Modeling of heat and mass transfer in a fractured porous medium

While fractured formations are possibly the most important contributors to the production of oil worldwide, modeling fractured formations with rigorou s treatments has eluded reservoir engineers in the past. To date, one of th e most commonly used fractured reservoir models remains the one that was su ggested by Warren and Root nearly four decades ago. ln this paper, a new mo del for fractures embedded in a porous medium is proposed. The model consid ers the Navier-Stokes equation in the fracture (channel flow) while using t he Brinkman equation for the porous medium. Unlike the previous approach, t he proposed model does not require the assumption of orthogonality of the f ractures (sugar cube assumption) nor does it impose incorrect boundary cond itions for the interface between the fracture and the porous medium. Also, the transfer coefficient between the fracture and matrix interface does not need to be specified, unlike the cases for which Darcy's law is used. In o rder to demonstrate the usefulness of the approach, a two-dimensional model of a fractured formation is developed and numerical simulation runs conduc ted. The proposed model is derived through a series of finite element modeling r uns for various cases using the Navier-Stokes equation in the channel while maintaining the Brinkman equation in the porous medium. Various cases stud ied include different fracture orientations, fracture frequencies, and ther mal and solutal constraints. The usefulness of the proposed model in modeli ng complex formations is discussed. Finally, a series of numerical runs als o provided validity of the proposed model for the cases in which thermal an d solutal effects are important. Such a study of double diffusive phenomena , coupled with forced convection, in the context of fractured formations ha s not been reported before.