# Flexible Design and Operation of Multi-Stage Flash (MSF) Desalination Process Subject to Variable Fouling and Variable Freshwater Demand

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}fouling resistance model developed earlier [11,12] are incorporated in the full steady state MSF mathematical model by using gPROMS model builder 3.0.3 [14]. For a different number of flash stages, operating parameters such as seawater rejected flow rate and brine recycle flow rate are optimised, while the total daily operating cost of the MSF process is selected to minimise.

## 2. Dynamic Freshwater Demand

## 3. Seawater Temperature Dynamic Profiles

## 4. MSF Process Model

#### 4.1. MSF Process Description

_{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}).

#### 4.2. Steady State MSF Process 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.

#### 4.2.1. Stage Model

_{R}for W

_{S}rejection stage)

_{R}for Ws rejection stage)

#### 4.2.2. Brine Heater Model

_{H})

#### 4.2.3. Splitter Model

#### 4.2.4. Mixers Model

## 5. Storage Tank and Level Control Models

#### 5.1. Storage Tank Model

_{out}represents the freshwater demand described by Equation (1).

#### 5.2. Storage Tank Level Control Model

_{max}) or below the minimum level (h

_{min}) as shown in Figure 5(a). At any time, this violation (V

_{1}, V

_{2}) of safe operation can be defined as [9]:

_{1}and V

_{2}versus time t is shown in Figure 5(b). The total accumulated violation for the entire period can be written using

_{max}and ≥h

_{min}throughout the 24 h operation.

## 6. Optimisation of MSF Parameters

_{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).

#### Optimisation Problem Formulation

^{*}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.

_{S}is steam consumption in kg/hr, T

_{s}is steam temperature in °C

_{M}is make-up flow rate in kg/hr, ρ

_{B}is brine density in kg/m

^{3}

_{d}is distillate product in kg/hr, ρ

_{w}is water density in kg/m

^{3}

_{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 Figure 1.

## 7. Case Study

^{7}kg/h with salinity 5.7 wt. %. The intermediate storage tank has diameter D = 18 m, and aspect ratio = L/D = 0.5.

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 |

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 |

_{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 Table 2. The total daily operating cost (TOC represented as $/day) is found to decrease as the number of stage increases. This is due to lower steam consumption rate with increasing number of stages contributing significantly to the TOC compared to any other cost components (chemical, power, etc.). Note, there is a small change in the C

_{2}, C

_{3}, C

_{4}and C

_{5}while a change in the C1 is relatively high (Table 2).

**Figure 6.**Stage temperature and fouling profile (N = 18). Note: In y axis, E+00 = 10

^{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}(Figure 7) and low R (Figure 8) from 00:00 to 08:00 when the water production rate is low due to low water demand (Figure 9 and Figure 10). However, the water production rate is sufficient to cover the demand (decreasing between 00:00 and 05:00) as well as to store meeting the increasing demand (beyond 06:00) (Figure 10 and Figure 11).

**Figure 7.**Optimum rejected seawater flow rate throughout profile. Note: In y axis, E+05 = 10

^{5}and likewise.

**Figure 8.**Optimum brine recycle flow rate throughout profile. Note: In y axis, E+05 = 10

^{5}and likewise.

_{w}and R reverse their profiles (Figure 7 and Figure 8) to increase the water production rate (Figure 9). Interestingly, up to 09.00, the water production rate is still more than the demand (thus increasing the storage tank level). Beyond 09:00, the water production rate is not sufficient to meet the demand and therefore it is being subsidized from the stored water (thus decreasing the tank level) (Figure 11). Although, the water demand drops down beyond 12:00, the trend of C

_{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.

