Analytical Development Of Vogel-Type Inflow Performance Relationships

Abstract

Summary In 1962, Vogel proposed an empirical inflow performance relationship (IPR) for solution-gas drive reservoirs based on numerical simulation results. This relationship isEquation 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. Introduction 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 byEquation 1 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 isEquation 2 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.

Self Consistent Approach to Construct Inflow Performance Relationship for Oil Well

“…However, this method also creates physically inadequate results when the skin-factor values are negative (then for the low values of wf p bottomhole pressure decrease leads to the oil flow rate decrease). As was subsequently proven [6,7] the presence of skin-factor should not influence to the shape of IPR curve. The results obtained by Standing are related to the mathematical representation of skin-factor as a non-dimensional pressure change around the wellbore which is linearly depended on the oil flow rate.…”

Control-Oriented Drift-Flux Modeling of Single and Two-Phase Flow for Drilling

“…The inflow from the reservoir is dependent on the pressure at the downhole boundary, usually given by a Vogel-Type Inflow performance relationship (IPR) [20], but within the operational range of a typical UBD operation an affine approximation should suffice, i.e.…”

An automation system for gas-lifted oil wells: Model identification, control, and optimization

“…Other IPR models are found in (Fetkovich, 1973), (Richardson and Shaw, 1982), (Raghavan, 1993), (Wiggins et al, 1996), and (Maravi, 2003). Fig.…”