Estimating oil/water relative permeability at SAGD steam chamber edge

Fluid flow at the edge of SAGD chamber where most of bitumen drainage occurs is of great importance. In this region, water condensate co-flows with the falling bitumen towards the production well. Since the bitumen viscosity varies at different locations due to temperature gradient across the edge of steam chamber, new correlations are required to consider the influence of fluid viscosity on the relative permeability curves. In this study, the objective is to remedy this deficiency by developing a new set of correlations for relative permeability estimation addressing in particular such effect at SAGD steam chamber edge. Various datasets from literature were obtained at different temperatures and oil viscosities. The data were used to develop new correlations which are a modification of the well-known Corey's equations for relative permeability estimation. Two mathematical approaches were applied and evaluated to achieve the best correlations: (1) at each temperature, herein substituted by viscosity ratio, relative permeabilities are functions of saturation, and (2) relative permeability is a function of viscosity ratio at a fixed saturation. Furthermore, different mathematical equations were used in the regression procedure in order to optimize the objective function and achieve the most reliable correlations. Results indicated a combined power and quadratic functionality of relative permeability to the phases' viscosity. The viscosity ratio was used in the new correlations as a dimensionless parameter which represents fluids' viscosities at different temperatures. The new correlations were compared against the original Corey's equations for various experimental datasets. Various statistical error formulation were employed: average relative error, average absolute relative error, root mean squared, correlation coefficient, and standard deviation. The accuracy of the new correlations was also graphically compared with Corey's model using cross-plot illustrations. Comparative evaluation of these correlation error analyses revealed that relative permeability estimations have been significantly improved when new correlations were employed which incorporate different temperature profiles and accordingly the viscosity variations. The application of the new correlation could improve the flow prediction in thermal simulators.