  This paper presents and analyses a Constraint Energy Minimization Generalized
Multiscale Finite Element Method (CEM-GMsFEM) for solving single-phase
non-linear compressible flows in highly heterogeneous media. The construction
of CEM-GMsFEM hinges on two crucial steps: First, the auxiliary space is
constructed by solving local spectral problems, where the basis functions
corresponding to small eigenvalues are captured. Then the basis functions are
obtained by solving local energy minimization problems over the oversampling
domains using the auxiliary space. The basis functions have exponential decay
outside the corresponding local oversampling regions. The convergence of the
proposed method is provided, and we show that this convergence only depends on
the coarse grid size and is independent of the heterogeneities. An online
enrichment guided by \emph{a posteriori} error estimator is developed to
enhance computational efficiency. Several numerical experiments on a
three-dimensional case to confirm the theoretical findings are presented,
illustrating the performance of the method and giving efficient and accurate
numerical.
