**5. Optimization parameters**

Optimization of the design of outfalls discharging pre-diluted or preconcentrated brine is considered here such that regulatory requirements on contaminant concentrations can be met at the end of the mixing zone with minimum cost. The end of the mixing zone is assumed to be at the impact point of the jets. Thus, the expressions for impact point dilution of a single port outfall and a multiport (unidirectional) diffuser can be used to calculate the "physical" dilution induced by the outfall.

The location of an outfall depends on many factors, such as the availability of deep water, absence of natural submerged sills, spits, and manmade jetties, and knowledge of the offshore bathymetry; hydrodynamic modeling is often utilized to test a proposed design before it is adopted. In addition, detailed analysis of the forces exerted on the outfall due to oceanographic conditions is also carried out to ensure its stability. These factors are site-specific and beyond the scope of this chapter. Here, we are considering generic outfall designs and calculating values of design variables, such as receiving water depth, discharge velocity, number of ports, etc., that result in minimum cost. For this calculation, the outfall is considered to be located at a place with uniformly sloping bottom in the offshore direction.

Optimization of outfall design requires identification of outfall cost, desired dilution and design alternatives, which are discussed below.

#### **5.1 Costs**

One of the major components of outfall cost is the cost of the conveyance system to carry brine to the offshore discharge location. Depending on the oceanographic conditions and the discharge location, this can be done by running a pipe through a tunnel or a trench, or laying a pipe on the seabed secured using ballast weights [28]. Here, we have assumed that high density polyethylene (HDPE) pipes are used.

The capital cost is considered to be composed of four major components. The first is the cost of laying the HDPE pipe to the required offshore distance. The cost per unit length of HDPE pipes was found to be proportional to the pipe diameter (*Dp*) [29, 30]. Thus, the cost of the pipe is proportional to the pipe diameter (*Dp*) times the length of the pipe (*X*Þ.

The most common way to secure HDPE pipes to the sea bed is to attach concrete ballast weights [28]. The cost of concrete weights per unit length of the pipe was found to increase with pipe diameter [29] and a linear fit was used. Thus, the total cost of anchor blocks was proportional to the product of pipe diameter and length. Combining the cost of the HDPE pipe and the concrete anchor blocks, the cost of laying the outfall pipe is:

$$CC\_1 = AD\_pX \tag{5}$$

At a location with uniformly sloping bottom (with slope ¼ Γ), the length of the pipe is related to the ambient depth required (*X* ¼ *H=*Γ). The pipe diameter depends on many factors including the size of the plant, construction material, water depth, available hydraulic head etc. [28]. Assuming the size of the pipe to be a function of the flow rate only, an analysis of the available data for outfalls around

the world (from [31, 32], shown in **Figure 1**) shows the following dependence of pipe size (in m) on flow rate (in m<sup>3</sup> /s):

$$D\_p = 0.98 Q\_0^{0.36} \tag{6}$$

The cost of the outfall pipe is then given by:

$$\text{CC}\_1 = \text{aQ}\_0^{0.36} \text{H/} \Gamma \tag{7}$$

where *a* ¼ 0*:*98*A*.

The second component is the cost of the diffuser manifold. Assuming that the diffuser manifold has the same diameter as the outfall pipe (*Dm* ¼ *Dp*) and that the spacing between adjacent nozzles is equal to the water depth (*l* ¼ *H*), the capital cost of the manifold becomes:

$$\text{CC}\_2 = \text{a}Q\_0^{0.36}\text{NH} \tag{8}$$

This component of cost is only considered for a multiport diffuser, i.e., *CC*<sup>2</sup> ¼ *aQ*<sup>0</sup> <sup>0</sup>*:*<sup>36</sup>*H* for a single port discharge is neglected in comparison to other costs.

The third component is the cost of nozzles. A linear fit to the cost per nozzle data, reported in [29, 30], was used to estimate the total cost of nozzles as:

$$\text{CC}\_3 = \text{N}(\text{B} + \text{CD}\_0) \tag{9}$$

The fourth component is the cost of pumps required to pump the effluent to the offshore location of the outfall. The cost of pumps increases with the flow rate and the total head loss in the outfall. Based on the cost of pumps for pumping product water reported by [29], this cost was found to be proportional to the product of effluent density, flow rate and total head loss (*HL*). Thus:

$$\text{CC}\_4 = \text{E}\rho\_0 \text{Q}\_0 \text{H}\_L \tag{10}$$

**Figure 1.** *Correlation between outfall pipe diameter and flow rate.*

The first three cost components (*CC*1,*CC*<sup>2</sup> and *CC*3) only include material costs. The installation cost is assumed to be 1.2 times the material cost (based on cost estimates from [30]) so that the total cost is 2.2 times the material costs. For the cost of pumps (*CC*4), the installation cost is already included in Eq. (10).

The total cost of the outfall also includes an operating cost which mainly consists of the cost of electricity for pumping the effluent, and operation and maintenance cost. It is assumed that the available pressure and elevation head before discharge are negligible and thus pumping is required to discharge the effluent with high velocity. The pumping cost is proportional to the product of effluent density, flow rate and total head loss. Thus, the pumping cost over the life of the plant is:

$$OC\_1 = F\rho\_0 Q\_0 H\_L \tag{11}$$

where *F* depends on the cost of electricity, discount rate and outfall lifetime.

Malcolm Pirnie [29] reported values of operation and maintenance cost for different scenarios which suggest that it is independent of design variables. Therefore, a constant value was used for the operation and maintenance cost.

**Table 2** provides a summary of the cost functions and typical values of cost coefficients (for costs in USD, as per May 2016 ENR index).

An estimation of head loss is required to calculate the total cost. Head loss is estimated by considering the components listed in **Table 3**. Here, *Vp* is the velocity inside the outfall pipe. The head loss incurred in conveying the effluent to the shoreline is not included as it is the same for all designs and does not affect the optimization analysis. Thus, the outfall costs calculated here represent the cost above the cost of the simplest (shoreline) discharge.

#### **5.2 Desired dilution**

Environmental regulations usually specify threshold concentrations for various contaminants. These are maximum acceptable concentrations in the water body that are considered to be safe for aquatic organisms. Thus, outfalls are required to reduce contaminant concentrations to threshold levels within a regulatory mixing zone. Here, the impact point of the jets is assumed to be the end of the mixing zone.

Threshold concentrations can be different at different locations as they are based on the toxicological adaptability of the marine species thriving in that location. Also, regulatory requirements vary from country to country, with international guidelines also referring to local regulations [34, 35]. In addition, source stream concentrations vary depending on the quality of feed water, desalination process etc.,


*b Assuming discount rate of 10% and plant lifetime of 20 years.*
