Mathematical modelling on transport of petroleum hydrocarbons in saturated fractured rocks

Abstract

The present paper addresses critical issues that describe the dissolution mass transfer of petroleum hydrocarbons in a saturated subsurface system. The field procedure associated with the estimation of Light Non-Aqueous Phase Liquid (LNAPL) thickness in site monitor wells is revisited. A brief theory has been included on the composition and transport of petroleum hydrocarbons following an onshore oil spill in order to demonstrate the level of complexity associated with the LNAPL dissolution mass transfer even in a classical porous medium. However, such studies in saturated fractured rocks are highly complex and limited, and hence, deserve a special attention as the fate and transport of the petroleum hydrocarbons are not uncommon in saturated fractured rocks. In this context, an improved mathematical model has been proposed that will better describe the dissolution kinetics of petroleum hydrocarbons in saturated fractured rocks at the scale of a single fracture using dual-porosity concept. The lumped mass transfer coefficient in a classical porous medium proposed depends on mean grain size, while the same parameter has been replaced by an equivalent average thickness of fracture aperture that better describes the LNAPL dissolution rate in a coupled fracture-matrix system. A set of nonlinear coupled partial differential equations is deduced for a coupled fracture-matrix system in analogy with the differential equations of a classical porous medium. The proposed mathematical model may work well for the fracture aperture thicknesses varying between 100 and 500 microns with a relatively low Reynolds Number and initial NAPL saturation.