Brine Discharge Plumes on a Sloping Beach

Transcription

1 Brine Discharge Pumes on a Soping Beach H.H. AL-BARWANI, Anton PURNAMA Department of Mathematics and Statistics, Coege of Science Sutan Qaboos Universit, PO Bo 6, A-Khod 1, Muscat, Sutanate of Oman E-mai: hamdi@squ.edu.om, antonp@squ.edu.om Abstract Large scae seawater desaination pants are operated aong the coasts and dispose of their brine waste stream b discharging into the sea. As the need for desainated seawater is steadi increasing, more new desaination pants are panned to be constructed. If desaination pants are cose custered together aong the coastines, the adverse environmenta impacts of the brine effuent discharges from pants such as these are strong inter-dependent. A far fied mathematica mode for continuous brine discharges from two desaination pants on a uniform soping beach is presented. The anatica soutions are iustrated graphica to stud the interaction of two brine discharge pumes. Asmptotic approimation wi be made to the shoreine's brine concentration to evauate the maimum sainit buid-up in the coasta waters. Kewords: Brine discharge, desaination pant, soping beach, two outfas Introduction More than haf of the word's seawater desaination pants are operated aong the coasts of the Arabian Guf (tota capacit of 1 miion m /da), Guf of Oman (1 miion m /da) and Red Sea (7.7 miion m /da). As the need for desainated seawater is steadi increasing, not on are the number of new arge scae desaination pants constructed aong the coasta areas growing, the eisting pants are aso gradua increasing their water production capacities. Seawater desaination pants generate two products, pure water and brine, a reject concentrate stream. The unwanted brine product is primari seawater but at a more concentrated eve, with the concentration factor as high as.5, which is to be disposed of b continuous discharging it back into the sea through an outfa. Therefore, ike an arge scae industria process, unfortunate seawater desaination aso has its potentia environmenta impacts [1]. Owing to the high variabe nature of the sea, we do not et have a fu understanding or description of the miing processes of brine discharges from coasta desaination pants []. Immediate after reease from the diffuser, vigorous and rapid diution of concentrate brine is governed b the effuents buoanc, momentum of the discharge and its interaction with the sea currents. At the end of this miing stage, the estabished stead discharge brine pume then continues to drift awa with 1

2 the currents. Due to reative shaow water depth, it is observed that the eongated brine pumes are spreading towards the shoreine and ma cause an increase in sainit in the coasta waters []. The merging of two or more brine pumes adds further compeit; such situations are not uncommon aong the coasts of the Arabian Guf, Guf of Oman, and Red Sea, where the arge scae desaination pants often tend to be tight custered together [1]. Considering the growth in desaination pants and their capacit, there is an urgent need to evauate the ocaized environmenta impacts from the individua pant, and the cumuative strategic impacts compounded from the neighbouring pants. As arge scae seawater desaination pants are buit predominant on the soping sand beaches, a mathematica mode is deveoped using a two-dimensiona advection-diffusion equation for continuous brine discharges from two coasta pants that incorporates the effect of soping beach. The soution is presented graphica to stud the interaction of two brine pumes. Asmptotic approimation wi be made to the shoreine's soution to assess the sainit buid-up in the coasta waters [4,5]. Long sea outfa on a soping beach As we are on concerned with the effect of seabed depth profie, for simpicit, the other compeities such as tida motions, densit, and temperature, are ignored. The shoreine is assumed to be straight and the sea wide, and we consider the concentrated brine stream to be steadi discharged with a rate Q 1 from a ong sea outfa at the position ( 0, α h0 ), where h 0 is an arbitrar reference water depth. As for modern desaination pants the discharge is made via diffusers and utiizes the best avaiabe technoog to promote rapid initia diution, we aso assume that the outfa s brine pume is vertica we-mied over the water depth. Furthermore, for shaow coasta waters, the dispersion in the vertica direction occurs much faster than in the atera direction. The coasta (drift) current is assumed to be stead with a speed U and remains in the -direction parae to the beach at a times. The dispersion mechanisms are represented b edd diffusivities, and diffusion in the -direction is negected, as the brine pumes in stead currents become ver eongated in the -direction. The variations in the -direction of drift current U and coefficient of dispersivit D are assumed as the power functions on of water depth h, and for appications, we take 1 U to be proportiona to h 0 and D to h 0. These scaings are appropriate for a turbuent shaow-water fow over a smooth bed [5,6,7]. In a uniform soping beach, the water depth varies increasing inear as ( ) h m, where the beach sope m and the beach is at 0, the far fied advection-diffusion equation for concentration c is c ( huc) hd Q δ ( ) δ ( α ) 1 h 0, (1)

3 with the boundar condition hd c 0 at the beach 0, and c is assumed to be utimate dissoved into the ocean. δ is the Dirac deta function. Foowing [,4,5], we define dimensioness quantities h 0, h 0, c c Q1 h0 U0, and b 1 setting U U 0 and D D 0, the anatica soution of (1) is given b c m 4 1 ep α [ α ] α I, () where I is a modified Besse function. As the water depth is gradua decreasing towards the beach, the brine pumes are eongated and turning towards the beach, and the genter the beach sope, the higher the buidup in concentration in the shaow water cose to the beach [4,5]. This is epected since deeper water has a more efficient transport mechanism. The mode parameter h0u 0 D0 represents the brine pume eongation in the -direction. To investigate the uncertaint in, Figure 1 shows the possibe vaues of for some reevant measured vaues of U 0 and D 0 [7] in the shaow water depth h0 10 m. Larger vaues of are most due to a stronger drift current U 0 with ess ongitudina dispersivit D 0. For the graphica iustrations, the vaues of 1 wi be used in a pots, and noting aso that the arger vaues of, the more eongated the brine pumes [4,5].

