Before revision:  We investigate global asymptotic stability in a modelwith finitely many species, Monod kinetics, different removal rates, and a constraint based on the Nernst and Butler-Volmer equations. If methanogens can grow at the lowest substrate concentration, then the equilibrium corresponding to competitive exclusion by methanogens is globally asymptotically stable.
After revision:  We investigate global asymptotic stability in two industrially relevant versions of the model. An important aspect of many chemostat models is the principle of competitive exclusion, which states that only the URLanisms which can grow at the lowest substrate concentration will survive. We show that if methanogens can grow at the lowest substrate concentration, then the equilibrium corresponding to competitive exclusion by methanogens is globally asymptotically stable.