pseudo-3D Model Research Articles

Automatic Generation of Stippling Illustrations from two Photographs

<p>In this paper we present a software tool that is able to reconstruct the depth field of the objects from two photographs and to obtain a pseudo 3D model. Using this information our system is able to difference background from foreground, and therefore, what are the interesting elements in the photographs and stipple them in different ways.<br />This tool needs almost no user interaction. The user simply has to align both photographs and indicate the level of detail according to the distance. The rest is decided by our software. Whereas a professional illustrator needs more than 20 hours to finish a similar illustration, our software is able to do it in just few seconds.</p>

Digital Representation of Historical Globes: Methods to Make 3D and Pseudo-3D Models of Sixteenth Century Mercator Globes

In this paper, the construction of digital representations of a terrestrial and celestial globe will be discussed. Virtual digital (3D) models play an important role in recent research and publications on cultural heritage. The globes discussed in this paper were made by Gerardus Mercator (1512–1594) in 1541 and 1551. Four techniques for the digital representation are discussed and analysed, all using high-resolution photographs of the globes. These photographs were taken under studio conditions in order to get equal lighting and to avoid unwanted light spots. These lighting conditions are important, since the globes have a highly reflective varnish covering. Processing these images using structure from motion, georeferencing of separate scenes and the combination of the photographs with terrestrial laser scanning data results in true 3D representations of the globes. Besides, pseudo-3D models of these globes were generated using dynamic imaging, which is an extensively used technique for visualisations over the Internet. The four techniques and the consequent results are compared on geometric and radiometric quality, with a special focus on their usefulness for distribution and visualisation during an exhibition in honour of the five hundredth birthday of Gerardus Mercator.

Linear Elastic and Cohesive Fracture Analysis to Model Hydraulic Fracture in Brittle and Ductile Rocks

Hydraulic fracturing technology is being widely used within the oil and gas industry for both waste injection and unconventional gas production wells. It is essential to predict the behavior of hydraulic fractures accurately based on understanding the fundamental mechanism(s). The prevailing approach for hydraulic fracture modeling continues to rely on computational methods based on Linear Elastic Fracture Mechanics (LEFM). Generally, these methods give reasonable predictions for hard rock hydraulic fracture processes, but still have inherent limitations, especially when fluid injection is performed in soft rock/sand or other non-conventional formations. These methods typically give very conservative predictions on fracture geometry and inaccurate estimation of required fracture pressure. One of the reasons the LEFM-based methods fail to give accurate predictions for these materials is that the fracture process zone ahead of the crack tip and softening effect should not be neglected in ductile rock fracture analysis. A 3D pore pressure cohesive zone model has been developed and applied to predict hydraulic fracturing under fluid injection. The cohesive zone method is a numerical tool developed to model crack initiation and growth in quasi-brittle materials considering the material softening effect. The pore pressure cohesive zone model has been applied to investigate the hydraulic fracture with different rock properties. The hydraulic fracture predictions of a three-layer water injection case have been compared using the pore pressure cohesive zone model with revised parameters, LEFM-based pseudo 3D model, a Perkins-Kern–Nordgren (PKN) model, and an analytical solution. Based on the size of the fracture process zone and its effect on crack extension in ductile rock, the fundamental mechanical difference of LEFM and cohesive fracture mechanics-based methods is discussed. An effective fracture toughness method has been proposed to consider the fracture process zone effect on the ductile rock fracture.

Effects of instrument orientation on small-loop electromagnetic induction surveys of localized 2D conductive targets

Frequency-domain electromagnetic induction (EMI) systems, composed of two coplanar small coils separated by a fixed distance (EMI or SLEM), enable the rapid detection of a great variety of near-surface structures. One coil generates a controlled, primary magnetic field and the other records the variations of the induced field while the instrument is moved over the studied area. The most usual acquisition configuration corresponds to horizontal coils, with the instrument axis parallel to the prospection lines. Usually, the interpretation is based on the direct visualization of the plan-views of the data measured at each frequency. In addition, to characterize the subsoil structure in-depth, 1D inversion methods are generally applied. The aim of this work is to analyse how the system orientation affects the ability of the method to detect localized, 2D conductive structures, buried at shallow depths, and the possibility of adequately characterizing these targets through 1D inversions. We performed a survey at a test site that contains two known structures of this type, buried in almost perpendicular directions. We performed parallel prospection lines in the direction of each structure, employing, aside from the usual configuration described before, other configurations that included horizontal and vertical coils, with the instrument axis parallel and perpendicular to the lines. For comparison, we also performed a geoelectric dipole–dipole line crossing one of the targets. The features of the anomalies observed in the graphs of the EMI apparent conductivity data strongly depend on the instrument orientation. In the horizontal coil configurations, a decrease of the apparent conductivity is observed just over the targets. Besides, each vertical configuration practically detects only the target aligned with the plane of the coils, as an important positive anomaly. Through numerical simulations, performed using a 2D forward modelling method, we demonstrate that these features are indeed 2D effects associated with the localized character of the studied conductive objects. Then, we applied to the data a 1D inversion method and drawing together the results generated pseudo 3D models of the subsoil. We found that the models obtained for the vertical coil configurations provide better results. They detect the targets as conductive structures and provide a rather good estimation of their depths. Finally, we compare the EMI results with the image obtained from the 2D inversion of the geoelectrical data and analyse the causes of the observed differences.

