Hydrocarbon production, gas recovery from shale, CO2 storage and water management have a common scientific underpinning: multiphase flow in porous media. This book provides a fundamental description of multiphase flow through porous rock, with emphasis on the understanding of displacement processes at the pore, or micron, scale. Fundamental equations and principal concepts using energy, momentum, and mass balance are developed, and the latest developments in high-resolution three-dimensional imaging and associated modelling are explored. The treatment is pedagogical, developing sound physical principles to predict flow and recovery through complex rock structures, while providing a review of the recent literature. This systematic approach makes it an excellent reference for those who are new to the field. Inspired by recent research, and based on courses taught to thousands of students and professionals from around the world, it provides the scientific background necessary for a quantitative assessment of multiphase subsurface flow processes, and is ideal for hydrology and environmental engineering students, as well as professionals in the hydrocarbon, water and carbon storage industries.

Multiphase Flow in Permeable Media: A Pore-Scale Perspective

Imaging and image-based fluid transport modeling at the pore scale in geological materials : a practical introduction to the current state-of-the-art

The theory of the dynamic bulk modulus, K(ω), of a porous rock, whose saturation occurs in patches of 100% saturation each of two different fluids, is developed within the context of the quasi-static Biot theory. The theory describes the crossover from the Biot–Gassmann–Woods result at low frequencies to the Biot–Gassmann–Hill result at high. Exact results for the approach to the low and the high frequency limits are derived. A simple closed-form analytic model based on these exact results, as well as on the properties of K(ω) extended to the complex ω-plane, is presented. Comparison against the exact solution in simple geometries for the case of a gas and water saturated rock demonstrates that the analytic theory is extremely accurate over the entire frequency range. Aside from the usual parameters of the Biot theory, the model has two geometrical parameters, one of which is the specific surface area, S/V, of the patches. In the special case that one of the fluids is a gas, the second parameter is a different, but also simple, measure of the patch size of the stiff fluid. The theory, in conjunction with relevant experiments, would allow one to deduce information about the sizes and shapes of the patches or, conversely, to make an accurate sonic-to-seismic conversion if the size and saturation values are approximately known.

Theory of Frequency Dependent Acoustics in Patchy-Saturated Porous Media

Humanity already possesses the fundamental scientific, technical, and industrial know-how to solve the carbon and climate problem for the next half-century. A portfolio of technologies now exists to meet the world's energy needs over the next 50 years and limit atmospheric CO2 to a trajectory that avoids a doubling of the preindustrial concentration. Every element in this portfolio has passed beyond the laboratory bench and demonstration project; many are already implemented somewhere at full industrial scale. Although no element is a credible candidate for doing the entire job (or even half the job) by itself, the portfolio as a whole is large enough that not every element has to be used.

“Stabilization wedges: Solving the climate problem for the next 50 years with current technologies” from science magazine (2004)

Obtaining structural information from tomographic images of porous materials is a critical component of porous media research. Extracting pore networks is particularly valuable since it enables pore network modeling simulations which can be useful for a host of tasks from predicting transport properties to simulating performance of entire devices. This work reports an efficient algorithm for extracting networks using only standard image analysis techniques. The algorithm was applied to several standard porous materials ranging from sandstone to fibrous mats, and in all cases agreed very well with established or known values for pore and throat sizes, capillary pressure curves, and permeability. In the case of sandstone, the present algorithm was compared to the network obtained using the current state-of-the-art algorithm, and very good agreement was achieved. Most importantly, the network extracted from an image of fibrous media correctly predicted the anisotropic permeability tensor, demonstrating the critical ability to detect key structural features. The highly efficient algorithm allows extraction on fairly large images of 500^{3} voxels in just over 200 s. The ability for one algorithm to match materials as varied as sandstone with 20% porosity and fibrous media with 75% porosity is a significant advancement. The source code for this algorithm is provided.

/pdf/versatile-and-efficient-pore-network-extraction-method-using-1sg2o4ihmo.pdf

Versatile and efficient pore network extraction method using marker-based watershed segmentation.

Digital rock physics benchmarks-Part I: Imaging and segmentation

Digital rock physics benchmarks-part II: Computing effective properties

Elastic upscaling of thinly layered rocks typically is performed using the established Backus averaging technique. Its poroelastic extension applies to thinly layered fluid-saturated porous rocks and enables the use of anisotropic effective medium models that are valid in the low- and high-frequency limits for relaxed and unrelaxed pore-fluid pressures, respectively. At intermediate frequencies, wave-induced interlayer flow causes attenuation and dispersion beyond that described by Biot’s global flow and microscopic squirt flow. Several models quantify frequency-dependent, normal-incidence P-wave propagation in layered poroelastic media but yield no prediction for arbitrary angles of incidence, or for S-wave-induced interlayer flow. It is shown that generalized models for P-SV-wave attenuation and dispersion as a result of interlayer flow can be constructed by unifying the anisotropic Backus limits with existing P-wave frequency-dependent interlayer flow models. The construction principle is exact and is ...

Anisotropic P-SV-wave dispersion and attenuation due to inter-layer flow in thinly layered porous rocks

This paper presents the first published 3D geomechanical modelling study of the CO2CRC Otway Project, located in the state of Victoria, Australia. The results of this work contribute to one of the main objectives of the CO2CRC, which is to demonstrate the feasibility of CO2 storage in a depleted gas reservoir. With this aim in mind, a one-way coupled flow and geomechanics model is presented, with the capability of predicting changes to the in situ stress field caused by changes in reservoir pressure owing to CO2 production and injection. A parametric study investigating the pore pressures required to reactivate key, reservoir-bounding faults has been conducted, and the results from the numerical simulation and analytical analysis are compared. The numerical simulation indicates that the critical pore fluid pressure to cause fault reactivation is 1.15 times the original pressure as opposed to 1.5 times for the comparable analytical model. Possible reasons for the differences between the numerical and analy...

Geomechanical modelling to assess fault integrity at the CO2CRC Otway Project, Australia

Summary Geothermal rapid screening is a workflow designed to quantify geothermal resources for electrical power and/or heat generation with its associated uncertainties. The tool enables a quick 1D estimate of the temperature vs. depth dependence considering the lithologies from existing wells at any depth. Machine learning methodologies are used to predict temperature at any other location in the same basin at any depth. The impact of subsurface uncertainty of each model parameter (e.g., temperature, heat flow, porosity, permeability, thermal conductivity) is estimated. The resulting risks associated with geothermal well candidates from converting existing water, oil, or gas wells are calculated for further investigations. 

Fabian Krzikalla

Papers

Digital rock physics benchmarks-Part I: Imaging and segmentation

Digital rock physics benchmarks-part II: Computing effective properties

Anisotropic P-SV-wave dispersion and attenuation due to inter-layer flow in thinly layered porous rocks

Geomechanical modelling to assess fault integrity at the CO2CRC Otway Project, Australia

Geothermal Rapid Screening