HydFrac

HydFrac is a numerical model based on a three-dimensional, two-phase thermal reservoir simulator. It incorporates fracture mechanics and formation plugging due to injected particles. “Special attention is paid to the analysis of fracture closure during injection shut-in and to the description of formation damage.”[1] The media are represented as heterogeneous, anisotropic and compressible and there is a thermo-poroelastic stress model.

After fracture initiation, propagation is described by a two-dimensional PKN model with a model for fracture plugging by particles. Internal and external filter cakes are considered.

Capabilities:

1. Three-dimensional, two-phase, thermal reservoir simulator for anisotropic, compressible media.
2. One injector and several producers can be modeled.
3. Injection can be specified by rate or pressure, at the wellhead or as bottomhole conditions.
4. Temperature can be applied as a bottomhole or wellhead condition.
5. When pressure/temperature are specified at the wellhead, heat exchange and pressure drop in the injector wellbore are represented.
6. The model computes pore pressure, saturation and temperature in the entire field.
7. From the pressure and temperature distributions, in-situ stress variations are computed using a thermo-poro-mechanical stress model and are solved using Koning’s method.
8. The displacement filed is represented as the gradient of a scalar function and the mechanical problem reduces to the Poisson’s equation. The temperature and pressure are the source terms of the equation with corresponding thermal expansion and poroelastic coefficients.
9. Thermal or hydraulic fracturing can be represented.
10. The fracture can increase or decrease in length at any time step.

The Fracture Model:

A two-dimensional model was used. A PKN representation was selected. Each vertical plane in the fracture is therefore assumed to deform independently of the others. The fracture widths in vertical planes are coupled by the fluid flow and continuity equations and the width is a function of the local pressure.

The equation for the width of the fracture is based on Sneddon’s equation and the propagation criterion is stress-based and takes the following form:

Mass Balance:

Once fracturing has been initiated, a fracture fluid flow model determines the fluid pressure profile in the fracture, accounting for friction, leakoff, changes in fracture volume and particle plugging. Solution is fully implicit.

Fracture Plugging:

Four mechanisms are cited:

1. Deposition on grain surface.
2. Formation of mono- or multiparticle bridges.
3. Internal cake formation (solids and oil) as soon as “the non-percolation threshold has been reached near the fracture face.” It is represented as a progressive permeability reduction function of the cumulative fluid filtration per unit fracture surface with a dependence on equivalent particle concentrations (oil and water). The depth of the permeability reduction is user-specified.
4. External filter cake and complimentary fracture filling. After internal plugging, particles accumulate on the surface of the fracture. This filter cake is assumed to be incompressible (i.e., constant permeability) but the thickness is allowed to increase. The thickness depends on the fracture evolution and the accumulated volume of particles in the fracture. The external cake is dynamic.

“For each fractured cell, the formation damage effect is represented by a modification of the transmissibility between the fracture and the reservoir. The damaged transmissibility is calculated using an equivalent fracture face permeability taking into account the pressure drop induced by internal and external plugging.” (Permeability in series.) “The damaged transmissibility is integrated in the coupled fluid flow description between fracture and reservoir, which is solved in an implicit manner. This description ensures a good representation of mass fluid balance in the fracture and the reservoir.”

This is a synopsis of the cited SPE paper. For additional information and examples, refer to the paper.

<Duke Engineering Model Duke Engineering   Click here to return to a summary of the Duke Engineering Model. This model considers many of the differences between conventional hydraulic fracturing and long term, lower rate water injection.

MWFlood> MWFlood   Click on this for a summary of the MWFlood model. MWFlood is a pseudo-three-dimensional simulator for predicting the pressure and geometry of conventional hydraulic fractures associated with waterflooding.