Steady-State Analysis of the Multiple Effect Evaporation Desalination Process

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Steady-State Analysis of the Multiple Effect Evaporation Desalination Process By Hisham El-Dessouky, Imad Alatiqi, S. Bingulac and Hisham Ettouney* Mathematical modeling of the multiple effect evaporation (MEE) desalination process has been carried out to determine the effects of the important design and operating variables on the parameters controlling the cost of producing fresh water. The model assumes the practical case of constant constant heat transfer areas for both the evaporators evaporators and feed preheaters preheaters in all effects. In addition, the model considered the impact of the vapor leak in the venting system, the variation in thermodynamic losses from one effect to another, the dependence of the physical properties of water on salinity and temperature, and the influence influence of nonconden noncondensable sable gases on the heat transfer transfer coefficien coefficients ts in the evaporators evaporators and the feed preheaters. preheaters. The modimodified fixed-point iterative procedure is used to solve the large number of highly nonlinear equations describing the MEE desalting desalting system. The algorithm algorithm consists consists of 10 calculatio calculation n blocks blocks and 6 logical logical blocks. blocks. The algorithm algorithm is implemente implemented d using L-A-S computer aided language. Results show that the heat transfer coefficients increase with the boiling temperature. Also, the heat transfer coefficient in the evaporator is always higher than that in the feed preheater at the same boiling temperature. The plant thermal performance ratio is nearly independent of the top brine temperature and strongly related to the number of effects. The specific heat transfer area increases by raising the number of effects and reducing the top brine temperature. The effect of the top brine temperature on the specific heat transfer area is more pronounced with a larger number of effects. The required specific heat transfer areas at a top brine temperature of 100 °C are 30.3% and 26% of that required at 60 °C when the number of effects are 6 and 12, respectively. The specific flow rate of cooling water is nearly constant at different values of top brine temperature and tapers off at a high rate as the number of effects is increased. Two correlations are developed to relate the heat transfer coefficients in the preheater and the evaporator to the boiling temperature. Design correlations are also developed to describe variations in the plant thermal performance, the specific heat transfer area, and the specific flow rate of cooling water in terms of the top brine temperature and the number of effects.

1 Introduction To live is to use water. Unfortunately, fresh water, like most other natural resources, is unevenly distributed in the universe. At the same time, many countries, especially, in the Middle East suffer from the increasing demand for fresh water and the limited available natural water resources. This gap is expected to widen dramatically in the near future, due mainly to the high rate of population growth and the improvement in the standard of living, which needs a large quantity of good quality water per capita. Desalination of sea water or brackish water is the logical or the only available solution to safeguard supplies of water so that the tap does not run dry. In the last four decades, the water desalination industry has developed at a very high rate. The number of desalination plants in 1960 was 5 units with a total production rate of 5000 m3/d, while in 1995 the number of units was

± [*] [*]

H. El-Dessouky El-Dessouky (to whom correspond correspondence ence should should be addressed), addressed), Chemical Engineering Department; I. Alatiqi, Chemical Engineering Department, S. Bingulac, Electrical & Computer Computer Engineering Department, and Hisham Ettouney, Chemical Engineering Department, Faculty of Engineering & Petroleum, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait; E-mail Address: [email protected]

Chem. Eng. Technol. 21 (1998) 5

11000 with a capacity of 18.6 ´ 106 m3/d [1]. This capacity is expected to double within the next 20 y. Nevertheless, many other countries still suffer from water shortage and cannot cannot afford afford the high high capita capitall requir required ed and the runnin runningg costs of desalination plants. Presently, the majority of desalin salinat atio ion n plan plants ts in oper operat atio ion n are are the the mult multis ista tage ge flas flash h (MSF) desalination systems. However, the MEE desalination process has recently acquired a potential interest. The author authorss strong strongly ly believ believee that that the high high tem temper peratu ature re MEE proces processs is a very very strong strong candidat candidatee for realizati realization on in the near future. The preeminent advantages of the MEE when operates at high temperature (about 100 °C) compared to the predominant MSF system are ± high thermal efficiency, efficiency, with a lower number of effects; effects; ± high heat transfer coefficient; coefficient; ± relatively low specific specific investment cost; ± low pumping pumping power; power; ± high operating flexibility with short start-up period and capabilitie capabilitiess for closely closely matching matching production production volume with water demand and energy supply; and ± a distinct advantage offered by the MEE system when compared with the MSF design is that tube leaks, if they occur, do not cause distillate contamination. This is because the vapor side has higher pressure than the sea water side. Thus, tube leaks result in loss of distillate without contamination of the product water.

Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 1998

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There are three different possible configurations for the MEE desalting systems, which differ in the flow directions of the heating steam and the evaporating brine. The backwardfeed arrangement is not suitable for application in sea water desalination. The parallel feed layout is by no means the most economical and is efficient only when the feed brine is nearly saturated to begin boiling inside the effects. The salt concentration reaches the maximum permissible value in all effects. Therefore, the parallel configuration is very appropriate for low top-brine temperature design. In the forwardfeed system, both the brine and the heating steam flow concurrently from the high temperature to the lower temperature effect. The concentration of the evaporated brine increases from the first effect to the last. The layout advantage is the absence of pumps for moving or rejecting brine from the effects. It has the disadvantage that all the feed has to be heated to the boiling temperature before boiling commences. In other words, a part of the heating steam when condensed does not accomplish any evaporation in the first or consecutive effects; thus, less vapor is generated from the heating steam, which lowers the performance ratio. Furthermore, the most concentrated brine is subjected to the coolest temperature, which reduces the heat transfer coefficient because of the viscosity increase. However, at the same time, this reduces the rate of scale formation. All these facts make the system very suitable for high temperature application. Most of the published work on the MEE water desalination process concentrated mainly on comparisons between it and the MSF process. Darwish and El-Dessouky [2] cited that the race for the second generation of sea water desalters had been settled between reverse osmosis (RO) and MEE. The MEE desalination system is more efficient from a thermodynamic and heat-transfer point of view than the predominant MSF desalination system. The pumping power and the specific heat transfer area required for the MEE system, in a respective way, are about 20% and 50% of that needed for the MSF plants. Moreover, instead of making partitions for 24 stages in the MSF plants, only partitions of 10 effects are made in MEE plants, having the same performance as that of the MSF plant. Thus, the capital cost of the MEE system is expected to be about 50% less than that of MSF system. Minnich, et al. [3] reported that the MEE process requires lower heat-transfer areas than the MSF plants at high top brine temperatures. Morin [4] carried out technical and economical comparisons of the low temperature MEE and the conventional MSF process. The study showed that the MSF process needs about half the heat transfer surface area required for the low temperature MEE process. The MEE process offers almost a 50% higher recovery than the MSF process at equal performance ratios. This results in reducing the size of the brine circulating pumps, the piping systems, and the pretreatment equipment. The electrical energy use for the pumping processes favors the MEE process over the MSF system by a factor of about 30% for the same performance ratio. Morin [4] showed that the capital and operating costs for the opti438


