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Desalination 181 (2005) 43–59

Thermoeconomic analysis of a seawater reverse osmosis plant

Vicente Romero-Terneroa*, Lourdes García-Rodrígueza, Carlos Gómez-Camachob

aDpto. Física Fundamental y Experimental, Electrónica y Sistemas, Universidad de La Laguna,Avda. Astrofísico Francisco Sánchez s/n, 38206 La Laguna (Tenerife), Canary Islands, Spain

Tel. +34 (922) 318102; Fax: +34 (922) 318228; email: [email protected]. bDpto. Ingeniería Energética y Mecánica de Fluidos, Universidad de Sevilla, E.S.I.,

Camino de los Descubrimientos s/n, 41092 Sevilla, Spain

Received 9 September 2004; accepted 11 February 2005

Abstract

Thermoeconomy is a useful and powerful tool that combines thermodynamics and economics. It can evaluate howirreversibility and costs of any process affect the exergoeconomic cost of the product flows. The thermoeconomicanalysis of a seawater reverse osmosis desalination plant with a 21,000 m3/d nominal capacity located in Tenerife(Canary Islands, Spain) is given. This analysis extends the exergy analysis performed in a previous paper where furtherdetails about features of desalination facility, flow diagram, equipment purposes and flows of the process are widelyprovided. The main result indicates that economics predominates over the thermodynamics aspect; thus the influenceof the operational parameters on the unit cost of the final product is significantly limited. Reverse osmosis skid is themost influential equipment on both the thermodynamic and economic aspects. As well, pretreatment has a largeinfluence on the unit cost of the final product, essentially due to O&M costs. The unit cost of external consumptionand the annual real discount rate are the most influential parameters on the sensitivity analysis of the final product andthe high-pressure pump efficiency the most important of the operational ones; conversely, membrane replacement isthe least important among the parameters analysed.

Keywords: Thermoeconomic analysis; Reverse osmosis plant

1. Introduction

This paper deals with a thermoeconomic anal-ysis of the Santa Cruz de Tenerife desalinationplant (a seawater reverse osmosis (SWRO) plantlocated at Santa Cruz de Tenerife, Tenerife,

*Corresponding author.

Canary Islands, Spain). For further informationabout this analysis see Romero-Ternero [1]. Someof latest references regarding thermoeconomy anddesalination processes have been reported inGarcía-Rodríguez et al. [2–4], Uche et al. [5,6]and El-Sayed [7,8].

Thermoeconomy is based on the thermody-namic potential exergy, which takes into account

V. Romero-Ternero et al. / Desalination 181 (2005) 43–5944

the energy as well as its potential use (quality).Thermoeconomic analysis provides valuableinformation about the influence of the efficiencyand cost of equipment on the efficiency of theglobal plant and the cost of the product. There-fore, this thermoeconomic analysis can identifywhere the major chances of improvements are inthe production process. In particular, the metho-dology of Valero and Lozano [9] has beenconsidered for this thermoeconomics analysis.

Previously, a comprehensive exergy analysisof the Santa Cruz de Tenerife desalination plantwas performed by Romero-Ternero et al. [10]where the main features, diagram flow, equip-ment purposes and flows of desalination facility,as well as a fuel product losses definition foranalysis were given in great detail. Thus, both theexergetic and the thermoeconomics analysis pro-vide an important overview of the performance ofthe Santa Cruz de Tenerife desalination plant.

2. Thermoeconomic analysis

The effects of irreversibility and fixed costs onthe exergoeconomic cost of the products wereevaluated. Details about fixed costs, thermoeco-nomics fundamentals and economic settings aregiven for the Santa Cruz desalination facility.

Fixed costs represent the sum of all those costsnot included as exergy terms in the flow chart(given by Fig. 1 in this case). Thus, fixed costsconsist of two main groups of costs: investmentand O&M. For the Santa Cruz de Tenerife desali-nation facility, O&M costs include properoperational and maintenance, spare parts, mem-brane replacement and auxiliary consumptionexpenditures. Auxiliary consumption representsall external consumption not included in the flowchart: chemical dosing, membrane cleaning, regu-lation and control, blowdown pumping, lightingand other minor consummables.

Fig. 1. Flow chart for the analysis of the Santa Cruz de Tenerife desalination plant.

V. Romero-Ternero et al. / Desalination 181 (2005) 43–59 45

2.1. Thermoeconomics fundamentals

The thermoeconomic analysis is based on thefollowing items:C For any flow, economic cost per unit of

exergy (unit exergoeconomic cost) isassigned. Exergoeconomic cost is equal to theunit exergoeconomic cost multiplied by theexergy rate.

