Open Collections

3D Simulation of Stimulated Rock Volume Evolution during Hydraulic Fracturing

Banff International Research Station for Mathematical Innovation and Discovery

Hydraulic fracturing in naturally fractured rocks often leads to the creation of a stimulated zone of enhanced permeability in which the target formation is irreversibly deformed through shear dilation of natural fractures, plastic deformation, and induced bulk damage. The current dominant modeling approach - explicitly accounting for each fracture with microscale resolution of the fracture network (e.g., discrete fracture network or distinct element method) is a computationally expensive and complex task. There also remain large uncertainties with respect to natural fracture distribution and reservoir parameters. Addressing these issues leads to identification of the need to develop up-scaled continuum model that is able to, in an average sense, capture the irreversible behavior of naturally fractured rock masses. We present a novel mathematical approach with the goal of simulating the evolution of the Stimulated Rock Volume (SRV) in a 2D/3D geomechanical model. This is achieved by introducing a homogenized non-local poro-elastic-plastic continuum zone for the stimulated region, described by an internal characteristic length scale. The up-scaled mechanism of fracturing and deformation is described by a non-local Drucker-Prager model coupled to a Biot poroelastic medium, and implemented within a standard Galerkin Finite Element Method framework. We first quantify the evolution of the SRV and pressure change in the reservoir for a typical example of hydraulic fracture stimulation in a tight formation. After the creation of a sufficiently large SRV, the well is shut-in for an extended period of time and the wellbore pressure is allowed to fall-off. The analysis of post-shut pressure curves confirms the existence of the well-known flow regimes- storage and bi-linear flow- characteristic of the simple bi-wing hydraulic fractures in homogenous rocks. Using the existing analytical solution for the finite conductive fracture, the flow capacity of the stimulated zone is calculated and correlated to the size of the stimulated zone through the non-local length scale. The performance of the developed methodology is tested by considering examples of 2D and 3D SRV calculations. For each example, the stimulated zone and the fluid pressure in relation to the local in-situ stress field are quantified. The influence of reservoir complexities, such as sedimentary layering, complex initial in-situ stress field, and wellbore effects on the evolution of the SRV and fluid pressure will be discussed.

Mathematics; Mechanics of deformable solids; Fluid mechanics

video/mp4

Author affiliation: U of Waterloo

2019-03-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68917

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/