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Production of hollow fibers by co-electrospinning of cellulose acetateKhalf, Abdurizzagh 03 1900 (has links)
Thesis (MScEng (Process Engineering))--University of Stellenbosch, 2009. / The study concerns the use of the electrospinning technique for the formation of
cellulose acetate hollow nanofibers. These hollow fibers are used to manufacture
hollow fiber membranes. Important properties that should be inherent to these
hollow-nanofibers include excellent permeability and separation characteristics, and
long useful life. They have potential applications in filtration, reverse osmosis, and
the separation of liquids and gases.
It is apparent from the available literature on electrospinning and co-electrospinning
that the diameter and the morphology of the resulting fibers are significantly
influenced by variations in the system and process parameters, which include the
solution concentration, solvent volatility, solution viscosity, surface tension and the
conductivity of the spinning solution.
The materials used include cellulose acetate (CA) (concentration = 11~14 wt %),
(feed rate = 1~3 ml/h), acetone:dioxane (2:1) and mineral oil (feed rate = 0.5~1
ml/h) with core and shell linear velocity of 2 and 0.7 mm/min respectively. These
materials were used as received without further purification.
The co-electrospinning setup used comprised a compound spinneret, consisting of
two concentric small-diameter capillary tubes/needles, one located inside another
(core-shell/co-axial design). The internal and external diameters of the inside and
outside needles were 0.3 and 1.2 mm respectively (0.3 mm shell/core gap space).
The liquids CA (shell) and mineral oil (core) are pumped to the coaxial needle by a
syringe pump, forming a compound droplet at the tip of the needle. A high voltage
source is used to apply a potential of several kilovolts over the electrospinning
distance. One electrode is placed into the spinning solution and the other oppositely
charged (or neutral) electrode attached to a conductive collector. If the charge build
up reaches approximately 15 kV the charged compound droplet, (poorly conductive
polymer solution) deforms into a conical structure called a Taylor cone. On further
increasing, the charge at the Taylor cone to some critical value (unique to each
polymer system) the surface tension of the compound Taylor cone is broken and a core-shell jet of polymer solution ejects from the apex of the Taylor cone. This jet is
linear over a small distance, and then deviates in a course of violent whipping from
bending instabilities brought about by repulsive charges existing along the jet length.
The core-shell jet is stretched and solvent is evaporated and expelled, resulting in the
thinning and alignment of the fiber. Ultimately dry (most solvent having been
removed) submicron fibers are collected in alignment form in a simple collector
design (water bath).
The shell to core solution flow rate ratio was chosen according to the parameter
response of shell-core diameter of the resulting fibers in order to achieve an optimal
hollow structure after removal of the mineral oil core. The mineral oil of the dry
collected core-shell fibers is removed by immersion in octane. The aforementioned
response is determined by measurement of core-shell diameters using scanning
electron microscopy (SEM) and transmission electron microscopy (TEM).
The obtained results showed that the ability of the spinning solution to be
electrospun was directly dependent on its concentration and the feed rate of the
spinning solution and also parameters such as the spinning distance and type of
solvents used. The preferable polymer solution concentration is 14 wt %, shell feed
rate of 3 ml/hr, core feed rate of 0.5 ml/hr (2 and 0.7 mm/s core and shell linear
velocity respectively), applied voltage of 15 KV, spinning distance of 8 cm and
coaxial spinnerets having internal diameters of 0.3 mm and 1.2 mm core and shell
needles respectively (0.3 mm shell/core gap space) have been found to make
uniform cellulose acetate hollow fibers with an average inside and outside diameter
of approximately 495 and 1266 nm, respectively.
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Methane and carbon dioxide sorption studies on South African coals.Gertenbach, Rosalind May 03 1900 (has links)
Thesis (MScEng (Process Engineering))--University of Stellenbosch, 2009. / Sequestration of carbon dioxide, CO2, has received large interest as a viable option for
mitigating the high atmospheric concentrations of this greenhouse gas. Each year 25
gigatons of anthropogenic CO2 (7.3 GtC/yr) are released into the earth’s atmosphere with the
combustion of fossil fuels being the major contributing source. Research in the field of
sequestration technology involves evaluating various geological structures as possible
reservoirs, determining adsorption capacities of natural formations and developing methods
for carbon dioxide injection and the monitoring thereof. Identified potential CO2 reservoirs for
geological carbon sequestration (GCS) include saline formations, depleted oil and gas fields
and deep coal seams. Carbon dioxide sequestration in coal seams provides the economic
opportunity of enhanced coalbed methane (CH4) recovery (ECBM).
In South Africa, some coal seams are considered a viable option for long term CO2
sequestration projects as they are abundant and closely situated to South Africa’s largest
concentrated CO2 point sources. Many studies have been conducted to determine the
sorption capacities for methane and carbon dioxide gases on various coals from around the
world; however, similar data have not been recorded for South African coals.
The objectives of this study are to determine the adsorption capacities for methane and
carbon dioxide of three South African coals over a pressure range of 0 – 50 bar. In the study,
single-component gas adsorption experiments were conducted and the absolute adsorption
capacities are reported. Isothermal adsorption experiments were conducted using both the
volumetric and gravimetric methods with the volumetric apparatus pressure range extending
up to 50 bar and the gravimetric apparatus up to 20 bar. Carbon dioxide adsorption
capacities are much higher than the methane adsorption capacities, which are expected.
Gravimetric experiments produce greater adsorption capacities than the volumetric method.
However, the relative CO2/CH4 ratios for each coal, as well as the relative CO2/CO2 ratios
between coals, remain almost identical. The difference in adsorption capacity is attributed to
the strength of the vacuum pump used on each apparatus. The gravimetric apparatus makes
use of a much stronger vacuum pump which can thus evacuate the coal pores more
adequately than in the volumetric apparatus. The methane and carbon dioxide adsorption
capacities of the three moisture-free coals compare well with literature data. The adsorption
isotherms fit conventional adsorption models (the Langmuir and Freundlich adsorption
equations) extremely well thus indicating that monolayer adsorption takes place.
Since no internationally recognised testing standards are in place regarding adsorption
procedures on coal, it is very difficult to compare adsorption results presented in the literature. Respective researchers determine their own experimental conditions for the many
variables in coal adsorption studies. It is recommended that international testing standards
be set in place to make coal research comparable. Such efforts would aid the development
of a coal adsorption database, another recommendation, which would advance sequestration
technology exchange and eliminate duplication of research efforts.
