An Experimental and Numerical Investigation of Crossflow Effects in Two-Phase Displacements

Y. Cinar, SPE, and K. Jessen, SPE, Stanford U. ; R. Berenblyum, SPE, Technical U. of Denmark; and R. Juanes, SPE,and F.M. Orr Jr., SPE, Stanford U.SummaryIn this paper, we present flow visualization experiments and nu-merical simulations that demonstrate the combined effects of vis-cous and capillary forces and gravity segregation on crossflow thatoccurs in two-phase displacements in layered porous media.We report results of a series of immiscible flooding experi-ments in 2D, two-layered glass bead models. Favorable mobility-ratio imbibition and unfavorable mobility-ratio drainage experi-ments were performed. We used pre-equilibrated immisciblephases from a ternary isooctane/isopropanol/water system, whichallowed control of the interfacial tension (IFT) by varying theisopropanol concentration. Experiments were performed for a widerange of capillary and gravity numbers. The experimental resultsillustrate the transitions from flow dominated by capillary pressureat high IFT to flow dominated by gravity and viscous forces at lowIFT. The experiments also illustrate the complex interplay of cap-illary, gravity, and viscous forces that controls crossflow. Theexperimental results confirm that the transition ranges of scalinggroups suggested by Zhou et al. (1994) are appropriate/valid.We report also results of simulations of the displacement ex-periments by two different numerical techniques: finite-differenceand streamline methods. The numerical simulation results agreewell with experimental observations when gravity and viscousforces were most important. For capillary-dominated flows, thesimulation results are in reasonable agreement with experimen-tal observations.IntroductionStreamline methods are very efficient numerical techniques forfield-scale reservoir simulation, but they are not without limita-tions. They treat flow along each streamline as independent ofadjacent streamlines and therefore do not typically represent cross-flow in the simulations. If users of streamline methods are tointerpret simulation results reliably, they will need to assess wheth-er any of the mechanisms not modeled in the simulations areimportant enough to limit the accuracy of the simulations appreciably.Transfer of fluid in the direction transverse to streamlines canresult from diffusion and dispersion, crossflow caused by viscousand capillary forces, and gravity segregation. The scaling of dif-fusion and dispersion has been investigated in a number of previ-ous studies. If the injected gas is miscible or partially miscible withthe oil, diffusion and dispersion mechanisms may play a signifi-cant role in the displacement (Mohanty and Johnson 1993; Fayersand Lee 1994; Tchelepi 1994; Jiang and Butler 1994; Burger andMohanty 1997). In particular, Burger and Mohanty (1997) showedthat diffusion through the oil phase can limit mass transfer from oilresiding in low-permeability regions. Similar arguments can alsoapply to other mechanisms of crossflow: viscous and capillarycrossflow as well as gravity segregation (Fayers and Lee 1994;Burger and Mohanty 1997; Zapata and Lake 1981; Zhou et al. 1994). Scaling analysis of crossflow mechanisms for displacements inheterogeneous media allows assessment of the relative contribu-tions of each driving force to flow (Tchelepi 1994; Zhou et al.1994; Shook et al. 1992). Starting from material balance equationsand defining them in dimensionless variables, scaling groups canbe obtained that determine the regime of flow during displacement.The relevant scaling groups for displacement of oil by water insystems that contain some simple heterogeneity such as layers arethe transverse gravity and capillary numbers, which are given by(Tchelepi 1994; Zhou et al. 1994):