C For any flow from the environment, externalvaluation of the unit exergoeconomic cost isperformed. For our system, this involvesseawater (free) and external consumption.

C For any flow without later usefulness (losses),zero unit exergoeconomic cost is assigned.This involves blowdown.

C For any equipment, fuel–product balance ofexergoeconomic cost is performed. In thisbalance, the sum of the exergoeconomic costsof the products (outlet useful flows) is equal tothe sum of the exergoeconomic costs of thefuel components (exergy flows which contri-bute to generate the products) and the fixedcosts: Product cost (AP) = fuel cost (AF) +fixed costs (Z).

2.2. Economic setting

For economic calculations, a 20-year lifetimeand a 5% real discount rate are considered. Thisdiscounting reflects the time value of money oncethe effect of inflation is removed (a real discountrate can be approximated by subtracting expectedor actual inflation from a nominal interest rate).Discounting is performed with respect to a basisyear, namely the previous year to production on-set. It is assumed that building of the desalinationplant is done in this basis year. Taxes, amorti-sation and salvage value are not taken intoaccount.

Discounting affects all the terms of the fuel–product balance. As a result, the unit exergo-economic cost of the product (cP) is given byEq. (1). It is determined by the unit costs (cF) and

exergy rates (ExF) of the fuel components, the rateof discounted fixed costs (X) and the exergy rateof the product (ExP). The rate of discounted fixedcosts (X) takes into account discounted fixedcosts during the lifetime of the desalinationfacility (Zn), availability (A) and discount factor(tr).

(1)

2.3. Investment costs

According to official figures [11], the totalinvestment cost of the SWRO plant is about

24.6 million. In accordance with specific costsof this type of plant [12,13], it is supposed that25% of the investment costs are due to freshwater distribution (additional, significant pipingand civil works were necessary to interconnectthe desalination facility and the municipal storagetanks). The remaining 75% distribution (see[12–16]) is shown in Fig. 2.

Civil works, piping and valves, instrumen-tation and control, electrical equipment and“other” represents 40% of the total investmentcosts without fresh water distribution (30% if the

Fig. 2. Distribution of the total investment cost of theSanta Cruz de Tenerife desalination plant (withoutdistribution).


Fig. 3. Investment cost (103 ) of the SantaCruz de Tenerife desalination plant byequipment. 1 seawater pumping, 2 pretreat-ment, 3 high-pressure pump, 4 regulationvalve, 5 reverse osmosis skid, 6 Peltonturbine, 7 posttreatment, 8 product pumping,9 distribution.

latter is included). These costs do not belong toany of the equipment of the flow chart of Fig. 1,and thus they will be shared among them, withtwo exceptions: the regulation valve, which has anegligible investment cost, and distribution. Thus,these shared costs contribute 4.3% per equipment.Besides that, half of the civil works is assigned toseawater pumping (70%) and posttreatment(30%) equipment. Finally, shared, own and totalinvestment costs for all equipment are shown inFig. 3.

It can be seen that reverse osmosis skid (19%)and distribution are the main contributions to thetotal investment costs. Seawater pumping, pre-treatment and high-pressure pump investmentcosts are about a 12% each. The Pelton turbine is7.5%, posttreatment and pumping product areabout 6% each, representing the smaller contri-butions (and this is the only equipment in whichthe contribution of the shared investment costs islarger than the contribution of their own invest-ment costs).

Distribution of investment costs amongmechanical equipment is based on its consump-tion ratio (5:2:1 for high-pressure pump, Peltonturbine, seawater and product pumping) [10] andcost data [17,18]. Therefore, 55% of the mechani-cal equipment investment cost is assigned to thehigh-pressure pump, 22.5% to the Pelton turbineand the remaining 22.5% to seawater and productpumping (half for each).

2.4. O&M costsThe costs needed for operation and main-

tenance (O&M) were analysed. Membrane re-placement costs are also included in O&M costs,since an annual membrane replacement rate isassumed.

Assumptions for O&M costs are shown inTable 1, itemized by equipment. With respect toshared costs, the percentages of investment coststhat have been considered for the calculation are:

Equipment: 20.25% (piping and valves,instrumentation and control and electrical equip-ment);C Building: 7.5% (half of civil works);C Insurance: 57.8% (all the investments costs

except for civil works, distribution and“other”).

The calculations for labour and insurance repre-sent about two-thirds of the O&M shared costs;the remaining one-third corresponds to equipmentand auxiliary consumption; building has a smallcontribution.

