  In this paper, we develop and analyze a rigorous multiscale upscaling method
for dual continuum model, which serves as a powerful tool in subsurface
formation applications. Our proposed method is capable of identifying different
continua and capturing non-local transfer and effective properties in the
computational domain via constructing localized multiscale basis functions. The
construction of the basis functions consists of solving local problems defined
on oversampling computational region, subject to the energy minimizing
constraints that the mean values of the local solution are zero in all continua
except for the one targeted. The basis functions constructed are shown to have
good approximation properties. It is shown that the method has a coarse mesh
dependent convergence. We present some numerical examples to illustrate the
performance of the proposed method.
