Engineering topics

Ladd, Anthony J. C.

Publications and source records attributed to Ladd, Anthony J. C..

5 records

DOE OSTI2021

Dissolution of periodic arrays of grains: Upscaling of pore-scale simulations with fast reactions

Upscaling methods are frequently used to derive transport equations at the macroscopic scale from more fundamental equations formulated at the pore scale. These methods typically give a suitable structure for the macroscopic equations and can also provide explicit expressions for the constitutive parameters, such as permeability and dispersion coefficients. Introducing chemical reactions complicates upscaling in at least two important ways. First, the interplay between chemical reactions and transport processes introduces a new length scale, which can be much smaller than the convective or dispersive length scales. A small reactive length scale breaks one of the key assumptions in upscaling; that there is a significant separation in length between the pore-scale and macro-scale processes. The second complication is that if reactions take place at mineral surfaces (dissolution or precipitation) then the pore space itself is evolving in time. In this paper we suggest ways in which these difficulties can be approached, based on analysis of pore-scale simulation data. First, we noticed that the concentration field in successive unit cells has an almost identical spatial variation, with a single scaling factor for each unit cell that is proportional to the incoming reactant flux. Using pore-scale simulations to determine the mass transfer coefficient in a few unit cells, we can calculate the concentration field in the whole domain, even when dissolution is entirely transport limited. Second, we have noticed a time-dependent mapping of the grain shapes from different unit cells. From these observations, we can deduce constitutive relations where the only time-varying parameter is the porosity. Here, we show that a model based on these ideas can quantitatively account for the pore-scale simulation data.

58 GEOSCIENCES↗

DOE OSTI2020

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

This manuscript presents a benchmark problem for the simulation of single-phase flow, reactive transport, and solid geometry evolution at the pore scale. The problem is organized in three parts that focus on specific aspects: flow and reactive transport (part I), dissolution-driven geometry evolution in two dimensions (part II), and an experimental validation of three-dimensional dissolution-driven geometry evolution (part III). Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex, and dissolFoam. These codes cover a good portion of the wide range of approaches typically employed for solving pore-scale problems in the literature, including discretization methods, characterization of the fluid-solid interfaces, and methods to move these interfaces as a result of fluid-solid reactions. A short review of these approaches is given in relation to selected published studies. Results from the simulations performed by the five codes show remarkable agreement both quantitatively--based on upscaled parameters such as surface area, solid volume, and effective reaction rate--and qualitatively--based on comparisons of shape evolution. This outcome is especially notable given the disparity of approaches used by the codes. Therefore, these results establish a strong benchmark for the validation and testing of pore-scale codes developed for the simulation of flow and reactive transport with evolving geometries. They also underscore the significant advances seen in the last decade in tools and approaches for simulating this type of problem.

58 GEOSCIENCES↗

DOE OSTI2018

The Development of Wormholes in Laboratory-Scale Fractures: Perspectives From Three-Dimensional Simulations

Here, we investigate the development of wormholes in laboratory–scale fractures using three–dimensional numerical simulations. Well–controlled initial conditions, involving a small perturbation near the inlet of an otherwise flat fracture aperture field, were used to make a systematic study of the effects of flow rate and reaction rate on the aperture evolution. We find at least two characteristic wormhole shapes, which can be grouped within a phase diagram in the space of Péclet and Damköhler numbers. We investigate how this phase diagram depends on fracture geometry, specifically the length ( L ) and width ( W ) in comparison to the initial aperture ( h 0 ). This information is used to determine an effective Damköhler number that leads to a Péclet and length–independent phase boundary between wormholes and uniform dissolution. We relate these observations to experimental studies of wormhole formation in dissolving fractures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Instabilities and finger formation in replacement fronts driven by an oversaturated solution: FINGER FORMATION IN MINERAL REPLACEMENT

We consider a simple model of infiltration-driven mineral replacement, in which the chemical coupling between precipitation and dissolution leads to the appearance of a reaction front advancing into the system. Such fronts are usually accompanied by a local increase of porosity. We analyze the linear stability of the replacement front to establish whether such a localized porosity increase can lead to global instability and pattern formation in these systems. We find that for a wide range of control parameters such fronts are unstable. However, both short- and long-wavelength perturbations are stabilized, whereas in a purely dissolutional instability only short wavelengths are stable. We analyze the morphologies of the dissolution patterns emerging in the later stages of the evolution of the system, when the dynamics are beyond the linear regime. Implications of these results for the natural systems are discussed, particularly in the context of karst formation in terra rossa-covered carbonate bedrock.

58 GEOSCIENCES↗

DOE OSTI2017

Use and misuse of large-density asymptotics in the reaction-infiltration instability

Analyzing the dissolution of rocks and other porous materials is simplified by the large dis-parity between mineral and reactant concentrations. In essence, the porosity remains frozen on the time scale of the reactant transport, which can then be treated as a quasi-stationary process. This conceptual idea can be derived mathematically using asymptotic methods, which show that the length scales in the system are, to a first approximation, independent of the ratio of reactant and mineral concentrations. Nevertheless, in a growing number of papers on dissolutional instabilities, the reactant-mineral concentration ratio has been incorrectly linked to the thickness of the dissolution front. In this paper we critically review the application of asymptotic methods to the reaction-infiltration instability. In particular, we discuss the limited validity of the thin-front or ‘‘Stefan’’ limit, where the interface between dissolved and undissolved mineral is sharp.

58 GEOSCIENCES↗