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184 S. Casimiro et al. / Desalination and Water Treatment 61 (2017) 183–195

plants as a means of renewable desalination. RO and MED For a given recovery rate, applied feed pressure (P )
f
were selected to be analyzed in this work as they present increases with the increasing feed osmotic pressure. It
the best performances within the mature technologies should be noted that there’s a minor drop in feed pressure
operating in the desalination market. as the feed solution passes from one membrane to another
in the pressure vessel due to friction. Pressure drop in the
concentrate side of an RO membrane can be estimated from
1.1. Methodology
the following equation:
The steps applied to perform this study are based on
freely available computer modelling tools used for the sim- P = 0.01nq 1.7
ulation of RO and CSP operation. These steps include, firstly cd fc (3)
the validation of the reverse osmosis system analysis (ROSA)
tool with operational data for nominal conditions from The average concentrate side flow rate (q ), is equal to
fc
a small scale water desalination plant in Alvor, Portugal. the arithmetic average of the feed and concentrate flow
Secondly, the utilization of the system advisor model (SAM) rates as in the following equation:
developed by the National Renewable Energy Laboratory
(NREL) to simulate a CSP plant, together with ROSA to sim- Q + Q c (4)
f
ulate the RO unit using data for the location of Trapani. The q = 2
fc
results of both models were combined to obtain the perfor-
mance of a CSP-RO co-generation scheme. Thirdly, an anal- In a typical RO process, as water flows thorough the
ysis and comparison between: 1) the CSP-RO modelled; 2) membrane and the membrane rejects salts, a boundary layer
a CSP-MED co- generation scheme previously studied in [2] is formed near the membrane surface in which salt concen-
adapted to the work shown in this paper; and 3) data from a tration exceeds the salt concentration in the bulk solution by
real TVC-MED plant that exists in Trapani, Sicily [3]. a factor equal to the concentration polarization value [5]. This
parameter can be calculated from the following equation:
2. Reverse osmosis system analysis (ROSA) tool C
ROSA can be used to estimate the performance of a new CP = C w (5)
RO system under design conditions, or the performance of b
an existing RO system under off-design conditions. This Experimentally, DOW FILMTEC has determined that
TM
projected performance is based on the nominal perfor- CP = EXP(0.7 R) where R is the recovery rate. Eq. (5) shows
mance specification for the DOW FILMTEC™ element(s) that the nominal salt rejection rate in RO membranes is low-
(or membranes) used in that system. Accurate results can be er than the true rejection rate. The actual rejection rate can
obtained very quickly using the ROSA computer program. be defined as the ratio between the permeate concentration
Thus, it can be used to modify and optimize the design of an to the feed concentration at the membrane surface:
RO system. The entire system calculation methods will not
be described in detail, however the major governing equa- R = 1 − (C /C ) (6)
tions and parameters will be briefly described in this sec- j p f
tion. These equations were also used previous work [4] to Although the membranes are designed for high rejec-
develop a computer model, similar to ROSA, to predict the tion, some amounts of salt always pass through the mem-
performance of RO systems based on membrane-to-mem- branes. In the ROSA design equations, the salt passage is
brane analysis (single element performance). by salt diffusion through the membrane. Thus, the salt flux
is proportional to the salt concentration difference between
2.1. Design equations and parameters both sides of the membrane. The proportionality constant is
known as the salt diffusion coefficient or the B factor.
The performance of a specified RO system, in ROSA, is
defined by its feed pressure (or permeate flow, if the feed
pressure is specified) and its salt passage (amount of salt NA = B (C − C ) (7)
f
p
passing through the membrane). In its simplest form, the
The quality of the permeate is proportional to the B fac-
permeate flow (Q) through an RO membrane is a function tor, concentration polarization, salt rejection, feed concen-
of the membrane active area (wet area) (S), the net driving tration and membrane active area. It can be calculate using
pressure (NDP) (∆P – ∆π) and the membrane permeability. the following equation:
The permeate water flux can be calculated from the follow-
ing equation [5]: s
C = B * C fc * CP R j * (8)
*
p
Q = (A)(S)(∆P − ∆π) (1) Q p
Van’t Hoff’s theoretical osmotic pressure equation is The permeate concentration C represents the quality of
p
adapted to operational conditions by DOW FILMTEC , the treated water which is a function of membrane type and
TM
and then used to calculate the osmotic pressure of the feed operational conditions such as feed water temperatures and
solution: total dissolved solids (TDS) levels. The permeate osmotic
pressure can be calculated using the feed osmotic pressure
π = 1.12 (273 + T) Σm (2) as a reference:
f j