ABSTRACT
A Pure water permeation constant of membrane (m/(s·Pa))
Aap Water permeation constant of membrane at PRO condition (m/(s·Pa))
B Solute permeation coefficient of membrane (m/s)
C Solute concentration of solution (mol/m3) Cr Assumed solute concentration of permea-
tion (mol/m3) d Diameter of hollow fiber (m) D Diameter of hollow fiber bundle (m) E Efficiency or combined efficiency of rotary
machine Eom Mechanical efficiency for ideal output Eoc Energy conversion efficiency for input
salinity gradient f Flushing ratio=F/∆V F Flow rate of flush out from the permeator
(m3/s) H Water head loss, head or lift (Pa) J Water permeation flux (m3/(m2·s)) or (mol/
(m2·s)) l Thickness of packed bed (fiber bundle)(m) L Length of hollow fiber (m) LD Width of compartment (m) m Number of hollow fiber M Loss factor with pressure drop for per-
meation flow rate (Pa·s/m3) n Number of compartments
P Pressure (Pa) Pa Atmospheric pressure (Pa)(value assumed
to be zero in this paper) S Membrane surface area in the permeator
(m2) Sv Surface area per unit volume of hollow
fiber (m-1) U Mean velocity (m/s) V Flow rate of salt water into the permeator
(m3/s) W Ratio of superficial output to ideal output Wnet Net power output (W) x Feed ratio=V/∆V α Proportional factor of salt water passage
for mean flow rate (Pa·s/m3) α´ Correction factor of salt water passage for
Kozeny equation ß Proportional factor of fresh water passage
for mean flow rate (Pa·s/m3) ß´ Correction factor of fresh water passage
for Hagen-Poiseuille equation γ Mean water head of tank (Pa) ∆N Flow rate of solute permeate through the
membrane (mol/s) ∆P Hydraulic pressure difference across fiber
wall or pressure drop of fluid passage (Pa) ∆V Flow rate of water permeate through the
membrane (m3/s) ∆Π Osmotic pressure difference across fiber
wall (Pa)
∆Π0 Osmotic pressure difference between salt water and fresh water at the source of supply (Pa)
ε Void fraction of hollow fiber bundle; 1-ε=packing ratio
Km Solute permeation coefficient in supporting layer (cm/s)
Ks Mass transfer coefficient on membrane surface (cm/s)
µ Viscosity coefficient (Pa·s) Π Osmotic pressure (Pa)
Subscripts A Epoxy tube sheet of the element B Interface of supporting layer to active
layer E Element of hollow fiber bundle in the cy-
lindrical shell F Filling up or filling pump G Generator H Surface of active layer i Inside M Motor o Outside P Epoxy partition wall S Solute, salt water side, or salt water pump T Turbine W Permeate water, fresh water side, or fresh
water pump
13.1 INTRODUCTION
Although the earth is called ‘the planet of water’ most of the water exists as sea water. The fresh water we can utilize is in the rivers, lakes and marshes. With the addition of subterranean water, these constitute less than 1% of the water on the earth.1 If we think about the fact that this precious fresh water evaporates from the surface of the sea because of solar radition, the water can be regarded as a major store of solar energy. Around estuaries the sea and fresh water mix and the energy is dispersed. Osmotic power generation, which is explained in this paper, is an attempt to extract the solar energy in the fresh water making use of fiber walls, or membranes. The process is the opposite of desalination.
