where, the lethal temperature of microalgae growth, optimal temperature

where,

 is
the density of air, the wind velocity is

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 and the viscosity of air is given by

.

The
conduction from the ground (

 is
calculated as referenced in 17.

where,

m from literature 17

The
temperature factor (

 which affects the specific growth rate of
microalgae is given by the following equation as reported in literature 6:

where,

 (oC),

 (oC)
and

 (oC)  are the lethal temperature of microalgae
growth, optimal temperature of microalgae growth and water temperature of the
culture medium, respectively.

 

 

Microalgae growth kinetics model

Nitrogen Uptake Modeling

            The uptake of nitrogen by the
microalgae was computed by solving the following set of equations 14,43:

  

where

 was
the cell quota of nitrogen in algal biomass (kg kg-1),

 was
the calculated specific uptake rate of nitrogen (kg kg-1 day-1),

 was
respiration constant of nitrogen (day-1) and

 was
the specific uptake rate of nitrogen (day-1). The

 was
related to the maximum specific uptake

 (kg kg-1 day-1), uptake
of internal nitrogen concentration efficiency (

) and uptake of external nitrogen
concentration efficiency (

) by the following equation:

  

The

 was
defined by the following equation where

 was
the minimum level of nitrogen present internally below which the cells do not
grow (kg/kg).

   

The

 was
treated as a Michaelis-Menten kinetic function and was computed according to
the following equation 22,44,45:

  

where 

 was
the concentration of nitrogen in the medium (kg m-3) and

 was
the half-saturation constant of uptake of nitrogen (kg m-3).

Phosphorus Uptake Modeling

            The
uptake of phosphorus by the microalgae was evaluated similarly to the nitrogen
uptake. The governing equations are as follows:

  

where

 was
the cell quota of nitrogen in algal biomass (kg kg-1),

 was
the calculated specific uptake rate of nitrogen (kg kg-1 day-1),

 was
respiration constant of nitrogen (day-1) and

 was
the specific uptake rate of nitrogen (day-1). The

 was
related to the maximum specific uptake

 (kg kg-1 day-1), uptake
of internal nitrogen concentration efficiency (

) and uptake of external nitrogen
concentration efficiency (

) by the following equation:

The

 was
defined by the following equation where

 was
the minimum level of nitrogen present internally below which the cells do not
grow (kg kg-1).

 

The

 was
treated as a Michaelis-Menten kinetics function and was computed according to
the following equation:

   

where 

 was
the concentration of phosphorous  in the
medium (kg m-3) and

 was
the half-saturation constant of uptake of phosphorous (kg m-3).

 

Carbon dioxide uptake modeling

            The
transfer and uptake of CO2 by microalgae is a complex process and was
modeled by coupling of two separate phenomena, CO2 transfer by
sparging from gas phase to liquid phase (bulk culture medium) and uptake by
microalgae during the growth phase. The following set of equations describing carbon
dioxide uptake used in the model was obtained from  literature 20,43,46,47.

CO2 transfer from gas phase to
bulk culture medium

            The
mass transfer of CO2 from the sparging phase to the bulk culture
medium was obtained by solving the following equations as obtained in
literature 20,21,43.

            An elemental height

 of
the pond depth was assumed and transfer of CO2 within the element was
expressed by the following equation: