A dimensionless inflow performance relationship (IPR) curve that is a function of horizontal permeability, average reservoir pressure, reservoir height, and reservoir drainage area has been developed for unfractured, horizontal gas wells. The Babu and Odeh horizontal oil well flow equations were modified to account for non-Darcy flow effects and mechanical skin effects and also transformed into pseudopressure form. The pseudopressure equations were solved using analytical methods and Monte Carlo simulation to yield dimensionless IPR curves. This effort showed that the proposed dimensionless IPR curve for unfractured, horizontal gas wells in pseudosteady-state flow is basically independent of all variables except horizontal permeability, average reservoir pressure, reservoir height, and reservoir drainage area. The proposed dimensionless IPR curve is similar in form to the familiar Vogel equation, but only has one coefficient, which is a function of horizontal permeability, average reservoir pressure, reservoir height, and reservoir drainage area. The proposed dimensionless IPR curve can be used to predict the deliverability of a horizontal gas well using a single-point test, as opposed to a standard four-point deliverability test, if the height of the reservoir is known.
Introduction
Deliverability testing refers to the testing of a gas well to measure its production capabilities at a given stage of reservoir depletion. Deliverability testing commonly yields a reservoir inflow performance relationship (IPR) curve. An IPR curve relates production rate to flowing bottomhole pressure for a given average reservoir pressure, the reservoir pressure at which the deliverability testing was performed. It is mainly used to predict current gas-well deliverability given a fixed backpressure.
Traditionally, deliverability testing of a gas well is accomplished using a four-point backpressure test, an isochronal test, or a modified isochronal test. All of these methods require testing a well at a minimum of four flow rates. These multi-point tests all yield very reliable results but are very expensive in terms of manpower and testing equipment. A method that can predict current gas well deliverability using only a single-point flowrate test is thus desirable.
Previous Studies
Vogel1 introduced the concept of dimensionless inflow performance relationship curves. As defined by Vogel, an IPR curve is made dimensionless by dividing the pressure for each point on the IPR curve by the maximum pressure for that particular curve and by dividing the corresponding production rate by the maximum producing rate for the same curve. Because it correlates q/qmax with pwf/p, a dimensionless IPR curve can be used to predict well performance. Vogel proposed his now famous inflow equation for solution-gas drive, oil wells: Equation (1)