Meeting Variable Freshwater Demand by Flexible Design and

ARTICLE pubs.acs.org/IECR

Meeting Variable Freshwater Demand by Flexible Design and Operation of the Multistage Flash Desalination Process E. A. M. Hawaidi and I. M. Mujtaba* School of Engineering Design & Technology, University of Bradford, West Yorkshire BD7 1DP, U.K. ABSTRACT: In this work, the design and operation of multistage flash (MSF) desalination processes are optimized and controlled in order to meet variable demands of freshwater with changing seawater temperature throughout the day and throughout the year. On the basis of actual data, the neural network (NN) technique has been used to develop a correlation which can be used for calculating dynamic freshwater demand/consumption profiles at different times of the day and season. A storage tank is linked to the freshwater line of the MSF process which helps avoiding dynamic changes in operating conditions of the process. A steady state process model for the MSF process coupled with a dynamic model for the storage tank is developed which is incorporated into the optimization framework within gPROMS modeling software. For a given design (process configuration), the operation parameters are optimized at discrete time intervals (based on the storage tank level which is monitored dynamically and maintained within a feasible limit) while the total daily cost is minimized.

1. INTRODUCTION Water is the most precious chemical compound as it is indispensable for all living things. Unfortunately freshwater, like most other natural resources, is unequally distributed in the world.1 Many countries around the Mediterranean Sea, in the Middle East and many other countries use desalinated seawater as a major water source.2 Of all desalination processes, the multistage flash (MSF) desalination process (Figure 1) is still a major source of freshwater around the world.3 Generally, energy and operation costs (such as electric, steam, power, chemical, etc.) are reduced through the selection of optimal operation strategy and design of a MSF desalination process. In these days it is essential to find out the optimal set points of the individual control loops on standard basis in any manufacturing process. Rather than playing with a plant in operation to determine the new set points, it is always economical to determine the optimal set points based on an accurate process model and accurate optimization techniques before the operating set-points are applied in the actual plant. In MSF desalination processes, modeling also contributed significantly in simulation, optimization, and control of the process.47 Seawater temperature is subject to variation during a 24 h day and throughout the year. This variation will affect the rate of production of freshwater using a MSF process throughout the year. Most recently, a number of authors including Tanvir and Mujtaba6 and Hawaidi and Mujtaba7 focused on optimal design and operation of MSF processes based on fixed freshwater demand 24 h a day, 7 days a week, and 365 days a year. However, the fact is that the demand and also the seawater temperatures vary throughout the day and throughout the year.8,9 For a given design and operating conditions, the freshwater production was observed to vary considerably with the variation of the seawater temperature, producing more freshwater at night (low seawater temperature) than during the r 2011 American Chemical Society

day (high temperature).6 Interestingly, this production pattern goes exactly counter to the demand profile, which is greater during peak hours (morning, noon, and evening) than after midnight. In addition, there is more freshwater demand in summer than in the winter season.8 Hawaidi and Mujtaba10 provided a study on the design and operation of the MSF process with variable demand but restricted to only one particular season of the year where variable demand was represented by a polynomial function. This work demonstrates how the design and operation of MSF process are to be optimized to meet a variable demand/ consumption of freshwater throughout the day and throughout the year, with varying seawater temperatures throughout the day and seasonally. An intermediate storage tank between the plant and the client is considered10 to provide additional flexibility in operation and maintenance of the MSF process throughout the day. Four main seasons such as summer, autumn, winter, and spring are considered in a year. For each season, with variable freshwater demand and seawater temperature, the operating parameters (such as makeup flow rate and brine recycle flow rate) are optimized at discrete time intervals (based on the storage tank level), while minimizing the total daily costs. In addition, based on the data from Alvisi et al. (2007), a NN based correlation is developed, which allows estimation of freshwater demand/consumption at different times of the day and seasons. Also, a simple polynomial based dynamic seawater temperature correlation is developed based on actual data. The software gPROMS models builder 2.3.4 is used for model development and optimization. Received: February 3, 2011 Accepted: July 27, 2011 Revised: July 12, 2011 Published: July 27, 2011 10604

dx.doi.org/10.1021/ie200253g | Ind. Eng. Chem. Res. 2011, 50, 10604–10614

Industrial & Engineering Chemistry Research

ARTICLE

Figure 1. Typical MSF desalination process with storage tank.

