blended in a 1:1 ratio (*RB* ¼ 2). The pre-dilution of excess salinity (¼ Δ*sb=*Δ*s*0) in this case is infinite. For high values of *RB*, the blended effluent may become positively buoyant (*RB* >2 for predilution with TWE and *RB* > 8*:*7 for pre-dilution with CW) in which case there is no


#### **Table 1.**

*Properties of brine and various pre-dilution streams.*

impact point. But the dilution equations for negatively buoyant effluent are used for this case too. These results are only meant to provide qualitative predictions.
