Development of a steady-state mathematical model

Desalination 351 (2014) 9–18

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Desalination journal homepage: www.elsevier.com/locate/desal

Development of a steady-state mathematical model for MEE-TVC desalination plants Ibrahim S. Al-Mutaz ⁎, Irfan Wazeer Chemical Engineering Department, College of Engineering, King Saud University, PO Box 800, Riyadh 11421, Saudi Arabia

H I G H L I G H T S • • • •

A steady-state mathematical model of MEE-TVC system was presented. Matlab program was used to solve the model. System performance of an MEE-TVC system was evaluated. Good agreement was obtained between model data and actual data.

a r t i c l e

i n f o

Article history: Received 18 January 2014 Received in revised form 13 July 2014 Accepted 14 July 2014 Available online xxxx Keywords: Steady-state modelling MEE-TVC MED-TVC Desalination plants

a b s t r a c t Multi-effect evaporation with thermal vapor compression (MEE-TVC) is one of the most effective desalination method. It plays a vital role in the production of fresh water in many regions of the world especially in the Arabian countries. A steady-state mathematical model of MEE-TVC system and its solution procedure are developed based on the basic laws of material balance, energy balance and heat transfer equations with correlations for physical properties estimation. The influence of important design and operating variables on the performance of the plant is investigated. These parameters include number of evaporation effects, motive steam pressure, top brine temperature, temperature difference across effects and feed water temperature. The purpose of this paper is to develop a mathematical model of the MEE-TVC systems and compare the results with the existing plants. A MATLAB program is also used to solve the model equations. The model validity is examined against some commercial MEE-TVC systems. Good agreement is obtained between data of these systems and model predictions. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Water is one of the most abundant element on the earth, but it is also a fact that clean water resources are drastically being reduced due to the human consumption around the world. There are different solutions for dealing with water shortages. Desalination is one of them. The process of removing dissolved salts from water to produce fresh water is called desalination. Multi-effect evaporation with thermal vapor compression (MEE-TVC) is gaining more interest as compared to other thermal desalination processes like multi stage flash desalination due to its low maintenance cost, simple geometry, easer operation and low energy consumption. Thermo-compressor plays a major role in multi-effect evaporation systems. It reduces energy consumption and increases system's efficiency. Energy consumption can be significantly influenced by the geometry and operating conditions of thermo-compressor [1–3]. Several studies have been reported since the last two decades concerning MEE-TVC desalination system. Some of which include field studies, and others describe different conceptual designs. Different ⁎ Corresponding author. E-mail address: [email protected] (I.S. Al-Mutaz).

http://dx.doi.org/10.1016/j.desal.2014.07.018 0011-9164/© 2014 Elsevier B.V. All rights reserved.

mathematical models have been developed, and most of these publications for simulation and economic evaluation purposes [4–15]. Minnich et al. [4] developed a simple model for the MEE-TVC system and reported that the proposed MEE-TVC system could operate in the parallel mode and at low temperatures. Furthermore, this model was used for the comparison of the performance and capital cost of the MEE-TVC against the MEE and MSF plants. On the other hand, it is also stated that the capital cost for the three systems was evaluated on the total heat transfer area basis. The results show that the MEE-TVC system gives higher heat transfer areas at low top brine temperatures, 60 °C, than the MSF system at performance ratios more than 6. Darwish and El-Dessouky [5] presented a simple mathematical model for parallel feed MEE-TVC. The model includes energy and mass balance equations in each effect as well as in the steam jet ejector. Graphical performance data for the ejector model is based on Power model [6]. They also stated that thermal vapor compression desalination systems are more cost-effective when compared with MSF desalination systems. The model assumed negligible pressure losses within the system components. Furthermore, equations for the heat transfer areas in the evaporators and the distillate flashing boxes were not included in the model. The results also show that MEE-TVC system

