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Desalination 204 (2007) 501–514 Simulation of large capacity MSF brine circulation plants Nabil M. Abdel-Jabbara,b,*, Hazim Mohameed Qiblaweya, Farouq S. Mjallic, Hisham Ettouneyd a Department of Chemical Engineering, Jordan University of Science and Technology, Jordan Tel: (+971) 65152907; Fax: +(971) 65152979; email: [email protected] b Chemical Engineering Department, American University of Sharjah, United Arab Emirates c Department of Chemical Engineering, University of Qatar, Qatar d Department of Chemical Engineering, Kuwait University, Kuwait Received 22 January 2006; accepted 15 February 2006 Abstract New multistage flashing desalination units (MSF) are being constructed with large capacity that may vary from 50,000 to 75,000 m3/d. This is almost 2–3 times the conventional unit capacity of 27,000–32,000 m3/d, which were common for the units installed in the 1980’s. Most of the Gulf States and several countries across the world are acquiring the large units to take the merits of reduced product cost caused by the large unit capacity. Literature studies and field reports indicate that the unit product in these units is almost identical to seawater reverse osmosis and the multiple effect evaporation, with an average of $0.5/m3. This paper focuses on modeling and simulation of the performance characteristics of these large units. Mathematical modeling of the MSF process is well established in the literature. However, several of the design parameters have to be adjusted in order to take into considerations the characteristics of the large unit capacity. The analysis focuses on evaluation of the weir loading, the dimensions of the condenser tube bundle, demister dimensions, stage dimensions, and temperature and flow rate profiles. The model predictions are validated against field data for a number of existing units. Keywords: Multistage flash desalination; modeling; design; costing 1. Introduction One of the striking features of the MSF is its reliability. Field experience shows that a large number of existing MSF plants has exceeded the intended life time [1–2]. Several of these plants are going through *Corresponding author. Presented at EuroMed 2006 conference on Desalination Strategies in South Mediterranean Countries: Cooperation between Mediterranean Countries of Europe and the Southern Rim of the Mediterranean. Sponsored by the European Desalination Society and the University of Montpellier II, Montpellier, France, 21-25 May 2006. 0011-9164/07/$– See front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2006.02.047 502 N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 rehabilitation. More efficient construction materials are used in the rehabilitation and newly designed and streamlined components. Such replacements are taking place in all areas of the plant, which may include venting system, demisters, tubing, partitions, and pumping units. Maintaining and updating of existing MSF plants is motivated by the excellent process reliability and the ability to continually operate for durations of more than 2 years. Success of the MSF process has resulted in drastic increase in the unit production capacity to large values of 50,000–75,000 m3/d. In the 1960’s the first MSF units had unit capacity of 500 m3/d. The unit capacity then increased to the well known capacity of 27,000–32,000 m3/d, which were introduced in the late 1970’s [3–4]. Recent economic evaluation of large desalination systems show that the competitive unit product cost of MSF, MED, and RO. Although, RO consumes a close to 25% of the total energy of MSF and MED, but, its unit product cost is almost similar, when membrane replacement cost is considered. In addition, competitive tendering, pricing, and less restrictive system design allowed for massive and economical increase in the unit capacity of the MSF and MED plants [5]. Modeling of the MSF process is well established in the literature [6–20]. Mathematical models include short cut techniques [6–8], which are very useful to provide quick estimates of main process characteristics, i.e., performance ratio (defined as the amount of distillate product per unit mass of heat steam), condenser heat transfer area, and flow rates of various streams. More detailed steady state models [9–14] are thought to evaluate additional design characteristics of the system, i.e., stage variations in the amount of flashed off vapor from the distillate stream, thermodynamic losses, heat transfer coefficient. MSF models include also system dynamics [15–18], which are used to study system transient behavior and to optimize system controllers. In addition, thermo-economic models are thought to optimize the unit product cost. [19–20]. This study is motivated by the need to present to the literature an integrated model on design of large scale MSF units. Such systems are becoming the industry standard. The analysis focuses on evaluation of various system design characteristics, which includes stage dimensions, weir loading, demister length, as well as flow rates and temperature profiles, and performance ratio. The next sections include system description, model, system analysis, and comparison against field data. 2. Process description Fig. 1 shows schematic of the MSF flashing stage. As is shown, the flashing stage includes the condenser tubes, demister, venting line, distillate tray, inlet/outlet brine orifices, and air baffle. The processes that take place inside the flashing stage are given below: The inlet brine flashes off as it enters the flashing stage. This is because the saturation Tube Bundle Air Baffle Vent line Demister Demister Distillate Tray Outlet Brine Flashed off Vapor Inlet Brine Brine Pool Fig. 1. MSF flashing stage. Submerged Orifice N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 temperature/pressure of the brine is higher than the stage temperature/pressure. Flashing implies that the formed vapor extracts its latent heat from the brine stream. Therefore, the brine temperature decreases as the brine flows across the stages. The brine orifice is designed to control the brine flow. Also, it maintains sufficient brine head within the stages to prevent vapor escape between stages. The stage width and length should be large enough to maintain the vapor velocity below 6 m/s. This is necessary to limit entrainment of brine droplets in the vapor stream and to allow for settling of the brine droplets. The flashed off brine flows through the demister, where most of the entrained brine droplets are captured by the demister wires. Continued removal of the droplets would result in the increase in the captured droplet size. This would result in detachment of the large droplets and settling back to the brine pool. As the vapor flows to the condenser tubes, where it releases its latent heat and condenses. The condensed vapor accumulates in the distillate tray and flows to the next stage. The inlet distillate stream has a higher temperature and it flashes off as it flows between stages. This flashed off vapor also condenses on the outside surface of the condenser tubes. Vapor condensation results in the increase of the temperature of the brine stream flowing inside the tubes. This is a very important design feature, where most of the thermal energy provided by the heating steam is recovered by the brine stream before entering the brine heater. Non-condensable gases are also released during the evaporation process. The noncondensable gases include oxygen, nitrogen, and carbon dioxide. Carbon dioxide 503 might be generated due to the decomposition of calcium carbonate at high temperature. The gases have very low thermal conductivity and it must be removed from the system. This is achieved by the use of vent lines, which are placed between the flashing stages. The vent lines, especially at the high temperature end, are directly connected to the vacuum steam jet ejector. This is because of the high release rate of the non-condensable gases. After the first few stages, the vent lines allow the non-condensable gases to flow across the stages until it reaches the last stage, where the vent line is attached to the vacuum steam jet ejector. The non-condensable gases act as an insulating blanket around the condenser tubes. Also, if it is left to accumulate within the stages, it would reduce the vapor partial pressure and its temperature. As a result, the brine flowing inside the tubes will not reach the desired design temperature. Another shortcoming of the non-condensable gases, especially oxygen and carbon dioxide, is the fact that it promotes corrosion reactions within the system. The air baffle shown within the stage is placed to control vapor flow through the vent line and to prevent condensate splashing in the vent line. Approximately, 2.5% of the vapor formed in each stage is lost through the vent line; however, close to 90% of this vapor is recovered in the steam ejector condenser. The MSF process with brine circulation is shown in Fig. 2. As is shown, the flashing stages are divided into two sections, which include the heat recovery and rejection sections. The heat recovery stages involve heating of the brine recycle stream inside the condenser tubes from the temperature of the 504 N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 Cooling Seawater Vacuum Steam Ejector Motive Steam Non-Condensable Gases Condenser Condensate Outlet Cooling Seawater Distillate Trays Condenser Tubes Cooling Seawater Intake Seawater Heating Steam Distillate Product Condensate Demister Brine Pool Feed Brine Brine Blowdown Brine Recycle Chemicals Fig. 2. Multistage flash desalination with brine recycle. brine blow down to a higher temperature close to the top brine temperature. Therefore, the amount of heating steam used in the brine heater is minimized. The heat rejection section usually contains three stages. The heat rejection section functions to control the temperature of the intake seawater and reject the excess heat added in the brine heater. As is shown the flow rate of the intake seawater is equal to the sum of the flow rates of the feed seawater and the cooling seawater. During winter operation part of the rejected cooling seawater is recycled and mixed with the intake seawater. This is to control the intake seawater temperature. This practice is common during winter operation. Control of the feed seawater temperature prevents reduction of the last stage system temperature, which would result in the increase of the specific volume of the flashed off vapor and subsequent increase in the vapor velocity as well as the amount of entrained brine. This would result in the increase of the product salinity. Therefore, the product stream might not be suitable for use as makeup boiler water. This problem is circumvented by using part of the distillate product in the first stages. It should be noted that the temperatures of the cooling and feed seawater steam leaving the condenser tubes from the heat rejection section is identical to the temperature of the brine blow down leaving the last flashing stage. This is necessary to prevent thermal shock upon mixing of the feed seawater in the brine pool of the last stage. If the temperature of the feed stream and the brine blow down are different then the calcium bicarbonate would decompose and result in precipitation of calcium carbonate inside the condenser tubes of the heat recovery section. Approximately, there are nine pumps used in the MSF system. The pumps are used for the intake seawater, rejected cooling seawater, recycled cooling seawater, feed seawater, brine blow down, distillate product, steam condensate, chemicals, and ejector condensate. The largest of these pumps is the N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 brine recycle pump. For example, a plant with a production rate of 30,000 m3/d, would require a brine recycle pump with a capacity of 300,000 m3/d. The feed seawater pump would be limited to 75,000 m3/d and the brine blow down pump would have a capacity of 45,000 m3/d. Other pumping units will have a much smaller capacity; where the heating steam condensate pump will have a capacity of 3000 m3/d and the ejector condensate pump will be limited to 1000 m3/d. The rejected cooling seawater pump will have a capacity of 150,000 m3/d and recycled cooling seawater pump will have a capacity of 90,000 m3/d. 3. Mathematical model The assumptions used to develop the mathematical model include the following: Stead state operation, which is the industry standard. Although, system operation may experience seasonal temperature variations of the intake seawater, but, such variations are slow and the system parameters are adjusted accordingly. Another factor that may change the system characteristics is the tube fouling, which results in the increase of the thermal resistance for heat transfer. This problem is encountered through the use of on-line ball cleaning system or tube acid cleaning, which restores conditions to near clean operation. Heat losses to the surroundings are negligible. This assumption is valid, since, the surface to volume ratio of the MSF plants is very small. Also, the temperature of the low temperature stage is very close to the ambient temperature, which reduces the rate of heat transfer to the surroundings. Equal heat transfer area in each flashing stage in the heat recovery section. 