A Review of Hydraulic Fracture Models and Development of an Improved Pseudo-3D Model for Stimulating Tight Oil/Gas Sand

Many injection/production wells have been hydraulically fractured to enhance injectivity/productivity. Various engineering models for fracture geometry have been developed, which define the propagation of a fracture with time and wellbore treatment pressure. These models combine with elasticity, fluid flow, material balance, and propagation criterion/in-situ stresses. When this combination describes the fracture dimensions, the fracture-geometry can be of two-dimensional (2D) and three-dimensional (3D), depending on the number of dimensional variables. For design purposes, several 2D and 3D models are already developed. But it is still a concern in the oil industry as to which model is beneficial to design optimum treatment parameters for a particular tight sand, because despite many successes, there have been many wells of poor post-fracture productivity. This article provides a review of 2D and 3D fracture models for prediction of fracture geometry. A P-3D (pseudo) model has been improved by incorporating Carter solution of material balance for the first time and was named P-3D-C model, which has predicted higher fracture conductivity. The improved model is highly potential for repetitive computation in hydraulic fracture design optimization.

Analysis of the classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers

This paper deals with the so-called “pseudo three-dimensional” (P3D) model for a hydraulic fracture with equilibrium height growth across two symmetric stress barriers. The key simplifying assumptions behind the P3D model are that (i) each cross section perpendicular to the main propagation direction is in a condition of plane-strain, and (ii) the local fracture height is determined by a balance between the effect of the stress jump across the barriers and that of the rock toughness. Furthermore, in the equilibrium height growth P3D models, the pressure is assumed to be uniform in each vertical cross-section. We revisit this particular model by first formulating the non-linear differential equations governing the evolution of the length, height, and aperture of the hydraulic fracture, in contrast to the numerical formulations adopted in many previous studies. Scaling of these equations shows that the solution depends, besides the dimensionless space and time coordinates, on only two numbers representing a scaled toughness and a scaled leak-off coefficient. Analysis of the governing equations enables us to determine explicitly the conditions under which breakthrough takes place (i.e., the onset of growth into the bounding layers), as well as the conditions of unstable height growth (i.e., the conditions of “runaway height” when the main assumptions of the equilibrium height model become invalid). The mathematical model is solved numerically using a novel implicit fourth order collocation scheme on a moving mesh, which makes explicit use of the fracture tip asymptotics. We then report the results of several numerical simulations conducted for different values of the dimensionless toughness and the dimensionless leak-off coefficients, as well as a comparison with closed-form small and large time similarity solutions that are valid under conditions where the fracture remains contained within the reservoir layer.

Trishear in 3D. Algorithms, implementation, and limitations

The algorithms and implementation of pseudo-3D and true-3D trishear models are explained, including a strategy to model lateral fault propagation. I show that the pseudo-3D algorithm is adequate and sufficient to model trishear in three-dimensions. Although ad-hoc, the pseudo-3D algorithm preserves volume in simulations without and with lateral fault propagation. A disadvantage of the pseudo-3D algorithm is that it produces very simple, and perhaps not realistic hanging wall geometries, specially in simulations in which the fault slip varies along strike. The true-3D algorithm has a more elaborate and richer kinematics that produces more realistic hanging wall geometries. However, the true-3D algorithm contains mathematical inconsistencies that result in considerable volume changes when the slip gradients along the tip line are high and the tip line is highly oblique to the slip vector and/or the fault strike. The volume changes occur to a large extent in the hanging wall, and to a minor extent in the forelimb and footwall areas.

