Summary
We describe the successful application of a new method to estimate
permeability and permeability anisotropy from transient measurements of
pressure acquired with a wireline straddle-packer formation tester. Unlike
standard algorithms used for the interpretation of formation-tester
measurements, the method developed in this paper incorporates the physics of
two-phase immiscible flow as well as the processes of mudcake buildup and
invasion.
An efficient 2D (cylindrical coordinates) implicit-pressure
explicit-saturation finite-difference algorithm is used to simulate both the
process of invasion and the pressure measurements acquired with the
straddle-packer formation tester. Initial conditions for the simulation of
formation-tester measurements are determined by the spatial distributions of
pressure and fluid saturation resulting from mud-filtrate invasion. Inversion
is performed with a Levenberg-Marquardt nonlinear minimization algorithm.
Sensitivity analyses are conducted to assess nonuniqueness and the impact of
explicit assumptions made about fluid viscosity, capillary pressure, relative
permeability, mudcake growth, and time of invasion on the estimated values of
permeability and permeability anisotropy.
Applications of the inversion method to noisy synthetic measurements include
homogeneous, anisotropic, single- and multilayer formations for cases of low-
and high-permeability rocks. We also study the effect of unaccounted
impermeable bed boundaries on inverted formation properties. For cases where a
priori information can be sufficiently constrained, our inversion methodology
provides reliable and accurate estimates of permeability and permeability
anisotropy. In addition, we show that estimation errors of permeability
inversion procedures that neglect the physics of two-phase immiscible fluid
flow and mud-filtrate invasion can be as high as 100%.
Introduction
Modular and multiprobe formation testers have proved advantageous in the
determination of permeability at intermediate-scale lengths because of the
increased distance between the observation and sink probes (Pop et al. 1993;
Badaam et al. 1998; Proett et al. 2000). Moreover, the use of dual-packer or
“straddle-packer” modules over point-probe modules is known to improve the
interpretation of pressure transient measurements when testing laminated,
shaly, fractured, vuggy, unconsolidated, and low-permeability formations (Ayan
et al. 2001). Several papers have been published to describe interpretation
techniques and applications of these new formation-testing approaches (Kuchuk
1998; Hurst et al. 2000; Onur et al. 2004).
The new method introduced in this paper interprets formation-tester
measurements acquired with wireline straddle-packer tools. It incorporates the
physics of two-phase, axisymmetric, immiscible fluid flow to simulate the
measurements, and it is combined with a nonlinear minimization algorithm for
history-matching purposes. Comparable inversion approaches have been documented
in the open technical literature (Proett et al. 2000; Xian et al. 2004; Jackson
et al. 2003) but they assumed single-phase fluid flow. Recently, Zeybek et al.
(2001) introduced a multiphase flow method to integrate formation-tester
pressure and fractional flow measurements with the objective of refining
relative permeability values estimated from openhole resistivity logs. The same
authors considered the manual inversion of radial invasion profiles, horizontal
permeability, and permeability anisotropy but did not assess the uncertainty of
their estimations introduced by a priori assumptions about multiphase flow
parameters. By contrast, the developments reported in this paper integrate the
flow simulator with a dynamically coupled mudcake growth and mud-filtrate
invasion algorithm (Wu et al. 2002), which improves the physical consistency
and reliability of the quantitative estimation of both permeability and
permeability anisotropy.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
14 July 2005
- Meeting paper published:
9 October 2005
- Revised manuscript received:
22 May 2007
- Manuscript approved:
29 May 2007
- Version of record:
20 September 2007
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