Mechanical equipment O&M affects seawaterand product pumping, the high-pressure pumpand the Pelton turbine (respectively, 1, 8, 3 and6). The percentage applied to mechanical equip-ment O&M costs varies in the literature from 2%[19] to 4% [12]. Specifically, it has been assumedthe latter, which represents a more expensive,preventive maintenance but consequently a betterperformance.


Fig. 4. Discounted O&M costs (103 ) of theSanta Cruz de Tenerife desalination plantover a lifetime (20 years with a real annualdiscount rate of 5%) itemized by equipment.

Table 1O&M cost assumptions (in ) itemized by equipment for the Santa Cruz de Tenerife desalination plant

1 Seawater pumping Mechanical equipments O&M: 4% of investment [12]Intake O&M: 1 % of investment

2 Pretreatment Chemicals: 3 c/m3 a [19]Cartridge filters replacement: 0.8 c/m3 [19]

3 High-pressure pump Mechanical equipment O&M: 4% of investment [12]5 Reverse osmosis skid Annual replacement rate: 8% [12,15,16,19], 780/membraneb [19]

O&M: 1% of investment6 Pelton turbine Mechanical equipment O&M: 4% of investment [12]7 Posttreatment Chemicals: 0.7 c/m3 [19]8 Product pumping Mechanical equipment O&M: 4% of investment [12]

Shared costs Equipment O&M: 2% of investmentBuilding O&M: 1% of investmentLabour: 25,000/worker/year [19] × 11 workers [12,19,20]Insurance: 2% of total equipment investmentc

Auxiliary consumption: 0.5 kWh/m3 [20] at 6 c/kWh

aPretreatment was designed with a specific cost of 5.5 c/m3; however, the high quality of seawater made a more soft,inexpensive actual pretreatment possible.bIn acceptable accordance with the literature [17,21,22].cWithout civil works, distribution and “other” costs.

Calculations establish total annual O&M costsclose to 1,557,000 (6.3% of the total invest-ment), 58% due to shared costs. The discountedO&M costs rise approximately to 19,400,000over the desalination facility’s lifetime. The dis-tribution by equipment is shown in Fig. 4.

Pretreatment and reverse osmosis are the mainexpensive equipment (and the only ones where

the contribution of their own O&M costs arehigher than shared O&M costs). Pretreatmentexhibits the highest O&M cost (27%) and reverseosmosis skid contributes 18% of the total. Theremaining equipment is about 9–14%. The regu-lation valve has negligible O&M costs. Distri-bution O&M costs were not considered aresponsibility of the desalination facility.


Fig. 5. Discounted fixed costs (103 ) of theSanta Cruz de Tenerife desalination plantover a lifetime (20 years with annual realdiscount rate of 5%), itemized by equipment.

2.5. Fixed costs

Fixed costs involve both investment andO&M. The sum of the discounted total fixed costsrises approximately to 44,000,000 over thedesalination facility’s lifetime. Distribution byequipment is shown in Fig. 5.

Seawater pumping (1), high-pressure pump (3)and reverse osmosis skid (5) have higher invest-ment than O&M costs. Pretreatment and reverseosmosis skid are the most important contri-butions, 18% each. The contribution of theprevious stages, namely seawater pumping andpretreatment, to the total fixed costs rise to 29%;the core stages, i.e., high-pressure pump, reverseosmosis skid and Pelton turbine, contribute 41%;and the final stages 30% (about half, due todistribution).

Shared fixed costs represent 43% of the total,17% investment and 26% O&M costs. Therefore,shared fixed costs have a contribution of 6% perpiece of equipment, which represents one-third ofthe reverse osmosis skid or pretreatment fixedcosts. The distribution of own fixed costs byequipment is shown in Table 2, with a contri-bution of investment and O&M costs of 25% and18%, respectively. Consequently, investment andO&M costs are balanced if distribution is notconsidered: 49–51% (56–44% if distribution isincluded).

Finally, the rate of discounted fixed costs forequipment is presented in Fig. 6 (with a total of

Table 2Contribution of the own fixed costs of equipment to thetotal fixed costs of the Santa Cruz de Tenerife desali-nation plant

Equipment Investment (%) O&M (%)

1: Seawater pumping 3.9 0.82: Pretreatment 4.2 8.23: High pressure pump 4.6 2.35: Reverse osmosis skid 8.4 4.16: Pelton turbine 1.9 0.97: Posttreatment 1.3 1.58: Product pumping 0.9 0.5Total 25.2 18.3

12.4 c/s). These values are needed to calculate thediscounted exergoeconomic cost of the productsgenerated by the equipment [see Eq. (1)]: 90%availability of the desalination plant, 5% annualreal discount rate and 20-year lifetime areassumed.

