420 research outputs found
Fractal Heterogeneous Media
A method is proposed for generating compact fractal disordered media, by
generalizing the random midpoint displacement algorithm. The obtained
structures are invasive stochastic fractals, with the Hurst exponent varying as
a continuous parameter, as opposed to lacunar deterministic fractals, such as
the Menger sponge. By employing the Detrending Moving Average algorithm [Phys.
Rev. E 76, 056703 (2007)], the Hurst exponent of the generated structure can be
subsequently checked. The fractality of such a structure is referred to a
property defined over a three dimensional topology rather than to the topology
itself. Consequently, in this framework, the Hurst exponent should be intended
as an estimator of compactness rather than of roughness. Applications can be
envisaged for simulating and quantifying complex systems characterized by
self-similar heterogeneity across space. For example, exploitation areas range
from the design and control of multifunctional self-assembled artificial nano
and micro structures, to the analysis and modelling of complex pattern
formation in biology, environmental sciences, geomorphological sciences, etc
A Multiscale Guide to Brownian Motion
We revise the Levy's construction of Brownian motion as a simple though still
rigorous approach to operate with various Gaussian processes. A Brownian path
is explicitly constructed as a linear combination of wavelet-based "geometrical
features" at multiple length scales with random weights. Such a wavelet
representation gives a closed formula mapping of the unit interval onto the
functional space of Brownian paths. This formula elucidates many classical
results about Brownian motion (e.g., non-differentiability of its path),
providing intuitive feeling for non-mathematicians. The illustrative character
of the wavelet representation, along with the simple structure of the
underlying probability space, is different from the usual presentation of most
classical textbooks. Similar concepts are discussed for fractional Brownian
motion, Ornstein-Uhlenbeck process, Gaussian free field, and fractional
Gaussian fields. Wavelet representations and dyadic decompositions form the
basis of many highly efficient numerical methods to simulate Gaussian processes
and fields, including Brownian motion and other diffusive processes in
confining domains
An FFT-based framework for predicting corrosion-driven damage in fractal porous media
Understanding fracture in cementitious materials caused by the deposition and
growth of corrosion products requires scale-bridging approaches due to the
large length-scale difference between the micro-pores, where deposition occurs,
and the structure, where deterioration manifests. Cementitious materials bear a
highly heterogeneous micro-structure owing to the fractal nature of
micro-pores. Simultaneously, a corrosion-driven fracture is a multi-physics
problem involving ionic diffusion, chemical reactions, and stress development.
This multi-scale and multi-physical character makes scale-bridging studies
computationally costly, often leading to the use of simplified fractal porous
media, which has important consequences for the quantitative interpretation of
the results. Recent advances in homogenization approaches using
Fast-Fourier-Transform (FFT) based methods have raised interest due to their
ease of implementation and low computational cost. This paper presents an
FFT-based framework for solving corrosion-driven fractures within fractal
porous media. We demonstrate the effectiveness of the Fourier-based spectral
method in resolving the multiple corrosion-driven mechanisms such as ionic
diffusion, stress development, and damage within a fractal porous
microstructure. Based on the presented methodology, we analyze the impact of
simplifying fractal porous media with simple Euclidean geometry on
corrosion-driven fracture. Our results demonstrate the importance of preserving
both the porosity and fractal nature of pores for precise and reliable modeling
of corrosion-driven failure mechanisms
Synthetic Fractal Modelling of Heterogeneous and Anisotropic Reservoirs for use in Simulation Studies: Implications on their Hydrocarbon Recovery Prediction
Optimising production from heterogeneous and anisotropic reservoirs challenges the modern hydrocarbon industry because such reservoirs exhibit extreme inter-well variability making them very hard to model. Reasonable reservoir models can be obtained using modern statistical techniques, but all of them rely on significant variability in the reservoir only occurring at a scale at or larger than the inter-well spacing. In this paper we take a different, generic, approach. We have developed a method for constructing realistic synthetic heterogeneous and anisotropic reservoirs which can be made to represent the reservoir under test. The main physical properties of these synthetic reservoirs are distributed fractally. The models are fully controlled and reproducible and can be extended to model multiple facies reservoir types. This paper shows how the models can be constructed and how they have been tested. Varying the fractal dimension and anisotropy factor of each of these physical properties can tell us how sensitive the reservoir is to uncertainties in its heterogeneity and anisotropy as well as how poroperm cross-plot shapes are controlled. Initial reservoir simulation results of the tested models with this approach show that heterogeneity in the reservoir's physical parameters has a little effect on high and moderate porosity and permeability reservoirs. The effect is more pronounced in the models representing tight reservoirs. The production from more heterogeneous reservoirs lasts a little longer, but eventually declines faster. This may be attributed to the fact that water channelling is more significant as heterogeneity increases
Study of Supercritical CO2 Displacing Water at the Pore Scale and Its Relevance at the Core Scale and Beyond
The advent of carbon sequestration and rapidly decreasing cost of computing creates opportunities in reservoir characterization for carbon storage. Reservoir description has been based on conventional seismic and well-log analysis which may be uncertain in real environments. In recent years, there had been interests in understanding the underlying physics behind multiphase flows in small scales. With the advancement in imaging technology, it is possible to reconstruct real porous media for simulation purposes. All the previous studies have the information gathered at the pore scale and have been limited by the uncertainty of how to use it. Upscaling of such information has always been a topic of great challenge in the fields of geology, hydrogeology, and petroleum engineering.
