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Effect of Diffusion on Foam Bubble Size Distribution and Gas Mobility: an Idealized 2D Model
In this thesis the effect of gas diffusion between bubbles on the bubble-size distribution and capillary resistance to foam flow in a bubble train is investigated using an idealized 2D pore model. First the shape of the model pore is discussed and how a lamella moves through it. Then the physical forces (lamella curvatures and pressure differences between bubbles) in the pores are explained and how they affect capillary resistance to foam flow. Next the parameters of the dimensionless model are related to measured fluid properties. Under certain conditions (large film permeability to gas, large surface tension, low pressure, small pores, and low velocity of flowing gas) it is possible that characteristic diffusion rate can be greater than imposed convection rate, and that all gas transport is from diffusion across lamellae, not bubble movement.
We present model results for different ratios of characteristic diffusion to convection rates. If bubbles are smaller than pores, diffusion reduces the number of bubbles and increases average bubble size, whether convection is imposed on the foam or not. If convection is imposed, lamellae disappear not in pore throats but after first colliding in jumps across pore bodies. If bubbles are larger than pores, diffusion does not increase average bubble size. Diffusion increases the capillary resistance to flow; the increase is greatest when the characteristic rate of diffusion is close to the convection rate. Diffusion increases capillary resistance to flow because lamellae spend more time in positions of greater curvature than in the absence of diffusion. For characteristic diffusion rates much greater or much less than the imposed convection rate the effect of diffusion on capillary resistance to foam flow is modest.
These results suggest that by itself, an increase in diffusion rate through lamellae does not make foam flow with less resistance. With diffusion lamellae spend more time in pore throats where capillary resistance to flow is greatest.
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Mining a Massive Reservoir Engineering Database for Determinants of Recovery Efficiency
A global and industry wide dataset was data mined for determinants of recovery efficiency. Understanding of the factors that are driving variance in reservoir performance is essential for benchmarking current performance and for the screening of new opportunities. The following insights in the origin of variance in reservoir performance could be extracted from this analysis. Global trends for recovery factor with drive mechanism, reservoir type, geological age, lithology and depositional environment were extracted through subgroup analysis. Other property trends, such as porosity with depth and geological age, were found to be basin specific. The internal structure of the database and correlations was revealed through principal component analysis. Relative importance of the predictor variables was determined using automatic multivariate linear regression. It was found that the predominant variables include: API gravity, permeability and reservoir temperature.
Additional data was identified through combination of literature review, dimensional- and statistical analysis. The following variables are suggested: dip angle, flow rate, fractional water cut, and pressure drop. Furthermore continuous scales for heterogeneity and fracture intensity, especially for carbonate reservoirs are suggested. To express the confidence level for each reservoir in the database, categorical variables for maturity and data quality are proposed. This research forms the basis for future data mining of the dataset and further improvement of the TQ EUR TOOL in which the data is stored. In a wider context this report presents a high level overview of observations on reservoir performance based on actual reservoirs worldwide rather than laboratory data or theory.
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Ground-Penetrating Radar
Measuring and analyzing ground penetrating radar data on different sand-clay soils as a function of water content
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Building and Evaluating Borehole-Image-Constrained Facies Models of a Complex Channelised Slope System, Karoo Basin, South Africa
As hydrocarbons become scarcer, submarine channelised slope systems have become a focus of exploration due to their reservoir potential. Outcrops of both levee-confined (Unit C) and entrenched (Unit D) channel systems are exposed in the Permian Fort Brown Formation, Karoo Basin, South Africa and have been extensively studied and interpreted. Full coring and logging of six research boreholes behind the outcrop surface has produced a comprehensive dataset including oriented borehole images.
Directional features from FMS borehole image logs can be subdivided into direct (cross-bedding and climbing ripples) and indirect (erosion- and amalgamation surfaces and syn-sedimentary faults) palaeoflow indicators. The distribution of these indicators is analysed qualitatively and statistically per well and per (sub)unit to arrive at a solid palaeoflow reconstruction. Distributions of features in unconfined external levee deposits yield the most unambiguous results, whereas levee- or valley-confined features display a higher level of scattering.
A borehole-confined, pseudo-2D and a well- and outcrop-confined 3D facies model are built to test the incorporation of the palaeoflow reconstruction. Erosion surface dip azimuths help to locally constrain (sub)unit bounding surfaces. The palaeoflow reconstruction serves to constrain the orientation of data analysis on conceptual facies models and to assign realistic orientations to the representation of multi-point facies patterns. Application of a multi-point statistics (MPS) algorithm maximises use of the available dataset and therefore yields the best results.
