Design Optimization of a Solar-Powered Reverse Osmosis Desalination System for Small Communities

1 Copyright © 2013 by ASME

Proceedings of IDETC/CIE 2013 ASME International Design Engineering Technical Conferences

& Computers and Information in Engineering Conference August 4-7, 2013, Portland, Oregon, USA

DETC2013-12654

DESIGN OPTIMIZATION OF A SOLAR-POWERED REVERSE OSMOSIS DESALINATION SYSTEM FOR SMALL COMMUNITIES

Jihun Kim Graduate Student Research Assistant

Dept. of Mechanical Engineering University of Michigan, Ann Arbor, MI 48109-2102

[email protected]

Karim Hamza Senior Research Fellow


[email protected]

Mohamed El Morsi Associate Professor

Dept. of Mechanical Engineering American University in Cairo, Cairo, Egypt

[email protected]

Ashraf O. Nassef Professor

Dept. of Mechanical Engineering American University in Cairo, Cairo, Egypt

[email protected]

Sayed Metwalli Professor

Dept. of Mechanical Design and Production Cairo University, Cairo, Egypt [email protected]

Kazuhiro Saitou Professor


[email protected]

ABSTRACT Fresh water availability is essential for the economic

development in small communities in remote areas. In desert

climate, where naturally occurring fresh water is scarce,

seawater or brackish water from wells is often more abundant.

Since water desalination approaches are energy intensive, a

strong motivation exists for the design of cost-effective

desalination systems that utilize the abundant renewable energy

resource; solar energy. This paper presents an optimization

model of a solar-powered reverse osmosis (RO) desalination

system. RO systems rely on pumping salty water at high

pressure through semi-permeable membrane modules. Under

sufficient pressure, water molecules will flow through the

membranes, leaving salt ions behind, and are collected in a

fresh water stream. Since RO system are primarily powered via

electricity, the system model incorporates photovoltaic (PV)

panels, and battery storage for smoothing out fluctuations in

the PV power output, as well as allowing system operation for a

number of hours after sunset. Design variables include sizing of

the PV solar collectors, battery storage capacity, as well as the

sizing of the RO system membrane module and power elements.

The objective is to minimize the cost of unit volume produced

fresh water, subject to constraints on production capacity. A

genetic algorithm is used to generate and compare optimal

designs for two different locations near the Red Sea and Sinai.

INTRODUCTION Fresh water availability is a significant factor in economic

growth and development of various areas around the world,

especially in remote semi-isolated areas that have limited or no

grid power. While access to brackish or seawater is often not

difficult, reduction of the salinity level to healthy limits for

human, animal and plant consumption through desalination

often involves expensive and/or energy-intensive processes.

This provides a motivation for design and development of

desalination plants that run on renewable energy sources and

are cost-effective at the small and medium scale capacity.

Towards that goal, this paper presents an optimization model

for solar-powered water desalination via reverse osmosis (RO).

Reverse osmosis is a process where pressure is applied on

a water stream with high salinity content in a setting that drives

water molecules to flow through semi-permeable membranes

into a lower salinity stream, leaving the salt ions behind. As a

concept, RO was initially developed by Reid and Breton [1] at

the University of Florida in the late 1950s. However, until the

development of composite polyamide membranes, desalination

via RO was neither sufficiently robust nor energy-efficient [2].

RO membranes evolved over the years [3-6] until the spiral

wound configuration (Fig. 1) practically became the one solely

used in practice [6]. RO currently accounts for about 50% of

the worldwide desalination capacity [7].

mailto:[email protected]







Fig. 1: Spiral wound RO module (www.membranes.com)

Solar energy harvesting technologies may be categorized

into two broad categories based on the energy conversion

mechanic [8]: i) thermal and ii) photovoltaic (PV) processes.

Thermal processes rely on redirecting solar radiation to a

receiver that heats a working fluid, which may then be used for

heating purposes, or to drive a Sterling-engine or steam turbine

connected to a generator. Photovoltaic processes on the other

hand convert solar energy directly into DC electricity.

Commercial PV has less overall efficiency of solar energy

conversion and higher cost per kilowatt-hour than large-scale

thermal systems. However, for smaller scale systems, thermal-

based electric power generation from solar energy is all but

economically infeasible. Accordingly, the strongest interest in

the literature for powering RO desalination systems via solar

power, is via photovoltaic energy harvesting.

Among the seawater PV-RO systems, tested on

Mediterranean and MENA countries up to 2008, six were

without batteries and five had battery storage, as listed in the

literature survey by Ghermandi et al [9]. The main advantage of

using batteries is continuous operation of RO desalination by

smoothing the power generated from PV arrays. However, the

use of batteries is accompanied with higher capital and

maintenance costs, which increases the investment capital cost,

but can reduce the overall unit cost of fresh water by increasing

the productivity. Studies in the literature have also considered

variable production operation of RO systems powered by PV

arrays. Thomson et. al. [10] suggested that a RO system may

operate over a wide operating range of feed pressure and flow

rate and, thus, operate with time-dependent energy sources,

such as solar photovoltaic power. It was shown via both

simulation [11, 12] as well as experimental studies [13, 14] that

operating a PV powered RO desalination system without

batteries at all is technically feasible.

Relatively little effort seems to have been made towards

design optimization of the RO desalination system powered by

PV modules. In a recent study [15], a design optimization

method of the RO desalination system power-supplied by PV

arrays and wind generator (WG) modules was proposed by

using a genetic algorithm (GA). The design variables

considered included the number of the RO desalination units,

PV modules, WG modules, and batteries. Although the optimal

sizing problem of the RO desalination unit and energy sources

was appropriately addressed, operational parameters, such as

feed pressure and feed flow rate, of the RO desalination were

not taken into consideration.

In Gilau et. al [16], various power systems were designed

in order to minimize the energy consumptions for the operation

of a RO desalination unit, which was designed by testing

various configurations using the commercial software, ROSA.

Once a RO configuration was determined to meet the water

demand, the energy systems were designed. The selected

configurations of the PV arrays and RO desalination units were

sequentially designed however, so they may not necessarily be

optimally matched. In addition, the operating feed pressure and

feed flow rate were not part of the optimization.

Bourouni et. al. [17] carried out a design optimization

study of RO desalination systems coupled with several

renewable energy sources, such as solar PV and/or WG. In

regards to the RO desalination systems combined with PV

arrays, the two different systems, without and with batteries,

were optimally designed, and their costs were compared. In

order to satisfy the water demand of the village of Ksar

Ghilène, the configurations of the RO desalination system was

first determined, and then the PV systems were then designed

such that the constraints for each system are satisfied. For the

PV-RO without batteries, the volume of fresh water remained in

the tank was required to be positive through a year (continuous

water supply), and for the one with batteries, the battery charge

state was required to remain between its nominal and minimal

operation values. The investigation focused on comparing the

various combinations of the RO desalination system and

renewable energy sources and selecting an optimal coupling

among them rather than finding optimal designs for each

coupling. In addition, designing the RO desalination unit was

based on simple rules rather than a formal optimization

The paper starts with a motivation and a brief review of

relevant work in the literature. Section 2 presents the modeling

details of the PV powered RO system. Sections 3 and 4 then

present case studies and design optimization results for two

locations in the Red sea and Sinai areas. The paper then

concludes with a discussion of relevance of the results and

possible future extensions.

2. SYSTEM MODEL

2.1. Overview A schematic diagram of the considered photovoltaic-powered

RO desalination system is shown in Fig. 2. Main components

of the system that are modeled include:

1. Photovoltaic solar panels, along with the voltage regulation

circuits and alternator

2. Battery storage system to allow some hours of operation

after sunset

3. Rack of pressure vessels for RO membrane modules. All

vessels assumed in parallel connection with RO modules

serially connected within each vessel.

4. Hydraulic power elements, which include:

http://www.membranes.com/


a. High pressure pumps that deliver pressurized salty

water to the RO rack

b. Pressure exchanger on the exiting brine stream, which

raises the pressure of a portion of the inlet stream to

the pumping station

c. Booster pumps that adjust the pressure of the portion

of inlet stream that goes through the pressure

exchanger

d. Electric motors that drive the pumps

Fig. 2: Schematic diagram of photovoltaic-power reverse osmosis desalination system

Salty water is assumed to come from an intake equipped

with proper filtering. High pressure pumps deliver the salty

water at a desired/design pressure value to the RO rack of

pressure vessels. As the pressurized water flows through the

membrane modules, a portion passes through the membranes

and is collected into a low-pressure fresh water stream

(product), while the rest exits are brine. To prevent formation of

an extremely high salinity boundary layer on the surfaces of the

membranes, which can lead to membrane fouling, the salty

stream is maintained at highly turbulent flow state. As such, the

exiting brine stream is typically still at high pressure and flow

rate, which would constitute wasted energy if discharged. A

pressure exchanger (PX) device [18] is often included in RO

desalination systems, which captures a good portion of the

hydraulic energy in the exiting brine stream. Control systems

govern the start-up, shut-down and pressure-regulation of the

various streams. The modeling in this paper however does not

encompass the details of the control systems, intake/filtering

nor disposal of the discharged brine; mainly due to the fact that

these systems are well-documented off-shelf components and

their selection/operation is primarily a fixed cost (treated as an

overhead) that does not depend on the design of the RO system.

