Reducing the Risk Associated to Desalination Brine Disposal on the Coastal Areas of Red Sea

Abstract

By the end of 2005 the global installed capacity for desalination of seawater was about 24.5·106 m³/day. The geographical distribution of the desalination plants was as follows: 77 % in the Middle East and North Africa, 10 % in Europe, 7 % in the Americas and 6 % in the Asia-Pacific region. The volume of brine discharged in the Red Sea increased from 6.4 million m³/day (in 1996) to 6.8 million m³/day (in 2008) and is still increasing due to the observed tendency to improve the average recovery ratio from 30 to 50 %. This will make the environmental concerns much more important in the future. There are two main sources of problems, i.e. the concentrate and chemical discharges and the cooling water effluent discharges. The salinity is expected to increase in the long term if larger and larger amounts of desalinated water are removed from the water bodies. A proper solution for the desalination waste brine disposal process requires a good balance between technical constraints (i.e. placing a pipe on the sea-bottom), environmental conditions (i.e., finding an optimum distance from the seashore where high salinity brine should be discharged without significant environmental impact; also, the availability for long run of brine disposal placement should be considered) and as low as possible overall economic costs.

Since the potential cumulative impacts of desalination activity on the marine environment is expected to be more significant in case of regional seas, in this chapter we focus on the desalination plants in Red Sea. The objective is to discuss a modeling framework for the environmental-hydraulic design of the outfall system for desalination plants. The chapter presents an interdisciplinary combination of environmental issues with physical processes and discharge modeling. We assess the technical viability of disposal the brine effluent produced by desalination plants into Red Sea coastal regions via submarine pipes.

There are several approaches to mitigate the environmental effects of the brine discharges. By tradition, the brine is discharged back to the sea in open channels. Impacts from high salinity may be avoided by pre-dilution of the desalination plant rejected stream with other waste streams, such as power plant cooling water. Impacts from high temperature may be avoided by ensuring heat dissipation from the waste stream to the atmosphere before entering the water body. However, simulations models for the brine plume dispersion from desalination power plants reveal the inadequacy of using surface discharging outfalls in order to brine discharging. Large capacity plants require submerged discharges which ensure a high dilution, reducing the harmful impacts on the marine environment. Mixing and dispersal of the discharge plume can be enhanced by installing a diffuser system, and by locating the discharge in a favorable oceanographic site which dissipates the heat and salinity load quickly.

The central concept of the brine disposal by submerged pipes is the available head at the discharge point. Higher values of the available head ensure larger jet dispersion lengths and better conditions for ejected brine dilution. We have shown that the quality of the dilution process is well quantified by the Froude number of the brine discharge jet, whose optimum values range between 20 and 25. Using the Froude number allowed us to find the optimum pipe length and the optimum depth of the discharge point.

About half of the Red Sea desalination plants are based on reverse osmosis. The percentage of RO plants is expected to increase, taking into account the lower production costs and the favorable technological evolution. The most representative RO desalination plants around the Red Sea coast are considered both by country and by capacity points of view. In order to provide relevant conclusions for the study reduced capacity desalination plants were selected due to their large number. For not available/existing desalination plants some hypothetic “case studies” were considered.

Optimum brine dispersion may be obtained by using underwater pipes for any sort of high capacity and low capacity RO desalination plants operating on the Red Sea coasts. In case of large capacities, a pipe length around lX = 1,000 m allows optimum operation. A pipe length about lX = 500 m is needed for low capacity RO desalination plants.

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1 Introduction

Countries with water resources of less than 1,000 m³/capita/year are usually listed among those with problems from both social and demographic aspects (Al-Gobaisi 1997). In this context, desalination is an important source of fresh water for the states which have seas or oceans as natural borders. In 1998 the total daily capacity of installed desalination plants worldwide was 22.7∙10³ m³. This is an increase of 70% from that previously reported in 1990 (Buros 1998; IDA 2006–2007). The cost of the desalination plants depends on their location and on the local unit costs and operations. Averagely speaking, these costs decreased from $1.5/m³ in 1990 to $0.50/m³ in 2003 (Pankratz 2004).

Seawater desalination may provide a constant supply of good quality drinking water, offering many human health and socio-economic benefits. Also, seawater desalination does not affect natural freshwater ecosystems. However, concerns are raised due to some potential negative impacts on coastal water quality and marine life. There are two main sources of problems, i.e. the concentrate and chemical discharges and the cooling water effluent discharges. The energy consumption and the land use are other aspects of concern in relation with seawater desalination plants operation (Tobias et al. 2009).

A good presentation about the waste products carried by the desalination plants into the coastal environment is made by Lattemann and Höpner (2003). The amount of intake water that can be desalted depends of the desalting process. It is about 10% for the thermal processes, such as multi-stage flash distillation (MSF) and up to 50% in case of reverse osmosis (RO). The rest of the seawater is usually discharged back to the sea. The reject streams from distillation plants consist in most cases in concentrated salt brine with increased temperature, residual chlorine levels, antiscalant and anti-foaming additives. Antiscalants and coagulants may be present in RO reject streams, if the backwash water from coagulation and media filtration is combined with the process wastewater before discharge. Low concentrations of metals from corrosion are usually found. Copper contamination may be a concern in the reject streams of those desalination plants with heat exchangers made of copper-nickel alloys. The reject streams of RO plants may contain harmful cleaning solutions if these are mixed with the concentrate and discharged into the sea.

By the end of 2005 the installed capacity for desalination of seawater was about 24.5∙10⁶ m³/day. The geographical distribution of the desalination plants was as follows: 77% in the Middle East and North Africa, 10% in Europe, 7% in the Americas and 6% in the Asia-Pacific region. Two thirds of this capacity was based on thermal processes, mainly in the Middle East. Membrane desalination was the dominating process on the rest of the globe.

