Format And Type Fonts CHEMICAL ENGINEERING TRANSACTIONS VOL. 45, 2015 A publication of The Italian Association of Chemical Engineering www.aidic.it/cet Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Sharifah Rafidah Wan Alwi, Jun Yow Yong, Xia Liu Copyright © 2015, AIDIC Servizi S.r.l., ISBN 978-88-95608-36-5; ISSN 2283-9216 DOI: 10.3303/CET1545076 Please cite this article as: Sowgath T.M., Mujtaba I., 2015, Meeting the fixed water demand of msf desalination using scheduling in gproms, Chemical Engineering Transactions, 45, 451-456 DOI:10.3303/CET1545076 451 Meeting the Fixed Water Demand of MSF Desalination using Scheduling in gPROMS Tanvir M. Sowgath* ,a , Iqbal Mujtaba b a Department of Chemical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka Bangladesh b Chemical Engineering Division, School of Engineering, University of Bradford, Bradford BD7 1DP, UK mstanvir@che.buet.ac.bd Multi-Stage Flash (MSF) desalination process has been used for decades for making fresh water from seawater and is the largest sector in desalination industries. In this work, dynamic optimisation of MSF desalination is carried out using powerful and robust dynamic simulation and optimisation software called gPROMS model builder. For a fixed freshwater demand, a number of optimal combinations of the factors such as heat transfer area, brine flow rate, cooling water flow rate, steam flow in brine heater, Top Brine Temperature, the number of stages, etc. are determined with the objective of maximising the performance ratio of the process (defined as the amount of fresh water produced per unit of energy input) considering the seasonal variations. An attempt has been made to develop an operational schedule for a particular day using dynamic optimisation. 1. Introduction Global thirst will turn millions into water refugees. Increasing in population and standards of living together with water pollution are diminishing the quantity of naturally available fresh water while the demand for it is increasing continuously. While fresh water is an absolute necessity for sustainable development, more than 90 % of the world’s surface water is saline. Multi Stage Flash (MSF) desalination process (Figure 1) has been used for decades for making fresh water from seawater (El-Dessouky and Ettouney, 2002). The MSF plant behaviour changes with time due to corrosion and scaling (Said et al., 2011). Therefore, use of one optimal set point operation decided at the time of commissioning the new plant will not guarantee the expected profitability while meeting the operational constraints. Dynamic model provides a better insight into the process dynamics without conducting the lengthy and expensive tests on real plant. A typical MSF dynamic process model includes mass and energy balances, the geometry of the stages and thermo-physical properties (Mazzotti et al. 2000). Al-Fulaij et al. (2011) studied the stability of MSF desalination process using a dynamic model. Alsadaie and Mujtaba (2014) studied the effect of venting system design of Once-Through MSF process using a dynamic model. Tayyebi and Alishiri (2014) studied MSF control using a dynamic model. However, none of these studies reflected on the effect of dynamic seawater temperature changes on the performance of MSF processes. In this work, we develop an operational schedule of a Brine-Recirculation MSF process for a particular day using dynamic modelling and optimisation. Models for flash chambers, brine heater, mixer, splitter and orifice are developed individually and connected according to the physical existence shown in Tanvir and Mujtaba (2008). A framework is developed to optimize steam temperature profile of the MSF process for maximizing the performance ratio. The daily time horizon is split into several zones. The dynamic seawater temperature profile is considered to be piecewise constant in each time zone. 2. MSF model development gPROMS allows user to model the transient behaviour of individual unit operations to be described in terms of mixed systems of integral, partial differential and algebraic equations (gPROMS, 2005). Like most 452 of the modern simulator package gPROMS also provides an interface to develop a complex system from several subsystems. The Sub model (i.e., equipment model) can be connected graphically in Master model (i.e., flowsheet, recovery stage (Figure 2)). The model equations for one recovery stage, one rejection stage, splitter, mixer, brine heater, etc. are written as unit models respectively. Note the number of rejection stage is fixed to three in this work. With reference to Figure 1, some of the main model equations are given in the following. Further details on the model equations can be found in Sowgath (2007) and