2. ESTIMATION OF DYNAMIC FRESHWATER DEMAND/ CONSUMPTION PROFILE USING NN Use of neural network (NN) based physical property correlation is not new in MSF desalination process modeling, simulation, and optimization.11 Table 1 presents typical hourly water demand/consumption for the Mondays of the week in winter, spring, summer, and autumn taken from Alvisi et al.8 These data were selected from the published data presented in graphical form with time range (024 h) for different seasons. In this work, a NN based correlation is developed to estimate the dynamic freshwater demand/consumption profile (flow_out) as a function of time (hour) and season S (S = 1, 2, 3, 4, winter, spring, summer, and autumn, respectively). A 4 layer NN architecture shown in Figure 2 is used for this purpose. A neuron (a) is a mathematical processing component of the NN. The neurons in the input layer are called the input, which receive information from the input layer and process them in a hidden way. The neurons in the output layer (e.g., a41) receive processed information from previous layers and sends output signals out of the system. Tanvir and Mujtaba11 provided the details of the development of a 4-layerd NN based correlation for estimating physical properties of saline water. In the NN architecture used in this work (4 layered) there is one input, two hidden layers, and one output layer. The transfer function between the input and the first hidden and between the hidden layers are a hyperbolic tangent function (f2j , f3j = tanh) and between the last hidden layer and output is a linear function (f4j = 1). For efficient development of a NN based correlation, data with wide range are usually scaled between (1,1) and descaled at the end.11 The data (time and season) shown in Table 1 are used as input data for the NN and are scaled up with mean and its standard deviation as timescaleup ¼ Sscaleup ¼

ðtime timemean Þ timestd

ðS Smean Þ Sstd

flow_outscaleup

ðflow_out flow_outmean Þ ¼ flow_outstd

ð1Þ

deviation of S values used to develop the correlation. The terms flow_outmean and flow_outstd are the average and standard deviation, respectively, of the freshwater demand/consumption. Equation 1 scales the time between (1.706, 1.548), eq 2 scales the value of S between (1.398, 1.298), and eq 3 scales the value of freshwater demand/consumption between (1.7616, 1.897). The mean values of time, S, and flow_out together with the standard deviation are presented in Table 2. There are two input neurons in the NN based correlations. The values are a11 ¼ timescaleup

where timemean is the average time, Smean is the average value of all S values, timestd is standard deviation of time, Sstd is standard

a12 ¼ Sscaleup

ð4Þ

There is one output neuron in the NN based correlations: a41 ¼ flow_outscaleup

ð5Þ

The output value is rescaled to find the value in original units. The values of the first, second, and third layer neurons can be written as a21 ¼ tanhðw211 timescaleup þ w212 Sscaleup þ b1 2 Þ

ð6Þ

a22 ¼ tanhðw221 timescaleup þ w222 Sscaleup þ b22 Þ

ð7Þ


ð8Þ


ð9Þ

a31 ¼ tanhðw311 a21 þ w312 a22 þ w313 a23 þ w314 a34 þ b31 Þ

ð10Þ

a32 ¼ tanhðw311 a21 þ w322 a22 þ w313 a23 þ w314 a34 þ b32 Þ

ð11Þ

The final NN based correlation for the estimation of demand/ consumption profile can be written as flow_outscaleup ¼ a41 ¼ w411 a31 þ w412 a32 þ b41

ð2Þ ð3Þ

and

ð12Þ

The total input data (Table 1) are divided into three sets: the first two input data points are selected for training (50%, bold), the next input data points are for validation (25%, italic), and the fourth one is selected for testing (25%, normal) (Table 1). The LevenbergMarquardt back-propagation algorithm11 is used for training to determine the weights and biases of a multilayered 10605

dx.doi.org/10.1021/ie200253g |Ind. Eng. Chem. Res. 2011, 50, 10604–10614


ARTICLE

Table 1. Demand Profile from Alvisi et al.8 and Input Data (Unscaled) for the NN season

S = 1 (winter)

S = 2 (spring)

S = 3 (summer)

S = 4 (autumn)

time (h)

flow_ out (L/s)

0

27.50

2 4

22.31 24.62

6

50.00

8

63.85

10

62.69

12

62.69

14

57.50

18

61.54

20 22

57.50 41.92

24

26.35

0

28.16

2

22.96

4

22.43

6

49.86

8 10

67.96 66.84

12

68.06

14

64.03

18

68.21

20

63.59

22

44.42

24

31.07

0

35.58

2

29.23

4

27.50

6 8

55.77 75.96

10

74.23

12

70.19

14

65.00

18

81.15

20

83.46

22

58.08

24

35.00

0

28.65

2

23.46

4

19.42

6

56.35

8

74.23

10 12

71.35 70.19

14

65.58

18

69.62

20

67.88

22

45.96

24

30.38

network. The weights and transfer functions are shown in Table 2. The statistical regression between calculated values of the average freshwater demand/consumption (flow_out) by NN correlations and experimental data is plotted to find the overall trends of the predicted data (Figure 3). The above correlation has a coefficient of determination equal to 0.98 (Figure 4), which clearly shows that NN based correlation can predict the freshwater demand/consumption profile very accurately and dynamically. The correlation is also used to predict the freshwater demand/consumption based on (time, season), which were never used for training, validation, or testing the correlation. For example, the NN correlation is used to predict the demand/consumption profile between winter and spring at S = 1.5 (Figure 5). The results clearly show that the prediction by correlation follow the expected trend.

3. ESTIMATION OF DYNAMIC SEAWATER TEMPERATURE PROFILE Figure 6 shows the actual seawater temperature (degrees Celsius) over 24 h in October (autumn season).9 With the use of regression analysis, the following polynomial relationship is obtained (also shown in Figure 6) with a correlation coefficient greater than 90%.10 T seawater ¼ 2 1016 t 6 þ 6 106 t 5 0:0003t 4 þ 0:0032t 3 þ 0:007t 2 0:1037t þ 28:918

ð13Þ

Equation 13 represents the relationship between the seawater temperature and time (hour). The temperature at t = 0 represents the seawater temperature at midnight. In this work, the seawater temperature profile in October is assumed to represent the temperature profile of the autumn season.

4. MSF PROCESS MODEL A steady state process model for the MSF process coupled with a dynamic model for the storage tank are developed and connected via a high-level modeling language using gPROMS. With reference to Figures 1, 7, and 8 the mathematical model description is therefore based on mass balance, energy balance, and heat transfer equations and supported by correlation for brine densities, boiling temperatures, brine and vapor enthalpies, and heat transfer coefficient, the temperature losses due to boiling point elevation, nonequilibrium allowance, and temperature losses in the demisters. Note, the overall process model consists of a steady state MSF process model plus the dynamic storage tank model leading to a coupled system of differential and algebraic equations. In this work, no disturbances in process input parameters (such as seawater feed rate, steam flow rate) are considered (which can make the MSF process dynamic) except the change in feed seawater temperature. However, in a particular season throughout the day, the variation of seawater temperature is very small (0.10.2 °C variation per hour) and the dynamics imparted due to this we believe will be very negligible.13,14 Hence 10606



ARTICLE

Table 2. Weights, Biases, Transfer Functions (TF), and Scaled Up Parameters for 4-Layered Network 2nd layer w211 = 4.031 69 w221 w231 w241

= 0.545 01 = 7.836 59 = 0.560 25

= 0.23998 = 0.68162

bias

TF

w212 = 0.006 19

b21 = 3.753 461

tanh

w222 w232 w242

3rd layer W311 W321

weights = 0.536 21

b22 = 0.546 13

tanh

= 0.045 66

b23 = 7.018 98

tanh

= 0.511 96

b24 = 0.579 75

tanh

weights W312 W322

bias W313 W323

= 28.67261 = 1.20067

4th layer

= 0.03723

W314 W324

= 0.14333

= 29.53401 = 1.13775

weights

bias

W411 = 4.29131

b41 = 167.8830

W412

b31 b32

TF

= 0.33252

tanh

= 2.74325

tanh TF 1

= 169.6067

timemean

Smean

flow_outmean

timestd

Sstd

12.5818

2.55

52.611

7.3727

1.1126

flow_outstd 17.304

Figure 2. A Four layer neural network.

Figure 3. Freshwater demand/consumption (flow_out) profiles at different seasons.

a steady state process model for the MSF is considered. However, the variation in the storage tank throughout the day is significant and therefore the dynamic model for the storage tank is considered. However, note, change in demand required changes in some of the operating parameters (e.g., R and F) which

Figure 4. Calculated and measured freshwater demand/consumption (flow_out).

are optimized at discrete time intervals. No doubt, discrete changes of these parameters will impart transient states into the process; however, for the sake of simplicity we assumed that these transient states will be of short period and therefore neglected. A steady state process model for the MSF and dynamic model for the storage tank are given in the following (all symbols are 10607



ARTICLE

Figure 5. Actual freshwater demand/consumption by Alvisi et al.8 and the predicted profile.

Figure 8. Storage tank.

Figure 6. Seawater temperature profiles.

Figure 9. (a) Typical storage tank level profile and (b) tank level violations during the operation.

