Thermodynamic optimization of multi-effect

Desalination 257 (2010) 195–205

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Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l

Thermodynamic optimization of multi-effect desalination plant using the DoE method M.E. Kazemian, A. Behzadmehr ⁎, S.M.H. Sarvari Mechanical Engineering Department, University of Sistan and Baluchestan, P.O. Box 98164-161, Zahedan, Iran

a r t i c l e

i n f o

Article history: Received 13 November 2009 Received in revised form 7 February 2010 Accepted 8 February 2010 Available online 19 March 2010 Keywords: Simulation Multi-effect desalination Optimization Design of experiment

a b s t r a c t Thermodynamic optimization of a multi-effect desalination (MED) plant has been performed. The effects of feed water flow rate, temperature of seawater, numbers of effects, temperature differences of preheaters and the outlet pressure have been studied. Tables for numerical calculations have been designed based on the DoE method. The effects of the foregoing parameters on the maximum and minimum distilled water have been investigated. In addition several contours have been presented to help a designer to find suitable conditions for a plant design. © 2010 Elsevier B.V. All rights reserved.

1. Introduction In the Middle East countries desalination of seawater is one of the main sources of potable water. Both thermal and physical desalination processes have being used in this region. The multi-effect desalination (MED) plant is one of the most efficient thermal desalination processes currently in use. Development of MED in the last few years has brought this process to the point of competing economically and technically with the multi-stage flashing (MSF) process. MED process is based on the pressure reduction of water in each effect. Many researchers have studied this process. Among them Sharmmiri and Safar [1] discussed the general aspects of some commercial MED plants and also some of their specifications such as type of plant configuration, gain output ratio, number of effects, operating temperature and the construction material for the evaporator, condenser and preheaters. Ophir and Lokiec [2] described the design principles of a MED plant and various energy considerations that result in an economical MED process and plant. They also provided an overview of various cases of waste heat utilization, and cogeneration MED plants operating. Aybar [3] considered a multi-effect desalination system using waste heat of a power plant as energy source. A simple thermodynamic analysis of the system was performed by using energy and mass balance equations. Khademi et al. [4] focused on the development of a steady-state model for the multi-effect evaporator desalination system. Hatzikioseyian et al. [5] reviewed and developed a simulation program based on design parameters of the plant. They used mass and energy balance through

each effect of the MED unit to predict the performance of the unit in terms of energy requirements. Kamali and Mohebbinia [6] showed that parametric study as one of the optimization methods on thermohydraulic data strongly helps to increase GOR value inside MED-TVC systems. El-Nashar [7] simulated part-load performance of small vertically stacked MED plants of the HTTF type using hot water as source of energy. Their model was validated with the experimental data obtained from an existing plant in operation. Ali and El-Fiqi [8] described a steady state mathematical model to analyze both multistage and multi-effect desalination systems. Relationships among the parameters which controlling the cost of fresh water production to the other operating and design parameters were presented. Parameters include plant performance ratio (PR), specific flow rate of brine, top brine temperature, and specific heat transfer area. In the present work the sensitivity of some important parameters on the minimum and maximum distilled water production is analyzed. Therefore the effects of feed water flow rate and its temperature, the number of effects, preheater temperature difference (performance of each preheater), and minimum pressure (at the end stage) are studied. Thus the mass, energy and salinity balance equations are solved for each effect to calculate temperature, pressure salinity of brine, enthalpies of outlet at each effect and mass flow rate of distilled water. For thermodynamic analysis and plant optimization, design of experiment method (DoE) is used to find the effective parameters on the minimum and maximum fresh water production. 2. Brief plant description

⁎ Corresponding author. E-mail address: [email protected] (A. Behzadmehr). 0011-9164/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2010.02.012

The multi-effect desalination is an important process that has been used for desalination particularly in large scale plants. This method reduces considerably the production cost [2]. The main parts of MED

