Velocities in Developed Five-Spot Patterns

Abstract

Laboratory experiments have shown that some oil recovery processes are rate sensitive, particularly Those employing surfactant-type materials. In this note, an ideal reservoir is analyzed to give a feel for proper rates in linear laboratory tests to best simulate proper rates in linear laboratory tests to best simulate a field pattern.We need to consider the distribution of frontal velocities* for field patterns. For the developed five-spot, velocities will range from very high in the well-bore vicinity to zero at the stagnation points halfway along each of the five-spot sides. Detailed frontal velocity distribution was determined from a computer streamline model for a homogeneous, isotropic, single mobility, confined five-spot octant. Each of the 12 equal volumetric rate stream channels in the octant had 40 cells with computer-generated values of volume and velocity.Fig. 1 shows the volumetric distribution of frontal velocities for the entire five-spot pattern (the same as for the octant). Velocities are on a normalized, but not dimensionless, basis, so the single curve applies for any pattern size, injection rate, and porosity. The median frontal velocity, 0.016, is that value at which half the five-spot volume has higher velocities and half lower. For example, a 10-acre five-spot with 20 percent porosity and an injection rate of 5 B/D-ft percent porosity and an injection rate of 5 B/D-ft would have a median frontal velocity of 0.016 X 5/(0.2 X the square root of 10) = 0.13 ft/D. Unless there is some other compelling consideration, this median value is probably a good single characterization of fluid velocity in a developed five-spot. Note that because of high near-wellbore velocities, the volumetric averaged velocity is somewhat higher than the median.A more detailed analysis would consider velocities at a displacement front in each of the stream channels as a function of total pattern injection. Fig. 2 shows the five-spot octant stream channels and location of a unit mobility ratio perfect piston front at various injection times. Velocities in Stream Channels 2, 4, 6, 8, 10, and 12 as a function of total pattern injection are shown in Fig. 3. Each curve is symmetrical about some vertical line. Consideration of Figs. 2 and 3 will give one a feet for just how realistic a particular linear laboratory experiment might be in simulating field five-spot rates. P. 550