505 Equal heat transfer area in each flashing stage in the heat rejection section. The heat capacities for feed seawater, brine, and distillate product depend on temperature and composition. The overall heat transfer coefficients in the evaporators depends on the following parameters: & Flow rate of the condensing vapor. & Flow rate of the brine inside the condenser tubes. & Temperatures of the condensing vapor and the brine. & Physical properties of the condensing vapor and the brine, which includes thermal conductivity, viscosity, density, and specific heat. & The tube material, diameter, and wall thickness. & The fouling resistance. & The percentage of the non-condensable gases. The overall heat transfer coefficient is the sum of the thermal resistances expressed in terms of the inside and outside heat transfer coefficient, the fouling resistance, and the thermal resistance of the condenser tube. The latent heat of formed/condensed vapor depends on temperature. Thermodynamic losses include the boiling point elevation (BPE), the non-equilibrium allowance (NEA), and demister losses (Tp). The distillate product is salt free. Schematics of the MSF variables in the flashing stage and the brine heater are shown in Figs. 3 and 4. The model equations are written for the heat recovery and the heat rejection sections. It should be noted that the balance are similar for the two sections; this is except for the balance of the first stage and the condenser balance equations in the heat rejection 506 N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 Inlet Seawater MR, XR, Tfj+1 Condenser Tubes Outlet Seawater MR, XR, Tfj Flashing Vapor Dj, Tcj Inlet Distillate j–1 ∑ Dk , Tcj – 1 Outlet Distillate j ∑ Dk, Tcj k =1 k=1 Brine Orifice Demister Inlet Brine Bj – 1, Xbj – 1, Tbj – 1 Outlet Brine Bj, Xbj, Tbj Flashing Vapor Dj, Tvj Brine Pool Design/Operation Parameters: Tube diameter Tube wall thickness. Number of Tubes. Stage Length, Width, Height. Tube Length Heat Transfer Area Distillate Flow Rate Brine Flow Rate Brine Recycle Flow Rate Temperature Rise of the Brine Recycle. Brine Temperature Drop. Brine Orifice Dimensions Demister width, Length, Thickness Fig. 3. Flashing stage and process variables. Design/Operation Parameters: Heating Steam Ms, Ts Brine Recycle MR, Tf1, XR Condensate Ms, Ts Brine Recycle MR, Tbo, XR Tube diameter Tube wall thickness. Number of Tubes. Shell diameter. Tube Length Heat Transfer Area Flow Rate of Heating Steam Heating Steam Temperature Temperature Rise of the Brine Recycle. Brine Recycle Flow Rate. Fig. 4. Brine heater process variables. section. The model equations include mass balance of stage j, which is given by Bj1 þ j1 X Dk ¼ Bj þ k¼1 j X Dk ð1Þ For the first stage Bj1 is equal to MR and Xbj1 is equal to XR. Therefore, the salt balance in the first stage is given by XR MR ¼ Xb1 B1 ð4Þ k¼1 It should be noted for the first stageP the term Bj1 is equal to MR and the term is j1 k¼1 Dk equal to zero. Therefore, the mass balance for the first stage is reduced to the following MR ¼ D1 þ B1 ð2Þ The stage salt balance is given by Xbj Bj ¼ Xbj1 Bj1 ð3Þ The energy balance for the flashing brine is given by Dj lvj ¼ Bj1 Cpb ðTbj1 Tbj Þ ð5Þ For the first stage, the term Bj1 is equal to MR and Tbj1 is equal to the top brine temperature Tbo . Therefore, the brine energy balance in the first stage is given by D1 v1 ¼ MR Cpb ðTbo Tb1 Þ ð6Þ N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 The energy balance for the condenser tubes is given by Dj cj þ Cpd ðTcj1 Tcj Þ j1 X MR CpR ðTfj Tfjþ1 Þ ¼ Urj Ar ðLMTDÞrj ð10Þ k¼1 ð7Þ It should be noted that in the last stage in the heat recovery section, the temperature Tfjþ1 isPequal Tbn . Also, for the first stage the term j1 k¼1 Dk is equal to zero; therefore, the condenser energy balance in the first stage is reduced to the following form Dj cj ¼ MR Cpf ðTfj Tfjþ1 Þ ð8Þ In the heat rejection section, the condenser tubes energy balance is given by Dj cj þ Cpd ðTcj1 Tcj Þ j1 X transfer equation for the condenser tubes in the heat recovery section is given by Dk ¼ MR Cpf ðTfj Tfjþ1 Þ where ðLMTDÞrj is given by ðLMTDÞrj ¼ ðTfj Tfjþ1 Þ=ln½ðTcj Tfjþ1 Þ=ðTcj Tfj Þ ð11Þ In the heat rejection section, the heat transfer equation for the condenser is given by ðMf þ Mcw ÞCpf ðTfj Tfjþ1 Þ ¼ Ucj Ac ðLMTDÞcj ð12Þ The flow of the brine recycle and its salinity are obtained by performing material balance on the mixer/splitter shown in Fig. 5. This gives the following relations MR ¼ Bn þ Mf Mb XR ¼ ðBn Xbn þ Mf Xf Mb Xbn Þ=MR Dk k¼1 ¼ ðMf þ Mcw ÞCpf ðTfj Tfjþ1 Þ 507 ð9Þ In the last stage of the heat rejection section, the temperature Tfj is equal to Tbn, and in the last stage of the heat rejection, the temperature Tfjþ1 is equal to Tcw. The heat The term Mb is obtained from performing overall material and