**7. Results and discussion**

## **7.1 Cost of outfalls**

**Figure 7** shows the comparison of total costs for the four designs (single jet and unidirectional diffuser with submerged and surfacing plume) with *Qb* <sup>¼</sup> 1 m<sup>3</sup> /s, Γ ¼ 0*:*01 and desired excess salinity of 2 ppt. It can be seen that for pre-dilution with SW and CW, the costs of all four designs increase with increase in *RB* in spite of the fact that the desired physical dilution decreases with increase in *RB*. The increase in total cost is caused due to the increase in discharge flow rate. For the case of blending with TWE, however, the costs of all four designs decrease with increasing *RB* for *RB* <2 due to the rapid reduction of desired physical dilution in that case. (The desired physical dilution goes down from 18 for *RB* ¼ 1 to 6 for *RB* ¼ 1*:*5.) The blended effluent is positively buoyant for *RB* >2 and *RB* >8*:*7 when brine is blended with TWE and CW, respectively, and the trends shown are

**Figure 7.** *Total costs of the four design alternatives to achieve desired excess salinity of 2 ppt at the impact point with Qb* <sup>¼</sup> <sup>1</sup> *<sup>m</sup>*<sup>3</sup>*=s and* <sup>Γ</sup> <sup>¼</sup> <sup>0</sup>*:*01*.*

different for *RB* in this range. For the case of pre-concentration, the desired physical dilution increases rapidly with *RC* leading to the increase in total cost.

**Figure 7** shows that for most of the pre-dilution cases, the design with a single jet is the optimum design when the regulations require the plume to be submerged. Thus, for these cases, the '*TCd* (single jet)' and '*TCd* (unidirectional diffuser)' curves overlap. For pre-dilution cases, the total cost can be significantly lower for the surfacing plume design as compared to the submerged plume design. For blending with SW (*RB* ¼ 2), TWE (*RB* ¼ 1*:*5) and CW (*RB* ¼ 5), the ratio of the total cost for surfacing plume design to that for the submerged plume design with a single jet is 0.84, 0.77 and 0.60, respectively. Using a unidirectional diffuser, this ratio is 0.60, 0.58 and 0.42 for blending with SW (*RB* ¼ 2), TWE (*RB* ¼ 1*:*5) and CW (*RB* ¼ 5), respectively.

For the discharge of brine without pre-dilution or pre-concentration, the total costs (in million USD) of the four designs are *TCd* ¼ 5*:*2 and *TCsh* ¼ 4*:*9 (for a single jet discharge), and *TCd* ¼ 3*:*1 and *TCsh* ¼ 3*:*0 (for a unidirectional diffuser). Thus, compared to the cost of a single jet design with submerged plume, the cost can be reduced by 40% if a multiport diffuser is used (with submerged plume), by 6% if the plume is allowed to hit the surface (but still using a single jet), and 42% if a multiport design with a surfacing plume is adopted.

When brine is concentrated, the desired physical dilution increases rapidly with increase in *RC*. Hence, discharge of concentrated brine is not preferable from an environmental standpoint. If brine is concentrated, it needs to be discharged with high (perhaps unrealistic) discharge velocity and/or using a large number of ports to generate adequate mixing. **Table 4** shows an example of the design variables calculated for *RC* ¼ 2. (Only designs with submerged plume are included because they are also the designs which minimize cost).

Pre-concentration of brine increases the concentrations of contaminants present in brine. Thus, the total cost of discharging concentrated brine increases with *RC* as shown in **Figure 7**. The processes used to concentrate brine also have some cost. Thus, whether brine should be concentrated prior to discharge depends on the value of the extra fresh water produced compared to the cost of pre-concentration and the additional cost of the outfall. At locations with regulatory restrictions on discharge concentrations, pre-concentration might not be possible. Pre-concentration could be beneficial if brine is concentrated to the extent that salts can be crystallized as there would be no cost of discharge.

The costs in **Figure 7** are calculated for salinity as the contaminant of concern. However, the relative importance of different types of contaminants (present in brine, TWE or CW) depends on the blending ratio (for pre-dilution with TWE and CW). At low blending ratio, the contaminants present in brine require higher dilution and are likely to be the constraining contaminants whereas contaminants present in TWE or CW require higher dilution at high blending ratio. Thus, the designs and the associated costs calculated above need to be adjusted at high blending ratio.


