Crossflow Mechanisms by Gas Drive in Heterogeneous Reservoirs

Abstract

In this paper a number of factors contributing to mass transfer by cross flow in gas displacement are examined. The mechanisms involved are diffusion, dispersive mixing, capillary pumping, interfacial tension variation, and relative permeability modification. The use of a modified Wilke-Chang correlation for bulk diffusion coefficients in multi-component systems is suggested. The performance of this correlation is tested against the limited experimental data available on diffusion coefficients. A general formulation of the terms needed to be included in compositional simulators for cross flow effects is reviewed, and thence some of the key aspects are analyzed using measurements from the IFP-diffusion experiment. The role of the gas phase tortuosity factor is investigated, but spatially varying capillary force is also found to be a dominating mechanism. An example reservoir application with a two-layer heterogeneous character is then studied to determine the relative magnitudes of cross flow, and how these compare between a nearly miscible displacement and a dry gas vaporizing process. Introduction In the study of gas displacement processes we are necessarily much concerned with the effects of a severely adverse viscosity ratio causing viscous fingering. The viscous fingering tendencies are now recognized to be augmented by, or perhaps dominated by, channeling through the higher permeability pathways of a heterogeneous medium. These effects take their most severe form when the mobility ratio is large, as is the case for heavy oils. Fractured systems provide examples of highly heterogeneous porous media where the fractures create pathways for a displacing gas to bypass and leave oil behind in the matrix system. The adverse fingering or channeling tendencies will be mitigated to varying degrees by cross flow effects induced by the following physical mechanisms:mass diffusion,dispersive mixing,capillary forces,gravity forces. All these factors are rate dependent, so that the effectiveness of a gas displacement process needs to be analyzed in a manner which takes quantitative account of these interacting mechanisms. We will discuss some aspects of the first three of the above factors in this paper. Gravity effects are also extremely important, but are not included in the scope of this discussion. In immiscible displacement it is expected that viscous fingering or channeling should be less dominant, because of the effects of relative permeabilities. The mobility ratio of the Buckley-Leverett front will often lie in the range 1.0 MBL2.0, even though / greater than, greater than 1.0. The further stabilizing effect usually associated with capillary forces when the flow rate is low, may not apply to a nonwetting phase invasion, since the capillary forces lead to preferential selection of the larger pores or higher permeability pathways for the displacement. However, an important mechanism contributing to the cross flow, and therefore potentially to the overall sweep factor, is that of capillary pumping. In the latter, substantial reduction of the oil saturation in the flow pathway causes a high saturation gradient with respect to an adjacent stagnant region. This implies that (Pc/ So) (So/ dn) is large (where n is normal to the flow), and oil as the wetting phase is induced to flow into the pathway. Necessarily gas counterflows and invades the stagnant region to reduce the saturation gradient (see Figure 1). The magnitude of this effect depends on go, the interfacial tension, which varies with phase behavior. Thus in considering the merits of multiple contact miscible processes, relative to nearly miscible processes, or to vaporization by dry gas cycling, there are a number of trade-offs in terms of economic performance to be considered. Because of the complexity of the cross flow phenomena, which necessarily interact with phase behavior and density differences causing gravity segregation, the only satisfactory route available for computing gas displacement is through compositional simulators. Care must be exercised in selecting both the grid details and the compositional representation to achieve a solution which is not overcome by numerical truncation errors. We will give illustrative solutions of some of the cross flow effects using a modified version of a commercial compositional simulator. Modeling of the mass diffusion term has uncertainties because of the lack of a good theory and measurements for bulk diffusion coefficients in multi-component systems. P. 827^

Scaling of Multiphase Flow in Simple Heterogeneous Porous Media

“…When the capillary force is neglected, only gravity and viscous forces contribute to flow. Dispersion and diffusion can influence to some degree the performance of miscible and near-miscible displacements [19], since they affect mixing and the contrasts in viscosity and density differences. However, dispersion can usually only be a significant contributor in displacements where capillary and gravity forces are small and injection rates are also relatively small.…”

“…and (19) The advantage of using Ngv and N cv is that they represent the magnitudes of the gravity and capillary forces in the transverse direction relative to the viscous forces in the logitudinal direction including the influence of aspect ratio as reflected by the shape factor (R,2).…”

The Role of Capillarity in VAPEX

“…The roles of asphaltene deposition, extended area of contact and capillarity (imbibition) have been re-emphasized in a more recent review by Das and Butler 8 . The role of capillary imbibition has also been recognized in enhanced recovery of conventional oil 9 . This is the phenomenon of the wetting phase being drawn into a porespace occupied by a nonwetting phase due to capillary forces.…”

Modelling Physical Dispersion in Miscible Displacement-Part 1: Theory and the Proposed Numerical Scheme

“…Since, C ικ = ρ κ Y ικ , a more general expression of the form: has also been used by many researchers (7,(26)(27)(28)(29) . Schmidt (25) For isotropic dispersion, individual elements of the tensor are given by (2,30) :…”