mized processes were as follows: ± unit capital cost/gpd: MSF $8.7 (PR at 10), MEE, $7.01 (PR at 8); ± operating and maintenance cost/kgal: MSF, $4.2, MEE, $3.35; ± total cost of water/kgal: MSF, $7.05, MEE, $5.65. On the other hand, Hess and Morin [5] presented results of two different studies comparing the cost of water produced from different desalination processes. The study indicated that the water cost at the distribution point is $1.35/m 3 for MEE and $1.058/m3 for RO (1997 basis). Rautenbach [6] stated that substantially lower primary energy consumption could be achieved in thermal desalination processes by the MEE principle. Horizontal tube MEE units can be operated economically with a very small driving force and can be designed with a high gain ratio even for low top brine temperatures. However, Rautenbach, et al., [7] pointed out that the MEE process has the potential of competing with MSF with respect to simplicity and with RO with respect to specific energy (or primary energy) consumption. However, although large units can be built, it remains an open question whether they will be ordered. Michels [8] reported the following outstanding features for the MEE process when combined with thermal vapor compression (MEE-TVC). These features include low corrosion and scaling, which is caused by low temperature operation (top brine temperature below 60 °C). Other features include low energy consumption, short delivery time, and easy operation and maintenance with proven reliability in the Gulf region. The cost of the plant erection, civil work, and the sea water intake is 35% cheaper than the MSF plants. A limited number of publications which focus on the modeling and simulation of MEE desalination process are available in the literature. El-Dessouky and Assassa [9] carried out a simple analysis for the process, assuming a constant heat transfer area in each effect, constant physical properties of water, and absence of feed heaters. They showed, for the first time, the advantages of the MEE-TVC system over any other thermal desalination system. In pioneering work, Darwish and El-Hadik [10] presented the basic characteristics, thermodynamic analysis, and the required heat transfer area for the MEE desalination system. Their model was based on the following postulates: ± Equal latent heat of evaporation in all effects. ± Equal specific heat for the brine, distillate, and feed. ± The temperature drop between the effects is equal. ± Equal temperature increase across the feed heaters. ± The amounts of vapor formed by boiling in the effects are equal. On the other hand, Hanbury [11] used the following assumptions in his analysis: ± The thermal loads in the second and subsequent effects are identical. ± The heat transfer coefficient falls linearly from the second to the last effect. ± Constant specific heat and latent heat.

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± The heat transfer coefficients and surface areas are equal for all feed preheaters. The assumptions employed in the analysis developed by Minnich et al. [3] are: ± Here are no feed preheaters. ± The feed flow rate is the same for all effects. ± The contribution of distillate flash is ignored. ± Constant heat transfer coefficients. ± Constant heat transfer area for each effect. ± Vent mass and energy is negligible. ± Temperature losses are equal in all effects. It is well established that the implementation of the assumptions listed in the previous sections in modeling and analysis of the MEE process can cause large discrepancies between the model predictions and actual data. Accurate modeling of the MEE process is a key component in understanding the process elements better, improving future design procedures, and predicting the performance of existing plants over a wide range of possible operating conditions. The main features of the model developed in this paper are summarized in the following points: ± Adopt the practice case of constant heat transfer areas in the evaporators and feed preheaters in all effects. This is necessary to improve the economics and the construction procedures of the plant. ± Consider the effect of vapor leak through the venting system. ± Model variations in the thermodynamic losses (boiling point elevation, non-equilibrium allowance inside the evaporators and the flashing boxes, temperature depression corresponding to the pressure drop in the demister, vapor transmission lines, and during the condensation process) from one effect to another. ± Study the effect of boiling temperature, the velocity of brine flowing through the tubes of feed heaters, the tube material of construction, and the tube bundle geometry on the required specific heat transfer area. ± Consider the effect of water temperature and salinity on the water physical properties such as density, latent heat of evaporation, viscosity, Prandtl number, and specific heat at constant pressure. ± Weight the effect of the presence of noncondensable gases on the heat transfer coefficients in the evaporators and the feed heaters. There are some software packaged that can be used for the design and rating of the MEE process. In many situations, however, these packages have limited capacities to determine necessary details, which are specific to local conditions. In addition, these packages are not available or easily accessible to many engineers in the field, not easy to use, and difficult to detect the errors. Moreover, the model on which these packages were built and the assumptions involved are not presented in details (black box syndrome).

2 Process Description A process diagram for the forward-feed Multiple Effect Evaporation (MEE) sea water desalination process is shown in Fig. 1. The effects are numbered 1 to n from the left to right (the direction of the heat flow) 1) The feed and vapor flow concurrently in the direction of the falling pressure. The system consists of a number of evaporators, n, a series of feed water preheaters, a train of flashing boxes, last effect or bottom condenser and a venting system. The number of effects, n, is closely allied to the relationship among the fixed charge and the steam operating cost. On the other hand, the upper number of effects is imposed by the difference between the heating steam temperature Ts and the boiling point in the last effect T 1. The number of the feed preheaters is n±2 while the number of flashing boxes is n±1. Each effect constitutes of a heat transfer area, vapor space, mist eliminator, and other accessories. The horizontal falling film evaporator is the most widely used in the MEE desalination process. The major advantage of the horizontal falling evaporator is its ability to handle sea water scaling, due to high wetting rates and efficient water distribution over the heat transfer surfaces by large spray nozzles. Thus, dry-patch formation or water maldistribution is eliminated. This configuration offers the additional advantages of positive venting and disengagement of vapor products and/or noncondensable gases, high heat transfer coefficients, and monitoring of scaling or fouling materials. A controlled amount of sea water (Mcw + Mf ) is introduced into the down condenser associated with the last effect, where its temperature increases from the sea water temperature Tcw to tf . A part of this water M cw is rejected back to the sea. The function of circulating the cooling water Mcw in the last stage condenser is the removal of the excess heat added to the system in the first effect. It is worth mentioning that the evaporators do not consume most of the supplied heat, it simply downgrades it. The remaining part of sea water Mf at tf is chemically treated, deaerated, and pumped through the preheaters. Feed preheating is an important means of improving the system performance ratio. The temperature of the feed water increases from tf to t2 as it flows inside the tubes of the preheaters. The heat necessary to heat the feed water is supplied by condensing a portion of vapor formed in each effect at the shell side of the preheaters. The feed water Mf is sprayed at the top of the first effect, where it falls in the form of thin film down the succeeding rows of tubes arranged horizontally. Within this effect, the brine temperature raises to the boiling temperature corresponding to the pressure in the vapor space T1 before a small portion of vapor D 1 is evaporated. The heat required to preheat the feed and for evaporating D1 is released by condensing a controlled mass of saturated steam

