When solving the MESH (Mass, Equilibrium, Summation and Heat) equations for an equilibrium absorption model (specifically CO2 absorption using monoethanolamine (MEA)), what is an acceptable tolerance for the residuals of the equations.

The mass equations are simply the component mass balances (X4), Equilibrium relations are of the form (Keq = y/x), where the Keq is polynomial f(mole fraction, temperature), Summation is simply adding the concentrations to 1, and the heat balance accounts for the change of enthalpies (as Cp*deltaT), CO2 heat of absorption, and H2O heat of vaporization.

I am using MATLAB (non-linear solvers, such as fsovle and fmincon) to reach to a solution but I am not able to achieve a 0 residual (perhaps 1e-5 or smaller). In the Process Separation Principles (Henley, Seader, and Roper. 3rd Edition), a convergence criterion was suggested as follows:

error = N(2C+1)(sigma(Fi))^2*e-10, where N is the number of stages, C is the number of components, and F is a feed stream (mainly the flue gas and lean solvent).

In a solved example of hydrocarbon separation, the value of the error was in the order of 1e-2. I am getting a similar error but using fsolve (and levenberg-marquardt algorithm) in my case. Yet, this criterion appears to be applicable when solving the MESH equations using the Newton Raphson method, as per the book.

I am getting reasonable answers for the variables, but subtle changes in the initial guesses can send me somewhere else, which is expected for such a system. Any ideas/thoughts on how to proceed, and whether I should accept the current error?