Simulating brine plumes discharged into the seawaters

Transcription

1 Desalination 1 (008) Simulating brine plumes discharged into the seawaters HH Al-Barwani*, Anton Purnama Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, PO Box 36, Al-Khod 13, Muscat, Sultanate of Oman Tel ; Fax ; hamdi@squeduom Received 31 January 007; accepted 4 February 007 Abstract A seawater desalination plant s reliability and service availability are essential to sustain and allow the continuing development in the arid climate countries As desalinated seawater is indispensably required at any cost, the conventional disposal method used for a large size desalination plant is to continuously discharge brine waste stream back into the sea via an outfall at some distance from the beach One major factor in assessing the potential environmental impact of brine discharges from desalination plants is the oscillatory nature of the coastal currents A model simulation of the long-time brine plumes steadily discharged into the seawaters is presented using a two-dimensional advection-diffusion equation The model parameters that minimize the impact of brine discharges are discussed Keywords: Brine discharges; Mathematical model; Sea outfall; Seawater desalination; Tidal flow 1 Introduction Seawater desalination is becoming the essential factor to address the continuously growing demands to supply freshwater in the arid countries Desalination, the process of removing salts and suspended solids from seawater, also produces brine, wastewater containing a high salinity to be disposed of into the environment It is common practice for the large-scale seawater desalination plants to discharge the brine waste *Corresponding author stream back into the sea via an outfall at some distance from the beach [1,] As the brine waste is produced daily in large volumes, it is important to understand how the long-time brine plumes is dispersed into the sea so that we can minimize its potential environmental impact [3,4] As the flow in the sea is dominated by the long shore tidal current, as illustrated in Fig 1, it is the oscillatory nature of the flow which produces physically and unpredictably interesting features [4] The brine stream discharged will be transported away from the outfall, and then Presented at the conference on Desalination and the Environment Sponsored by the European Desalination Society and Center for Research and Technology Hellas (CERTH), Sani Resort, Halkidiki, Greece, April 5, /06/$ See front matter 006 Elsevier BV All rights reserved doi:101016/jdesal

2 HH Al-Barwani, A Purnama / Desalination 1 (008) Fig 1 The distance travelled by brine plumes over four tidal cycles afterwards as the flow reversal, the plume is returned back towards the outfall With the net result however, as shown by the dashed line in Fig 1, the flow carries the brine plume away from the outfall Within two tidal periods after being discharged, the plume may have returned to the outfall 3 times before eventually leaving it If brine waste stream is continuously discharged at a constant rate, then the coastal water which is closed to the outfall at the time of flow reversal, where the flow speed drops to zero and there is no dispersion, will be carrying an undesirably high salinity Thus, as simulated in Fig a, at a certain time within a tidal cycle the concentration peaks will appear on both sides of the outfall There is an increased public concern and scientific awareness on the environmental impact of desalination plants [1,,5] It has become a key issue to obtain permits to build a new plant, often considerably influencing plant commissioning and design The long-time effect of a tidally oscillating flow on the mixing and dispersion of brine plumes are simulated and illustrated graphically by plotting contours of concentration As the plume travels downstream, it eventually heads towards the beach (Fig a) Using the peak concentration at the beach as a measure Fig (a) Brine plumes at T i = 415p, and (b) concentration at Y = a and at the beach (Fig b), the impact of brine stream discharges into the sea is assessed with respect to the model parameters Mathematical model Since we are only concerned with the effect of a tidally oscillating flow on the long-time (or far field) brine plume, a highly simplified vertical beach profile is considered [4], where the coast is straight and of a constant water depth, with the beach at y = 0 The brine waste stream is continuously discharged from large desalination

