Network Simulation of Relative Permeability Curves Using a Bond Correlated – Site Percolation Method of Pore Structure
Kantzas, A., and Chatzis, I.,
Chemical Engineering Communications
Volume 69, Issue 1, 1988
This paper deals with the conductivity and relative conductivity properties of irregular 3-D networks of pores that represent the continua of the oil phase and the aqueous phase respectively, during steady slate two phase flow in porous media. The relative conductivity properties presented, correspond to the saturation history defined by the drainage, imbibition and secondary drainage capillary pressure curves respectively. Use has been made of the pore accessibility history of a 20 × 20 × 20 network and a 10 × 10 × 10 nodes core portion of the network is used to write the flow equations. A set of 1001 linear equations is solved using the Preconditioned Conjugate Gradients Method for the conductivities of the wetting phase and the non-wetting phase respectively, as a function of network saturation and saturation history. The effects of pore throat size distribution and pore body size distribution on relative permeability behaviour has been investigated. Furthermore, the effect of conductivity function q(D) proportional to Dn (n = 0, 1, 2, 3, 4) on relative permeability behaviour was investigated, where D stands for pore throat diameter and n is an exponent depending on pore geometry.
The results of this work are very significant in elucidating the following points that are not clearly stated in the literature: 1) using the bypassing as the only trapping mechanism, the primary drainage and secondary drainage relative permeability curves are in agreement with experimental findings; 2) more realistic displacement mechanisms in secondary imbibition are required to have better agreement with experimental findings; 3) the correlated network models after the site type problem of percolation theory are realistic models of pore structure; 4) the conductivity function q(D) proportional to D 3 is the most appropriate pore throat conductivity function because of lamelar like pore geometries; and 5) accurate prediction of the effective permeability requires knowledge of the porosity and the detailed pore geometry in the pore network, in addition to pore size distributions used in the network simulation.