Analytical Development Of Vogel-Type Inflow Performance Relationships
- Michael L. Wiggins (School of Petroleum & Geological Engineering, University of Oklahoma) | James E. Russell (Department of Petroleum Engineering) | James W. Jennings (Department of Petroleum Engineering, Texas A&M University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 1996
- Document Type
- Journal Paper
- 355 - 362
- 1996. Society of Petroleum Engineers
- 5.3.2 Multiphase Flow, 3.1 Artificial Lift Systems, 5.2 Reservoir Fluid Dynamics, 4.1.2 Separation and Treating, 5.6.8 Well Performance Monitoring, Inflow Performance, 4.6 Natural Gas, 5.3.1 Flow in Porous Media, 5.2.1 Phase Behavior and PVT Measurements, 5.5 Reservoir Simulation
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In 1962, Vogel proposed an empirical inflow performance relationship (IPR) for solution-gas drive reservoirs based on numerical simulation results. This relationship is
and was based on a wide range of rock and fluid properties. This generalized relationship gained almost immediate acceptance in the industry due to its relative ease of use and because it gave reasonable engineering accuracy. This paper presents a theoretical basis for Vogel's IPR based on the physical nature of the multiphase flow system. The resulting analytical IPR follows from a Taylor series expansion of the multiphase flow equations and is verified by computer simulation results.
Predicting the performance of individual oil wells is an important responsibility of the petroleum engineer. Estimates of well performance allow the engineer to determine the optimum production scheme, design production and artificial lift equipment, design stimulation treatments and forecast production for planning purposes. Each of these activities is integral to the efficient operation of producing wells and successful reservoir management.
When estimating oilwell performance, engineers often assume that fluid inflow is proportional to the difference between reservoir pressure and wellbore pressure, One of the first relationships to be used based on this assumption was the Productivity Index (PI). This straight-line relationship is derived from Darcy's law for the steady-state incompressible flow of a single-phase fluid and is the ratio of the producing rate to the pressure difference. In equation form, the PI is defined by
However, Evinger and Muskat1 pointed out that a straightline relationship should not be expected when two phases, oil and gas, are flowing in the reservoir. They presented theoretical calculations that showed a curved relationship between flow rate and pressure. Their method, however, did not gain wide acceptance by petroleum engineers since it required extensive knowledge of rock and fluid properties.
Vogel2 later developed an empirical inflow performance relationship (IPR) for solution-gas drive reservoirs that accounted for the flow of two phases, oil and gas, in the reservoir based on computer simulation results. The resulting IPR equation is
Vogel's relationship gained almost immediate use within the industry due to its simplicity and accuracy. The method, which required knowledge only of a single flow rate, flowing wellbore pressure and average reservoir pressure, was easy to use and gave good approximations of the pressure-production behavior of an oil well over a wide range of operating conditions.
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