Gas Condensate Relative Permeability for Well Calculations

This paper addresses several issues related to the modeling and experimental design of relative permeabilities used for simulating gas condensate well deliverability. Based on the properties of compositional flow equations, we make use of the fact that relative permeability ratio k_rg/k_ro is a purely thermodynamic variable, replacing saturation, when flow is steady-state. The key relation defining steady-state flow in gas condensate wells is relative permeability k_rg as a function of k_rg/k_ro. Consequently, determination of saturation and k_r as a function of saturation is not important for this specific calculation. Once the k_rg=f(k_rg/k_ro) relationship is experimentally established and correlated with capillary number (N_c), accurate modeling of condensate blockage is possible. A generalized model is developed for relative permeability as the function of k_rg/k_ro and capillary number. This model enables us to link the immiscible or rock curves with miscible or 'straight-line curves by a transition function dependent on the capillary number. This model is also extended to the case of high-rate, inertial gas flow within the steady-state condensate blockage regionand locally at the wellbore. We have paid particular attention to the effect of hysteresis on the relation k_rg=f(k_rg/k_ro), based on our observation that many repeated cycles of partial/complete imbibition and drainage occur in the near-well region during the life of a gas condensate well. Finally, the composite effect of condensate blockage is handled using a Muskat pseudopressure model, where relative permeabilities are corrected for the positive effect of capillary number dependence and the negative effect of inertial high velocity flow. Special steady-state experimental procedures have been developed to measure k_rg as a function of k_rg/k_ro and N_c. Saturations, though they can be measured, are not necessary. An approach for fitting steady-state gas condensate relative permeability data has been developed and used for modeling relative permeability curves.