in Tanvir and Mujtaba (2008). The total number of stages are NS = NR+NJ (where, NR = number of stages in the recovery section, NJ = number of stages in the rejection section). From the degrees of freedom analysis, the total number of free variables is: 7NS + 11 and the differential state variables are 2NS+1. In optimization, a set of these variables are relaxed and optimized. The initial conditions are equal to the number of dynamic variables. This means 7NS+11 variables and the initial conditions must be specified before the model equations could be solved. The initial conditions (at time t = 0) of all the differential variables (such as , , , , , , B D W B D F j j j j j j BH M M M h h h h ) has to be given. Each model of different equipment can be presented as graphical form and connected graphically in process flowsheet (Figure 2). A 1 1 W TFj CR W TFj+1 CR Dj TDj Bj TBj CBj Bj-1 TBj-1 CBj-1 Dj-1 TDj-1 FLASHING BRINE DISTILLATE COOLING BRINE Figure 1: A typical MSF Process and its stage j Figure 2: Internal Connection of Stages in Recovery Section in gPROMS 453 2.1 Stage Model Total Mass Balance for the flashing brine: jjj B j VBB dt dM  1 (1) Salt Mass for the flashing brine:   1 1 B B j j j j j j d M X B CB B CB dt        (2) Enthalpy balance for the flashing brine:     11 j j j j B B B B V B j j j j M h B h h V h h         (3) Mass balance for the distillate tray: 1    D j j j j d M D D V dt (4) Total Mass Balance for the Cooling Brine Tube: 1j j T W W W    (5) Salt Mass for the Cooling Brine Tube: 1 1j j j j W CF W CF      (6) Enthalpy Balance:         1 1 1 ln D F j jF F F F F F j j j j j j T j jD F j j T Td M h U A T T W h h dt T T            (7) Overall Enthalpy Balance of Stage is given by,    1 1 1 1 1 D B j jD V D D B D B F F j j j j j j j j j j j T j j dh dM M h h D h B h D h B h W h h dt d                     (8) Distillate and flashing brine temperature relation: Bj Dj j j j T = T +TE + EX +  (9) The stage pressure relationship:     log10      C V j j P X a b X c X d X P T (10) Brine and Distillate tray Holdup calculation: B B B B j j j j j M Oh L V    (11) D D D D j j j j j M Oh L V    (12) 2.2 Brine Heater Model Mass Balance: BH T B W (13) Salt mass Balance: BH R C C (14) Enthalpy balance:    11 1ln F F Fsteam BH BH H H BH T BH steam BH d T T M h U A T T W h h T Tdt                 (15)   11 ln F F steam steam steam H H BH steam BH T T W U A T T T T             BH T B W (16) 2.3 Blowdown splitter D NS B B R  (17) 2.4 Reject seawater splitter: W S C W F  (18) 2.5 Makeup Mixers Model Mass balance: R W = R + F (19) Salt Balance: BNS S R R R C + F C = W C   (20) The correlations for physical and chemical properties (except the calculation of TE) and the above are taken from Rosso et al., (1996). Husain et al. (2003) also used similar correlations. Instead of an empirical correlation an NN based correlation (Tanvir and Mujtaba, 2006) is used here to calculate the temperature elevation (TE) due to salinity. Detailed development of MSF process model is found in Sowgath (2007). All symbols of the model are defined in Rosso et al. (1996) and in more recent work of Tanvir and Mujtaba (2006). 454 3. Optimisation problem formulation The dynamic optimization problem (DOP) can be described mathematically as shown below. DOP PRMax Wsteam CRT ,, s.t.  fttvuxxtf ,equations) model(0,,,, 0 .          (21)  o93 (101 )L U osteam steam steamC T T T C  (22) (33 C) (39 C) o L U o seawater seawater seawater T T T  (23) 5 9 10 N D D     (24) Subscripts/superscripts L and U refer to lower and upper bounds of the parameter. The daily time horizon is split into several zones. The dynamic seawater temperature profile is considered to be piecewise constant in each time zone. Also the stage temperatures are constrained within a narrow limit to reduce heat exchanger fouling. 4. Results and discussions Table 1 lists all the constant parameters of the model equations including various dimensions of the brine heater and flash stages. Table 2 also shows the sample validation results of the dynamic process. There is a close agreement between the predictions of the dynamic model at steady state condition with those presented by Rosso et al. (1996). Table 1: Constant parameters and Model validation Table 2: Constant parameters and Model validation F kg/h BD kg/h WR kg/h Wsteam kg/h CR wt/wt 5.68 × 10 6 4.76 × 10 6 1.203 × 10 7 1.348 × 10 5 6.29 × 10 -2 5.68 × 10 6 4.78 × 10 6 1.203 × 10 7 1.316 × 10 5 6.27 × 10 -2 Stage Profiles (Brine heater stage j =0; TBT = TB0) Stage Bj kg/h Dj kg/h CBj wt/wt TFj °C TDj °C TBj °C Brine heater 1.203 × 10 7 0.0629 89.74 1.203 × 10 7 0.0627 88.66 1 1.197 × 10 7 5.94 × 10 4 0.06295 83.68 86.04 85.58 1.197 × 10 7 5.98 × 10 4 0.0632 83.33 85.75 86.89 16 