Mass Balance

[amolpatil1983]

Hi, there!
Thanks for such a nice implementation.
I take this opportunity to know more about mass Balance equations to be fed to the program. E.g.,

Consider the following system

CD + MEA = CBNAC
CD + MEA = CBMAC
CD + MEA = OZD + Water

What will be the mass Balance equations to be used here?

Using,

CD + CBNAC+CBMAC
MEA+CBNAC+CBMAC

Seems to give better in comparison when using

CD + CBNAC+CBMAC+OZD
MEA+CBNAC+CBMAC+OZD

Or

CD + CBNAC+CBMAC
MEA+CBNAC+CBMAC
OZD-WATER

It seems that I am failing to understand the logic

[mtod92]

Hi Patil,

Let's say that you start with 5 CD and 10 MEA (initial concentrations).
Let's say that your reaction 3 is dominating in your system and all your CD and MEA react through that.
In this case we can neglect the first two reactions.
This means that at equilibrium you will have consumed your 5 CD and 5 MEA, so your final product will be 5 OZD, 5 WATER and 5 leftover MEA (given the initial excess).

Your mass conservation has to keep this into account. Let's try with the following:
OZD + WATER + CD == CD (initial) <-- you can easily see that this cannot be, because at equilibrium we would have 5 + 5 + 0 != 5

The issue here is that the total number of OZD and WATER (OZD + WATER) molecules produced in your reaction 3 is going to be double of whatever amount of CD (or MEA) was consumed to form them.
Keeping this into account, the correct mass conservations will be instead:
0.5OZD + 0.5WATER + CD == CD (initial) <-- 2.5 + 2.5 + 0 == 5
0.5OZD + 0.5WATER + MEA == MEA (initial) <-- 2.5 + 2.5 + 5 == 10

Including the other reactions (1 and 2), I would then set the following mass conservations:
1CD + 1CBNAC + 1CBMAC + 0.5OZD + 0.5WATER == CD (initial)
1MEA + 1CBNAC + 1CBMAC + 0.5OZD + 0.5WATER == MEA (initial)

We can now rewrite this problem in a form suitable for equipy:

species_names = {'CD':0, 'MEA':1, 'CBNAC':2, 'CBMAC':3, 'OZD':4, 'WATER':5}
stoichiometry = np.array([[-1, -1, +1, 0, 0, 0],[-1, -1, 0, +1, 0, 0],[-1, -1, 0, 0, +1, +1])
K = np.array([1, 2, 3]) # whatever your equilibrium constants are going to be
total_masses = np.array([5, 10]) # whatever your initial concentrations for CD and MEA are going to be, I am using 5 and 10
mass_conservation = np.array([[1, 0, 1, 1, 0.5, 0.5],[0, 1, 1, 1, 0.5, 0.5]])

Theoretically, since OZD and WATER are not taking part in any other reaction and you know that they are the same at equilibrium, you could make this problem more digestible, either using a placeholder instead of (OZD + WATER) or (they are formally the same) ignoring one of the two. This would lead to your second set of mass conservation equations.
I would say that the main problem with this "simplifying" approach is that you have to be really careful when redefining your equilibrium constants.

Please let me know if this makes sense to you, I have quickly gone through it so I may have misunderstood or missed something.

Best,
Marco

[amolpatil1983]

Thanks for the quick reply !

Your reasoning was extremely helpful in clearing my doubts.

Well I must admit that I did not know that we can use fractions there in equpy.

I take this opportunity to ask if there are any extensive advices on the proper usage of equpy..e.g. can we multiply a whole mass Balance equations with some number etc..

Of course, my actual task is much more complicated than these three reactions...I used these as surrogate to the problem I faced. Actually I am a quantum chemist but very new to the field of kinetics and dynamics. Your program is a real help in time...It works fast and smooth.

Since I am new to this practical computation of thermodynamic equilibria, can you recommend me any books, just in case these might be helpful for me to elevating my understanding. I tried over internet but couldn't find much on practical mass balances etc. for complicated reaction networks...most of the texts I came across deal with very introductory level...