The stage salt balance is given by X bj Bj ¼ X bj1 Bj1

ð15Þ

mass balance for distillate tray : j

∑

k¼1

Figure 7. Typical flash stage j.

j1

∑ Dk þ Dj

k¼1

ð16Þ

enthalpy balance on flash brine :

defined in the list of symbols). See further details on the process model in Hawaidi and Mujtaba.7 The assumptions used to develop the mathematical model include the following: (1) Heat losses to the surroundings are negligible. (2) The heat capacities, specific enthalpy, and physical properties for feed seawater, brine, and distillate product are functions of temperature and composition. (3) The fouling resistance is constant for the recovery and rejection section. (4) Thermodynamic losses include the boiling point elevation (TE), the nonequilibrium allowance (δ), and demister losses (Δ). (5) The distillate product is salt free. (6) Heat of mixing is negligible. (7) No subcooling of condensate leaving the brine heater. Stage Model. mass balance in the flash chamber : Bj1 ¼ Bj þ Dj

Dk ¼

ð14Þ

Bj =Bj1 ¼ ðhBj1 hvj Þ=ðhBj hvj Þ

ð17Þ

hvj ¼ f ðT vj Þ hBj ¼ f ðT Bj , X Bj Þ overall energy balance on stage :

W R CPj ðT Fj T Fjþ1 Þ ¼ jk ¼ 11 Dk CPDj1 T Dj1 T jk ¼ 1 Dk CPDj T Dj T ð18Þ þ Bj1 CPBj1 ðT Bj1 T Þ Bj CPBj ðT Bj T Þ

∑

∑

heat transfer equation : W R CPj ðT Fj T Fjþ1 Þ ¼ U j Aj LMTDj

ð19Þ

The logarithmic mean temperature difference in the recovery stage is 10608


Industrial & Engineering Chemistry Research LMTDj ¼

ðT Fj T Fjþ1 Þ ðT Dj T FJþ1 Þ ln ðT DJ T Fj Þ

ARTICLE

ð20Þ

where UJ is calculated in terms of WR, TFj, TFj+1, TDj, ID, OD, and fj CPj ¼ f ðT FJþ1 , T Fj , XR Þ, CPBj ¼ f ðT Bj , XBj Þ, CPDj ¼ f ðT Dj Þ

distillate and flashing brine temperature correlation : T Bj ¼ T Dj þ TEj þ Δj þ δj distillate flashed steam temperature correlation : T Vj ¼ T Dj þ Δj

ð21Þ

5. STORAGE TANK LEVEL CONSTRAINTS In Figure 8, the storage tank is assumed to operate without any control on the level,10 and therefore h goes above the limit hmax or below the limit hmin during the operation of the MSF process as shown in Figure 9a. At any time, this violation (v1, v2) of safe operation can be defined as ( ðhðtÞ hmax Þ2 if h > hmax v1 ¼ ð34Þ 0 if h < hmax and

(

v2 ¼ ð22Þ

ðhðtÞ hmin Þ2 0

if h < hmin if h > hmin

ð35Þ

ð23Þ

A typical plot of v1 and v2 versus time t is shown in Figure 9b. The total accumulated violation for the entire period can be calculated using Z tf ðv1 ðtÞ þ v2 ðtÞÞ dt ð36Þ VT ¼

B0 CPRH ðT B0 T F1 Þ ¼ W Steam λs

ð24Þ

Therefore,

λs ¼ f ðT Steam Þ

ð25Þ

Δj ¼ f ðT Dj Þ;

TEj ¼ f ðT Bj , X Bj Þ; δj ¼ f ðT BJ , H j , W j Þ

Brine heater model: B0 ¼ W R ,

X B0 ¼ X R

heat transfer equation : W R ðT BO T F1 Þ ¼ U H AH LMTD ðT B0 T F1 Þ ðT Steam T F1 Þ ln ðT Steam T B0 Þ

ð26Þ

ð27Þ

where UH is calculated in terms of WR, TFj, TB0, TSteam, ID, OD, and fbh Splitters model: BD ¼ BNS R;

CW ¼ W S F

ð28Þ

makeup mixers models: W R ¼ R þ F;

RX BNS þ FX F ¼ W R X R

W R hm ¼ RhR þ FhF

dV T ¼ v1 ðtÞ þ v2 ðtÞ dt ¼ ðhðtÞ hmax Þ2 þ ðhðtÞ hmin Þ2

The logarithmic mean temperature difference in brine heater is LMTDj ¼

t¼0

ð29Þ ð30Þ

hM ¼ f ðT FM , X R Þ, hF ¼ f ðT FNR , X F Þ, hR ¼ f ðT BNS , X BNS Þ

Equation 37 is added to the overall process model equations presented in section 4. In the optimization problem formulations (presented in the next section), a terminal constraint (0 e VT(tf) e ε) is added, where ε is a very small finite positive number (106). The above constraint will ensure that h(t) will always be equal or less than hmax and equal or above hmin throughout the 24 h.10