2.6. Exergoeconomic cost of the flows

Once fixed costs have been calculated, Eq. (1)provides the discounted unit exergoeconomic costor concise unit cost (c/MJ). For any stream, therate of discounted exergoeconomic cost (c/s), orbrief cost, is given by the product of its unitexergoeconomic cost and its exergy rate (kW).


Fig. 6. Rate of discounted fixed costs (c /s) of the Santa Cruz de Tenerife desalination plant (90% availability, 5% discountrate and 20-year lifetime) itemized by equipment.

Fig. 7. Exergoeconomic cost (c /s) of the flows of the Santa Cruz de Tenerife desalination plant. 10 seawater, 21 pumpedseawater, 32 feed (pretreated seawater), 43 high-pressure feed, 54 high-pressure feed to skid, 65 high-pressure blowdown,06 blowdown, 75 product, 87 posttreated product, 98 pumped product, 09 final product, W10 seawater pumping;W30 external consumption of high-pressure pump, W36 Pelton turbine recovery, W80 product pumping.

For equipment, this cost reflects the influence ofirreversibility (related to the thermo-dynamicperformance of the process inside the equipment)and fixed costs in the generation of the products(useful outlet flows).

The cost of the flows is shown in Fig. 7.Seawater (10) has zero cost (no process is neededto generate it). Blowdown (06) has zero cost aswell because it is a useless outlet of the globalprocess. The unit cost of external consumption isimposed by the market price (1.67 c/MJ or6 c/kWh).

The highest cost is for high-pressure feed flow(43), with a value of 19.6 c/s (high-pressure feedto skid (54) has the same value because the fixedcosts of the regulation valve are null). This result

is justified since the high-pressure pump has thehighest consumption of fuel (4362 kW), and thisconsumption has a mean unit cost of 4.12 c/MJ,which is approximately two and a half times moreexpensive than the external one. Moreover, abouthalf of the cost of the high-pressure feed flow isdue to energy recovery. As a consequence, ifenergy recovery would be removed, the meanunit cost of fuel would decrease to 2.53 c/MJ andthe cost of the high-pressure feed flow to 12.7 c/s.However, energy recovery is a suitable processsince it increases the performance of the globalprocess and reduces the cost of the final product.Finally, costs by stages (previous, core and finalstages) are shown in Fig. 8.


Fig. 8. Exergoeconomic cost diagram of the Santa Cruz de Tenerife desalination plant by stages.

Fig. 9. Unit exergoeconomic cost (c /MJ) of the flows of the Santa Cruz de Tenerife desalination plant.

As shown, the fuel–product increase is widelydominated by fixed costs in the previous and finalstages. In the core stages, the cost of the productis penalized by the blowdown with a 5% contri-bution (see Appendix B), given that the potentialuse of its chemical exergy rate with respect toseawater is wasted.

The unit cost of any flow is presented in Fig. 9(see appendix A). First of all, a remarkableincrease of the unit cost of the products involvingthe previous stages is shown. This increase isbased on the significant influence of the fixedcosts (29% of the total) but the small exergy gainassociated with the previous stages (mainly pre-treatment). Consequently, the equipment repre-sents the highest fuel–product increase of the unit

costs (with reverse osmosis skid) and moreoverthe unit cost of feed (14.8 c/MJ) is the mostexpensive one. As expected, the fuel–productincrease of the unit costs of the previous stages islargely dominated by fixed costs (higher than90%).

With regard to core stages, the influence offixed costs and thermodynamic performance arepractically balanced (about 50% each for wholecore stages). The mean unit cost of fuel (the sumof the cost divided by the sum of the exergy ratefor feed and high-pressure pump external con-sumption) is 3.07 c/MJ. Thus, the fuel–productincrease of the unit cost due to core stages is6.31 c/MJ, the difference with respect to the unitcost of product (9.38 c/MJ).


In core stages, a considerable reduction in unitcosts between the high-pressure feed (43) andfeed (32) is disclosed. This reduction is due to thehigher increase of exergy yields by the high-pressure pump with respect to the exergy destruc-tion of the process. The mean unit cost of the fuelof the high-pressure pump (feed, external con-sumption and energy recovery) is 4.12 c/MJ. Forthe high-pressure pump, the influence of the fixedcosts on the fuel–product increase of the unit cost(0.70 c/MJ) reaches 57%. The rise of the unit costof the high-pressure feed to skid (54) is exclu-sively due to the exergy destruction in theregulation valve, since negligible fixed costs areconsidered for this equipment.

