Summary
Unsteady-state relative permeability experiments followed by automatic
history matching have been used in the past for estimating relative
permeability and capillary pressure simultaneously. The performance of the
automatic history matching largely depends on the simulator, the functional
form of the flow functions, and the optimization tool. The Newton method is
commonly used as the optimization tool for the automatic history matching; we
have used a genetic algorithm (GA) as the optimization tool in this work. One
of the advantages of GA is that it requires only function evaluations for the
solution searching and not Jacobian or gradient calculations as required by the
Newton method. The Corey model and piece-wise spline interpolation were used to
represent the relative permeability. A new coding method in GA was developed
for piece-wise spline interpolation. In-situ saturation data were collected
during an unsteady-state primary drainage experiment by CT scanning. Simulation
and experimental data were used to test the performance of the algorithm. Test
results showed a good match between the simulation data and experimental data
for low-injection-rate primary drainage. At higher rates, GA did not converge
to the global optimum.
Introduction
Relative permeability and capillary pressure are two important functions for
describing multiphase flow through porous media. They depend on saturation,
saturation history, wettability, porous medium microstructure, capillary
number, and Bond number, in general. Pore network models are being developed to
estimate these functions, but most researchers rely on experimental
measurements of these functions.
Capillary pressure and relative permeability have been measured separately
in previous works. Capillary pressure can be measured by the porous-plate
method, the centrifuge method, or by mercury porosimetry. Relative permeability
can be measured by steady-state or unsteady-state coreflooding experiments. The
drawback of determining capillary pressure and relative permeability separately
is that the capillary pressure measured in this manner gives a static capillary
pressure curve, while it is the dynamic capillary pressure that influences the
flow. As pointed out by Bentsen and Manai and then in Bentsen, the capillary
pressure in a dynamic system may be different from that in a static case,
because the dynamic capillary pressure is affected by many factors including
flow rate, possible variations of the wetting property, and microheterogeneity.
Therefore, simultaneously estimating the capillary pressure and the relative
permeability for a given flow system is preferable. In the present work, we use
unsteady-state experiments followed by the history-matching method to estimate
relative permeability and capillary pressure.
History-matching techniques have been developed to estimate relative
permeability and capillary pressure simultaneously. Functional forms with a set
of parameters are presumed for relative permeability of each phase and
capillary pressure. A series of forward simulations is run with the parameters
taking a certain set of values. The parameters are automatically tuned by an
optimization tool to match the simulation data (generally the pressure drop and
the production) with the experimental data.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
28 January 2004
- Revised manuscript received:
18 March 2005
- Manuscript approved:
3 April 2005
- Version of record:
15 December 2005
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