**Table 4.**

*Example showing calculated design variables for the discharge of concentrated brine (RC* ¼ 2*) with* Γ ¼ 0*:*01*.*

### **7.2 Effect of threshold concentrations on outfall design**

Since the outfall design depends on desired physical dilution, which in turn, depends on the threshold concentrations, it is important to analyze the effect of threshold concentrations on the optimum design. This is illustrated through an example in **Figure 8** in which the threshold concentration of salinity (Δ*sth*) varies between 0.5 and 5 ppt (above ambient). The variation in required depths and total costs with the threshold salinity is shown for discharge of brine without pre-dilution or pre-concentration.

The required depths and total costs (for designs with submerged and surfacing plume) decrease with increase in threshold concentrations (for discharge through a single jet) because the additional mixing required to achieve those concentrations is less. For a design with multiple ports which requires the plume to be submerged and has the discharge velocity fixed to ensure uniform flow, the required depth is proportional to the inverse of desired dilution, i.e., the depth is proportional to Δ*sth*. This can be seen for Δ*sth* > 3*:*3 ppt. When the discharge velocity is not fixed (for Δ*sth* < 3*:*3 ppt), the required depths and total costs reduce with increase in Δ*sth* similar to the case of a single jet discharge.

#### **7.3 Effect of bottom slope**

The optimum design at a location with a mild bottom slope, such as the Arabian Gulf which has bottom slopes as little as about 4 � <sup>10</sup>�<sup>4</sup> [2], can be quite different as compared to the design at a location with a steep slope. With a mild bottom slope, the offshore distance to locate the outfall in sufficient depth of water can be long which also increases the total cost significantly. In that case, it costs less to achieve the desired dilution in small water depth by increasing the discharge velocity and/or the number of ports. This is illustrated by considering outfall designs at two locations with Γ ¼ 0*:*01 and 0*:*001. For discharge using a single jet in deep water (submerged plume), the design variables are independent of Γ (Eqs. (12)–(14)) but the total cost is higher for a location with smaller bottom slope because of the increased offshore distance. For discharge using a single jet with a surfacing plume and discharge through a unidirectional diffuser, the design variables can be adjusted to reduce the total cost. But, the total costs are still significantly higher for smaller Γ. **Figure 9** shows the effect of Γ on the total cost to discharge brine pre-diluted with SW using a single jet and a multiport diffuser. The total cost for a submerged plume

#### **Figure 8.**

*Variation of Hd*, *Hsh, TCd and TCsh with threshold salinity for discharge of brine through a single jet and a tee diffuser with Qb* <sup>¼</sup> <sup>1</sup> *<sup>m</sup>*<sup>3</sup>*=s and* <sup>Γ</sup> <sup>¼</sup> <sup>0</sup>*:*01*.*

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

design with Γ ¼ 0*:*001 is approximately 10 times the corresponding cost for Γ ¼ 0*:*01.

A comparison of optimum design variables at locations with different bottom slopes is shown in **Table 5** for discharge of brine without pre-dilution or preconcentration. For this example, two bottom slopes (Γ ¼ 0*:*01 and Γ ¼ 0*:*001) are considered. The design of a single jet with surfacing plume for Γ ¼ 0*:*001 has a discharge velocity of 20.8 m/s which is not realistic. The designs with multiple ports are preferable with reasonable velocities. It can be seen from **Table 5** that the cost of the unidirectional diffuser design is about 60% of the cost of a single jet design for Γ ¼ 0*:*01 but only 25% of the single jet cost for Γ ¼ 0*:*001 which suggests that a multiport design is more realistic at locations with small Γ.

For the unidirectional diffuser designs in **Table 5**, the required water depths are 1.4 m and 0.8 m (for Γ ¼ 0*:*001). Thus, the lengths of outfall pipe to outfall location are 1.4 km and 0.8 km, which are quite long. For such locations, a staged diffuser [37] can also be used which has ports along the length of the outfall pipe. For the same diffuser length, water depth, flow rate and discharge velocity, the dilution of a staged diffuser in quiescent conditions is less than the dilution of a unidirectional diffuser [18]. But considering that the length of the outfall pipe is much longer as compared to the diffuser length for a unidirectional diffuser design, the staged diffuser design will get much higher dilution than the unidirectional diffuser. In fact, if a staged diffuser is designed to achieve the desired physical dilution, its offshore distance would be less that the 1.4 km (or 0.8 km) distance for the unidirectional diffuser design.

## **7.4 Comparison with the cost of discharging brine without pre-dilution or pre-concentration**

As shown in **Figure 7**, the cost of discharging brine blended with TWE is less than the cost of discharging brine without pre-dilution for *RB* <2. However, the total costs (for all four designs) for other pre-dilution cases increase as *RB* increases (except when brine is blended with CW with *RB* >8*:*7), which means that the cost of discharging pre-diluted brine is higher than the cost of discharging brine without pre-dilution. However, these costs should be compared to the cost of two outfalls for discharging brine and the pre-dilution stream separately (for blending with

#### **Figure 9.**

*Comparison of total costs at locations with* Γ ¼ 0*:*01 *and* Γ ¼ 0*:*001 *for the discharge of brine pre-diluted with SW using a single jet and a tee diffuser with Qb* <sup>¼</sup> <sup>1</sup> *<sup>m</sup>*<sup>3</sup>*=s and* <sup>Δ</sup>*sth* <sup>¼</sup> <sup>2</sup> *ppt.*


#### **Table 5.**

*Example showing calculated design variables for discharge of brine (without pre-dilution or pre-concentration) at two locations with* Γ ¼ 0*:*01 *and* Γ ¼ 0*:*001*.*

TWE and CW; since these effluents have to be discharged anyway), which will likely be more than the cost of discharging the blended effluent.

Unlike TWE and CW, SW does not need a separate outfall. In fact, intake of seawater for pre-dilution adds an extra cost. Also, as shown in **Figure 7**, the total cost increases with increase in *RB* for the case of pre-dilution with SW. Thus, pre-diluting brine with SW is not economical. But it might be needed if there are regulatory restrictions on discharge concentrations themselves which are not met without pre-dilution.

For the calculations in this paper, a wide range of *RB* (1 to 10) is considered. The flow rate of condenser cooling water from power plants is usually quite high as compared to the flow rate of brine. Therefore, a high value of *RB* is possible for CW. However, the availability of TWE for blending with brine can be limited as it can be re-used or used for other purposes (e.g., irrigation).

### **8. Conclusions**

Brine management strategies cause changes to the discharge flow rate, discharge concentrations of contaminants and the density difference between the effluent and seawater, and thus require changes to the outfall design. It is shown that predilution with seawater is less economical than the discharge of brine without any pre-dilution. Thus, seawater should only be used for pre-dilution if there are restrictions on discharge concentrations of contaminants and other effluents (TWE or CW) are not available for pre-dilution. Concentration of brine is also not viable from an environmental standpoint. On the other hand, pre-dilution with TWE or CW is likely to be economically beneficial.

For the design of a new outfall for a desalination plant with known amount of pre-dilution or pre-concentration, design variables are calculated for both a single *Desalination Brine Management: Effect on Outfall Design DOI: http://dx.doi.org/10.5772/intechopen.99180*

port and a multiport outfall. Depending on the environmental regulations which might have restrictions on plume visibility, design parameters are evaluated for a submerged plume or a surfacing plume. It is shown that when the plume is allowed to hit the water surface (no restrictions on plume visibility), the required water depth and total cost of the outfall can be significantly reduced. For such cases, the required water depth and the offshore distance decrease as the blending ratio increases. At locations which require the plume to be submerged, the design with a single jet is found to have lower cost than a design with multiple ports (for most values of the blending ratio). However, for locations with no restrictions on plume visibility, use of a multiport diffuser is recommended as it can result in much lower cost than a single jet.

The effect of bottom slope and threshold concentrations on outfall design is also explored. Locations with mild bottom slope encourage the use of outfalls with multiple ports which can reduce the required water depth and, in turn, the offshore distance of the outfall from the shoreline. An increase in threshold concentrations usually leads to a reduction in outfall cost as the outfall needs to achieve a smaller dilution. Similarly, more stringent regulations (smaller threshold concentrations) can lead to a rapid increase in outfall cost.

### **Acknowledgements**

This work was supported by Kuwait-MIT Center for Natural Resources and the Environment (CNRE), which was funded by Kuwait Foundation for the Advancement of Sciences (KFAS).