The approach used is thought to be applicable to analogous channelised slope systems and is designed to work with a subsurface dataset.
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Weathering of fluvial sands as a compositional linear process: a new modeling approach
Geological data is often compositional (i.e. positive and sum to unity). The constrained nature of compositional data can lead to severe problems during data analysis. Transforming from the simplex to centered log-ratio (CLR) space can solve these problems, converting constrained non-linear processes into unconstrained linear processes (transforming perturbation and power transformation into addition and multiplication). Using this transformation, techniques were developed to analyze weathering (a compositional process) in the fluvial system. Detailed knowledge of the weathering process will improve reservoir characterization by providing in- sights into the spatial distribution of reservoir rock, provenance regions, basin evolution and composition of sediment at the time of burial (an important input of diagenesis models).
To analyze the CLR-transformed compositional data, several methods were developed. The SVD method uses principal component analysis (PCA), singular value decomposition (SVD) and cluster analysis to extract weathering directions from bedload samples (models usually ignore the bedload due to its complicated relation with time and its high level of noise, even though bedload is the main component of reservoir rock in fluvial reservoirs). The pairwise p-vector method combines directional derivatives with simple geological knowledge to obtain weathering directions and drainage patterns. Combined use of both methods creates the best results. The techniques were tested on a dataset including fluvial bedload samples taken in the Orinoco drainage basin. Two different grain type groupings were used; [Q F R] and [Qms Qmu Qp2 Qp3x F R]. To restrict the influence of non weathering processes, mineral groups with deviating densities or shapes were discarded.
The developed techniques are able to extract directional information from CLR transformed data, which can provide a prediction of spatial trends in reservoir quality across a fluvial basin. Cluster analysis techniques can divide samples into distinct lithological regions, of which the upstream ones coincide with different provenance regions. The actual flow directions between the different clusters can be reproduced with a fair amount of reliability. A more detailed drainage pattern can be obtained by creating a flow direction vector plot using a grid over the geographical area. The weathering direction can be obtained with a reasonable degree of reliability with the techniques in this thesis (the ranking of elements in the weathering direction vectors, which reflects their durability, is in accordance with geological knowledge). With the weathering direction vector and the created drainage pattern one can start to predict compositional change across a fluvial basin. The results of this thesis contain the first building blocks towards a compositional linear process (CLP) model for reservoir-quality assessment in fluvial systems.
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Experimental Investigation of Non Optimum Conditions of Alkaline Surfactant Polymer Flooding
Alkaline Surfactant Polymer (ASP) flooding is a chemical EOR technique that takes advantage of both interfacial tension reduction and mobility control. Core flooding tests show almost 100% recovery when the experiment is carried out under optimal conditions, i.e., a middle phase micro-emulsion characterized by extremely low interfacial tension is formed when a phase behavior test is done. In the field, reservoir heterogeneity causes mixing, which takes the system away from its optimal condition. Another major drawback of the ASP floods is the high cost of the associated chemicals. In some cases the logistics can also be a major challenge.
Therefore this thesis considers the application of ASP at non optimal conditions. We study this application by performing series of core flood experiments. For a given surfactant concentration we determined the optimal condition by varying the alkali concentration, which turns out to be 1.75 w/w% of Sodium Carbonate (Na2CO3). Subsequently we performed vertical flow experiments using alkaline weight percentages from 1.0 % to 2.25 % with increments of 0.25% around the optimum. Initially we used a 38.3 cm core, which gave an unexpected low recovery of 68% to residual oil, after injection of two pore volume (PV). Injection of over-optimum solutions resulted in even worse recoveries, while injection of under-optimum solutions led to higher recoveries at chemical break-through for 1.5 w/w% and 1.25 w/w% before it dropped again for 1.0 w/w%.
To understand this behavior we repeated the experiment with shorter cores (30 cm and 17 cm) at optimum conditions, which gave a recovery of more than 90% (95% of the oil initially in place (OIIP)), which value is often encountered in literature.
We propose that instabilities may be the cause of the low recoveries after a stability analysis shows that the system apparent viscosity is higher than the viscosity of the displacing ASP solution.
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Dimensionering van onderwaterbetonvloeren
Samenvatting is verwerkt in document, hoofstukken omvatten:
- gevoeligheidsanalyses
- betontechnologische aspecten
- gebruik van 2D-rekenmodel
- toetsing in BGT en UGT
- constructieve veiligheide in geval van paaluitval
- bepaling axiale veerstijfheid
- bepaling normaaldrukkracht
- staalvezelversterkt beton
Summary in English is included in document, key words:
- dimensioning of underwater concrete floors
- dutch recommendation CUR77
- sensitivity analyses
- concrete technology
- use of 2D calculation models
- SLS and ULS
- axial stiffness of tension piles and sheet piles
- tension pile failure
- normal forces
- steel fibre reinforced concrete
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Utilization of Rice husk ash in GeoTechnology: Applicability and effect of the burning conditions
Rice husk ash is an attractive pozzolan. Due to its low cost and high activity it has a promising perspective in sustainable construction. In combination with lime, its effect in soil improvement can be equal to cement treatment but its production process consumes much less energy.
The main component of the rice husk ash is silica, which is the element that governs the reactivity of the ash. A delicate burning process is required to eliminate the organic components in the rice husk but keep the silica to be amorphous so that a highly reactive rice husk ash can be obtained. A too high temperature would transform amorphous silica to crystalline silica, which would reduce the reactivity. The suggested burning process in literature is 2 hours at 500oC. However, due to the exothermic property of the burning rice husk it is difficult to control the exact burning temperature, hence there is still a possibility that the carbon and the crystallized silica are present and hinder the activity of the rice husk ash. Based on the silica state and the carbon content, the rice husk ash is classified in three types: C-RHA which is collected from a quick and open-air burning and contains a large amount of carbon; Cr-RHA which is collected form slow burning at above 600oC and contains a large amount of crystallized silica; and A-RHA which is collected from the suggested burning process which is 500oC in 2 hours and is considered to be the most active.
The activity of these three types of rice husk ash and their effect in soil improvement were tested. As expected, the higher reactivity of the A-RHA compared with the Cr-RHA confirmed the capability of these burning conditions. Surprisingly, the C-RHA appeared to be the most reactive and its effect to the soil was also the most positive despite of the large carbon content and the detected crystalline silica. The high reactivity of the C-RHA derives that there is a hierarchy of the solubility depending on the burning duration so that although all the three types of ash were mainly amorphous, the C-RHA is the most soluble. From the experiments, the role of the carbon was seen in only the term of quantity as it reduce the proportion of the silica, but might it have any support to the reactivity of the material in those experiments then it needs more investigation.
The results of the treated soil showed that the rice husk ash need the lime to be activated, but then it helped to enlarge the possitive effect of the lime. The immediate effect of the additives to the plasiticity of the soil were seen to be the results of the lime only, but the long-term effect of the strength and the compression of the soil were seen to be the results of the combination between rice husk ash and lime. Especially in the case of C-RHA, it can reduce half the amount of lime in the case of 6% lime mixing to give similar undrained shear strength which was about 410 kPa. Because the carbon is not a serious harmful factor in the soil, and the soil can also take the advantage of the firmness of the quartz, so between the two cases, the rice husk ash with large carbon content and also considerable amount of quartz but higher reactivity, and the rice husk ash which is almost purely amorphous silica but less reactive, the former is the preferred for the soil improvement purpose.
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Leak-off of oil-based drilling fluids in saturated porous media: a CT scan-aided study
The static leak-off of oil-based drilling mud into liquid-saturated cores was studied experimentally. A simple model for the leak-off was first developed extending an earlier model for the static filtration into unsaturated core. CT scan aided static filtration experiments were performed in brine and oil and brine saturated cores, simulating reservoir saturation regimes. Formation of external filter cake and internal filtration of solid particles were visualized and leak-off volumes were determined as function of time. At the end of the experiments the formed external filter cake and internal particle deposition were characterised with the aid of an Electron Scanning Microscope. Using drilling fluids containing carbonate particles it was found that leak-off volumes for saturated cores are larger than for unsaturated cores. It was observed further that leak-off volumes increase with the particle size, i.e. consistently with a more permeable external filter cake and limited internal filtration. Leak-off volumes decreased when using smaller hematite particles or using larger range of (barite) particles sizes. The filtration volumes for the smaller sized drilling fluid components in brine saturated core experiments were found to be larger than filtration volumes found for dry core experiments in previous work.
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Model for gas sweep with foam
In this BSc-thesis a Surfactant-Alternating-Gas (SAG) foam displacement is represented by an idealized model. Shan and Rossen show in the article ‘Optimal Injection Strategies for Foam IOR’ (2004) that this model, though greatly simplified, is a useful representation of a foam displacement in the physical world, where pressure gradient is the most important factor in controlling gravity override.