The observed tendency of the installed desalination capacity is to follow the future increase in regions population. Another observed tendency is to improve the average recovery ratio from 30 to 50%. Both tendencies will have as a result the increase of the brine salt concentration. This will make the environmental concerns much more important in the future.

Most of the Middle East desalination plants are located on the borders of the Arabian Gulf (AG) and Red Sea (RS). These semi-enclosed seawater bodies are characterized by very low annual precipitations, from 90 to 150 mm and very high evaporation rates, from 1.2 to 2 m annually. Therefore, the AG and RS waters have a higher salt content than the planetary ocean (Anton et al. 2005). The salinity is expected to increase in the long term if larger and larger amounts of desalinated water are removed from the water bodies.

Since the potential cumulative impacts of desalination activity on the marine environment is expected to be more significant in case of regional seas, in this chapter we focus on the desalination plants in Red Sea. The countries bordering the Red Sea are: Egypt, Israel, Jordan, Sudan, Eritrea, Saudi Arabia, Yemen and Djibouti. The objective is to discuss a modeling framework for the environmental-hydraulic design of the outfall system for desalination plants. The chapter presents an interdisciplinary combination of environmental issues with physical processes and discharge modeling.

2 Desalination Plants on Red Sea Coasts

The Red Sea surface area is about 450,000 km². Other characteristics are as follows: a gross length of about 2,000 km, a mean width of about 225 km, a mean depth of around 500 m and a maximum depth of 3,040 m (Anton et al. 2005).

No river enters the Red Sea. Therefore, there is virtually no surface water runoff. The Red Sea exchanges water with the Gulf of Aden at the strait of Bab el Mandab (Shahin 1989; Morcos 1970). The water exchange rate is about 0.5∙10⁶ m³/s during November to May while during June to October this quantity is about 0.16∙10⁶ m³/s (Thompson 1939; Murray and Johns 1997). The annual mean Red Sea outflow transport is estimated to about 0.37∙10⁶ m³/s (Murray and Johns 1997). This agrees with Siedler’s (1969) estimated amount of 0.33∙10⁶ m³/s. The rainfall over the Red Sea and its coasts is about 60–100 mm/y with an average volume of about 233,000 km³. The renewal of water in the Red Sea is estimated to take 20 years (Red Sea 2008).

In 1996 about 6.4∙10⁶ m³/day brine water was discharged into the Red Sea. In 2008, this figure has increased to 6.8∙10⁶ m³/day. The estimate for 2050 is 26.6∙10⁶ m³/day. Table 12.1 shows the desalination capacity for several countries located on the border of the Red Sea.

Table 12.1 Desalination capacity and amount in cubic meters per capita per year at the end of 1996, 2008 and 2050, for countries on the Red Sea shore

Figure 12.1 shows that the desalination technologies used in Red Sea area are Reverse Osmosis, Multi-stage Flash Distillation and Multi-effect Distillation (MED) (Lattemann and Höpner 2008; IDA 2006). Saudi Arabia owns large desalination plants. On the other hand, the desalination plants in Egypt are larger in number but of smaller capacity. Therefore, the capacity values shown in Fig. 12.1 for Egypt are cumulated values for small desalination plants located in the same area.

Fig. 12.1

Seawater desalination capacity in the Red Sea (m³/day). Desalination technologies are: RO Reverse Osmosis, MSF Multi-stage Flash Distillation,MED Multi-effect Distillation (Adapted from Lattemann and Höpner (2008)) (Source of background: Esri, i-cubed, USDA, USGS, AEX, GeoEye, Getmapping, Aerogrid, IGN, IGP, and the GIS User Community)

2.1 Perspectives for Desalination Technologies in Red Sea Area

Table 12.2 shows that the reverse osmosis technology is dominating the world market (Wittholz et al. 2008). Most of the desalination capacities installed in the last 25 years were based on this technology.

Table 12.2 World’s installed desalination capacity by technology (IDA 2002)

However, in the Middle East and North Africa (MENA) region, most of the installed desalination capacities are using the MSF technology although the installed capacity for reverse osmosis has increased in the last years (Table 12.3). The lower percentage of the RO technology in MENA region is mainly due to the fact that this technology is used for small capacities.

Table 12.3 Cumulative contracted capacity by technology since 1944 in the Middle East and North Africa (MENA) region (Source GWI 2010)

Since 2000 the recovery ratio of the RO technology has significantly increased at 44% (for a seawater intake salinity value of 41.7 ppt and brine outlet of 74 ppt – Raed et al. 2007). The production cost of the reverse osmosis seawater desalination decreased from 2.5 to less than 0.5 $/m³, mainly in those locations which are favourable in terms of water intake access point and cost operation. Table 12.4 shows that RO technology is in most cases more competitive than the MSF and MED technologies. An Australian case study shows that because of its lower cost and improved membranes RO became competitive for large size desalination plants (Table 12.5) (Karagiannis and Soldatos 2008; Wittholz et al. 2008).

Table 12.4 Relative operating costs of desalination process ($/m³) (Bushnak 2010; GWI 2010)

Table 12.5 A summary of costs for different technologies for four different capacities (Wittholz et al. 2008 – case study Adelaide Australia)

The desalination technologies will face various technical and economical issues as well as environmental issues due to the increase of the amount and the salinity of the discharged waters, associated to the increase of the fresh water demand. The volume of brine discharged in the Red Sea increased from 6.4 million m³/day (in 1996) to 6.8 million m³/day (in 2008) – (Bashitialshaaer et al. 2011) and is still increasing. The larger amount of brine will increase locally the salinity of the seawater used as intake by the desalination plants. As a result, the recovery ratio is expected to decrease and this will raise the cost of desalinated water – this can already be observed in some areas of the Arabian Gulf.

