Numerical model for NAPL migration in double-porosity subsurface systems

Abstract

The double-porosity concept has been successfully applied by many researchers to simulate fluid flow in oil reservoirs over the past few decades. These oil reservoirs were typically considered to be made of fractured or fissured rock, hence the usance of the double-porosity concept. Nonetheless, double-porosity may also exist in soil either through soil aggregation, or through soil features such as wormholes, cracks and root holes. These attributes in soil that cause the occurrence of double-porosity are also known as secondary porosity features and are akin to the reservoir rock fractures or fissures. In the case of groundwater contamination, the occurrence of double-porosity in soil is highly influential since immiscible fluids have been found to flow preferentially through the secondary porosity features. Ergo, a numerical model for non-aqueous phase liquids (NAPL) migration in double-porosity groundwater systems was developed. This model was modified from the conventional double-porosity model applied in the petroleum industry. The difference is that while the standard double-porosity models usually simulate the fluid flows in both continua making up the doubleporosity medium, the double-porosity model presented here focuses the modelling on the secondary porosity features in the soil, therefore making it more pertinent in the context of groundwater contamination. In the modified model, the phase saturations and relative permeabilities are expressed as functions of the capillary pressures. The resultant nonlinear governing partial differential equations are solved using numerical methods. The problem is discretized spatially using the Galerkin’s weighted-residual finite element method whereas a fully implicit scheme is used for temporal discretization. Verification of the developed model has been done against similar works in the open literature and the preferential flow of NAPL through the secondary porosity features was validated.