The process of building the model and numerical problems and solutions are discussed. The foam displacement is extended beyond the range computed by Shan and Rossen, to an dimensionless position XD of 4. The following cases are considered: kv = kh, 0<kv<kh and kv = 0. A comparison shows that the smaller the kv, the less convex the foam displacement front is. Ironically, in this case, increasing vertical permeability reduces the extent of gravity segregation of gas and increases vertical sweep.
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Salt Reserve Estimate for the Twenthe-Rijn concession
AkzoNobel has been producing salt from solution-mined brine since 1919. Production in the Hengelo area started in 1933, and is still ongoing today. Because at some point in time the mineable salt will all be mined and preparations for extension of the concession will need to be made, it is important to know the remaining amount of salt in the Hengelo area. To date no singular method for estimation of these reserves has been adopted. This leaves room for the development of a local method. It was chosen to develop this method in accordance with international standards. Due to its worldwide influence and being recognised by the Amsterdam Stock Exchange that AkzoNobel is registered on, it was opted to use the code of the Joint Ore Reserves Committee (JORC) of the Australasian Institute of Mining and Metallurgy (AusIMM).
The geology of the Hengelo area was modelled using a modified version of the ordinary Kriging algorithm to take into account the presence of faults. Kriging was used because it also provides an estimate of uncertainty in the horizons that are modelled. To factor in the uncertainty about the continuity of the salt body, the resources in three areas were calculated: the area was investigated as a whole, and two sub-areas were investigated separately:
· Sub-area 1 is the area within 500m distance of any measurement in the area.
· Sub-area 2 is the area for which the geology was previously studied in great detail by GeoWulf Laboratories[5]. This area is essentially the area in-between the different measurements.
The modelled horizons and their uncertainty values were then used in a Monte Carlo simulation, yielding cumulative probability distributions for the estimated amount of salt in the three scenarios. The total amount of salt was also calculated deterministically, meaning all calculations were performed using expected values. This produced the same values as the expectations of the probabilistic approach. It was decided that the probabilistic approach of the total area produced an over-optimistic value of the total Resource, and to only use the expected values of the three areas to distinguish between Inferred, Indicated and Measured Resources.
Reserves were estimated for three scenarios:
1. Salt has been produced in the past in this area using a no longer used leaching strategy that results in large caverns with multiple wells. What would be the Salt Produced if the same locations had been chosen to produce salt using the modern Single Completion Cavern design? And what would be the historical recovery?
2. Assuming no production had taken place in the past, what would be the total Salt Reserve if the field would be developed now?
3. What is the Salt Reserve left in the area?
It was found that the recovery percentages per cavern as asked for in scenario 1 were so widespread that no conclusive numbers could be given.
The cavern lay-out throughout the area in scenarios 2 and 3 was not optimized, but because the overall estimation process was conservative the numbers could still be used as minimal values in future evaluations of the area. The results of scenario 3 are given in the table below.
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Pavement Fracture Analysis of open Devonian Anticline, Tata, Morocco
Three fracture sets have been found and analysed in the Tata anticline. The analysis consists of an analysis of the strike directions, the length of the fractures, the spacing between the fractures and the fracture intensity.
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Testing reagents to improve the recovery of ilmenite flotation at Titania A/S
Mineral processing plays an important part in providing our society with much needed resources. These processes, however, could be made much more efficient. Advancements in this field would enable a population to make economical use of its resources. One widely-used ore processing method to separate target minerals from other minerals is froth flotation. This report summarizes the method and outcome of 48 flotation experiments, performed at the Titania A/S Ilmenite mine, Hauge i Dalane, Norway, in which 6 different tall oil collectors and 2 paraffin solvents were used in a pilot scale batch process. The approach used is controlling the types and amounts of reagents, as well as the ratio between reagents. The amount of feed, rotor speed, air consumption and conditioning time are kept constant. The time of tapping concentrate is noted, dry concentrate is weighed and the TiO2-contents of the feed, tailings and concentrate are assayed. Results are qualitatively analyzed with a TiO2 recovery vs. concentrate TiO2 grade graph created in Microsoft Excel. Within the randomly occurring unmeasured ore variation the combination of Sylvatal 20S tall oil and ExxonMobil Exxsol D80 paraffin in a 2:1 volume ratio yields the best TiO2 recovery at the same concentrate grade.
