Lincoln Paterson

Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions

Previous studies of fluid convection in porous media have considered the onset of convection in isotropic systems and the steady convection in anisotropic systems. This paper bridges between these and develops new results for the onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. These results are relevant to sedimentary formations where the average vertical permeability is some fraction γ of the average horizontal permeability. Linear and global stability analyses are used to define the critical time tc at which the instability occurs as a function of γ and the dimensionless Rayleigh-Darcy number Ra* for both thermal and solute-driven convection in an infinite horizontal slab. Numerical results and approximate analytical solutions are obtained for both a slab of finite thickness and the limit of large slab thickness. For a thick slab, the increase in tc as γ decreases is approximately given by (1+γ)4∕(16γ2). One important application is to the geological sto...

Safe storage and effective monitoring of CO2 in depleted gas fields

Carbon capture and storage (CCS) is vital to reduce CO2 emissions to the atmosphere, potentially providing 20% of the needed reductions in global emissions. Research and demonstration projects are important to increase scientific understanding of CCS, and making processes and results widely available helps to reduce public concerns, which may otherwise block this technology. The Otway Project has provided verification of the underlying science of CO2 storage in a depleted gas field, and shows that the support of all stakeholders can be earned and retained. Quantitative verification of long-term storage has been demonstrated. A direct measurement of storage efficiency has been made, confirming that CO2 storage in depleted gas fields can be safe and effective, and that these structures could store globally significant amounts of CO2.

Coupling of geochemical reactions and convective mixing in the long-term geological storage of carbon dioxide

Abstract The effect of coupling of geochemical reactions with convective mixing of dissolved carbon dioxide during geological storage is investigated by both analytical and numerical techniques. In the limit of fast reactions, scaling arguments and stability analysis show that the time for the onset of convection could be increased by up to an order of magnitude due to consumption of the dissolved carbon dioxide in mineralization. Numerical simulations are then used to investigate the effect of general reaction rates in two contrasting mineralogies, including overall dissolution and the distribution of ion and mineral concentrations.

Direct and Stochastic Generation of Network Models from Tomographic Images: Effect of Topology on Residual Saturations

We generate the network model equivalents of four samples of Fontainebleau sandstone obtained from the analysis of microtomographic images. We present the measured distributions of flow-relevant geometric and topological properties of the pore space. We generate via bond dilution from a regular lattice, stochastic network models with identical geometric (pore-size, throat-size) and topological (coordination number distribution) properties. We then simulate the two-phase flow properties directly on the network model and the stochastic equivalent for each sample. The simulations on the stochastic networks are found to provide a poor representation of the results on the direct network equivalents. We find that the description of the network topology is particularly crucial in accurately predicting the residual phase saturations. We also find it necessary to introduce into the stochastic network geometry both extended pore-pore correlations and local pore-throat correlations to obtain good agreement with flow properties on the rock-equivalent network.

Fractional Lévy motion as a model for spatial variability in sedimentary rock

A new approach to the modeling of spatial variability in sedimentary formations is introduced. This approach avoids the assumption of Gaussian behavior. Specifically, borehole measurements of physical properties of sedimentary rock from contrasting geological settings are shown to have a statistical character consistent with fractional Levy motion. Successive increments in the measurement sequences are accurately modeled as having Levy-stable distributions. The Levy parameters are similar for boreholes in the same sedimentary basin, but vary from basin to basin. Thinly bedded formations have smaller values for the Levy index, suggesting that the Levy index may be a useful measure of heterogeneity. The measurement sequences are also statistically self-similar and have long-range negative dependence among the increments (antipersistence). In addition to reproducing the statistical properties of well logs, the new model also mimics the most striking visual features of sedimentary formations.

Pore-scale network model for drainage-dominated three-phase flow in porous media.

Drainage displacements in three-phase flow under strongly wetting conditions are completely described by a simple generalisation of well understood two-phase drainage mechanisms. As in two-phase flow, the sequence of throat invasions in three-phase flow is determined by fluid connectivity and threshold capillary pressure for the invading interface. Flow through wetting and intermediate spreading films is important in determining fluid recoveries and the progress of the displacement in three-phase flow. Viscous pressure drops associated with flow through films give rise to multiple filling and emptying of pores. A three-phase, two-dimensional network model based on the pore-scale fluid distributions and displacement mechanisms reported by Øren et al. and which accounts for flow through both wetting and intermediate fluid films is shown to correctly predict all the important characteristics of three-phase flow observed in glass micromodel experiments.