± 1) Chem. Eng. Technol. 21 (1998) 5

List of symbols at the end of the paper.


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Figure 1. Process flow diagram for the multiple effect evaporator (MEE) desalination process.

Ms inside the tube bundle. The steam is supplied to the system from an external boiler. The high quality condensate from the first effect is returned to the boiler. The temperature of the vapor formed in the first effect T v1 is less than the boiling temperature T1 by the boiling point elevation (BPE)1. The vapor generated therein flows through a knitted wire mist separator known as a wire mesh demister to remove the entrained brine droplets. The saturation temperature of the vapor departing the demister is less than that of the formed vapor due to the frictional pressure loss in the demister. The vapor flows from the demister have to be transported to the second effect. This transport inevitably involves a pressure drop and hence a corresponding decrease in the saturation temperature. Another pressure fall and consequent depression in the saturation temperature of the vapor is associated with vapor condensation inside the heat transfer tubes in the evaporators or over the heat transfer area in the preheaters. The latent heat of condensation of D1 is exploited for further evaporation in the second effect. The remaining unevaporated brine in the first effect (Mf ± D1) goes to the second effect, which operates at a lower pressure. The vapor is formed inside the second effect by two different mechanisms. First, by boiling over the heat transfer surfaces D2. Second, by flashing or free boiling within the liquid bulk d2. The temperature of the vapor formed by flashing T¢v2 is less than the effect boiling temperature T2 by the boiling point elevation (BPE)2 and the nonequilibrium allowance (NEA)2. Another small quantity of vapor d2 is formed in the flashing box due to the flashing of distillate condensed in the second effect D 1. The flashed off vapor d 2 is produced at a temperature T² v2 which is lower than the condensation temperature of distillate Tc1 by the nonequilibrium allowance (NEA)2. The flashing boxes offer a way to recover heat from condensed fresh water. The boiling point elevation 440


BPE and temperature depression corresponding to pressure loss in the demister DTm, transmission lines DTt, and during the condensation process DTc reduces the available driving force for heat transfer in the evaporators and the preheaters. Thus, it is necessary to provide excess surface areas to compensate for these temperature degradations. In other words, the temperature losses present an extra resistance to the flow of heat between the condensing steam and the boiling sea water. Nonetheless, the temperature downgrading does not influence the plant thermal performance ratio PR or steam economy. The plant performance ratio depends on the heat balance consideration and not on the rate of heat transfer. The vapors formed by flashing inside the effect and the flashing box (d2 + d 2) are condensed on the shell side of the preheaters. The heat given up results in a heating of the brine flowing inside the preheater tubes. The distillate condensed in the preheater (d2 + d2) is carried with the vapor formed by boiling D2 into the tubes of the third effect. Although the vapors formed by evaporation and flashing are drawn separately in the flow diagram to show the process, they flow from the evaporator and the flashing box to the feed heater in the same line. The processes that take place in the second effect are repeated in each effect all the way down to the last. Fig. 2 shows the different processes that take place inside effect number (i). It is worth mentioning that the amount of steam generated by evaporation in each effect is less than the amount generated in the previous effect. This is due to the increase in the specific latent heat of vaporization with the decrease in the effect temperature. Consequently, the amount of vapor generated in an evaporator by boiling is less than the amount of condensing steam used for heating in the following evaporator. The unevaporated brine flowing into the last effect reaches its final concentration X n by eva-

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Figure 2. Different processes in effect (i).

porating more vapors. The remaining brine M b is rejected to the sea. The vapor formed by boiling and flashing in the last effect (Dn + d n) and in the end flashing box dn passes to the bottom condenser. The condenser and the brine heaters must be provided with good vents, first for purging during start-up and then for removing noncondensable gases, which may have been introduced with the feed or drawn in through leaks to the system. The presence of the noncondensable gases not only impedes the heat transfer process but also reduces the temperature at which steam condenses at the given pressure. This occurs partially because of the reduced partial pressure of vapor in a film of poorly conducting gas at the interface. To help conserve steam economy venting is usually cascaded from the steam chest of one preheater to another. The effects operate above atmospheric pressure are usually vented to the atmosphere. The noncondensable gases are always saturated with vapor. The vent for the last condenser must be connected to vacuum-producing equipment to compress the noncondensable gases to the atmosphere. This is usually a steam jet ejector if high-pressure steam is available. Steam jet ejectors are relatively inexpensive but also quite inefficient. Since the vacuum is maintained on the last effect, the unevaporated brine flows by itself from effect to effect and only a blow down pump is required in the last effect. It is interesting to note that the MSF process, the most frequently encountered in standard desalination practice, is a special case of the MEE system. This occurs when the entire vapor formed in the effects is needed to preheat the feed in the preheaters and none is available for the evaporator tubes. In this case, the brine heater, distillate collecting trays, and the heat rejection section in MSF are replaced by the first effect, flashing boxes, and bottom condenser in the MEE process.