Since solar energy from photovoltaic panels is unavailable

after sunset, and can be highly variable throughout the day, an

off-grid system requires battery storage to maintain steady

operation. RO systems are typically require around 4 hours of

maintenance per day for back-washing the membrane modules,

changing defective modules and other repairs. During the

maintenance period, there is no production of fresh water, but

the power draw of the desalination plant is significantly

reduced. To take advantage of the typical daily power

availability cycle, the maintenance period is assumed to happen

between midnight and 4:00am every day. Aside from

maintenance, the RO system has no hard restrictions on being

run at partial load or even complete shutdown( in case of power

unavailability) so long as: i) turbulence flow levels in the

membrane modules are maintained to prevent fouling, and ii)

change of state happens via a smooth ramp-up/down.

2.2. Optimization Problem Formulation The objective of the optimization in the desalination system is

to minimize the cost of unit produced fresh water [$/m3], while

observing constraints on production and operating conditions of

the RO membrane modules. Summary of the optimization

problem in negative null form is:

Minimize )(

)()(

2

1

x

xx

f

ff (1)

Subject to: 0)(

1)(min,

21

pQ

fg

xx (2)

01)(

)(max,

22

pQ

fg

xx (3)

01)(

)()(

4

33

x

xx

f

fg (4)

0)(

)(1)(

6

54

x

xx

f

fg (5)

01)(

)()(

max,3

75

iRf

fg

x

xx (6)

f1(x) is the equivalent cost per day of the whole system [$]

f2(x) is the average daily fresh water production [m3]

Qp,min is the target minimum average daily fresh water

production [m3]

Qp,max is the target maximum average daily fresh water

production [m3]

f3(x) is the inlet salty water flow rate [m3/hr] into a single

pressure vessel of the RO rack, at nominal maximum

flow rate and pressure conditions

f4(x) is the maximum allowable flow rate [m3/hr] per RO

membrane module

f5(x) is the exiting brine flow rate [m3/hr] from a single

pressure vessel of the RO rack, at nominal maximum

flow rate and pressure conditions

f6(x) is the minimum permissible flow rate [m3/hr] per RO

membrane module

f7(x) is fresh water flow rate [m3/hr] from the first RO

membrane module in a pressure vessel, at nominal

maximum flow rate and pressure conditions

Ri,max is the maximum recommended recovery ratio per

single RO membrane module [dimensionless]

Brine

Pressurized

Brine

Pressure

Exchanger

Fresh Water

RO Rack

Battery

PV Panels

Pumping

Station

Motors

Alternator

Salt Water

Intake

Voltage Regulator

& Power Dispatch


The constraint g1(x) specifies that the average daily production

of fresh water should not be less than a desired minimum. A

reason the is treated as a single objective rather than a trade-off

between cost and productivity is that in small communities in

remote areas, producing more fresh water than the estimated

need would be a waste of investment. As such, constraint g2(x)

is set for a maximum daily production limit. Constraints g3(x)

and g4(x) are for keeping the flow rate within RO membrane

modules between the maximum and minimum allowable flow

rate. g5(x) is a constraint on the maximum recovery ratio per

single RO modules, which is an indicator of the flow rate

across the membranes (from salty stream to fresh water

stream). The condition on minimum flow rate, which is least at

the exit from the pressure vessels, ensures that the flow within

the membrane modules remain turbulent so to avoid formation

of high salinity boundary layer that leads to fouling of the

membranes. On the other hand, constraints on maximum flow

rates, which are highest at the entry to pressure vessels, are a

safeguard against damaging the membrane modules. While

small amounts of salt passage to the fresh water stream occurs,

it is practically impossible to exceed the recommended safe

limits with the adopted single-stage RO configuration, and thus

no constraints on salinity were considered in the optimization

model.

The design variables of the system include both discrete

and continuous quantities, as summarized in Table 1. x1 – x3 are

discrete design decisions for the setup of the RO rack; number

of pressure vessels, number of membrane modules per vessel,

and the membrane modules type (which inherently identifies

the diameter and flow capacities), respectively.

Table 1: Summary of Design Variables

Var. Description Type Units

x1 Number of pressure vessels in RO

rack Discrete

Dimen-

sionless

x2 Number of RO membrane modules per pressure vessel

Discrete Dimen-sionless

x3 Selected RO membrane module type

from catalogued list Discrete

Dimen-

sionless

x4 Nominal salty water intake flow rate Continuous m3/hr

x5 Nominal operating pressure for the high-pressure pumps

Continuous bar

x6 Ratio of the nameplate DC power of

the PV panels to the maximum

operating power of the RO system

Continuous kW/kW

x7 Ratio of the battery storage capacity to

the maximum operating power of the

RO system

Continuous kW.hr/kW

x8 Proportional constant for power

dispatch controller Continuous

Dimen-

sionless

x9 Derivative constant for power

dispatch controller Continuous hr

All other design variables are continuous: x4, x5 are the

pumping station nominal (full load power) flow rate and

pressure respectively. Full load power conditions are used for

sizing selection of the pumps, motors and pressure exchanger.

