An introduction to the derivation of surface balance equations without the excruciating pain

Abstract

Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the interface and boundary conditions between various domains. This paper provides an elegant, straightforward and universal method that considers the nature of those shared boundaries and derives the appropriate conditions at the interface, irrespective of the governing equations being solved. As a first example, a well-known interface condition is derived using this method. For a second example, the set of boundary conditions necessary to solve a baseline aerothermodynamics coupled plain/porous flow problem is derived. Finally, the method is applied to two more flow configurations, one consisting of an impermeable adiabatic wall and the other an ablating surface.

A critical review on coupled geomechanics and fluid flow in naturally fractured reservoirs

“…( 9) in different continuums. Therefore, it is essential to specify the initial and boundary conditions, and the continuity equation must be detected at different interfaces between distinct continua in terms of pressures, concentrations and mass fluxes (Martin et al, 2017). Fig.…”

“…In addition, the fully coupled scheme requires enormous software development efforts and large computational costs (Kim et al, 2013) whereas the iterative coupling scheme combines the conventional reservoir geomechanics and fluid flow simulators through a data exchange interface (Chin et al, 2002). Despite several research efforts (Ashworth and Doster, 2019;Martin et al, 2017;Weishaupt et al, 2019), coupled geomechanics and multiphase flow is still a challenging issue related to mathematical, numerical models and discretization schemes to capture the hydrodynamic behaviours, such as fracture deformation and fluid flow interaction at fracture matrix interface in naturally fractured reservoirs.…”