The Effect of Fouling on Performance and Design Aspects of Multiple-Effect Desalination Systems

Abstract

Multiple-effect desalination systems are attractive water desalination units for large capacity production since the brine temperature does not exceed 65 °C and there is less power consumption compared to other thermal desalination systems. The system is modeled for performance prediction as well as for the assessment of design aspects such as the total heat transfer area in the effects, the preheaters and the system down condenser. Then, the system degradation with time due to fouling is considered for both rating and design aspects. It is therefore believed that the results presented can provide guidelines for designers and engineers using multiple-effect desalination systems for specifying system sizes and/or scheduling maintenance of the existing systems.

Nomenclature

A _c

Condenser area (m²)

A _ej

Area of jth effect, j = 1 to n(m²)

A _pj

Area of jth pre-heater, j = 2 to n-1 (m²)

B _j

Brine leaving jth effect, j = 1 to n (kg/s)

BPE _j

Boiling point elevation in jth effect, j = 1 to n (°C)

BPE _j ′

Boiling point elevation of flashed vapour in jth effect, j = 2 to n (°C)

C _p

Specific heat of water (kJ/kg-K)

d _i

Internal diameter of tube (m)

d _o

Outer diameter of tube (m)

D _j

Distillate formed in jth effect, j = 1 to n (kg/s)

ΔT _j

Temperature difference across jth effect, j = 1 to n(°C)

d _dj

Distillate formed due to flashing in jth effect, j = 2 to n(kg/s)

d _fj

Flashed distillate in the jth flashing box, j = 2 to n(kg/s)

g

acceleration due to gravity, m/s²

η _c

Efficiency of condenser

η _p

Efficiency of pre-heater

h _in

Heat transfer co-efficient inside the tube (kW/m²-K)

h _o

Heat transfer co-efficient outside the tube (kW/m²-K)

h _fgcj

Latent heat of condensation inside the tubes at T _cj of the jth effect, j = 2 to n(kJ/kg)

h _fgcj ′

Latent heat of condensation of the flashed vapor at T _cj ′ in the jth effect, j = 2 to n(kJ/kg)

h _fgcj ^′′

Latent heat of condensation of the flashed vapor at T _cj ^′′ in the jth effect, j = 2 to n(kJ/kg)

h _fgs

Latent heat of steam (kJ/kg)

h _fgvj

Latent heat of vaporization in jth effect, j = 1 to n(kJ/kg)

h _fgvj ′

Latent heat of vaporization of the flashed vapour in the jth effect, j = 2 to n(kJ/kg)

h _fgvj ^′′

Latent heat of vaporization of the flashed vapor from jth flashing box, j = 2 to n (kJ/kg)

k _w

Thermal conductivity of the tubes (W/m-K)

k_sw

Thermal conductivity of the seawater (W/m-K)

k _LC

Thermal conductivity in the liquid phase (W/m-K)

LMTD _c

Log mean temperature difference across the condenser (°C)

LMTD _pj

Log mean temperature difference across the jth pre-heater, j = 2 to n-1 (°C)

m _b

Total mass flow rate of brine (kg/s)

m _cw

Mass flow rate of cooling water (kg/s)

m _d

Total mass flow rate of distillate (kg/s)

m _s

Mass flow rate of steam (kg/s)

m _f

Feed flow rate (kg/s)

μ _sw

Seawater viscosity, kg/m-s

μ _L

Viscosity in the liquid phase, kg/m-s

n

Total number of effects

NEA _j ′

Non equilibrium allowance within the jth effect, j = 2 to n (°C)

NEA _j ^′′

Non equilibrium allowance for the flashing box for the jth effect, j = 3 to n (°C)

PR

Performance ratio of the plant

Pr

Prandtl number outside the tubes

Pr _v

Prandtl number inside the tubes

q

Heat transfer within each effect (kW)

q _c

Heat transfer within the condenser (kW)

q″

Heat flux (kW/m²)

ρ _sw

Density of seawater (kg/m³)

ρ _LC

Density in the liquid phase (kg/m³)

ρ _VC

Density in the vapor phase (kg/m³)

r _o

Outside radius of the tubes (m)

r _i

Inside radius of the tubes (m)

Re

Reynolds number outside the tubes

Re _i

Reynolds number inside the tubes

R _fo

Fouling factor outside the tubes (kW/m²-K)

R _f

Fouling factor inside the tubes (kW/m²-K)

sA

Total specific area of the system (m²/(kg/s))

sM _cw

Specific mass of cooling water flow rate

t _pj

Temperature at the outlet of the jth pre-heater, j = 2 to n-1 (°C)

T _cw

Temperature of cooling water (°C)

T _cj

Condensation temperature of the distillate in jth effect, j = 1 to n (°C)

T _cj ′

Condensation temperature of the flashed vapor in jth effect, j = 2 to n (°C)

T _cj ^′′

Condensation temperature of flash distillate from the flashing box, j = 2 to n (°C)

ΔT _cj

Vapor condensation losses inside the tubes of jth effect, j = 2 to n (°C)

ΔT _cj ′

Vapor condensation losses associated with the flashed vapor within the jth effect, j = 2 to n (°C)

ΔT _cj ^′′

Vapor condensation losses associated with the flashing box of jth effect, j = 2 to n (°C)

T _f

Temperature of feed (°C)

T _j

Temperature of brine at jth effect, j = 1 to n (°C)

T _j ′

Temperature of flashing brine within the jth effect, j = 2 to n (°C)

T _j ^′′

Temperature of flashing brine in flash boxes at the jth effect, j = 2 to n (°C)

T _s

Temperature of steam (°C)

T _vj

Vapor saturation temperature in the jth effect, j = 1 to n (°C)

T _vj ′

Vaporization temperature of flashed vapor in the jth effect, j = 2 to n (°C)

T _vj ^′′

Vaporization temperature of flashed vapor within the flashing box at the jth effect, j = 2 to n (°C)

U

Generalized overall heat transfer coefficient (kW/m²-K)

U _c

Overall heat transfer coefficient of the condenser (kW/m²-K)

U _j

Overall heat transfer coefficient of jth effect, j = 1 to n (kW/m²-K)

U _p

Overall heat transfer coefficient of the pre-heaters, j = 2 to n-1 (kW/m²-K)

V _c

Seawater velocity inside the tubes (m/s)

x

vapor phase mass fraction

X _f

Feed salinity (ppm)

X _j

Salinity of brine leaving each effect, j = 1 to n (ppm)

X _b (X _n )

Salinity of brine leaving the last effect (ppm)