Neither Vogel nor Standing's extension of Vogel's work takes into account the non-Darcy flow term. A constant flow efficiency is usually assumed and determined from two flow tests with knowledge of the static pressure at the well in question.
In this paper, a method is presented to construct the true Inflow Performance Relationships with rate-dependent skin (variable flow efficiency) from a two flow test knowing the static pressure. If the fluid properties and oil permeabilities are also known the non-Darcy flow term can be determined. The Inflow Performance Relationships with a constant flow efficiency is also discussed, showing how the coefficient in the Vogel equation varies with flow conditions.
Stimulation or treatment cannot remove the rate dependent skin and may result in increasing it. Therefore, knowing the non-Darcy flow term will be helpful in deciding to see if remedial work is needed for improving the well productivity.
In some oil wells, the productivity index (PI). the ratio of flow rate to pressure drawdown, does not remain constant; i.e., the flow rate is not directly proportional to the bottomhole pressure drawdown over a wide variation in flow rate. The cause of this nonlinearity in flow rate has been attributed to producing below the bubble point pressure and non-Darcy flow effect. However, it is widely known to reservoir engineers that the non-Darcy flow effect dominates the total skin factor at high flow rates in gas wells and is neglected in oil wells. This is not the case in oil wells testedby Fetkovich (1) where the non-Darcy flow term causes the exponent (n) of the backpressure equation to be less than 1. Fetkovich showed that the exponent (n) for oil well tests determined from a log (q) vs. log (Δp2) plot was found to lie between 0.568 and 1.000 which isvery near the 1imits commonly accepted for gas well back-pressure curves. Morris et al(2) have also presented the production test data foe naturally fractured, liquid- dominated geothermal reservoirs, with the similar behavior at high flow rates. This production data indicates that the pressure drawdown relationship with flow rate has a component that is proportional to flow rate squared in a manner similar to turbulent flow in high-rate gas wells. They concluded that the turbulent flow theory does describe the observed behavior of most 'f/ells in naturally fractured formations.
The analysis of pressure buildup data does show the effect of non-Darcy flow in terms of skin component, Dq. That is
Equation (Available in full paper)
The true skin effect component, s, is caused by a physical occurrence to the well such as drilling mud filtrate and partial penetration. This skin damage can be removed by remedial work. The non-Darcy flow term, however, cannot be removed and is usually determined from a two rate test where the total skin effects, s' from both flows are known.
This paper uses the theoretical basis of two rate test to develop a simplified solution to the problem of determining the non-Darcy flow term, D, without knowledge of the total skin factors, and the true IPR for oil wells.
