Summary
This paper builds on a model for single-phase, non-Darcy flow in porous
media presented in by Barree and Conway (2004). In this work, the generalized
equation for single-phase non-Darcy flow is extended to multiphase-flow
conditions. Laboratory measurements of gas/water flow were conducted in several
flow cells to determine relative permeability curves and the nonlinear
relationship between individual-phase flow rate and induced potential gradient
over a wide range of input fractional-flow conditions and over a range of
Reynolds numbers (Re). A model is presented to predict
multiphase non-Darcy flow in porous media that is applicable to
high-deliverability reservoirs and hydraulically fractured wells.
Introduction
The importance of multiphase non-Darcy flow on well productivity and
impairment has been recognized widely (Martins et al. 1990; Blom and Hagoort
1998; Vincent et al. 1999; Wang and Mohanty 1999; Barree et al. 2003; Lolon et
al. 2004; Miskimins et al. 2005; Mohan et al. 2006). The combination of
high-velocity and multiphase flow has great effects on productivity and
stimulation effectiveness in hydraulically fractured wells. It is also
important in near-well pressure drop in high-permeability retrograde-condensate
reservoirs and fracture-pack or gravel-pack completions.
Many papers have addressed methods to predict the combined effects of
non-Darcy and multiphase flow (Evans et al. 1987; Penny and Jin 1995; Jin and
Penny 1998; Jin and Penny 2000; Olsen et al. 2004; Civan and Evans 1991; Civan
and Evans 1993; Milton-Tayler 1993). Several of these are based on work
conducted previously at Stim-Lab (Core Laboratories, Houston, USA) (Penny and
Jin 1995; Jin and Penny 1998, 2000). All these previous works have assumed a
constant value of the Forchheimer inertial coefficient (β), have relied
on a combined average Reynolds number to define the non-Darcy-flow state, or
both. In most cases, the combined effects of inertial losses and multiphase
flow have been expressed by use of a modified value of β. These earlier
methods neglect the fact that each phase flows at a different velocity in
separate pore channels and each experiences a different phase Reynolds number.
Further, phase velocity varies with saturation of each phase and relative
permeability to each phase.
The current work presents an alternative method of predicting the non-Darcy
multiphase relationship between potential gradient and phase-flow rate. The
model is based on extensive laboratory measurements of many proppants at
elevated confining stress, pore pressure, and temperature. The results can be
applied to flow in proppant packs for hydraulically fractured wells and to
high-velocity flow in reservoir rocks, typically in the near-wellbore
region.
© 2009. Society of Petroleum Engineers
View full textPDF
(
1,908 KB
)
History
- Original manuscript received:
27 July 2008
- Meeting paper published:
11 November 2007
- Revised manuscript received:
14 October 2008
- Manuscript approved:
13 November 2008
- Published online:
1 May 2009
- Version of record:
1 May 2009
View Cart