salt balance on the plant, where Mf ¼ Md þ Mb Cooling Seawater Removes Excess Heat Feed Seawater Heating Steam Feed and cooling Seawater MSF Plant ð13Þ ð14Þ Distillate Product Flashing vapor Energy Recovery Brine Blow Down Mixer/splitter Brine Recycle Fig. 5. Heat and mass transfer in MSF brine circulation plant. ð15Þ 508 N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 Xf Mf ¼ Xbn Mb ð16Þ The heat transfer equation for the brine heater is given by Ms ls ¼ Uh Ah ðLMTDÞh ð17Þ ntj ¼ 4ðMcw þ Mf Þ=ðVcw dj 2 Þ The vapor temperature below the demister is less than the brine boiling temperature by the boiling point elevation and the non-equilibrium allowance. This relation is given by Tvj ¼ Tbj BPEj NEAj where ðLMTDÞh ¼ ðTbo Tf1 Þ=ln½ðTs Tf1 Þ=ðTs Tbo Þ ð18Þ The energy balance equation for the brine heater Ms s ¼ MR Cph ðTbo Tf1 Þ ð19Þ The width of all stages is set equal the width of the first stage, which has the highest brine load. This relation is given by Wst ¼ MR =wb ð20Þ Demister length is given Lp ¼ ðDvv Þ=ðVv Wst Þ ð21Þ The vapor velocity through the demister varies between 2 m/s in the first stage and 12 m/s in the last stage. The stage length is given Lst ¼ Lp þ Ltb ð22Þ The tube bundle length is obtained as a function of number of tubes, tube diameter, and tube spacing, where Ltb ¼ nt 1=2 dSt ð23Þ The number of condenser tubes in the heat recovery and the heat sections are obtained as a function of the stream flow rate and velocity. These equations are given by ntr ¼ 4MR =ðVR dr 2 Þ ð24Þ ð25Þ ð26Þ The vapor temperature above the demister is given by Tcj ¼ Tvj Tpj ð27Þ 4. Degree of freedom analysis and solution method Each flashing stage contains five balance Equas (1, 3, 5, 7–8) and five unknowns ðDj ; Bj ; Xbj ; Tbj ; and Tfj Þ. Also, there are two constraints that apply to the system; the first is the equality of the system production capacity and the summation of the distillate produced in each flashing stage. The second constraint is the equality of the outlet seawater temperature from the condenser tubes in the first stage in the heat rejection section and the brine blow down temperature. Therefore, the number of system unknowns is equal to the heat transfer areas per stage in the heat recovery and heat rejection stages as well as the 5 unknowns in each flashing stage. Solution of the system equations would define the temperature, flow rate, and salinity profiles across the flashing stages. The flow rate and salinity of the outlet streams are then used to calculate the brine recycle flow rate and salinity. Also, the brine heater energy balance and the heat transfer equation are used to calculate the heating steam flow rate and the brine heater heat transfer area. The model Eqs (1–24) are highly non-linear. This is because the equations are interlinked and contains non-linear terms. Therefore, an N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 iterative procedure is needed to solve the equation system. Newton’s method is used to solve the model equations. The solution scheme is shown in Fig. 6. As is shown, the solution starts with definition of the system design parameters, which includes capacity (Md), cooling seawater flow rate (Mcw), number of flashing stages (n), 509 vapor velocity in the last stage (Vv), brine velocity inside the tubes (Vb), heating steam temperature (Ts), top brine temperature Tbo , intake seawater salinity (Xf), outer diameter of condenser tube (do), wall thickness of the condenser tubes (dw), thermal conductivity of the condenser tubes (kw), discharge coefficient of the brine weirs (Cd), brine loading per unit Define System Parameters: Md, Mcw, n, Vv, Vb, Ts, Tf, Tbo, Xf, do, dw, kw, Cd, ε, wb, Lp, ρp, dp, Rfh, Rfc Calculate the Flow Rates of the Brine Blow Down and Feed (Eqs. 15-16) Mf, Mb Calculate Initial Guess for: MR, XR, Ac, Ar, Tfj, Tbj, Xbj, Dj, Bj For Each Stage Calculate: Tvj, Tcj, Hj, HGj, NEAj, BPEj, Cpf, Cpb, Cpd, μb, kv, hij, hoj, Ucj vvj, ΔTpj, ΔPpj Evaluate the Residuals of the Balance Equations in Each Stage: Eqs. 1-12 Solve the Residual Equations Using Newton’s Method Check Convergence: |error difference in the calculated variables in two iterations| ≤ ε Yes Calculate the Heating Steam Flow Rate and the Brine Heater Heat Transfer Area Ms, Ah, Uh Print Solution Fig. 6. Solution scheme for the MSF mathematical model. No 510 N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 length of the interstage weirs (wb), demister thickness (Lp), demister bulk density (rp), demister wire diameter (dp), condenser fouling resistance Rfc , brine heater fouling resistance Rfh , and error tolerance for the solution method (e). The flow rates of the feed and brine blow down (Mf and Mb) are calculated by simultaneous solution of Eqs. (15–16). This is followed by constructing an initial guess for the condenser areas in heat recovery and heat rejection stages (Ar and Ac), the temperature profiles of the flashing brine (Tbj) and the feed seawater flowing inside the condenser tubes (Tfj), and the profiles of the brine salinity (Xbj), brine flow rate (Bj), and distillate product (Dj). Also, the brine recycle flow rate and salinity (MR and XR) are obtained by solution of Eqs. (13–14). This guess is used to calculate various parameters in each stage, which include the physical properties (Cpf, Cpb, Cpd, b, kv) the heat transfer coefficients (hbj, hvj), the overall heat transfer coefficient (ucj), the vapor and condensation temperatures, and the thermodynamic losses (BPE, NEA), and the drop in temperature and pressure drop across the demister (Pp, Tp). The residuals of Eqs. (1–12) are then evaluated and new profiles are established for the system temperatures, flow rates, and salinity. The solution error, which is the summation for the difference between the calculated variables in two successive iterations, is checked against the error tolerance (e). If the solution error is less than the tolerance the iterations are terminated; if not then a new iteration is performed. Newton’s method is known to give quadratic convergence as the exact solution of the residual equations is approached. This criterion is found to hold upon solution of the model equations for wide range system parameters, which includes number of stages, capacity, feed seawater temperature and salinity, top brine temperature, and heating steam temperature. 5. Results and discussion Results and analysis of the MSF system includes calculations of the stage dimensions, tube bundle length, the demister length, and the flow rate and temperature profiles. Other design characteristics include the system performance ratio, specific heat transfer area, and specific flow rates of various streams. The analysis is made for the conditions shown in Table 1. Variations in the specific heat transfer area as a function of the system production capacity and top brine temperature are shown in Fig. 7. As is shown, the specific heat transfer area decreases with the increase in the top brine temperature. This is because of the increase in the flashing range and the temperature drop per stage, which increase the driving force for heat transfer. Also, the specific heat transfer area increases with the increase in the production capacity. This is because of the increase in the system thermal load. Variations in the stage length as a function of the top brine temperature and the production capacity are shown in Fig. 8. As is shown, the top brine temperature has small effect on the stage length. There is small decrease in the stage length is caused by the reduction in the dimension of the tube bundle upon the increase in the top brine Table 1 Design parameters Variable Value 24 43,200–77,760 m3/d 36,000 ppm 30 C 105–115 C Heating steam temperature (Ts) (Tbo þ 10) C 70,000 Salinity of brine reject Xbn Stage width 20 m Performance ratio 9 Number of stages (n) Distillate flow rate (Md) Intake seawater salinity (Xcw) Intake seawater temperature ( C) Top brine temperature Tbo Specific Heat Transfer Area (m2/(kg/s)) N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 210 Product Flow Rate (m3/d) 205 900 700 500 200 195 190 185 180 175 104 106 108 110 112 Top Brine Temperature (°C) 114 116 Fig. 7. Variations in the specific heat transfer area as a function of the top brine temperature and product flow rate. 9 Product Flow Rate (m3/d) 900 700 500 Stage Length (m) 8 7 6 5 4 3 104 106 108 110 112 Top Brine Temperature (°C) 114 116 Fig. 8. Variations in the stage length as a function of the top brine temperature and product flow rate. temperature. On the other hand, the increase in the production capacity requires larger heat transfer area, which causes increase in the tube bundle dimensions and the stage length. A similar behavior is found for the change in stage height, where it vary between 5.7 and 7 m upon the increase in the production capacity and decrease of the top brine temperature. Upon the increase in the top brine temperature from 105 to 110 C, the specific flow 511 rate for cooling water varies over a range of 7.4–8.5 and the specific flow rate of brine recycle varies over a range of 7.42–8.54. On the other hand, increasing the production capacity has no effect on the specific flow rate of cooling water or the specific flow rate of brine recycle. This is because the system performance ratio is kept constant at a value of 9. This implies that the amount of input heat per unit product is also kept constant, which implies use of a constant amount of cooling seawater and brine recycle per unit product. 