Viscous Fingering, Gravity Segregation, and Reservoir Heterogeneity in Miscible Displacements in Vertical Cross Sections

Abstract

SPE Members Abstract Combined effects of gravity segregation, viscous fingering and reservoir heterogeneity are examined in particle-tracking simulations of flow in vertical cross sections. Differences in model formulation from previous descriptions are reviewed briefly. The accuracy of the simulation representation of the physical flow mechanisms is tested. For homogeneous cross physical flow mechanisms is tested. For homogeneous cross sections, simulator calculations are presented that illustrate the transition from flow in a single gravity-dominated tongue at low viscous to gravity ratio (N) to flow dominated by viscous fingering at high values of N. Quantitative accuracy of the simulator is tested against the experimental results of Pozzi and Blackwell. Simulation results agree with experimental results wide ranges of mobility ratio, viscous to gravity ratio, and aspect ratio. Additional simulations also agree well with Stalkup's correlation of breakthrough recovery as a function of mobility ratio and N. The validated simulator is then used to augment Stalkup's correlation with results for additional mobility ratios. In addition, plots are presented of recovery after breakthrough as a function of N for several mobility ratios. The results confirm that in homogeneous porous media, better displacement performance is observed at high viscous to gravity ratio for any performance is observed at high viscous to gravity ratio for any mobility ratio. For heterogeneous porous media, however, that conclusion must be qualified. Example simulation results show that for injection of light solvent into a layered reservoir with high permeability low in the reservoir, better displacement efficiency is observed at intermediate values of N than at high or low values. If the high permeability is at the top of the reservoir, high N is still preferred. Introduction Many factors influence the displacement performance of a miscible flood. According to the accepted description of development of miscibility, phase behavior acts to generate high local displacement efficiency in the zone swept by injected fluid. The fraction of a reservoir swept at a given time in a flood is determined partly by injection and production well patterns, permeability variations in the reservoir rocks, gravity patterns, permeability variations in the reservoir rocks, gravity segregation of fluids, and viscous fingering that arises from the unfavorable ratio of displaced oil mobility to injected fluid mobility. Understanding of the relative importance of these factors is a key part of scaling of predictions of Miscible flood performance. performance. In an earlier paper, a particle-tracking technique for calculation of the growth of viscous fingers was described. In that paper, results of the particle-tracking simulations were shown to agree well with experimental results of Blackwell et al. for displacements in homogeneous porous media. The simulator was then used to investigate how viscous fingers grow in heterogeneous porous media. The simulations showed that if high and low permeabilities are randomly distributed, fingering patterns observed are similar to those that occur in homogeneous porous media. On the other hand, finger patterns can be dominated by the permeability distribution if the permeability is sufficiently variable and there is enough correlation permeability is sufficiently variable and there is enough correlation of high and low permeability. In such cases, the fingers that develop simply follow the high permeability flow paths, and there is little difference between the flow patterns at unit mobility ratio and those at adverse mobility ratio. Hence, a porous medium with enough correlation of high and low porous medium with enough correlation of high and low permeability behaves as if it is layered, and the viscous fingers permeability behaves as if it is layered, and the viscous fingers follow the high permeability layers. In this paper, we consider only layered systems. Here we focus on the interplay of viscous fingering, gravity segregation and simple examples of reservoir heterogeneity layers within two-dimensional vertical cross sections. In what follows, the effects of phase behavior are ignored, therefore, though phase behavior certainly plays a key role in many Miscible floods. We begin with a brief review of the model formulation, which differs slightly from that described previously. Next we compare simulation results with experimental previously. Next we compare simulation results with experimental data for homogeneous cross sections that demonstrate the interaction of viscous fingering with gravity segregation. Finally we report results of simulations in layered systems that illustrate the combined effects of viscous instability, gravity segregation, and reservoir heterogeneity. MATHEMATICAL MODEL The model used is based on the following assumptions:Fluids are incompressible and first-contact miscible but have differing densities and viscosities. P. 39