Modelling and simulation of reactive transport phenomena

Mathematical modelling and numerical simulation of chemical transport phenomena are very challenging due to large numbers of species and reactions involved. Reactive transport models for such systems have high degrees of freedom, and therefore, are computationally expensive to solve. In this discussion, we present and numerically analyse stoichiometric decoupling method for reducing the high degrees of freedom and hence, cost of simulation. This method is a model reduction procedure that is based on some key properties of chemical systems. A multi-scale model of a passive treatment method for acidic mine effluents is used to test the efficacy of the reduction procedure. Moreover, reduced models are characteristically non-linear and stiff, thus, we used numerical techniques to study the reduction error in order to establish compatibility/efficiency of the reduction procedure.AEA acknowledges support from the Pilot Bursary of the University of Pretoria, the African Institute of Mathematical Sciences and University of Stellenbosch. This work is also supported in part by the National Research Foundation of South Africa (Grant Number: 93099 and 93476).http://www.elsevier.com/locate/jocs2019-09-01hj2018Mathematics and Applied Mathematic

A stoichiometric method for reducing simulation cost of chemical kinetic models

Mathematical models for chemically reacting systems have high degrees of freedom (very large) and are computationally expensive to analyse. In this discussion, we present and analyse a model reduction method that is based on stoichiometry and mass balances. This method can significantly reduce the high degrees of freedom of such systems. Numerical simulations are undertaken to validate and establish efficiency of the method. A practical example of acid mine drainage is used as a test case to demonstrate the efficacy of the procedure. Analytical results show that the stoichiometrically-reduced model is consistent with the original large model, and numerical simulations demonstrate that the method can accelerate convergence of the numerical schemes in some cases.AEA acknowledges support from the Pilot Bursary of the University of Pretoria, the African Institute of Mathematical Sciences and University of Stellenbosch. MKB is grateful to the African Institute for Mathematical Sciences (AIMS) for hosting him while finalising this work. This work is also supported in part by the National Research Foundation of South Africa (Grant number: 93099 and 93476).http://www.elsevier.com/locate/com/pchemeng2019-04-06hj2018Mathematics and Applied Mathematic

Numerical simulation of chemical kinetics transport and flow processes

In this thesis, numerical solution procedures are developed for simulating chemical phenomena. Mathematical models for phenomena involving flow, transport and reaction of chemical species are computationally challenging to simulate due to stiffness, high degrees of freedom and spatial dependence. Such challenges are resolved (in this thesis) by combining model decoupling techniques with compatible efficient numerical schemes. Chemical phenomena is decomposed into well-mixed chemical systems, poorly-mixed systems (or spatial dependent kinetics) and flow with reactive transport systems. Mathematical models for the systems are Ordinary Differential Equations (ODEs), parabolic Partial Differential Equations (PDEs) and hyperbolic PDEs, respectively. In the ODE model, stiffness is resolved by positivity-preserving implicit schemes while the large degrees of freedom is reduced by stoichiometric and continuous-time iteration methods. In the parabolic model, model decoupling techniques are employed to reduce the degrees of freedom while Implicit-Explicit numerical schemes are presented for resolving stiffness. Further, numerical schemes that have dispersion-dissipation-preserving properties have also been discussed. In the hyperbolic model, model decoupling techniques have been presented for reducing the degrees of freedom while shock-capturing, well-balanced numerical schemes have been presented for resolving nonlinear hyperbolic effects. The results from experiments show that the proposed numerical solution procedures can efficiently resolve the challenges in simulating chemical phenomena.Thesis (PhD)--University of Pretoria, 2020.Mathematics and Applied MathematicsPhDUnrestricte

Flow and reactive transport processes in porous media

Thesis (MSc)--Stellenbosch University, 2013.ENGLISH ABSTRACT: Flow and reactive transport of chemical species is a very common phenomenon that occurs in natural and artificial systems. However in this study, the topic is related to acid mine drainage in the South African mining environment. Due to the hazards associated with acid mine drainage, prevention or treatment of mine effluent water before discharging to receiving waters and other environments is a necessity. A new time-dependent mathematical model is developed for a passive treatment method, based on multi-scale modelling of the coupled physico-chemical processes such as diffusion, convection, reactions and filtration, that are involved in the treatment process. The time-dependent model is simulated on a two-dimensional domain using finite volume discretization to obtain chemical species distributions.AFRIKAANSE OPSOMMING: Vloei en reagerende transport van chemiese spesies is ’n baie algemene verskynsel wat in natuurlike en kunsmatige stelsels plaasvind. In hierdie studie is die onderwerp egter verwant aan suurmyndreinering in die Suid-Afrikaanse mynbou-omgewing. As gevolg van die gevare wat verband hou met suurmyndreinering, is die voorkoming of die behandeling van die afval-mynwater voor dit in opvangswaters en ander omgewings beland ’n noodsaaklikheid. ’n Nuwe tydafhanklike wiskundige model vir ’n passiewe behandelingsmetode is ontwikkel. Dit is gebaseer op die multi-skaal modulering van gekoppelde fisies-chemiese prosesse soos diffusie, konveksie, reaksies en filtrasie, wat by die behandelingsproses betrokke is. Die tydafhanklike model word gesimuleer op ’n twee-dimensionele domein met behulp van eindige volume diskretisasie om die verspreiding van chemiese spesies te bepaal