I have a problem, where I'm trying to solve the mass balance of a multi-step process with limited information available.

What I have is a material supply of known flow and composition. This supply is split into multiple streams (in my current case 7). For these streams, I do not know the individual flows, I only know they are not all equal.

Each of these streams is supplied to a separation process where they are separated into a product and a waste stream. I know the composition of each of those product and waste streams, bot no flows at all.

As such, the system looks like this: Process layout

From the compositions, I can easily calculate the ratio of product and waste stream for each separation process (i.e. the values of x1 ~ x7 above).

My problem is that I can't figure out how to calculate each of the process flows 1 through 7, or whether or not this is even possible with the information available.

I know that if I can set up a system of linear equations, where I have the same number of independant equations as unknowns, then it can easily be solved. However, I seem to only have 1 equation with 7 unknowns (sum of all process flows = total supply flow).

I would appreciate any help here.

  • $\begingroup$ you can't get there from here $\endgroup$
    – Tiger Guy
    Commented Jan 8 at 13:56
  • $\begingroup$ Thanks @Tiger Guy, after several failed attempts I came to the same conclusion. In the end, I had to gather some more data and then I could create a solver scenario in Excel, which performs some iterative guess work until the mass balance is correct. $\endgroup$ Commented Jan 9 at 17:06
  • $\begingroup$ If there is equal division of Feed or Feed split is specified...then it is is easy to perform calculations using system of linear equations $\endgroup$ Commented Feb 21 at 14:19


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.