CHEMICAL ENGINEERING TRANSACTIONS

VOL. 57, 2017

A publication of

The Italian Association

of Chemical Engineering
Online at www.aidic.it/cet

Guest Editors: Sauro Pierucci, Jiří Jaromír Klemeš, Laura Piazza, Serafim Bakalis
Copyright © 2017, AIDIC Servizi S.r.l.

ISBN 978-88-95608- 48-8; ISSN 2283-9216

Minimise the Operation Schedule Time to Meet the Daily
Fixed Water Demand of MSF Desalination

Tanvir M. Sowgath*a,b
a Department of Chemical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh
b School of Engineering, University of Bradford, Bradford BD7 1DP, UK
mstanvir@che.buet.ac.bd

Multi Stage Flash (MSF) desalination process is the largest sector in providing fresh water to the gulf region.
The production of fresh water from an MSF process can vary with daily temperature variation of seawater
producing more water during the night than during the day whereas the demand during the day is usually
more than at night. In this work, a Dynamic Optimisation (DO) problem is formulated and solved within
gPROMS based on Control Vector Parameterisation (CVP) where the minimum schedule time problem for
fixed water demand is solved to achieve the optimal trajectories. The dynamic seawater temperature profile is
considered to be piecewise constant or linear in each time zone.

1. Introduction

Steady and source of water supplies ensures quality of life for a community. Existing fresh water supplies are
over exploited due to population growth, higher living standards and growth of both agriculture and industry
(Patroklou et al. 2013). With almost 90% of the surface water being saline desalination is becoming one of the
stable and sustainable source of freshwater around the world. MSF desalination process (Figure 1) is the
oldest and is still leading in desalination industry (Alsadaie and Mujtaba, 2016). In the MSF process, vapour is
formed from flashing of seawater in stages and condenses into freshwater.
When then design and the operation are fixed, the production of freshwater from an MSF is more in winter
than in summer (Tanvir and Mujtaba, 2006). To maintain water production at the same level during both
season, the common industrial practice is to operate the plant at higher temperature. However, this results in
increased fouling and corrosion of heat exchanger (other plant equipment) leading to frequent shutdown of the
plant interrupting the freshwater supply or resulting in the increased amount of antiscallant (Al-Hangary et al.,
2007). Also note, the plant operation changes with time due to different uncertainty that originates from
corrosion, equipment failure, raw material shortages, fluctuation in pricing, change in demand, change in
weather condition, etc. Therefore, the short-term operational decision needs to be addressed to maintain the
desired supply and expected profitability. Optimisation can help finding the short-term optimised plant
operating schedule. Several works have been found in the literature considering dynamic and optimisation
study of MSF desalination. Sowgath and Mujtaba (2015) presented DO framework to develop the real-time
schedule and to maximize the performance while maintaining fixed water demand with daily variation of
seawater temperature. They vary the steam temperature for discrete change of seawater temperature to offset
its effect.
In this work, a number of DO problems are formulated to: (a) maximise the performance ratio (PR) for a given
time to get to one steady state to other due to discrete change in seawater temperature (b) minimise the time
between one steady state to other due to discrete change in seawater temperature and finally (c) minimise the
time between one steady state to other due to continuous change in seawater temperature. In all cases, a
fixed water demand is maintained optimum operation policies for in terms of brine heater steam temperature,
recycled brine flowrate and rejected seawater flowrate are obtained. A set of Differential and Algebraic
Equations (DAEs) that describe the transient behaviour of MSF process is incorporated in the DO problems.

DOI: 10.3303/CET1757078

Please cite this article as: Sowgath M.T., 2017, Minimise the operation schedule time to meet the daily fixed water demand of msf
desalination, Chemical Engineering Transactions, 57, 463-468 DOI: 10.3303/CET1757078

463

Recycle Brine,R

Rejection stages
Recovery stages

Steam

WSTEAM

DEND

Seawater, Ws

Blowdown,BD

1 NR
NR+1 NR+NJ

Stage

Freshwater

Figure 1: A typical MSF Process and Stage j.

