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. / text

Single-probe formation testers have been used since the 1950s to measure pore pressure and estimate mobility in fluid-bearing formations penetrated by a well. They are widely used in the oil and gas industry, with tens of measurements often made in every newly drilled well as part of the formation evaluation program. Each measurement consists of placing the tool in the wellbore in direct contact with the face of the formation, extracting a small amount of fluid (from 1 to 50 cc) from the rock and analyzing the fluid pressure response of the system. Pressure interpretation is based on models that assume that temperature within the formation tester flowline remains constant during the tool operation. However, formation pressure measurement involves relatively fast volume and pressure changes within the flowline, which result in temperature changes. These temperature changes are modeled semi-analytically and their effect on pressure transients is analyzed. Temperature variations are accounted for by describing the pressure and temperature dependence of fluid density in the continuity equation, and that temperature varies with both space and time. It is considered here that once a temperature change is imposed on the system, the primary mechanism of thermal transport to achieve equilibrium is conduction. Including temperature in the analysis requires taking into account flowline geometry, and well environmental conditions during the measurement-- namely, wellbore temperature and type of drilling fluid in the wellbore, all of which are immaterial in the isothermal analysis. Arguably, pressure behavior during formation tester measurements could be influenced by several factors. All previous studies related to formation testers assume perfect tool performance and provide explanations to pressure behaviors from the reservoir point of view (e.g., Stewart and Witmmann, 1979; Phelps et al., 1984; Proett and Chin, 1996, etc.). The approach followed here is diametrically opposite. The formation is considered `perfect' from the point of view of pressure measurement, and physical phenomena (thermal transients) that may affect the measured pressure signal are studied. The focus is to understand fundamental aspects of the tool performance that can be studied analytically while minimizing, as much as possible, external parameters that add uncertainty. This dissertation was motivated by inconsistencies observed between the pressure behavior in field measurements and existing (isothermal) theory. For instance, false buildups, buildup overshoots and long time required to reach pressure equilibration, have puzzled those involved in the interpretation of formation tester pressure transients for many years. These behaviors can be reproduced in pressure computations when accounting for temperature variations. The focus of this dissertation is on modeling the tool capability to sense pressure transients associated with recompression of formation fluids several inches away from the wellbore, accounting for temperature variations during the measurement. This is relevant because it is desirable to characterize formation properties beyond the region affected by drilling mud filtrate invasion. In practice, a discrepancy is often observed between formation mobility obtained from drawdown, which depends mostly on formation properties near the wellbore, and mobility obtained from the analysis of late-time buildup pressure, which in theory depends on formation properties farther from the wellbore (Moran and Finklea, 1962). This dissertation examines the influence of late-time tool storage effects caused by thermal equilibration of the flowline fluid on the pressure equilibration and buildup mobility interpretation. It was found that in some cases such late-time storage effects could exhibit a behavior that resembles that expected from spherical flow, that is, the flow regime characteristic of single-probe formation testers; and could therefore invalidate mobility determined by isothermal transient pressure analysis. Formation tester flowline and probe design, test parameters (rate and volume), and environmental conditions during the measurement, mostly type of drilling fluid and wellbore temperature, are important variables in determining the magnitude of late-time storage effects, and hence the tool capability to detect a deep formation signal (spherical flow). Temperature variations affecting late-buildup pressure transients were observed to be more pronounced (listed in order of importance): as wellbore temperature increases; drilling fluid is oil-based mud; flowline with large radius components (e.g. > 1 cm); large flowline volume; small probe radius (< 1 cm); and, large drawdown rate. Temperature effects on the late-buildup also tend to be more significant when mobility is in the 0.1 to 10 md/cp range, that is for those formations more likely, in theory, to exhibit spherical flow regime during buildup. / text

Well logs and formation testers are routinely used for detection and quantification of hydrocarbon reserves. Overbalanced drilling causes invasion of mud filtrate into permeable rocks, hence radial displacement of in-situ saturating fluids away from the wellbore. The spatial distribution of fluids in the near-wellbore region remains affected by a multitude of petrophysical and fluid factors originating from the process of mud-filtrate invasion. Consequently, depending on the type of drilling mud (e.g. water- and oil-base muds) and the influence of mud filtrate, well logs and formation-tester measurements are sensitive to a combination of in-situ (original) fluids and mud filtrate in addition to petrophysical properties of the invaded formations. This behavior can often impair the reliable assessment of hydrocarbon saturation and formation storage/mobility. The effect of mud-filtrate invasion on well logs and formation-tester measurements acquired in vertical wells has been extensively documented in the past. Much work is still needed to understand and quantify the influence of mud-filtrate invasion on well logs acquired in horizontal and deviated wells, where the spatial distribution of fluids in the near-wellbore region is not axial-symmetric in general, and can be appreciably affected by gravity segregation, permeability anisotropy, capillary pressure, and flow barriers. This dissertation develops a general algorithm to simulate the process of mud-filtrate invasion in vertical and deviated wells for drilling conditions that involve water- and oil-base mud. The algorithm is formulated in cylindrical coordinates to take advantage of the geometrical embedding imposed by the wellbore in the spatial distribution of fluids within invaded formations. In addition, the algorithm reproduces the formation of mudcake due to invasion in permeable formations and allows the simulation of pressure and fractional flow-rate measurements acquired with dual-packer and point-probe formation testers after the onset of invasion. An equation-of-state (EOS) formulation is invoked to simulate invasion with both water- and oil-base muds into rock formations saturated with water, oil, gas, or stable combinations of the three fluids. The algorithm also allows the simulation of physical dispersion, fluid miscibility, and wettability alteration. Discretized fluid flow equations are solved with an implicit pressure and explicit concentration (IMPEC) scheme. Thermodynamic equilibrium and mass balance, together with volume constraint equations govern the time-space evolution of molar and fluid-phase concentrations. Calculations of pressure-volume-temperature (PVT) properties of the hydrocarbon phase are performed with Peng-Robinson's equation of state. A full-tensor permeability formulation is implemented with mass balance equations to accurately model fluid flow behavior in horizontal and deviated wells. The simulator is rigorously and successfully verified with both analytical solutions and commercial simulators. Numerical simulations performed over a wide range of fluid and petrophysical conditions confirm the strong influence that well deviation angle can have on the spatial distribution of fluid saturation resulting from invasion, especially in the vicinity of flow barriers. Analysis on the effect of physical dispersion on the radial distribution of salt concentration shows that electrical resistivity logs could be greatly affected by salt dispersivity when the invading fluid has lower salinity than in-situ water. The effect of emulsifiers and oil-wetting agents present in oil-base mud was studied to quantify wettability alteration and changes in residual water saturation. It was found that wettability alteration releases a fraction of otherwise irreducible water during invasion and this causes electrical resistivity logs to exhibit an abnormal trend from shallow- to deep-sensing apparent resistivity. Simulation of formation-tester measurements acquired in deviated wells indicates that (i) invasion increases the pressure drop during both drawdown and buildup regimes, (ii) bed-boundary effects increase as the wellbore deviation angle increases, and (iii) a probe facing upward around the perimeter of the wellbore achieves the fastest fluid clean-up when the density of invading fluid is larger than that of in-situ fluid. / text