Sizing of the PV collectors and battery storage are inferred

based on the full load power of the pumping station; x6 is the

ratio of total nameplate DC power of the PV panels to the full

load power, and x7 is the ratio of battery storage capacity (in

kW.hr) to the full load power. A power dispatch strategy, which

is discussed in detail in section 2.3, employs a PD controller for

deciding the fraction of full-load power to operate the

desalination system at. x8, x9 are respectively the proportional

and derivative constants of the controller.

Design optimization of the system is performed via a

genetic algorithm (GA), with the recommended crossover and

mutation operators suggested by Michalewiz [19]. Listing of

the operators is provided in Table 2. Since the problem only

includes 9 design variables, a population size of 120 and 200

generations are deemed sufficient, but multiple runs (with

different random number seed) are conducted in order to assess

the consistency of the attained results. GA based optimization

only requires simulation models of objectives and constraints.

These models are discussed in section 2.3 and 2.4.

Table 2: Genetic algorithm operators

Operator Percentile of Newly

Generated Members

Heuristic Crossover 14.3%

Uniform Crossover 14.3%

Arithmetic Crossover 14.3%

Boundary Mutation 14.3%

Uniform Mutation 14.3%

Non-uniform Mutation 14.3%

Whole non-uniform Mutation 14.3%

2.3. System Performance Simulation Given an instance of the design variables x, simulation of the

system performance (fresh water production and constraint

feasibility) involves hour by hour simulation of the state of the

PV collectors, battery and RO plant for one complete year, with

representative weather data of the site location. To avoid using

excessive computational resources on poor designs, it is notable

that the most severe conditions for the constraints g3(x), g4(x)

and g5(x) all happen at the full-load power conditions. Thus

these constraints are used for pre-screening design variables

instances in the GA; if any of these constraints is violated, a

penalty value is returned to GA for the values of f(x), g1(x) and

g2(x), alongside the estimated values for g3(x), g4(x) and g5(x),

but without performing the hourly simulations.

Given an instance design variables x, the maximum and

minimum flow rates through the RO membrane modules (f4(x),

f6(x) respectively) are identified from the catalogued properties

of the selected type of RO membrane modules (decided by the

design variable x3). The maximum flow rate f3(x) occurs at the

inlet of the pressure vessels, and is used along with f4(x) to

calculate the value of g3(x). f3(x) is calculated as:

1

43 )(

x

xf x (4)

A finite-difference model of a pressure vessel containing

the RO membrane modules is used for predicting the outlet


conditions and fresh water productivity of each membrane

module in the pressure vessel. Main details of the finite

difference model are explained in the Appendix. In the system

model, the finite difference solution is treated as a “black box”

type simulation. Given the inlet conditions (qin, pin, sin) to the

pressure vessel, the finite difference model computes the output

conditions (qout, pout, sout), as well as the fresh water flow in the

first membrane module (qp1) and total produced fresh water (qp)

by the pressure vessel.

qin is the instantaneous inlet salty water flow rate to the

pressure vessel [m3/hr]

pin is the instantaneous inlet salty water pressure to the

pressure vessel [bar]

sin is the inlet salty water salinity [ppm]

qout is discharged brine flow rate [m3/hr]

pout is the discharged brine pressure at the exit from the

pressure vessel (inlet to the pressure exchanger) [bar]

sout is the salinity of the discharged brine [ppm]

When the inlet conditions are set to qin = f3(x), and pin = x5, then

the exit flow rate will be f5(x) = qout/x1, f7(x) = qp1, and f8(x) =

pout. After the finite difference simulation, f3(x), f5(x), f6(x) and

f7(x), are used to calculate g4(x) and g5(x)

When a design is feasible, hourly simulations using

weather data for the site location are performed. Prediction of

the hourly electric power output is performed via SAM 2012

[20]. Sizing of the PV panels and battery are respectively

controlled by the design variables x6 and x7 in reference to the

full-load operating power of the RO system. The full-load

power Pmax(x) is calculated as:

)()(1

)( 85154max xxx ffxxxP rp

(5)

p is a combined efficiency factor to account for the

pumping station hydraulic efficiency, as well as motor

and transmission [dimensionless]

r is the energy recovery efficiency of the pressure

exchanger [dimensionless]

The full load operating power is then used to estimate the sizing

of the PV collectors and battery, as:

)()( max6 xx PxPPVN (6)

)()( max7 xx PxCB (7)

PPVN is the nameplate DC power of the PV panels [kW]

CB is the battery storage capacity [kW.hr]

A sample simulation (generated via SAM 2012) of the hourly

harvested energy by PV panels is shown in Fig. 3. Deciding the

fraction of full-load power (y(t)) to operate the RO desalination

system at, is based on the battery state of charge (z(t)) through a

PD controller. Once decided on a value for fraction operating

power, it is assumed to remain in effect for one complete hour.