## 8. Conclusions

## Nomenclature

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

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

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

B_{0} | Flashing brine mass flow rate leaving brine heater (kg/h) |

BBT | Bottom brine temperature (°C) |

B_{D} | Blow-down mass flow rate (kg/h) |

B_{j} | Flashing brine mass flow rate leaving stage j (kg/h) |

C_{B0} | Salt concentration in flashing brine leaving brine heater (wt. %) |

C_{Bj} | Salt concentration in flashing brine leaving stage j (wt. %) |

C_{BNS} | Salt concentration in brine recycle (R) (wt. %) |

C_{R} | Salt concentration in feed seawater (WR) (wt. %) |

C_{S} | Salt concentration in makeup seawater (F) (wt. %) |

C_{W} | Rejected seawater mass flow rate (kg/h) |

D_{j} | Distillate flow rate leaving stage j (kg/h) |

D | Diameter of storage tank (m) |

EX_{j} | Non-equilibrium allowance at stage j |

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

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

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

h | freshwater level in the storage tank (m) |

h_{Bj} | Specific enthalpy of flashing brine at stage j (kcal/kg) |

h_{R} | Specific enthalpy of flashing brine at T _{F} (kcal/kg) |

h_{vj} | Specific enthalpy of flashing vapor at stage j (kcal/kg) |

h_{W} | Specific enthalpy of brine at T _{F} (kcal/kg) |

H_{j} | Height of brine pool at stage j (m) |

L_{H} | Length of brine heater tubes (m) |

L | Length of storage tank (m) |

L_{j} | length of tubes at stage j (m) |

M | storage tank holdup |

ID | Internal diameter of tubes (m) |

OD | External diameter of tubes (m) |

W_{steam} | Steam mass flow rate (kg/h) |

R | Recycle stream mass flow rate (kg/h) |

SB_{j} | Heat capacity of flashing brine leaving stage j (kcal/kg/°C) |

SD_{j} | Heat capacity of distillate leaving stage j (kcal/kg/°C) |

SR_{j} | Heat capacity of cooling brine leaving stage j (kcal/kg/°C) |

TBT | Top brine temperature (°C) |

T_{Bj} | Temperature of flashing brine leaving stage j (°C) |

T_{BNS} | Temperature of the brine in the recycle flowrate (°C) |

T_{BO} | Temperature of flashing brine leaving brine heater (°C) |

T_{Dj} | Temperature of distillate leaving stage j (°C) |

TE_{j} | Boiling point elevation at stage j (°C) |

T_{Fj+1} | Temperature of cooling brine leaving stage j (°C) |

T_{FNR+1} | Temperature of makeup flowrate (F) (°C) |

T_{Fm} | Temperature of the brine in feed entering recovery stage (°C) |

T_{Vj} | Temperature of flashed vapour at stage j (°C) |

T_{steam} | Steam temperature (°C) |

T_{seawater} | Seawater temperature (°C) |

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

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

ww_{j} | Width of stage j (m) |

W_{S} | Seawater mass flow rate (kg/h) |

X | LMTD, logarithmic mean temperature difference at stages |

Y | LMTD, logarithmic mean temperature difference at brine heater |

Δ_{j} | Temperature loss due to demister (°C) |

ρ_{j} | Brine density (kg/h) |

λ_{s} | Latent heat of steam to the brine heater (kcal/kg) |

## IDEX

H | Brine heater |

j | Stage index |

* | Reference value |

## Conflicts of Interest

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**MDPI and ACS Style**

Said, S.A.; Emtir, M.; Mujtaba, I.M.
Flexible Design and Operation of Multi-Stage Flash (MSF) Desalination Process Subject to Variable Fouling and Variable Freshwater Demand. *Processes* **2013**, *1*, 279-295.
https://doi.org/10.3390/pr1030279

**AMA Style**

Said SA, Emtir M, Mujtaba IM.
Flexible Design and Operation of Multi-Stage Flash (MSF) Desalination Process Subject to Variable Fouling and Variable Freshwater Demand. *Processes*. 2013; 1(3):279-295.
https://doi.org/10.3390/pr1030279

**Chicago/Turabian Style**

Said, Said Alforjani, Mansour Emtir, and Iqbal M. Mujtaba.
2013. "Flexible Design and Operation of Multi-Stage Flash (MSF) Desalination Process Subject to Variable Fouling and Variable Freshwater Demand" *Processes* 1, no. 3: 279-295.
https://doi.org/10.3390/pr1030279