This paper presents generalized liquid inflow performance relationships(IPR's) for three-phase flow in bounded, homogeneous reservoirs and new methodsto predict present and future performance during boundary-dominated flow.
IPR's are empirical relationships based on linear regression analysis ofsimulator results that cover a wide range of reservoir fluid and rockproperties. The IPR's developed are compared with other three-phase methods andyield similar results for production-pressure behavior duringboundary-dominated flow while being much simpler to use.
The proposed IPR's were developed from analysis of multiphase flow inbounded, homogeneous reservoirs without external influx of fluids into thereservoir and apply to the boundary-dominated flow regime. The relationshipsare limited by the assumptions that (1) the reservoirs are initially at thebubblepoint, (2) no initial free gas phase is present, (3) a mobile water phaseis present for three-phase studies, (4) Darcy's law for multiphase flowapplies, (5) isothermal conditions exist, (6) no reactions take place betweenreservoir fluids and reservoir rock, (7) no gas solubility exists in the water,(8) gravity effects are negligible, and (9) the wellbore is fullypenetrating.
Development of Simulator Results
To develop generalized equations to predict inflow performance, IPR curveswere generated from simulator results for four basic sets of relativepermeability and fluid property data. Each data set was used to generatesimulator results from irreducible water saturation to residual oil saturation(ROS). A total of 16 theoretical reservoirs were examined from initial pressureto minimum flowing bottomhole pressure in 91 simulator runs. Reservoirproperties varied as follows: porosity, 12% to 24%; permeability, 10 to 100 md;height, 10 to 25 ft; temperature, 150 to 200°F; initial pressure, 1,500 to3,500 psi; oil gravity, 15 to 45°API; gas gravity, 0.6 to 0.7; water solids,12% to 30%; ROS, 5% to 45%; irreducible water saturation, 10% to 50%; criticalgas saturation, 0% to 7.5%; and drainage radius, 506 to 1,085 ft.
Simulator results were obtained for a radial flow geometry and constant oilrate production. The model grid was established geometrically so that eachsucceeding radius was 1.1 times larger than the previous radius. The initialcellblock radius was 0.329 ft, with a wellbore radius of 0.328 ft. Refs. 1 and2 give additional reservoir property details and simulator parameters.