In 1968, Vogel used a computer program to predict inflow performance relationships (IPR) of a well producing from a wide variety of solution-gas drive reservoirs. In dimensionless form, these curves relating flowing, bottom-hole pressures to oil production rates were found to share a common characteristic shape which was correlated by a parabola. Because Vogel studied cases of differing rock and PVT properties, his work became well accepted in the industry. Most of the papers published on inflow performance deal with vertical wells and should not be applied to performance deal with vertical wells and should not be applied to horizontal wells without verification. There are no analytical models available at present to compute IPRs from two phase flow theory. In such a case, it is necessary to use numerical simulation. Unfortunately, most commercial black oil simulators do not include the feature necessary for predicting IPRs of horizontal wells. predicting IPRs of horizontal wells. In this paper, two commercial simulators are utilized to develop IPRs for horizontal wells producing from solution-gas drive reservoirs. The development parallels the work of Vogel for vertical wells. First, a base case is considered with typical fluid, rock and reservoir properties. Then, variations from the base case are investigated. Changes from the base case, -i fluid properties included variations in relative permeability and PVT properties. Changes in reservoir properties included variations in drainage area, pay thickness, and absolute permeability. Changes in well properties included variations in skin, well location, and well length with properties included variations in skin, well location, and well length with respect to reservoir boundaries. The resulting IPRs were made dimensionless in order to compare their curvature, or the rate of change of oil production rate with flowing bottom-hole pressure. These curves were found to be sensitive to the stage of reservoir depletion. However, they were not affected significantly by changes in the fluid reservoir, or well properties. properties. An attempt was made to develop a simple correlation to represent numerical results. Both Vogel's and Fetkovich's equations were tried, but neither of them fully reproduced the characteristic shape of the dimensionless IPRs. A new two-parameter equation, that results from combining the two previous equations was found to provide an adequate correlation.
A step in the analysis of the deliverability of a well is to estimate the production rate for any given flowing bottom-hole pressure. In single phase production rate for any given flowing bottom-hole pressure. In single phase flow of oil, inflow into a well is usually directly proportional to the pressure differential between the reservoir and the wellbore. But in two pressure differential between the reservoir and the wellbore. But in two phase flow of oil and gas, this relationship between the production rate phase flow of oil and gas, this relationship between the production rate ana the wellbore pressure is no longer linear. An equation that describes this relationship is known as the inflow performance relationship of a well (IPR).
Vogel has proposed an empirical IPR equation that has been used in the industry successfully. Because flow into a horizontal well is different from the flow into a vertical well, IPR equations developed for vertical wells should not be applied to horizontal wells without verification. Since the analytical calculations necessary to compute IPRs from two phase flow theory axe tedious, numerical simulation is used. Most commercial black oil simulators do not include the feature of making complete IPR predictions for a reservoir. predictions for a reservoir. In this paper, available commercial simulators are nevertheless utilized to generate IPRs of a horizontal well producing from a solution-gas drive reservoir. First, IPRs are generated for a base case reservoir. Then, variations of the base case are examined. These variations cover a wide range of fluid, reservoir and well characteristics. Fluid characteristics include crude oil PVT properties and relative permeability data. Reservoir characteristics include absolute permeability data. Reservoir characteristics include absolute permeability, drainage area, and formation thickness. Well characteristics permeability, drainage area, and formation thickness. Well characteristics include skin, location, and length with respect to the reservoir dimensions.