Anna Suzuki

Analysis of Water Injection in Fractured Reservoirs Using a Fractional-Derivative-Based Mass and Heat Transfer Model

This research proposes a numerical scheme for evaluating the effect of cold-water injection into a geothermal reservoir. A fractional heat transfer equation (fHTE) is derived based on the fractional advection–dispersion equation (fADE) that describes non-Fickian dispersion in a fractured reservoir. Numerical simulations are conducted to examine the applicability of the fADE and the fHTE in interpreting tracer and thermal responses in a fault-related subsidiary structure associated with fractal geometry. A double-peak is exhibited when the surrounding rocks have a constant permeability. On the other hand, the peak in the tracer response gradually decreases when the permeability varies with distance from the fault zone according to a power law, which can be described by the fADE. The temperature decline is more gradual when the permeability of surrounding rocks varies spatially than when they have a constant permeability. The fHTE demonstrates good agreement with the temperature profiles for the different permeabilities of surrounding rocks. The retardation parameters in the fADE and the fHTE increase with the permeability of the surrounding rocks. The orders of the temporal fractional derivatives in the fADE and the fHTE vary with the permeability patterns.

Fracture network created by 3‐D printer and its validation using CT images

Understanding flow mechanisms in fractured media is essential for geoscientific research and geological development industries. This study used 3-D printed fracture networks in order to control the properties of fracture distributions inside the sample. The accuracy and appropriateness of creating samples by the 3-D printer was investigated by using a X-ray CT scanner. The CT scan images suggest that the 3-D printer is able to reproduce complex three-dimensional spatial distributions of fracture networks. Use of hexane after printing was found to be an effective way to remove wax for the posttreatment. Local permeability was obtained by the cubic law and used to calculate the global mean. The experimental value of the permeability was between the arithmetic and geometric means of the numerical results, which is consistent with conventional studies. This methodology based on 3-D printed fracture networks can help validate existing flow modeling and numerical methods.

Contributions of 3D Printed Fracture Networks to Development of Flow and Transport Models

Conventional experiments using natural rock samples have trouble in observing rock structures and controlling fracture properties. Taking advantage of 3D printing technologies, a complex fracture network was made by using a 3D printer. This approach allowed us to control the properties of the fracture networks and to prepare identical geometries for both simulation and experiment. A tracer response curve from the flow experiment was obtained and compared with numerical simulations. The result of the computational fluid dynamics (CFD) simulation based on the Navier–Stokes equations was in good agreement with experimental result, which suggested that the results of experiment and the CFD simulation are reliable. On the other hand, comparison with an equivalent permeability model based on the cubic law showed a discrepancy from the experimental result. This validation approach enabled discussion of the limitation of the flow model. Because 3D printed fracture networks could reduce uncertainty between numerical simulation and laboratory experiment, they will be useful for understanding more detailed and more complicated phenomena in fracture networks.

Experimental tests of truncated diffusion in fault damage zones

Fault zones affect the flow paths of fluids in groundwater aquifers and geological reservoirs. Fault-related fracture damage decreases to background levels with increasing distance from the fault core according to a power law. This study investigated mass transport in such a fault-related structure using nonlocal models. A column flow experiment is conducted to create a permeability distribution that varies with distance from a main conduit. The experimental tracer response curve is preasymptotic and implies subdiffusive transport, which is slower than the normal Fickian diffusion. If the surrounding area is a finite domain, an upper truncated behavior in tracer response (i.e., exponential decline at late times) is observed. The tempered anomalous diffusion (TAD) model captures the transition from subdiffusive to Fickian transport, which is characterized by a smooth transition from power-law to an exponential decline in the late-time breakthrough curves. This article is protected by copyright. All rights reserved.

Mathematical Modeling of Rock Pore Geometry and Mineralization: Applications of Persistent Homology and Random Walk

Mathematical methods used to model heterogeneous pore geometry of natural rocks and their temporal evolution (mineralization processes) are explored. Recent development of X-ray microcomputed tomography enables high-resolution (micrometers) pore geometry of rock to be obtained. Nevertheless, exploring the complex spatial distribution of pore bodies, and relating this information to hydraulic and elastic properties, remains a challenge. In this study, persistent homology is first applied to describe heterogeneous rock pores, which captures the appearance and disappearance of topological features. The persistence diagram derived from this analysis shows the characteristic features of rock pore. Next, random walk is used to model rock mineralization processes. The results show that rock pore evolution is successfully modeled using random walk by defining the probability of mineral precipitation and dispersion degree in each grid cell of a modeled rock body. The mineralization parameter can be flexibly changed and a short computation time used when using random walk; this approach may thus be practical when simulating rock evolution processes such as long-term chemical reactions in a reservoir.