where,

is

the density of air, the wind velocity is

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: