Instantaneous equations for multiphase flow in porous media without length-scale restrictions using a non-local averaging volume

The aim of this paper is to propose a framework to obtain a new formulation for multiphase flow conservation equations without length-scale restrictions, based on the non-local form of the averaged volume conservation equations. The simplification of the local averaging volume of the conservation equations to obtain practical equations is subject to the following length-scale restrictions: d ≪ ℓ ≪ L, where d is the characteristic length of the dispersed phases, ℓ is the characteristic length of the averaging volume, and L is the characteristic length of the physical system. If the foregoing inequality does not hold, or if the scale of the problem of interest is of the order of ℓ, the averaging technique and therefore, the macroscopic theories of multiphase flow should be modified in order to include appropriate considerations and terms in the corresponding equations. In these cases the local form of the averaged volume conservation equations are not appropriate to describe the multiphase system. As an example of the conservation equations without length-scale restrictions, the natural circulation boiling water reactor was consider to study the non-local effects on the thermal-hydraulic core performance during steady-state and transient behaviors, and the results were compared with the classic local averaging volume conservation equations.