Section 15. SEAFOOD WASTES
MODELING OF ULTRAFILTRATION
FOR TREATING FISHERY WASTEWATERS
Allen C. Chao, Associate Professor
Leon Tzou, Graduate Assistant
David Green, Graduate Assistant
Department of Civil Engineering
North Carolina State University
Raleigh, North Carolina 27650
INTRODUCTION
The ultrafiltration process has been successfully employed to separate soluble organic substances
from different aqueous solutions [1, 2]. This process uses a semi-permeable membrane which selectively passes solutes based on their molecular weight and size. When the solution is pressurized within
an enclosure of the membrane, substances of small molecular weight pass through the membrane
pores with water molecules as a "permeate stream" thus leaving substances of large molecular weight
in the enclosure as a "concentrate stream". The removal efficiency of an ultrafiltration process is
dependent on the molecular size of the solute and that of the membrane pore. If a membrane of
relatively large pore size is used, more solute will pass through the membrane to reach the permeate
stream and the ultrafiltration process will have a low rejecting coefficiency or low treatment efficiency. The removal efficiencies of the ultrafiltration process for treating a number of fishery wastewaters has been reported in previous publications [3-5]. Modeling and computer simulations of the
laboratory results are presented herein.
MODEL DEVELOPMENT
Basic Model
The ultrafiltration membrane is characterized by the presence of numerous pores in the membrane. During the operation, substances which have physical diameter larger than the pore diameter
are unable to pass through the membrane and thus are removed or rejected from the permeate stream.
Water and substances with a diameter smaller than the pore diameter may pass throug these pores
to reach the permeate stream. A basic model has been developed to delineate the relationship between
the rejection coefficient or removal efficiency of the substances which have a diameter smaller than
the membrane pore diameter. In developing the basic model, several simplifying assumptions were
made, such as the membrane pores are assumed to be cylindrical pipes and the solutes in water are
assumed to be spherical in shape. When traveling in the cylindrical pores, these spherical solute
particles are assumed to be evenly distributed in the liquid and their concentration is the same as that
in the feeding stream. The liquid is assumed to be Newtonian and have a laminar flow pattern with
a parabolic velocity distribution. When water flows through the membrane pore, the solutes are
assumed to travel at the same velocity as the surrounding liquid. Ignoring diffusion of solute, concentration polarization and membrane-solute interactions, the following equation has been derived
16]:
P = [ R(2-R)]2 for R < I (1)
Where: P  = Rejection Coefficient or Removal Efficiency
R =    Solute to Membrane Pore Diameter Ratio
Paine and Scherr [6] considered that when the solute sphere moves through the cylindrical membrane pore, it always moves at a slower velocity than that of the surrounding fluid. The moving
solute will then experience a drag force F which can be calculated by the following equation:
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