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plant are: 1-Condenser, 2-Evaporator, 3-Collector (thermal source) and 4-Preheaters (heat exchanger). Each effect except the last one includes a preheater and an evaporator. The hot water circulates between the top effect evaporator and solar collector to supply thermal energy to the evaporator in the form of hot water flowing through the tube bundle of the first effect. The preheated sea water is sprayed on the tube bundle of first evaporator and vapor is generated. In the other effects, vapor is generated by both boiling and flashing processes. Pressure reduces on each effect to produce more vapors. Fig. 1 shows a vertical configuration of MED plant.

vapor and condensed water) of the previous preheater. This is shown in Fig. 2d. The balance equations can be written as follows: Mass balance equation m˙ b ði−1Þ = m˙ b ðiÞ + m˙ v ðiÞ; m˙ oe ðiÞ = m˙ ie ðiÞ :

3. Mathematical modeling A schematic of main multi-effect desalination plant's parts is shown in Fig. 2. As seen in Fig. 2a the mass, energy and salinity balance equations for evaporator at the first effect (top effect) are as follows: Mass balance equation: m˙ f = m˙ b ð1Þ + m˙ v ð1Þ:

ð1Þ

Balance of salinity: m˙ f Xsw = m˙ b ð1ÞXb ð1Þ:

ð2Þ

Balance of energy: Q˙ + m˙ f hfo ð1Þ = m˙ b ð1Þhb ð1Þ + m˙ v ð1Þhv ð1Þ:

ð3Þ

It is well known that the enthalpy of brine in each effect could be considered a function of salinity and temperature while the enthalpy of saturated vapor is only a function of temperature. Thus these equations are used to find temperature and salinity relationship. As shown schematically in Fig. 2b, preheaters are considered as being shell and tube heat exchangers. The mass and energy balance for all preheaters are as follows:Mass balance equation m˙ d ðiÞ = m˙ v ðiÞ

ð4Þ

Energy balance equation: m˙ d ðiÞhd ðiÞ + m˙ f hfo ðiÞ = m˙ f hfi ðiÞ + m˙ v ðiÞhv ðiÞ

ð5Þ

Fig. 2c shows the evaporator of the second effect. The mass, energy and salinity balance equations for this part are: Mass balance equation: m˙ b ð1Þ = m˙ b ð2Þ + m˙ v ð2Þ; m˙ oe ð1Þ = m˙ d ð1Þ :

ð6Þ

Salinity balance equation: m˙ b ð1ÞXb ð1Þ = m˙ b ð2ÞXb ð2Þ:

ð7Þ

Energy balance equation: m˙ b ð1Þhb ð1Þ + m˙ d ð1Þhd ð1Þ = m˙ b ð2Þhb ð2Þ + m˙ v ð2Þhv ð2Þ + m˙ oe ð2Þhoe ð2Þ:

ð8Þ

Other evaporators are fed from both outlet of the previous evaporator and from the exit of distilled water side (mixture of

Fig. 1. Schematic diagram of MED plant.

ð9Þ


197

Fig. 2. Control volume MED parts.

Balance of salinity:

hicon =

m˙ b ði−1ÞXb ði−1Þ = m˙ b ðiÞXb ðiÞ:

4. Numerical procedure

m˙ b ði−1Þhb ði−1Þ + m˙ ie ðiÞhie ðiÞ = m˙ b ðiÞhb ðiÞ + m˙ v ðiÞhv ðiÞ + m˙ oe ðiÞhoe ðiÞ

ð11Þ

where: m˙ ie ðiÞ = m˙ oe ði−1Þ + m˙ d ði−1Þ; m˙ oe ði−1Þhoe ði−1Þ + m˙ d ði−1Þhd ði−1Þ ; m˙ oe ði−1Þ + m˙ d ði−1Þ

i = 3; 4; :::; n

ð12Þ

i = 3; 4; :::; n :

ð13Þ

The last effect of MED plant just includes a condenser (see Fig. 2e). The mass and energy balance in this stage are: Mass balance equation m˙ icon = m˙ dis :

ð14Þ

Energy balance equation: m˙ icon hicon + m˙ sw hsw = m˙ f hfi ðnÞ + m˙ dis hdis

ð15Þ

where: m˙ icon = m˙ oe ðnÞ + m˙ d ðnÞ

ð17Þ

ð10Þ

Balance of energy equation:

hie ðiÞ =

m˙ oe ðnÞhoe ðnÞ + m˙ d ðnÞhd ðnÞ : m˙ oe ðnÞ + m˙ d ðnÞ

ð16Þ

The Eqs. (1)–(17) are simultaneously solved to predict the thermodynamic properties of water and steam (temperature, pressure, enthalpy and salinity) at each part. The thermodynamic properties of distilled water, water vapor and brine are calculated for known parameters; ṁf, Tsw, Xsw, Q̇ , n, ΔTpr, ΔTcon and Pout in the simulation code. In order to validate the code, comparisons are done with the results of Hatzikioseyian [5]. These are shown in Figs. 3–5. As seen the concordance between the results are good. They considered a constant water concentration at each effect thus as seen in these figures, there are differences between the results. Since in the present code concentration difference at each effect is calculated by solving the balance equations (mass, energy and concentration). As mentioned, the parameters ṁf, Tsw, Xsw, Q̇ , n, ΔTpr, ΔTcon have been specified in the simulation code, the input heating energy (Q̇ ) must be limited to a particular range based on these parameters in order to achieve the balanced thermodynamic conditions at all parts of MED plant. Therefore for given input parameters minimum and maximum values for the heating energy is calculated Eqs. (1)– (17) would be thermodynamically balanced with real physical conditions. The parameter Q̇ is an important and an effective parameter on the MED process which has direct effect on the final costs of distilled water. The higher heat flux results higher final cost. In addition if the

198


Fig. 3. Comparison of salt concentration profile with [5].

Fig. 5. Comparison of power input on performance ratio with [5].

input heat flux is unconditionally increased in the first effect, all the feed water would be vaporized in the first effect and the rest does not involve in the process. This is not acceptable for a MED plant. Therefore the increase of heat flux is restricted by Eq. (18). hd = α hv ;

0bαb1

ð18Þ

Different values of α has been tested. Fig. 6 shows the effects of α on the values of maximum heat flux (Qmax/100), maximum distilled water (dismax), plant performance for the maximum algorithm (Prmax), minimum heat flux (Qmin/100), minimum distilled water (dismin), and plant performance for the minimum algorithm (Prmin). The values corresponding to these parameters (which is specified on the x axis) could be read on the y axis. As shown the desirable input heat flux and the amount of distilled water are increased by increasing the value of α. However the performance ratio (pr) is fairly constant. It means the cost of construction will also increase. In this study α = 0.9 is considered. These equations could be solved by assuming the amount of heating energy and condenser temperature differences as known

Fig. 4. Comparison of temperature profile with [5].

values. However this approach is not adequate since these parameters are not optimized. In addition selecting these parameters prior to the thermodynamic calculation may result a plant for which the thermodynamic balance of the properties at some parts of the plant do not present a real condition. Therefore, to avert these problems, two algorithms; minimum and maximum distilled water, are designed. These are shown in Figs. 7 and 8. So the amount of heating energy, condenser temperature difference and other unknown parameters must be determined by the optimization algorithm. Minimum and maximum distilled water algorithms give the minimum and maximum distilled water for which the thermodynamic balance at different parts of plant could be established.

5. Results and discussions By using foregoing equations and algorithms the effects of different parameters such as feed water flow rate, temperature of feed

Fig. 6. Effect of α on the maximum distilled water and maximum performance.


199

Fig. 7. Calculation procedure of minimum distilled water.

water, number of effects, temperature difference of preheaters and output pressure on the rate of fresh water production have been studied. Therefore to be more efficient the test conditions are design based on the method of design of experiment (DoE). DoE is performed on k parameters at two or more than two levels to understand their direct effects and also their interactions on the desired responses [9]. First a 2k factorial design is chosen to con-

struct the tests table. Five parameters are selected to study their effects on the minimum and maximum distilled water. These parameters are: feed water flow rate (A), temperature of feed water (B), numbers of effects (C), temperature difference of preheater (D) and output pressure (E). A 2k factorial with two levels for the minimum distilled water has been performed to see if there are any non significant parameters. It should be mentioned that

200


Fig. 8. Calculation procedure of maximum distilled water.

the signification of the parameters are quantified by the p-value, a p-value less than 0.05 indicates significance [9] and are specified as significant parameter. The results show that the effects of these parameters on the minimum distilled water are significant (see Fig. 9). Thus in order to have more accuracy a new DoE with three levels is performed to study the effects of these parameters on the minimum distilled water.

A 3k factorial test table is designed which is shown in Table 1. Therefore 243 (35) tests have been executed to find the response of the objective function (minimum distilled water) on the variations of these parameters. Analysis variance of the 3k factorial tests is shown in Table 2. Then a regression has been performed on the results of 3k factorial to show and also to predict the effects of these parameters on the minimum water distilled. Eq. (19) is the regression


201

Table 3 Error percentage of minimum distilled water.

Within range Out of range

Fig. 9. Response of first DoE for minimum distilled water.

function estimated from DoE analysis of minimum amount of distilled water. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðm˙ d Þmin = 11:01593−0:023307 mf + 0:35466 Tsw + 0:014194 n −3 + 2:64044 ΔTpr + 3042:42454 Pout + 1:73109 × 10 mf −3 −4 × Tsw −1:177766 × 10 mf × n + 1:39631 × 10 mf −3 × ΔTpr + 6:08346 mf × Pout + 3:14011 × 10 Tsw × n−0:090929 Tsw × ΔTpr −95:27274 Tsw × Pout + 0:049661 n × ΔTpr −26:34805 n × Pout −749:91251 ΔTpr

Prediction

Actual

Error%

8.958 34.398

8.896 36.8249

0.69 6.59

For given values of the parameters the prediction contours of minimum water distilled can be plotted by this equation. In order to see the precision of the predicted results by these contours, comparisons are done with the results obtained directly from the simulation code. As seen in Table 3, within the range of performed tests, these results are very close while out of the range of executed tests the concordance between the results is acceptable (6.59%). The same approach is also adopted for the maximum distilled water. The results of 2k factorial tests for the maximum amount of distilled water shows that the effect of parameter B (Tsw) on the maximum amount of distilled water is negligible (see in Fig. 10).

−5

× Pout + 1:71863 × 10 mf × Tsw × n −1:19483 −4 × 10 mf × Tsw × ΔTpr −0:34827 mf × Tsw × Pou t −4 + 5:14699 × 10 mf × n × ΔTpr + 0:28864 mf × ΔTpr −4 × Pout + 0:19816mf × n × Pout −9:56007 × 10 Tsw × n × ΔTpr + 0:18593 Tsw × n × Pout + 24:71972 Tsw × ΔTpr × Pout + 1:57852 n × ΔTpr × Pout : ð19Þ Table 1 Parameters and their three levels value for 3k factorial model of minimum distilled water. Factors Parameters A B C D E

Feed water (kg/s) 30 Temperature of seawater (°C) 25 Numbers of effects 12 Temperature difference of 1 each preheater (°C) Output pressure (MPa) 0.003

60 30 15 3 0.004

90 32.5 18 5 0.005

Table 2 Analysis variance of 3k factorial model for minimum distilled water. Source Sum of squares

Fig. 10. Response of first DoE for maximum distilled water.