Some aspects related to the brine discharge in Red Sea by RO desalination plants will be considered next.

3 Hazards for Brine Disposal

The total dissolved solids in the Red Sea is 41 g/L, which is higher than 34.5 g/L for typical seawater (Magazine 2005). The desalination processes produce a concentrate which contains residues of pretreatment and cleaning chemicals, their reaction (by-) products, and heavy metals due to corrosion. Depending on the desalination technology, the concentrate may be increased in temperature. Most desalination plants are using chemical pretreatment and cleaning. In thermal plants these include the treatment against biofouling, scaling, foaming and corrosion while the membrane plants are using treatments against biofouling, suspended solids and scale deposits. The chemical residues and by-products are usually discharged into the sea along with the concentrate. The effluent is a mix of these pollutants, which may have effects on marine life.

The amount of natural evaporation in Red Sea is much larger than the total amount of water extracted for desalination. However, evaporation takes place all over the surface area but the amount extracted for desalination is local and may have a greater effect than evaporation. The salt concentrations of the brines are usually found to be close to double that of natural seawater (Vanhems 2001). The salinity may increase by 70% after the brine of RO desalination plants is discharged into the sea (Ruiz-Mateo et al. 2007). Constructions close to the coastline give opportunities for one or more outfalls to the sea. This may reduce the local environmental impact of brine discharge (Raed et al. 2007). At the level of the whole Red Sea the increase in brine discharge raises significantly the salt concentration. The salinity of Red Sea in late 1996 and 2008 and predictions for 2050 is (in g/L) 0.22, 0.49 and 1.16, respectively. As seawater salinity increases, the recovery ratio decreases, which raises the cost of desalinated water.

Some of the environmental impacts of desalination plants, such as the land use, are similar to other development projects. Specific effects are the impingement and entrainment of organisms due to the intake of large quantities of seawater. The construction of the intake structure and pinping causes an initial disturbance of the seabed. This results in the re-suspension of sediments, nutrients or pollutants into the water column. After installation, the structures can affect water exchange and sediment transport, act as artificial reefs for organisms, or may interfere with shipping routes or other maritime uses.

The concentrate and chemical discharges to the marine environment are the key concerns of desalination plants. They may have adverse effects on water and sediment quality, impair marine life and the functioning of coastal ecosystems. The most negative effects occur when high waste water discharges coincide with sensitive ecosystems. The impacts on the marine environment depend on both, the properties of the reject streams and the biological features of the receiving environment. More sensitive to desalination plant discharges are the shallow sites with abundant marine life. Less sensitive are the open-sea locations, which are more capable to dilute and disperse the discharges.

The distribution of marine species is mainly controlled by salinity and temperature. Most organisms can adapt to minor deviations from optimal salinity and temperature conditions. Extreme situations may be tolerated temporarily. A continuous exposure to unfavourable conditions has however bad consequences on the survival rate. Thus, a constant brine discharge of high salinity and temperature may be fatal for marine life. This may change the composition and abundance of species in the discharge site. The more adapted species to the new situation will eventually prevail in the discharge site.

The discharge brines of RO and thermal plants have different effects on the seawater. The brine of RO plants has higher density than seawater. It will spread over the sea floor in shallow coastal waters unless it is dissipated by a diffuser system. The most affected by the high salinity and chemical residues will be the benthic communities, such as seagrass beds. The brine of the thermal plants are typically positively or neutrally buoyant, especially when combined with power plant cooling waters. They will affect mainly the open water organisms.

The regulations usually refer to the limiting pollutant levels in the reject streams at the point of discharge (ES – effluent standards) and in the receiving environment (AS – ambient standards). For instance, the ratio ES/AS for copper is about 100 while for chlorine is 27. For most chemical and physical parameters (such temperature) the ratio ES/AS ranges between 5 and 1,000. This ratio describes appropriately the impact of the pollutants on the eco-system. Indeed, the ES may be considered to protect against acute (lethal) effects on organisms, while the AS is supposed to prevent long-time chronic influences. The necessary dilution that must be attained through physical mixing or by biological decay and chemical transformation processes may be equally well described by the ratio ES/AS.

A “combined approach” has been proposed in case of distillation brine discharge (Tobias et al. 2009). In analogy to wastewater discharges, it requires a regulatory mixing zone regulation. The mixing zone is defined as follows (Tobias et al. 2009):

“The ambient standards apply in the case of point sources outside and at the edge of the mixing zone. The mixing zone is a spatially restricted region around the point source whose dimensions shall be specified either according to water body type and use or on an ad-hoc basis.”

A similar approach is already used in the United States, the Sultanate of Oman and other countries (Tobias et al. 2009).

4 Brine Disposal by Submerged Pipe

There are several approaches to mitigate the environmental effects of the brine discharges. By tradition, the brine is discharged back to the sea in open channels. In the case of membrane technologies, dense RO effluent flow behave as negatively buoyant plume and spread on the sea floor. In the case of thermal technologies the effluent from thermal desalination plants could behave both neutral to positive buoyant flux causing the brine to rise and spread on the sea surface. Therefore effluent properties (i.e. flow, temperature, density, salinity etc.) have to be calculated at the discharge point. Impacts from high salinity may be avoided by pre-dilution of the desalination plant rejected stream with other waste streams, such as power plant cooling water. Impacts from high temperature may be avoided by ensuring heat dissipation from the waste stream to the atmosphere before entering the water body. Cooling towers may be used for this purpose. In the case of submerged disposal using long pipes the effluent temperature is decreasing while flowing towards the output section. However, simulations models for the brine plume dispersion from desalination power plants reveal the inadequacy of using surface discharging outfalls in order to brine discharging (Alameddine and El-Fadel 2007).

