Page 7 - Water-energy_2020

F. Calise, et al. Energy Conversion and Management 220 (2020) 113043
includes only the parabolic concentrator: the following equations:
4 4 4 4
tot
A PVT σε PVT T ( PVT − T conc ) + I A conc α conc = A conc σε conc back, T ( conc − T ) + W ̇ p i, = AA· membranes ·(ΔPr i − ΔΠ ) i (10)
sky
w
A conc h c conc front, , T ( conc − T ) + A conc h c conc back, , T ( conc − T )
a
a
ṁ s i, = B A· s membranes ·( c f i, − c ) i, p (11)
(5)
where, W ̇ p i, is the permeate water flowrate [m /s], Bs is the salt per-
3
Due to the radiative terms, the system of equations is not linear and
meability coefficient [m/s], ΔPr i is the pressure of the seawater feed
it must be solved iteratively. This CPVT model is stationary, but this
assumption can be removed by adding capacitive terms in the balances, flowrate on the inlet of the RO module [Pa], A w is the water perme-
2
3
ability coefficient [m /(Pa m s)], ΔΠ i is the osmotic pressure of the
and consequently, converting the system into a differential equations
system that can be solved using well-known techniques also included in seawater [Pa], c f,i and c p,i are the feed seawater and the permeate water
3
salt concentration [mol/m ], and ṁ si, is the mass flowrate of salt that is
the EES tool. It is possible to calculate thermal and electrical efficiencies
able to pass across the membrane [kg/s].
using the following equations:
ΔΠ i is evaluated step by step according to the Van't Hoff's law:
mh( out − h )
̇ f
in
η CPVT th, = ΔΠ i = kRT c( f i, − c ) i, p (12)
i
s
ap
AI b (6)
where, T i is the absolute temperature of the seawater (obtained by
I η η
C PVT A PVT b opt PV adopting the hourly data measured by the ISPRA institute [37]), R is the
η CPVT el , =
ap
AI b (7) universal gas constant [J K −1 mol −1 ], and k s is the number of ions of
the salt molecule.
A w and B s show the performance of the RO membrane/module and
3.2. District heating and cooling networks
they depend on T i and on the type of the selected membrane. To con-
sider the effect of the membrane compaction due the high pressure on
District heating and cooling networks bring several short- and long-
term benefits for communities. In this paper, energy generation from the membrane, the value of the A w is modified step by step as a function
of the value of the pressure on the membrane, by considering this
the proposed renewable energy systems is distributed to communities, empirical correlation [33,38]:
offering the opportunity for higher penetration of renewable energy to
community members and remote areas that may otherwise not permit R membranes i, ⎜ ⎛ ΔPr 0 ⎟ ⎞
viable on-site renewable energy use. In addition, the use of renewable- = exp 1 −
R membranes,0 ⎝ ΔPr i ⎠ (13)
based energy for heating and cooling purposes reduces the use of fossil
fuels, reducing the overall environmental impact of energy conversion. where, R membranes is equal to 1/A w and it represents the hydraulic re-
To evaluate some technical requirements of the heating and cooling sistance of the membranes.
systems assumed in this study, basic simplified indicators and costs of Further details, concerning the equations implemented for the
the piping system have been calculated. The pipe length required per evaluation of the RO module performance, in terms of Rejection Rej
building has been calculated using the equation: (i.e., the capability of the RO module to reject the salt, and to achieve
drinkable water with a lower salinity), Recovery Recov (the amount of
= 1207.36 ρ −0.5894
L spec (8)
building drinkable water that is produced thought the RO module with respect to
2
where ρ building is the building density, i.e., the buildings per km [34].A the amount of feed seawater), and PX efficiency, are provided in re-
smaller number of buildings needs a smaller piping network, reducing ference [8].
the cost of the system. The total annual energy of the systems in this
study include the heating and cooling or the domestic hot water supply 3.4. Energy, economic and environmental model
to the communities. The cost of the distribution network is calculated as
The proposed plants are analyzed from an energy, economic and
CAPEX = C( 1 + C d L) p2 a (9) environmental point of view by a suitable model calculating the pri-
A A 0.5 mary energy saving (PES), the simple payback period (SPB), the profit
with L p = 0.02 DH + 0.4 DH , d a is the diameter of the pipes and C 1
and C 2 the construction cost constant and the construction cost coeffi- index (PI), and the avoided carbon dioxide (CO 2 ) emissions (ΔCO 2 ). In
cient. The diameter of the pipes can be calculated using the logarithmic particular, indexes are evaluated by comparing the proposed systems
equation presented by Persson and Werner [35]. However, the two (PS) with a reference system (RS). In the RS?? the thermal energy de-
regions investigated in this study are rural areas with low population mand of the district buildings for the space heating and DHW is pro-
vided by traditional boilers (η B,RS = 0.80) and space cooling is supplied
density that include a high number of secondary or vacation residences
with relatively low annual energy demand. The linear density of the by electrically-driven air-to-air heat pumps (COP CH,RS = 3). Regarding
the electric energy demand, it is considered that the local grid, based on
case studies is, thus, found to be smaller than 1 MWh/m and the
average pipe diameter of the networks has been assumed to be 35 mm diesel engine power plants (with an electric efficiency η RS,el assumed
equal to 0.35), is the main source to cover the demand of the district
[34]
(note that it is common for remote islands to not be linked to the na-
tional electric grid). The fresh drinkable water demand is provided by
3.3. RO model
water-tankships.
PES is calculated as follows:
The model of the RO unit has been developed in-house using a zero-
dimensional approach and is based on a pressure driven membrane
⎛ E th heat RS, , + E th DHW RS, , E th cool RS, , E el RS,
process [36], equipped by a Pressure Exchanger (PX). PX is a device PES = ∑ ⎜ η + η + η
,
that transfers the hydraulic energy of the pressurized brine directly to i ⎝ AH RS, COP CH RS RS el, RS el,
the feed seawater without an intermediate conversion to mechanical E el fromGRID PS, , E el toGRID PS, , E th AH PS, , ⎞
energy, resulting in high efficiencies. The model, written in MATLAB, is − η RS el, + η RS el, − η AH PS, ⎟ (14)
subsequently linked to TRNSYS. The input parameters to the RO si- ⎠i
mulation model are: i) seawater temperature ii) seawater concentra- where, E th,heat,RS and E th,DHW,RS are the thermal energy demand for space
tion, iii) seawater feed flowrate to the RO membranes and iv) seawater heating and DHW of the district in RS, respectively; E th,cool,RS is the
feed pressure to the RO membranes. The in-house RO model is based on thermal energy demand for space cooling in RS; E el,RS is the electric
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