Modelling breakthrough curves and investigating the impact of models and numerical properties on parameter estimation

Silavwe, Davy Danny (2019-04)

Thesis (DEng)--Stellenbosch University, 2019.

Thesis

ENGLISH ABSTRACT: The research investigated and applied several Eulerian numerical methods of the advection-dispersion model (AD-Model) for the analysis of concentration-time curves, also known as breakthrough curves (BTCs), to develop empirical models for predicting stream longitudinal dispersion coefficients. Typically, measured BTCs are analysed to estimate solute transport parameters which are then used to develop empirical equations by correlating optimised longitudinal dispersion coefficients with the bulk flow and channel properties. The investigation attempted to determine the impact of numerical methods and nondimensional numerical properties on optimised parameters and subsequently on constructed empirical models for predicting longitudinal dispersion coefficients. Four concerns related to the construction of empirical models for estimating stream longitudinal dispersion coefficient based on estimates by numerical methods were addressed. (a) Dependence of estimated parameter values on the method used. (b) Influence of numerical properties on values of estimated parameters (c) Identification of model structure, and (d) Characterising model performance. To address the concern (a), six optional numerical methods were assessed using a set of synthetic BTCs simulated for a hypothetical stream reach. This was followed by a selection of three numerical methods for the analysis of observed BTCs to determine parameter values for the development of empirical models. The selected numerical methods are well-known methods, namely, Backward-time/centred space (BTCS), Crank-Nicolson, Implicit QUICK, QUICKEST, MacCormack and third-order upstream-differencing methods. Shortlisted methods were Crank-Nicolson, MacCormack and QUICKEST methods. To address issue (b) parameter values for the development of empirical models were obtained over a range of numerical properties. To address issue (c) dimensional analysis and least-squares regression was used. To address issue (d) a combination of several model performance measures focusing on several features were used for a broad evaluation of models. The study shows that optimal parameter values of the AD-Model determined by Eulerian numerical methods vary with numerical methods and model resolution, such that there is a possibility of overestimating or underestimating parameter values, especially the dispersion coefficient. Consequently, in this research, the Crank-Nicolson and the MacCormack methods were observed to overpredict the dispersion coefficient with an increase in Peclet number, while the the QUICKEST method was observed to underpredict dispersion coefficients with increase in Peclet number. Consequently, structures of developed empirical models and predictions varied with solution method used and nondimensional numerical parameters under which optimised parameters were determined. Based on performance analysis measures, adequate and comparable empirical models were developed for a range of 0.599 – 12.818 of the Peclet number. However, the quality of concentration predictions using predicted dispersion coefficients requires the use of numerical methods and model resolutions under which empirical models were developed. Therefore, empirical models may be well-founded within their calibrated conditions and channel characteristics.

AFRIKAANSE OPSOMMING: Hierdie navorsing was gefokus op die ondersoek van verskeie Euleriese numeriese metodes wat tipies gebruik word in die adveksiespreidingsmodel (AD-Model). Die metodes was toegepas op die analise van konsentrasie-tydkrommes, ook bekend as deurbreekkrommes (BTCs), om empiriese modelle te ontwikkel vir die voorspelling van longitudinale verspreidingskoëffisiënte. Gemete BTC's word tipies ge-analiseer om opgeloste vervoerparameters te bereken, wat dan verder gebruik word om empiriese vergelykings te ontwikkel deur ge-optimaliseerde longitudinale verspreidingskoëffisiënte met massa vloei en kanaal eienskappe te korreleer. Daar was gepoog in hierdie ondersoek om die impak van numeriese metodes en nie-dimensionele numeriese eienskappe op ge-optimaliseerde parameters te bepaal. Daar was ook voort gegaan om die verdere impak hiervan op empiriese modelle vir die voorspelling van longitudinale verspreidingskoëffisiënte te bepaal. Vier kwessies wat verband hou met die konstruksie van empiriese modelle vir die bepaling van stroom longitudinale verspreidingskoëffisiënte, gebaseer op beramings deur numeriese metodes, was aangespreek: (a) afhanklikheid van beraamde parameterwaardes op die metode wat gebruik word, (b) invloed van numeriese eienskappe op waardes van geskatte parameters, (c) identifikasie van modelstruktuur en (d) karakterisering van modelprestasie. Om kwessie (a) aan te spreek, was ses opsionele numeriese metodes ge-assesseer met 'n stel sintetiese BTC's wat gesimuleer was vir 'n hipotetiese stroom lengte. Dit was gevolg deur ‘n verdere ondersoek van drie gekose numeriese metodes gebruik vir die analise van die waargenome BTCs om parameterwaardes vir die ontwikkeling van empiriese modelle te bepaal. Die ondersoekte numeriese metodes het algemeen bekende metodes ingesluit, naamlik: die “Backward-time/centred space (BTCS)” metode, die “Crank-Nicolson” metode, die “Implicit QUICK” metode, die “QUICKEST” metode, die “MacCormack” metode en derde-orde stroomopwaartse differensiëringsmetodes. Finaal geselekteerde metodes was die “Crank-Nicolson”, “MacCormack” en “QUICKEST” metodes. Om kwessie (b) aan te spreek, was parameterwaardes vir die ontwikkeling van empiriese modelle oor 'n verskeidenheid numeriese eienskappe verkry. Dimensionele analise en kleinste-kwadrate regressie was gebruik om kwessie (c) aan te spreek. ‘n Kombinasie van verskeie modelprestasiemaatreëls wat op verskeie funksies gefokus het was gebruik vir 'n breë evaluering van modelle onder kwessie (d). Die studie het getoon dat optimale parameterwaardes van die AD-model, wat deur Euleriese numeriese metodes bepaal was, gewissel het volgens numeriese metodes en modelresolusie. Dit beteken dat daar 'n moontlikheid is om parameterwaardes, veral die verspreidingskoëffisiënt, te oorskat of te onderskat. In hierdie ondersoek was die “Crank-Nicolson” en die “MacCormack” gebaseerde modelle waargeneem om die verspreidingskoëffisiënt te oorskat met toename in Peclet-nommer, terwyl die “QUICKEST” gebaseerde modelle waargeneem was om verspreidingskoëffisiënte te onderskat met toename in Peclet-nommer. Gevolglik het die strukture van ontwikkelde empiriese modelle en voorspellings gewissel met oplossingsmetode wat gebruik was sowel as met die nie-dimensionele numeriese parameters waarvolgens ge-optimaliseerde parameters bepaal was. Op grond van prestasie analise maatreëls, was voldoende en vergelykbare empiriese modelle ontwikkel vir 'n reeks van 0.599 - 12.818 van die Peclet-nommer. Die kwaliteit van konsentrasie voorspellings wat gedoen word deur gebruik te maak van voorspelde verspreidingskoëffisiënte, vereis egter die gebruik van numeriese metodes en modelresolusies waaronder die empiriese modelle ontwikkel is. Dus mag empiriese modelle goed gegrond wees binne hul gekalibreerde toestande en kanaal eienskappe.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/105964
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