Large capacity plants require submerged discharges which ensure a high dilution, reducing the harmful impacts on the marine environment. Mixing and dispersal of the discharge plume can be enhanced by installing a diffuser system, and by locating the discharge in a favorable oceanographic site which dissipates the heat and salinity load quickly.

5 Technical and Environmental Evaluation

In this section we assess the technical viability of disposal the brine effluent produced by desalination plants into Red Sea coastal regions via submarine pipes. The largest operating capacities of desalination plants along Red Sea coast are located in Saudi Arabia, Egypt, Israel and Jordan. Thus, we shall consider a number of such facilities in order to assess technical and environmental solution for an optimum brine disposal. For other countries such as Yemen, Eritrea and Sudan similar case studies may be elaborated in the future.

Figure 12.2 shows the largest RO desalination plants operation on the Red Sea border. Most of these plants are located in Saudi Arabia. Smaller RO desalination plants are spread over the Egyptian coast. The Red Sea area belonging to Saudi Arabia has the following geographical characteristics: sea-surface area = 215,978 km², seabed area = 216,274 km², mean seabed slope = 1.42°, maximum seabed slope = 31.32° and the maximum depth offshore is −2,284 m (Costello et al. 2010). These values may be considered as representative for all calculations in this chapter.

Fig. 12.2

Several RO desalination plants on Red Sea coast (El-Sadek 2010; Lattemann and Höpner 2008; Mohsen 2007; Khalil 2004; Semiat 2001) (Source of background: Esri, i-cubed, USDA, USGS, AEX, GeoEye, Getmapping, Aerogrid, IGN, IGP, and the GIS User Community)

Details about the technical and economical evaluation are presented in Sect. 12.5 for the particular case of the Rabigh desalination plant. This plant is using an Independent Water Steam Power Production unit (IWSPP) to generate electrical power with a 5 × 115 MW Steam Turbine Power Plant for supplying 16 trains RO units. The total installed capacity is about 192,000 m³/day. Results for all representative stations in Fig. 12.2 are presented and discussed in Sect. 12.6.

The top of the hypothetical submarine pipe is located at a particular place on the Saudi Arabia coast. The pipe is couched on the bottom of the sea following a straight-line direction through Red Sea axis as shown in Fig. 12.3a.

Fig. 12.3

(a) Course of the desalination concentrate pipe hugging the sea-bottom from Jeddah; (b) Cross section through region A

Preliminary results obtained by the authors in case of a desalination plant located at Jeddah are reported in Badescu et al. (2012). The maximum length of the submarine pipe in that study was 10,000 m. This value has been obtained under the constraint of a maximum dispersion for the brine plume. The same maximum pipe length of 10,000 m is adopted in the present work since the geographical characteristics of Jeddah and Rabigh are quite similar. It corresponds to region A in Fig. 12.3a. In this chapter pipes of different length are considered in region A, which has been split in five sections. The sea-bottom in these regions is delimitated by the points described in Table 12.6. Points A1 to A5 in Fig. 12.3b are associated to the sea water free surface while points A1^’ to A5’ in Table 12.6 represent potential discharge points of the underwater duct.

Table 12.6 Several parameters for pipes with discharge points A1’ to A5’ inside region A in Fig. 12.3b

5.1 Optimization of Brine Pipe Diameter

A simple hydraulic model is developed here. It involves computation of the optimum brine pipe diameter. A detailed presentation of the model is made in Badescu et al. (2012) and a brief presentation is included here. The input data for this model consists of temperature values as well as salinity values for both the seawater and the brine inside the duct, at various depths. The influence of natural sea currents as well as seasonal climate variations is neglected.

These assumptions allow using data for seawater temperature and salinity provided by Tomczak and Godfrey (2003). Relationships from Millero et al. (1980) were used to calculate brine and seawater density as function of salinity, pressure and temperature. For convenience the brine salinity inside the pipe is a constant in time and space (S_B = 74 ppt), according to Raed et al. (2011), and the seawater salinity at the intake of the desalination plant in S_I = 41.7 ppt. Therefore, the brine density at the discharging end of the pipe is function just of pressure and temperature. Data for relevant discharge points A1’ to A5’ (see Fig. 12.3b) are presented in Table 12.7.

Table 12.7 Data for pipes with discharge points A1’ to A5’ in Fig. 12.3b

Figure 12.4 shows the brine basin of the desalination plant and the pipe. This figure is used to derive the equations for the optimization of the discharge pipe diameter. The brine level in respect to the seashore basin is denoted h. The basic scenario assumes h = 0 m, i.e. the surface of the brine in the basin is at the level of the sea surface. The discharging end of the pipe may be placed at the deeper extremity of one of the discharge points A1’ to A5’ in Fig. 12.3a, b.

Fig. 12.4

Brine pipe layout for the hydraulic model considered

For convenience, here we denote by X (=A1,A2,A3,A4,A4) any of the five sub-regions of region A. Similarly, n’(=1’,2’,3’,4’,5’) denotes any of the five points on Fig. 12.3a, b and Table 12.6 . These points are placed at depth H _n’ .

