Equilibrium Reactor with three Reactions fails

[nrgeng]

The three reactions solve in a Gibbs Reactor in Reaction Package mode, but do not solve in an Equilibrium Reactor although each reaction solves individually in an Equilibrium Reactor. The flowsheet fails when the third reaction is added. Two solve together. One would expect all three to solve together also. What is missing here?

The fsd was e-mailed to you.

[jasper]

The problem is numeric in nature, and related to the previous problems. The methanol concentration that you are trying to solve for is so close to zero that the solver has a hard time getting this value by difference.

In the situation where you just have reaction M, the reactor convergences with 7e-11 mol fraction methanol. Adding the other two reactions shifts the equilibrium such that there is less methanol. The reactor now fails to converge at a mol fraction of methanol at a final value of 6e-12 and the equilibrium constant says that the ratio methanol over its other reaction partners is still about 2 times too high. This makes the accuracy with which the conversion of reaction M needs to be determined something like the ratio of mol fraction methanol in the feed and the target method, i.e. 3e-12/5e-3 = 6e-10. On a conversion of - say - unity, the solver would need to be able to accurately tell the difference between a conversion of 1 and 1.0000000006. Given a finite precision of the numbers you are operating on, which are molar concentrations following from density calculations using an equation of state that is configured to terminate at a precision of 1e-6 (see the numerical options in the property package configuration), this is simply not feasible. Even setting that tolerance to 1e-12 does not fix the problem.

Again my solution would be - unless you are actually interested in knowing the exact very small amount of methanol that solves your system - to take out the methanol equation away from the equilibrium and consider it as instantaneous irreversible (that is, as with a conversion of 100% of methanol). You can do this in a separate reactor before performing the other two reactors, provided that the amount CO2 in your feed is not limiting, which it is not in the example you sent me.

A solver that would solve for the (log transformed) compositions using balances and equilibrium conditions as equations might do the trick, but such a setup is complicated by the fact that the reactor allows for multiple equilibrium bases, e.g. log of concentration would be required. And this is not how this particular reactor implementation is set up, it attempts to solve for the reaction extents. In those terms, the solution of your particular system is very hard if not impossible to accomplish.