For the reverse osmosis skid, the high-pres-sure feed to skid (54) and high-pressure blow-down (65) are the same unit cost (inlet and outletcomponents of a fuel must have the same exergo-economic unit cost), and consequently, ineffi-ciencies and fixed costs of the equipment areexclusively loaded on the product (75). Fixedcosts contribute 35% to the fuel–product increaseof the unit cost (4.39 c/MJ); therefore, thermo-dynamic performance dominates (exergy destruc-tion is 54% and losses 11%).

With reference to the Pelton turbine, the unitcost of energy recovery is 5.80 c/MJ. This isabout 3.5 times higher than the unit cost of exter-nal consumption. This increase is due to theinefficiencies and fixed costs of the high-pressurepump (seed of the hydraulic energy of high-pressure blowdown) and the Pelton turbine, alsoloaded on a stream with a lower exergy rate. Aspointed out previously, this result does not meana more expensive final product. In this way, aPelton turbine rate of discounted fixed costs/recovery exergy rate ratio lower than the unit costof external consumption is requisite to improvethe unit cost of the final product using energyrecovery. Consequently, for the desalination sys-tem analysed, energy recovery is economicallysuitable for a unit cost of external consumption

higher than 2.4 c/kWh (far enough from theactual 6 c/kWh).

With reference to final stages, the mean unitcost of the fuel is 7.87 c/MJ, and the fuel–product increase is 4.22 c/MJ. Fixed costs domi-nate with a fraction close to 60% (70% withoutdistribution). The pumped product (98) presentsa lower unit cost than the previous one becausethe cost associated with pump operation is lowerthan the generated exergy rate increase. The unitcost of the final product is 12.1 c/MJ and theglobal fuel–product increase is 10.4 c/MJ.

A summary of unit costs by stages is shown inFig. 10. As observed, the product cost ispenalized by blowdown (see also Fig. 8). The unitcost of blowdown is determined in accordancewith the balance of the desalination plant as awhole.

Finally, the cost per cubic meter (c/m3) for anymass flow is shown in Fig. 11. It can be seen thatthere are some significant differences with respectto unit exergoeconomic costs. In contrast with theunit exergoeconomic cost, feed (32) is not themore expensive flow because the high unitexergoeconomic cost is compensated for by lowspecific exergy. Similarly, since the high-pressurefeed flow (43) has a high specific exergy, its costis substantially increased. Another significantincrease takes place between high-pressure feedto skid (54) and product (75), the latter with acost of 58.5 c/m3. The cost of the final product(09) is 76.7 c/m3 (10% previous, 66% core and27% final stages).

2.7. Final considerations

In the analysis performed, the major influenceof the reverse osmosis skid equipment wasdisclosed. This equipment, with the highestexergy destruction [10], presents the highest fixedcosts as well (see Figs. 5 and 6).

Influence of exergy destruction (D) and fixedcosts (Z) by equipment on the unit cost increase


Fig. 10. Exergoeconomic unit cost diagram by stages of the Santa Cruz de Tenerife desalination plant.

Fig. 11. Cost (c /m3) of the mass flows of the Santa Cruz de Tenerife desalination plant.

Table 3Influence of exergy destruction (D) and fixed costs (Z) by equipment on the exergoeconomic unit cost increase of pumped(98) and final (09) product with respect to the exergoeconomic unit cost of global fuel (external consumption)

Equipment Pumped product Final product

D (%) Z (%) D + Z D (%) Z (%) D + Z

1: Seawater pumping 0.5 9.8 10.3 0.4 8.5 8.92: Pretreatment 0.5 16.5 17.0 0.4 14.4 14.83: High pressure pump 3.7 11.8 15.5 3.2 10.2 13.44: Regulation valve 1.7 0.0 1.7 1.5 0.0 1.55: Reverse osmosis skid 8.6 16.8 25.4 7.4 14.6 22.06: Pelton turbine 5.9 8.1 13.9 5.1 7.0 12.17: Posttreatment 1.0 8.0 9.0 0.9 6.9 7.88: Product pumping 0.4 6.8 7.2 0.3 5.9 6.29: Distribution — — — 2.3 11.0 13.3Total 22.2 77.8 100 21.5 78.5 100

of pumped (98) and final (09) product withrespect to unit cost of global fuel (external con-sumption) is shown in Table 3. As shown, thereis a wide influence of fixed costs, close to 80%.

This is an essential result since prospectiveimprovements in thermodynamic performanceare clearly restricted by the economics of theprocess.