2. Process model

Due to the availability of process engineering computational tools for model development and optimisation
(e.g. Aspen Plus, Aspen Custom Modeler, gPROMS etc.), growing implementation of such tools in process
design and operations over the past decades is observed. In gPROMS the “CVP_SS” solver act as a single

solver manager for the solution of both dynamic and steady-state, continuous and mixed integer optimization
problems. CVP technique can handle large Differential Algebraic Equation systems (DAE) of the dynamic
process very faster than other methods. gPROMS enables user to construct the model in hierarchical
structure.
Here, a dynamic model developed within gPROMS is taken from Sowgath and Mujtaba (2015) which is based
on the work of Rosso et al. (1996), Hussain et al. (2003) and Mazzotti et al. (2000). Models for each unit
operations such as flash chambers, brine heater, mixer, splitter and orifice are developed individually and
connected according to the physical existence. 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 stage is
fixed. MSF dynamic model is constructed in hierarchical structure where lower hierarchy includes flashing
stages, brine heater, mixers, splitter and physical properties models while higher hierarchy combines them in
a process flowsheet model. Sowgath and Mujtaba (2015) validated the model using steady state data from
Rosso et al. (1996) which showed a good agreement.

3. Optimization problem formulation and constraints

3.1 Optimization Problem 1 (OP1)

The optimization problem is described as:
Given: Fixed water demand throughout the year, fixed number of rejection stages, fixed

amount of seawater flow, heat exchanger areas in stages, design specifications
of each stages

Optimise: The number of recovery stages, steam temperature, recycled brine flowrate,
rejected seawater flowrate while there is a step change in seawater temperature

So as to Maximise: Performance ratio (PR) ( 310 amount of freshwater energy consumption )
Subject to: Process constraints: Equality constraints such as process model, Inequality

constraints such as linear bounds on optimisation variables and other
parameters.

The optimization problem (OP1) can be described mathematically by:

     

, ,

, , , , 0,[ , ] Model

w SteamR C T

Max PR

f t x t x t x t v t t
 

 
 

END

END
D D

464

(93 C) (97 )

(4.7 10 ) (7

L U o

steam steam steam

T T T C

R R R

 

  
6

6 6

.85 10 )

(4.1 10 ) (5.9 10 )

1.13 10 ,

L U

w w w

C C C

W Seawa



   

 

1 1 2

5.7 %

1 ( 0, ), 2 ( , ),

seawater seawater

terConcentrration wt

T X t t T X t t



  

2
2 10t 

ENDD is the total amount of fresh water produced and
*
ENDD is the fixed water demand (= kg/hr). steamT is the

steam temperature. TBT is the Top Brine Temperature. R is the Recycle flowrate; wC is the Rejected seawater
flow rate. Subscripts/superscripts L and U refer to lower and upper bounds of the parameters. The bounds of
the parameters are shown in brackets above. Water demand *ENDD is fixed over schedule time. X1 and X2 are
seawater temperatures in the first (t1) and second interval (t2). The minimum and maximum value of (t1) are 1
and 5 seconds respectively and the minimum and maximum value of second interval (t2) is 5 and 10 seconds
respectively.

3.2 Optimization Problem 2 (OP2)

The optimization minimum time problem (OP2) can be described mathematically by:
For fixed water demand Minimum time problem (OP2) can be expressed as.

     

, ,

, , , , 0,[ , ] Model

w Steam

f
R C T

Min t

f t x t x t x t v t t
 

 
 

Other Constraints are ame as 1s OP

4. Results

The results of the first two optimisation problems (OP1 and OP2) are presented in Table 1. In Table 1, the
MSF process is assumed to be at steady-state condition at seaw aterT = 33

oC. An external disturbance of
seawater temperature is considered where it increases from 33oC to 35oC. The optimizer reaches the steady
state again in 35oC in both OP1 and OP2 where the fixed water demand is maintained from 510 10endD   to

5
8.5 10

end
D   for different case studies (1-4). For case 1, the objective is to minimize schedule time for fixed
water demand for operation schedule time. For case 2, the objective is to maximise PR for fixed water
demand for operation schedule time. For OP1, operation schedule time hits the upper bound 9 except the
water demand 58.5 10endD D   , while for OP2, except the water demand 510 10endD D   , operation
schedule time hit the lower bound of the controller time horizon. In Case 2, the step changes are minimum to
go for stable operation. It is interesting to note that water production per unit energy is increased with
decrease of water demand for both OP1 and OP2.
For OP1, with decrease in fixed water demand Reject seawater Cw, top brine temperature TBT is increase,
while recycle flowrate R, Amount of steam Wsteam also decrease to maintain the fixed water demand for
increase in seawater temperature. For OP1, Tsteam hits the higher bound while for OP2, it decreases with
decrease of water demand.
For OP1, it is found that PR is increased at the cost of more time to reach stable operation and larger step of
manipulated variable is found. From the Table 1, it can be concluded that the minimum time problem (OP2)
leads to the smaller step changes and optimum steady condition reaches for lesser time than maximum
problem (OP1). Therefore minimum time optimisation is more desirable with respect to operation of the
process.

