The rate of transfer of CO2 from the gas phase to the bulk culture medium ( ) was estimated by the following equation: where, was the mass transfer coefficient from the gas phase to the liquid phase, and was the concentration of dissolved CO2 in the liquid phase which was in equilibrium with the concentration of CO2 in the gas phase. was estimated by the following equation: As the residence times of the gas in the culture medium was small, pseudo steady state conditions were assumed.
Thus, the following equation was obtained by combining equation the above equations: The saturation concentration of CO2 ( ) was computed using Henry’s Law according to the following: where, H was the Henry’s constant and p was the partial pressure of CO2 in the atmosphere.Combining equations 68 and 69 and then integrating within the proper limits, the following equation was obtained: ( ) (70) Thus, the moles of CO2 transferred from the gas phase to the culture medium ( ) was given by the following equation: ( )) (71) Uptake of Carbon by microalgaeThe bio uptake of carbon by microalgae during the growth phase was modeled using an approach described in the literature 20,21. The dissociation of CO2 in water was given by the following equations: where, and were the dissociation constants of and respectively.
The total dissolved concentration of carbon in the medium could be obtained by adding the concentration of , , and , respectively. Several studies considered the total dissolved concentration of carbon species in water to determine the carbon uptake by microalgae 20,47. In this study, it was assumed that the pH of the solution was between 7.67-6.
83 where the dominant species was bicarbonate 21. Thus, the bio uptake of carbon by microalgae was assumed to take place only in the form of bicarbonate and the concentration of dissolved CO2 ( ) was essentially the concentration of bicarbonate in the solution. Assuming that the culture medium was thoroughly mixed, molar balance of dissolved carbon in the culture medium provided the following equation: The carbon uptake rate by microalgae ( ) was estimated utilizing the following equation: Thus, combining the above equations, the main governing equation was obtained as follows: ( )) – Modeling carbon uptake by microalgae in the growth phase was provided in greater detail in literature 20,21,43,46,47. Effect of relative components on capital and operating costsThe following charts give the effect of various components on the capital cost and operating cost estimates.