Level 1 (−1) Level2 (0) Level 3 (+1)

df

Mean square

Model 2076.82 20 103.841 A-mf 597.2135 1 597.2135 B-Tsw 3.868855 1 3.868855 C-n 549.1412 1 549.1412 D-ΔTpr 539.6624 1 539.6624 E-Pout 42.44459 1 42.44459 AB 0.617234 1 0.617234 AC 87.78436 1 87.78436 AD 86.38329 1 86.38329 AE 6.796065 1 6.796065 BC 1.162114 1 1.162114 BD 0.561878 1 0.561878 BE 4.281921 1 4.281921 CD 126.191 1 126.191 CE 5.539345 1 5.539345 DE 1.563831 1 1.563831 ABE 0.684065 1 0.684065 ACD 20.19142 1 20.19142 ACE 0.884603 1 0.884603 BCD 0.431494 1 0.431494 BDE 1.416334 1 1.416334

F-value

pvalue

846.4712 4868.251 31.5374 4476.385 4399.118 345.9918 5.031455 715.5839 704.1629 55.39888 9.473101 4.580208 34.90455 1028.66 45.15458 12.74774 5.576231 164.5926 7.210942 3.517369 11.5454

0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0464 0.0001 0.0001 0.0001 0.0105 0.0556 0.0001 0.0001 0.0001 0.0044 0.0377 0.0001 0.0212 0.0875 0.0060

Table 4 Parameters and their three levels value for 3k factorial model of maximum distilled water. Factors

Parameters

Level 1 (−1)

Level2 (0)

Level 3 (+ 1)

A B C

Feed water (kg/s) Numbers of effects Temperature difference of each preheater (°C) Output pressure (MPa)

30 12 2

50 15 3

70 18 4

D

Significant Significant Significant Significant Significant Significant Significant Significant Significant Significant Significant Non Significant Significant Significant Significant Significant Significant Significant Significant Non Significant Significant

0.003

0.0045

0.006

Table 5 Analysis variance of 3k factorial model for maximum distilled water. Source

Sum of Squares

df

Model A-mf B-n C-deltpr D-Pout

4974.632 2447.064 661.6533 1583.357 0.278922

11 452.2393 1 2447.064 1 661.6533 1 1583.357 1 0.278922

AB AC AD BC CD ABC ACD

70.48853 168.8939 0.03011 29.61552 9.119239 3.161682 0.970699

1 1 1 1 1 1 1

Mean Square

70.48853 168.8939 0.03011 29.61552 9.119239 3.161682 0.970699

F-value

p-value

3444.212 18636.61 5039.089 12058.69 2.124243

0.0001 0.0001 0.0001 0.0001 0.1495

536.834 1286.28 0.229317

0.0001 0.0001 0.6335

225.549 69.45126 24.07907 7.392755

0.0001 0.0001 0.0001 0.0083

Significant Significant Significant Significant NonSignificant Significant Significant NonSignificant Significant Significant Significant Significant

202


Prediction

Actual

Error%

water consists of 81 tests (34) which is presented in Table 5. The estimated function resulted from DoE analysis for maximum distilled water is as follow:

13.724 43.0413

13.5522 44.9896

1.27 4.33

ðm˙ d Þmax = −9:98114 × 10

Table 6 Error percentage of minimum distilled water.

Within range Out of range

−3

+ 3:24331 × 10 −3

× 10

+ 0:02892 mf + 1:11264 × 10

−4

n

ΔTpr −0:7575 Pout + 5:17374

mf × n−0:012606 mf × ΔTpr −21:07516 mf × Pout −4

Thus another tests routine with 3k factorial is performed. The parameters and their levels (three for each) are shown in Table 4. The tests table for analysis of variance of maximum amount of distilled

−3

−1:28832 × 10

+ 6:04926 × 10

Tsw × n + 0:34856 ΔTpr × Pout

−3

mf × n × ΔTpr + 6:70371 mf × ΔTpr

× Pout :

Fig.11. Contour of minimum distilled water for n = 15, ΔTpr = 3 °C, Pout = 0.004 MPa.

Fig. 12. Contour of minimum distilled water for Tsw = 30 °C, ΔTpr = 3 °C, Pout = 0.004 MPa.