The objectives of the project were achieved by determining the absolute adsorption
capacities for carbon dioxide and methane gas of the three South African coals within a
pressure range of 0 – 50 bar. Further work is required to investigate adsorption capacities of
South African coals under supercritical conditions (above 73 bar abs and 31.1 oC).
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Development of Pichia pastoris as a production system for HPV16 L1 virus-like particles as component to a subunit vaccineKotze, Lara 03 1900 (has links)
Human papillomavirus (HPV) is a sexually transmitted virus and known precursor to
cervical cancer, the second most lethal cancer in females across the world. Two virus-like
particle (VLP) vaccines exist that provide immunity against the main serotypes of the
disease and are produced in Saccharomyces cerevisiae (S. cerevisiae) and baculovirus
infected insect cells. Pichia pastoris (P. pastoris) was chosen as an alternative expression
system for HPV VLP production based on its history as prolific heterologous protein
producer that circumvent many of the problems associated with aforementioned
expression systems. The strongly inducible AOX promoter allows three-phase
fermentations (1.3 L bioreactors) in which high cell densities (>100gCDW.L-1) are
obtained prior to induction with methanol. During the induction phase the dissolved
oxygen concentration may be used to control addition of methanol. It is also possible to
use predetermined methanol feed rates and to adjust the amount of additional oxygen
sparged to maintain a constant dissolved oxygen level. The effects of these control
strategies, different gene constructs and multiple gene integrations were quantified
through monomer-, VLP- and mRNA production levels.
Increased biomass concentrations in the 20% dissolved oxygen control strategy led to the
highest volumetric VLP concentration (68.53 mg.L-1). VLPs were located intracellularly
in both the cytoplasm and membranes of the yeast cells. Despite lower codon adaptation
of the h-L1 gene expressed in the X33[h-L1] strain it still had higher volumetric VLP
concentrations under 40% dissolved oxygen control than the X33[Syn-L1] and
X33[SA-L1] strain containing the SA-L1 and Syn-L1 genes. This was ascribed to the
possible presence of rare codons in the Syn-hL1 and SA-L1 genes and a lower A+T
content in the h-L1 gene. Multiple gene integrations of the h-L1 gene had a negative
effect on VLP production and this conclusion was supported by lower mRNA
concentrations indicating lower transcriptional efficiency. Increased methanol induction
efficiency in the DO control strategies was indicated by higher specific L1 monomer
levels. Decreased VLP to monomer ratios in the DO control strategies indicated that a
bottleneck existed in the assembly process due to increased L1 monomer concentrations. Due to the hydrophobic region on the L1 protein, these proteins associated with the
membranes within the yeast cells especially when efficient assembly to VLPs did not
occur. HPV16 L1 VLP concentrations obtained in P. pastoris in this study are
comparable to the study by Li et al., (2003), but much lower than expression levels
obtained in baculovirus infected insect cells. Based on the expression levels of HBsAg
VLPs obtained in P. pastoris, this system, with the necessary recommended optimisation,
has the capacity for increased HPV VLP production ability.
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Flottasie van 'n growwe pirieterts in 'n luggeborrelde hidrosikloonBurger, Andries Jacobus 12 1900 (has links)
Thesis (MScEng) -- Stellenbosch University, 1986 / ENGLISH ABSTRACT: High turbulence, high shear forces and high centrifugal forces characterise the flow in hydrocyclones. These characteristics are employed advantageously in the air-sparged hydrocyclone so that a space time of only one second is necessary for effective flotation. Conventional flotation processes on the other hand require a few minutes.
Flotation of pyrite from a coarse Witwatersrand ore (100%
-300 micron; 92% +38 micron) produces a sulphur recovery of
90% with a sulphur grade of 40% in the concentrate when the content of solids of the slurry feed equals 10%. Higher recoveries up to 93% are possible when slurries with a higher content of solids (e.g. 30%) are used. However, the sulphur grade then decreases to about 35%. Flotation in a batch cell produces a recovery of sulphur of 95% with a sulphur grade of 40%, but in this case a flotation time of 5 minutes is required.
A hydrocyclone with a diameter of 50 mm and a length of 410 mm produces optimum results at a slurry feed rate of 35 to
40 l/min and an air-flow rate of 200 l/min. An air-flow rate of about 150 l/min is adequate at slurry feed rates lower than 35 l/min. Flotation of particles finer than 38 micron is more successful at higher slurry feed rates. The optimum flotation of coarse particles (i.e. +106 micron) occurs at lower feed rates. The best flotation results are obtained in the size fraction between 38 and 75 micron, which produces a recovery and content of sulphur of 95% and 51% respectively.
A collector concentrate of 160 g/ton, which is thrice the quantity used in conventional processes, is required. The best recoveries at slurry feed rates lower than 35 l/min are obtained when the frother concentrate is low (approximately 20 mg/l). A higher frother concentrate, i.e. between 50 to 60 mg/l, is required at higher feed rates.
The air-sparged hydrocyclone may be used effectively for rougher flotation and especially for the flotation of ore finer than 150 micron. The use of a specially designed pedestal can minimize blockage of the underflow. Such a pedestal has been designed and tested successfully. / MINTEK
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Detecting change in complex process systems with phase space methodsBotha, Paul Jacobus 12 1900 (has links)
Model predictive control has become a standard for most control strategies in modern
process plants. It relies heavily on process models, which might not always be
fundamentally available, but can be obtained from time series analysis. The first step
in any control strategy is to identify or detect changes in the system, if present. The
detection of such changes, known as dynamic changes, is the main objective of this
study. In the literature a wide range of change detection methods has been developed
and documented. Most of these methods assume some prior knowledge of the system,
which is not the case in this study. Furthermore a large number of change detection
methods based on process history data assume a linear relationship between process
variables with some stochastic influence from the environment. These methods are
well developed, but fail when applied to nonlinear dynamic systems, which is focused
on in this study.
A large number of the methods designed for nonlinear systems make use of statistics
defined in phase space, which led to the method proposed in this study. The
correlation dimension is an invariant measure defined in phase space that is sensitive
to dynamic change in the system. The proposed method uses the correlation
dimension as test statistic with and moving window approach to detect dynamic
changes in nonlinear systems.
The proposed method together with two dynamic change detection methods with
different approaches was applied to simulated time series data. The first method
considered was a change-point algorithm that is based on singular spectrum analysis.
The second method applied to the data was mutual cross prediction, which utilises the
prediction error from a multilayer perceptron network. After the proposed method was
applied to the data the three methods’ performance were evaluated.
