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Entropy generation in multi-stage flash desalination plants

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Abstract

A second-law analysis of two types of MSF desalination plants (once-through OT and with heat rejection section HR) is conducted. Fixing the number of stages to 20, the HR configuration is found to present clearly less entropy generation but more specific area than the OT configuration. The detailed investigation showed that heat transfer is responsible of more than 65% of the irreversibility occurring in a stage. The 30% reduction of the entropy generation number when passing from OT to HR is totally due to the reduction of the heat-transfer irreversibility. The variation of the number of stages for OT configuration has no effect on the entropy generation. Besides, we noted that beyond 10 stages the specific area is not expected to vary noticeably. For the HR configuration, there is a continuous decrease of the entropy generation number accompanied by a continuous increase of the specific area. The comparison between the two plants showed that HR is not necessarily better than OT. The decision of which of them is the most competent depends on the number of stages and on the relative importance we attach to the irreversibility and to the specific area.

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Abbreviations

\(A\) :

Area (m²)

\(A^{*}\) :

Relative specific area

BPE:

Boiling point elevation (°C)

\(c_{p}\) :

Specific heat capacity (kJ/kgK)

\(D\) :

Distillate flow rate (kg/s)

GOR:

Gain output rate

\(h\) :

Specific enthalpy (kJ/kg)

\(N_{\text{S}}\) :

Dimensionless rate of entropy generation

\(n^{*}\) :

Relative dimensionless rate of entropy generation

\(P\) :

Pressure (bar)

\(P^{0}\) :

Saturation pressure (bar)

\({ \Pr }\) :

Performance ratio

\(Q\) :

Heat-transfer rate (kW)

\(R\) :

Recycling ratio

\(\dot{S}_{\text{g}}\) :

Entropy generation rate (kW/K)

\(s\) :

Specific entropy (kJ/kgK)

\(sA\) :

Specific area (m²/(kg/s))

\(sW\) :

Specific flow rate (kg/kg)

\(T\) :

Temperature (°C)

\(U\) :

Overall heat-transfer coefficient (kW/m²K)

\(W\) :

Feed flow rate (kg/s)

\(x\) :

Salinity (ppm, g/kg or kg/kg)

\(y,y^{\prime}\) :

Vapor flow rate (kg/s)

\(\Delta T\) :

Temperature difference (°C)

\(\lambda\) :

Latent heat of evaporation (kJ/kg)

av:

Average

\({\text{BH}}\) :

Brine heater

b:

Brine

bd:

Blowdown

c:

Condenser tubes

\({\text{cS}}\) :

Condensate of steam

\({\text{cv}}\) :

Condensate of vapor

\({\text{cw}}\) :

Cooling water

D :

Distillate

f:

Feed

HR:

Plant with heat rejection section

HT:

Heat transfer

\(i\) :

ith stage, inlet

in:

Inlet

\({\text{lm}}\) :

Logarithmic mean

mw:

Make-up water

\({\text{MT}}\) :

Mass transfer

\(n\) :

nth stage

\({\text{OT}}\) :

Once-through plant

out:

Outlet

S:

Steam

s:

Seawater solution

sw:

Seawater

v:

Vapor

w:

Water

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Correspondence to Ali Snoussi.

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Appendix: Thermodynamic properties of pure water and seawater

Appendix: Thermodynamic properties of pure water and seawater

Thermodynamic properties of pure water and seawater are calculated using equations from [2, 19]. In all the equations, the temperature is in °C.