ð20Þ


203

Fig. 13. Contour of minimum distilled water for Tsw = 30 °C, n = 15, Pout = 0.004 MPa.

To show the precision of this equation comparisons are done with the direct results of the simulation code. As seen in Table 6 within the range of performed tests, the results are very close while at the out of range the concordance between the results is acceptable (4.33%). Thus at this step the contours for prediction of minimum and maximum distilled water could be presented and discussed. As mentioned the regression functions are obtained by using the responses of the parameters on the objective function. These functions are composed of the effective parameters and their interactions. The contours of responses on each parameter could be plotted using these equations. These contours are an excellent tools to show the effect of each parameter rather than calculating by the simulation code.

Several contours are shown in Figs. 11–16. It is shown that the amount of feed water mass flow rate has a significant effect on increasing the amount of minimum distilled water. As seen in Fig. 11, for a given feed water mass flow rate, increasing the temperature of the inlet feed water slightly augments the amount of minimum distilled water. There are two parallel phenomena to increase the amount of minimum distilled water by increasing the numbers of effects (see Fig. 12). The top brine temperature is increased by increasing the effects, so the salt concentration in the first effect is increased and more vapors is produced. On the other hand, the pressure and temperature differences of effects are decreased by increasing the effects. Therefore

Fig. 14. Contour of maximum distilled water for ΔTpr = 3 °C, Pout = 0.0045 MPa.

204


Fig. 15. Contour of maximum distilled water for n = 15, ΔTpr = 3 °C.

the salt concentration differences at each effect would be decreased and the amount of distilled water would be increased. The influence of increasing temperature difference of preheaters on the minimum distilled water production is fairly the same as the one that was seen by increasing the numbers of effects (Fig. 13). In the case of maximum distilled water, the top brine temperature and also salt concentration of the first effect are increased by the numbers of effects. Consequently the amount of vapor on the first effect is augmented. Therefore it causes to enhance the amount of maximum distilled water which can be seen in Fig. 14. The temperature difference of condenser is reduced by augmenting pressure output, thus the top brine temperature is decreased and the heating energy is increased. On the other hand increasing of heating energy is restricted with the maximum distilled water. So as seen in Fig. 15

the sensitivity of pressure output on the maximum distilled water is negligible. The influence of increasing temperature difference of preheaters on the maximum distilled water is fairly similar to the one that was seen in the minimum distilled water approach (see Fig. 16). 6. Conclusion MED plant has been studied numerically. In order to investigate the effects of feed water flow rate, temperature of seawater, numbers of effects, temperature differences of preheaters and the outlet pressure on the distilled water production, method of Design of Experiment (DoE) has been adopted. It is shown that the minimum distilled water is increased by augmenting the feed water temperature. However the

Fig. 16. Contour of maximum distilled water for n = 15, Pout = 0.0045 MPa.


latter does not have significant effect on the maximum distilled water. Choosing higher Tsw, n and ΔTpr could increase the fresh water production. In addition, despite of increasing the fresh water production, lower value of heating energy is also needed. However more efficient preheaters must be used. Different contours have been presented to show the effects of feed water flow rate, temperature of seawater, numbers of effects, temperature differences of preheaters and the outlet pressure on the fresh water production. These contours could help a designer to find suitable thermodynamic conditions at different situations for which the plant would operate close to its optimum condition.

f o, out pr sw b

Nomenclature h Enthalpy, kJ/kg ṁ Mass flow rate, kg/s n Number of effect P Pressure, MPa Q̇ Heat flux, kW T Temperature, °C X Salt concentration, TDS

References

Subscript b con d, dis e

Feed water Outlet Pre heater Seawater vapor

Acknowledgment The authors would like to thank Sistan and Baluchestan Water and Wastewater Company for their financial support of this research.

[1] [2] [3] [4] [5]

[6]

Brine Condenser Distilled water Evaporator

205

[7] [8] [9]

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