3 System Analysis

mass of fresh product water or the thermal performance ratio PR, the required specific heat transfer surface area sA, the temperature profile in various effects Ti, and the amount of cooling water flowing to the condenser of the last effect Mcw. The analysis of MEE systems is based on developing a steady state mass and heat balances coupled with the heat transfer rate equations for each individual effect and con joining them with the ratio between the mass of feed to that of product fresh water. In most cases, the number of equations which can be developed are equal to the number of unknown variables. The dry saturated or very slightly superheated steam admitted into the first evaporator is used to increase the temperature of the feed brine M f from the inlet temperature t2 to the boiling temperature T1, supply the latent heat required to evaporate a specified mass of vapor D1, and account for heat losses to the surroundings q. This is (1) Where Cp is the specific heat at constant pressure of the brine and l is the latent heat of evaporation. The specific heat depends on water temperature and salinity, while the latent heat relies only on the boiling temperature. The generated vapor has a saturation temperature Tv1 corresponding to the pressure in the evaporator vapor space. This temperature is less than the boiling temperature T1 by the boiling point elevation (BPE)1; or (2) The boiling point rise caused by the hydrostatic head DTh has a negligible effect in the horizontal falling film evaporators. The boiling point elevation BPE at a given pressure is the increase in the boiling temperature due to the salts dissolved in the water. The boiling point elevation, BPE, is calculated from the following empirical formula. (3) with (3a)

Where T is the temperature in °C and X is the salt concentration in ppm. The above equation is valid over the following ranges: 20000 < X < 160000 ppm, 20 < T < 180 °C. The dimensions of the evaporator heat transfer surface area Ae is obtained from the amount of transferred heat Qe, the overall heat transfer coefficient Ue, and the temperature difference of condensing steam T s and the boiling brine. This is

The main data usually required for the analysis of the MEE system are the amount of steam consumed per unit Chem. Eng. Technol. 21 (1998) 5


(4)

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The effects of steam superheating and condensate subcooling have negligible roles on the heat transfer process in the evaporators of the MEE system. The most critical step in determining the heat transfer area is the settlement of the overall heat-transfer coefficient U. The overall heat transfer coefficient based on the outside surface area Uo is related to the individual thermal resistance by the following expression.

(5)

Where h is the heat transfer coefficient, Rf is the fouling resistance, kw is the thermal conductivity of tube material, and r is the radius. The subscripts i and o refer to the inner and outer tube surface, respectively. The evaporator heat transfer surface area Ae is usually, but not always, taken as that in contact with the boiling liquid, whether on the inside or the outside of the tubes. Han and Fletcher [12] developed the following experimental correlation to calculate the boiling heat transfer coefficient ho for thin water film flowing over the outside of smooth horizontal tubes,

(6)

In the above equation Re and Pr are Reynolds and Prandtl numbers, respectively, q² is the heat flux, m is the viscosity, r is the density, and k is the thermal conductivity of the fluid. The above correlation is valid over the following ranges: 770 £ Re £ 7000, 1.3 £ Pr £ 3.6, 30 £ q² £ 80 kW/m2, and 49 £ T £ 127 °C. The maximum deviation for the equation is ± 10%. There are a wealth of corrections in the literature that can be used to calculate the heat transfer coefficient of condensation inside a horizontal tube for a particular flow pattern. However, the correlations, which can be used for all flow patterns, are limited. Perhaps the most verified predictive general technique available for all flow regimes in horizontal tubes is the following correlation of Shah [13]:

Where hl is the heat transfer coefficient, when all the flowing mass is liquid, and is calculated by the well-known Dittus-Bolter equation, (10) The above correlation is valid over the following ranges: 2.8 £ di £ 40 mm, 21 £ TV £ 355 °C, 0 £ w £ 1, 0.158 £ q £ 16000 kW/m2, 11 £ G £ 4000 kg/m2 s, 0.7 £ P £ 1 bar, 0.0019 £ Pr £ 0.82, 350 £ Re £ 100000. The average heat transfer coefficient is obtained by linear interpolation between the values of local heat transfer coefficient hi at the values of w ranging from 0 to 1. Proper venting of the evaporators reduces significantly the impairing effects of the noncondensable gases on the condensation heat transfer coefficient. Continuous withdrawal of gases prevents their accumulation and minimizes their effect on the heat transfer coefficient. A decrease of less than 5% occurs in the heat transfer coefficient for a gas concentration of 10% in the vent stream. Standiford [14] modeled the effect of noncondensable gases as an additional fouling resistance, with a value of 6.5 ´ 10 ±5 (m2 °C/W), which is then multiplied by the volume percentage of the gases. In water desalination plants, the volumetric concentration of noncondensable gases is about 4% [15]. Boiling and flashing mechanisms form the vapor in the second effect. Boiling takes place over the outer surface of the heating surface. Flashing or free boiling occurs within the liquid bulk. The mass of vapor generated by boiling is calculated from (11) The amount of vapor flashed off from the brine flowing to the second effect d 2 is estimated from (12) Where T2© is the temperature to which the brine (Mf ±D1) cools down as it flows to the second effect. This temperature is higher than the boiling temperature by the nonequilibrium allowance (NEA¢)2. That is (13)

(7) The parameter Z is defined as:

(8)

The nonequilibrium allowance is a measure for the efficiency of the flashing process. Miyatake, et al. [16] developed the following equation to correlate data obtained from flash evaporation experiments in a pool of pure water, which simulates to the flashing processes inside the evaporators and the flashing boxes,

Where w is the vapor mass fraction. The local superficial heat transfer coefficient hf is calculated from (9) 442


(14) with

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(15) and (16)

Where Z is the length of the pipe, di is the pipe inside diameter, and Mv is the vapor mass flow rate. The pressure drop during the vapor condensation inside the evaporator tubes is the sum of the frictional DPr, gravitational DPg, and acceleration DPa components. That is

On the other hand, the mass of vapor formed by flashing in the flashing box of the second effect d 2 is given by

(17) with (18) The condensation temperature of vapor inside the tube bundle of the second effect T c1 is less than the boiling temperature in the first effect T1 by the boiling point elevation (BPE)1 and the saturation temperature depressions associated with the pressure loss during the vapor flow in the demister (DTm)1, vapor transmission lines (DTt)1 and vapor condensation inside the horizontal tubes (DTc)1. Thus,

(23) The two terms on the right hand side of Eq. (23) have opposite signs. The first gives a fall in pressure due to wall friction, while the second represents a rise in pressure because of the pressure recovery from the flow deceleration and the gravitational force. For the condensation inside horizontal tubes, the gravitational component of the pressure drop DPg is equal to zero. However, it is usual to design the condenser with a small angle of inclination such that the condensate tends to run out of the end of the tubes at the opposite end to the steam inlet. This makes the flow much more stable than if the tubes are horizontal. It also improves the efficiency of the venting system [17]. This component of pressure drop is estimated from this expression: (24)

(19) In general, the pressure loss during the vapor flow through a wire mesh pad, which is widely used as the mist eliminator in water desalination industry, is relatively small because of the high void fraction of these pads. Losses in the mist separator are about 10 cm of water for 0.15 m. For the dry steam (free of any entrained droplets), the pressure loss through the mesh pad is given by

Where a is the vapor phase void fraction, Z is the pipe length, and y is the inclination angle. There are many correlations for the void fraction a. The one suggested most frequently in the literature for condensation in tube is by Zivi [18].

(25) (20)

Where V is the vapor superficial velocity (m/s), a is the specific area per unit volume (approximately = 85±115 m2/ m3), rv is the vapor density, e is the bed void fraction (varied from 0.97 to 0.99), Lm is the mesh pad thickness, and f is the friction factor. The value of f depends mainly on the extent of the modified Reynolds number as follows

(21) The pressure fall due to the vapor flow in the steam line connecting the vapor space of the first effect and the condenser tubes of the second one can be calculated from the Unwin formula

The acceleration pressure drop is calculated from this formula

(26)

The subscripts (1) and (2) refer to the inlet and outlet conditions, respectively. The two-phase pressure losses due to friction (dPr/dZ) are generally expressed as a function of the corresponding single-phase pressure losses, which is multiplied by a correction factor f21. That is

(22)



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Friedel [19] developed the following correlation for calculating f21

(28)

(37)

with (38)

Where After rearrangement, (29) (39) (30)

(31)

(32)

The pressure of saturated vapor at T v1 is predicted from the steam table or from equation (A±1), which is obtained by fitting the steam table data. The vapor formed by flashing inside the evaporator and the flashing box (d2 + d2) is used to heat the feed water M f flowing inside the tubes of the feed heater. The heat balance around the feed heater yields:

(33) (40) Where f g and f l are the friction factors for the total mass flux flowing with vapor and liquids, respectively, G is the mass flux, m is the dynamic viscosity, and s is the surface tension. The density of the two phase mixture rTP is defined as

(34)

Hewitt [20] recommended the use of Friedel equation when the value of (ml/mv) is less than 1000. In the MEE system this ratio ranges from 65.12 at T = 315 K to 19.856 at T = 385 K. The frictional pressure drop term usually calculated in a stepwise manner. The tube is divided into a number of short lengths DZ over which the conditions change only moderately. On the other hand, assuming that the condensation process takes place completely inside the tubes for w1 = 0 and w2 = 1 yields (35) and (36)

The temperature depression or the vapor saturation temperature decrease (Tv1 ±Tc1 = DTt1), because of the pressure drop in the demister DPm, vapor transmission line DPt, and during condensation process DPc, can be calculated using the Clausius-Clapeyron equation as follows: 444


Where t2 and t3 are the outlet and inlet temperatures of the feed preheater respectively, l¢vc2 and l² vc2 are the latent heat of condensation at T¢c2 and T² c2, respectively, and Z2 is the feed heater thermal efficiency. This efficiency accounts for the heat loss to the surrounding and the vapor escape with the vented noncondensable gases. The condensation temperatures T¢c2 and T² c2 are calculated from the following equations: (41) and (42) Where DTm and DTc are the temperature losses corresponding to the pressure drop associated with the vapor flow through the demister pad and vapor condensation outside the tubes of the preheater. Eq. (20) predicts the pressure drop due to the vapor flow through the demister. On the other hand, the pressure drop due to the vapor flow over the preheater tubes can be calculated, at best, only roughly because changing velocity and flow pattern during condensation process [21]. This overall pressure drop associated with the vapor condensation process is the algebraic sum of pressure losses due to the vapor flow in the nozzles and headers, static pressure head, two phase friction-loss, and momentum change. The static head and baffle losses are insignificant in the condensers. The momentum change or flow slow down during condensation results in a pressure recovery [22]. The magnitude of this pressure recovery is high in vacuum operation. The pressure regain can approach or exceed the friction

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loss [23]. Since most effects in MEE plants operate at vacuum, it seems reasonable to assume that the pressure recovery due to flow slow down can compensate for the friction pressure drop component; therefore, the net pressure fall and consequently the saturation temperature depression in the condensation process can be neglected. The heat transfer between the condensing vapor and the sea water in the feed preheater of the second effect can be written in terms of an overall heat transfer coefficient Up, preheater heat transfer area Ap, and the logarithmic mean temperature difference LMTD, thus:

(48)

The correction factors C1 and C2 consider the influence of the condensate dripping down and the presence of noncondensable gases, when they constitute less than 4% by weight, on the condensation heat transfer coefficient, respectively. The size of the coefficients C 1 and C2 are given by the following equations [26] (49)

(43) (50) Neglecting the small difference between T¢c2 and T² c2 , the (LMTD)2 is defined as:

(44)

Combining Eqs. (43) and (44) produces

(45)

Where NTU2 is the number of transfer units. The above equation can be solved for the outlet temperature of feed water to give:

Where Xnc is the percentage weight of the noncondensable gases and N is the number of tube rows in the vertical direction inside the condenser. The value of N depends on the total number of tubes Nt, tube arrangement pitch Pt, number of tube passes, and nozzle diameter. It is customary practice to arrange the tubes in the feed heaters with a square pitch pattern to provide adequate mechanical cleaning for the outer surface of the tubes. In this arrangements each four tubes occupy an area of (4 Pt 2) and the number of tubes in the vertical direction is 2. Thus, the total number of tubes, which can be installed in a shell of diameter Ds and with a pitch of Pt, can be approximated by this equation: (51) The following relation determines the number of tubes in the vertical direction N to the shell diameter and pitch:

(46) (52) The term (T¢c2 ± t2) is the preheater terminal temperature difference, and its value has a strong impact on the preheater heat transfer area. Eq. (4) can be used to relate the overall heat transfer coefficient Up to the individual coefficients. The inside tube heat-transfer coefficient hi is calculated from the empirical formula developed by Wangnick [24] especially for desalination plants.

For tubes arranged in an equilateral triangular pitch, the following equation can be used (53) The total number of tubes in the feed heater is calculated by (54)

(47)

Where Xf is the salt concentration in ppm, T f is the film temperature, and di and do are the inside and outside tube diameters, respectively. Henning, et al. [25] developed the following equation to calculate the heat transfer coefficient during vapor condensation outside the tubes. Chem. Eng. Technol. 21 (1998) 5

Where Z is the tube length, do and di are the tube outside and inside diameters, respectively, and V is the feed water velocity. The value V is limited at the top end by erosion damage to the tube materials and excessive pumping costs and at the bottom end by higher fouling rates and the need to maintain high side heat transfer coefficients. It ranges, in thermal desalination units, between 1.3±2.2 m/s. Differences of the second effect and other effects, i.e., effect number i are the brine flow rate to the second effect is (Mf ±D1) while it is


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(63)

for stage number (i) and the mass flow rate of distillate entering the flashing box of the second effect is D1 while it is

The heat transfer area for the feed heater

(64)

for effect number i. Taking these differences into consideration and following the same procedure presented in the previous sections, the following equations can be developed for effect number i. The mass of vapor formed by evaporation D i is (55) The amount of vapor flashed off from the unevaporated brine di is

(56)

The outlet temperature of feed water flowing inside the feed preheater tubes is (65) There are two basic distinctions between the feed preheaters of any effect and the last effect condenser. The first one is that the mass of vapor condensed in the shell side is not only the vapor formed by flashing inside the last evaporator and flashing box (dn + n), but also the vapor formed by boiling Di. The other difference is that the mass of water flowing inside the tubes of the last condenser is the feed water plus the cooling water (Mcw +Mf ). Accordingly, the following relationships can be developed for the last effect condenser.

with (57)

(66)

and

Themassofvaporformedbyflashingintheflashingboxd i is

Where Tcw is the sea water temperature and Mcw is the mass flow rate of cooling water. Arranging the above two equations and substituting the value of (LMTD) cw from Eq. (44) produces

(59)

(67)

(58)

and with

(68) (60)

and

On the other hand, the overall mass balances around the plant assuming that the product fresh water is free of salt (Xd = 0) gives

(61) The concentration of salt in the effect is

(69) and (70)

(62)

The heat transfer surface area is 446


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(71) Where Md is the total mass of distillate formed by boiling and flashing in all effects and flashing box. Thus: (72) The mass of heating steam Ms is calculated from Eq. (1). The exercise of the basic design requirement of constant surface area for the preheater and the evaporator in all effects produces (73) and (74)

4 Computational Algorithm The model developed in the preceding section is composed of a set of highly nonlinear equations. Thus, the use of any numerical procedure to solve them such as the wellknown Newton-Raphson, TDM, and like methods is tedious, because it requires the linearization and/or differentiation a high number of nonlinear relationships. The modified fixed point iteration procedure developed by El-Dessouky and Bingulac [27] is a simple, but yet powerful and convergent algorithm. According to this technique, the whole algorithm consists of 10 calculation blocks denoted by B through B 10 and 6 logical blocks expressed by L1 through L6 as shown in Fig. 3. The algorithm is implemented using the L-A-S Computer Aided Language [28]. To facilitate the understanding of the algorithm, calculations of some variables in the following flowchart are represented symbolically by corresponding functions (subroutines). These variables are l, m, rl, rv, and Pr; LMTD, Eq. (44); ho and hi for the preheater sections, Eqs. (47 and 48), these functions are called hop and hip, respectively; ho and hi for the evaporator sections, Eqs. (6 and 7), these functions are called hoe and hie, respectively; and Dtl the total thermodynamic losses. The first block B1 defines all necessary geometrical constants of the plant and design values as well as the initial guesses for subsequent iterative calculations. The most outer loop consisting of blocks B2 through B7 and L6 performs sequential effect-by-effect solution of equations describing the MEE system. The calculation process starts at the lower temperature side, i.e., effect n. The block B2 sets the initial guesses for the preheater in effect i. The loop consisting of the blocks B 3 and L1 solve iteratively the equations describing the preheater of effect i. This involves calculations of outlet temperature from the Chem. Eng. Technol. 21 (1998) 5

s

| |

s

| |

Figure 3. Computational Algorithm.


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preheater of effect i, i.e., t 2 = ti, given the temperature t3 = ti+1 at the inlet of the preheater of effect i. The loop consisting of blocks B 2 ± B5 and L3 iteratively adjusts the temperature T2 = T, at the outlet of the i th effect of the evaporator, so that the temperature difference Ti±1 ± Ti is equal to the difference Z(ti ± ti+1 ), as required by the heat balance. The blocks B 7, B8, and L5 constitute the loop where iterative solution of equations describing the i th effect of the evaporator. In other words, the quantity D satisfying Eqs. (11, 73, and 74) is calculated. Block B9 stores the results of the ith effect of the evaporator as well as sets the initial guesses for the next effect of both the preheater and evaporator. Finally, in the block B 10 overall plant effectiveness parameters are calculated and stored, which include the plant thermal performance PR, the specific heat transfer area sA, and the specific cooling water flow rate sMcw. Figure 4. The overall heat transfer coefficients in the evaporator and the con-

5 Results

denser.

The model developed and the suggested algorithm are used to obtain the data required from modeling the MEE desalination process. The parameters needed in process optimization and product water cost calculations are the plant thermal performance PR, the specific heat transfer surface area sA, and the specific flow rate of cooling water sM cw. These parameters are computed as a function of the most important design variables, namely, the top brine temperature T1 and the number of effects. The main assumptions upon which these relationships were generated are ± The sea water temperature Tcw and salinity Xcw are 25 °C and 42000 ppm. ± The temperature of rejected cooling water Tf is 35 °C. ± The boiling temperature in the last effect Tn is 40 °C. ± The sum of the heat transfer resistances due to the tube material, fouling inside the tube, and fouling outside the tube is 731 ´ 10±6 m2 °C/W. ± The thermal efficiency of the preheater Zi is 90%. ± The tubes outside diameter do is 31.75 mm and the inside diameter di is 19.75 mm. ± The brine velocity inside the preheater tubes V is 1.55 m/s. Fig. 4 shows the effect of the boiling temperature of the brine on the overall heat transfer coefficients in the evaporator and the feed preheater. The heat transfer coefficient is augmented with the boiling temperature; however, the heat transfer coefficient in the evaporator is always higher than that of the feed preheater. The heat transfer in the evaporator is associated with change of phases on the two sides of the tubes. In the preheater, steam condenses in the shell side and the feed water is heated by single phase forced convection inside the tubes. The increase of the heat transfer coefficient with the boiling temperature can be attributed to the effect of boiling temperature on the water physical properties, specially the dynamic viscosity. The viscosity of the water at 40 °C and 100 °C are 665 ´ 10±6 N s/m2 and 279 ´ 10±6