Reverse osmosis skid leads with about one-quarter of the total increase. About half is attri-buted to four items (pretreatment, high-pressurepump, Pelton turbine and distribution), with anindividual contribution in the range of 12–15%.The remaining one-quarter is due to seawater andproduct pumping, posttreatment and the regula-tion valve. Similar results are obtained for thepumped product flow.

With respect to the plant as a whole, thecontribution of global external consumption onthe unit cost of the final product is about 30%(23% high pressure pumping + 7% seawater andproduct pumping, half each); useless exergy ofblowdown and fixed costs contribute around 5%and 65%, respectively. The contribution of theannual real discount rate is about 14%, since theunit cost of the final product is reduced to65.8 c/m3 for r = 0%.

Finally, the influence of environmental para-meters on the unit costs is negligible for the SantaCruz de Tenerife desalination plant, with varia-tions less than 1%.

3. Sensitivity analysis

The main thermodynamic and economic para-meters of the desalination facility were changedto analyse how they affect the unit cost of thefinal product.

First, performance of mechanical equipment(seawater and product pumps, high-pressurepump and Pelton turbine) is considered. Alter-natively, for all this equipment, a performancereduction of 5% is analysed (i.e., with anefficiency decreasing from 85% to 80%). High-pressure pump performance, with a 2.5% in-crease, presents the most important sensitivity onthe unit cost of the final product. For the Peltonturbine a moderate 0.8% increase is achieved,despite that exergy destruction has a higher con-tribution on the unit cost increase of the finalproduct (see Table 3). Lastly, seawater and

product pump performance present a weakinfluence.

The availability of the desalination plant isanother operational parameter with a significantpotential influence on the unit cost of the finalproduct. The calculations indicate a 3.3% reduc-tion on the unit cost of the final product for anavailability increasing from 90% to 95%. Hence,its influence is slightly higher than that of high-pressure pump performance, but in a similar orderof magnitude.

With regard to the main economic parameters,the external consumption unit cost and annualdiscount rate are considered. For external con-sumption, a 1 c/kWh drop yields a reduction ofabout 6%. For the discount rate, the decreasefrom 5% to 4% provides a 3.3% drop (thus, thesame effect as a 5% increase on availability).Consequently, the unit cost of the final productpresents a higher sensitivity to economicparameters.

Finally, the influence of the most importantO&M parameters (chemicals for pretreatment,membrane replacement in reverse osmosis skid)is evaluated. The increase of the chemical costsfrom 3 c/m3 to 4 c/m3 provides a 1.7% reductionof unit cost of the final product. A lowersensitivity is obtained for membrane replacementsince only a 1% decrease is achieved when 5%annual membrane replacement cost and the costof 700 membranes are taken into account.

4. Conclusions4.1. Fixed costs

1. When distribution is not considered, invest-ment costs and discounted O&M costs—including replacement as well—along the lifetimeof the desalination plant with an annual discountrate of 5% and a lifetime of 20 years, contributeequally to fixed costs. A reduction of the annualdiscount rate or an increase of the lifetime wouldincrease the contribution due to discounted O&Mcosts. Additionally, it is important to point out


that half of the fixed costs without distribution areshared costs, thus representing a noteworthycontribution.

2. The highest fixed costs are located in thereverse osmosis skid and pretreatment equipmentwith a contribution slightly greater than one-thirdof the total fixed costs (about half for each one).The first represents the highest investment costand the second the highest O&M costs for equip-ment. This is the first evidence where majorimprovements on fixed costs may be made, andtherefore, any line of work designed to the reduc-tion of fixed costs relating to the pretreatment andmembrane cost is a suitable and realistic option.In this way, for example, it would be advisable tofit the pretreatment design to the intake seawaterquality to avoid unnecessary over-scale.

3. Core stages contribute only to 40% of thetotal fixed costs, in contrast to the 80% of thetotal exergy destruction [10]; therefore, it dis-closes a significant influence of the no-corestages on the fixed costs. While this happens, itseems reasonable to operate with high-perfor-mance mechanical equipment in the core stages,even though it represents an increase of theirfixed costs.

4.2. Exergoeconomic analysis

1. High-pressure feed mass flow has the high-est exergoeconomic cost, about half of which isdue to energy recovery by the Pelton turbine.Consequently, as a universal result, energy recov-ery always increases the exergoeconomic cost ofthe high-pressure feed, but conversely, it de-creases the exergoeconomic cost of the product inthe final stages. However, as a consequence of itshigh specific exergy, the exergoeconomic unitcost of the high-pressure feed mass flow isrelatively low.