The length of the pipe whose discharging end is placed at the deepest point n’ (=1’,2’,3’,4’,5’) of region X(=A1,A2,A3,A4,A5) in Fig. 12.3b is denoted l _X . That pipe has a constant diameter denoted d _X . One denotes by ρ _B,0 and t ₀ , respectively, the mass density and the temperature of the brine in the basin of the desalination plant. Also, ρ _B,X denotes the average mass density of the brine in the pipe, for a certain region X. This quantity is calculated as the arithmetical mean between the density of the brine in the basin (ρ _B,0 ) and the brine density ρ _B,n’ at the appropriate discharge point n’(=1’,2’,3’,4’,5’) of the pipe, respectively:

$$ {\rho_{{B,X}}} = \frac{{{\rho_{{B,0}}}\left( {{t_0},{p_{{atm}}},{S_B}} \right) + {\rho_{{B,{n^{^\prime}}}}}\left( {{t_{{sw,{n^{^\prime}}}}},{p_{{{n^{^\prime}}}}}{S_B}} \right) }}{2} $$

(12.1)

Equation 12.1 shows that the brine density in the basin, ρ _B,0 , depends on the atmospheric pressure p _atm and on the brine salinity S _B . The brine density in point n’ depends on the brine temperature (t _n’ ) and pressure (p _n’ ) as well as on the brine salinity S_B, which is a constant along the pipe. The seawater density in points n(=1,2,3,4,5) at sea surface level and in points n’(=1’,2’,3’,4’,5) is denoted ρ _sw,n and ρ _sw,n’ , respectively. The average density of the seawater column of height H _n’ is denoted ρ _sw,X . It is computed as an arithmetical mean between the seawater density at surface (ρ _sw,n ) and at the depth H _n’ (ρ _sw,n’ ) of the appropriate discharge point n’(=1’,2’,3’,4’,5’):

$$ {\rho_{{sw,X}}} = \frac{{{\rho_{{sw,n}}}({t_{{sw,n}}},{p_{{atm}}},{S_{{sw,n)}}} + {\rho_{{sw,n^\prime}}}({t_{{sw,n^\prime}}},{p_{{n^\prime}}},{S_{{sw,n^\prime}}})}}{2} $$

(12.2)

Equation 12.2 shows that the seawater density in points n (=1,2,3,4,5’) at sea surface level depends on the seawater temperature and salinity in that point, t _sw,n and S _sw,n , respectively. Similarly, the seawater density in points n’(=1’,2’,3’,4’,5’) depends on the seawater temperature, pressure and salinity in that point, t _sw,n’ , p _sw,n’ and S _sw,n’ , respectively.

One denotes by V _n’ the brine discharge velocity in point n’ (=1’,2’,3’,4’,5’). The energy balance for the steady-state brine flow is:

$$ {\rho_{{B,X}}}g\left( {h + {H_{{n^\prime}}}} \right) = \frac{{{\rho_{{B,X}}}V_{{n^\prime}}^2}}{2} + {\rho_{{sw,X}}}g{H_{{n^\prime}}} + \Delta {p_{{lin,X}}} + \Delta {p_{{loc,X}}} $$

(12.3)

The l.h.s. of Eq. 12.3 represents the pressure due to the brine’ weight at the discharge point n’ (=1’,2’,3’,4’,5’) of the pipe. The first and second terms in the r.h.s. of Eq. 12.3 are, respectively, the kinetic pressure of the brine at the discharge point and the seawater static pressure at the same point. Finally, Δp _lin,X and Δp _loc,X in Eq. 12.3 are de linear and local pressure losses inside the pipe, respectively. These last two quantities may be computed by (Florea and Panaitescu 1979):

$$ \Delta {p_{{lin,X}}} + \Delta {p_{{loc,X}}} = \frac{{\rho {{_B}_{{,X}}}}}{2}{\left( {\frac{{4{Q_B}}}{{\pi d_X^2}}} \right)^2}\left( {{\lambda_{{lin,X}}}\frac{{{l_X}}}{{{d_X}}} + {\zeta_{{loc,X}}}} \right) $$

(12.4)

where ζ _loc,X and λ _lin,X are the coefficients of local and linear pressure losses, respectively. Local pressure losses may be neglected in case of very long pipes, as we shall do here. The coefficient λ _lin,X has been computed by:

$$ \lambda = \frac{{8g}}{{{C^2}}}, $$

(12.5)

where the Chézy coefficient C could be calculated, in this stage, by using Bazin’s formula (Florea and Panaitescu 1979):

$$ C = \frac{{87}}{{1 + \frac{\gamma }{{\sqrt {R} }}}} ,$$

(12.6)

For an average pipe roughness (fabric pipe tape, for instance), R = d/4 and γ = 0.6 in Eq. 12.6. Usage of Eqs. 12.3, 12.4, 12.5, and 12.6 yield another form of the energy balance equation:

$$ {\rho_{{B,X}}}g\left( {h + {H_{{n^\prime}}}} \right) = {\rho_{{sw,X}}}g{H_{{n^\prime}}} + \frac{{{\rho_{{B,X}}}}}{2}{\left( {\frac{{4{Q_B}}}{{\pi d_X^2}}} \right)^2}\left( {0.01036\frac{{{{\left( {\sqrt {{{d_X}}} + 0.32} \right)}^2}}}{{d_X^2}}{l_X} + 1} \right) $$

(12.7)

The available head in the discharge section of the brine pipe is given by:

$$ {H_a} = {H_t} - {h_d} ,$$

(12.8)

where H _t is the total head and h _d is the friction losses in the pipe, associated to the waste brine discharge point n’ in section X. These quantities are given by:

$$ {H_t} = \frac{{H(\rho_{{B,X}} - \rho_{{sw,X}})}}{{\rho_{{sw,X}}}};{h_d} = \frac{{\Delta {p_{{linX}}}}}{{\rho_{{B,X}}g}} $$

(12.9a,b)

where H is seawater depth. Equation 12.7 may be used to obtain the optimum diameter of the underwater pipe which maximizes the available head H _a . Results are shown in Table 12.8 for the sub-regions A1 to A5 of region A in Fig. 12.3a, b.

Table 12.8 Results for the optimum pipe diameter in sub-regions A1’ to A5’ of region A in Fig. 12.3a, b

A few explanatory comments follow. The optimum pipe diameter d _X is about 1.4 m, for all input values for the pipe length l _X . The available head H _a increases by increasing the pipe discharge depth H_n’. However, the linear losses increase by increasing H_n’, since this means a longer pipe length l _X . Therefore, using pipes longer than about 2,000 m is not justified from a hydraulic point of view. Indeed, using longer pipes is not associated to a decrease of the pipe diameter, which would result in a relative decrease of pipe cost.

