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A higher-order finite element reactive transport model for unstructured and fractured grids.

ABSTRACT: This work presents a new reactive transport framework that combines a powerful geochemistry engine with advanced numerical methods for flow and transport in subsurface fractured porous media. Specifically, the PhreeqcRM interface (developed by the USGS) is used to take advantage of a large library of equilibrium and kinetic aqueous and fluid-rock reactions, which has been validated by numerous experiments and benchmark studies. Fluid flow is modeled by the Mixed Hybrid Finite Element (FE) method, which provides smooth velocity fields even in highly heterogenous formations with discrete fractures. A multilinear Discontinuous Galerkin FE method is used to solve the multicomponent transport problem. This method is locally mass conserving and its second order convergence significantly reduces numerical dispersion. In terms of thermodynamics, the aqueous phase is considered as a compressible fluid and its properties are derived from a Cubic Plus Association (CPA) equation of state. The new simulator is validated against several benchmark problems (involving, e.g., Fickian and Nernst-Planck diffusion, isotope fractionation, advection-dispersion transport, and rock-fluid reactions) before demonstrating the expanded capabilities offered by the underlying FE foundation, such as high computational efficiency, parallelizability, low numerical dispersion, unstructured 3D gridding, and discrete fraction modeling.

SUBMITTER: Moortgat J

PROVIDER: S-EPMC7511411 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature

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A higher-order finite element reactive transport model for unstructured and fractured grids.

Moortgat Joachim J Li Mengnan M Amooie Mohammad Amin MA Zhu Di D

Scientific reports 20200923 1

This work presents a new reactive transport framework that combines a powerful geochemistry engine with advanced numerical methods for flow and transport in subsurface fractured porous media. Specifically, the PhreeqcRM interface (developed by the USGS) is used to take advantage of a large library of equilibrium and kinetic aqueous and fluid-rock reactions, which has been validated by numerous experiments and benchmark studies. Fluid flow is modeled by the Mixed Hybrid Finite Element (FE) method ...[more]

PMID: 32968113

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Project description:BACKGROUND: Biological mass transport processes determine the behavior and function of cells, regulate interactions between synthetic agents and recipient targets, and are key elements in the design and use of biosensors. Accurately predicting the outcomes of such processes is crucial to both enhancing our understanding of how these systems function, enabling the design of effective strategies to control their function, and verifying that engineered solutions perform according to plan. METHODS: A Galerkin-based finite element model was developed and implemented to solve a system of two coupled partial differential equations governing biomolecule transport and reaction in live cells. The simulator was coupled, in the framework of an inverse modeling strategy, with an optimization algorithm and an experimental time series, obtained by the Fluorescence Recovery after Photobleaching (FRAP) technique, to estimate biomolecule mass transport and reaction rate parameters. In the inverse algorithm, an adaptive method was implemented to calculate sensitivity matrix. A multi-criteria termination rule was developed to stop the inverse code at the solution. The applicability of the model was illustrated by simulating the mobility and binding of GFP-tagged glucocorticoid receptor in the nucleoplasm of mouse adenocarcinoma. RESULTS: The numerical simulator shows excellent agreement with the analytic solutions and experimental FRAP data. Detailed residual analysis indicates that residuals have zero mean and constant variance and are normally distributed and uncorrelated. Therefore, the necessary and sufficient criteria for least square parameter optimization, which was used in this study, were met. CONCLUSION: The developed strategy is an efficient approach to extract as much physiochemical information from the FRAP protocol as possible. Well-posedness analysis of the inverse problem, however, indicates that the FRAP protocol provides insufficient information for unique simultaneous estimation of diffusion coefficient and binding rate parameters. Care should be exercised in drawing inferences, from FRAP data, regarding concentrations of free and bound proteins, average binding and diffusion times, and protein mobility unless they are confirmed by long-range Markov Chain-Monte Carlo (MCMC) methods and experimental observations.

Project description:Isolating the role(s) of microstructural pathological features in affecting diastolic filling is important in developing targeted treatments for heart diseases. We developed a microstructure-based constitutive model of the myocardium and implemented it in an efficient open-source finite element modeling framework to simulate passive inflation of the left ventricle (LV) in a representative 3D geometry based on experimentally measured muscle fiber architecture. The constitutive model was calibrated using previous tissue-level biaxial mechanical test data derived from the canine heart and validated with independent sets of measurements made at both the isolated constituent and organ level. Using the validated model, we investigated the load taken up by each tissue constituent and their effects on LV passive inflation. The model predicts that the LV compliance is sensitive to the collagen ultrastructure, specifically, the collagen fiber azimuthal angle with respect to the local muscle fiber direction and its waviness. The model also predicts that most of the load in the sub-epicardial and sub-endocardial regions is taken up, respectively, by the muscle fibers and collagen fiber network. This result suggests that normalizing LV passive stiffness by altering the collagen fiber network and myocyte stiffness is most effective when applied to the sub-endocardial and sub-epicardial regions, respectively. This finding may have implication for the development of new pharmaceutical treatments targeting individual cardiac tissue constituents to normalize LV filling function in heart diseases. STATEMENT OF SIGNIFICANCE: Current constitutive models describing the tissue mechanical behavior of the myocardium are largely phenomenological. While able to represent the bulk tissue mechanical behavior, these models cannot distinguish the contribution of the tissue constituents and their ultrastructure to heart function. Although microstructure-based constitutive models can be used to isolate the role of tissue ultrastructure, they have not been implemented in a computational framework that can accommodate realistic 3D organ geometry. The present study addresses these issues by developing and validating a microstructure-based computational modeling framework, which is used to investigate the role of tissue constituents and their ultrastructure in affecting heart function.

Dataset Information

A higher-order finite element reactive transport model for unstructured and fractured grids.

Publications

A higher-order finite element reactive transport model for unstructured and fractured grids.

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