items detailed in Eqs。 (32), (38) and  (39)

Cdewatering   ¼ Cenergy  þ Cdepreciation  þ Clabor ð40Þ

It is anticipated that this overall cost as defined in Eq。 (36)can be  minimized  by  identifying  the  optimal  operating     conditions

including the filtration vacuum pressure, p, and the filter    rotation

where k is the ratio of heat capacities of air at constant pressure and constant volume。 The energy required to maintain the rotation of the filter drum is assessed by Eq。 (30) [28],

5。 Results and discussion

5。1。 Algal  cake-layer thickness

The sized filter has a drum diameter of 0。9 m and a drum length

of 0。6 m, and it provides a working area of 1。69 m2。 The thickness

where x is the angular velocity of the rotating drum filter, k is the ratio of radius of the drum filter to that of the feed tank, the first term is the drag force experienced by the rotating filter in the feed tank, and the second term is the torque resistance。

Therefore, the total energy of the RDVF dewatering system   is

Wtotal   ¼ Wwater  pump  þ Wvacuum  þ Wrotation ð31Þ

Assuming the price of industrial electricity is 0。05 US$/kWh, the energy cost is thus

Cenergy   ¼ 0:05 · Wtotal ð32Þ

Supposing the unit price of the rotary filter is Pc, the capital cost for purchase of the filters  is

C1  ¼ n · Pc ð33Þ

As a rule of thumb, the installation of the dewatering system can be considered to be 60% of the major capital cost [35,36] of the process。

C2  ¼ 0:6 · n · Pc ð34Þ

The room temperature operation of the process also requires the dewatering facility and the accompanying system to be installed indoors。 Infrastructure cost is assessed by assuming the space required by the whole system and the open space needed for process maintenance and operation, which  is  estimated  at 50% of the capital cost。

C3  ¼ 0:5 · n · Pc ð35Þ

Empirically, it has been shown that the maintenance cost is usually 10% [35,36] of the sum of the above three  items,

C4  ¼ 0:21 · n · Pc ð36Þ

Therefore, the total capital investment  is

Ccapital  ¼ 2:31 · n · Pc ð37Þ

Assuming the life span of the filter with maintenance is 20 years [35], the hourly depreciation of the investment is estimated   as

Cdepreciation   ¼ 2:31 · n · Pc=20=365=24 ð38Þ

of algal cake-layer as shown in Fig。 3 was investigated over a wide range of operating conditions: vacuum pressure ranging from 5 to 60 kPa, and filter rotation cycle time varying from 10 to 120 s。 Nat- urally, for a specific operating pressure, a thicker algal cake-layer corresponds to a longer cycle time。 As shown in Fig。 3, the impact of the working pressure on the cake-layer thickness is more com- plicated。 Roughly speaking, algae-dewatering benefited from using a higher filtration pressure under 10 kPa, as indicated by the increased algal cake-layer thickness。 Negative impact  was observed instead when the filtration  pressure  was  higher  than 20 kPa。 It was seen that the buildup rate of algal cake-layer was remarkably slowed by the increased working pressure。 This resulted from the compressibility of algae。 For a compressible algal cake-layer, the filtration pressure plays two roles, one is the driving force for the filtration, and the other is the driver for cake-layer compression, and the other occurs when the working pressure is raised higher than the critical pressure (17 kPa) of algae compres- sion。 Any pressure surpassing this critical pressure densifies the algal cake-layer, and causes a higher transport resistance for fil- trate water, resulting in a reduced throughput for water and a cor- responding lesser algal cake-layer thickness。 It is shown in Table 1 that the porosity of the algal cake-layer is strongly dependent upon the working pressure。 There is almost 45% cake-layer porosity loss