6. Comparison against field data Comparison of model predictions against field data is made for a number of existing MSF units in the Gulf States. The comparison results are shown in Table 2. The input design data include the number of flashing stages, the system capacity, the top brine temperature, and the stage width. The data were obtained from web site of the manufacturing company Italimpianti (http://www.italimpianti.it). The calculated variables include the performance ratio, the stage length, the stage height, the demister length, and the specific flow rates of the cooling water and brine recycle. The results shown in the table are for small, medium, and large production capacity systems, where it varies from 15,000 to 75670 m3/d. The stage width for these systems varies over a range of 8–23.8 m, as the system capacity increases. As is shown, the MSF performance ratio varies between 8 and 9.5. This is except for the unit with a capacity of 15,000 m3/d, which has a performance ratio of 6. Also, it should be noted that specific flow rate of the cooling seawater and brine recycle varies over a range of 8–9. Similarly, the stage length and height varies over a range of 3.5–7 m. 8.6 8.85 8 8 9.27 8.6 9.3 8.45 8.6 8 12.82 8.88 8.6 8.57 8 7.9 8 7.4 198 141 184 189 194 197 199 199 205 2.1 2.3 2 2 2.5 2 2.2 2.3 2 260 193 226 237 282 242 270 311 288 5.6 4.7 5.4 5.8 6.4 5.5 5.9 6.6 6.2 4.66 3.64 4.25 4.7 5.7 4.4 5 6 5.2 9 6 8.8 9 8 8.9 8.6 9 9.5 107–112 105–112 115 105 105 110 105 111 110 37000 15000 34080 45480 60530 34000 45400 75670 58000 14.2 8 14 17.8 23 14 18 23.8 20 9.53 174 2.3 293 6.2 5.58 8 19 112 57600 The results shown in Table 2 indicate that stage dimensions of the MSF system are strongly dependent on the stage width. The stage width is set to maintain the weir loading within a range of 200–300 kg/(m s). Lower weir loading would imply high residence time for the brine stream within the stage, which would result in high brine levels. In this case, the minimum distance between the top of the brine pool and the demister will not be achieved. As a result, brine entrainment in the distillate vapor will increase and would result in higher product salinity. Higher weir loading is also not desirable because it may result in increased vibrations within the system and subsequent damage to the weir components. Although, no actual data were available for the stage length, stage height, demister length, the specific heat transfer area, and the specific flow rates of the brine recycle and cooling seawater, but, the predicted values are well within known field practice, For example stage height and length are known to vary to vary between 4 and 6 m. Also, the specific flow rate of the brine recycle is known to vary over a range of 9– 10. Similarly, the specific flow rate of the heat transfer area is reported in several studies to vary between 200 and 300 m2/(kg/s) 21 15 21 21 19 21 21 21 24 20 7. Conclusions Al Taweelah ‘‘B’’ (Abu Dhabi–UAE) Al Hidd (Bahrain) Ruwais (UAE) Jebel Ali ‘‘G’’ (Dubai UAE) Jebel Ali ‘‘K’’ (Dubai UAE) Jebel Ali ‘‘K’’ 2 (Dubai UAE) Mirfa (Abu Dhabi–UAE) Ras Laffan (Qatar) Shuweihat (Abu Dhabi–UAE) Subyia (Kuwait) Plant 8.36 N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 Top brine Stage PR Stage Stage Weir Demister Specific heat Number Capacity temperature width length height loading length transfer area of stages (m3/d) sMCW sMR ( C) (m) (m) (m) (m) (m) [m2/(kg/s)] Table 2 Comparison of model predictions against field data 512 This paper presented a mathematical model and analysis for large capacity MSF process. Analysis is presented for variations in main design parameters, which includes stage dimensions, performance ratio, specific heat transfer area, and specific flow rates of cooling seawater and brine recycle. The analysis is made as a function of system capacity, top brine temperature, and number of stages. The main outcome of this analysis is that the system design is strongly dependent on N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 capacity and stage width. The width is set to achieve weir loading of 200–300. Also, the width is limited to a value of 20–25 m, which is set by the available tube length for the cross flow configuration. As a result, the remaining stage dimensions vary over a narrow range of 3.5–7 m for the stage height and length. Also, the demister length vary between 1 and 2 m. Similarly, maintaining the system performance ratio between 8 and 10 result in limited variations in the specific flow rate of the cooling seawater and the brine recycle. 