Effect of Transverse Diffusion on Fingering In Miscible-Phase Displacement

Abstract

The importance of transverse diffusion on the fznger development in a miscible-phase displace-ment at an adve.rse mobility ratio of three was studied in a porous plate 1I4-in. thick, 3-in. wide and i8-in. long. Fast displacement rates (29 ftlD) and slow rates (1. 6 ftlD) were used to determine t~e effect of residence time on the geometry of the fzngers. The shape of the fingers was observed directly by use of the X-ray technique. At fast rates numerous narrow fingers were observed, but at slow rates a single somewhat bulging finger was produ~ed. !he amount of material moved transversely by dlffuslOn across the plate was sufficient to modify the finger geometry in the slow-rate run because of the long residence time. These results are in contradiction to some of the postulates in the literature. The composition of the effluent stream, however, was not affected by the flow rate. This result is not inconsistent with the observed change in the shape of the finger in a short model, but it seems likely that a short model does not offer adequate and proper scaling of the reservoir. The model used was probably a valid one for studying the effect of transverse diffusion on the finger geometry, but .a longer model would be needed for proper scalzng of the effect of the change in the finger shape on the efficiency of displacement as measured by the composition of the effluent stream.