Proceedings of the Second International Energy 2030 Conference,
November 4-5, 2008, Abu Dhabi, U.A.E.

Stability of Two-Phase Vertical Flow in EOR Applications

Amir Riaz
University of Maryland, USA

Hamdi Tchelepi
Stanford University, USA

Abstract
This paper investigates the interfacial instability that occurs due to the displacement of reservoir oil by an injected solvent of lesser viscosity and density than oil. Instability in the form of interfacial distortions arises due to unfavorable contrasts of both density and viscosity between the injected solvent and reservoir oil. The resulting viscous and gravitational fingers lead to the formation of large channels of the injected solvent that bypass the reservoir oil and lower the sweep efficiency substantially compared to the hypothetical stable displacement. Instability characteristics are quantified in terms of the width of unstable fingers and their rate of propagation and growth. We employ a normal mode, matched asymptotic expansion method to obtain analytical expressions governing the incipient stability behavior of such flows. We show that in the case of vertically oriented injection, instability can occur at two fronts moving in opposite directions with unique characteristics such that the maximum growth rate decreases both when the mobility ratio is increased at the front end and decreased at the back end. Linear stability analysis indicates that the most important parameters governing instability behavior are the shock viscosity ratio, capillary number and the relative permeability functions. We systematically explore the influence on instability due to the variation of these parameters. We carry out high accuracy numerical simulations based on spectral methods to investigate nonlinear instability properties related to the long term development of unstable structures. Our high accuracy numerical simulations are able to resolve all the relevant length and time scales of the unstable displacement that are determined from the stability analysis. This provides a rigorous validation of the numerical simulator. The late time nonlinear behavior is marked by interactions between the fingers, similar to that for miscible displacements and the wavelength coarsening characteristics follow a linear growth in time for a wide range of the parameters.