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Algorithms for numerical modeling and inversion of multi-phase fluid flow and electromagnetic measurements
textThe focus of this dissertation is the estimation of petrophysical properties of rock
formations based on the combined use of electromagnetic and fluid-flow measurements.
Traditionally, borehole electromagnetic measurements are interpreted independently in
terms of spatial variations of electrical resistivity. The estimated spatial variations of
electrical resistivity are subsequently interpreted in terms of variations of fluid saturation
and porosity. Such a strategy can lead to erroneous conclusions concerning the
petrophysical evaluation of rocks because the spatial distribution of electrical resistivity
is often governed by the interplay between salt concentration, absolute permeability,
relative permeability, and capillary pressure. To date, no consistent effort has been
advanced to use the physics of multi-phase fluid flow as the leading phenomenon in the
interpretation of borehole electromagnetic measurements.
This dissertation develops several efficient nonlinear inversion algorithms that
quantitatively combine borehole electromagnetic and fluid-flow phenomena. These
inversion algorithms also provide a measure of uncertainty and non-uniqueness in the
presence of noisy and imperfect measurements. The combined use of electromagnetic and
fluid-flow measurements drastically reduces non-uniqueness and uncertainty of the
estimated petrophysical parameters and, therefore, increases the accuracy of the
estimates. Specific problems considered in this dissertation are the estimation of spatial
distributions of porosity, permeability, and fluid saturation, as well as the estimation of
relative permeability and capillary pressure.
Joint and independent nonlinear inversions are performed for large-scale
petrophysical properties from in-situ permanent sensor data and near-borehole scale
petrophysical variables of rock formations from wireline formation tester and
electromagnetic induction logging measurements. For cases where fluid-flow related
measurements are absent, the coupled dual-physics inversion strategy allows quantitative
interpretation of electromagnetic measurements consistent with the physics of fluid flow.
It is conclusively shown that the simultaneous use of fluid-flow and
electromagnetic data sets reduces non-uniqueness in the inverted petrophysical model.Petroleum and Geosystems Engineerin
Capillarity and phase-mobility of a hydrocarbon gas–liquid system
When oil fields fall during their lifetime below the bubble point gas comes out of solution. The key questions are at which saturation the gas becomes mobile (“critical gas saturation”) and what the gas mobility is, because mobile gas reduces the production of oil significantly. The traditional view is that the gas phase becomes mobile once gas bubbles grow or expand to a size where they connect and form a percolating path. For typical 3D porous media the saturation corresponding to this percolation limit is on the order of 20%. However, significant literature report on gas mobility below lower limits of percolation thresholds i.e. below 0.1%. A direct experimental insight for that is lacking because laboratory measurements are notoriously difficult since the formation of gas bubbles below the bubble point includes thermodynamic and kinetic aspects, and the pressure decline rates achievable in laboratory experiments are orders of magnitude higher than the decline rates in the field. Here we study the nucleation and transport of gas coming out of solution in-situ in 3D rock using X-ray computed micro tomography which allows direct visualization of the nucleation kinetics and connectivity of gas. We use either propane or a propane–decane mixture as model system and conduct pressure depletion in absence of flow finding that – consistent with the literature – observation of the bubble point in the porous medium is decreased and becomes pressure decline rate dependent because of the bubble nucleation kinetics. That occurs in single-component systems and in hydrocarbon mixtures. Pressure depletion in absence of flow results in critical gas saturations between 20 and 30% which is consistent with typical percolation thresholds in 3D porous structures. That does not explain experimentally observed critical gas saturations significantly below 20%. Also, the respective pore level fluid occupancy where pores are filled with either gas or liquid phase but not partially with both as in normal 2-phase immiscible systems rather diminishes connectivity of gas and liquid phases. This observation indicates that likely other mechanisms play a role in establishing gas mobility at saturations significantly below 20%. Experiments under flow conditions, where gas is injected near the bubble point suggest that diffusion may significantly contribute to the transport of gas and may even be the dominant transport mechanism at field relevant flow rates. The consequence of diffusive transport are compositional gradients where locally the composition is such gas nucleation may occur. That would lead to a disconnected but mobile gas distribution ahead of the convective front. Furthermore, diffusive exchange leads to ripening and anti-ripening effects which influences the distribution for which we see evidence in pressure depletion experiments but not so much at low rate gas injection. Respective relative permeability computed from the imaged fluid distributions using a lattice Boltzmann approach show distinctly different behavior between pressure depletion and flowing conditions. These findings suggest that capillarity in a gas–liquid hydrocarbon mixture is far more complex than in a 2-phase immiscible system. Capillarity is coupled to phase behavior thermodynamics and kinetics on a fast time scale and diffusion-dominated mechanisms such as ripening and anti-ripening effects at a slow time scale. While the consequences for the current experimental and field modelling approaches are not yet fully clear, this shows that more research is needed to fully understand these effects and their implications