Micromechanical Analysis of Relative Permeability Hysteresis

This paper represents the model of relative permeability hysteresis in drainage and imbibition with help of percolation theory. The following processes are considered. First of all the hydrophilic core is totally saturated by water. Oil displaces water under the pressure gradient – this process is called drainage. During this process oil firstly goes to large pores, because they have small hydrodynamic resistance and small capillary pressure. After the core is maximally saturated by oil the displacing of this oil by water begins under the pressure gradient. This process is called imbibition. During drainage oil changes the surface properties of some part of capillaries through which it passed. The cause of it is formation of thin hydrocarbon film during drainage. So one part of capillaries (ӕ) has unchanged hydrophilic surface properties, and the other part (1-ӕ) has changed surface properties, which can become both hydrophobic and hydrophilic with another angel of contact (θ1 and θ2 – angles of contact before and after oil pass through, α=cosθ1/cosθ2). Different variants of ӕ and α are considered in this paper. The cubic lattice of capillaries is taken for the basic model of porous media which has lognormal density of radius distribution function. The received results of relative permeability calculations for drainage and imbibition demonstrate the availability of hysteresis. The closest to experiment results are for ӕ=0.75 and α=-1. This shows that in proposed model after drainage oil changed surface properties from hydrophobic to hydrophilic in 25% of capillaries that is 1/3 of capillaries, trough which oil passed. Represented model is rather universal and allows taking into consideration different mechanisms of changing the surface properties of porous media. The best accordance with represented experiment is achieved by choosing the hydrophobisation of porous media during drainage as the main mechanism. Comparing with the experiment allows to find the right ӕ and α. This method can be used instead long and difficult experiments for plotting the relative permeability. It’s necessary to use the mineral structure data and the experimental density of radius distribution function in the calculating algorithm of represented model and the relative permeability will be plotted.