Power dispatch to the RO system is thus calculated as:

)()()( max xPtytPRO (8)

)()()( 98 tzxtzxty (9)

otherwise )(

))()),((()(

if )(

))),(()(()(

)1(

x

-x

x

x

B

ROPVNPVB

PVROB

PVNPVRO

C

tPtPPtz

PPC

tPPtPtz

tz

(10)

t is the time from start of the year [hr]

y(t) is the fraction of full-load power Pmax(x) at which the

RO system is operated (limited to a maximum of

100%) at time t [dimensionless]

zt) is the battery state of charge as a fraction of the battery

energy storage capacity [dimensionless]

PRO(t) is the power at which the RO system is operated at

time t [kW]

PPV(PPVN (x), t) is the estimated average harvested power by

the PV panels at time t [kW]

B is the battery charging efficiency [dimensionless]

Some exceptions Eqn. (9) for setting the fraction operating

power are assumed:

If the state of charge z(t) falls below a minimum threshold

(selected as 10% in this paper), the RO system is shut

down. And if the system is shut down, it does not begin

operation again unless the state of charge is above another

threshold (selected as 20%)

If the state of charge reaches 100% (full), the RO system is

operated at full power

If t is at a designated daily maintenance hour (midnight to

4:00am), the RO system is assumed not to be producing

any fresh water, but is constantly drawing a small amount

of power (assumed to be 2.5% of PPVN)

Given the operating power PRO(t) at a point of time, the flow

rate per pressure vessel is assumed to be maintained at the

nominal operating conditions (i.e. qin(t) = f3(x)), but the number

of pressure vessels that are operated nv(t), and their inlet

pressure pin(t) are adjusted to values allowed by the dispatched

power:

)(

)(Round)(

3

4

xf

xtytnv (11)

otherwise

1)(

)()( if

)(

)()(

)(

5

1

max5

1

max

in

x

tPx

Ptnx

tPx

Ptn

tpRO

v

RO

v xx

(12)

When at least one pressure vessel is operation (i.e. nv(t) 1),

the finite difference simulation model of the RO pressure is run

with the inlet conditions (qin = f3(x), pin(t), sin) to obtain the

fresh water production of a single pressure vessel. The daily

production average f2(x) is then estimated by averaging over the

hours in one complete representative year:

8760

1

2 )()(8760

1)(

t

pv tqtnf x (13)


2.4. Cost Estimation For project budgeting, a component pricing survey (including

offers from potential component suppliers) should be

conducted. In this paper however, average world cost values [6,

21-23] are used for the estimation. First-order cost models are

used for estimation of the investment costs of the hydraulic

power components as:

4,1, xaac pumppumpopump (14)

)(51,1, xfxaac pxpxopx (15)

)(max,1, xPaac motormotoromotor (16)

Initial investment cost of the RO rack of membrane modules

(including pressure vessels, piping, valves and controls) are

estimated based on the number and type of modules used:

)( 321 xcxxc modulerack (17)

RO membrane modules, unlike hydraulic power components,

require (fairly predictable) regular year-round replacements,

with a replacement rate rack of 13 to 15%. Thus, the effective

investment cost in RO modules is corrected as:

)1(~ nROYearscc rackrackrack (18)

Battery costs are assumed proportional to the installed storage

capacity. Since the battery storage is stationary, weight is not a

primary concern, and as such, the most cost economical values

(corresponding to lead-acid batteries [23]) are used:

)(,1 xBbatterybattery Cac (19)

Investment cost per installed nameplate DC power of the PV

panels cpv(PPVN(x)) is estimated via SAM 2012 simulations.

Since the lifetime expectancy of PV panels is typically different

than the RO plant (20 to 30 years compared to 10 years), the

effective yearly and daily costs are estimated as:

nROYears

ccccc

nPVYears

cf

batteryrackmotorpxpumppv )~()(9

x

(19)

365/)()( 91 xx ff OH (20)

OH is a lumped overhead correction coefficient to account

for installation [6, 24], investment devaluation, as well

as operation and maintenance costs [dimensionless]

ao and a1 are respectively the constant and linear

coefficients of the first-order cost models. Values for

the adopted values in this paper are listed in Table 3.

Table 3: Cost Estimation Coefficients

Coefficient Value Unit

ao,pump 75,000.00 $

a1,pump

375.00 $/(m3/hr)

ao,px 40,000.00 $

a1,px

400.00 $/(m3/hr)

ao,motor 25,000.00 $

a1,motor

125.00 $/kW

a1,battery

170.00 $/kW.hr

OH 1.30 Dimensionless

3. CASE STUDIES Two case studies of two locations in the Red sea and Sinai

region were considered. The locations are: i) brackish water

from desert wells in El-Arish valley, ii) and seawater from a

location along the southern Egyptian Red sea coast, as shown in

Fig. 3. The closest locations with recorded weather data are the

cities of El Arish and Hurgada (Fig. 3). While the city and plant

locations are an appreciable distance apart (more than a

100km), the weather data from locations to the North of the

desalination plants provide conservative estimates of the

harvestable energy. Sample simulations via SAM of the hourly

harvested energy for El Arish and Hurgada are shown in Fig. 4,

5 respectively. For both plants, the minimum and maximum

average daily fresh water production was set to 100 and 150 m3

respectively. Intake salinity for brackish water is assumed to be

2000 ppm (which is an upper bound as most wells in the area

are around 1000 ppm), and seawater salinity is assumed to be

45,000 ppm (also an upper bound for the Red Sea).

Fig. 3: Potential locations for desalination plants – map obtained from https://maps.google.com/

Fig. 4: Hourly simulation of harvested energy at El Arish for nameplate DC power 20kW of PV panels

Ho

url

y H

arv

este

d E

ner

gy

[kW

.h]

Red

Sea

Mediterranean Sea

El Arish

Hurgada

Brackish

water site

Seawater site

https://maps.google.com/


Fig. 5: Hourly simulation of harvested energy at Hurgada for nameplate DC power 20kW of PV panels

4. RSULTS AND DISCUSSION Twenty runs of a C++ implementation of GA were conducted

for each of the considered desalination plants. Population size

and number of generations for the GA was set to 120 and 200

generations respectively, and convergence plots are shown in

Fig. 6-7. Details of the best obtained designs are listed in Table

4. To better understand the cost break-down and power dispatch

behavior, pie charts of the main cost elements and hourly fresh

water productivity are shown in Fig. 8, 9 respectively. While

GA is a random search technique, thus not always guaranteed to

find the true optimum of a problem, the number of runs that

have been conducted and their convergence plots (Fig. 6, 7)

suggest that the best obtained designs are close to optimal.

An observation in Table 4, is that the cost of unit produced

fresh water is close to (or less) than $3 per m3, which is around

the lower limit of the other major technology for solar-powered

water desalination at the same production scale: humidification-

dehumidification (HDH) [25]. While HDH tends to be

insensitive to the salinity level in water and scalable to smaller

scale production, RO appears to be a more economical choice

for the considered plant capacity. Also observable in the results

of both plants is that the main active constraint appears to be

the maximum production (g2(x)), which implies that relaxing

that constraint should allow for lowering the unit cost of fresh

water even further. In other words, the PV-powered RO

desalination system would be more favorable had the studies

been for larger sized plant, and will likely be less favorable for

smaller-scale. This might also imply that hard-constraining the

production rate might not necessarily be the best setup of the

optimization problem. An alternative setup could be the

maximization of yearly fresh water production while subject to

a total budget constraint.

A notable difference between the brackish and seawater

plants is that the energy consumption is much higher at higher

salinity, which seems to drive the best obtainable designs to

different configurations. For brackish water, the best design has

a relatively larger PV array, along with a small battery. This lets

the system achieve larger peak fresh water production (Fig.

9.a), but also has a higher percentage down time (~30%). On

the other hand, the best obtained design for seawater employs a

relatively smaller PV array and a much larger battery. This

allows for a more steady operation with very little down time.

Fig. 6: Convergence of 20 GA runs for design optimization of brackish water desalination plant

Fig. 7: Convergence of 20 GA runs for design optimization of seawater desalination plant

Fig. 8: Desalination costs breakdown

(a) Brackish water (b) Seawater

PV System

Battery

RO Modules

RO – Other

Overheads

2.50 0 2000 4000 6000

3.00

3.50

4.00

4.50

Number of Model Evaluations

f [$

/m3]

2.50 0 2000 4000 6000

3.00

3.50

4.00

4.50

Number of Model Evaluations

f [$

/m3]

Ho

url

y H

arv

este

d E

ner

gy

[kW

.h]


Fig. 9: Hourly fresh water production

5. CONCLUSION AND FUTURE WORK This presented an optimization model for off-grid photovoltaic-

powered RO water desalination systems. The design variables

consider the RO system configuration, sizing of the hydraulic

power elements and their operating conditions, as well as sizing

of the PV collectors, battery storage and power dispatch. Two

case studies for brackish and sea water in Sinai and the Red sea

areas are considered. Estimated cost per unit volume of

produced fresh water appeared favorable in comparison with

reported values for other solar-powered HDH technology.

Examining the best obtained designs however implies PV-RO

may not be suited for small-scale capacities.

Future extensions of this research may include further

examination of power-dispatch strategies instead of the fairly

simple approach adopted in this paper, which may also lead to a

multi-level optimization model, with the power dispatch being

a sub-problem in the overall system. Future work may also

include detailed comparisons with other solar-powered water

desalination technologies such as HDH for varying production

capacity and salinity levels.

ACKNOWLEDGEMENT

This research was supported by the U.S. Department of

Agriculture and Egypt Science and Technology Development

Fund. STDF Project #3832.

Table 4: Details of best obtained desalination plant designs

Quantity Brackish

Water Plant

Seawater

Plant

Unit

x1 5 5 Dimensionless



x4 17.10 34.26 m3/hr

x5 55.26 59.24 bar

x6 3.42 1.97 kW/kW

x7 4.98 5.00 kW.hr/kW

x8 1.52 1.99 Dimensionless

x9 1.93 2.00 hr

f 2.696 3.044 $/ m3

g1 -0.499 -0.499 Dimensionless





Average Daily

Production 150.00 150.00 m3

Max. RO Sys.

Power 40.36 86.73 kW

Nameplate PV

DC Power 138.04 170.87 kW

Battery size 201.00 433.68 kW.hr

Percentage

downtime 30.7% 17.9% Dimensionless

(a) Brackish water plant

(b) Seawater plant

Fre

sh W

ater

Pro

du

ctio

n [

m3/h

r]

0.0

10.0

5.0

0.0

15.0

10.0

5.0

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec


REFERENCES

[1] Reid, C., Breton E. (1959). “Water and ion flow across

cellulosic membranes,” Journal of Applied Polymer

Science, 1: 133-143

[2] Peterson, R., Cadotte, J. and Buttner, J. (1982). “Final

Report: development of FT-30 membrane in spiral wound

modules,” Contract No. 14-34-0001-8547 for US

department of Interior

[3] Sourirajan S., 1977, Reverse Osmosis and Synthetic

Membranes: Theory-Technology-Engineering, National

Research Council, Ottawa, Canada.

[4] Bray, D. and Menzel, H., 1966, “Design study of reverse

osmosis pilot plant,” Office of Saline Water Research and

Development Progress, Report No. 176.

[5] Mahon, H. and Lipps, B., 1971, Encyclopedia of Polymer

Science and Technology, 15, Interscience publishers, New

York. USA.

[6] Wilf, M., 2007, The Guidebook to Membrane

Desalination Technology, 1st Edition, Desalination

Publications, L’Aquila, Italy.

[7] Global Water Intelligence, 2006 IDA Worldwide Desalting

Plants Inventory Report

[8] Garma, S., Wayman, E. and Bradford, T. (2008).

Concentrating Solar Power – Technology, Cost and

Markets, Green-Tech Media 2008 Industry Report

[9] A. A. Ghermandi, and R. Messalem, 2009, "Solar-driven

desalination with reverse osmosis: the state of the art,"

Desalination and Water Treatment, 7, pp. 285-296.

[10] Thomson, M., Miranda, M., Infield, D. (2003). “A small-

scale seawater reverse-osmosis system with excellent

energy efficiency over a wide operating range,”

Desalination, 153(1–3): 229-236

[11] Thomson, M., Infield, D. (2003). “A photovoltaic-

powered seawater reverse-osmosis system without

batteries,” Desalination, 153(1–3): 1-8

[12] Riffel, D., Carvalho, P. (2009). “Small-scale photovoltaic-

powered reverse osmosis plant without batteries: Design

and simulation,” Desalination, 247(1–3): 378-389

[13] Thomson, M., Infield, D. (2005). “Laboratory

demonstration of a photovoltaic-powered seawater

reverse-osmosis system without batteries,” Desalination,

183(1–3): 105-111

[14] Mohamed, E., Papadakis, G., Mathioulakis, E.,

Belessiotis, V. (2008) “A direct coupled photovoltaic

seawater reverse osmosis desalination system toward

battery based systems — a technical and economical

experimental comparative study,” Desalination, 221(1–3):

17-22

[15] Koutroulis, E., Kolokotsa, D. (2010). “Design

optimization of desalination systems power-supplied by

PV and W/G energy sources,” Desalination, 258(1–3):

171-181

[16] Gilau, A., Small, M. (2008). “Designing cost-effective

seawater reverse osmosis system under optimal energy

options,” Renewable Energy, 33(4): 617-630

[17] Bourouni, K., Ben M’Barek, T., Al Taee, A. (2011).

