Variations of Gas/Condensate Relative Permeability With Production Rate at Near-Wellbore Conditions: A General Correlation
Authors: Jamiolahmady Mahmoud , Danesh Ali , Tehrani D.H. , Sohrabi Mehran 
Published: December 2006

Summary
It has been demonstrated, first by this laboratory and subsequently by other researchers, that the gas and condensate relative permeability can increase significantly by increasing rate, contrary to the common understanding. There are now a number of correlations in the literature and commercial reservoir simulators accounting for the positive effect of coupling and the negative effect of inertia at near-wellbore conditions. The available functional forms estimate the two effects separately and include a number of parameters, which should be determined with measurements at high-velocity conditions. Measurements of gas/condensate relative permeability at simulated near-wellbore conditions are very demanding and expensive.
Recent experimental findings in this laboratory indicate that measured gas/condensate relative permeability values on cores with different characteristics become more similar if expressed in terms of fractional flow instead of the commonly used saturation. This would lower the number of rock curves required in reservoir studies. Hence, we have used a large data bank of gas/condensate relative permeability measurements to develop a general correlation accounting for the combined effect of coupling and inertia as a function of fractional flow. The parameters of the new correlation are either universal, applicable to all types of rocks, or can be determined from commonly measured petrophysical data. The developed correlation has been evaluated by comparing its prediction with the gas/condensate relative permeability values measured at near-wellbore conditions on reservoir rocks not used in its development. The results are quite satisfactory, confirming that the correlation can provide reliable information on variations of relative permeability at near-wellbore conditions with no requirement for expensive measurements.

Introduction
The process of condensation around the wellbore in a gas/condensate reservoir, when the pressure falls below the dewpoint, creates a region in which both gas and condensate phases flow. The flow behavior in this region is controlled by the viscous, capillary, and inertial forces. This, along with the presence of condensate in all the pores, dictates a flow mechanism that is different from that of gas/oil and gas/condensate in the bulk of the reservoir (Danesh et al. 1989). Accurate determination of gas/condensate relative permeability (kr) values, which is very important in well-deliverability estimates, is a major challenge and requires an approach different from that for conventional gas/oil systems.
It has been widely accepted that relative permeability (kr) values at low values of interfacial tension (IFT) are strong functions of IFT as well as fluid saturation (Bardon and Longeron 1980; Asar and Handy 1988; Haniff and Ali 1990; Munkerud 1995). Danesh et al. (1994) were first to report the improvement of the relative permeability of condensing systems owing to an increase in velocity as well as that caused by a reduction in IFT. This flow behavior, referred to as the positive coupling effect, was subsequently confirmed experimentally by other investigators (Henderson et al. 1995, 1996; Ali et al. 1997; Blom et al. 1997). Jamiolahmady et al. (2000) were first to study the positive coupling effect mechanistically capturing the competition of viscous and capillary forces at the pore level, where there is simultaneous flow of the two phases with intermittent opening and closure of the gas passage by condensate. Jamiolahmady et al. (2003) developed a steady-dynamic network model capturing this flow behavior and predicted some kr values, which were quantitatively comparable with the experimentally measured values.