10

I.S. Al-Mutaz, I. Wazeer / Desalination 351 (2014) 9–18

uses a much smaller heat transfer area than MEE and MSF systems with the same energy consumption. They also developed a model to evaluate the performance of a four effect MEE-TVC system, and results show a performance ratio of 7.65 for a top brine temperature of 62 °C. In addition, it is reported that the gain output ratio of four effects of MEE-TVC is very close to that of eleven effects and twenty four stages MEE and MSF systems, respectively. El-Dessouky et al. [7,8] proposed extensive mathematical models than can be used for the analysis of the single effect thermal vapor compression (TVC) process and the multi-effect desalination systems (MEE). The single-effect TVC model and the stand-alone MEE model form the basis for the development of the more complicated MEE-TVC models. El-Dessouky and Ettouney conducted a model to evaluate the performance of the MEE-TVC system. The obtained MEE-TVC model is based on the two models proposed by El-Dessouky in 1997 for the single-effect TVC and multi-effect MEE model of El-Dessouky et al. [9]. It was found that a new developed model (MEE-TVC) has higher potential than the stand-alone MEE system because of its higher performance ratio. In addition, a large decrease in the specific flow rate of cooling water is obtained. They also developed a computer package for the design and simulation of thermal desalination processes. Temstet et al. [10] conducted a case study for a desalination plant in Sicily. The plant consists of 12 effects and thermo-compression. The design gain output ratio of the units is close to 17. The description of plants units, heat and mass balance flow diagram and overall plant layout were described. The main construction detail and data of the first production period were also presented. El-Dessouky and Ettouney also presented analysis of the MEE-TVC system. Their model was basically based on the two models proposed by El Dessouky for the single-effect TVC and the multi-effect MEE model developed by El-Dessouky et al. As a result, the MEE-TVC model used sound physical phenomena in order to take care of various processes happening in the system. Large increase in the performance ratio was observed against the stand-alone MEE system, with increase varying from 20% to 50%. In addition, the specific flow rate of cooling water exhibited large reduction. Habshi used a steady-state simulation program to develop a mathematical model to analyze the performance of an MEE-TVC plant [11]. He studied the effect of the thermodynamic losses on the specific flow rate of the cooling water, specific heat transfer area and thermal performance ratio in his research. Ji et al. [12] developed a theoretical model to examine a single-effect thermal vapor compression (TVC) desalination system. They investigated the effects of varying operating conditions including intake seawater temperature and cooling water mass flow rate on the system performance. The results and discussions showed that the efficiency of the plant can be increased by increasing the cooling water mass flow rate (higher than the design value) when the temperature of intake seawater is higher than the design value. Kamali et al. performed parametric study of MEE-TVC process to obtain higher gain output ratio (GOR) [13]. They presented a simulation model for the development and optimization of MEE-TVC plants. To perform the parametric analysis, a mathematical model was also developed. This model was used to study the influence of all factors on performance ratio, total production and temperature difference across effects and pressure on each effect under different operating conditions. In 2009, Kamali et al. [14] presented another simulation model which provides a cost effective tool for development and optimization of MEE-TVC plants. A mathematical model was developed to study the effect of all parameters on temperature and pressure, heat transfer coefficients, total production and performance ratio of the system. Results showed that the plate type evaporators and more suitable for the system rather than shell and tube heat type. Bin Amer used Engineering Equations Solver (EES) and developed a steady-state mathematical model for MEE-TVC desalination system to analyze the system performance [15]. The model was evaluated against

three commercial MEE-TVC systems. The comparison between the simulation results and commercial data well proves the model validity. A MATLAB program was also developed to find the optimum design and operating conditions of the MEE-TVC desalination plants. To obtain the maximum gain output ratio value, two methods were used in MATLAB: (1) Smart Exhaustive Search Method and (2) Sequential Quadratic Programming. Furthermore, results also showed the total production capacity can be increased significantly by combining MEE-TVC desalination system with conventional multi-effect system. Kouhikamali and Sharifi investigated the influence of thermocompressors in multi-effect desalination units [16]. They examined the influence of constant area zone on thermo-compressor performance. They changed the throat diameter of thermo-compressor and compared the numerical and experimental results of this modified thermo-compressor with the old thermo-compressor. The overall efficiency of the modified thermo-compressor was increased. In this paper, a mathematical model is developed based on the steadystate operating condition. Also, all aspects of the design procedure for an MEE–TVC system are considered. The validity of the model is tested against some available data of commercial units. 2. Process description Fig. 1 shows a conventional MEE-TVC system. The main components include the n number of evaporation effects in which fresh water is obtained as a result of the evaporation of water, a condenser and a thermal vapor compressor. There are different configurations (forward feed, parallel feed and backward feed) of MEE system. These arrangements differ in the flow direction of evaporating brine and heating steam. Among these configurations, parallel feed arrangement is the most common one. In the parallel feed configuration, the direction of brine and vapor flow is same, and feed water is divided into set of parallel streams to feed into each evaporation effect. The configuration of parallel feed system is simpler as compared to the other two configurations. As shown in Fig. 1, feed seawater leaves the condenser at Tf where it exchanges heat with the vapors formed in the last effect. The greater portion of this feed seawater is rejected back to the sea as cooling water while remaining feed seawater (F) is divided equally between the effects. Cooling water is used to remove the excess heat enter the system by the hot motive steam. Generated vapor flows in the direction of falling pressure, i.e., from left to right while feed seawater is sprayed in a perpendicular direction. Motive steam from the external source goes through the thermal vapor compressor, which entrains and compresses portion of the vapor generated in the last effect. Compressed steam from the thermal vapor compressor is supplied into the tube side of the first effect as heating medium to heat the feed seawater (F), while feed seawater (F) is sprayed on the outside surface of tube. Heating steam form thermal vapor compressor is condensed inside the tubes, which warms up feed seawater to the boiling temperature of the first effect (T1), which is also known as top brine temperature. Part of feed evaporates and generates an amount of vapor (D1), which is directed to the second effect as the heat source at the lower temperature and pressure than the previous effect. The temperature of vapor initiated in the first effect (Tv1) is lower than the boiling temperature (T1) by a small value known as the boiling point elevation (BPE). A wire mist separator, the so-called wire mesh demister, is also used in each effect for the removal of entrained brine droplets. Part of the condensate from the first effect goes back to its source while the remnant enters the first flashing box. In order to the utilize the energy of brine leaving the first effect (B1), it is directed to the next effect and so on it goes to the last effect at a lower pressure than the preceding effect. The vapor is formed inside the effects 2 to n by two different mechanisms. It is formed, first, by boiling over the surface of the tubes and, second, by flashing inside the liquid bulk. Flashing also takes place in the flashing box due to the condensation of the distillate in the second


11

Fig. 1. MEE-TVC system with n number of effects.

effect and so on; it goes to the last effect, which generates small amount of vapors. The purpose of the flashing boxes is to recover the heat from the condensed fresh water. In the last effect, produced vapor (Dn) is split into two streams. One stream (Dev) is entrained and compressed by the thermal vapor compressor, and the other stream (Dc) is directed to the condenser where it increases the temperature of feed seawater from Tcw to Tf. Representation of the system variables in the effect i and the associated flash box is given in the Fig. 2 which includes salinity, flow rate and temperature of different streams.

3. Assumptions and mathematical model 3.1. Assumptions The following assumptions were used to drive the mathematical model: • Temperature difference across each effect is assumed to be the same. • The distillate is salt free, Xd = 0.

Why Tci-1 at the output? Fig. 2. A schematic representation of the variables in evaporator and flash boxes of effect i.

Shouldn't we write Tvi+NEA?

12


• Steady-state operation. • Specific heat capacity for feed seawater is equal to that of brine and distillate water. • Equal flow rate in each effect. • Boiling point elevation (BPE) is equal for all effects. • Thermodynamic losses are negligible. 3.2. Mathematical model

−3892:7 þ 9:5 P s ¼ 1000 exp T s þ 273:15−42:6776

P ev ¼ 1000 exp

A mathematical model of MEE-TVC system (Fig. 1) is developed in this section to study the effect of design parameters on the system performance. The model is based on material and energy balances around evaporation effects, thermal vapor compressor, flash chambers and end condenser. Input parameters include top brine temperature(T1), boiling temperature of the last effect (Tn), total feed flow rate (F), motive steam flow rate (Dm), cooling water temperature (Tcw), feed seawater temperature (Tf), feed seawater salinity (Xf), motive steam pressure (Pm) and number of effects (n). The mathematical model is divided into three sections, which include mass balances, energy balances and heat transfer equations. The model also includes equations for the heat transfer coefficients and the physical properties of water. Temperature difference across the effects is assumed to be the same in this model and can be calculated as follows: ΔT ¼

Pressure of compressed vapors (Ps) and entrained vapors (Pev) is obtained from the correlation developed by EI-Dessouky et al. [4]:

T 1 −T n n−1

ð1Þ

Temperature of compressed steam (Ts) can be obtained by using the following equation: T s ¼ T 1 þ ΔT

ð2Þ

Vapor temperature in the last effect can be calculated as follows: T vn ¼ T n −BPE

ð3Þ

The boiling point elevation (BPE) is the increase in the boiling temperature at a given pressure due to the dissolved salts in the water. The following relation is used to calculate the boiling point elevation which is almost the same for each effect: −3

BPE ¼ Xb ½B þ ðC XbÞ ð10Þ

ð4Þ

! ð7Þ

where P is in kPa and T is in °C. To calculate the ratio of motive steam to entrained vapor (Dm/Dev) in jet ejectors is the most important part in modeling the MEE-TVC systems. An optimum value of this ratio will improve system performance by reducing the amount of motive steam. This ratio is a function of compressed vapors pressure (Ps), motive steam pressure (Pm) and the pressure of entrained vapor (Pev), as follows ER ¼

Pm P ev

ð8Þ

CR ¼

Ps P ev

ð9Þ

There are several methods available to calculate entrainment ratio, but most of them requires very lengthy mathematical procedures. Two methods that are most widely used are as follows: (1) Power's graphical data method [17] and (2) El-Dessouky and Ettouney's semiempirical model. By using the Power method, entrainment ratio can be calculated directly in term of expansion ratio and compression ratio from the Fig. 3. The semi-empirical model is simpler one, but it is only applicable when the motive stream is steam and entrained fluid is water vapor. The model equation to calculate entrainment ratio (Ra) is given as follows: 1:19

Ra ¼ 0:235

ðP s Þ 1:05 ðERÞ ðP ev Þ1:04

ð10Þ

The amount of the entrained vapor (Dev) can be obtained by using the following equation:

With −2 −5 2 −3 B ¼ ½6:71 þ 6:34 ð10Þ T n þ ð9:74 ð10Þ ðT n Þ ð10Þ h i −3 −5 2 −8 C ¼ 22:238 þ 9:59 ð10Þ Tn þ 9:42 ð10Þ ðTn Þ ð10Þ

T vn

−3892:7 þ 9:5 þ 273:15−42:6776

ð6Þ

Dev ¼

Dm Ra

ð11Þ

Heat capacity of the water can be obtained by using the following relation:

The brine temperature in an effect is less than that of the previous one by ΔT. Hence, it is assumed that the brine temperature in an effect i is Ti, then the brine temperature in the next effect i + 1 can be obtained by using the following equation:

h i 2 3 −3 C P ¼ a þ ðb T 1 Þ þ c ðT 1 Þ þ d ðT 1 Þ ð10Þ ;

T iþ1 ¼ T i −ΔT; i ¼ 1; 2; 3; …; n

ð5Þ

where −2 2 a ¼ 4206:8−ð6:6197 SÞ þ 1:2288 ð10Þ ðSÞ −2 −4 2 b ¼ −1:1262 þ 5:4178 ð10Þ S − 2:2719 ð10Þ ðSÞ −2 −4 −6 2 − 5:3566 ð10Þ S þ 1:8906 ð10Þ ðSÞ c ¼ 1:2026 ð10Þ −7 −6 −9 2 þ 1:517 ð10Þ S − 4:4268 ð10Þ ðSÞ d ¼ 6:8777 ð10Þ And S ¼

Xf 1000

where T1 is the temperature in °C and S is the water salinity in g/kg.

ð12Þ

Vapor temperature in an effect i is described in terms of the boiling temperature (Ti) and boiling point elevation (BPE) since vapor temperature in the effect is below the boiling temperature of the brine by the boiling point elevation: Tvi ¼ Ti−BPE

ð13Þ

The feed seawater flow rate F is distributed equally to all effects at a rate equal to Fi and can be calculated by using the following formula: Fi ¼

F ; n

i ¼ 1; 2; 3; …; n

ð14Þ


The condensation temperature of vapor T ci is less than the boiling temperature Ti by the boiling point of elevation losses caused by pressure losses in the demister (ΔTp), friction in the connecting line (ΔTt) and during condensation (ΔTc). T ci ¼ T i −BPE−ΔT p −ΔT t −ΔT c

The cooldown temperature of brine when it enters the effects can be calculated by using the following equation: 0

T i ¼ T i þ NEAi;

ð15Þ

Latent heat of steam (λs), distillate vapors (λi) and condensate (λci) can be calculated by using the following equations: λs ¼ 2589:583 þ 0:9156 T s −4:834 10

−2

−2

λi ¼ 2589:583 þ 0:9156 T i −4:834 10

Ts Ti

2

ð16Þ

2

−2

T ci

0

0

ðDm þ Dev Þ λs − F 1 C p ðT 1 −T f Þ λ1

ð19Þ

where

Vapor flashed off from the brine entering to the effects 2 − n is given 0 Bi−1 C p T i−1 −T i λi

;

i ¼ 2; 3; 4; …; n

F1 X ð F 1 −D1 Þ f

ð27Þ

Nonequilibrium allowance (NEA) for flash boxes can be determined by using the following equation: 0

NEAi ¼

0:33 T ci−1 −T vi T vi

;

i ¼ 2; 3; 4; …; n

ð28Þ

Cooling temperature of condensing vapors when it enters to flash boxes can be obtained by using the following relation: 00

0

ð29Þ

The amount of vapor flashed off in the flash boxes is given by 0 1 00 T ci−1 −T i @ A; i ¼ 2; 3; 4; …; n di ¼ Di−1 C p 0 λi 0

Brine leaving the first effect enters into the second effect can be calculated by considering material balance as follows: Salinity of brine leaving the first effect can be obtained by applying salt balance: X b1 ¼

ð26Þ

by

T i ¼ T vi þ NEAi ; i ¼ 2; 3; 4; …; n motive steam flow rate entrained vapors flow rate latent heat of evaporation at temperature Ts latent heat of evaporation at temperature T1

