Multiscale Numerical Simulation

The difficulty in analyzing multi-phase fluid flow in real reservoirs is mainly caused by the strong heterogeneity of the reservoirs. The multiple scales in reservoirs may span several orders of magnitude. It takes a long time to calculate multi-scale problem by utilizing conventional numerical method. Multi-scale method incorporates the small-scale information into the base functions; therefore, multiple scale method has exclusive advantages when it is applied to reservoir numerical simulation. The multi-scale methods only need to carry out the coarse mesh on the macro scale. The multi-scale basis function, constructed by solving the partial differential equations on the coarse mesh, could capture the small scale information. It aims at reducing the computational amount and capturing the small scale characteristics. Besides, the efficiency can be further improved by applying parallel computation. In this chapter, we present some applications of multi-scale methods to fluid flows in carbonate reservoirs. We discuss multi-scale methods for transport equations and their coupling to flow equations which are solved using MsFEMs.