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Abstract

Probe-type formation testers are often used to estimate permeability and permeability anisotropy from pressure transient measurements. The interpretation of these measurements is not trivial in the presence of oil-base mud-filtrate invasion due to miscibility with formation oil and gas. Simple analytical expressions of spherical and linear single-phase flow may not give correct estimates of permeability in miscible or partially miscible flow regimes. A computationally demanding three-dimensional (3D) numerical model is required to provide accurate and reliable estimates of formation properties. Because pressure transients are nonlinearly dependent on the permeability of the formation, repeated 3D numerical simulations are necessary to match the measured pressure transients.

We describe the development and successful implementation of a new inversion method that efficiently estimates permeability and permeability anisotropy with a cascade sequence of least-squares minimizations. Measurements consist of pressure transients acquired at the sand face with a probe-type wireline formation tester (WFT). The new inversion method executes the forward 3D problem only in an outer loop. In the inner loop, we perform fast minimizations with an equivalent two-dimensional (2D) cylindrical grid. Transient measurements of pressure at the sand face simulated with the 2D cylindrical grid are correlated to the corresponding measurements simulated with the 3D grid. Once the 2D minimization is completed, we perform a 3D simulation of transient pressure to update the 2D-3D correlation parameter and a new 2D minimization is performed until convergence is reached.  The process repeats itself until the simulated 3D pressure transients reproduce the field measurements within pre-stipulated error bounds.

We perform tests of the new inversion algorithm on synthetic and field data sets acquired in the presence of oil-base mud-filtrate invasion. Results successfully confirm that our coupled 2D/3D hybrid inversion approach enables significant savings in computer time and provides reliable and accurate estimates of permeability and anisotropy. In most cases, we are able to estimate permeability under 2% error within 20% of the computational time required by 3D minimization. Sensitivity analysis indicates that permeability estimates may be biased by noisy measurements and uncertainty in (a) flow rates, (b) relative permeability, (c) radial extent of invasion, (d) formation damage, and (e) location of bed boundaries.