Time series data were obtained from simulating three systems with mathematical
equations and observing one real process, the electrochemical noise produced by a
corroding system. The three simulated systems considered in this study are the
Belousov-Zhabotinsky reaction, an autocatalytic process and a predatory-prey model.
The time series obtained from observing a single variable was considered as the only
information available from the systems. Before the change detection methods were
applied to the time series data the phase spaces of the systems were reconstructed with
time delay embedding.
All three the methods were able to do identify the change in dynamics of the time
series data. The change-point detection algorithm did however produce a haphazard behaviour of its detection statistic, which led to multiple false alarms being
encountered. This behaviour was probably due to the distribution of the time series
data not being normal. The haphazard behaviour reduces the ability of the method to
detect changes, which is aggravated by the presence of chaos and instrumental or
measurement noise. Mutual cross prediction is a very successful method of detecting
dynamic changes and is quite robust against measurement noise. It did however
require the training of a multilayer perceptron network and additional calculations that
were time consuming. The proposed algorithm using the correlation dimension as test
statistic with a moving window approach is very useful in detecting dynamic changes.
It produced the best results on the systems considered in this study with quick and
reliable detection of dynamic changes, even in then presence of some instrumental
noise.
The proposed method with the correlation dimension as test statistic was the only
method applied to the real time series data. Here the method was successful in
distinguishing between two different corrosion phenomena. The proposed method
with the correlation dimension as test statistic appears to be a promising approach to
the detection of dynamic change in nonlinear systems.
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Modelling the thermal, electrical and flow profiles in a 6-in-line matte melting furnaceSnyders, Cornelius Albert 12 1900 (has links)
Thesis (MScEng (Process Engineering))--Stellenbosch University, 2008. / The furnace at Polokwane is designed to treat high chromium containing concentrates
which requires higher smelting temperatures to prevent or limit the undesirable
precipitation of chromium spinels. The furnace has therefore been designed to allow for
deep electrode immersion with copper coolers around the furnace to permit the
operation with the resulting higher heat fluxes.
Deep electrode immersion has been noted to result in dangerously high matte
temperatures. Matte temperatures however can be influenced by a number of furnace
factors which emphasize the need to understand the energy distribution inside the
furnace. Computational fluid dynamics (CFD) has therefore been identified to analyze
the flow and heat profiles inside the furnace. The commercial CFD software code Fluent
is used for the simulations.
Attention has been given only to a slice of the six-in-line submerged arc furnace
containing two electrodes or one pair while focusing on the current density profiles, slag
and matte flow profiles and temperature distribution throughout the bath to ensure the
model reflects reality. Boundary conditions were chosen and calculated from actual plant
data and material specifications were derived from previous studies on slag and matte.
Three dimensional results for the current, voltage and energy distributions have been
developed. These results compare very well with the profiles developed by Sheng, Irons
and Tisdale in their CFD modelling of a six-in-line furnace. It was found the current flow
mainly takes place through the matte, even with an electrode depth of only 20%
immersion in the slag, but the voltage drop and energy distribution still only take place
in the slag.
Temperature profiles through-out the entire modelling domain were established. The
vertical temperature profile similar to Sheng et al. 1998b was obtained which shows a
specifically good comparison to the measured temperature data from the Falconbridge
operated six-in-line furnace. The temperature in the matte and the slag was found to be
uniform, especially in the vertical direction.
It has been found that similar results with Sheng et al. (1998b) are obtained for the slag
and matte velocity vectors. Different results are, however, obtained with different
boundary conditions for the slag/matte interface and matte region; these results are still
under investigation to obtain an explanation for this behaviour.
The impact of the bubble formation on the slag flow was investigated and found to be a
significant contributor to the flow. With the bubble formation, it is shown that possible
‘dead zones’ in the flow with a distinctive V-shape can develop at the sidewalls of the
furnace with the V pointing towards the centre of the electrode. This behaviour can have
a significant impact on the point of feed to the furnace and indirectly affect the feed rate
as well as the settling of the slag and matte. These results are not validated though.
Different electrode immersions were modelled with a constant electrical current input to
the different models and it was found that the electrode immersion depth greatly affects
the stirring of the slag in the immediate vicinity of the electrode, but temperature (which
determines the natural buoyancy) has a bigger influence on the stirring of the slag
towards the middle and sidewall of the slag bath.
The sensitivity of the model to a different electrode tip shape with current flow
concentrated at the tip of the electrode was also modelled and it was found that the
electrode shape and electrical current boundary conditions are very important factors
which greatly affect the voltage, current density and temperature profiles through the
matte and the slag. A detailed investigation to determine the electrode tip shape at
different immersions, as well as the boundary conditions of the current density on the tip
of the electrode is necessary as it was proven that the model is quite sensitive to these
conditions.
Several recommendations arose from this modelling work carried out in this
investigation. Time constraints, however, did not allow for the additional work to be
carried out and although valuable results were obtained, it is deemed to be a necessity if
a more in-depth understanding of furnace behaviour is to be obtained. Future work will
include the validation of the results, understanding the liquid matte model, investigating
the MHD effects and modelling different furnace operating conditions.
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Leaching of nickel laterite with a solution of ammonia and ammonium carbonate utilizing solids liquid separation under pressureErasmus, Mothobi 03 1900 (has links)
ENGLISH ABSTRACT: Leaching of nickel laterite was conducted with a solution of ammonia and ammonium carbonate in a closed vessel. The vessel used in this study was designed to leach and perform solid-liquid separation at the same time. For solid-liquid separation, stainless steel sintered metal filter media were used. The sintered metal filter medium was selected for its high strength to withstand pressure, chemical resistance to caustic solution and back flushing properties.
Optimum leaching conditions were determined by varying temperature, ammonia concentration, ammonium carbonate concentration and oxygen pressure. After leaching and filtration, the pH of the leach liquor was measured and samples were analyzed for dissolved metals (Ni, Fe and Co) using atomic absorption spectrophotometry.
The most significant variable effect on leaching of nickel was the ammonia concentration. The maximum dissolution of nickel from the unroasted ore was 11.90% at 4 M NH3, 100oC, 2 M (NH4)2CO3 and 2 bar O2 pressure. Optimization from the leaching data was done using response profiling and desirability in Statistica software. Optimum leaching conditions were determined to be 3 M NH3, 2 M (NH4)2CO2, 100oC and 2 bar O2 pressure. The mineralogy of the ore before and after leaching was studied to understand why nickel extraction from unroasted ore was poor. XRF analysis of solids after leaching showed that iron, silicon, and magnesium remained the same. The only metal which showed significant decrease from solids was nickel. XRD analysis of solids after and before leaching showed that most mineral phases present in the ore are not affected by the leaching solution. SEM with EDS detection was used to determine nickel distribution within the ore. The results showed that nickel is mostly associated with iron. The iron is surrounded by magnesium and silicon. Silicate minerals do not react with ammonia and ammonium carbonate solution.
From filtration experiments, the filtration differential pressure had no significant effect on the filtration rate. An average filtration rate of 0.29±0.07 ml/min.cm2 was obtained. The filtration rate from these experiments was very low. The main reason was due to quick pore clogging of sintered metals. Pore clogging was found to be mainly on the surface of the filter medium. Laterites have been found to have low permeability due a lot of clay present in the ore. Rheological studies on this ore showed that the ore has shear thickening behavior. However, a very clear filtrate was obtained. After each leach and filtration experiment, the sintered metals was unblocked by back flushing with water and air. Back flushing was successful because all 18 experiments were carried out using the same sintered filter medium.
The effect of roasting the ore prior to leaching was investigated using optimum conditions obtained when leaching the unroasted ore. There was a slight improvement in nickel extraction when the ore was roasted. The average percentage extraction of nickel from 3 experimental runs was 19.25%±0.19 at 100oC, 3M NH3, 2M (NH4)2CO3, and 5 bar oxygen pressure. Some part of nickel in the ore was unextractable due to association of nickel with recrystallized silicate minerals in the reduced ore. Roasting improved permeability of the ore. The filtration rate improved significantly after roasting the ore. The average filtration rate was 2.60±0.05 ml/min.cm2.
Dissolution kinetics of the unroasted and roasted saprolitic laterite were investigated with regard to the effects of temperature, ammonia concentration, ammonium carbonate concentration, and oxygen pressure. For the unroasted ore, it was found that dissolution rate and degree of nickel extraction increases with increasing temperature. Increase in ammonia concentration improves the degree of nickel extraction. Nevertheless, nickel extraction does not depend entirely on ammonia concentration because even when ammonia concentration is high and ammonium carbonate concentration is zero nickel extraction is low. An increase in ammonium carbonate concentration also increases the degree of nickel extraction. Ammonium carbonate is critical for the extraction, since ammonium ions in the solution prevent hydrolysis of the nickel ammine complex. Oxygen did not have a significant effect on the degree of nickel extraction. The leaching of nickel laterite was found to be a two stage leaching process. In the first stage, the dissolution of nickel is faster but after 15 minutes, the reaction rate is reduced. The reaction rate is reduced by inert minerals which host nickel. These minerals contain iron magnesium and silicon. The fast dissolution of nickel in the first stage represents leaching of free nickel in the ore. The data for the second stage of leaching was analyzed by the shrinking core model, and the results suggested that the dissolution rate is controlled by mixture kinetics (ash layer diffusion and surface reaction control). The activation energy for the dissolution reaction was calculated as 56.5 KJ/mol. The reaction order with respect to ammonia and ammonium carbonate were determined to be 0.3 and 0.26 respectively. For the roasted ore, the highest degree of nickel extraction was obtained at 60oC, 3M NH3, 2M (NH4)2CO3, and 5 bar oxygen pressure. The percentage extraction under these conditions was 28.7%. Temperature did not have a significant effect on the leaching rate. An increase in NH3 and (NH4)2CO3 increased the final extraction of nickel but did not have any effect on leaching rate in the first stage of leaching. In the absence of ammonium carbonate, nickel extraction is almost zero. The experimental data did not give linear fit to the shrinking core models investigated for the unroasted ore. The reason for this could be due to the sampling time interval which was too far apart, or the leaching behavior of roasted nickel is complicated and cannot explained by shrinking core model alone.
Leaching experiments demonstrate that for a high degree metal extraction and improved reaction kinetics with ammonia and ammonium carbonate, the solution temperature should be high (>100oC) for the unroasted ore. In order to leach at high temperature with ammonia and ammonium carbonate a closed vessel is required to prevent reagent loses. The reaction kinetics showed that the reaction is controlled mostly by ash layer diffusion; this indicates that a low degree of nickel extraction in the unroasted saprolitic laterite is due to inert minerals (ash layer) which host nickel within the ore.
In order to obtain a high degree of nickel extraction, the ore needs to be roasted under reducing conditions. Roasting conditions need to be carefully controlled to ensure high dissolution of nickel. In fact optimum roasting conditions which will give maximum dissolution of nickel, must be determined before working with the bulk of the ore. / AFRIKAANSE OPSOMMING: Logingstoetse van saprolitiese lateriet met 'n oplossing van ammonia en ammonium karbonaat is gedoen in 'n druk houer. Die logingsvat vir hierdie studie is ontwikkel om die loging sowel as die vloeistof – vastestof skeiding te doen. Gesinterde metaal filter medium was gebruik vir die vloeistof – vastestof skeiding aangesien dit die volgende eienskappe vertoon; die vermoë om druk te weerstaan, die chemiese weerstand teen bytsoda oplossing, asook voordelige terugspoel eienskappe.
Optimum loogkondisies is bepaal deur die temperatuur, ammoniak konsentrasie, ammonium karbonaat konsentrasie, en suurstof druk te varieer. Na loging en filtrasie is die pH van die loogvloeistof gemeet en monsters is deur atoom absorpsie spektrofotometrie geanaliseer vir opgeloste metale (Ni, Fe en Co).
Die veranderlike wat die grootste effek op die loging van nikkel gehad het was die ammoniak konsentrasie. Die maksimum herwinning van nikkel van uit ongeroosterde erts was 11.9 % by 4 M NH3, 100 oC, 2 M (NH4)2CO3 en 2 bar O2 druk. Optimisering van die loogdata is gedoen deur die respons profiel te analiseer met Statistica sagteware. Optimum loogkondisies was bepaal as 3 M NH3, 2 M (NH4)2CO2, 100 oC en 2 bar O2 druk.