Dm Dev λs λ1

02

Ti

ð18Þ

In above three equations, temperature is in °C, and latent heat is in kJ/kg. Vapor generated in the first effect by the boiling only can be calculated by applying energy balance as follows: D1 ¼

−2

λi ¼ 2589:583 þ 0:9156 T i −4:834 10

ð17Þ 2

ð25Þ

i ¼ 2; 3; 4; …; n

Latent heat of evaporation at temperature T'i:

di ¼ λci ¼ 2589:583 þ 0:9156 T ci −4:834 10

13

ð20Þ

ð30Þ

The amount of vapor released from the effects 3 − n can expressed as follows: Di ¼

0 0 Di−1 λi−1 þ di−1 λi−1 þ di−1 λi−1 −F i C p T i −T f þ Bi−1 C p ðT i−1 −T i Þ λi

ð31Þ The mass of vapor generated in the second effect is calculated from

D2 ¼

D1 λ1 − F 2 C p T 2 −T f þ B1 C p ðT 1 −T 2 Þ λ2

where i = 3, 4,…, n. Total amount of distillate (Dt) is given by ð21Þ Dt ¼ D1 þ D2 þ D3 þ þ Dn ¼

n X

Di ;

i ¼ 1; 2; 3; ; n

ð32Þ

i¼1

Brine leaving the second effect and its salinity can be calculated by using the following two material balance equations: B2 ¼ F 2 þ B1 −D2

X b2 ¼

ð22Þ

X f F 2 þ X b1 B1

ð23Þ

B2

Miyatake et al. [18] developed the following correlation to calculate nonequilibrium allowance (NEAi) for effects 2 − n, which is a measure for the efficiency of the flashing process: 0:55

NEAi ¼

33 ðT i−i −T i Þ Tvi

; i ¼ 2; 3; 4; ::; n

ð24Þ

The amount of brine leaving the effects and brine salinity for the effects 3 − n is calculated from the following two equations: Bi ¼ F i þ Bi−1 −Di;

X bi ¼

i ¼ 3;

X f F i þ X bi−1 Bi−1 Bi

;

4; …; n

ð33Þ

i ¼ 3; 4; …; n

ð34Þ

The vapors generated in the last effect are divided into two parts, one is directed to the condenser (Dc) while other is entrained by thermal vapor compressor (Dev). The amount of vapor goes to the condenser can be calculated as follows: Dc ¼ Dn −Dev

ð35Þ

14


Fig. 3. Entrainment ratio for different compression and expansion ratios.

Overall heat transfer coefficient (Ui) can be obtained as follows:

Ui ¼

2 3 1939:4 þ 1:40562 T i −0:0207525 ðT i Þ þ 0:0023186 ðT i Þ

−5

2 T vn ð41Þ

1000 ð36Þ

Heat transfer area for the first effect is calculated from the following formula: ðD þ Dev Þ λs A1 ¼ s U 1 ðT s −T 1 Þ

ð37Þ

Heat transfer area for the effects 2 − n can be obtained as follows: Ai ¼

−2

U c ¼ 1:7194 þ 3:2063 10 T vn −1:5971 10 3 −7 þ 1:9918 10 T vn

Di λi ; U i T ci −T i

i ¼ 2; 3; 4; …; n

ð38Þ

Total heat transfer area of the effects (Ae) is given by the following equation: Ae ¼ A1 þ A2 þ A3 þ þ An ¼

n X

Ai ; i ¼ 1; 2; 3; ; n

ð39Þ

i¼1

Logarithmic mean temperature difference and overall heat transfer coefficient of the condenser can be obtained by using the following two equations: ðT f −T cw Þ " # ðLMTDÞc ¼ T vn −T cw ln T cn −T f

ð40Þ

Condenser heat transfer area can be obtained from the following equation: Ac ¼

Dc λn U c ðLMTDÞc

ð42Þ

The flow rate of cooling seawater (Mcw) can be obtained by applying the energy conservation law on the condenser as shown in the following equation: Mcw ¼

Dc λn C p ðT f −T cw Þ

ð43Þ

Specific heat transfer area (Ad) is equal to the sum of effects and condenser heat transfer area per total product: Ad ¼

Ae þ Ac Dt

ð44Þ

The system performance of the MEE-TVC model is calculated in term of gain output ratio (GOR) as follows: GOR ¼

Dt Dm

ð45Þ

One of the most important characteristic of thermal desalination units is specific heat consumption. It is defined as the thermal energy


consumed by the system to produce 1 kg of distilled water. It relies on the first law of thermodynamics and can be calculated as follows: Q¼