N s/m2. Moreover, the salt concentration in the forward feed MEE system increases with the boiling temperature decrease. The sea water viscosity is directly related to the salt concentration. The rate of heat transfer is impeded as the viscosity increases. The variation of the plant thermal performance ratio with both the top brine temperature and the number of effects is illustrated in Fig. 5. As can be seen, the performance ratio is nearly independent of the top brine temperature and is strongly related to the number of effects. The performance ratio is measured by the kg of distillate water produced per kg of heating steam condensed in the first effect. In n-effect evaporator system, there is approximately n kg of water produced per kg of steam supplied. In other words, the number

448


Figure 5. Effect of the top brine temperature and number of effects on the

plant thermal performance.

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of effects is directly allied to the number of reusing the heating steam in generating nearly the same amount of this steam. Fig. 6 depicts the impact of the top brine temperature and the number of effects on the specific heat transfer area. The specific heat transfer area or the heat transfer area required

Figure 7. Effect of top brine temperature and number of effects on the speci-

fic flow rate of the cooling water.

Figure 6. Effect of top brine temperature and number of effects on the speci-

fic heat transfer area.

per unit mass of product water increases by reducing the top brine temperature and raising the number of effects. The overall heat transfer coefficient and the available driving force for heat transfer affect the specific heat transfer area for heat transfer in each effect. The heat transfer coefficients in the evaporator and the feed preheater are improved with the boiling temperature as shown in Fig. 4. Furthermore, the total effective temperature difference between the heating steam and the bottom condenser is directly related to the top brine temperature. Note that in all calculations, the boiling temperature at the last effect is kept constant at 40 °C. On the other hand, the increase in number of effects is connected with a reduction in the temperature difference for heat transfer across the heat transfer area by a factor approximately equal to the number of effects. That is, the increase of required specific heat transfer area is the compensating disadvantage to the increase in thermal performance resulting from increasing the number of effects. Fig. 7 displays the effects of the top brine temperature and the number of effects on the specific flow rate of cooling water. The figure shows that the specific flow rate of cooling is nearly constant at different values of top brine temperature and decreases at a high rate as the number of effects goes up. The cooling water is required mainly to condense the vapor formed by boiling in the last effect. The total capacity of an MEE desalination system remains basically unchanged if the number of effects is varied and if the total temperature difference is kept constant. This means that the fraction of the vapor formed by boiling in the last effect diChem. Eng. Technol. 21 (1998) 5

minishes with respect to the total plant capacity as the number of effects increases. The result of this is the reduction of the thermal load of the condenser and consequently the required cooling water flow rate per unit mass of fresh water produced. It is necessary to emphasis that the increase of the top brine temperature from 60 °C to 100 °C decreases the required specific heat area tremendously. This behavior is more pronounced with a high number of effects. For example, the required specific heat transfer areas at 100 °C are 30.3% and 26.1% of that required at 60 °C when the number of effects are 6 and 12, respectively. The top brine temperature has minor effects on the plant performance ratio and the specific flow rate of cooling water.

6 Design Correlations The model predictions are used to develop the following correlations. These correlations are useful in the design and optimization of the MEE desalination plants.


(75)

(76)

(77)

(78)

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(79)

The standard deviations for the above equations are 1.76 , 2.03 , 2.4, 5.67, and 1.6%, respectively.

7 Conclusions The present study introduces an efficient and accurate mathematical model describing the Multiple Effect Evaporation desalination system. The following conclusions are made in the light of results and analysis performed in this study: ± The heat transfer coefficients in the evaporators and the preheaters augmented with boiling temperature. ± The heat transfer coefficients in the evaporator are always high when they are compared to that in the preheater at the same boiling temperature. ± The plant thermal performance ratio is nearly independent of the top brine temperature and strongly related to the number of effects. ± The specific heat transfer area increases by reducing the top brine temperature and raising the number of effects. ± The effect of top brine temperature on the specific heat transfer area is more pronounced at high number of effects. ± The specific flow rate of cooling water is nearly constant at different values of different top temperature and decreases at high rate as the number of effects is increased. Received: July 8, 1997 [CET 929]

Symbols Used a

[m2/m3]

A BPE Cp

[m2] [°C] [kJ/kg °C]

Cp

[kJ/kg °C]

d

[kg/s]

d

[kg/s]

D [kg/s] Ds [m] f [±] g [m/s2] G [kg/m2s] h [W/m2 °C] k [W/m °C] L [m] LMTD[°C]

450

Specific surface area per unit volume of the demister Heat transfer surface area Boiling point elevation Specific heat at constant pressure of sea water Specific heat at constant pressure of distillate water Mass of vapor formed by flashing inside the effects Mass of vapor formed by flashing in the flashing boxes Mass of vapor formed by boiling Shell inside diameter Friction factor gravitational acceleration Mass flux Heat transfer coefficient Thermal conductivity. Length Logarithmic mean temperature difference


M n N NT NTU NEA P Pt PR

[kg/s] [±] [±] [±] [±] [°C] [kPa] [m] [±]

DP

q q² Q R r Rf sA sMcw t

[Pa] [W] [W/m2] [W] [kJ/kg °C] [m] [m2 °C/W] [m2/(kg/s)] [m2/(kg/s)] [°C]

T

[°C]

T¢

[°C]

T²

[°C]

DT

[°C]

U

[W/m2 °C]

V X Z

[m/s] [ppm] [m]

Mass flow rate Total number of effects Number of rows of horizontal tubes Total number of tubes Number of transfer units Nonequilibrium allowance Pressure Tube pitch Thermal performance ratio, kg of distillate/kg of heating steam Pressure drop due to flow acceleration Heat loss to the surroundings Heat flux Heat transfer rate Universal gas constant Tube radius Thermal resistance of the fouling Specific heat transfer area Specific heat transfer area Temperature of sea water flowing inside the feed heaters Temperature of brine boiling in the effects Temperature of vapor formed by flashing inside the effects Temperature of vapor formed by flashing inside the flashing boxes Temperature decrease corresponding to pressure drop Overall heat transfer coefficient in the evaporator Velocity Salt concentration Pipeline length