2. Mass flows for previous stages present thehighest fuel–product increases of the exergo-economic unit cost, with an influence of the fixedcosts greater than 90%. Like this, the product

from previous stages (feed) exhibits the highestunit cost—a significant influence of fixed costsand low gain of exergy (while feed exergy repre-sents only 11% of the core fuel, feed exergo-economic cost means 51% of the core fuelexergoeconomic cost). In summary, previousstages have a significant influence on the exergo-economic analysis (supporting conclusion 4.1.2)but is weak on an exergetic one [10] with respectto the final product.

3. Core stages as a whole are characterised bya more balanced contribution between thermo-dynamic performance and fixed costs (contribu-tion of fixed costs is slightly lesser than 60%) onthe fuel–product increases of their exergo-economic unit costs. Similarly, reverse osmosisskid presents the lowest influence of fixed costs(35%) and a significant influence of exergydestruction (53%); the remaining 11% is due tolosses (blowdown). Hence, given that pressuredrop in membranes has a negligible effect onexergy destruction [10], any thermodynamicimprovement on the membrane performance (e.g.,development of membranes with similar permeatemass flow rate but operating with a lesserpressure), have an appreciable influence on theunit cost of the final product. Since the theoreticalminimum of specific consumption is about1 kWh/m3 for the actual recovery factor of aseawater desalination plant (40–45%) and theactual specific consumption range is close to3 kWh/m3, it seems reasonable to expect futureadvancement in this way, even though otherfactors like mechanical equipment performanceare involved in this specific consumptiondecrease.

4. Final stages without distribution present aninfluence of fixed costs near to 70% and lowerfuel–product increases of the exergoeconomicunit cost than previous stages. In view of thisresult and conclusion 4.2.2, it can be stated thatthe previous stages are a greater influence onthermoeconomic analysis and particularly on unitexergoeconomic cost of the final product.


5. There is a strong predominance of fixedcosts (79%) on the fuel–product increase of theexergoeconomic unit cost of the final productwith respect to global fuel (external consump-tion). Thus, improvements of the thermodynamicperformance of the process are clearly limited byfixed costs. In order to reach a reasonable influ-ence of thermodynamic performance, it is neces-sary to reach a notable reduction of these fixedcosts.

6. When influence of equipment on the fuel–product increase of the exergoeconomic unit costof the final product with respect to global fuel isconsidered, reverse osmosis skid contributesapproximately one-fourth of this increase; pre-treatment, the high-pressure pump, the Peltonturbine and distribution contribute about a half (inan individual range of 12–15%); and the remain-der is due to seawater and product pumping,regulation valve and posttreatment.

7. Core and previous stages contribute 55%and 27% (the latter almost exclusively due tofixed costs), respectively, on the fuel–productincrease of the exergoeconomic unit cost of thefinal product when distribution is not considered.

8. Results for the fuel–product increase of theexergoeconomic unit cost with respect to globalfuel are similar in magnitude when distribution isnot taken into account, and thus the main con-clusions can be applied to pumped product aswell.

9. Energy recovery is economically suitableonly when the external consumption unit costfrom the grid is higher than 8.6 c/MJ (2.4 c/kWh),far enough from the actual 6 c/kWh.

10. Exergoeconomic unit cost of the finalproduct is 12.1 c/MJ, 30% due to external con-sumption—23% high-pressure pump and 7% sea-water and product pumping (half each one)—68% to fixed costs and 4% to losses (blowdown).Finally, the cost per cubic meter is 76.7 c/m3.

4.3. Sensitivity analysis

1. The exergoeconomic unit cost of the finalproduct presents the highest sensitivity withrespect to external unit consumption cost and theannual real discount rate, parameters whoseinfluence is determined by market considerations.

2. The next greatest influences are due toavailability, high-pressure pump performance andchemical costs for pretreatment. The latter sup-ports some previous conclusions, but it can belimited by a possible drop in availability. Thesecond one indicates the possible advantages ofchoosing a high-performance pump even thoughit were more expensive.

3. From among the parameters analysed, thelower sensitivity corresponds to the Pelton tur-bine’s performance and membrane replacementcosts; and thus intensification of the pretreatmentdoes not seem beneficial for reducing only mem-brane replacement costs.

5. Recommendations

First, as a general recommendation, Con-clusion 4.2.5 indicates an overall reduction offixed costs without which the influence of equip-ment performance on the unit cost of final pro-duct would be rather limited. The correspondingtechnological and market tests must be performedboth on invest-ment and O&M costs as a result ofConclusion 4.1.1. About this general reduction,pretreatment is a principal focus (Conclusion4.2.7), and it would be suitable to find a higherbalance bits role in the process and the fixed costswhich its operation generates.