6. OPTIMIZATION PROBLEM FORMULATION The optimization problem is described below. Given: the MSF plant configurations, fixed design specification of each stage, volume of the storage tank, seawater flow, variable seawater temperature, top brine temperature (TBT) and freshwater demand profile. Determine the optimum total number of stages, optimum recycled brine flow rate R; makeup seawater, F at different intervals within 24 h. Minimize the total daily cost (TDC). Subject to process constraints. The optimization problem (OP) is described mathematically over 24 h period as OP

plant performance measure: GOR ¼ Dj =W Steam

ð31Þ

TDC ðmodelequationsÞ

TBT ¼ TBT ð0:1Þ hmin e h e hmax

ð10:5Þ

0 e V T ðt f Þ e ε

ð32Þ

Relation between liquid level and holdup: M ¼ FAs h

Min R, F

s:t: f ðt, x_ , x, u, vÞ ¼ 0

Tank Model. The dynamic mathematical model of the tank process takes the follwing form. Mass balance

dM ¼ Flow_in Flow_out dt

ð37Þ

ð33Þ 10609

ð2 106 Þ

RL e R e RU

ð7:55 106 Þ

ð2 106 Þ

FL e F e FU

ð7:55 106 Þ



ARTICLE

Table 3. Constant Parameters and Input Data Aj /

IDj/

ODj/

AH

IDH

ODH

fj/fbh

wj/LH

brine heater

3530

0.022

0.0244

1.864 104

12.2

recovery stage

3995

0.022

0.0244

1.4 10 4

12.2

0.457

rejection stage

3530

0.024

0.0244

2.33 10 5

10.7

0.457

Hj

Figure 12. Variation of total daily costs with total number of stages for different seasons.

Figure 10. Seawater temperature profiles for different seasons.

Figure 13. Variation of optimal daily operation costs for different seasons.

Figure 11. Freshwater consumption/demand profiles for different seasons.

Table 4. Summary of Optimization Results for All Seasons season

NR

STC ($/day)

CPC ($/day)

TOC ($/day)

TDC ($/day)

summer

16

176.06

26 750.10

21 307.62

48 233.67

autumn

13

176.06

23 372.75

21 028.86

44 577.61

spring

12

176.06

22 187.85

20 316.55

42 673.27

winter

11

176.06

20 967.75

19 669.16

40 810.63

where TBT* is the fixed top brine temperature (90 °C). Subscripts L and U refer to the lower and upper bounds of the parameters. The model equations presented in the previous section can be described in a compact form by f(t, x_ , x, u, v), where x_ represents all the state variables, x represent nonlinear sets of all algebraic and deferential variables, u is the control variable, such as seawater makeup, recycle flow rate, etc., and v is a set of constant parameters. The values of seawater makeup (F) and brine recycle (R) between 2 106 and 7.55 106 are chosen based on controlling the velocity in the condenser tubes between of 1 m/s as a minimum to a maximum of 3 m/s. The lower limit is dictated by heat transfer and flashing efficiency considerations and the higher

Figure 14. Variation of optimal daily steam costs for different seasons.

limit by the tube erosion damage and higher pumping costs.12 The minimum and maximum levels of storage tank are arbitrarily assumed as 0.1 and 10.5 m, respectively. The objective function TDC is given by TDC = (TAC/365), where total annual cost (TAC) is defined as TAC ð$=yearÞ ¼ CPC þ STC þ TOC

ð38Þ

where CPC ðMSF annualized capital cost; $=yearÞ ¼ 182 8000 NR 0:65

ð39Þ

STC ðstorage tank; $=yearÞ ¼ ½2300 ðstoragetankvolume ðm3 ÞÞ0:55 3:1 0:0963 10610

ð40Þ



ARTICLE

Figure 15. Optimum seawater makeup (F) and brine recycle flow rate (R) profiles for different seasons.

Figure 16. Variations of steam temperature and consumption profiles for different seasons.

TOC ðtotal annual operating cost; $=yearÞ ¼ C3 þ C4 þ C5 þ C6 þ C7

ð41Þ

where C3 ðstream cost; $=yearÞ ¼ 8000 Wstream ½ðTstream 40Þ=85 ð0:004 15Þ

ð42Þ

C4 ðchemical cost; $=yearÞ ¼ 8000 ½Dj =1000 0:025

ð43Þ

C5 ðpower cost; $=yearÞ ¼ 8000 ½Dj =1000 0:109

ð44Þ

C6 ðmaintenance and spares cost; $=yearÞ ¼ 8000 ½Dj =1000 0:082 C7 ðlabor cost; $=yearÞ ¼ 8000 ½Dj =1000 0:1

ð45Þ ð46Þ

The detailed references on the calculation of TOC can be found in Hawaidi and Mujtaba.7 The storage tank has a diameter (D = 20 m) and aspect ratio L/D = 0.55. The depreciation period of the storage tank is 15 years with 5% interest rate giving the capital recovery factor equal to 0.0963. The detailed references on the calculation of CPC of the MSF plant can be found in Tanvir and Mujtaba.6 (the depreciation period/interest rate and the capital recovery factor are assumed to be included). For the variable seawater temperature change (eq 13) and variable freshwater demand/consumption profile (eq 12), the optimization problem presented above minimizes the total daily

Figure 17. Storage tank level profiles for all seasons.

cost while optimizing R and F over 3 intervals (within 24 h period) meeting the storage tank height constraints.

7. CASE STUDY For a different total number of stages, here, the total daily cost of the process including pro-rata capital cost of the storage tank is minimized by optimizing operation parameters at discrete time intervals with the storage tank level being monitored dynamically between a maximum and minimum limit. The feed seawater flow rate is 1.13 107 kg/h with salinity 5.7 wt %. The rejection section consists of three stages. The initial level of the storage tank is 0.1 m. The total operating time is 24 h, and midnight is considered to be the starting time. In this work, three discrete time intervals are used. The lengths of these intervals and in each interval seawater make up “F” and brine recycle “R” are optimized. hmin = 0.1 m and hmax = 10.5 m are used as lower and upper tank levels. Table 3 10611



ARTICLE

Figure 18. Variations of freshwater production of MSF and consumption and freshwater holdup during a day for all seasons.

lists all the constant parameters of the model equations including various dimensions of the flash stages and brine heater. During a particular day of the autumn season, the daily variation of average seawater temperature is calculated using eq 13. The average seawater temperatures profiles are assumed to increase by 4 °C (in the summer season) and fall by 10 °C (in the winter season) and 1 °C (in the spring season) as shown in Figure 10. The daily freshwater demand/consumption profiles for four seasons are calculated using the NN based correlation (eq 12) are as shown in Figure 11. Note, the actual freshwater consumption at any time and season is assumed to be 5 times more than that shown in Figure 3. Table 4 summarizes the cost of the storage tank, capital cost of the MSF process based on total number of stages, total operating cost, total cost on a daily basis, and the optimum total number of stages for four seasons. Figure 12 illustrates the variations of total cost with a different number of stages in different seasons. Figures 13 and 14 represent the optimum operating cost components in different seasons. Figure 15 represents the optimum recycle flow rate (R) and makeup flow rate (F) at discrete time intervals in different seasons. Figure 16 illustrates the steam temperature and demand/consumption profiles in different seasons. It is noticed from the optimization results that the total daily cost and total number of stages required in the summer season (Table 4 and Figure 12) are the highest due to higher seawater temperature and freshwater consumption (Figures 10 and 11). In addition, F and R (Figure 15) and therefore total operating costs are higher in the summer season. Although the steam consumption decreases slightly compared to the other seasons except the winter season (Figure 14), the contribution of the other operating and capital costs are relatively higher (Figure 13). Figure 12 proves this fact in terms of minimum total cost as a function of the total number of stages policy. Observation also shows that to meet the demand of variable freshwater in summer, there has to be an increase in the total number of stages from 11 to 16 (compare the results of the summer and winter seasons in Table 4). Observation also shows that the total cost has been increased by about 18% in the summer season compared with that for the winter season to meet the variable freshwater demand.

