A Dual-Grid Automatic History-Matching Technique With Applications to 3D Formation Testing in the Presence of Oil-Based Mud-Filtrate Invasion
- Mayank Malik (University of Texas at Austin) | Carlos Torres-Verdin (University of Texas at Austin) | Kamy Sepehrnoori (University of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2009
- Document Type
- Journal Paper
- 164 - 181
- 2009. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 5.5 Reservoir Simulation, 5.2.1 Phase Behavior and PVT Measurements, 5.3.2 Multiphase Flow, 5.5.11 Formation Testing (e.g., Wireline, LWD), 4.1.2 Separation and Treating, 5.2.2 Fluid Modeling, Equations of State, 1.8 Formation Damage, 5.2 Reservoir Fluid Dynamics, 1.11 Drilling Fluids and Materials, 5.5.8 History Matching, 5.6.1 Open hole/cased hole log analysis
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Probe-type formation testers are often used to estimate permeability and anisotropy from pressure-transient measurements. The interpretation of these measurements is not trivial in the presence of oil-based-mud (OBM) -filtrate invasion because of 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. Because pressure transients are nonlinearly dependent on permeability, repeated 3D numerical simulations become necessary to honor measured pressure transients.
We describe the development and successful implementation of a new inversion method that efficiently estimates permeability and anisotropy with a cascade sequence of least-squares minimizations. Measurements consist of pressure transients acquired at the sandface 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 2D cylindrical grid. Transient measurements of pressure at the sandface 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 initialized until convergence is reached. The process repeats itself until the simulated 3D pressure transients reproduce the field measurements within prestipulated error bounds.
We perform tests of the new inversion algorithm on synthetic and field data sets acquired in the presence of OBM-filtrate invasion. Results 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 as well as by uncertainty in flow rates, relative permeability, radial extent of invasion, formation damage, and location of bed boundaries.
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