Laboratory measurements of saturation-dependent relative permeability are commonly used to construct reservoir models. However, because of sample size and paucity, their reliability to predict real-time production behavior of heterogeneous formations remains questionable. This paper introduces a new method to estimate near-wellbore hydrocarbon-water relative permeability from measurements acquired with production logging tools (PLT). Production logs (PL) are simulated in time-lapse mode by effectively coupling fluid flow regimes taking place in both wellbore and hydrocarbon-producing formations.
To simulate production logs, the reservoir-borehole coupled flow model assumes slightly compressible oil bubbles flowing through the incompressible phase of water in the wellbore. We apply a one dimensional isothermal two-fluid formulation to calculate wellbore fluid properties in the presence of velocity differences between fluid phases. Subsequently, a nonlinear inversion algorithm estimates saturation-dependent relative permeability by minimizing quadratic differences between borehole measurements of velocity, pressure, and holdup of the two phases, and their numerical simulations.
Estimations of relative permeabilities using the new method are within 5% of actual values in various synthetic cases. Estimation accuracy decreases to 30% in the presence of 5% additive Gaussian noise for intervals where phase saturation is close to the end-point value of relative permeability. Additionally, ignoring low-pressure compartments in multilayer reservoirs with differential depletion causes underestimation of relative permeability. We also examine time-lapse production logs acquired in multilayer reservoirs supported by an active aquifer. Incremental water production over time enables the inference of layer-by-layer relative permeability. Feasibility studies with synthetic measurements indicate that relative permeability can be estimated with errors lower than 10%. However, the reliability of the estimation method is limited by the effective water saturation window monitored in the wellbore during the life of producing reservoirs.