Shell 2 Model

 

Introduction

This is a pseudo-three-dimensional fracture growth model which permits the description of elliptical fractures in a multi-layered reservoir.  Symmetrical vertical growth is not a pre-requisite.

 

Principles

This model is analytical and it is coupled with a reservoir simulator.  It is assumed that fracture growth and development of the pressure field can be decoupled.  This permits modelling of the pressure field in the reservoir using a constant fracture length.  The transient pressure is approximated by applying the Laplace equation with a moving boundary for the pressure disturbance. 

 

Fracture friction (shear) is ignored although pressure drop along the length of the fracture can result due to plugging.  It is assumed that when multiple layers are present that there is no crossflow in the reservoir.

 

Pressure Distribution

Pressure distribution is represented by coupling the three-dimensional solution for a radial fracture in an unbounded reservoir with a two-dimensional solution (far-field) for an elliptically symmetric, pseudo-steady state situation.  There is a discontinuity at the transition between the two regimes.  This transition concept also applies for multiple mobility zones.  Thermo- and poroelastic effects are considered.

 

Damage

The external filter cake is represented as a zone of altered mobility.  “In the previous 2D model, the filtercake was assumed to be uniformly distributed over the fracture wall, with a possible tip plug at the end of the fracture where no water could penetrate.  However, this resulted in often very high simulated bottomhole pressure as the friction in the very narrow “sheet” of fluid would become excessive.  This observation pointed us to introduce “channeling” as a mechanism to release pressure.”