Reactive transport in the underground leaching of uranium: Asymptotic analytical solution for multi-reaction model

2016 ◽  
Vol 160 ◽  
pp. 60-72 ◽  
Author(s):  
Mikhail Panfilov ◽  
Bolat Uralbekov ◽  
Mukhambetkali Burkitbayev
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.


Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2502 ◽  
Author(s):  
Phuong Thanh Vu ◽  
Chuen-Fa Ni ◽  
Wei-Ci Li ◽  
I-Hsien Lee ◽  
Chi-Ping Lin

Fractures are major flow paths for solute transport in fractured rocks. Conducting numerical simulations of reactive transport in fractured rocks is a challenging task because of complex fracture connections and the associated nonuniform flows and chemical reactions. The study presents a computational workflow that can approximately simulate flow and reactive transport in complex fractured media. The workflow involves a series of computational processes. Specifically, the workflow employs a simple particle tracking (PT) algorithm to track flow paths in complex 3D discrete fracture networks (DFNs). The PHREEQC chemical reaction model is then used to simulate the reactive transport along particle traces. The study illustrates the developed workflow with three numerical examples, including a case with a simple fracture connection and two cases with a complex fracture network system. Results show that the integration processes in the workflow successfully model the tetrachloroethylene (PCE) and trichloroethylene (TCE) degradation and transport along particle traces in complex DFNs. The statistics of concentration along particle traces enables the estimations of uncertainty induced by the fracture structures in DFNs. The types of source contaminants can lead to slight variations of particle traces and influence the long term reactive transport. The concentration uncertainty can propagate from parent to daughter compounds and accumulate along with the transport processes.


1991 ◽  
Vol 65 (5-6) ◽  
pp. 925-939 ◽  
Author(s):  
E. Cl�ment ◽  
P. Leroux-Hugon ◽  
L. M. Sander

2021 ◽  
Author(s):  
Jinyun Tang ◽  
William J. Riley ◽  
Qing Zhu

Abstract. Reliable soil biogeochemical modeling is a prerequisite for credible projections of climate change and associated ecosystem feedbacks. This recognition has called for frameworks that can support flexible and efficient development and application of new or alternative soil biogeochemical modules in earth system models (ESMs). The BeTR-v1 code (i.e., CLM4-BeTR) is one such framework designed to accelerate the development and integration of new soil biogeochemistry formulations into ESMs, and to analyze structural uncertainty in ESM simulations. With a generic reactive transport capability, BeTR-v1 can represent multi-phase (e.g., gaseous, aqueous, and solid), multi-tracer (e.g., nitrate and organic carbon), and multi-organism (e.g., plants, bacteria and fungi) dynamics. Here, we describe the new version BeTR-v2, which adopts more robust numerical algorithms and improves on structural design over BeTR-v1. BeTR-v2 better supports different mathematical formulations in a hierarchical manner by allowing the resultant model be run either for a single topsoil layer, a vertically resolved soil column, or fully coupled with the land component of the Energy Exascale Earth System Model (E3SM). We demonstrate the BeTR-v2 capability with benchmark cases and example soil BGC implementations. By taking advantage of BeTR-v2’s generic structure integrated in E3SM, we then found that calibration could not resolve biases introduced by different numerical coupling strategies of plant-soil biogeochemistry. These results highlight the importance of numerically robust implementation of soil biogeochemistry and coupling with hydrology, thermal dynamics, and plants— capabilities that the open-source BeTR-v2 provides.


2019 ◽  
Vol 12 (05) ◽  
pp. 1950059 ◽  
Author(s):  
Ved Prakash Dubey ◽  
Rajnesh Kumar ◽  
Devendra Kumar

Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists. In this paper, an effective and powerful mathematical technique, viz. fractional homotopy analysis transform method (FHATM), is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives. The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm. This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure. The Caputo-type fractional derivatives are considered in the present paper. Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically. The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order [Formula: see text] is also analyzed. In the context of stability discussion, we have used the fractional Routh–Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.


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