The phase behavior of the continuous shouldered well model fluid proposed
by Franzese [J. Mol. Liq. 136 (2007) 267] was examined using the
Monte Carlo computer simulations in the grand canonical ensemble. The essential
parts of the vapour-liquid and liquid-liquid coexistence envelopes were
obtained. The Widom lines departing from coexistence envelopes were calculated
using maxima of the fluctuations of the number of particles as a function of
chemical potential along various isotherms. The region embracing anomalies in
the properties of the model was located using the approximate criterion that
involves the excess pair entropy.. The temperature of maximum density line was
built by performing canonical Monte Carlo simulations. Our results are
consistent with previous results from molecular dynamics constant
pressure-constant temperature simulations and provide wider insight into the
phase behavior of the model by using the chemical potential as the external
parameter.