  The dual continuum model serves as a powerful tool in the modeling of
subsurface applications. It allows a systematic coupling of various components
of the solutions. The system is of multiscale nature as it involves high
heterogeneous and high contrast coefficients. To numerically compute the
solutions, some types of reduced order methods are necessary. We will develop
and analyze a novel multiscale method based on the recent advances in
multiscale finite element methods. Our method will compute multiple local
multiscale basis functions per coarse region. The idea is based on some local
spectral problems, which are important to identify high contrast channels, and
an energy minimization principle. Using these concepts, we show that the basis
functions are localized, even in the presence of high contrast long channels
and fractures. In addition, we show that the convergence of the method depends
only on the coarse mesh size. Finally, we present several numerical tests to
show the performance.
