Summary
Relative permeability curves (kr) control 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 the 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 the 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 that takes into account the various mechanisms of the process: bubble nucleation(pre-existing bubbles model), phase transfer (volumetric transfer function), and gas displacement (bubble flow). In our model, we have identified a few"invariant" parameters that are not sensitive to depletion rate and are specific to the rock/fluid system (mainly the pre-existing bubble-size distribution and a proportionality coefficient relating gas and oil velocity for the dispersed-phase regime). These invariant parameters are determined by history matching one experiment at a given depletion rate.
The calibrated model is then used to generate synthetic data at any depletion rate, especially at very low depletion rates representative of the reservoir conditions. Relative permeabilities are derived from these"numerical" experiments in the same way as they are from real experiments. The calculated kr is finally used 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 very good accuracy. Finally, we present an example of determination of relative permeabilities at reservoir depletion rates.
Introduction
In the case of conventional recovery processes (waterflooding and gasflooding), experiments that are conducted in the laboratory can mimic the conditions that prevail in the reservoir. Hence, the kr data derived from these experiments can be used in a practically straightforward manner for field-simulation purposes (upscaling is often needed to account for heterogeneities).
The problem is more complicated for recovery by solution-gas drive. In this case, the laboratory experiments fail in reproducing the reservoir conditions. In reservoirs, the depletion rates are at least several times lower than what can be obtained in the laboratory. Because the depletion rate controls the gas topology (bubble density), the diffusion of gas from solution (out of equilibrium), and the gas displacement (dispersed flow), it also dramatically affects the shape of the kr curves. Therefore, the depletion experiments cannot be used to derive field kr data directly.
