Uniform Flux & Infinite Conductivity Model

Introduction

The AFA uniform flux model is derived from the work of Olivier Houze [1983]. The work assumed a Dual Porosity medium (pseudo-steady state interporosity flow assumption).

Below, the dimensionless Laplace space pressure drop at a point (xD, yD) at a time “s” caused by constant production through a uniform-flux fracture:

In this solution, the fracture is divided into “m' elements of equal length 2/m. It is then assumed that the contribution of each segment is equivalent to the effect an equal line source at the centre of the segment.

Extension to Infinite-Conductivity Solution

In the infinite conductivity case, the pressure within the fracture is assumed to be uniform. The partition of rates is uniform at early times while linear flow lasts. Post linear flow, the flow rates increase at the ends of the fracture as they are open to the greater reservoir.

Houze et al [1988] showed that the uniform flux model can replicate the infinite conductivity model if the uniform-flux case pressure response is measured at the point (0.732xf ,0).

Nomenclature (Dimensionless)

xi = center of the segment

yD, xD = dimensionless coordinate from origin point

s = Laplace Parameter

m = Number of points

tD = dimensionless time

f(s) = represents the dual porosity function.

All dimensionless variables are referenced to xf.

Reference

• Pressure-Transient Response of an Infinite-Conductivity Vertical Fracture in a Reservoir with Double Porosity Behavoir, Oliver P. Houze, Roland N. Horne. Henry J. Ramey, SPE Fonnation Evaluation, September 1988