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.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
28 January 2004
- Revised manuscript received:
10 May 2005
- Manuscript approved:
24 May 2005
- Version of record:
15 August 2005
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