However, the optimization of the pipe diameter should take into account the brine dispersion process at the outlet section of the pipe. Discharging the desalination brine on the seabed of the Red Sea increases locally the salt concentration of the seawater. This may disrupt the ecosystem in the dilution zone, leading to dehydration, decrease of turgor pressure, and death of benthic marine organisms. The distance the plume travels before it contacts the ocean bottom is defined as the mixing zone (Kimes 1995). The mixing zone is a function of both pipe diameter d _X and available head H _a .

5.2 Optimization of Pipe Length and Brine Jet Dispersion Length

The environmental issues considered in the Sect. 12.5.1 require calculation of the maximum brine flow velocity at discharge, the optimum pipe length related to emitted jet length and the extent of the maximum dilution zone. The most efficient method for brine discharging into the seawater is a subject of intense R&D. A common solution to ensure better dilution is to use inclined under-sea jets, (30–45° above horizontal) obtained by throttling the cross-section of the pipe end. This requires knowledge of the hydraulic energy available at the outlet pipe cross-section. Results in Sect. 12.5.1 show that the discharge point A1’ (i.e.l _X  = 2,000 m, H _n’  = 110 m, h = 0 m) is the best solution from the hydraulic point of view. However, a more precise value of the available head H _a is needed in order to evaluate more accurately the available brine jet length. Several parameters have been computed for the discharge points A1’ to A5’ (see Table 12.7). For all these points, the notation and computational procedure of Sect. 12.5.1 have been used. Jet velocities emissions produced by a nozzle placed at each discharge points A1’ to A5’ have been computed by using a relationship similar to Eq. 12.4:

$$ {\rho_{{B,X}}}g{H_{{n^\prime}}} = {\rho_{{sw,X}}}g{H_{{n^\prime}}} + \frac{{{\rho_{{sw,X}}}V_{{nozzlen^\prime}}^2}}{2}\left( {1 + {\zeta_{{nozzle}}}} \right) + \frac{{{\rho_{{B,X}}}V_{{n^\prime}}^2}}{2}{\lambda_X}\frac{{{l_X}}}{{{d_X}}} $$

(12.10)

Here the notation of Fig. 12.4 has been used while V _n’ and V _{nozzle n’} is the velocity of the brine along the pipe and at nozzle discharge point, respectively. In Eq. 12.10, ζ _nozzle is the coefficient of local head losses related to the d _nozzle /d _X ratio (Florea and Panaitescu 1979). Note that V _nozzle enters the flow equation:

$$ {\left( {\frac{{{d_{{nozzlen^\prime}}}}}{{{d_X}}}} \right)^2} = \frac{{{V_{{n^\prime}}}}}{{{V_{{nozzlen^\prime}}}}} $$

(12.11)

Three values of the ratio d _nozzle /d _X have been considered as input.

Figure 12.5 shows the geometrical configuration of the brine jet. A point (x, y) on brine jet trajectory obeys the following standard kinematic relationships:

Fig. 12.5

Geometrical configuration of the brine jet

$$ x = {V_{{nozzle}}}t;y = {H_a} - \frac{{{{g^\prime}_0}{t^2}}}{2} $$

(12.12)

where:

$$ {g^\prime_0} = g\frac{{\rho_{{B,X}} - \rho_{{sw,X}}}}{{\rho_{{sw,X}}}} $$

(12.13)

is the reduced gravity. Using Eqs. 12.12 and 12.13 yields:

$$ y = {H_a} - \frac{{g(\rho_{{B,X}} - \rho_{{sw,X}})}}{{2\rho_{{sw,X}}V_{{nozzle}}^2}}{x^2} $$

(12.14)

Equation 12.14 allows deriving the jet horizontal length L, taking into account that y = 0 is associated to x = L:

$$ L = {V_{{nozzle}}}\sqrt {{\frac{{2{H_a}}}{{g\frac{{\rho_{{B,X}} - \rho_{{sw,X}}}}{{\rho_{{sw,X}}}}}}}} $$

(12.15)

Equation 12.15 and Table 12.8 are used now to compute the jet horizontal length L for the five discharge points A1’ to A5’ defined in Table 12.7. Results are given in Table 12.9. The dependence of the jet length L on the sea water depth H in shown in Fig. 12.6.

Table 12.9 Horizontal length L of the brine jet for given discharge point and values of the ratio d_nozzle/d_X

Fig. 12.6

The horizontal brine jet length L as a function of seawater depth H for three values of nozzle diameter ratio, d _nozzle /d _X (▲-0.2; ▪-0.25; ♦- 0.33)

Table 12.9 shows that the values of V _nozzlen’ range between 3.53 and 6.41 m/s for d _nozzle values ranging between 0.47 and 0.28 m. This is in reasonable agreement with results of similar calculations (Tobias et al. 2009). Generally, larger ejection nozzle velocities increase the horizontal length of the brine jet. Also, the jet length increases by increasing the depth of the discharge point. However, knowing the length L of the brine jet is not enough to evaluate the efficiency of the brine dispersion process. It remains to be assessed whether the surface area covered with brine on the sea-bottom is large enough to obey the ecological constraints. The space distribution of brine concentration depends on the sitting of the outfall and the amount of mixing and transport capacities of the prevailing marine current. High mixing efficiencies occur at high-flow velocities at offshore discharge location (Bleninger and Jirka 2008). A few models were developed previously to predict dispersion and mixing of brine discharges (see CORMIX (Cornell Mixing Zone Expert) by Doneker and Jirka 2001). However, they have limited relevance since data concerning pollutant concentration along the brine plume are not readily available. Indeed, obtaining consistent data sets requires monitoring to be carried out every 6 months for a period of 4 years on a radius of 200 m around the submarine outfall point . From this point of view evaluation of sediment chlorite levels enables the desalination effects to be quantified (Alharbi et al. 2012). Since elevated chlorite levels are directly linked to the desalination technology and site specific feature it is suggested that such studies be undertaken at desalination plants on regular basis. In practice, the appropriate value of the brine dilution is obtained by choosing a value of the densimetric Froude number F _o within the (empirically derived) recommended range of variation. Next, this value is used to compute the surface area of the pipe discharge section. However, our method computes the optimum brine flow geometrical data associated to the maximum available head H _a . Therefore, a reversed approach is adopted here to assess the quality of the dilution process. It uses the Froude (F_o) and Reynolds (Re) numbers of the brine discharge jet, defined as follows (Bleninger et al. 2009)

