Production Technology - Displacement Mechanism in Multi-Well Systems

A procedure for determining the behavior of a reservoir under a gas or water injection program was reported by Buckley and Levertt in 1942.1 This method, which allowed the calculation of the phase saturation distribution behind the front of a displacing fluid, has been extended to apply to a more general situation. The reservoir may initially contain flowing quantities of the displacing fluid, or the fluid in the reservoir may be above saturation pressure SO that solution effects are present. Production may occur behind the front as in the case of a well which is produced after breakthrough of the displacing fluid. The calculating procedure is simplified in that the graphical integration necessary to determine breakthrough saturation is eliminated by performing a direct integration and the graphical differentiation necessary to determine saturation distribution is eliminated by representing the displacing phase fraction of the flowing stream by an empirical equation. This representation results in simple expressions for the producing gas or water/oil ratio and cumulative production. INTRODUCTION A method for the calculation of the saturation distribution behind the front (interface between the displaced and displacing phases in a gas injection or water flooding operation) was reported by Buckley and Leverett in 1942. The method leads to a curve for the saturation distribution which is double-valued; consequently, part of' the curve was interpreted to be physically meaningless. That part of the curve which has physical significance was determined by a graphical integra-tion (material balance). In this paper it is shown that the integration may be performed analytically with a resulting equation for the saturation of the displacing phase at the front. The case in which the displacing fluid is initially flowing and the case in which the reservoir is initially above the saturation pressure so that some injected gas goes into solution are included in the integration. The calculations are considerably simplified by representing the fraction of the flowing stream which is oil by an exponential function of saturation. The methods is extended to apply approximately to reservoirs in which wells located between the injection well and the front are produced. An illustrative example utilizing the methods presented is included. RESERVOIR BELOW SATURATION PRESSURE In the case of a water flooding operation or in the case of a gas injection operation in which no gas goes into solution in the displaced oil, the equation for saturation in a linear flow system as a function of time and position as given by Buckley and Leverett is where* q = total reservoir volume flow rate, rvb/day A = cross sectional area of system, sq ft / = porosity of formation x = distance from injection point, ft t = time, days Pj = saturation of the displacing phase /dx velocity of planes of constant saturation, ft/day *The nomenclature used here is not the same as that used by Buckley and Leverett A complete nomenclature is given in Appendix A.