1.110 × 10 7 9.34 × 10 5 0.0681 38.17 39.80 41.40 1.113 × 10 7 9.04 × 10 5 0.0682 38.07 39.98 41.51 The results of this work are shown in bold In Figure 3, an external disturbance of seawater temperature is considered where it increases from 23 °C to 45 °C and steam T remaining at 97 °C. Note that in reality the plant will not experience such a big step change in a short period of time. However, this case is considered to test the robustness of the dynamic model in terms of handing large step change. With the change in the seawater temperature, the plant will or j H A A m 2 or i i j H D D m or o o j H D D m or i i j H f f hm 2o C/kcal , or j j H w L L m j H m Brine heater 3,530 0.022 0.0244 1.86 × 10 -4 12.2 Recovery stage 3,995 0.022 0.0244 1.4 × 10 -4 12.2 0.457 Rejection stage 3,530 0.024 0.0254 2.33 × 10 -5 10.7 0.457 S W steam T seawater T S C R 1.131 × 10 8 kg/h 97 °C 35 °C 5.7 wt% 6.35 × 10 6 kg/h 455 reach to a different steady state condition (producing less freshwater). To produce the same amount of freshwater, the steam temperature needed to be changed to 116.5 °C (Figure 3). Figure 3: Dynamic Model Prediction of Fresh Water Production due to Steam Temperature Disturbance 4.1 Case study: The desired steam temperature to maintain the fixed water demand It is assumed that during a particular day of the spring season, the seawater temperature increases from 33 (9 am in the morning) to 39 ºC (at 12 pm noon) and falls back to 33 ºC (at 3 pm in the afternoon) as shown in Figure 4. Although the temperature change will be gradual, but for the sake of convenience it is assumed that they change at discrete points as shown. It is also assumed that the steam temperature also changes at these discrete points. The purpose of this exercise is to find out optimum steam temperature at these discrete points which will be needed to off-set the change in seawater temperature while maintaining the same level of water demand and maximising the performance ratio (note, for a fixed water demand, steam temperature determines the amount of steam). Table 2: Summary of the Optimisation Results Run Tsteam Tseawater PR 1 5 9 10 N D D     93.96 33 11.4481 95.76 35 2 5 9 10 N D D     95.76 35 11.5376 97.55 37 3 5 9 10 N D D     97.55 37 11.6261 99.35 39 4 5 9 10 N D D     99.35 39 11.5376 97.51 37 5 5 9 10 N D D     97.51 37 11.4481 95.72 35 6 5 9 10 N D D     95.72 35 11.3575 93.94 33 The results are presented in Table 3 which clearly show that the change in steam temperature can off-set the change in seawater temperature while maintaining the fixed water demand. Also note, the PR values during the period (9 am to 3 pm) is almost constant. Note, it is assumed that the plant is operating at steady state right up to the point of changes of seawater temperature and reaches to the next steady state after 8 s of the step change in the seawater temperature (as can be seen from Figure 4). Therefore, the results only include 16 s operations prior and after the step change. Basically, the second 8s operation is dynamic (as shown in Figure 4 for TBT) during the period (9 am to 3 pm). Tsteam = 97 °C Tseawater = 23 °C Tsteam = 97 °C Tseawater = 45 °C Tsteam = 116.5 °C Tseawater = 45 °C 456 Figure 4: Seawater Temperature profile and TBT Response of the Optimised Tsteam Profile 5. Conclusions A detailed dynamic MSF process model describing the physical behaviour of the plant is considered here to study the impact of dynamic seawater temperature change on the performance of the process. gPROMS software package has been used to construct the model. The model included non-equilibrium effects, demister pressure drop and the brine and distillate hold up equations. The model is used within a dynamic optimisation framework to optimise the steam temperature profile subject to several step changes in seawater temperature while ensuring fixed water demand and maximum Performance Ratio. The seawater temperature profile is considered to be piecewise constant in each time zone. It clearly offers potential to explore flexible design, scheduling and operation of MSF desalination process simultaneously without compromising the freshwater demand. In future, the dynamic model will be used for control study. Acknowledgement Authors would like acknowledge the BUET authority for all logistic and financial support. References Al-Fulaij H., Cipollina A., Ettouney H., Bogle D., 2011, Simulation of stability and dynamic multistage flash desalination, Desalination, 281, 404-412. Alsadaie S.M., Mujtaba I.M., 2014, Modelling and simulation of MSF desalination plant: The effect of venting system design for non-condensable gases, Chemical Engineering Transactions, 39, 1615-20. 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