Geothermal history and petroleum generation in the Norwegian South Viking Graben revealed by pseudo-3D basin modelling

Hydrocarbon exploration in the Norwegian South Viking Graben (57°45′–60°15′N) began in the late 1960s and has now entered a mature phase. A map-based pseudo-three-dimensional (3D) basin modelling study is performed in order to unravel regional trends in hydrocarbon generation and expulsion and to evaluate the remaining potential of this mature petroleum province. Generation and expulsion from all major source rock horizons in the area, the Draupne, Heather, Hugin and Sleipner Formations, is simulated using a pseudo-3D model comprising 36 isochronous geological events. The map-based pseudo-3D model is built from 1D models, combined with subsurface and source rock quality maps. Hydrocarbon expulsion from the Middle and Upper Jurassic source rocks in the area occurred in two major phases. The first phase lasted from Palaeocene to Middle Miocene with peak oil and gas expulsion during the Early Miocene. The second, Quaternary, phase of expulsion, which supplied 11% and 13% of all oil and gas, respectively, is related to increased subsidence rates during this period. A total of 74×10 9 Sm 3 oil and 8.2×10 12 Sm 3 gas has been expelled in the area. The Frigg area in the north is with 2.9×10 12 Sm 3 gas expelled the most gas-prone area, and the Greater Balder area seems to be the most oil-prone area with 17×10 9 Sm 3 oil expelled. The lower, syn-rift section of the Upper Jurassic Draupne Formation dominated oil expulsion (54% of all expelled oil), whilst the Heather Formation dominated gas expulsion with 37% of all gas expelled. Model predictions were successfully applied to explain the fill and secondary alteration history of the Greater Balder Area, Norway. The modelling supports the Draupne Formation origin of the oils in the Greater Balder Area, as well as the presence of oils deriving from multiple charge phases found in correlation studies. Based on the modelled cumulative volumes expelled and estimates for in-place volumes in the area, generation–accumulation efficiencies (GAEs) of 1.01–1.05% for oil and 9.67–12.89% for gas have been estimated for the South Viking Graben. In light of comparisons with other petroleum systems and critical evaluation of the elements of the petroleum systems, the estimated GAEs should be regarded as encouraging for further exploration of the area.

Image Interpolation Using Enhanced Multiresolution Critical-Point Filters

There are increasing demands for image interpolation in various fields such as virtual reality, computer animation, and video transmission. The critical-point filters (CPF) we have proposed previously enable completely automatic matching of two images. In our previous method, however, it has taken a long time to compute the optimal parameter values by iterative searches. This paper proposes an improved algorithm called the enhanced critical-point filters (ECPF) where the parameters are stably computed using together the inverse mapping from the destination to the source. It takes only a second to match images whose size is 64 × 64. The algorithm is also improved in its precision by directly handling color images while the previous algorithm has taken only the intensity value into account. We apply ECPF to keyframe interpolation of video sequences. We also apply ECPF to interpolating two different views of an object to generate any intermediate views. In this case, there are many constraints that can be used to determine the mapping between the images. We propose a method to use such constraints to improve the accuracy of the mappings. As the results, image-based pseudo-3D models are easily created from a set of views without any special devices.

95/01253 Super-barge saddles up for drilling duties

Hydrocarbon exploration in the Norwegian South Viking Graben (57°45′–60°15′N) began in the late 1960s and has now entered a mature phase. A map-based pseudo-three-dimensional (3D) basin modelling study is performed in order to unravel regional trends in hydrocarbon generation and expulsion and to evaluate the remaining potential of this mature petroleum province. Generation and expulsion from all major source rock horizons in the area, the Draupne, Heather, Hugin and Sleipner Formations, is simulated using a pseudo-3D model comprising 36 isochronous geological events. The map-based pseudo-3D model is built from 1D models, combined with subsurface and source rock quality maps.Hydrocarbon expulsion from the Middle and Upper Jurassic source rocks in the area occurred in two major phases. The first phase lasted from Palaeocene to Middle Miocene with peak oil and gas expulsion during the Early Miocene. The second, Quaternary, phase of expulsion, which supplied 11% and 13% of all oil and gas, respectively, is related to increased subsidence rates during this period. A total of 74×109 Sm3 oil and 8.2×1012 Sm3 gas has been expelled in the area. The Frigg area in the north is with 2.9×1012 Sm3 gas expelled the most gas-prone area, and the Greater Balder area seems to be the most oil-prone area with 17×109 Sm3 oil expelled. The lower, syn-rift section of the Upper Jurassic Draupne Formation dominated oil expulsion (54% of all expelled oil), whilst the Heather Formation dominated gas expulsion with 37% of all gas expelled.Model predictions were successfully applied to explain the fill and secondary alteration history of the Greater Balder Area, Norway. The modelling supports the Draupne Formation origin of the oils in the Greater Balder Area, as well as the presence of oils deriving from multiple charge phases found in correlation studies.Based on the modelled cumulative volumes expelled and estimates for in-place volumes in the area, generation–accumulation efficiencies (GAEs) of 1.01–1.05% for oil and 9.67–12.89% for gas have been estimated for the South Viking Graben. In light of comparisons with other petroleum systems and critical evaluation of the elements of the petroleum systems, the estimated GAEs should be regarded as encouraging for further exploration of the area.

