Can effective porosity be used to estimate near-well protection zones in fractured chalk?

Abstract

Protection of fractured carbonate aquifers is often based on a single-porosity description of a dual-porosity system. However, it is difficult to assess a trustworthy value of the effective porosity based on scientific principles; thus, a range of estimates is often suggested. The complexity of the problem is compounded by the fact that the effective porosity may be scale-dependent. This paper investigates whether it is possible to describe solute transport in fractured carbonate rocks with an equivalent porous medium model using a constant value of effective porosity. It is assumed that the dual-porosity model provides an acceptable description of transport mechanisms in fractured porous rock and that it is possible to estimate the parameters needed in the single-porosity models from results generated by the dual-porosity model. The effective porosity is estimated from the dual-porosity results that are used as targets. For Danish chalk, an effective porosity of 13% (11–17%) is estimated. However, it is demonstrated that the estimated effective porosity is only valid at the specific transport time (1 year) from which simulation results of the dual-porosity model were extracted. The effective porosity is shown to increase with travel time until equilibrium conditions are realised between the fractures and matrix, following which, the effective porosity equals the matrix porosity and will maintain this value at larger transport times. Assuming that the dual-porosity model provides a trustworthy description of solute transport in fractured chalk and limestone, a method to estimate the effective porosity of an equivalent porous medium model is presented.