The optimized interval lengths within which R and F are optimized are found to be 6, 14, and 4 h (Figure 15) within the 24 h operation. Figure 16 illustrates that the steam temperature and consumption for different seasons are low at night time (first interval) and approximately constant for all seasons except the winter season. The freshwater demand is higher between morning and evening; therefore, steam temperature and the consumption rate reach to the maximum (second interval) except for the winter season. At night time (8 p.m. to midnight) when the freshwater demand drops, the steam temperature and consumption rate becomes considerably lower (third interval) for all seasons. Note, steam cannot be supplied at the same temperature throughout the day for any season to meet fixed TBT and variable demand. Also note, the highest steam cost is noted in the autumn season and the lowest steam cost in the winter season (Figure 14). The dynamic storage tank levels for all seasons are shown in Figure 17. Freshwater production from the MSF process and consumption (as per demand, Figure 11) and accumulated freshwater hold-up (in storage tank) profiles for all seasons are shown in Figure 18. It can be seen from the results that when the freshwater demand is more than the freshwater production rate, the freshwater hold-up decreases (Figure 18) and the storage tank level falls down (Figure 17) for all seasons. The opposite happens when the freshwater consumption rate is less than the freshwater production rate. The highest tank level h is noted at 8 a.m. and the lowest level at 10 p.m. On the basis of the results, it can be proposed to design a plant with a storage tank based on the summer conditions, make the design of individual flash units as a stand-alone module, and connect as many of them as needed15 due to variation in the weather conditions (Figure 10) to supply a variable amount of freshwater (Figure 11) throughout the day and throughout the year. This clearly shows the benefit of using the intermediate storage tank which adds the operational flexibility, e.g., maintenance could be carried out without interrupting the production of water or full plant shut-downs at any time throughout the day and the year just by adjusting the number of stages and controlling the seawater makeup and brine recycle. Note, although the 10612


Industrial & Engineering Chemistry Research optimum total number of stages in summer is 16, the same freshwater demand can be fulfilled by using 15 stages (Figure 12) although the operating cost will be higher. Note, the demand cannot be fulfilled using lower than 15 stages.

8. CONCLUSIONS Here, on the basis of actual data, the neural network (NN) technique is used to develop a correlation which allows calculation of freshwater demand/consumption profile at different times of the day and seasons of the year. Also, a simple polynomial dynamic seawater temperature profile is developed based on actual data to predict seawater temperature at a different time of the day and at different seasons. An intermediate storage tank is considered between the MSF process and the client to add flexibility in meeting the customer demand throughout the day and throughout the year. A steady state process model for the MSF process coupled with a dynamic model for the storage tank is developed within gPROMS modeling software. The intermediate storage tank helps to avoid dynamic changes in operating conditions of the process and restricts these changes only at discrete times. The total number of flash stages and some significant operating parameters such as recycle brine and seawater makeup at a discrete time interval are optimized, minimizing the total daily cost (including capital cost component of the process and the storage tank and the operating cost) of the process for all seasons. The optimization results show that summer operation requires the desalination process to use more flash stages than in other seasons to meet the variable demand of freshwater. This consequently demands higher F and R at higher seawater temperature and freshwater demand during a day leading to higher total cost (daily) by about 18% in the summer season compared with that for the winter season. Note, the steam cannot be supplied at the same temperature throughout the day for any season to meet the variable demand with varying seawater temperature at fixed TBT. The results clearly also show that the benefit of using the intermediate storage tank adds flexible scheduling and maintenance opportunity of individual flash stages and makes it possible to meet variable freshwater demand with varying seawater temperatures without interrupting or fully shutting down the plant at anytime during the day and for any season. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ NOMENCLATURE AH = heat transfer area of brine heater (m2) AJ = heat transfer area of stage j (m2) As = cross section area of storage tank (m2) B0 = flashing brine mass flow rate leaving brine heater (kg/h) BBT = bottom brine temperature (°C) BD = blow-down mass flow rate (kg/h) fbh = brine heater fouling factor (m2 h K/kcal) BJ = flashing brine mass flow rate leaving stage j (kg/h) BNS = flashing brine mass flow rate leaving last stage j (kg/h) CPBj = heat capacity of flashing brine leaving stage j (kcal/kg °C) CPDj = heat capacity of distillate leaving stage j (kcal/kg °C) CPj = heat capacity of cooling brine leaving stage j (kcal/kg °C) CPRH = heat capacity of brine leaving brine heater (kcal/kg °C)