Die mineralogie van die erts voor en na loging is bestudeer om te bepaal waarom die nikel opbrengs van ongeroosterde erts so laag was. XRF analise van die vastestof na loging het gewys dat yster, silikon en magnesium nie deur loging affekteer is nie. Slegs nikkel het 'n merkwaardige afname getoon. XRD analsiese van die vastestof voor en na loging wys dat die meeste mineraal fases teenwoordig in die erts nie deur die loogoplossing affekteer is nie. SEM met EDS deteksie is gebruik om die nikkel verspreiding in die erts te bepaal. Die resultate wys dat nikkel meestal met yster assosieer. Die yster is omring deur magnesium en silikon. Silikaat minerale reageer nie met ammoniak en ammonium karbonaat oplossing nie. In filtrasie eksperimente is daar gevind dat die filtrasie differensiële druk geen noemenswaardige effek op die filtrasie tempo gehad het nie. Die gemiddelde filtrasietempo was 0.29+0.07 ml/min.cm2. Die filtrasie tempo van hierdie eksperimente was baie laag, hoofsaaklik as gevolg van blokkasie van porieë van die sinter metaal filter medium. Dit is gevind dat blokkasie van porieë hoofsaaklik op die oppervlak van die filter medium plaasvind. Lateriedes toon 'n lae deurlaatbaarheid as gevolg van die erts se hoë klei inhoud. Rheologiese studies op hierdie erts wys dat die erts skuif verdikking (“shear thickening”) gedrag vertoon. 'n Baie helder filtraat is egter verkry. Die gesinterde metale is na elke loog en filtrasie eksperiment skoongemaak deur terugspoeling met water en lug. Hierdie procedure was suksesvol, aangesien al 18 eksperimente met dieselfde filter medium uitgevoer is.
Die effek van erts roostering voor loging is ondersoek by die optimum kondisies wat verkry was vir die loging van ongeroosterde erts. Nikkel ekstraksie het effens verbeter met geroosterde erts. Die gemiddelde persentasie ekstraksie van nikkel van drie eksperimentele lopies was 19.25 % + 0.19 by 100 oC, 3 M NH3, 2 M (NH4)2CO3, en 5 bar suurstofdruk. 'n Gedeelte van die nikkel in die erts was onherwinbaar as gevolg van die assosiasie van nikkel met her-gekristaliseerde sillikaat-minerale in die gereduseerde erts. Die porositeit van die erts is verbeter deur dit te rooster. Die filtrasie tempo het merkwaardig verbeter nadat die erts gerooster is. Die gemiddelde filtrasie tempo was 2.6+0.05 ml/min.cm2.
Kinetika vir die oplossing van ongeroosterde en geroosterde saprolitiese lateriet is ondersoek, met in ag geneem die effekte van temperatuur, ammonia konsentrasie, ammonium karbonaat konsentrasie en suurstofdruk. Vir ongeroosterde erts is gevind dat die oplossingstempo en graad van nikkel ekstraksie toeneem met toenemende temperatuur. Toename in ammoniak konsentrasie lei tot 'n toename in nikkel ekstraksie, maar nikkel ekstraksie is nie alleenlik afhanklik van ammoniak nie. 'n Toename in ammonium karbonaat konsentrasie lei ook tot 'n toename in nikkel ekstraksie. Ammonium karbonaat is krities vir die ekstraksie, aangesien ammonium ione in die oplossing die hidrolise van die nikkel-amien kompleks verhoed. Suurstof het nie 'n merkwaardige effek op die totale nikkel ekstraksie gehad nie. Vir die bepaling van reaksie kinetika is 100˚C gebruik as die logingstemperatuur. Die loging van saprolitiese nikkel lateriet vind in twee stadia plaas. In die eerste fase is die oplossing van nikkel vinnig, maar na 15 minute neem die reaksietempo af. Die reaksietempo word verlaag deur inerte minerale wat teenwoordig is in die nikkel erts. Hierdie minerale bevat yster, magnesium en silikon. Die vinnige oplossing van nikkel in die eerste fase verteenwoordig die loging van vry nikkel in die erts. Die data vir die tweede stadium is geanaliseer deur die krimpende kern model, en die resultate dui aan dat die oplossingstempo deur 'n gemengde meganisme beheer word (as laag diffusie en oppervlak reaksie beheer). Die aktiveringsengergie vir die oplossingsreaksie was bereken as 56.5 kJ/mol. Die reaksieorde ten opsigte van ammoniak en ammonium karbonaat is onderskeidelik bepaal as 0.3 en 0.26.
Die hoogste graad van nikkel ekstraksie vir die geroosterde erts is verkry by 60oC, 3 M NH3, 2 M (NH4)2CO3, en 5 bar O2 druk. Die persentasie ekstraksie by hierdie kondisies was 28.7 %. Temperatuur het nie 'n merkwaardige effek op loogtempo gehad nie. 'n Toename in NH3 en (NH4)2CO3 het die graad van nikkel ekstraksie laat toeneem, maar het nie enige effek op die loogtempo gehad nie. In die afwesigheid van ammonium karbonaat het byna geen nikkel ekstraksie plaasgevind nie. Die eksperimentele data het nie 'n lineêre passing vir die krimpende kern model soos vir die ongeroosterde erts ondersoek gegee nie. Die rede hiervoor is dat die monsternemings interval te groot was, of dat die logings karakteristiek van geroosterde nikel gekompliseerd is en nie alleen deur die krimpende kern model voorspel kan word nie.
Logings eksperimente wys dat die temperatuur hoog moet wees (> 100 oC) om 'n hoë graad van nikkel ekstraksie te verkry met die ongeroosterde erts. 'n Geslote reaktor word benodig om by 'n hoë temperatuur met ammoniak en ammonium karbonaat te loog om reagens verliese te verhoed. Die reaksie kinetika word grootliks deur aslaag diffusie beheer. Hieruit kan gesien word dat 'n lae graad van nikkel ekstraksie uit die ongeroosterde saprolitiese lateriet die gevolg is van nie-reaktiewe minerale (aslaag) waarin die nikkel binne die erts bevat word.
Om 'n hoë graad van nikkel ekstraksie te verkry moet die erts onder reduserende kondisies gerooster word. Rooster kondisies moet versigtig beheer word om hoë oplossing van nikkel te verseker. Optimum rooster kondisies om maksimum nikkel oplossing te verkry, moet bepaal word voordat daar met groter hoeveelhede erts gewerk kan word.
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Chemical and physical modification of wood based hemicelluloses for use in the pulp and paper industryPostma, Dirk 03 1900 (has links)
Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Hemicelluloses are the most abundant plant polysaccharides available next to cellulose. The industrial usage of hemicelluloses however is very limited to nonexistent. As wood is processed in the Kraft pulping process, a large fraction of these hemicelluloses is degraded to low molecular weight isosaccharinic acids, which end up in the black liquor with the degraded lignin. The extraction of hemicelluloses prior to pulping and re-introducing them as a wet-end additive has been shown to improve the paper tensile -, burst- and tear index properties. It has also been proven that the pre-extraction of hemicelluloses does not negatively affect the downstream paper products.
The objective of this project was to study the modification of extracted wood based hemicelluloses, focusing on glucuronoxylan in Eucalyptus grandis (E. grandis), by chemical and physical methods identified from literature. The methods investigated were; cationisation, carboxymethylation and ultrasound treatment. The modified hemicelluloses were applied as a wet-end additive to E. grandis pulp to test their effect on strength properties. An addition protocol for the new hemicelluloses additives was developed in this investigation.
The E. grandis glucuronoxylan was extracted by using the mild alkali extraction method of Höije et al. The characterization of the extracted solids from the pure E. grandis chips showed that 4-O-methylglucuronoxylan was extracted with an average uronic acid content of 17.3 wt.%. The hemicelluloses yield was 50.75 wt.%, based on dry biomass, containing 40.76 wt.% xylose units. The solids still contained 26.6 wt.% lignin after extraction. The presence of lignin in the extracted solids indicated that the delignification step in the extraction method used, was not sufficient for the E. grandis biomass. The molecular weight of the extracted glucuronoxylan was 51 589 g.mol-1.
It was proven that the modification methods from literature are applicable to E. grandis glucuronoxylan, producing cationic, carboxymethyl and low uronic acid content 4-O-methylglucuronoxylan. The cationic E. grandis glucuronoxylan produced had a degree of substitution between 0.05 and 0.73 and an uronic acid content ranging between 6.12 and 12.70 wt.%. The carboxymethylated E. grandis glucuronoxylan had a degree of substitution between 0.05 and 0.11 with a uronic acid content between 10.2 and 21.4%. The sonication of E. grandis glucuronoxylan resulted in products with molecular weights ranging from 54 856 to 57 347 g.mol-1 and uronic acid contents between 13.0 and 18.4 wt.%.
Handsheet formation with the modified hemicelluloses added, showed that the cationic E. grandis glucuronoxylan improved handsheet strength and surface properties the best. Cationic E. grandis glucuronoxylan also outperformed the industrial additive, cationic starch at a dosage level of 1.0 wt.%. The addition protocol development for cationic E. grandis glucuronoxylan showed it is possible to add cationic hemicellulose before refining, which results in maximum contact time with the pulp fibres without inhibiting the effect of the additive. Cationic hemicellulose additive added before refining led to a decrease in refining energy required to reach the desired strength properties.
It was concluded that the cationisation and carboxymethylation methods chosen from literature were applicable to the South African grown E. grandis glucuronoxylan. The cationic glucuronoxylan showed the best improvement in handsheet strength and surface properties. Cationic E. grandis glucuronoxylan could be added before refining in the papermaking process for maximum effectiveness of this new strength additive. The use of hemicellulosic additives will be more sustainable than starch, due to the presence of hemicelluloses in the initial biomass that enters the pulp and paper process. / AFRIKAANSE OPSOMMING: Hemiselluloses is die mees volopste plantpolisakkariede naas sellulose, alhoewel die industriële gebruik van hierdie hemiselluloses tans nog beperk is. In die huidige verwerking van hout met behulp van die Kraft verpulpingsproses word die hemiselluloses gedegradeer na lae molukulêre massa isosakkariniese sure wat saam met die lignien in die swartloog afvalstroom eindig. Die ekstraksie van hierdie hemiselluloses vóór die verpulpingsproses, en latere byvoeging as ‘n sterktebymiddel in die papier vervaardigings proses, kan die papier treksterkte, bars-, en skeur eienskappe verbeter. Dit is aangetoon dat die ekstraksie van hemiselluloses vóór die verpulpingsproses nie die opbrengs en kwaliteit van papierprodukte negatief beïnvloed nie.
Die doelwit van hierdie projek was om die modifikasie van hemiselluloses, ge-ekstraheer uit Eucalyptus grandis (E. grandis) hout vóór verpulping, deur middle van chemiese en fisiese metodes uit literatuur te ondersoek. Die projek het spesifiek gefokus op glukuronoxilaan verkry uit E. grandis en wat gemodifiseer is met met behulp van kationisasie, karboksimetilering en ultraklank behandeling. Die gemodifiseerde hemiselluloses is daarna benut as ‘n nat-kant bymiddel tot E. grandis pulp, om die sterkte eienskappe van papier te ondersoek. ‘n Toevoegingsprotokol is vir die nuwe hemisellulose bymiddel ontwikkel in hierdie ondersoek.
Die glukuronoxilaan is deur middle van die matige alkali-ekstraksie metode van Höije geekstraheer. Karakterisering van die vastestof residu wat uit die suiwer E. grandis biomassa geekstraheer is het getoon dat 4-O-metielglukuronoxilaan geëkstraheer is, met ‘n gemiddelde glukuronosuurinhoud van 17.3 massa%. Die hemisellulose opbrengs was 50.75 massa%, gebaseer op droë biomassa, en dit het 40.76 massa% xylose-eenhede bevat. Die lignieninhoud van die soliedes was 26.6 massa% na ekstraksie. Die teenwoordigheid van die lignien het daarop gedui dat die delignifikasie (van die metode) van E. grandis biomassa nie voldoende was nie. Die molekulêre massa van die geëkstraheerde glukuronoxilaan was 51 589 g.mol-1.
Dit is bewys dat die modifikasiemetodes toepasbaar is op die E. grandis glukuronoxilaan, en dat kationiese, karboksiemetiel en lae glukuronosuur 4-0-metielglukurono-xilaan geproduseer is. Die kationiese glukuronoxilaan het ‘n graad van substitusie tussen 0.05 en 0.73 gehad, met ‘n glukuronosuur inhoud tussen 6.12 en 12.70 massa%. Die karboksiemetielglukuronoxilaan het ‘n graad van substitusie tussen 0.05 en 0.11 gehad, met glukuronosuurinhoude tussen 10.2 en 21.4 massa%. Die ultraklankbehandelde glukuronoxilaan het molekulêre massas tussen 54 856 en 57 347 g.mol-1 gehad met glukuronosuurinhoude tussen 13.0 en 18.4 massa%.