465

Table 1: Comparison of the Results for different fixed water demand for Case 1 and Case 2

Tseawater Tsteam TBT R Cw WSTEAM PR t2

OP1

Case 1 510 10endD D  
33 94.41 84.59 7.14E+06 4.10E+06 1.49E+05 10.3 9
35 97.00 87.07 7.23E+06 4.10E+06 1.51E+05 10.4

Case 2 59.5 10endD D  
33 97.00 89.07 4.70E+06 4.10E+06 1.25E+05 11.5 8.80
35 97.00 88.20 5.94E+06 4.10E+06 1.36E+05 10.9

Case 3 59 10endD D  
33 93.00 86.91 4.70E+06 5.90E+06 1.00E+05 12.1 9.0
35 97.00 89.21 4.80E+06 4.10E+06 1.23E+05 11.5

Case 4 58.5 10endD D  
33 94.66 88.01 4.76E+06 5.45E+06 1.08E+05 12.0 8.30
35 97.00 90.06 4.70E+06 5.02E+06 1.12E+05 11.9

OP2

Case 1 510 10endD D  
33 93.00 84.64 6.35E+06 4.89E+06 1.30E+05 10.9 4.5
35 95.32 85.20 7.85E+06 4.25E+06 1.53E+05 10.1

Case 2 59.5 10endD D  
33 93.00 84.64 6.35E+06 4.89E+06 1.30E+05 10.9 1.0
35 94.33 84.78 7.85E+06 4.85E+06 1.45E+05 10.3

Case 3 59 10endD D  
33 93.00 84.64 6.35E+06 4.89E+06 1.30E+05 10.9 1.0
35 93.53 84.88 7.30E+06 5.30E+06 1.34E+05 10.6

Case 4
5

8.5 10
end

D D


   33 93.00 84.64 6.35E+06 4.89E+06 1.30E+05 10.9 1.0
35 93.09 85.37 6.50E+06 5.57E+06 1.21E+05 11.0

Objective function values are in bold & italic

Based on the Kuwait the daily seawater temperature profile of October 27, 2016 (timeanddate, 2017),
seawater temperature discrete profile is divided into several zones (Figure 2). Seawater temperature
increases from 23oC (at 2:00 am) to 35oC (at 1:00 pm noon) and again decreases form 35oC to until 23oC (at
midnight). As before in Table 1, the MSF process is assumed to be at steady-state condition for at the
beginning of time horizon and an external disturbance of seawater temperature is considered piecewise
constant where it increases or decreases 2oC increment for each time horizon (Figure 2). The optimizer
reaches the steady state for different temperature change during the day where the fixed water demand is
maintained. A minimum schedule operation time for different time horizon of that particular day without
compromising the freshwater demand is studied where the optimum operation policies is obtained which will
offset the change in seawater.
The results for optimum operation schedule time for particular day are presented in the Table 2. For the
simplicity, the steam temperature is kept constant. The operation schedule time value hit the lower bound of
control time horizon. R and Wsteam increase while PR, TBT and Cw are decrease with increase of seawater
temperature from 2:00 am to 1:00pm. The opposite trends is observed with decrease of seawater temperature
form 1 pm to midnight.

