Effect of Pore Pressure on Conductivity and Permeability of Fractured Rocks
Authors: Berumen Sergio , Tiab Djebbar 
Published: December 2007

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Abstract
This paper discusses a new approach for interpreting the effect of pore pressure on the conductivity and permeability of artificially fractured rocks. The mathematical model formulated includes the non-linear effect of pressure dependence of fracture conductivity and formation permeability through a modified concept of fracture conductivity. New type curves for pressure-sensitive fracture formation systems were generated and a method of pressure analysis to interpret this effect is provided.
The pressure behavior of wells intercepting pressure-sensitive finite conductivity fractures was investigated by solving numerically the non-linear mathematical model. A conductivity modulus in the fracture (fD) and a permeability modulus in the formation (D) determine the intensity of the pore pressure effect.
Results of our investigation demonstrate that when the fracture conductivity is pressure dependent, the use of conventional techniques to evaluate fractured wells may lead to incorrect estimates of the fracture-formation properties. The slope of the pseudo-bilinear flow period () becomes function of CfD and fD, ranging from 0.25 to 0.35. The interpretation of pressure data is carried out through a graph of p vs t . However the pore pressure effect has no influence on the one-half slope of the linear flow.
A novel correlation to detect the approximate time and pressure when the fracture closure occurs is presented. Equations relating the pseudo-bilinear slope with CfD and fD were obtained by using multivariate non-linear regression analysis. The expressions facilitate the analysis of well-test data and detect the pore pressure effect on conductivity.

Introduction
Conductivity and permeability of porous media are known to depend on pore pressure and/or stress field. The pore pressure dependency of conductivity is even stronger in fractured porous media, particularly on artificially fractured formations. As pore pressure declines, deformations on the proppant material-fracturing fluids-porous media make the conductivity of the fractured system to become quite sensitive to pore-pressure. Mathematically this phenomenon constitutes a non-linear problem. An approach used to solve this non-linear problem is the use of transformations to linearize the modeling equations. A modified form of Kirchoff transformation has been extensively used to formulate the non-linear problem. However, this approach presents the disadvantage of the requirement of extensive experimental data of permeability-pore pressure.
An important result of the experimental work on pressure and stress dependence of porosity and permeability published in the literature, is that the rock permeability or conductivity behaves in an exponential manner with the pore pressure variation. The same variation has been found for the porosity, but the magnitude of the pressure dependence of porosity is considerably lower than it is for permeability. Experimental results on permeable rocks have shown that permeability is a function of both the confining pressure and pore pressure.
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