Variations of Gas-Condensate Relative Permeability with Production Rate at Near Wellbore Conditions: A General Correlation
Authors: Jamiolahmady M. , Danesh A. , Henderson G. , Tehrani D. 
Published: December 2007

Abstract
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 using measurements at high velocity conditions. Measurements of gas-condensate relative permeability at simulated near wellbore conditions are very demanding and expensive.

Introduction
The process of condensation around the wellbore in a gas-condensate reservoir, when the pressure falls below the dew point, creates a region in which both gas and condensate phases flow. The flow behaviour in this region is controlled by the viscous, capillary and inertial forces. This along with the presence of condensate in all the pores dictate a flow mechanism that is different to that of gas-oil and also gas-condensate in the bulk of the reservoir[1]. Accurate determination of gas-condensate relative permeability (kr) values, which is very important in well deliverability estimates, is a major challenge and requires a different approach compared to 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[2–5]. Danesh et al.[6] were first to report the improvement of relative permeability of condensing systems due to an increase in velocity as well as that caused by a reduction in interfacial tension. This flow behaviour, named as the positive coupling effect, was subsequently confirmed experimentally by other investigators[7–10]. Jamiolahmady et al.[11] were first to study the positive coupling effect mechanistically capturing the competition of viscous and capillary forces at the pore level where there is a simultaneous flow of the two phases with intermittent opening and closure of gas passage by condensate. Jamiolahmady et al.[12] developed a steady-dynamic network model capturing this flow behaviour and predicted some kr values, which were quantitatively comparable with the experimentally measured values.
There are also several empirical correlations in the literature and commercial simulators accounting for the positive effect of coupling at near wellbore conditions as a function of capillary number (ratio of viscous to capillary forces). These correlations can be divided into two main classes:using Corey functions in which the Corey coefficients are interpolated between the immiscible and miscible limits[9,13] andinterpolation between miscible and immiscible relative permeability curves[14–16].
In both methods the interpolation is weighted by capillary number (Nc) dependent functions. Blom and Haggort[17]reviewed fifteen different correlations, all of which had capillary number and saturation as the main independent variables.
At high velocities where the inertial effect (non-Darcy flow) is significant the competition of inertial and coupling effects complicates the flow in this region even further. Henderson et al.[18], through some steady state kr measurements, confirmed the significant effect of positive coupling effect even at very high velocities contrary to the conventional view that kr would reduce with increasing velocity. They observed that the presence of condensate initially decreased the permeability due to inertia, before the positive coupling effect became dominant.