Calculation of Relative Permeability Using Well Test Data in Gas-Condensate Reservoirs

Abstract

Analysing well test data from gas-condensate reservoirs can be challenging, particularly when pressure drops below the dew point and condensate forms near the well. Usually, a single-phase pseudo-pressure approach is used to analyse the corresponding pressure transient well test data in combination with a composite reservoir model, but this approach has its shortcomings. A two-phase pseudo-pressure approach has been shown to give better results, but it requires relative permeability (kr) data which are not readily available. The paper demonstrates the reliability of calculating a pressure versus radius profile from pressure versus time build up data from tests on wells in gas-condensate reservoirs. The calculation is based on the probe radius concept originally proposed for single-phase systems. It also evaluates the possibility of obtaining, analytically, kr data affected by pressure and velocity in single-rate and multi-rate tests. The calculation is based on Darcy's law using the pressure derivative with respect to distance obtained from the pressure versus radius profile. The theory of these calculations is verified by comparing the results with the output from a numerical simulator based on a single-layer single-well radial reservoir model. A simple binary rich gas condensate fluid was used in the numerical simulation. The results demonstrate that the pressure versus radius profile using probe radius theory reasonably matches the corresponding pressure versus radius profile output from the numerical simulation. This also shows that the method can reliably predict the condensate bank radius. At first, the analytical approach used to calculate kr, as a function of radius, resulted in oscillations due to the nature of derivative calculation involved. The source of the kr noise was treated following two separate approaches that can be used depending on the level of noise versus ease of use. The calculated kr versus radius data showed good agreement with the corresponding grid block kr versus radius data predicted by the simulator for various rock types and flow rates. The method described in this paper provides a practical tool to estimate kr data that can be used to calculate two-phase pseudo pressure and hence potentially improve the analysis of gas-condensate test data affected by condensate banking and velocity. The derived kr data may also have other applications.