Dm λm Dt

ð46Þ

4. Computational algorithm The model developed in the previous section is composed of a set of highly nonlinear equations. Eqs. (1)–(43) were solved by using MATLAB software to evaluate the system performance Eqs. (44)–(46) of the model. Since the model equations are highly non-linear, therefore,

15

iterative solution for direct substitution is proposed to solve these equations simultaneously. Design parameters and constrains should be defined properly in order to perform the parametric study of any system. A standard design optimization model is developed in Fig. 4 to solve the problem for MEE-TVC units varying from 4 to 12. A constant value of boiling point elevation (BPE) is considered for each effect. The system performance is obtained in term of gain ratio, specific heat transfer area, specific heat consumption and distillate production. The constraints of compression and entrainment ratios are 4 ≤ CR ≥ 1.81 and Ra = 4, respectively [19]. A general description of some commercial MEE-TVC plants is given below.

Fig. 4. Computational algorithm of the MEE-TVC system.

16


Table 1 Mathematical model comparison against three commercial plants with different number of effects. Desalination plants

Tripoli [20]

Yanbu Phase II

Trapani [10]

Model

Actual

Model

Actual

Model

Actual

Operating and design conditions Number of effects n Motive pressure Pm, kPa Top brine temperature T1, °C Minimum brine temperature Tn, °C Temperature drop per effect, °C Feed seawater temperature Tf, °C Cooling seawater temperature Tcw, °C Motive steam flow rate Dm, kg/s

4 2300 60.1 45.4 4.9 41.5 31.5 8.8

4 2300 60.1 45.4 4.9 41.5 31.5 8.8

5 1500 63 45 4.5 43 30 101.7

5 1500 63 45 4.5 43 30 101.7

12 4500 62.2 37 2.3 35 25 6.25

12 4500 62.2 37 2.3 35 NA 6.25

TVC design Entrainment ratio Ra Expansion ratio ER Compression ratio CR

1.14 240.9 2.66

1.14 NA NA

0.84 104.4 1.97

0.82 100.4 1.91

1.8 736.1 4

NA 730 4

System performance Distillate production D, kg/s Gain output ratio GOR Specific heat consumption Q, kJ/kg Specific heat transfer area Ad, m2/kg/s

58.02 6.59 370.8 277.1

57.8 6.51 NA NA

792.5 7.79 312.03 373.7

793.1 7.84 NA NA

102.9 16.47 148.6 761.1

105.2 16.7 NA NA

4.1. Plant description 4.1.1. Tripoli Two units of 5000 m3/day low temperature horizontal tube multi-effect evaporation with thermal vapor compressor were built by the General Electricity Company in Tripoli West plant to supply the makeup water to the boilers. Each unit consists of four effects and a condenser. One preheater is also used for each unit to increase the feed seawater temperature of the first effect using active steam [20].

4.1.2. Yanbu II Yanbu Phase 2 expansion seawater desalination plant features the world's largest MED unit desalination plant [21]. The plant was commissioned in December 2012. It has production capacity of 15 MIGD, which is more than twice the capacity of Fujairah F2 IWPP desalination plant in UAE (8.5 MIGD). Each unit consists of two effects and the total production capacity of plant is around 146,160 m3 per day.

4.1.3. Trapani The desalination plant in Trapani consists of four MEE units with thermal vapor compressor. The MEE-TVC was setup in Sicily in April 1995. The thermal vapor compressors are fed with 45 bar steam raised by dedicated boilers. It is fitted between the last effect and the first effect and recompresses the part of low energy vapor from the last effect towards the first cell. Each unit produces 9000 m3/day of fresh water and consists of twelve effects. The design GOR of the units is 16.7, which is very high. Feed preheaters are also used in some of the effects so that the vapor generated by the effects is condensed by the feed seawater which is preheated at the same time. [10]. 4.1.4. Umm Al-Nar The Umm Al-Nar (UAN) plant is the integrated power and desalination plant, located on Sas Al Nakhl Island on the east side of Abu Dhabi city. The Umm Al-Nar plant consists of two UAN east and UAN west plants and the UAN B “Sas Al Nakhl” Plant. UAN B “Sas Al Nakhl” Plant consists of seven multi stage flash (MSF) desalination units and two MEE units. The unit capacity of MEE plant is 3.5 MIGD, and the thermal

Table 2 Mathematical model comparison of MEE-TVC against three commercial plants with same number of effects. Desalination plants

Umm Al-Nar [22]

Rabigh Plant [23]

Al-Taweelah A1 [24]

Model

Actual

Model

Actual

Model

Actual

Operating and design conditions Number of effects n Motive pressure Pm, kPa Top brine temperature T1, °C Minimum brine temperature Tn, °C Temperature drop per effect, °C Feed seawater temperature Tf, °C Cooling seawater temperature Tcw, °C Motive steam flow rate Dm, kg/s