  • For pure water, the saturation pressure (bar) [20] and the latent heat of evaporation (kJ/kg) are:

    $$\begin{aligned} & \ln (P^{0} ) = \left[ {23.1698 - \frac{3799.8871}{226.346 + T}} \right]10^{ - 5} \\ & \lambda_{i} = 2501.689845 - 2.407064037T_{i} + 1.192217 \times 1 0^{ - 3} T_{i}^{2} - 1.5863 \times 1 0^{ - 5} T_{i}^{3} . \\ \end{aligned}$$
  • The specific enthalpies (kJ/kg) of saturated liquid and saturated vapor are:

    $$\begin{aligned} h_{\text{w}} & = \left( {141.355 + 4202.07T - 0.535T^{2} + 0.004T^{3} } \right)10^{ - 3} \\ h_{\text{v}} & = 2501.689845 + 1.806961015T + 5.987717 \times 1 0^{ - 4} T^{2} - 1.221 \times 1 0^{ - 5} T^{3} . \\ \end{aligned}$$
  • The specific entropies (kJ/kgK) of saturated liquid and saturated vapor are:

    $$\begin{aligned} s_{\text{w}} & = \left( {0.1543 + 15.383T - 2.996 \times 1 0^{ - 2} T^{2} + 8.193 \times 1 0^{ - 5} T^{3} - 1.37 \times 1 0^{ - 7} T^{4} } \right)10^{ - 3} \\ s_{\text{v}} & = s_{\text{w}} + \frac{\lambda }{(T + 273.15)}. \\ \end{aligned}$$
  • The boiling point elevation (°C) of seawater is function also of the salinity (ppm)

    $$\begin{aligned} & BPE = x\left( {B + xC} \right)10^{ - 3} \\ & B = \left( {6.71 + 6.34 \times 10^{ - 2} T + 9.74 \times 10^{ - 5} T^{2} } \right)10^{ - 3} \\ & C = \left( {22.238 + 9.59 \times 10^{ - 3} T + 9.42 \times 10^{ - 5} T^{2} } \right)10^{ - 8} . \\ \end{aligned}$$
  • The specific heat (kJ/kg °C) is function of the temperature (°C) and the salinity (g/kg):

    $$\begin{aligned} C_{p} & = \left( {A + BT + CT^{2} + DT^{3} } \right)10^{ - 3} \\ A & = 4260.8 - 6.6197x + 1.2288 \times 10^{ - 2} x^{2} \\ B & = - 1.1262 + 5.4178 \times 1 0^{ - 2} x - 2.2719 \times 10^{ - 4} x^{2} \\ C & = 1.2026 \times 1 0^{ - 2} - 5.3566 \times 1 0^{ - 4} x + 1.8906 \times 10^{ - 6} x^{2} \\ D & = 6.87774 \times 1 0^{ - 7} + 1.517 \times 1 0^{ - 6} x + 4.4268 \times 10^{ - 9} x^{2} . \\ \end{aligned}$$
  • The specific enthalpy (kJ/kg) and the specific entropy (kJ/kgK) of saturated liquid as functions of the temperature (°C) and the salinity (kg/kg) are, respectively,

    $$\begin{aligned} h_{s} & = h_{w} - x\left( \begin{aligned} & 2.438 \times 10^{4} + 3.152 \times 10^{5} x + 2.803 \times 10^{6} x^{2} - 1.446 \times 10^{7} x^{3} + 7.82610^{3} T - 4.417 \times 10^{1} T^{2} \\ & + 2.139 \times 10^{ - 1} T^{3} - 1.991 \times 10^{4} Tx + 2.77810^{4} Tx^{2} + 9.728 \times 10^{1} T^{2} x \\ \end{aligned} \right)10^{ - 3} \\ s_{s} & = s_{w} - x\left( \begin{aligned} & - 4.231 \times 10^{2} + 1.463 \times 10^{4} x - 9.8810^{4} x^{2} + 3.09510^{5} x^{3} + 2.562 \times 10^{1} T - 1.443 \times 10^{ - 1} T^{2} \\ & + (5.879 \times 10^{ - 4} T^{3} - 6.111 \times 10^{1} Tx + 8.041 \times 10^{1} Tx^{2} + 3.035 \times 10^{ - 1} T^{2} x \\ \end{aligned} \right)10^{ - 3} . \\ \end{aligned}$$

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Snoussi, A., Chekir, N. & Ben Brahim, A. Entropy generation in multi-stage flash desalination plants. Int J Energy Environ Eng (2020). https://doi.org/10.1007/s40095-020-00337-1

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Keywords

  • Entropy generation
  • MSF desalination
  • Specific area