Figure 2: Discrete Seawater Temperature Profile during the Day assuming temperature as piecewise constant

466

Table 2: Summary of the optimum operation for fixed water demand DEND=9x10
5

Tseawater Tsteam TBT R Cw WSTEAM PR t2

23 93 85.85 4.70E+06 5.79E+06 1.17E+05 12.1
1

25 93 85.64 5.19E+06 5.88E+06 1.20E+05 11.8
25 93 85.64 5.19E+06 5.88E+06 1.20E+05 11.8

1
27 93 85.41 5.63E+06 5.86E+06 1.22E+05 11.6
27 93 85.40 5.63E+06 5.86E+06 1.22E+05 11.6

1
29 93 85.16 6.00E+06 5.74E+06 1.25E+05 11.4
29 93 85.17 6.00E+06 5.74E+06 1.25E+05 11.4

1
31 93 84.89 6.42E+06 5.60E+06 1.28E+05 11.1
31 93 84.90 6.42E+06 5.60E+06 1.27E+05 11.1

1
33 93 84.58 6.91E+06 5.43E+06 1.31E+05 10.8
33 93 84.58 6.91E+06 5.43E+06 1.31E+05 10.8

1
35 93 84.23 7.47E+06 5.24E+06 1.35E+05 10.5
35 93 84.23 7.47E+06 5.24E+06 1.35E+05 10.5

1
33 93 84.58 6.91E+06 5.43E+06 1.31E+05 10.8
33 93 84.58 6.91E+06 5.43E+06 1.31E+05 10.8

1
31 93 84.89 6.42E+06 5.60E+06 1.28E+05 11.1
31 93 84.90 6.42E+06 5.60E+06 1.27E+05 11.1

1
29 93 85.17 5.99E+06 5.72E+06 1.25E+05 11.4
29 93 85.17 6.00E+06 5.74E+06 1.25E+05 11.4

1
27 93 85.41 5.63E+06 5.86E+06 1.22E+05 11.6
27 93 85.40 5.63E+06 5.86E+06 1.22E+05 11.6

1
25 93 85.64 5.19E+06 5.88E+06 1.20E+05 11.8
25 93 85.64 5.19E+06 5.88E+06 1.20E+05 11.8

1
23 93 85.85 4.70E+06 5.79E+06 1.17E+05 12.1
Objective function values are in italic.

The optimised TBT temperature profile is shown in Figure 3. Recycle flow rate and Reject seawater flowrate offset the
seawater temperature change.

Figure 3: TBT Response of the Optimised Profile

5. Conclusions

The objective is to improve in design, operation and control of the MSF desalination process to ensure the
quality of water at a cheaper rate. Firstly, series of maximum problem and minimum time problem is solved.
Since the maximum problem leads to the larger step changes. It optimum steady condition reaches for longer
time. Secondly, the different operation policies have been studied for MSF process by a series of minimum
time interval problem for fixed water demand for particular day. Thirdly, in the daily temperature variation is
varied in linearly (timeanddate, 2017), seawater temperature changes linearly and its effects are compared
with piecewise constant step changes. Operational policies obtained can be implemented by designing an
appropriate controllers.

467

Acknowledgments

The author is extremely grateful to the University of Bradford, UK and BUET, Bangladesh for support.

Reference

Alsadaie S. M., Mujtaba I. M., 2016, Generic Model Control (GMC) in Multistage Flash (MSF), Journal of
Process Control, 44, 92-105.

Husain A., 2003, Integrated Power And Desalination Plants. Eolss, Oxford, UK
Mazzotti M., Rosso M., Beltramini A., Morbidelli M., 2000, Dynamic modeling of multistage flash desalination

plants, Desalination, 127(3), 207-218.
Patroklou G., Sassi K. M., Mujtaba I. M., 2013, Simulation of boron rejection by seawater reverse osmosis

desalination, Chemical Engineering Transactions, 32, 1873-1878
Rosso M., A. Beltramini, Mazzotti M., Morbidelli M., 1997, Modeling multistage flash desalination plants,

Desalination, 108(1–3), 365-374.
Sowgath, T. M. and Mujtaba I., 2015, Meeting the fixed water demand of MSF desalination using scheduling in

gPROMS, Chemical Engineering Transactions, 45, 451-456
Tanvir M. S., Mujtaba I. M., 2006, Modelling and simulation of MSF desalination process using gPROMS and

neural network based physical property correlation, Computer Aided Chemical Engineering, 21, 315-320.
Eds. W. Marquardt and C. Pantelides, Elsevier, Amsterdam, the Netherlands..

Tanvir M. S.,Mujtaba I. M., 2008, Optimisation of design and operation of MSF desalination process using
MINLP technique in gPROMS, Desalination, 222(1–3), 419-430.

timeanddate, 2017, Weather in Kuwait City, Kuwait < www.timeanddate.com/weather> accessed 09.01.2017

468