“Design and optimization of desalination reverse osmosis

plants driven by renewable energies using genetic

algorithms,” Renewable Energy, 36(3): 936-950

[18] http://www.energyrecovery.com/px-pressure-exchanger-

energy-recovery-devices

[19] Michalewiz, Z. and Fogel, D. B. (2000). How to Solve it:

Modern Heuristics, Springer-Verlag, New York

[20] National Renewable Energy Laboratory (2012). System

Advisor Model, https://sam.nrel.gov/

[21] Peters, M., Timmerhaus, K., West, R. (2003). Plant

Design and Economics for Chemical Engineers, 5th

Edition, McGraw-Hill Higher Education

[22] http://www.che.com/business_and_economics/economic_

indicators.html

[23] http://www.allaboutbatteries.com/Battery-Energy.html

[24] http://www.dowwaterandprocess.com/support_training/de

sign_tools/rosa.htm

[25] Narayan, G.., Sharqawy, M., Summers, E., Lienhard, J.,

Zubair, S., Antar, M. (2010). “The potential of solar-

driven humidification–dehumidification desalination for

small-scale decentralized water production,” Renewable

and Sustainable Energy Reviews, 14: 1187-1201

APPENDIX: FINITE DIFFERENCE MODEL OF REVERSE OSMOSIS MEMBRANE MODULES A one-dimensional finite-difference (FD) model is used for

input-output simulation of a pressure vessel containing RO

membrane modules similar to the model presented in [6], and is

calibrated verses the public-domain software ROSA [24]. Fluid

flow in one FD element is illustrated in Fig. 10. In this paper,

each RO membrane module was divided into 10 FD elements.

Inlet conditions (pi, qi, si, qfi, sfi) to a FD element are used to

calculate the conditions (pi+1, qi+1, si+1, qfi+1, sfi+1) at the outlet,

which then become the inlet conditions for the next element in

the pressure vessel.

Fig. 10: Schematic diagram of fluid flow in one finite difference element

Assuming the pressure drop within one element to be

small, and the salinity concentration in the salty stream to be

much higher than in the fresh water stream, the flow rates and

salinity concentration are estimated from:

2

1iiimi

ssOSpSPq (20)

miii qqq 1 (21)

Membrane

Salty water stream

Fresh water stream

(pi, qi, si)

(qfi, sfi) (qmi, smi) (qfi+1, sfi+1)

(pi+1, qi+1, si+1)

http://www.energyrecovery.com/px-pressure-exchanger-energy-recovery-devices

http://www.energyrecovery.com/px-pressure-exchanger-energy-recovery-devices

https://sam.nrel.gov/

http://www.che.com/business_and_economics/economic_indicators.html

http://www.che.com/business_and_economics/economic_indicators.html

http://www.allaboutbatteries.com/Battery-Energy.html

http://www.dowwaterandprocess.com/support_training/design_tools/rosa.htm

http://www.dowwaterandprocess.com/support_training/design_tools/rosa.htm


2

1

iimi

mi

ss

QS

qSRs (22)

11

i

mimiiii

q

qsqss (23)

mififi qqq 1 (24)

11

fi

mimififi

fiq

qsqss (25)

where OS is the osmotic pressure constant, which solely

depends on the composition of the dissolved salts (standard

value used in this paper is for sodium chloride). SP, SR, QS are

specific permeability, salt rejection and membrane flow rate in

standard conditions respectively. The parameters are estimated

via standard test conditions data, which is available in the

documentation provided by the membrane manufacturers.

Equations 20-23 are solved for (qmi, qi+1, qmi, si+1) given (pi,

qi, si). Although the system of equations exhibits nonlinear

terms, it is fairly easy to solve numerically as there is only one

meaningful solution in the ranges 0 qmi qi, 0 qi+1 qi

Finally, an estimate of the pressure drop in the salty stream

(assuming turbulent flow is maintained, as is the case in RO

modules) is calculated as:

21 iii qPCpp (26)

where PC is a pressure constant estimated from the standard

test conditions of the RO membrane modules

After estimation of the fresh water production of a

complete pressure vessel, correction factors are introduced to

account for partial fouling of the membranes (15% less fresh

water production is the typical conservative estimate [6]), as

well as time lost during smooth ramp-up/down (10% less fresh

water production is the adopted conservative estimate for 5min

ramp time per hour).

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