A Numerical Model Study of Gravitational Effects and Production Rate on Solution Gas Drive Performance of Oil Reservoirs

Abstract

Ultimate oil recovery by solution gas drive can be greatly affected by variations in production rates --- in general the higher the rate the higher the recovery. However, the quantitative relationship for a given field will be influenced by factors other than rate and vertical permeability: reservoir thickness, gas solubility, shrinkage factor, oil permeability: reservoir thickness, gas solubility, shrinkage factor, oil viscosity, relative permeability, and capillary pressure. Introduction The relationship between ultimate oil recovery and rate of oil production has been the subject of many investigations since 1924 when Cutler published a study of field data. Cutler concluded that higher oil production rates yielded higher ultimate oil production rates yielded higher ultimate oil recoveries. Subsequent studies of performance from a variety of fields showed that factors other than producing rate caused so much variation in total oil producing rate caused so much variation in total oil recovered that no conclusion could be reached concerning the effects attributable to this single factor. Because of the impossibility of imposing different production histories on a given reservoir to observe production histories on a given reservoir to observe the difference in ultimate oil produced, confirmation of any such relationship had to depend on analytical studies and laboratory model tests. Analytical approaches using simplified models, in which effects of capillary pressure and gravity forces were ignored, led to the conclusion that any effect of production rate upon ultimate recovery was negligible. They did show gross differences in horizontal saturation distributions imposed by production rate variations. In 1953 and 1954 the foundation was laid for solution of the unsteady-state fluid flow equations by use of difference approximations and high-speed computers. The development of these techniques led to numerous mathematical model investigations of fluid displacement in one and two dimensions. These works treated a range of fluid systems in one and two dimensions; generally they were confined to incompressible fluids, and included gravity and capillary, effects. When simulating compressible fluid systems, gravity and capillary forces were ignored. Levine et al. and Heuer et al. studied the effects of production rate on ultimate oil recovery by solution gas drive, using these more sophisticated mathematical techniques. Both efforts neglected the effect of gravity, but Levine included capillary forces. Both concluded that producing rate had a negligible effect on ultimate recovery. Ridings et al. showed that performance of long horizontal laboratory systems performance of long horizontal laboratory systems coincided closely with performance calculated by numerical modeling techniques, with one exception. Noticeably increasing recovery was observed with increasing production rate in the laboratory system, whereas the numerical model showed no rate effect. Gravity was not a factor in either system. Since the production rate sensitivity was less on very long production rate sensitivity was less on very long laboratory systems than for the shorter ones, it was concluded that the rate effect observed on the short laboratory system was, for reasons not specified, typical only of short systems. It bas been recognized for some time that, under certain conditions, gravitational forces can be very important in the displacement of oil from natural reservoirs. Muskat treats exhaustively the performance of wells and reservoirs in which gravity is performance of wells and reservoirs in which gravity is the sole driving mechanism. JPT P. 625