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Composiet versus Staal in de Geothermie deel 2
In dit verslag zal wordt er gekeken naar effecten van formatiewater, dat een temperatuur heeft van 333 Kelvin, op een stuk casingwand. Deze onderzochte materialen zijn composiet en staal. Langs deze twee materialen wordt een stroming gecreerd met het formatie water. Hierbij zullen verschillen ontstaan tussen, voor de omstroming en na de omstroming. Ook zal er gekeken worden naar onderlinge effecten van het composiet op het staal.
Uiteindelijk is gebleken dat composiet niet tot nauwelijks wordt aangetast en staal daarentegen wel. Het onderlinge effect is dat het composiet de corrosie processen 2x versneld.
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1-D Approximation for the Simulation of Preferential Flow in Heterogeneous Landfill Conditions
The latest stage in treating Municipal Solid Waste Landfills is the aftercare of these waste sites. An important issue, concerning the aftercare of landfills, is the reduction of long term emission potentials. The research in this field, which has been carried out the last couple of decades, has lead to different concepts for describing the processes occurring inside the landfills. The knowledge gained has resulted in two approaches for enhanced stabilization of the landfill body.
The first approach is based on infiltration and recirculation of landfill leachate, which stimulates the anaerobic degradation of solid organic matter and leads to enhanced methane production. The second is based on stimulated aeration of the landfill body leading to enhanced degradation of organic matter by creating local aerobic conditions. The infiltration and recirculation of leachate has an impact on the flow of water and transport of solutes inside the landfill.
A significant amount of the research on this matter involves the interpretation of such phenomena by using water flow models for soils. Many of these models are implemented to describe such events. The research objective of this project is to create a one-dimensional two-domain model that simulates preferential flow inside landfills. In order to reach this objective an implementation of a model, which couples a two-domain flow along with the transport of solutes throughout these domains, is required. The outcome of this study will be used for an up-scaling process of the numerical modeling of the preferential flow events.
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Control of Fluvial Architecture on the Spatial Distribution of Arsenic Rich Ground Water
In Bihar, India, arsenic rich aquifers are used as a drinking water source by millions of people, even though the arsenic concentration in some places is so high it causes serious health issues. The arsenic concentrations in the aquifers show a large spatial variability, one that is presently unpredictable. The most important factors which play a role in arsenic distribution are the source (natural occurring minerals) and the redox conditions, which enable the arsenic to be released from the minerals. There is a relation between fluvial deposits and redox conditions. In addition, fluvial deposits are known to be heterogeneous, which has large influence on flow regimes. The objective of this study is therefore to investigate the fluvial deposits in the region, and to predict the control they have on the distribution of arsenic. To do so, the architecture of a point bar attached to a clay plug is mapped in the region of Bakhorapur, Bhojpur District, Bihar, India. This was done by interpreting Google Earth satellite images, with executing a transient electromagnetic survey and by drilling two boreholes of 50 m (including well logs); the cores were ultimately studied in detail. The three methods indicate that up to 28 m, two stacked, heterogeneous and laterally continuous 10-15 m thick point bars are present. Below these extensive conglomerate and coarse sand bodies of braided river origin are recognized. The end result is a geological model concept, in which fluvial reservoir architecture elements of importance for flow regimes are highlighted. The geological model concept suggests that both the initial place of release and the spreading of arsenic are to a large extent controlled by the 3D architecture of the fluvial deposits. The concept can be turned into a static model and used for flow calculations such that the user is able to predict arsenic spreading in the case of arsenic release from specific fluvial sediment bodies. Considering the region being full of similar point bar deposits, the concept is generally applicable throughout the region. With this, arsenic safe drinking spots can be located, helping a great number of people.
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The design and development of CaveCad : A state of the art integrated cave management system
This thesis describes and substantiates the design and development of CaveCad, a state of the art integrated cave management system. CaveCad is Rio Tinto proprietary software.
The scope of this project is to design, develop and implement an integrated cave management system for Rio Tinto Underground Technology Centre. A successful outcome will result in the implementation of CaveCad on all Rio Tinto caving operations.
The block caving mining method is being increasingly applied as a mass mining method used to exploit base metals and diamond resources. In block cave mining, geotechnical monitoring is fundamental to the successful management and operation of the mine. Current state of the art in monitoring, although innovative and useful, has lacked the collective integration of multiple systems from which collective information can be used to make unambiguous and timely decisions. This is the reason for the design, development and subsequent application of CaveCad.
