Fractured Reservoirs Modeling by Embedded Fracture Continuum Approach: Field-Scale Applications

Modeling the Effect of Intersected Fractures on Oil Production Rate of Fractured Reservoirs by Embedded Fracture Continuum Approach

“…Based on the hypothesis that the flow in the fractured element is principally conducted through the fracture inside the domain and flow in fracture is assumed to be laminar between two infinite parallel smooth plates (cubic law), the permeability K f is defined as K f � w 2 /12, where w is the aperture of fracture. By equivalence of the flux flow through the fracture cell and one through the fracture, we have the formula to determine the isotropic equivalent permeability of the fracture cell of type I [7][8][9]15]:…”

“…Regarding the dimension of the well, the saturated reservoir of 200 m width and 200 m length (with respect to the center of the well) was selected. e initial pore pressure and total isotropic horizontal stress are assumed to be equal to 10.0 MPa and 24.46 MPa, respectively, which corresponds to the values measured at the depth of 725 m in the Sellafield site [7][8][9]. Otherwise, concerning the boundary conditions, we consider that the top and right boundaries are closed and fixed while a zeroconstant pressure is imposed on the wall of the well.…”

“…Following this model, the closure/opening of fractures is principally affected by the effective normal stress acting on their surfaces (shear stress is neglected). In equation (8), w init and k init n are the aperture and normal stiffness of fracture at the initial state, respectively; w f is the actual fracture aperture calculated from the variation of the effective normal stress Δσ n ′ � σ n ′ − σ n,o ′ (σ n ′ and σ n,o ′ indicate the actual and initial effective normal stress acting on the fracture plane, respectively). Otherwise, through the definition of the effective stress σ n ′ � σ n − b.p (we can consider the simplest case b � 1), if the variation of the total stress is negligible, the evolution of fracture aperture can be defined as a function of the pressure drawdown p drawdown :…”

“…e flexibility and performance of this hierarchical approach were demonstrated by these authors in modeling the complex fractured rock masses. In this paper, the embedded fracture continuum (EFC) approach [7][8][9] will be used to model a hypothetical reservoir whose natural fractures coincide with that of the Sellafield site [10]. e objective is to illustrate the effects of intersected fractures on the oil production rate of a fractured reservoir.…”

“…is well surface is explicitly considered in our model through which the production rate (fluid flux) will be calculated directly while the drop of pressure in the fractures is decided by the transient flow in their corresponding fracture cells. e implementation of these fractures in the model at the present stage seems easy by using the EFC approach based on the fracture cell concept [7][8][9]. Note that each fracture cell in the model represents a porous medium which has its own porosity and permeability and is different from those of the fractured matrix.…”