| Summary: | Thesis (MEng)--Stellenbosch University, 2014. === ENGLISH ABSTRACT: Current numerical methods in the eld of hydraulic fracturing are based mainly on
continuum methods, such as the Finite Element Method (FEM) and the Boundary Element
Method (BEM). These methods are governed by Linear Elastic Fracture Mechanics
(LEFM) criteria, which su er from the inherent
aw of a non-physical stress representation
at the fracture tip. In response to this, a non-local method is proposed, namely
the peridynamic theory, to model sleeved hydraulic fracture. A 2D implicit quasi-static
ordinary state based peridynamic formulation is implemented on various benchmark
problems, to verify the ability to capture constitutive behaviour in a linear elastic solid,
as well as, the quanti cation of adverse e ects on the accuracy of the displacement solution,
due to the nature of the non-local theory. Benchmark tests consist of a plate in
tension, where convergence to the classical displacement solution, non-uniform re nement
and varying cell sizes are tested, as well as, a thick walled cylinder with internal
pressure, where three di erent loading techniques are tested. The most accurate loading
technique is applied to the sleeved fracture model, in order to simulate fracture initiation
and propagation. This model is then veri ed and validated by using the Rummel &
Winter hydraulic fracturing model and experimental results, respectively. Displacement
error minimisation methods are implemented and as a result, the displacement solutions
for a plate in tension converges to the analytical solution, while the thick walled cylinder
solutions su er from inaccuracies due to an applied load on an irregularly discretized
region. The fracture initiation test captures the fracture tip behaviour of the Rummel
& Winter model and the fracture propagation test show good correlation with experimental
results. This research shows that the peridynamic approach to sleeved hydraulic
fracture can yield a realistic representation of fracture initiation and propagation, however,
further research is needed in the area of a pressure load application on a solid using
the peridynamic approach. === AFRIKAANSE OPSOMMING: Huidige numeriese metodes in die veld van hidrouliese breking is hoofsaaklik gebaseer
op kontinuum metodes, soos die Eindige Element Metode (EEM) en die Rand Element
Metode (REM). Hierdie metodes word beheer deur Linie^ere Elastiese Breukmeganika
(LEB) kriteria, wat ly aan die inherente gebrek van 'n nie- siese voorstelling van die
spanning by die fraktuur punt. Om hierdie probleme aan te spreek, word 'n nie-lokale
metode voorgestel, naamlik die peridinamiese teorie, om gehulsde hidrouliese breking
te modelleer. 'n 2D implisiete kwasi-statiese ordin^ere toestand gebaseerde peridinamika
formulering word ge mplimenteer op verskeie norm probleme, om te veri eer of dit oor
die vermo e beskik om die konstitutiewe gedrag van 'n linie^ere elastiese soliede materiaal
te modeleer, asook die kwanti sering van nadelige e ekte op die verplasings oplossing as
gevolg van die natuur van die nie-lokale teorie. Normtoetse bestaan uit 'n plaat in trek
spanning, waar konvergensie na die klassieke verplasings oplossing, nie-uniforme verfyning
en vari^eerende sel groottes getoets word, asook 'n dikwandige silinder onder interne
druk, waar drie verskillende belasting aanwendingstegnieke getoets word. Die mees akkurate
belasting aanwendingstegniek word dan gebruik in die gehulsde hidrouliese breking
model, om fraktuur aanvangs en uitbreiding na te boots. Die model word dan geveri-
eer deur die Rummel & Winter hidrouliese breking model en eksperimentele resultate,
onderskeidelik. Fout minimering metodes word toegepas en as 'n resultaat, konvergeer
die verplasing oplossing vir die plaat na die analitiese oplossing, terwyl die oplossing
van die dikwandige silinder onakuraathede toon as gevolg van 'n toegepaste belasting
op 'n onre elmatig gediskretiseerde gebied. Die modellering van die fraktuur inisi ering
by die fraktuur punt, stem goed ooreen met die Rummel en Winter voorspelling en die
fraktuur uitbreiding stem goed ooreen met eksperimentele resultate. Hierdie navorsing
toon dat die peridinamiese benadering tot gehulsde hidrouliese breking wel die fraktuur
inisi ering en uitbreiding realisties kan modelleer, maar nog navorsing word wel benodig
in die area waar 'n druk belasting op 'n peridinamiese soliede model toegepas word.
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