Appraisal of Erosional Sequence Boundaries and Facies Successions in Periglacial Environment by Pseudo-3D Modelling: ABSTRACT

Appraisal of Erosional Sequence Boundaries and Facies Successions in Periglacial Environment by Pseudo-3D Modelling: ABSTRACT

Pseudo-3D Modeling of the Combined Evolution of Salt and Sediments - A North Sea Case History: ABSTRACT

Pseudo-3D Modeling of the Combined Evolution of Salt and Sediments - A North Sea Case History: ABSTRACT

A magnetotelluric investigation of the structural geology beneath Charlevoix Crater, Quebec

The results of ten tensor magnetotelluric soundings recorded within the Charlevoix crater are presented. The geological complexity of the region (the crater is located at the junction of two major geological provinces, i.e. the crystalline basement of the Canadian shield and the more conductive sediments of the Appalachian system) and the amount of cultural noise present in our data prevent a highly definitive interpretation of the shallow structure. A subhorizontal conductive fault related to Rondot's (1971) structural sketch of the original impact structure may exist within the upper 5 km, but it is not completely constrained by the data. Pseudo 3D modelling using stacked thin sheets indicates that superficial patches of high conductivity may explain the large anisotropy observed at the long periods and suggests that our deeper structures fit well with the 2D model previously proposed by Kurtz (1982) for the region.

Quantitative Analysis of Factors Influencing Vertical and Lateral Fracture Growth

Summary This paper presents contributions to the modeling of the vertical and lateral propagation of hydraulic fractures. The first part presents a method for the quantitative analysis of factors controlling vertical height growth in three-dimensional (3D) fracture propagation. Included are confining stress contrast, elastic stiffness contrast, fracture toughness, and influence of settled (or buoyant) proppant on height growth. A composite propagation function was formulated that can be implemented in a pseudo3D model of fracture geometry or in hand calculations. The second part extends the formulations of the lumped models for lateral fracture growth to handle dynamic conditions existing in the field. The new formulation can handle variable injection rates, fluid rheology changes, and multiple fluids and includes fracture toughness at the tip. The results are presented in the form of dimensionless charts, and their use is explained through an example.

Comparison of Hydraulic Fracture Models for Highly Elongated Fractures of Variable Height

There is a pressing need to compare and evaluate hydraulic fracture models which are now being used by industry to predict variable fracture height. The fractures of concern here are vertical fractures which have a pronounced elongation in the direction of the payzone, i.e., there is a dominant one-dimensional fluid flow along the payzone direction. A summary is given of the modeling entailed in the basic ORU fracture model, which calculates fracture height as a function of distance from the wellbore in the case of a continuous sand bounded by zones of higher (but equal) minimum in-situ stress. The elastic parameters are assumed the same in each layer, and injected flow rates and fluid parameters are taken to be constant. Leak-off is included with spurt loss, as well as non-Newtonian flow. An advantage of the model is its small computer run time. Predictions for wellbore height and pressure from the ORU model are compared separately with the AMOCO and MIT pseudo-3D models. In one instance of high stress contrast the ORU wellbore pressure agrees fairly well with the AMOCO model, but the AMOCO wellbore height is greater by 32 percent. Comparison between the ORU and MIT models in two cases (also high stress contrast) indicates height disagreement at the wellbore by factors of 1.5–2.5 with the MIT model giving a lower height. Thus it appears there can be substantial discrepancies between all three models. Next we compare the ORU model results with six cases of elongated fractures from the TERRA-TEK fully-3D model. Although two of these cases are precluded due to anomolous discrepancies, the other four cases show reasonable agreement. We make a critical examination of assumptions that differ in all the models (e.g., the effective modulus-stiffness multiplier approximation in the AMOCO model, the effect of finite fluid flow in the vertical direction in the MIT model, and the effect of 2D flow and limited perforated height in the TERRA-TEK model). Suggestions are made for reconciling some of the discrepancies between the various models. For example, the ORU/AMOCO height discrepancy appears to be resolved; for other discrepancies we have no explanation. Our main conclusion is that the AMOCO, TERRA-TEK and ORU models for fracture height and bottomhole pressure are in reasonable agreement for highly elongated fractures. Despite the difficulties in understanding the different models, the comparisons herein are an encouraging first step towards normalizing these hydraulic fracture models.