Summary
We use upscaling through homogenization to predict oil recovery from
fractured reservoirs consisting of matrix columns, also called vertically
fractured reservoirs (VFRs), for a variety of conditions. The upscaled VFR
model overcomes limitations of the dual-porosity model, including the use of a
shape factor. The purpose of this paper is to investigate three main physical
aspects of multiphase flow in fractured reservoirs: reservoir wettability,
viscosity ratio, and heterogeneity in rock/fluid properties. The main
characteristic that determines reservoir behavior is the Péclet number that
expresses the ratio of the average imbibition time divided by the residence
time of the fluids in the fractures. The second characteristic dimensionless
number is the gravity number.
Upscaled VFR simulations, aimed at studying the mentioned features, add new
insights. First, we discuss the results at low Péclet numbers. For only small
gravity numbers, the effect of contact angle, delay time for the nonequilibrium
capillary effect, the heterogeneity of the matrix-column size, and the matrix
permeability can be ignored without appreciable loss of accuracy. The ultimate
oil recovery for mixed-wet VFRs is approximately equal to the Amott index, and
the oil production does not depend on the absolute value of the phase viscosity
but on viscosity ratio. However, large gravity numbers enhance underriding,
aggravated by large contact angles, longer delay times, and higher viscosity
ratios. Layering can lead to an improvement or deterioration, depending on the
fracture aperture and permeability distribution. At low Péclet numbers, the
fractured reservoir behaves very similarly to a conventional reservoir and
depends largely on the viscosity ratio and the gravity number. At high Péclet
numbers, after water breakthrough, the oil recovery appears to be proportional
to the cosine of the contact angle and inversely proportional to the sum of the
oil and water viscosity. In addition, the mixed-wetting effect is more
pronounced; there are significant influences of delay time (nonequilibrium
effects), matrix permeability, matrix-column size, and the column-size
distribution on oil recovery. At low gravity numbers and an effective
length/thickness ratio larger than 10, the oil recovery is independent of the
vertical-fracture-aperture distribution. For the same amount of injected water,
the recovery at low Péclet numbers is larger than the recovery at high Péclet
numbers.
© 2010. Society of Petroleum Engineers
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History
- Original manuscript received:
8 December 2009
- Revised manuscript received:
2 June 2010
- Manuscript approved:
17 June 2010
- Published online:
23 December 2010
- Version of record:
17 June 2011
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