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This work describes how the design and operation parameters of the Multi-Stage Flash (MSF) desalination process are optimised when the process is subject to variation in seawater temperature, fouling and freshwater demand throughout the day. A simple polynomial based dynamic seawater temperature and variable freshwater demand correlations are developed based on actual data which are incorporated in the MSF mathematical model using gPROMS models builder 3.0.3. In addition, a fouling model based on stage temperature is considered. The fouling and the effect of noncondensable gases are incorporated into the calculation of overall heat transfer co-efficient for condensers. Finally, an optimisation problem is developed where the total daily operating cost of the MSF process is minimised by optimising the design (no of stages) and the operating (seawater rejected flowrate and brine recycle flowrate) parameters.

At present, there is a shortage in the freshwater resources all over the world. About 40% of the world’s populations are suffering from the water crisis. This is due to the continuous growth of the world population and economic activities. Moreover, 96% of the water on the earth is located in oceans and seas and out of 1.7% groundwater only 0.8% is considered to be the freshwater [

During the last decades, modelling played a very important role in the simulation, optimisation and control of multistage flash (MSF) desalination process. Many models have been developed to find a functional relationship between the design and operating variables [

A recent study [

Most recently, [_{3} fouling resistance model developed earlier [

Fresh water consumption profile on holiday (Saturday).

The variation in seawater temperature throughout the day is shown in

Seawater temperature profile during the day and night.

Note, between 0 and 10 h, 5th order polynomial shows a very good mapping with the actual data. Beyond 10 h, although the polynomials do not show a close map, the trend of temperature change is retained.

The MSF process mainly consists of three sections: brine heater section, recovery section with NR stage and rejection sections with NJ stage (_{S}) and passes through series of tubes to remove heat from the stages. Before the recovery section seawater is partly discharged to the sea (C_{W}) to balance the heat. The other part (F) is mixed with recycled brine (R) from the last stage of the rejection section and fed (W_{R}) before the last stage of the recovery section. Seawater is flowing through the tubes in difference stages to recover heat from the stages and the brine heater raises the seawater temperature to the maximum attainable temperature (Top brine temperature TBT). After that it (B_{0}) enters into the first flashing stage and produce flashing vapour. This process continues until the last stage of the rejection section. The concentrated brine (B_{N}) from the last stage is partly discharged to the sea (B_{D}) and the remaining (R) is recycled as mentioned before. The vapour from each stage is collected in a distillate tray to finally produce the fresh water (D_{N}). Vapour from each stage is collected in a distillate tray to finally produce the fresh water (D_{N}).

Typical Multi-Stage Flash (MSF) Process.

With reference to

The following assumptions are made in the model:

The distillated from any stage is salt free

Heat of mixing are negligible

No sub cooling of condensate leaving the brine heater

There are no heat losses and

There is no entrainment of mist by the flashed vapour.

The model equations are presented below for the sake of completeness.

Mass Balance in the flash chamber:
_{R} for W_{S} rejection stage)

The logarithmic mean temperature difference in the recovery and rejection stages:
_{R} for Ws rejection stage)

Heat capacity of cooling brine leaving stage j:

Mass and salt balance for the brine heater
_{H})

Mass balance on seawater splitter

Mass balance on mixer

These models are taken from Hawaidi and Mujtaba [

The dynamic mathematical model of the tank process shown in _{out} represents the freshwater demand described by Equation (1).

Storage tank.

The storage tank described above is assumed to operate without any control on the level(h), therefore and during the MSF operation process, the tank level goes above the maximum level (h_{max}) or below the minimum level (h_{min}) as shown in _{1}, V_{2}) of safe operation can be defined as [

A typical plot of V_{1} and V_{2} versus time

_{max} and ≥h_{min} throughout the 24 h operation.

(a) Tank level profile and (b) tank level violations during the MSF operation.

The seawater temperature and the freshwater demand are subject to vary during a day. Therefore, to supply freshwater meeting a variation in the seawater temperature and variable freshwater demand throughout the day, the operation parameters of the MSF process has to be adjusted. In this section, the MSF process model and the CaCO_{3} fouling resistance model coupled with the storage tank model developed has been used to adequate the variations in the seawater temperature and freshwater demand during a day. For different number of flash stages, operating parameters such as seawater rejected flow rate and brine recycle flow rate are optimised, while the total annual operating cost of the MSF process is selected to minimise using gPROMS models builder 3.0.3 (version 3.0.3.; PSE: London, UK).

