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.
Singularity crossing phenomena in DAEs: A two-phase fluid flow application case study
