Multicontinuum description of flow in composite heterogeneous media

Adequacy of the description of flow and transport processes in subsurface d epends on how well a model represents the heterogeneity. One of the simples t models to describe the heterogeneity structure is a so-called composite s ystem. Flow and transport 'simulation in composite systems can be reduced t o solving equations and averaging the solutions. A different approach relat ed to averaging the equations leads to new equations. This description is d esignated as monocontinuum description. If the homogeneous components of a composite system, so-called phases, have different hydrodynamic and/or geom etric parameters, it is natural to study averaging on the individual phases along with the global averaging. This approach takes into consideration th e mean fields in the individual continuum phase as well as the cross flows and cross forces between continua. However, this description is nonclosed. To overcome this difficulty, the phenomenological theory usually postulates a special interaction mechanism for closing the equations. This paper pres ents the exact equations of mass balance and moment balance for each phase. The exact sense of exchange terms in the multicontinuum models is explaine d. We demonstrate that joint consideration of the monocontinual and multico ntinual systems in the case of two-phase random composite leads to a closed description and that we can find the exchange terms. For a periodic compos ite system the same approach leads to a closed description for any number o f phases. The terms describing the interactions between continua for system s with a random and periodical structure are calculated. We examine the hyp othesis customarily made in the phenomenological models.