3 610 HH Al-Barwani, A Purnama / Desalination 1 (008) plants starting from the initial time t i at a rate Q from the sea outfall at a distance a from the beach, and as the discharge is commonly made via diffusers, we assume that the brine plume is vertically well-mixed over the water depth The dominant diffusive processes are represented by the longitudinal diffusivity D x and lateral diffusivity D y We assume also that the complexities of flow in coastal water, such as temperature and density, will be ignored except for timedependence and the current to be uniform over water depth and remain in the x-direction parallel to the beach A simple model of a tidally oscillating flow [6,7] can be represented by U(T) =V +sin T, where V = n/u 0 is the relative strength of the longitudinal current, U 0 is the tidal amplitude, T = wt and p/w is the tidal period The solution of the advection-diffusion equation in a tidally oscillating flow for the brine plume s concentration is given by [4] T i X VT T C = d 0 0 λ exp + cost T T ( T T ) cos 0 λη ( Y α) exp T 0, λη ( Y + α) + exp T0 (1) where C = 4π c DxDy Q, T i = T wt i, l = U 0 / 4wD x, X =wx/u 0, Y =wy/u 0 and h=d x /D y For illustration, the simulation of brine plumes discharged from an outfall at (0, a =04) is shown in Fig a, where the actual plumes are elongated in the x-direction by a factor of 40 As the flow direction is reversed at T i =415p, a peak is created on the upstream side of the outfall Further downstream, the plume travels towards the beach As we are only interested in the long-time for more than l tidal periods, as shown in Fig a, the concentration of the brine plume that peaks away from the outfall has been dispersed [8] The brine plume concentration along the line Y = a parallel to the outfall distance is shown in Fig b as a dashed curve Conversely, the concentration at the beach Y = 0 is gradually increased and reaches a maximum value C max at a downstream distance X max Note that there are three model parameters which characterize the brine plume: V the longitudinal current to tidal amplitude, l the distances by which the brine plume is transported and spread over by advection to that by longitudinal diffusion, and h the longitudinal to lateral diffusivities Due to the unpredictable sea conditions, very little information is available on these parameters Typical numerical values used [9,10] are the tidal amplitude U 0 =0ms 1 with the tidal period p/w = 1 h, which give a longitudinal scale U 0 /w of about 4 km [4] Assuming that the longitudinal diffusion is a very efficient process, the value h could be at least 0 [11] However, it is the lateral diffusion that spreads over the concentration towards the beach The coefficients of diffusivity are reported to be D x 35 m s 1 and D y 1m s 1 To investigate the uncertainty in the model parameters, Fig 3 Fig 3 The model parameter l for a 1-h tidal period

4 HH Al-Barwani, A Purnama / Desalination 1 (008) shows the graphs of l for some relevant measured values of U 0 and D x For example, larger values of l are mostly due to a larger current with smaller values of D x Thus, l in the range of 5 5 are suitable for a moderate current In all simulations the values of V = 0, l = 10 and h = 30 are used, unless stated otherwise 3 Concentration at the beach The potential environmental impact of seawater desalination can be associated with brine plume concentrations in coastal waters Therefore, an appropriate measure for assessing the impact of brine discharges into the sea would be the concentration at the beach, which can be obtained from Eq (1) by substituting Y = 0 [4] It deserves emphasis that the extremely long-time, ie in the limit as T i, allows the neglect of the term cos (T T 0 ) in evaluating the concentration of the brine plume [6] But the flow periodicity enables us to restrict our observation time T in a single representative tidal cycle, and thus the concentration at the beach is given by ( { }) C( 0) 4exp λv X + cost K 0 λv X + cost { } + ηα () where K 0 is a modified Bessel function of the second kind Using the asymptotic approximation for K 0 we can approximate further C ( 0) 4π λv X + cost { } λvηα exp X + T cos (3) The concentration at the beach from an outfall at a = 04 is shown in Fig 4 at T = p and T =p of a tidal cycle As the maximum concentration C max remains constant throughout the tidal cycle, this implies that there is no time at which the maximum possible concentration level at the beach is worse than at any other Fig 4 The concentration levels along the beach time Thus, the maximum concentration C max, which remains constant throughout the tidal cycle, can be used as the numerical upper limit for the long-time brine discharges Next, by differentiating with respect to X, the maximum value of the concentration at the beach is given by C max 1 π (4) λvα eη, which occurs at X max =lvha cos T As shown in Fig 4, over one tidal cycle, X max =lvha ± 1 Therefore, the range of X max is over a large distance of w/u 0 along the beach It is also important to note the very long tail feature of the concentration at the beach From a regulatory viewpoint, this could be used as a standard distance to grant a new desalination plant from the existing large plant The exponential term in Eq (3) implies that we can reduce the concentration levels at the beach by increasing the values of a, ie, the plant s brine outfall length [4] Fig 5 shows the graphs of C max with respect to the outfall distance a for the three different values of l For a given outfall length, increasing values of l, ie, larger tidal amplitude, will decrease the maximum

5 61 HH Al-Barwani, A Purnama / Desalination 1 (008) Fig 5 Maximum concentration at the beach for three values of l concentration at the beach For example if a = 04, the reduction of 60% in the value of C max is achieved by increasing the values of l =10 to l =5 4 Conclusions Seawater desalination has contributed significantly to ensuring a safe, sustainable and adequate water supply for the arid climate countries As desalination plants carry a large volume of brine wastewater into the sea [1,,5], environmental impact studies are required to define regulatory strategies on protection and conservation of the marine environment in a sustainable way In general there is little information available on the impacts of desalination plants on the marine environment [1,13] Even less data is available to quantify such impacts for regulatory and design purposes [14] Higher salinity or fluctuations in salinity is expected near the outfall, and a long outfall s plume is often observed drifting along the coast [3,4] Environmental risks can be reduced and regulated by restricting the levels of brine at the discharge point using some treatment and recycling technologies or by imposing the maximum criteria (concentration limit) within the coastal Fig 6 C max as a function of X max waters [15] In searching for the maximum concentration in the coastal waters, using a twodimensional advection-diffusion equation, the long-time effect of a tidally oscillating flow on mixing brine discharges into the sea is investigated It is found that the maximum value of the concentration at the beach remains constant throughout the tidal cycle, and thus can be used as an impact measure Finally, as it is observed that X max is a long distance downstream the outfall, and it appears to be getting longer as the model parameters values increase, C max can be expressed as α 8πη Cmax = (5) Xmax + cos T e As shown in Fig 6 for an outfall at a =04 with T = p and T = p of a tidal cycle, the maximum concentration C max is a decreasing function of X max References [1] S Lattemann and T Hopner, Seawater desalination: impacts of brine and chemical discharges on the marine environment, Desalination Publ, L Aquila, Italy, 003, pp 14, com, ISBN:

6 HH Al-Barwani, A Purnama / Desalination 1 (008) [] R Einav and F Lokiec, Environmental aspects of a desalination plant in Ashkelon, Desalination, 156 (003) [3] A Purnama, HH Al-Barwani and M Al-Lawatia, Modeling dispersion of brine waste from a coastal desalination plant, Desalination, 155 (003) [4] A Purnama and HH Al-Barwani, Spreading of brine waste discharges into the Gulf of Oman, Desalination, 195 (006) 6 31 [5] A Hashim and M Hajjaj, Impact of desalination plants fluid effluents on the integrity of seawater, with the Arabian Gulf in perspective, Desalination, 18 (005) [6] A Kay, Advection-diffusion in reversing and oscillating flows: Flows with multiple reversals, IMA J Appl Math, 58 (1997) [7] GJ Macdonald and RN Weisman, Oxygen-sag in a tidal river, J Environ Eng Div, Proc Amer Soc Civil Eng, 103 (1977) [8] KA Mohamed, A Arieqat and M Odeh, Set-up of a mid-field model to investigate the recirculation of effluents in the Mirfa power and desalination plant, Desalination, 166 (004) [9] WE Johns, GA Jacobs, JC Kindle, SP Murray and M Carron, Arabian marginal seas and gulfs, Technical Report , RSMAS, University of Miami, zantopp/amsg-reporthtml [10] CN Flagg and HS Kim, Upper ocean currents in the northern Arabian Sea from shipboard ADCP measurements collected during the US JGOFS and ONR programs, Deep Sea Res II, 45 (1998) [11] R Smith and CF Scott, Mixing in the tidal environment, J Hydraulic Eng, Am Soc Civil Eng, 13 (1997) [1] JLP Talavera and JJQ Ruiz, Identification of the mixing processes in brine discharges carried out in Baranco del Toro beach, south of Gran Canaria (Canary Islands), Desalination, 139 (001) [13] JJ Malfeito, J Diaz-Caneja, M Farinas, Y Fernandez-Torquemada, JM Gonzalez-Correa, A Carratala-Gimenez and JL Sanchez-Lizaso, Brine discharge from the Javea desalination plant, Desalination, 185 (005) [14] GL Meerganz von Medeazza, Direct and sociallyinduced environmental impacts of desalination, Desalination, 185 (005) [15] RL Doneker and GH Jirka, CORMIX-GI systems for mixing zone analysis of brine wastewater disposal, Desalination, 139 (001) 63 74