This work presents a complete reformulation of the Hall method involving
both pre- and post-breakthrough situations. Two approaches involving both
transient and pseudosteady-state methods produced very similar solutions, which
were verified with the results of coupled geomechanical/fluid-flow simulations.
The new formulations allow tracking the expanding water-bank radius from
inception to breakthrough. Pressure of this bank at the water/oil interface is
evaluated at every timestep, thereby allowing continuous update of the
'external pressure' in Hall's formulation. We show that Hall's formulation is a
particular case of the proposed approach. Several simulated and field examples
demonstrate the value of reformulated Hall analysis.
Because Hall's formulation involves an integral, the resultant signature, by
nature, is insensitive in revealing clues about subtle changes that may occur
during formation fracturing or plugging. We observed that the derivative of the
modified-Hall integral, obtained analytically, provides definitive signatures
about fracturing or plugging.
The new interpretation approach is particularly suitable for projects at the
inception of flooding. Mature projects can benefit equally from the new tool.
Perhaps the biggest appeal of the proposed tool lies in the green fields where
real-time data are readily available.
Significant advances have been made in recording, transmitting, filtering,
and interpreting real-time production data. However, data interpretation from
injection wells has not gained as much attention. Traditional water-injection
well evaluation involves pressure-transient analysis, which predictably
improved over the years, as testified by the contributions from Hazebtoek et
al. 1958; Kazemi et al. 1972; Marrill et al. 1974; Sosa et al. 1981; Abbaszadeh
and Kamal 1989; Yeh and Agarwal 1989; and Bratvold and Horne 1990. Falloff
analysis allows estimation of permeability, skin, and drainage-area pressure.
Because formation parting is quite common, van den Hoek (2005) presented a
method for discerning shrinkage of fracture height or length from falloff
While great strides have been made in interpreting falloff tests, Hall
(1963) plot appears to be one of the few tools available for ongoing
performance monitoring. Others have attempted modifications of the Hall plot by
introducing the use of bottomhole-flowing and reservoir pressures (Buell et al.
1990) or evaluating the reservoir pressure from a slope-analysis method (Silin
et al. 2005a, 2005b). Ideally, the Hall method is suitable for either the early
injection period or during the post-breakthrough period because the notion of
single reservoir pressure is entertained. Both reciprocal-injectivity index, or
RII (Hearn 1983; Abou-Sayed et al. 2007), and evolving skin (Zhu and Hill 1998)
are other alternatives to monitoring real-time well performance.
This study presents a new formulation of the Hall analysis. To that end, the
development of an analytic derivative expression turns out to be much more
discriminating for yielding the desired diagnostic clues. Ascertaining the
variable radial distance of the injection bank and pressure at the water/oil
interface (pe) makes the new formulation robust and suitable
for prebreakthrough situation. Our study shows that pe
practically becomes time invariant in postbreakthrough situation, suggesting
applicability of the original Hall formulation.
© 2009. Society of Petroleum Engineers
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- Original manuscript received:
19 July 2007
- Meeting paper published:
11 November 2007
- Revised manuscript received:
23 April 2008
- Manuscript approved:
9 May 2008
- Published online:
2 March 2009
- Version of record:
26 February 2009