The optimisation problem is described as:

Given: Design specifications of each stage, fixed amount of seawater flow, heat exchanger areas in stages, variable seawater temperature, steam temperature, freshwater demand profile, and volume of the storage tank.

Optimise: Recycle brine flow rate, rejected seawater flow rate, at different time intervals within 24 h.

To minimise: The total operation cost (TOC, $/day).

The optimisation problem (OP) can be described mathematically by:
^{*} is the fixed top brine temperature. R is the recycle flowrate and C_{w} is the rejected seawater flowrate. Subscripts L and U refer to lower and upper bounds of the parameters.

The objective function, TOC (total operating cost) is defined as [_{S}_{s} is steam temperature in °C
_{M} is make-up flow rate in kg/hr, _{B}^{3}
_{d} is distillate product in kg/hr, _{w}^{3}

This optimisation problem minimises the total operating cost while optimises R and C_{w} for variable seawater temperature and freshwater demand throughout 24 h. Note, the actual freshwater consumption at any time is assumed to be 40,000 times more than that shown in

A steady state process model for the MSF process coupled with a dynamic model for the storage tank (as described earlier) has been used in the case study. The constant parameters of the MSF process model equations including various dimensions of the brine heater and flash stages are listed in ^{7} kg/h with salinity 5.7 wt. %. The intermediate storage tank has diameter D = 18 m, and aspect ratio = L/D = 0.5.

Constant parameters.

Unit | A_{j}/A_{H} |
D_{j}^{i}/D_{H}^{i} |
D_{j}^{0}/D_{H}^{0} |
w_{j}/L_{j}/L_{H} |
H_{j} |
---|---|---|---|---|---|

Brine heater | 3530 | 0.022 | 0.0244 | 12.2 | |

Recovery stage | 3995 | 0.022 | 0.0244 | 12.2 | 0.457 |

Rejection stage | 3530 | 0.024 | 0.0254 | 10.7 | 0.457 |

Summary of optimisation results.

Case | N | C1, $/d | C2, $/d | C3, $/d | C4, $/d | C5, $/d | TOC, $/d |
---|---|---|---|---|---|---|---|

1 | 16 | 46,184,583 | 37,498,047 | 17,220,256 | 12,954,688 | 15,798,400 | 129,655,973 |

2 | 17 | 44,026,301 | 37,597,628 | 17,358,817 | 13,058,927 | 15,925,521 | 127,967,194 |

3 | 18 | 41,403,746 | 37,222,956 | 17,250,642 | 12,977,547 | 15,826,277 | 124,681,167 |

Six time intervals within 24 h are considered within which both R and C_{W} are optimised with the interval lengths. The total operating cost on daily basis and the other plant cost (steam cost (C1), chemical cost (C_{2}), power cost (C_{3}), spare cost (C_{4}) and labour cost (C_{5})) for three different number of stages (16, 17 and 18) are listed in _{2}, C_{3}, C_{4} and C_{5} while a change in the C1 is relatively high (

Stage temperature and fouling profile (^{0}; E−06 = 10^{−6} and likewise.

_{w}) and recycle flow rate (R) throughout 24 h at different number of stages. The plant operates at the high flow rate of C_{w} (

Optimum rejected seawater flow rate throughout profile. Note: In y axis, E+05 = 10^{5} and likewise.

Optimum brine recycle flow rate throughout profile. Note: In y axis, E+05 = 10^{5} and likewise.

Fresh water plant production profile. Note: In y axis, E+05 = 10^{5} and likewise.

Fresh water demand profile. Note: In y axis, E+05 = 10^{5} and likewise.

Storage tank level profiles (case 1).

As the water demand increases between 05:00 and 12:00 (_{w} and R reverse their profiles (_{w}, R and water production rate continues at the same level right up to 18:00. During this period, storage tank level continues to drop down to the minimum. Beyond 18:00 C_{w} are R are adjusted to have sufficient water production to meet the demand until 24:00 and to store at the same time.

However, the intermediate storage tank adds the operational flexibility, and maintenance could be carried out without interrupting the production of water or full plant shut-downs at any time throughout the day by adjusting the number of stage. Note, the optimal results in this case are almost the same for the all the number of stages considered.

In this work, for a given design, an optimal operation scheme for an MSF desalination process subject to variable seawater temperature and variable freshwater demand is considered. An intermediate storage tank is considered between the MSF process and the customer to add flexibility in meeting the customer demand. A dynamic model for the storage tank level has been implemented with steady state MSF process model using gPROMS 3.0.3 model builder. Unlike previous work, a stage temperature based fouling correlation is added and the effect of non-condensable gases on the condenser heat transfer co-efficient is reflected into the process model.