$$ {F_0} = \frac{{{V_{{nozzle{n^{{{{\prime}} }}}}}}}}{{\sqrt {{\left| {g_0^{{\prime}}} \right|}} {d_{{nozzle}}}}};{\rm Re} = \frac{{{V_{{nozzle{n^{{\prime}}}}}}{d_{{nozzle}}}}}{{{v_{{brine}}}}}; $$

(12.16)

Here ν_brine (= 1,3 10⁻⁶ m²/s) is the brine kinematic viscosity. Good mixing conditions are fulfilled if F_o >10 (with an optimum ranging between 20 and 25) and Re >4,000 (Tobias et al. 2009). Results are shown in Table 12.9. A pipe length l_X = 2,000 m (associated to the discharge point A1’, which has been found in Sect. 12.5.1 to be the optimum hydraulic solution) corresponds to a Froude number F_o = 18, which is not in the optimum range 20–25. Thus, the hydraulic optimum of the pipe length does not coincide with the optimum pipe length from the point of view of brine jet dissipation.

Figure 12.7 shows the dependence of the Froude number F _o on the sea depth H for several values of the maximum speed V _nozzlen ’. Using Fig. 12.7 and Table 12.9 one sees that an optimum dissipation of the brine jet is obtained for pipes of lengths ranging between 3,000 and 4,000 m. This is not acceptable from a technical and economical viewpoint.

Fig. 12.7

Dependence of Froude number at maximum nozzle velocity V _{nozzle n’} on seawater depth H

Therefore, other design solutions should be found in order to ensure a good dissipation of the brine discharge. A few comments follow concerning the methods of increasing the brine jet dilution effectiveness. Higher values of the available head H _a are needed in order to obtain higher values of the jet length L (see Eq. 12.15). Higher values for H _a may be obtained by using longer pipes. However, this solution is not always acceptable from an economic point of view (see Sect. 12.5.3). A second solution is to use a seashore basin for brine storage placed at a certain level h above the sea level (see Fig. 12.4). This second solution is considered and analyzed in some details next. A brine storage basin placed at h = 5 m above current sea level is considered. Also, the pipe discharge end is placed in point A1’ (i.e. H _n’  = 110 m; l = 2,000 m; see Table 12.8). Equations 12.7, 12.8, 12.9, 12.10, 12.11, 12.12, 12.13, 12.14, and 12.15 are used. Results are shown in Table 12.10.

Table 12.10 Pipe diameter d _X and horizontal length L of the brine jet related to F _o numbers for discharge point A1’

The best results are obtained for F_o = 26. Indeed, higher Froude numbers are associated to higher pressure losses (Bleninger et al. 2009).

A proper solution for the desalination waste brine disposal process requires a good balance between technical constraints (i.e. placing a pipe on the sea-bottom), environmental conditions (i.e., finding an optimum distance from the seashore where high salinity brine should be discharged without significant environmental impact; also, the availability for long run of brine disposal placement should be considered) and as low as possible overall economic costs. First, the technical constraints required to properly design, place and operate a submerged pipe. This means, for the bottom-line, calculation of the optimum brine pipe diameter d _X and pipe length l _X for which the maximum available head H _a is obtained. The basic scenario for region A1 (see Table 12.9) may be used as a reference. Second, the environmental issue requires us to obtain the maximum horizontal discharge jet length L. This ensures a high dilution near the pipe end. The basic scenario for region A1 (see Table 12.10) may be used again as a reference. Third, cost estimates are briefly outlined in Sect. 12.5.3. A short discussion on these lines of thought follows. Common practice of extant desalination plants shows that 200 m from shore is the geographical limit to intake seawater while the ordinary limit to brine discharge is at least 500 m. Thus, we shall consider a pipe of length l = 1,000 m discharging in point A1” at seawater depth H = 56 m. These assumptions agree with the seabed slope of Fig. 12.3a, b. A brine basin placed at height h = 5 m above sea level is assumed. Results are presented in Table 12.11.

Table 12.11 Pipe diameter d _X and horizontal length L of the brine jet related to F _o numbers for discharge point A1” (l _x  = 1,000 m, H _n’  = 56 m)

As expected, the values of the Froude number in Table 12.11 for discharge point A1” are higher than those of Table 12.10 for discharge point A1’. The values in Table 12.11 correspond to very good dilution. The best solution is found for F_o =21.6. Further decreasing of the pipe length may increase the water salinity near the Red Sea border.

A competing solution, with similar effects, is to use free-surface channels for brine disposal. This solution is cheaper but has two major weaknesses. First, gravitational brine falling towards the seabed may be perturbed uncontrollably by natural and unnatural marine currents. Second, increasing the desalination process efficiency will increase the brine salinity, which, in turn, will increase the negative environmental impacts.

5.3 Cost Estimates

Only building costs are considered here. Maintenance costs and other costs such as costs associated to damage repairs are not considered. Details can be found in Badescu et al. (2012). To compute the cost of the brine discharge pipe first its capacity is estimated, as a function of the length l _X and diameter d _X . Results are shown in 2010 US dollars in Fig. 12.8.

