Streamline-based modeling and interpretation of formation-tester measurements
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Formation testing is a critical component of modern petrophysical analysis for determining pore pressure, pressure gradients, and reservoir connectivity, and for estimating static and dynamic formation properties. However, petrophysicists tend to avoid the analysis of transient formation-tester measurements because of the physical and mathematical complexities involved, including time-consuming numerical simulations, rock heterogeneity, anisotropy, presence of mud-filtrate invasion, and saturation-dependent properties. Additional technical challenges arise when modeling formation-tester measurements in heterogeneous reservoirs penetrated by high-angle wells. A new method is developed in this dissertation to efficiently simulate formation-tester measurements acquired in heterogeneous reservoirs penetrated by vertical and deviated wells. The method is based on tracing flow streamlines from the reservoir into the formation tester’s probe. Before tracing streamlines, an initial reservoir condition is imposed due to the pressure-saturation field resulting from mud-filtrate invasion. Subsequently, the spatial distribution of pressure is calculated via finite differences to account for the negative flow-rate source originating from the tester’s probe. Streamlines are retraced at various time intervals upon updating the pressure distribution resulting from dynamic fluid flow toward the source. The streamline-based simulation method is efficient and flexible in accounting for various probe configurations, including dual packers and point focused-sampling probes. Streamlines are also used to trace reservoir fluid and contamination into sample probes. In addition, graphical rendering of streamlines permits rapid assessment of flow regimes as a function of time. Simulation results obtained with finite-difference and streamline methods agree well, although the streamline-based method is computationally more efficient. However, the streamline method is not well suited for complicated fluid displacement, such as that arising in the presence of highly compressible flow, strong capillary-pressure effects, and variable phase behavior. Furthermore, criteria for enforcing pressure updates with finite differences raise additional difficulties in accurately modeling formation-tester measurements. Despite these limitations, forward simulation results indicate that both faster computation time and reduced computer-memory requirements resulting from use of the streamline-based method are ideal for inversion of formation-tester measurements used in estimating static and dynamic petrophysical properties. Synthetic and field examples of streamline-based inversion are considered to estimate petrophysical properties from transient data acquired with packer and probe-type formation testers. The method is applied to measurements acquired in two offshore field reservoirs penetrated by vertical and deviated wells to estimate permeability, anisotropy, and relative permeability. In the documented examples, each streamline-based simulation used to calculate the Jacobian matrix is up to 8.7 times faster than that obtained by using the finite-difference method. Inversion results also indicate that streamline trajectories are valuable in ascertaining the sensitivity of estimated formation properties in the presence of variable pressure/fluid sampling locations, variable wellbore orientations with respect to formation bedding, and reservoir heterogeneity in deviated and horizontal well models.