Simulating reactive transport in time dependent multiphase flow problems

2004 ◽  
Vol 92 (9-11) ◽  
Author(s):  
Maarten Saaltink ◽  
Francisco Batlle ◽  
Carlos Ayora ◽  
Jesús Carrera
Keyword(s):  
Multiphase Flow ◽  
Reactive Transport ◽  
Pyrite Oxidation ◽  
Time Dependent ◽  
Time Varying ◽  
Mass Balances ◽  
Flow Properties ◽  
Flow And Transport ◽  
Flow Problems ◽  
Time Stepping

SummaryThis paper discusses issues on time stepping and time weighing when simulating reactive transport in time dependent multiphase flow problems. It proposes to solve the flow and transport equation with different time increments. We analyze how the time varying flow properties should be evaluated in order to obtain correct solute mass balances. The proposed algorithm is illustrated by an example that models pyrite oxidation in an unsaturated soil. The example shows that flow and transport may require completely different time steps for numerical reasons and illustrates well the utility of using different time steps.

Special Issue: Advanced numerical modeling and algorithms for multiphase flow and transport

2020 ◽  
Vol 408 ◽  
pp. 109222
Author(s):  
Yalchin Efendiev ◽  
Abbas Firoozabadi ◽  
Shuyu Sun ◽  
Mary F. Wheeler ◽  
Bo Yu
Keyword(s):  
Numerical Modeling ◽  
Multiphase Flow ◽  
Special Issue ◽  
Flow And Transport

scholarly journals Mineralogical, numerical and analytical studies of the coupled oxidation of pyrite and coal

2003 ◽  
Vol 67 (2) ◽  
pp. 381-398 ◽  
Author(s):  
K. A. Evans ◽  
C. J. Gandy ◽  
S. A. Banwart
Keyword(s):  
Reactive Transport ◽  
Transport Model ◽  
Pyrite Oxidation ◽  
Spoil Heap ◽  
Reaction Fronts ◽  
Order Of Magnitude ◽  
Magnitude Variation ◽  
Discharge Chemistry ◽  
Analytical Expressions

Mineralogical, bulk and field leachate compositions are used to identify important processes governing the evolution of discharges from a coal spoil heap in County Durham. These processes are incorporated into a numerical one-dimensional advective-kinetic reactive transport model which reproduces field results, including gas compositions, to within an order of magnitude. Variation of input parameters allows the effects of incorrect initial assumptions on elemental profiles and discharge chemistry to be assessed. Analytical expressions for widths and speeds of kinetic reaction fronts are developed and used to predict long-term development of mineralogical distribution within the heap. Results are consistent with observations from the field site. Pyrite oxidation is expected to dominate O2 consumption in spoil heaps on the decadal timescale, although C oxidation may stabilize contaminants in effluents on the centennial scale.

scholarly journals A Tutorial on Evaluating the Time-Varying Discrimination Accuracy of Survival Models Used in Dynamic Decision Making

2018 ◽  
Vol 38 (8) ◽  
pp. 904-916 ◽  
Author(s):  
Aasthaa Bansal ◽  
Patrick J. Heagerty
Keyword(s):  
Decision Making ◽  
Statistical Methods ◽  
Sensitivity And Specificity ◽  
Prognostic Model ◽  
Dynamic Decision Making ◽  
Time Dependent ◽  
Survival Models ◽  
Biliary Cirrhosis ◽  
Time Varying ◽  
Over Time

Many medical decisions involve the use of dynamic information collected on individual patients toward predicting likely transitions in their future health status. If accurate predictions are developed, then a prognostic model can identify patients at greatest risk for future adverse events and may be used clinically to define populations appropriate for targeted intervention. In practice, a prognostic model is often used to guide decisions at multiple time points over the course of disease, and classification performance (i.e., sensitivity and specificity) for distinguishing high-risk v. low-risk individuals may vary over time as an individual’s disease status and prognostic information change. In this tutorial, we detail contemporary statistical methods that can characterize the time-varying accuracy of prognostic survival models when used for dynamic decision making. Although statistical methods for evaluating prognostic models with simple binary outcomes are well established, methods appropriate for survival outcomes are less well known and require time-dependent extensions of sensitivity and specificity to fully characterize longitudinal biomarkers or models. The methods we review are particularly important in that they allow for appropriate handling of censored outcomes commonly encountered with event time data. We highlight the importance of determining whether clinical interest is in predicting cumulative (or prevalent) cases over a fixed future time interval v. predicting incident cases over a range of follow-up times and whether patient information is static or updated over time. We discuss implementation of time-dependent receiver operating characteristic approaches using relevant R statistical software packages. The statistical summaries are illustrated using a liver prognostic model to guide transplantation in primary biliary cirrhosis.

Sign in / Sign up

Export Citation Format

Share Document