Papers - - Reservoir Engineering - The Performance of Bottom Water-drive Reservoirs (TP 2060, Petr. Tech., Sept. 1946, with discussion)

A theory has been developed describing the behavior of wells and reservoirs producing by the action of bottom water drives. It is assumed that the pressures are maintained above the bubble point, and that the permeability to viscosity ratio of the water in the flooded zone is the same as for the oil in the oil-saturated pay. Accordingly, the treatment is based on the homogeneous fluid potential theory. The effect of the difference in density between the oil and water is neglected. .4fter deriving the proper potential distrihutions, the nature of the rise of the water-oil interface below the producing wells is calculated. The primary clean-oil-production phase is expressed in terms of the displacement efficiency, defined as the fraction of the pay flooded out by the rising water table at tlle time of first water entry. The variation of this displacement efficiency is calculated as a function of the well spacing, pay thickness, the ratio of the horizontal to vertical permeability, and the well penetration. The important parameter, other than the well penetration, is found to be the ratio of the well separation to the thickness of the oil pay multiplied by the square root of the ratio of vertical to horizontal permeability. It was found that the displacement efficiency continually decreases as this parameter increases, and for values of the latter >3.5, the efficiency varies inversely as the square of the parameter. It also increases with decreasing well penetration. Perhaps the most striking result of this phase of the analysis is the conclusion that in order to explain the delay in entry of water in wells producing by bottom water drives for periods longer than a few days normal production, with drawdowns large compared with the differential density head between the oil and water, it is necessary to assume that the vertical permeability is a very low fraction of the horizontal permeability. An analysis is also given of the production history after the water has broken through, on the assumption that the production mechanism and details of the flow distribution continue to be the same as during the phase of clean-oil production. As is to be expected, it is found that the water cut will increase at an accelerated rate as production proceeds. However, the initial differences between systems of different well penetrations or well spacings with respect to the total clean-oil production gradually decrease in terms of the variation of the water-oil ratio with cumulative production. In particular, by the time the water-oil ratio has reached values of the order of 5 or greater the cumulative recoveries will generally differ much less among various producing systems than their corresponding clean-oil recoveries. Introduction On the basis of elementary geological principles, one may classify effective water-drive fields in two groups. In the first, the entry of water into the oil-producing formation may be characterized as an edge-water encroachment. This term is used to suggest that the motion of the water proceeds largely in a direction parallel to the planes of stratification. This type of water intrusion occurs usually in thin producing zones and in strata lying along structural flanks of appreciable dip. In the second group—"bottom water-drive" fields—the water-oil interface lies in a plane of zero or slight inclination to the