Fig. 12.8

Cost of pipes of various lengths, depending on the depth of discharge point and pipe diameter. Discharge point at the end of regions A1 to A5 in Table 12.7. The presumed pipe material is steel

The costs range from 48∙10⁶ $ for discharge point A1 to 237∙10⁶ $ for discharge point A5. Costs are significantly reduced when plastic or fabric is used (see Badescu et al. 2012 for details). In case of plastic pipes the cost ranges from 39∙10⁶ $ for discharge point A1 to 190∙10⁶ $ for discharge point A5. When fabric pipes are considered, the cost ranges from 44∙10⁶ $ for discharge point A1 to 163∙10⁶ $ for discharge point A5.

6 Data for Some Desalination Plants Located on the Red Sea Coasts

Figures 12.1 and 12.2 show that about half of the Red Sea desalination plants are based on reverse osmosis. The percentage of RO plants is expected to increase, taking into account the lower production costs and the favorable technological evolution. The most representative RO desalination plants around the Red Sea coast are considered next both by country and by capacity points of view. In order to provide relevant conclusions for the study reduced capacity desalination plants were selected due to their large number. For not available/existing desalination plants some hypothetic “case studies” were considered. Also, the same bathymetric conditions were selected. The method described in Sects. 12.5.1 and 12.5.2 is used to estimate the optimum design solution of the underwater discharge pipes associated to all these plants.

The best brine dispersion on the sea bottom is associated to values of the Froude number ranging from 21 to 23. Table 12.12 shows that these Froude number values may be obtained by changing the free-surface level h of the brine in the desalination plant’s basin. A few comments about the results obtained for a ratio d _nozzle /d _x  = 0.33 follow.

Table 12.12 Optimum brine dispersion – for similar F_o numbers – using underwater pipes for any sort of high capacity and low capacity RO desalination plants operating on the Red Sea coasts

Large and very large desalination plants (exceeding 25,000–50,000 m³/day) are first considered. In Sect. 12.5.1 it has been shown that the optimum pipe length is about l _X  = 1,000 m. Optimum Froude number values associated to this optimum pipe length, are obtained for a brine free-surface level h = 5 m.

In case of smaller desalination plants, ranging between 4,000 and 10,000 m³/day, the same brine free-surface level h = 5 m yields optimum values of the Froude number for pipe length around l _X  = 1,000 m. Shorter pipes should be also considered, since such smaller plants are subjected to more restrictive economical constraints. For example, in case of shorter pipes around l _X  = 500 m a smaller brine free-surface level (around h = 3 m) is needed to obtain optimum Foude number values.

For very small desalination plants, ranging between 500 and 3,500 m³/day, the brine free-surface level should be increased to about h = 8 m in order to obtain optimum Froude numbers for pipe length around l _X  = 1,000 m. In case of shorter pipes (l _X  = 500 m) the brine free-surface level should be decreased to about h = 3 m.

Table 12.12 shows that the optimum brine dispersion may be obtained by using underwater pipes for any sort of high capacity and low capacity RO desalination plants operating on the Red Sea coasts. In case of large capacities, a pipe length around l _X  = 1,000 m allows optimum operation. A pipe length about l _X  = 500 m is needed for low capacity RO desalination plants. Desalination capacities exceeding 15,000 m³/day need longer underwater pipes and brine basins located on the sea shore. Optimum dispersion is associated to Froude numbers ranging between 20 and 23 and corresponds to a brine free-surface level in the basin around h = 5 m.

The model developed in this chapter covers a large range of brine flow rates. The linear pressure losses increase by decreasing the underwater pipe diameters. Thus, the range of optimum Froude number values should be extended towards larger values. However, using the recommended optimum Froude number values (Tobias et al. 2009) is a conservative attitude.

7 Conclusion

Increasing the efficiency of the seawater desalination process increases the salt concentration in the waste brine. This may raise ecological problems if the brine disposal is made by free-surface channels into the nearby Red Sea. A solution to avoid these problems is to use submerged pipes for brine disposal. The geometry of these pipes should be optimized in order to allow larger brine dispersion lengths. A case study is presented in this paper, focusing on brine disposal for the desalination plant Rabigh in Saudi Arabia, on its Red Sea shoreline.

The central concept of the brine disposal by submerged pipes is the available head at the discharge point. This quantity should be as high as possible. Higher values of the available head ensure larger jet dispersion lengths and better conditions for ejected brine dilution. We have shown that the quality of the dilution process is well quantified by the Froude number of the brine discharge jet, whose optimum values range between 20 and 25. Using the Froude number allowed us to find the optimum pipe length and the optimum depth of the discharge point.

Higher values for the available head may be obtained either by extending the desalination brine waste pipe length or by using an onshore basin for brine storage placed at a certain level h above the existing local sea-level. The first solution may be economically prohibitive. The case treated in this paper shows that an onshore brine storage basin placed about 5 m above sea-level allows a good brine jet dispersion even for relatively short discharge pipes.

A proper decision about the brine disposal method must take into account technical, environmental, as well as economic constraints. The cost depends on pipe length and pipe material, as expected. Costs are significantly reduced when plastic or fabric pipes are used instead of traditional steel-made pipes.

About half of the Red Sea desalination plants are based on reverse osmosis. The percentage of RO plants is expected to increase, taking into account the lower production costs and the favorable technological evolution. Using underwater pipes for avoids some of the hazards of brine disposal. Optimum brine dispersion may be obtained by using underwater pipes for any sort of high capacity and low capacity RO desalination plants operating on the Red Sea coasts. In case of large capacities, a pipe length around l _X  = 1,000 m allows optimum operation. A pipe length about l _X  = 500 m is needed for low capacity RO desalination plants.