Abstract
The relative permeability curves (Kr) control the production and are of primary importance for any type of recovery process. In the case of production by displacement (waterflood or gasflood) the Kr curves obtained in laboratory can be used in numerical simulators to predict hydrocarbon recovery (after upscaling to account for heterogeneity). In the case of reservoirs produced under solution gas drive (depressurized field, foamy oils), the experiments conducted in laboratory depend on the depletion rate and cannot be used directly for reservoir simulations.
We have developed a novel approach for calculating representative field-relative permeabilities. This new method is based on a physical model, which takes into account the various mechanisms of the process: bubble nucleation (preexisting bubbles model), phase transfer (volumic transfer function), gas displacement (bubbles flow). In our model, we have identified a very few number of "invariant" parameters that are not sensitive to depletion rate and are specific of the rock-fluids system (mainly the preexisting bubble size distribution and a factor between gas velocity and oil velocity in the dispersed phase regime). These invariant parameters are determined by history matching of one experiment at a given depletion rate.
The calibrated model is then used to generate synthetic data at any depletion rate, and especially at very low depletion rates representative of the reservoir conditions. Relative permeability are derived from these "numerical" experiments in the same way as real experiments. The calculated Kr are finally introduced in commercial reservoir simulators.
We have tested our model by using several series of published experiments with light and heavy oils. After adjusting the invariant parameters on one or two experiments, we are able to predict other experiments performed at different depletion rates with a very good accuracy.
Finally, we present an example of determination of relative permeabilities at reservoir depletion rates.