8. Acknowledgement The authors wish to acknowledge the financial support of the Middle East Desalination Research Center (MEDRC), Oman, project # 04-AS-001. Nomenclature Heat transfer area, m2 Brine flow from each flashing stage, kg/s BPE Boiling point elevation, C Cp Specific heat at constant pressure, kJ/kg K D Distillate formed in each flashing stage, kg/s L Length, m LMTD Logarithmic mean temperature difference, C M Mass flow rate, kg/s Number of tubes nt NEA Non-equilibrium allowance, C Tube spacing, m St T Temperature, C U Overall heat transfer coefficient, kW/(m2 C) v Specific volume, m3/kg V Velocity, m/s Brine loading per unit width of the wb flashing stage, kg/(m s) A B Wst X 513 Stage width, m Salinity, ppm Greek Symbols Latent heat, kJ/kg Density, kg/m3 Subscripts 1 b c cw d f h j n p r R s st t tb v First stage Brine Condensation temperature Cooling seawater Distillate product Feed stream Brine heater Heat rejection section Last stage Demister Heat recovery section Brine recycle Heating steam Stage Tube Tube bundle Vapor References [1] C. Thirumeni, Deutsche Babcock Rehabilitation and uprating of Ras Abu Fontas MSF, desalination units: process optimisation and life extension. Desalination 182 (2005) 63–67. [2] A.M. Helal Uprating of Umm Al Nar East 4–6 MSF desalination plants. Desalination, 159 (2003) 43–60. [3] Al-Zubaidi, Sea water desalination in Kuwait – A report on 33 years experience. Desalination, 63 (1987) 1–55. [4] A. Al-Shuaib, M. Al-Bahu, H. El-Dessouky, and H. Ettouney, Progress of the Desalination Industry in Kuwait, IDA World Congress on Desalination and Water Reuse, San Diego, U.S.A., 29Aug to 3-Sep, 1999. [5] R. Borsani, R. Rebagliati, S., Fundamentals and costing of MSF desalination plants and comparison with other technologies. Desalination, 182 (2005) 29–37. 514 N. M. Abdel-Jabbar et al. / Desalination 204 (2007) 501–514 [6] M.A. Soliman, A mathematical model for multistage, flash desalination plants. J. Eng. Sci., 7 (1981) 2–10. [7] M.A. Darwish, Thermal analysis of multi stage flash desalination systems. Desalination, 85 (1991) 59–79. [8] H.T. El-Dessouky, I. Alatiqi and H.M. Ettouney, Process synthesis: the multi-stage flash desalination system. Desalination, 115 (1998) 155–179. [9] A.M. Omar, Simulation of M.S.F. desalination plants, Desalination, 45(1983)65–76. [10] A.M. Helal, M.S. Medani, M.A. Soliman and J.R. Flower, Tridiagonal matrix model for multi-stage flash desalination plants. Comp. Chem. Engin., 10 (1986) 327–342 [11] A. Husain, A. Woldai, A. AI-Radif, A. Kesou, R. Borsani, H. Sultan and P.B. Deshpandey, Modelling and simulation of a multistage flash (MSF) desalination plant. Desalination, 97 (1994) 555–586. [12] H. El-Dessouky, H.I. Shaban and H. Al-Ramadan, Steady-state analysis of multi-stage flash desalination process. Desalination, 103 (1995) 271–287. [13] M. Rosso, A. Beltramini, M. Mazzotti, and M. Morbidelli, Modeling multistage flash desalination plants, Desalination, 108 (1997) 365–374. [14] H.M. Ettouney, H.T. El-Dessouky and F. AlJuwayhel, Performance of the once through multistage flash desalination, Proc. Inst. Mech. Eng. Part A, Power and Energy, 216 (2002) 229–242. [15] B. Fumagalli and E. Ghiazza, Mathematical modelling and expert systems integration for optimum control strategy of MSF desalination plants. Desalination, 92 (1993) 281–293. [16] A. Husain, A. Hassan, D.M.K. Al-Gobaisi, A. Al-Radif, A. Woldai and C. Sommariva, Modelling, simulation, optimization and control of multistage flashing (MSF) desalination plants Part I: Modelling and simulation. Desalination, 92 (1993) 21–41. [17] M. Mazzotti, M. Rosso, A. Beltramini and M. Morbidelli, Dynamic modeling of multistage flash desalination plants. Desalination, 127 (2000) 207–218. [18] M.F. Falcetta and E. Sciubba, Transient simulation of a real multi-stage flashing desalination process. Desalination, 122 (1999) 263–269. [19] I. Kamal, Thermo-economic modeling of dualpurpose power/desalination plants: steam cycles. Desalination, 114 (1997) 233–240. [20] P. Fiorini and E. Sciubba, Thermoeconomic analysis of a MSF desalination plant Desalination, 182 (2005) 39–48