Fingering with miscible fluids in a Hele Shaw cell

Unstable, two‐fluid miscible displacements in a Hele Shaw cell of plate spacing b are analyzed by considering viscous dissipation of energy. A perturbation theory is presented that predicts the wavelength of fingers, λ, as λ≊4b. Experiments with a circular Hele Shaw cell are shown to support this result. In a porous medium, the analogous fingers are demonstrated to be the size of a pore, which is much larger than the corresponding fingers in the analogous Hele Shaw cell. These results provide the lower limits of finger wavelength for the theories of Saffman and Taylor, and Chuoke, van Meurs, and van der Poel.

Direct laboratory observation of patchy saturation and its effects on ultrasonic velocities

Maximizing the recovery of known hydrocarbon reserves is one of the biggest challenges facing the petroleum industry today. Optimal production strategies require accurate monitoring of production-induced changes of reservoir saturation and pressure over the life of the field. Time-lapse seismic technology is increasingly used to map these changes in space and time. However, until now, interpretation of time-lapse seismic data has been mostly qualitative. In order to allow accurate estimation of the saturation, it is necessary to know the quantitative relationship between fluid saturation and seismic characteristics (elastic moduli, velocity dispersion, and attenuation). The problem of calculating acoustic properties of rocks saturated with a mixture of two fluids has attracted considerable interest (Gist, 1994; Mavko and Nolen-Hoeksema, 1994; Knight et al., 1998. For a comprehensive review of theoretical and experimental studies of the patchy saturation problem see Toms et al., 2006).

Statistical characterization of gas-patch distributions in partially saturated rocks

Reservoirrocksareoftensaturatedbytwoormorefluidphases forming complex patterns on all length scales. The objective of thisworkistoquantifythegeometryoffluidphasedistributionin partially saturated porous rocks using statistical methods and to modeltheassociatedacousticsignatures.BasedonX-raytomographic images at submillimeter resolution obtained during a gasinjection experiment, the spatial distribution of the gas phase in initially water-saturated limestone samples are constructed. Mapsofthecontinuousvariationofthepercentageofgassaturationarecomputedandassociatedbinarymapsobtainedthrougha global thresholding technique. The autocorrelation function is derived via the two-point probability function computed from thebinarygas-distributionmapsusingMonteCarlosimulations. The autocorrelation function can be approximated well by a single Debye correlation function or a superposition of two such functions. The characteristic length scales and show sensitivity andhencesignificancewithrespecttothepercentageofgassaturation. An almost linear decrease of the Debye correlation length occurs with increasing gas saturation. It is concluded that correlation function and correlation length provide useful statistical information to quantifyfluid-saturation patterns and changes in these patterns at the mesoscale. These spatial statistical measuresarelinkedtoamodelthatpredictscompressionalwave attenuationanddispersionfromlocal,wave-inducedfluidflowin randomly heterogeneous poroelastic solids. In particular, for a limestone sample, withflow permeability of 5 darcies and an average gas saturation of 5%, significant P-wave attenuation is predictedatultrasonicfrequencies.

Outcrop Analog for Sandy Braided Stream Reservoirs: Permeability Patterns in the Triassic Hawkesbury Sandstone, Sydney Basin, Australia

Permeability and porosity measurements on 1228 core plugs taken from the Triassic Hawkesbury Sandstone in the Sydney basin, Australia, were analyzed by both sedimentological and geostatistical approaches to assess horizontal and vertical permeability and porosity variations in deposits of braided river systems. The samples are variably cemented with porosities ranging from 5 to 20%, and permeabilities range from 0.1 to 1200 md. The permeability of the Hawkesbury Sandstone does not show any obvious relationship to its porosity. The permeability variations are closely related to sedimentary facies type, while the porosity distribution primarily reflects postdepositional diagenesis of the sandstone. Statistical analysis of all plug data shows a strong azimuth-directional permeability in the horizontal plane. The horizontal semivariogram correlation length ranges for two adjacent orthogonal outcrops are 4.5 and 2.5 m, respectively. The permeability correlation length ranges in the vertical direction for the two outcrops are similar, ranging from 1.3 to 1.6 m. Permeability is much more variable in the vertical direction than in the horizontal direction. The high degree of spatial variability observed in the permeability data is not consistent with fractal models based on the Gaussian-normal probability distribution. Subdivision of the sandstone into genetically related sedimentary facies significantly improves the predictability of the permeability distribution. Alternatively, the high degree of the permeability heterogeneity can be described using a new model based on the Levy-stable family of probability distributions.