For several process configurations (the design), some of the operation parameters of the MSF process such as seawater recycle flow rate and brine recycle flow rate at discrete time interval are optimised, while minimising the total daily operating costs. The optimisation results show increase in the total operating cost with decreasing number of stages. During the low consumption of freshwater, there is an increase in the tank level and plant production. Consequently, the plant operates at maximum value of rejected seawater flowrate and at minimum value of recycled brine flowrate. On the other hand, optimum results show decrease in the plant production and tank level when there is an increase in the freshwater consumption and consequently the plant operate at minimum value of rejected seawater flowrate and slightly increase in recycled brine flowrate. The results also clearly show that the use of the intermediate storage tank adds flexible scheduling in the MSF plant to meet the variation in freshwater demand with varying seawater temperatures without interrupting or fully shutting down the plant at any time during the day by connecting the desired number of stages (see [

_{H}

Heat transfer area of brine heater (m^{2})

_{j}

Heat transfer area of stage j (m^{2})

_{S}

cross sectional area of storage tank (m^{2})

_{0}

Flashing brine mass flow rate leaving brine heater (kg/h)

Bottom brine temperature (°C)

_{D}

Blow-down mass flow rate (kg/h)

_{j}

Flashing brine mass flow rate leaving stage j (kg/h)

_{B0}

Salt concentration in flashing brine leaving brine heater (wt. %)

_{Bj}

Salt concentration in flashing brine leaving stage j (wt. %)

_{BNS}

Salt concentration in brine recycle (R) (wt. %)

_{R}

Salt concentration in feed seawater (WR) (wt. %)

_{S}

Salt concentration in makeup seawater (F) (wt. %)

_{W}

Rejected seawater mass flow rate (kg/h)

_{j}

Distillate flow rate leaving stage j (kg/h)

Diameter of storage tank (m)

_{j}

Non-equilibrium allowance at stage j

Make-up seawater mass flow rate (kg/h)

_{j}

^{H}

Brine heater fouling factor ( h m^{2} °C/kcal)

_{j}

^{i}

Fouling factor at stage j ( h m^{2} °C/kcal)

freshwater level in the storage tank (m)

_{Bj}

Specific enthalpy of flashing brine at stage j (kcal/kg)

_{R}

Specific enthalpy of flashing brine at T_{F} (kcal/kg)

_{vj}

Specific enthalpy of flashing vapor at stage j (kcal/kg)

_{W}

Specific enthalpy of brine at T_{F} (kcal/kg)

_{j}

Height of brine pool at stage j (m)

_{H}

Length of brine heater tubes (m)

Length of storage tank (m)

_{j}

length of tubes at stage j (m)

storage tank holdup

Internal diameter of tubes (m)

External diameter of tubes (m)

_{steam}

Steam mass flow rate (kg/h)

Recycle stream mass flow rate (kg/h)

_{j}

Heat capacity of flashing brine leaving stage j (kcal/kg/°C)

_{j}

Heat capacity of distillate leaving stage j (kcal/kg/°C)

_{j}

Heat capacity of cooling brine leaving stage j (kcal/kg/°C)

Top brine temperature (°C)

_{Bj}

Temperature of flashing brine leaving stage j (°C)

_{BNS}

Temperature of the brine in the recycle flowrate (°C)

_{BO}

Temperature of flashing brine leaving brine heater (°C)

_{Dj}

Temperature of distillate leaving stage j (°C)

_{j}

Boiling point elevation at stage j (°C)

_{Fj+1}

Temperature of cooling brine leaving stage j (°C)

_{FNR+1}

Temperature of makeup flowrate (F) (°C)

_{Fm}

Temperature of the brine in feed entering recovery stage (°C)

_{Vj}

Temperature of flashed vapour at stage j (°C)

_{steam}

Steam temperature (°C)

_{seawater}

Seawater temperature (°C)

_{H}

Overall heat transfer coefficient at brine heater (Kcal/m^{2} h K)

_{j}

Overall heat transfer coefficient at stage j (Kcal/m^{2} h K)

_{j}

Width of stage j (m)

_{S}

Seawater mass flow rate (kg/h)

LMTD, logarithmic mean temperature difference at stages

LMTD, logarithmic mean temperature difference at brine heater

_{j}

Temperature loss due to demister (°C)

_{j}

Brine density (kg/h)

_{s}

Latent heat of steam to the brine heater (kcal/kg)

Brine heater

Stage index

Reference value

The authors declare no conflict of interest.