6 2500 61.8 42.8 3.74 40 30 10.6 × 2

6 2500 61.8 42.8 3.74 40 30 10.6 × 2

6 1770 70 49.4 4.1 32 23 7.06

6 1770 70 49.4 4.1 32 NA 7.06

6 280 63 44 3.8 40 30 12.3 × 2

6 280 63 44 3.8 40 30 12.3 × 2

TVC design Entrainment ratio Ra Expansion ratio ER Compression ratio CR

1.36 299.7 3.12

1.36 NA NA

1.47 151.4 3.22

NA NA NA

0.72 17.8 1.75

NA 18.3 1.7

System performance Distillate production D, kg/s Gain output ratio GOR Specific heat consumption Q, kJ/kg Specific heat transfer area Ad, m2/kg/s

183.2 8.64 282.4 384.2

184.4 8.6 NA NA

56.6 8.01 298.5 312.5

57.9 8.2 NA NA

192.5 7.83 311.1 382.1

198 8.0 NA NA

I.S. Al-Mutaz, I. Wazeer / Desalination 351 (2014) 9–18 Table 3 Operating conditions. Motive steam flow rate, Dm (kg/s)

6.8

Motive steam pressure, Pm (kPa) Feed seawater temperature, Tf (°C) Cooling seawater temperature, Tcw (°C) Feed seawater salinity, Xf (ppm) Boiling point elevation, BPE (°C)

2500 40 30 46,000 0.8

energy requirement is 85 ton of low-pressure steam per hour. Each unit consists of 6 effects and a condenser with GOR close to 8 [22]. 4.1.5. RABIGH Saudi Aramco's RABIGH Refinery in Saudi Arabia installed a facility for 10000 TPD seawater desalination for their industrial use. The two 5000 m3/day multi-effect evaporation (MEE) systems were used to produce process water and potable water to Saudi Aramco's Refinery and their community. The net capacity of the desalination plant is 10,000 m3/day. It consists of 4000 m3/day of process water as well as 6000 m3/day of potable water. High purity distillate is produced by the MEE systems, which can be used as process water after remineralization as potable water. The designed GOR is 8.0. The actual capacity can be more than 10000 TPD with a GOR of 8.2. Thermal vapor compression (TVC) is used in the MEE system. The following are the designed criteria: • Seawater total dissolved salts (TDS) 41,500 ppm. • Low-pressure (LP) heating source steam at 3.5 kg/cm2g minimum pressure. • Medium-pressure (MP) steam to vacuum system at 17 kg/cm2g minimum pressure. • Distillate purity 5 mg/l TDS. • Condensate purity 5 mg/l TDS. • Design capacity of 5000 m3/day each with turndown to 50% of design capacity [23]. 4.1.6. Al-Taweelah A1 Al-Taweelah A1 is power and desalination plant with the heat being used for seawater desalination. The plant was commissioned in 2002 in Abu Dhabi as the largest MEE-TVC plant in the world to use multi-effect evaporation (MEE) technology, which is more energy efficient than multi-stage flash (MSF) technology. It is one of the world's largest cogeneration facilities. It consists of 14 units; each unit has 3.77 MIGD production capacity and gain output ratio equal to Each unit consists of six effects arranged in two parallel rows of three effects which is one of the latest example of the developed MEE system. The motive steam is introduced from a steam turbine in a combined gas-steam turbine cycle at low pressure of 280 kPa. Part of the vapor produced in the third effect of each row is entrained by a steam jet ejector with the help of motive steam. The remnant goes to the conventional MEE systems with three effects [24].