With regard to pretreatment, any intensi-fication of chemical treatment that only involvesimprovements on membrane replacement and noton availability would be unsuitable for theexergoeconomic unit cost of the final product,according to Conclusions 4.3.2 and 4.3.3. In


addition, this intensification would be opposed toconclusions 4.1.2, 4.2.6 and 4.2.7, which indicatehigh fixed costs and greater influence on theexergoeconomic unit cost of the final product forpretreatment. However, on the other hand, theinfluence of a possible reduction in the pretreat-ment level on availability must be analysed indetail. In summary, the optimisation of standardpretreatment or the integration of innovativetechniques—like other membrane processes—isentirely justified and clearly supported by reportsin the literature.

With reference to the Pelton turbine, perfor-mance increase is not a priority from the point ofview of the product cost according to Conclusion4.3.3. To improve the influence of the Peltonturbine performance on product cost, it is neces-sary to decrease the fixed costs of the no-corestages (Conclusion 4.1.3) or to increase the influ-ence of equipment performance in agreementwith the general recommendations. Conclusion4.2.9 indicates the cost-effective operation of thePelton turbine, since the unit cost of externalconsumption (6 c/kWh) is clearly separate fromprofitable energy recovery value (2.4 c/kWh).

The influence of reverse osmosis skid onproduct cost must be mainly focused on invest-ment cost: membrane technology must pointtowards a fixed cost reduction (Conclusion 4.1.2)without availability loss (Conclusion 4.3.2) andkeep or improve current operational features.According to Conclusion 4.3.3, the influence ofmembrane replacement on product cost wouldhave a less important order of magnitude.

Since fixed costs of the core stages are only40% of the total (Conclusion 4.1.3) and perfor-mance of high-pressure pump is the most influ-ential operational parameter (Conclusions 4.3.1and 4.3.2), it is reasonable to choose a high-quality pump like that selected for the Santa Cruzde Tenerife desalination plant, despite its highercost. However, possible reduction of fixed costs

for no-core stages would make a new analysisnecessary.

6. Symbols

A — Availability of the desalination plantc — Exergoeconomic unit cost or unit

cost, /kJEx — Exergy rate, kWn — Lifetime, yr — Annual real discount rate

tr — Discount factor (years) =

X — Rate of discounted fixed costs, /s)

=

Z — Fixed costs, Zn — Discounted fixed costs over a life-

time, Subscripts

F — FuelP — Product

Greek

A — Rate of discounted exergoeconomiccost or exergoeconomic cost, /s

Acknowledgements

This work was financially supported by theSpanish Ministerio de Ciencia y Tecnología(project SOLARDESAL REN 2000-0176-P4-04)and the Consejería de Educación, Cultura y De-portes of the Autonomous Government of theCanary Islands (project PI2001/012).

The authors thank the manager of the SantaCruz de Tenerife desalination plant, Mr. JorgeMotas Pérez, for his valuable technical adviceand especially for his friendly cooperation.


References

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Appendix A

Table A.1Exergoeconomic unit costs of flows from thermoeconomic balance

Flows Exergoeconomic unit cost

21 Pumped seawater

32 Feed (pretreated seawater)

43 High-pressure feed

54 High-pressure feed to skid

65 High-pressure blowdowna

75 Product b

W36 Energy recovery

06 Blowdowna

87 Posttreated product

98 Pumped product

09 Final product

aBy methodological considerations of Valero-Lozano thermoeconomic analysis.bTerm representing the waste of rejected brine chemical exergy rate, i.e., the waste of its potential use with respect toseawater (cW: unit cost of external consumption).c, exergoeconomic unit cost ( /kJ).Ex, exergy rate (kW).X, rate of discounted fixed costs ( /s).


Appendix BUnit cost of final product (plant as a whole)

From exergy and exergoeconomic balanceof the plant as a whole:

where c09 is the exergoeconomic unit cost of thefinal product ( /kJ), cW the unit cost of externalconsumption ( /kJ), ExD the rate of exergydestruction of the desalination plant as a whole(kW), ExD,k, rate of exergy destruction in equip-ment k (kW), Ex06, exergy rate of blowdown (kW),Ex09, exergy rate of final product (kW), X the rate

of discounted fixed costs of desalination plant asa whole ( /s) and Xk is the rate of discounted fixedcosts of equipment k ( /s).

Fig. B1. Contributions to unit cost of final product (plantas a whole): exergy destruction, fixed costs and potentialuse of rejected brine chemical exergy rate.

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