**Calculation of specific energy demand (SED) of crossflow membrane**

This example shows a method of calculating SED for a single tube tubular membrane system, where water flows through a uniform channel from the entrance to the exit without changing channel size. Due to low pressure loss, membrane channel length can be extended up to 48 m (vs 10-15 m for typical tubular membranes) for the same total pressure loss of 5-6 bar. As a result, higher permeate recovery is possible with single tube system than with multi-tube system at one feed circulation. It must be noted that the estimated SED for single tube system in this example will fall into the low end of the SED known for crossflow filtration.

If inlet pressure is known, total energy consumption can be calculated by estimating the power demand to pressurize the liquid and to move the liquid at certain speed in membrane system. The condition given is as follow.

*P _{in }*= inlet pressure (550 kPa)

*ρ*= liquid density (1,000 kg/m

^{3})

*ν*= liquid velocity in membrane module (3.7 m/s)

*D*= internal diameter of membrane (0.0254 m)

_{i }*n*= number of channels (10 ea)

*ε*= pump efficiency ( 0.6 -)

_{p}*ε*= motor efficiency ( 0.9 -)

_{M }*J*= average flux (83 LMH, 2 m/d, 2.31×10

_{avg }^{-5}m/s, or 49 gfd)

*L*= effective membrane length (48 m)

The liquid flow rate to membrane system, *Q _{feed}* (m

^{3}/s), can be calculated using equation (1)

—————————————(1)

m^{3}/s or 67.5 m^{3}/hr

Note that the inlet pressure already includes the pressure required to overcome longitudinal pressure loss and head loss/gain from the difference in the elevations of inlet and outlet. Power demand, (kW), can be calculated using the equation here. The velocity head in the equation is not neglected here since it can be significant due to the high liquid velocity.

= 18.4 kW

Total permeate flow rate, *Q _{p}* (m

^{3}/s) can be calculated as

*Q _{p} = (πD_{i}Ln)^{.}J* ————————————- (2)

=(3.14 x 0.0254 x 48 x 10) x 2.31 x 10^{-4} = 8.86 x 10^{-4} m^{3}/s (or 3.19 m^{3}/hr)

Finally *SED _{filtration}* is calculated as follow.

= 5.8 kWh/m^{3}

The permeate recovery from a single pass of the mixed liquor is calculated at only 4.7% (=3.19/67.5, *Q _{feed}/Q_{p}*) , which means 21 times more liquid recirculation is required to obtain certain volume of permeate. Due to the very optimistic assumption of the long tubular membrane with 48 meter channel, the SED obtained above falls into the low end of the literature values,

*i.e*. 4-12 kWh/m

^{3 }(Côté, 2000).

Despite of the optimistic assumption, it is very apparent that SED of side-stream filtration is more than an order of magnitude higher than that of submerged membrane system (0.09-0.5 kWh/m^{3}). This is a significant handicap when tubular membranes are used for the process that does not create high value, *e.g*. municipal wastewater treatment. In general, tubular membranes can be considered as a competitive option only when specific reasons exist to the benefit of it.

© Seong Hoon Yoon