In tight reservoirs development such as shale gas it is important and yet difficult to predict the size and orientation of the drainage area around a hydraulically fractured well. Often the drainage area is determined by near-well fractures. Diagnostic fracture injection test (DFIT) is an effective way of predicting many reservoir parameters. However, it is challenging to uniquely interpret fractures' geometry, dimension and spacing. A forward model is desired to correlate the DFIT responses with different fracture configurations and the associated drainage area.

We present a 2D model that couples fluid flow with geomechanical deformations in hydraulically fractured reservoirs by solving Biot's equation. Both fluid pressure/velocity and deformations are solved on a finite element mesh. Fracture space is distinguished from the rest of the matrix by high porosity/permeability and low elastic strength. The FEM mesh is adaptively refined at the fractured area to allow the fractures to be reasonably thin and arbitrarily spaced. Pseudo time iteration is applied to seek for convergence between fracture opening/closure and fluid pressure changes. DFIT is simulated with the new numerical model with a single (bi-wing) fracture case and a complex fracture case. The complex fracture case is made by adding transverse fractures to the two wings of a single fracture. The numerical results reveal pressure changes of reservoir fluid due to matrix and fracture deformations as well as due to fluid leak-off. The model is able to generate synthetic well pressure data that show all the type curves given by analytical DFIT theory. The complex fracture case results in pressure transient such that the flow regime rapidly evolves into pseudo-radial flow.

For idealized bi-wing fracture cases, this model is consistent with existing analytical tools for DFIT interpretation. The advantages of this model are the ability to implement complex fractures, and the ability to extend to 3D for non-vertical fractures (briefly mentioned in the appendices).

Synthetic DFIT data from the model developed in this study has been compared to a field example from a shale gas reservoir. The discrepancy between the model result and field example suggests that some special constitutive law is needed for the modeled fracture areas to appropriately capture the real fracture closure process.


When a well is subjected to production or fracturing injection, the fluid flow is likely accompanied by the solid deformation. In most cases of conventional reservoirs, the initial pore volume is much larger than the volume changes that are caused by the matrix strain with competent rock grains. For this reason, the fluid flow is often modeled independently without coupling with deformation. In the cases of tight and shale gas reservoirs however, the pore volume is comparable to the strain caused volume changes. The fluid flow modeling then needs to be coupled with the solid deformation.

We present our work on modeling a hydraulically fractured reservoir subjected to production or injection, where the fluid and solid are coupled by solving Biot's equation. The model is capable of generating synthetic well test data that show all the characteristic type curves given by the analytical DFIT theory. The paper is organized as follows:

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