17

The model validity was tested against some available data of six commercial plants: Trapoli, Yanbu Phase II, Trapani, Umm Al-Nar, Rabigh and Al-Taweelah A1 plants. Good agreement is obtained between model data and actual data, as shown in Tables 1 and 2. In Table 1, each plant has different number of effects than the other. Table 2 shows the optimal results of three 6-effect MEE-TVC desalination plants. It is clearly visible from Tables 1 and 2 that some of the parameters of the plants are not available in the literature like specific heat consumption, compression ratio and expansion ratio. In order to evaluate the system performance of any plant, the developed mathematical model is used to predict the missing values. It can be concluded from Table 2 that gain output ratio (GOR) depends upon operating and design conditions of the system. For same number of effects, GOR is different for each plant due to difference in other operating and design parameters like top brine temperature, entrainment ratio, etc. Hence, a parametric analysis must be done to get the maximum GOR. It can be seen in the literature that most of the MEE-TVC units operate with low top brine temperature (not more than 75 °C) to avoid corrosion and scaling problem. Hence, 67.1 °C is set here as upper limit of top brine temperature. The lower limit of top brine temperature is assumed to be 56.1 °C. The brine temperature in the last effect (Tn) is assumed to be 10 °C greater that the cold temperature of the intake seawater and it is normally kept at least 2 °C greater than the feed water temperature (Tf). It is also assumed that there are no thermodynamic losses in the system. It is considered that the steam is available directly from a boiler at 2500 kPa. The input parameters are listed in Table 3. 5. Results and discussion A parametric analysis was performed by using MATLAB program. The parameters include motive steam pressure, top brine temperature, entrainment ratio and temperature difference across each effect. The impact of these parameters on the system's performance is investigated. All feasible solutions are presented in Table 4. It can be reported from Table 4 that the number of effects in MEE-TVC system is limited by the temperature difference across each effect, ΔT. MEE-TVC can operate at top brine temperature below 60 °C with a maximum gain output ratio 11.64 for 7 effects. It can also be seen that the maximum gain ratio varies between 7.34 and 15.04 for 4 effects and 12 effects. It is also clear from Table 4 that the entrainment ratio and GOR increases by increasing the number of effects while specific heat consumption decreases. 6. Conclusion This paper presents an efficient and accurate mathematical model describing the MEE-TVC desalination system. MATLAB algorithm is developed and used to solve the mathematical model of the MEE-TVC system. The analysis is based on the first and second law of thermodynamics. This paper shows that the simulation model is an effective tool to design MEE-TVC system for different number of effects with any desired capacity. Also, it provides an effective tool to evaluate the

Table 4 Optimal operating conditions for different number of effects of MEE-TVC system. N

4 5 6 7 8 9 10 11 12

Temperature (°C)

TVC design

Performance parameters

T1

Tn

ΔT

CR

ER

Dm/Dev

Ad (m2/kg/s)

Q (kJ/kg)

D (kg/s)

GOR

56.1 56.1 57.1 58.9 60.1 61.5 63.1 65.5 67.1

46.0 46.0 46.0 44.8 42.8 42.8 42.5 45.0 46.5

3.37 2.53 2.30 2.35 2.47 2.34 2.29 2.05 1.87

2 1.93 2.03 2.31 2.73 2.89 3.14 3.04 2.99

253.92 253.92 253.92 270.09 299.73 299.73 304.49 267.32 247.52

0.79 0.79 0.84 0.97 1.16 1.24 1.37 1.34 1.33

440.17 636.08 725.44 707.01 665.32 716.89 736.65 850.13 971.24

336.77 258.55 225.70 211.74 204.87 191.07 183.52 171.70 161.11

51.44 67.06 76.65 81.47 83.97 89.80 93.17 99.10 105.3

7.34 9.58 10.95 11.64 12.00 12.83 13.31 14.16 15.04

18


system performance of any MEE-TVC unit. Good agreement is obtained between model data and actual data. Parametric analysis of MEE-TVC system was also performed. Gain output ratio of the model for each plant is close to the actual plant gain output ratio.

i m n s

Effect number i Motive steam Last effect Discharge stream

Symbols A Ac Ad Ae B BPE Cp CR D Dc Dev Dm Dt ER F GOR LMTD Mcw MEE-TVC MIGD NEA n Pev Pm Ps ppm Ra Q S T T1 Tcw Tf Tv TVC ΔT U X

Heat transfer area, m2 Condenser heat transfer area, m2 Specific heat transfer area, m2/kg Total heat transfer of the effects, m2 Brine flow rate, kg/s Boiling point elevation, °C Specific heat capacity of water, kJ/kg. K Compression ratio Distillate, kg/s Non entrained vapor, kg/s Entrained vapor to the ejector, kg/s Motive steam flow rate, kg/s Total amount of distillate, kg/s Expansion ratio Feed flow rate, kg/s Gain output ratio Logarithmic mean temperature difference Cooling seawater flow rate, kg/s Multi-effect evaporation with thermal vapor compression Million imperial gallons per day Non equilibrium allowance, °C Number of effects Entrained pressure in the last effect, kPa Motive steam pressure, kPa Discharge pressure, kPa Parts per million Entrainment ratio Specific heat consumption, kJ/kg Motive steam goes back to the power plant, kg/s Brine temperature, °C Top brine temperature, °C Cooling seawater temperature, °C Feed seawater temperature, °C Saturated vapor temperature, °C Thermal vapor compression Temperature difference per effect, °C Heat transfer coefficient, kW/m2 K Salt concentration, ppm

Greek symbol λ Latent heat of evaporation, kJ/kg Subscripts b Brine c Condenser or cooling e Effect ev Entrained vapor f Feed

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