Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Flow and Leakoff in a Hydraulic Fracture Using the Finite Volume Method
Submission Author:
Keveen Tenereli , SC
Co-Authors:
Keveen Tenereli, Hermínio Tasinafo Honório, Clovis Maliska
Presenter: Keveen Tenereli
doi://10.26678/ABCM.COBEM2021.COB2021-0207
Abstract
Hydraulic fracturing is an important stimulation technique mainly applied to tight reservoirs. It consists of injecting a fracturing fluid at high pressure through a well with the intention of initiating and propagating fractures. These fractures ultimately increase the formation permeability and thus the well productivity. Although fracture propagation plays an important role in this process, the present work focuses on the numerical modeling of the fluid flow through the fracture and the surrounding porous rock, where a rigid solid skeleton is assumed. The fluid flow inside the fracture is considered to be one-dimensional and it is mathematically modeled in two different ways. In the first model, the Navier-Stokes equations are solved for both the pressure and velocity fields. Alternatively, a cubic law, obtained through the Poiseuille solution for a flow between parallel plates, is employed to evaluate velocities in the mass conservation equations, so the pressure field is the only unknown. These two models carry different assumptions and simplifications, so a comparison is carried out in terms of accuracy and computational cost. The fracture (flow) models are discretized through the Finite Volume Method (FVM) in a one-dimensional grid. For the fluid flow through the porous medium, on the other hand, the Element based Finite Volume Method (EbFVM) is employed for the discretization of the mass conservation equation in two-dimensional unstructured grids. The two physical processes (i.e. fluid flow inside fracture and porous medium) are coupled through the fluid exchange between the channel and the rock formation, the so called leakoff. The numerical strategy for treating the coupling between these two physical processes is described in details. The results show that the two models for fluid flow inside fractures produce almost the same results in most practical situations. Discussions and physical interpretations of the results are also provided in this work. Finally, the coupling strategy is shown to provide physically consistent results.
Keywords
Hydraulic fracturing, Finite volume method, unstructured grids
