[pierrest]

Hello,

I am building a simulator with Simulink (MATLAB). I need to simulate a photobioreactor and there is carbone dioxyde involved (the phytoplancton culture does photosynthesis in order to grow). It enters in the photobioreactor in gaseous form at 20 mL/minute. I need the mass-balance equation for the CO2 uptake. In this equation there is a therm called the «CO2 saturation concentration» (I don't really know it is). I don't have a huge background in chemistry. I don't know if it's a constant or a variable and I don't know how to find and/or calculate it. It seems to be in relation with the Henry's Law. The liquid in the photobioreactor is mostly a replica of seawater. Hope to hear from someone soon!

Thank You.

Regards,

Pierrest 

[Stepan]

For any given liquid it is a function of temperature and CO2 partial pressure. The constant itself depends on liquid nature and pH (if water)

[pierrest]

Thank you for your answer!
So if I understand, the CO2 saturation concentration is a variable?
Please, can you type the function. I know how to find the partial pressure and I know the temperature.
Also, which constant are you talking about?

Thanks again!

[typhoon2028]

It sounds like a transient process.  It does not appear to be at equilibrium; you need to consider mass transfer.

[pierrest]

OK, so its a variable. That's what I thought. I have found the following equation in litteratue:

CO2* = ((10^3)(R)(T)([CO2]))/H

where CO2* is the saturation concentration, R is a constant, T is the temperature (in my case constant), H is a constant but I not really sure which constant and [CO2] is the concentration (and it varies). Thus, CO2* is a variable. The thing is that I am not sure if it's a general equation and if it applies in my case.

Thanks again!!

Pierrest

[Stepan]

I did not verify the details, but the publication below sounds quite professional. You mostly need chapter 2. It also gives you some references:
http://www.thuisexperimenteren.nl/infopages/Carbondioxide%20in%20water%20equilibrium.doc
another reference
http://www.engineeringtoolbox.com/gases-solubility-water-d_1148.html 

This one is particularly talks about seawater equilibrium

http://cdiac.ornl.gov/ftp/cdiac74/chapter5.pdf

for more try to search for :"Carbon Dioxide seawater Solubility"

[pierrest]

Thank You for the info. I've printed the documents but have a really hard time understanding, because like I've mentionned earlier, I don't have a good background in chemistry. Can you tell me if the equation I wrote is valid?

CO2* = ((10^3)(R)(T)([CO2]))/H

where CO2* is the saturation concentration, R is a constant, T is the temperature (in my case constant), H is a constant and [CO2] is the concentration (and it varies). Thus, CO2* is a variable. The thing is that I am not sure if it's a general equation and if it applies in my case.


Thank You

[Stepan]

It does not look right if used as a general equation. It is likely something developed for a particular application or solution. On a top, I do not understand what are the units, what is H, is R - gas constant or what, and so on. It is too sketchy. In general:
C(CO2)=K*P(CO2)

if pH and Temperature are constants. When P(CO2) is high, the function would become nonlinear.

[pierrest]

Is C(CO2)=K*P(CO2) Henry's law? With C(CO2) being the equilibrium mole fraction of solute in liquid phase and P(CO2) being the partial pressure and K being Henry's constant? If so, maybe I could use it. I know Henry's constant. What would be the partial pressure?

Thanks again for your *delete me*

[Stepan]

Henry's constant depends on your solution properties. Be careful if you use handbook numbers, they might be not applicable to your particular solution and different by orders of magnitude from the book value for H2O. this is true and especially for CO2, which a) physically dissolved in liquid, b) reacts with liquids.


You do not have to use partial pressure:
 http://en.wikipedia.org/wiki/Partial_pressure 

Use whatever units work the best for your project.