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We analyze a proposed experiment {[Boixo} et al., Phys. Rev. Lett. 101, 040403 (2008)] for achieving sensitivity scaling better than {1/N} in a nonlinear Ramsey interferometer that uses a two-mode {Bose-Einstein} condensate {(BEC)} of N atoms. We present numerical simulations that confirm the analytical predictions for the effect of the spreading of the {BEC} ground-state wave function on the ideal {1/N3/2} scaling. Numerical integration of the coupled, time-dependent, two-mode {Gross-Pitaevskii} equations allows us to study the several simplifying assumptions made in the initial analytic study of the proposal and to explore when they can be justified. In particular, we find that the two modes share the same spatial wave function for a length of time that is sufficient to run the metrology scheme.