Greek Symbols a w d e Z m n f r rTP s

[±] [±] [m] [±] [±] [kg/sm] [m2/s] [rad.] [kg/m3] [kg/m3] [N/m]

Vapor phase void fraction Vapor phase mass fraction Tube diameter Wire mesh void fraction Thermal efficiency Dynamic viscosity Kinematic viscosity Angle of inclination Mass density Density of the two phase mixture Surface tension

Dimensionless Numbers

Nu Pr Re We

[±] [±] [±] [±]

Nusselt number, hD/k Prandtl number, Cp m/k Reynolds number, rVD/m Weber number, rV2L/s

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1,2,...,n a b c cw d e f g i l m o p r s t v w

Effect number Acceleration component Reject brine Condensate or condenser Cooling sea water Product fresh water Evaporator Feed sea water Gravitational component Inside the tubes Liquid phase Demister Outside the tubes Preheater Frictional component Heating steam Transmission line component vapor phase Tube wall

[21] Sinnott, R.K., Coluson & Richardson's Chemical Engineering, Vol. 6, 2nd ed., Butterworth Heinemann, Oxford, 1996. [22] Marto, P.J., Heat Transfer in Condensers, in: Boilers, Evaporators and Condensers, (S. Kakac, Ed.), John Wiley, NY 1991. [23] Muller, A.C., Condensers, in: Hemisphere Handbook of Heat Exchanger Design, (G. F. Hewitt, Ed.) Hemisphere, NY 1991. [24] Wangnick, K., How Incorrectly Determined Physical and Constructional Properties in the Sea Water and Brine Regimes Influence the Design and Size of an MSF desalination plant ± stimulus for further thoughts, Proceedings of the IDA World Congress on Desalination and Water Science, Abu Dhabi, November, 1995, Vol. II, pp. 201-218.

[25] Hennig, S; Wangnick, K., Comparison of Different Equations for the Calculation of Heat Transfer Coefficients in MSF Multi-Stage Flash Evaporators, Proceedings of the IDA World Congress on Desalination and Water Sciences, Abu Dhabi, November, 1995, Vol. III, pp. 515-524. [26] Oak Ridge National Laboratory (ORNL), United States Department of the Interior, Research and Development Progress Report No. 315 , December 1967. [27] El-Dessouky, H.T.; Bingulac, S., Computer Methods in Applied Mechanics and Engineering 141 (1997) pp. 95-115. [28] Bingulac, S.; Van Landingham, H.F., Alogrithms for Computer Aided Design of Multivariable Control Systems, Marcel Dekker, NY 1993.

APPENDIX: Physical Properties of Water and Water Vapor 1 Vapor Pressure of Saturated Water

References [1] IDA, Int. Desalination Association, Gnarrenburg, Worldwide Desalting Plants Inventory, Wangnick, K., Report No. 13, December, 1995. [2] Darwish M.A.; El-Dessouky, H.T., Applied Thermal Engineering 18 (1996) pp. 523-537. [3] Minnich, K.; Tonner, J.; Neu, D., A Comparison of Heat Transfer Requirement and Evaporator Cost for MED-TC and MSF, Proceedings of the IDA World Congress on Desalination and Water Sciences, Abu Dhabi, November, 1995, Vol. III, pp. 233-257. [4] Morin, O.J., Desalination 93 (1993) pp. 69±109. [5] Hess, G.; Morin, O.J., Desalination 87 (1992) pp. 55±68. [6] Rautenbach, R., Desalination 93 (1993) pp. 1±13. [7] Rautenbach, R.; Widua, J.; Schafer, S., Reflections on Desalination Processes for the 21st Century, Proceedings of the IDA World Congress on Desalination and Water Sciences, Abu Dhabi, November, 1995, Vol. I, pp. 117±136. [8] Michels, T., Desalination 93 (1993) pp. 111±118. [9] El-Dessouky, H.T.; Assassa, G.R., Desalination 55 (1985) pp. 145±168. [10] Darwish, M.A.; El-Hadik, A.A., Desalination 60 (1986) pp. 251±265. [11] Hanbury, W.T., An Analytical Simulation of Multiple Effect Distillation Plant, Proceedings of the IDA World Congress on Desalination and Water Sciences, Abu Dhabi, November, 1995, Vol. IV, pp. 375±382. [12] Han, J.; Fletcher, L., Ind. Eng. Chem. Process Des. Dev. 24 (1985) pp. 570±597. [13] Shah, M.M., Heat Transfer, Pressure Drop, Visual Observations, Test Data for Ammonia Evaporating Inside Tubes, ASHRAE Trans., Vol. 84, Part 2, 1978. [14] Standiford, F.C., Evaporators and Evaporation, Encyclopedia of Chemical Processing and Design (Meketta, Ed.) Vol. 20, Marcel Dekker, Inc., NY 1984. [15] Office of Saline Water (OSW)±United States Department of the Interior, Distillation Digest, Research and Development Progress Report No. 538, March 1970. [16] Miyatake, O.; Murakami, K.; Kawata, Y.; Fujii, Heat Transfer Jpn. Res. 2 (1973) pp. 89±100. [17] Whalley, P.B., Boiling-Condensation and Gas-Liquid Flow, Oxford Science Publications 1987. [18] Zivi, S.M., J. of Heat Transfer 86 (1964) pp. 247±252. [19] Friedel, L., New Friction Pressure Drop Correlations for Upward, Horizontal and Downward Two-Phase Pipe Flow, Proceedings of the HTFS Symposium, Oxford 1979. [20] Hewitt, G.F., Gas-Liquid, in: Handbook of Multiphase Systems, Hemisphere Publishing, NY 1982. Chem. Eng. Technol. 21 (1998) 5

(A.1)

Where P is kPa and T is °C. 2 Saturation Temperature

(A.2) Where P is in kPa and T is in °C. 3 Specific Volume of Water Vapor

(A.3)

Where V is in m 3/kg and T is in °C. 4 Specific Volume of Water

(A.4) Where V is in m 3/kg and T is in °C. 5 Latent Heat

(A.5) In the above equation, T is the saturation temperature in °C and l is the latent heat in kJ/kg.


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