Modeling hydraulic fracturing fully coupled with reservoir and geomechanical simulation

Unconventional fracturing applications such as long-term waterflooding at fracturing pressure, produced water re-injection and waterfracs, etc., are characterized by very high fluid leakoff velocity, long operation time and significant changes in stress, pore pressure, and/or permeability and porosity, affecting possibly large regions around the wellbore and/or fracture. These special characteristics make fracturing modeling methods developed for conventional fracturing applications inadequate. Some of the problems encountered include grid effects resulting in oscillation of fracture growth with time (limiting the stability of conventional fracture modeling models), singularity of material balance constraint on injected fluid and geomechanical effects caused by the changes in reservoir pressure and temperature and caused in turn by the existence and propagation of fracture. Therefore proper representation of dynamic (propagating) fractures which requires modeling the propagation in a manner coupled with reservoir response is the central issues for simulation of these unconventional fracturing processes.;This work focuses on improving fracturing modeling techniques by coupling fracture propagation with reservoir and geomechanical simulation. The coupled models developed here intentionally use only one common stationary grid system for fracturing modeling, reservoir and geomechanical simulation, treat fracture as a highly-permeable part of reservoir matrix for flow simulation (using the concept of transmissibility multipliers) and treat the fracture as a dynamic boundary condition in the geomechanical simulation.;This research first developed a transmissibility modification model to couple a static hydraulic fracture with reservoir simulation, which averages fracture and matrix transmissibility based on fracture size and permeability. This method was validated by comparing it with analytical production model of a well with infinite and finite fracture conductivity.;Then, as the first step in developing a fracturing model fully coupled with reservoir and geomechanical simulation, the method of coupling the static hydraulic fracture with reservoir simulation was extended to model propagating fracture by coupling reservoir model and a simplified geomechanical model with using dynamic transmissibility multipliers, which are computed based on length and width of a 2-D GDK-shaped fracture. Fracture length is calculated based on minimum net pressure criteria, instead of the conventional material balance constraints of injected fluid directly while fracture width is calculated according to the 2-D analytical GDK formula. Four different mathematical approaches are derived to calculate transmissibility multiplier for the fractured grids by averaging fracture and matrix transmissibility based on fracture and grid sizes. This method was extended to model propagating fracture by pressure-dependent or stress-dependent dynamic transmissibility multiplier and was further implemented into a modular coupled (finite difference) reservoir and (finite element) geomechanical simulator Geosim. A model to reduce oscillation of pressure and stabilize fracture propagation was derived by including the derivative of the transmissibility multiplier with respect to pressure in the Jacobian matrix for solving the reservoir flow equations with Newtonian Iteration. This method decreased the number of time steps required to model fracture propagation by an order of magnitude. Finally, a new fracturing model to fully couple the fracture mechanics with reservoir and geomechanical simulation was developed. The model consists of a conventional 3-D finite difference reservoir model, a 3-D finite element geomechanical model, and a 3-D fracture propagation model implicitly included in the 3-D finite element geomechanical model via the node displacements on the fracture face. The flow and geomechanics/fracturing are coupled in an iterative manner equivalent to a full coupling between these components. The 3-D (planar) fracture geometry, pressure and temperature in the fracture are the common dynamic boundary conditions and loads for the flow and stress model. A new Aitken Delta2 iterative process yielding smooth fracture propagation has been developed and the model has been tested on classical fracturing problems. This methodology allows modeling fracture initialization and propagation, post-frac multiphase cleanup in the reservoir and fracture, pre- and post-frac well performance in a changing stress and pressure environment, all within the same system.;Field examples demonstrate the validity and advantages of the approach and show that the model is capable of matching complex history of injections and calibrating stress-dependency of formation permeability.