Papier handvelproduksie van die pulp waar tydens die gemodifiseerde hemiselluloses toe gevoeg is, het aangedui dat die kationiese E. grandis glukuronoxilaan die grootste sterkte- en oppervlakeienskappe verbetering getoon het. Die kationiese glukuronoxilaan het ook, in terme van verbetering van pulpeienskappe, die industrieële kationiese stysel bymiddel oortref, by ‘n doserings vlak van 1.0 massa%. Die toevoegingsprotokol ontwikkeling vir die kationiese E. grandis glukuronoxilaan het getoon dat hemiselluloses byvoeging tot die papiermaakproses vóór die raffinerings stadium die mees gunstige was, met dosering tussen 0.5 en 2.0 massa%. Die byvoeging van kationiese hemiselluloses vóór raffinering het gelei tot ‘n afname in raffineringsenergie wat benodig word om die verlangde sterkteeienskap te verkry.
Dit is bevesting gekose kationisasie- en karboksimetilerings metodes toepasbaar op die Suid Afrikaanse E. grandis glukuronoxilaan was. Die kationiese glukuronoxilaan het die grootste verbetering in pulpeienskappe, in terme van handvelsterkte en oppervlakeienskappe, getoon. Kationiese glukuronoxilaan moet vóór raffinering tot die papiermaakproses bygevoeg word vir maksimum doeltreffendheid van hierdie nuwe sterktebymiddel. Die gebruik van hemisellulose bymiddels sal meer volhoubaar wees as stysel, omdat die hemiselluloses wat in die biomassa aanwesig is, in die proses teruggrplaas word.
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Computational fluid dynamic modelling of an electric smelting furnace in the platinum recovery processBezuidenhout, Johan Jacobus 12 1900 (has links)
Thesis (MScEng (Process Engineering))--Stellenbosch University, 2008. / The electric smelting furnace is found at the heart of the platinum recovery process where the power
input from the electrodes produces a complex interplay between heat transfer and fluid flow. A
fundamental knowledge of the dynamic system hosted by the electric furnace is valuable for
maintaining stable and optimum operation. However, describing the character of the system hosted
by the electric furnace poses great difficulty due to its aggressive environment. A full-scale threedimensional
Computational Fluid Dynamics (CFD) model was therefore developed for the circular,
three-electrode Lonmin smelting furnace.
The model was solved as time dependent to incorporate the effect of the three-phase AC current,
which was supplied by means of volume sources representing the electrodes. The slag and matte
layers were both modelled as fluid continuums in contact with each other through a dynamic interface
made possible by the Volume of Fluid (VOF) multi-phase model. CO-gas bubbles forming at electrode
surfaces and interacting with the surrounding fluid slag were modelled through the Discrete Phase
Model (DPM).
To account for the effect of concentrate melting, distinctive smelting zones were identified within the
concentrate as assigned a portion of the melting heat based on the assumption of a radially
decreasing smelting rate from the centre of the furnace. The tapping of slag and matte was neglected
in the current modelling approach but compensation was made for the heating-up of descending
material by means of an energy sink based on enthalpy differences.
Model cases with and without CO-gas bubbles were investigated as well as the incorporation of a third
phase between the slag and matte for representing the ‘mushy’ chromite/highly viscous slag
commonly found in this region. These models were allowed to iterate until steady state conditions has
been achieved, which for most of the cases involved several weeks of simulation time.
The results that were obtained provided good insight into the electrical, heat and flow behaviour
present within the molten bath. The current density profiles showed a large portion of the current to
flow via the matte layer between the electrodes. Distributions for the electric potential and Joule heat
within the melt was also developed and showed the highest power to be generated within the
immediate vicinity of the electrodes and 98% of the resistive heat to be generated within the slag.
Heat was found to be uniformly distributed due the slag layer being well mixed. The CO-gas bubbles
was shown to be an important contributor to flow within the slag, resulting in a order of magnitude
difference in average flow magnitude compared to the case where only natural buoyancy is at play.
The highest flow activity was observed halfway between electrodes where the flow streams from the
electrodes meet. Consequently, the highest temperatures are also observed in these regions. The
temperature distribution within the matte and concentrate layers can be characterized as stratified.
Low flow regions were identified within the matte and bottom slag layer which is where chromite and
magnitite deposits are prone to accumulate.
The model results were partially validated through good agreement to published results where actual
measurements were done while also falling within the typical operating range for the actual furnace.
The modelling of the electric furnace has been valuably furthered, however for complete confidence in
the model results, further validation is strongly recommended.
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Modeling & optimisation of coarse multi-vesiculated particlesClarke, Stephen Armour 03 1900 (has links)
Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Multi-vesiculated particles (MVP) are synthetic insoluble polymeric particles containing a multitude
of vesicles (micro-voids). The particles are generally produced and used as a suspension in an
aqueous fluid and are therefore readily incorporated in latex paints as opacifiers. The coarse or suede
MVP have a large volume-mean diameter (VMD) generally in the range of 35-60μm, the large VMD
makes them suitable for textured effect paints.
The general principle behind the MVP technology is as the particles dry, the vesicles drain of liquid
and fill with air. The large refractive index difference between the polymer shell and air result in the
scattering of incident light which give the MVP their white opaque appearance making them suitable
as an opacifier for the partial replacement of TiO2 in coating systems.
Whilst the coarse MVP have been successfully commercialized, insufficient understanding of the
influence of the MVP system parameters on the final MVP product characteristics coupled with the
MVP’s sensitivity towards the unsaturated polyester resin (UPR) resulted in a product with significant
quality variation. On the other hand these uncertainties provided the opportunity to model and
optimise the MVP system through developing a better understanding of the influence of the MVP
system parameters on the MVP product characteristics, developing a model to mathematically
describe these relationships and to optimise the MVP system to achieve the product specifications
whilst simultaneously minimising the variation observed in the product characteristics.
The primary MVP characteristics for this study were the particle size distribution (quantified by the
volume-mean diameter (VMD)) and the reactor buildup.1
The approach taken was to analyse the system determining all possible system factors that may
affect it, and then to reduce the total number of system factors by selecting those which have a
significant influence on the characteristics of interest. A model was then developed to
mathematically describe the relationship between these significant factors and the characteristics of
interest. This was done utilising a set of statistical methods known as design of experiments (DoE).
A screening DoE was conducted on the identified system factors reducing them to a subset of factors
which had a significant effect on the VMD & buildup. The UPR was characterised by its acid value and
viscosity and in combination with the identified significant factors a response surface model (RSM)
was developed for the chosen design space, mathematically describing their relationship with the
MVP characteristics. Utilising a DoE method known as robust parameter design (specifically
propagation of error) an optimised MVP system was numerically determined which brought the MVP
product within specification and simultaneously reduced the MVP’s sensitivity to the UPR.
The validation of the response surface model indicated that the average error in the VMD prediction
was 2.16μm (5.16%) which compared well to the 1.96μm standard deviation of replication batches.
The high Pred-R2 value of 0.839 and the low validation error indicates that the model is well suited
for predicting the VMD characteristic of the MVP system. The application of propagation of error to
the model during optimisation resulted in a MVP process and formulation which brought the VMD
response from the standard’s average of 44.56μm to the optimised system’s average of 47.84μm
which was significantly closer to the desired optimal of 47.5μm. The most notable value added to the system by the propagation of error technique was the reduction in the variation around the mean of
the VMD, due to the UPR, by over 30%1 from the standard to optimised MVP system.
In addition to the statistical model, dimensional analysis, (specifically Buckingham-Π method) was
applied to the MVP system to develop a semi-empirical dimensionless model for the VMD. The model
parameters were regressed from the experimental data obtained from the DoE and the model was
compared to several models sited in literature. The dimensionless model was not ideal for predicting
the VMD as indicated by the R2 value of 0.59 and the high average error of 21.25%. However it
described the VMD better than any of the models cited in literature, many of which had negative R2
values and were therefore not suitable for modelling the MVP system. / AFRIKAANSE OPSOMMING: Sintetiese polimeer partikels wat veeltallige lugblasies huisves en omhul, staan beter bekend as MVP
(verkort vanaf die Engelse benaming, "multi-vesiculated particles"). Tipies word hierdie partikels
berei en gestabiliseer in 'n waterige suspensie wat dit mengbaar maak met konvensionele emulsie
sisteme en dit dus in staat stel om te funksioneer as 'n dekmiddel in verf. Deur die volume
gemiddelde deursnee (VGD) te manipuleer tot tussen 35 en 60μm, word die growwe partikels geskik
vir gebruik in tekstuur verwe, soos byvoorbeeld afwerkings met 'n handskoenleer (suède) tipe
tekstuur.
Die dekvermoë van MVP ontstaan soos die partikels droog en die water in die polimeer partikel
vervang word met lug. As gevolg van die groot verskil in brekingsindeks tussen die polimeer huls en
die lugblasies, word lig verstrooi in alle rigtings wat daartoe lei dat die partikels wit vertoon. Dus kan
die produk gebruik word om anorganiese pigmente soos TiO2 gedeeltelik te vervang in verf.
Alhoewel growwe MVP al suksesvol gekommersialiseer is, bestaan daar nog net 'n beperkte kennis
oor die invloed van sisteem veranderlikes op die karakteristieke eienskappe van die finale produk.
Dit volg onder andere uit waarnemings dat die kwaliteit van die growwe MVP baie maklik beïnvloed
word deur onbekende variasies in die reaktiewe poliëster hars wat gebruik word om die partikels te
maak. Dit het egter die geleentheid geskep om die veranderlikes deeglik te modeleer en te
optimiseer om sodoende 'n beter begrip te kry van hoe eienskappe geaffekteer word. 'n
Wetenskaplike model is opgestel om verwantskappe te illustreer en om die sisteem te optimiseer
sodat daar aan produk spesifikasies voldoen word, terwyl produk variasies minimaal bly.
Die oorheersende doel in hierdie studie was om te fokus op partikelgrootte en verspreiding (bepaal
met behulp van die VGD) as primêre karakteristieke eienskap, asook die graad van aanpaksel op die
reaktorwand gedurende produksie.
Vanuit eerste beginsel is alle moontlike veranderlikes geanaliseer, waarna die hoeveelheid verminder
is na slegs dié wat die karakteristieke eienskap die meeste beïnvloed. Deur gebruik te maak van
eksperimentele ontwerp is die wetenskaplike model ontwikkel wat die effek van hierdie eienskappe
statisties omsluit.
'n Afskerms eksperimentele ontwerp is uitgevoer om onbeduidende veranderlikes te elimineer van
dié wat meer betekenisvol is. Die hars is gekaraktiseer met 'n getal wat gebruik word om die aantal
suur groepe per molekuul aan te dui, asook die hars se viskositeit. Hierdie twee eienskappe, tesame
met ander belangrike eienskappe is gebruik om 'n karakteristieke oppervlakte model te ontwikkel
wat hul invloed op die VGD van die partikels en reaktor aanpakking beskryf. Deur gebruik te maak
van 'n robuuste ontwerp, beter beskryf as 'n fout verspreidingsmodel, is die MVP sisteem numeries
geoptimiseer. Dit het tot gevolg dat die MVP binne spesifikasie bly en die VGD se sensitiwiteit vir
variasie in die hars verminder het.
Geldigheidstoetse op die oppervlakte model het aangetoon dat die gemiddelde fout in VGD 2.16μm
(5.16%) was. Dit is stem goed ooreen met die 1.96μm standaard afwyking tussen herhaalde lopies.
Hoë Pred-R2 waardes (0.839) en lae geldigheidsfout waardes het getoon dat die voorgestelde model
die VGD eienskappe uiters goed beskryf. Toepassing van die fout verspreidingsmodel gedurende
optimisering het tot gevolg dat die VGD vanaf die standaard gemiddelde van 44.56μm verskuif het na
die geoptimiseerde gemiddelde van 47.84μm. Dit is aansienlik nader aan die verlangde optimum
waarde van 47.5μm. Die grootste waarde wat toegevoeg is na afloop van hierdie studie, is dat die afwyking rondom die gemiddelde VGD, toegeskryf aan die eienskappe van die hars, verminder het
met oor die 30%1 (vanaf die standaard tot die optimiseerde sisteem).
Verdere dimensionele analise van die sisteem deur spesifiek gebruik te maak van die Buckingham-Π
metode het gelei tot die ontwikkeling van 'n semi-empiriese dimensielose VGD model. Regressie op
eksperimentele data verkry uit die eksperimentele ontwerp is vergelyk met verskeie modelle beskryf
in ander literatuur bronne. Hierdie dimensionele model was nie ideaal om die VGD te beskryf nie,
aangesien die R2 waarde 0.59 was en die gemiddelde fout van 21.25% relatief hoog was. Nietemin,
hierdie model beskryf die VGD beter as enige ander model voorgestel in die literatuur. In talle gevalle
is negatiewe R2 waardes verkry, wat hierdie literatuur modelle geheel en al ongeskik maak vir
toepassing in die MVP sisteem.
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