In addition to the design and development process of CaveCad, this study includes background information on block caving and cave monitoring, data research on the relevant monitored data types and a comprehensive case study. It also includes software research into the different system components and the testing of the Geotech module, a GOCAD Mining Suite geotechnical plug-in. Finally, the first CaveCad module, which was released in December 2011, is fully described. The report concludes with a discussion, recommendations and a conclusion.
The database and system architecture comprising CaveCad has been successfully designed and developed. However, this thesis does not include the implementation phase as the first released version lacked essential functionality. The estimated release and site implementation date of the updated CaveCad module is March 2012.
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Sand Erosion in Cold Heavy Oil Production with Sand
Cold Heavy Oil Production with Sand (CHOPS) is a production method to produce heavy oil (>100 cP). It is mainly applied onshore Canada in unconsolidated sand reservoirs. Different theories exist about how the erosion process takes place inside the reservoir. This research project focused on the influence of the grain stress on the sand erosion process.
Laboratory experiments were performed to investigate the influence of grain stress on the sand erosion process. In order to carry out these experiments a high pressure radial flow cell has been developed. Inside this flow cell, oil was injected into a compressed sand pack and produced via a single perforation. During this process the sand pack was scanned using a X-ray computed tomography (CT) scanner.
Experiments were carried out at different confining pressures between 30 and 100 bar, using both oil and water as pore fluids. CT scans have revealed that the erosion process does not change when different grain stresses are applied. However, different erosion patterns were observed for experiments with the two different pore fluids.
In both oil-sand and water-sand experiments a cavity was observed at the periphery of the sample. Although it could not be visualised using the CT-scanner, calculations have shown that a “weak zone”, must have developed between the injector and the producer before a cavity became visible.
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A 3-D stress and strain analysis in a three layered model with a single fractured layer: A finite element approach
Natural fracture systems are often influenced by the presence of different layers with contrasting rock mechanical properties. Understanding the distribution of stress between different mechanical layers is essential to the interpretation of fracture networks within these systems. Knowledge of the fracture system’s geometry and spatial distribution is crucial in understanding the planning and development of any fractured reservoir.
In this study, stress/strain distributions and deformation patterns in a three layered medium with and without pre-existing fracture set are analysed. Starting from the most simple to a complex configuration, finite element models are used to understand these patterns. Stress distribution in the presence of fractures gives a better understanding of the type of failures that the rock can undergo. Stress and strain localizations at fracture tips are observed. The study indicates that tensile stresses will result in the fractured layer in response to remote compression alone given sufficient input parameters. In this case, tensile stress arises without the requirement for an additional body force such as internal fluid pressure.
Frictional sliding (displacement) causes localization of deformation at the fracture tips. The displacement intensity varies as a function of fracture orientation (α) (α: angle between the fracture strike and the bulk compression orientation). This displacement along the fractures present in the middle layer of the model also impacts the stress distribution within the surrounding layers as well. Any change in the orientation of the remote stress may lead to significant differences in the stress magnitude within the three layers.
Similar analyses have been done with increasing complexity and the impact of fracture length, spacing and overlap/underlap between the adjacent fractures are studied. It is observed that all these parameters not only impact the stress and strain distribution within the fractured layer but also have a significant or subtle impact on the surrounding layers.
The study also aims to predict if these patterns are localized or if deformation between the fractures is also influenced by these parameters. The scenario with two fractures is therefore used to investigate the influence of one fracture on the other and it is observed that the stresses are compressive in nature and the magnitude is influenced by the fracture spacing and fracture overlap/underlap.
The study gives a confirmation on why finite element modelling is one of the better tools to do such an analysis and more importantly that it gives a first-hand understanding of the impact on such a system under external stress.
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Computing the vertical density and seismic velocity profiles from multi-angle reflection data: error analysis
Numerical models were used to recursively compute the density profile and the seismic velocity profile of three different artificial models of the underground from primary reflection images obtained from multi-angle incident plane wave reflection data. The aim is to investigate the effect of errors in the obtained primary reflection amplitudes on the recursive construction of the vertical density-velocity profiles. The reflection coefficients needed for the computations were obtained by solving the Marchenko equation for different angles of incidence. The recursive computation shows errors occur in every layer, but the error does not necessarily grow with each step. This implies the error does not propagate into the recursive scheme. Adding a random error to the reflection coefficients yielded results in a greater error in each individual layer with respect to the values obtained without an added error. Using a too large angle of incidence can result in too few primary events in the autofocused data, distorting the computed values.
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