4 Figure 1. The mode parameter for water depth h0 10 m. Again foowing [4,5], the appropriate measure for assessing the impact of brine discharges from coasta desaination pants woud be the concentration eves at the beach. Letting 0 and repacing I in () b its imiting form, we obtain the concentration at the beach 5 4 α c ep. () ( 0) m π Figure. The effects of varing outfa ength α on the maimum concentration at the beach c 1 m (eft) and on the position of maimum concentration 1 (right). B differentiating, the maimum vaue of the concentration at the beach is 5 c1 m mα, which occurs at 1 α 5 downstream of the outfa. As shown in Figure, c 1 m does not depend on, and is inverse proportiona to the outfa ength α. Note aso that, for an eisting outfa with ength α, the ocation of the maimum concentration 1 is on governed b. Two ong sea outfas As iustrated in Figure, we consider the concentrated brine stream to be steadi discharged from two arge scae desaination pants at L distance apart at a rate Q 1 from the first (od) outfa at the position ( 0, α h0 ), and at a different rate Q from the second (new) outfa at the position ( L, βh 0 ). As an etension of the previous 4

5 5 mode [4,5], the two-dimensiona advection-diffusion equation for the far fied pume concentration c from the two outfas is ( ) ( ) ( ) ( ) h L Q h Q c hd c hu β δ δ α δ δ. (4) Figure. Diagram of two brine outfas. In terms of the dimensioness variabes, and b apping a inear superposition, the anatica soution of (4) is given b [ ] ( ) [ ] 4 4 ep 1 ep 1 I m q I m c β β β α α α, (5) where 1 Q Q q and 0 L h. The interaction of two discharged brine pumes is aso governed b the outfa engths α and β, the separation distance between them, and the discharge ratio q of the second (new) outfa. For etreme arge separation distances, the contribution of the new outfa is negigibe; this is because the two pumes are we separated and become two individua pumes. However, for shorter distances 5 β, the two pumes are merging, and in the imit 0, we have a singe outfa with two ports.

6 Figure 4. Merging of two brine pumes when the separation distance (top) and when 0 (bottom). The effect of a soping beach with sope m on the miing and dispersa of brine discharges from two desaination pants with q 0. 5 is iustrated graphica b potting the concentration contour of (5). Figure 4a shows a tpica merging brine pume drifting aong the coasta waters from two outfas where α 8 and β 10 with separation distance. The case of a singe outfa ( 0 ) with two ports where α 8 and β 1 is shown in Figure 4b. Net, the compounded concentration at the beach can be approimated b ( ) α ep β c 0 ep q. (6) m π As cear shown in Figure 4, the position of maimum compounded concentration at the beach occurs downstream of the first (od) outfa. That is, the presence of the second (new) outfa wi not change the ocation of maimum concentration 1 of the first (od) outfa; however, it wi contribute to the maimum vaue c 1 m of concentration at the beach. Therefore, b substituting 1 to (6), the maimum vaue of compounded concentration at the beach can be written as 6

7 5 α 5 1 β c ep m c1m q 1. (7) α β α β Note aso that, in the imit 0, the maimum vaue of the compounded 5 β concentration (7) reduces to cm c1m 1 q ep 1. α Figure 5. The compounded concentration at the beach. Figure 5 shows the compounded concentration at the beach from two outfas, where α 8 and β 10 with q 0. 5, for three vaues of the separation distance 0.5, and. For comparisons, the concentration at the beach from the first (od) outfa is aso shown b the dotted ine. The onger the separation distance between the two outfas, the smaer the contribution of the new outfa. Fina, the maimum vaue of the compounded concentration at the beach is shown in Figure 6 as a function of the separation distance between two outfas with q 0. 5 for β α, β 1. 5α and β α. The on wa to keep the effect of the (new) second outfa minima is to buid a onger new outfa. A reduction of 0% in the maimum vaue can be achieved b etending the new outfa ength b 50%. 7

8 Figure 6. The maimum vaue of the compounded concentration. Concusion If two or more arge scae seawater desaination pants are operated cose together aong the coastines, the maimum vaue of the compounded concentration at the beach is strong dependent on the outfa engths, the separation distance between the outfas, and the discharge ratio of each outfa. Therefore, when assessing the individua potentia environmenta impact of desaination pants, nearb pants' discharges shoud aso be taken into the consideration. Modern ocean outfas have been constructed with the mutiport diffusers to enhance initia diution, which is essentia in minimizing the impact of outfa pumes. In the imit 0, the equation (6) can be etended for cacuating the compounded concentration at the beach foowing discharges from a singe outfa with mutiport diffusers. References [1] Lattemann, S. and Hopner, T. Environmenta impact and impact assessment of seawater desaination, Desaination, Vo. 0 (008) 1-15 [] Purnama, A. and A-Barwani, H.H. Spreading of brine waste discharges into the Guf of Oman, Desaination, Vo. 195 (006) 6-1 [] Purnama, A. and A-Barwani, H.H. Some criteria to minimize the impact of brine discharges into the sea, Desaination, Vo. 171 (004) [4] A-Barwani, H.H. and Purnama, A. Re-assessing the impact of desaination pants brine discharges on eroding beaches, Desaination, Vo. 04 (007) [5] Ka, A. The effect of cross-stream depth variations upon contaminant dispersion in a vertica we-mied current, Estuarine and Coasta Shef Science, Vo. 4 (1987)

9 [6] Smith, A. Longitudina dispersion of buoant contaminant in a shaow channe, Journa of Fuid Mechanics, Vo. 78 (1976) [7] Ostendorf, D.W. Longshore dispersion over a fat beach, Journa of Geophsica Research, Vo. 87 (198)