ARTICLE

CW = rejected seawater mass flow rate (kg/h) DJ = distillate flow rate leaving stage j (kg/h) DN = total distillate flow rate (kg/h) F = makeup seawater mass flow rate (kg/h) fj = fouling factor at stage j (m2 h K/kcal) GOR = gained out ratio or performance ratio hBj = specific enthalpy of flashing brine at stage j (kcal/kg) hF = specific enthalpy of makeup water (kcal/kg) Hj = height of brine pool at stage j (m) hM = specific enthalpy of brine at TFM (kcal/kg) hR = specific enthalpy of flashing brine recycle (kcal/kg) hvj = specific enthalpy of flashing vapor at stage j (kcal/kg) ID = internal diameter of tubes (m) LH = length of brine heater tubes (m) LJ = length of tubes at stage j (m) OD = external diameter of tubes (m) R = recycle stream mass flow rate (kg/h) TBJ = temperature of flashing brine leaving stage j (°C) TBNS = temperature of blow-down (°C) TBO = temperature of flashing brine leaving brine heater (°C) TBT = top brine temperature (°C) TDJ = temperature of distillate leaving stage j (°C) TEJ = boiling point elevation at stage j (°C) TFJ = temperature of cooling brine leaving stage j (°C) TFM = temperature of cooling brine to the heat recovery section (°C) TFNR = temperature of makeup (°C) Tseawater = seawater temperature (°C) Tsteam = steam temperature (°C) TVJ = temperature of flashed vapor at stage j (°C) UH = overall heat transfer coefficient at brine heater (kcal/m2 h K) UJ = overall heat transfer coefficient at brine heater (kcal/m2 h K) VJ = linear velocity of brine (m/s) WJ = width of stage (m) WR = cooling brine mass flow rate to the heat recovery section (kg/h) WS = seawater mass flow rate (kg/h) WSteam = steam mass flow rate (kg/h) X = salt concentration (wt %) XBJ = salt concentration in flashing brine leaving stage j (wt %) XBNS = salt concentration in flashing brine leaving last stage (wt %) XF = salt concentration in makeup water (wt %) XR = salt concentration in cooling brine (wt %) XS = salt concentration in seawater (wt %) Δj = temperature loss due to demister (°C) F = water density (kg/m3) λS = latent heat of steam to the brine heater (kcal/kg) δ = nonequilibrium allowance (°C)

’ INDICES H = brine heater J = stage index / = reference value ’ REFERENCES (1) El-Dessouky, H.; Bingulac, S. Solving equations simulating the steady-state behaviour of the multi-stage flash desalination process. Desalination 1996, 107, 171. 10613



ARTICLE

(2) Gille, D. Seawater intakes for desalination plants. Desalination 2003, 156, 249. (3) El-Dessouky, H. T.; Ettouney, H. M. Fundamentals of Salt Water Desalination: Elsevier Science Ltd.: Amsterdam, The Netherlands, 2002. (4) Maniar, V. M.; Deshpande, P. B. Advanced controls for multistage flash (MSF) desalination plant optimization. J. Process Control 1996, 6, 49–66. (5) Mussati, S. F.; Aguirre, P. A; Scenna, N. J. A rigorous mixedinteger non lineal programming model (MINLP) for synthesis and optimal operation of cogeneration seawater desalination plants. Desalination 2004, 166, 339–345. (6) Tanvir, M. S.; Mujtaba, I. M. Optimization of design and operation of MSF desalination process using MINLP technique in gPROMS. Desalination 2008, 222, 419–430. (7) Hawaidi, E. A. M.; Mujtaba, I. M. Simulation and optimization of MSF desalination process for fixed freshwater demand: Impact of brine heater fouling. Chem. Eng. J. 2010, 165, 545–553. (8) Alvisi, S.; Franchini, M.; Marinelli, A. A short-term pattern-based model for water-demand forecasting. J. Hydroinf. 2007, 91, 39–50. (9) Yasunaga, K.; Fujita, M.; Ushiyama, T.; Yoneyama, K.; Takayabu, Y. N.; Yoshizaki, M. Diurnal Variations in Perciptible Water Observed by Shipborne GPS over the Tropical Indian Ocean. SOLA, Sci. Online Lett. Atmos. 2008, 4, 97–100. (10) Hawaidi, E. A. M.; Mujtaba, I. M. Fresh Production by MSF Desalination Process: Coping with Variable Demand by Flexible and Operation. In Computer Aided Chemical Engineering, Vol. 29; Pistokopoulos, E.N., Georgiadis, M.C., Kokossis, A., Eds.; Elsevier: Oxford, U.K., 2011; pp 11801184. (11) Tanvir, M. S.; Mujtaba, I. M. Neural network based correlations for estimating temperature elevation for seawater in MSF desalination process. Desalination 2006, 195, 251–272. (12) El-Nashar, A. M. Optimization of operating parameters of MSF Plants through automatic set point control. Desalination 1998, 116, 89–107. (13) Tanvir, M. S. Neural network based hybrid modelling and MINLP based optimization of MSF desalination process within gPROMS. Ph.D. Thesis, University of Bradford, West Yorkshire, U.K., 2007. (14) Aly, N. H.; Marwan, M. A. Dynamic behaviour of MSF desalination plants. Desalination 1995, 287–293. (15) Tanvir, M. S.; Mujtaba, I. M. Less of the foul play: Flexible design and operation can cut fouling and shutdown of desalination plants. The Chemical Engineer, June, 2829, 2008.

10614


Meeting Variable Freshwater Demand by Flexible Design and

Recommend Documents