Multiphase lattice Boltzmann method (LBM), a proven tool to simulate flows in porous media, was applied to simulate flows in porous media at the pore scale (above the representative element volume (REV) size threshold) to gather permeability and relative permeability data. Artificially created fields of permeability and relative permeability are used as benchmarks. Cores extracted from these fields were used in kriging to recreate the fields. Pores from the cores were extracted and used as individual data points for kriging. Comparing the core kriged and pore kriged fields showed that while only modest improvements in permeability field accuracy of 4-16% was seen, large accuracy improvements in relative permeability fields of 55-82% was observed
Design and Topology Optimisation of Tissue Scaffolds
Tissue restoration by tissue scaffolding is an emerging technique with many potential applications. While it is well-known that the structural properties of tissue scaffolds play a critical role in cell regrowth, it is usually unclear how optimal tissue regeneration can be achieved. This thesis hereby presents a computational investigation of tissue scaffold design and optimisation. This study proposes an isosurface-based characterisation and optimisation technique for the design of microscopic architecture, and a porosity-based approach for the design of macroscopic structure. The goal of this study is to physically define the optimal tissue scaffold construct, and to establish any link between cell viability and scaffold architecture. Single-objective and multi-objective topology optimisation was conducted at both microscopic and macroscopic scales to determine the ideal scaffold design. A high quality isosurface modelling technique was formulated and automated to define the microstructure in stereolithography format. Periodic structures with maximised permeability, and theoretically maximum diffusivity and bulk modulus were found using a modified level set method. Microstructures with specific effective diffusivity were also created by means of inverse homogenisation. Cell viability simulation was subsequently conducted to show that the optimised microstructures offered a more viable environment than those with random microstructure. The cell proliferation outcome in terms of cell number and survival rate was also improved through the optimisation of the macroscopic porosity profile. Additionally artificial vascular systems were created and optimised to enhance diffusive nutrient transport. The formation of vasculature in the optimisation process suggests that natural vascular systems acquire their fractal shapes through self-optimisation
Design and Topology Optimisation of Tissue Scaffolds
Tissue restoration by tissue scaffolding is an emerging technique with many potential applications. While it is well-known that the structural properties of tissue scaffolds play a critical role in cell regrowth, it is usually unclear how optimal tissue regeneration can be achieved. This thesis hereby presents a computational investigation of tissue scaffold design and optimisation. This study proposes an isosurface-based characterisation and optimisation technique for the design of microscopic architecture, and a porosity-based approach for the design of macroscopic structure. The goal of this study is to physically define the optimal tissue scaffold construct, and to establish any link between cell viability and scaffold architecture. Single-objective and multi-objective topology optimisation was conducted at both microscopic and macroscopic scales to determine the ideal scaffold design. A high quality isosurface modelling technique was formulated and automated to define the microstructure in stereolithography format. Periodic structures with maximised permeability, and theoretically maximum diffusivity and bulk modulus were found using a modified level set method. Microstructures with specific effective diffusivity were also created by means of inverse homogenisation. Cell viability simulation was subsequently conducted to show that the optimised microstructures offered a more viable environment than those with random microstructure. The cell proliferation outcome in terms of cell number and survival rate was also improved through the optimisation of the macroscopic porosity profile. Additionally artificial vascular systems were created and optimised to enhance diffusive nutrient transport. The formation of vasculature in the optimisation process suggests that natural vascular systems acquire their fractal shapes through self-optimisation
Numerical Modeling of Fluid Migration in Hydraulically Fractured Formations
Economic production from low permeability shale gas formations has been made possible by the introduction of horizontal drilling and hydraulic fracturing. To ensure that gas production from these formations is optimized and carried out in an environmentally friendly approach, knowledge about the patterns of gas flow in the shale reservoir formation is required. This work presents the development of a shale gas reservoir model for the characterization of flow behavior in hydraulically fractured shale formations. The study also seeks to develop more computationally efficient approaches towards the modeling of complex fracture geometries. The model evaluates the migration patterns of gas in the formations, and investigates the range of physical conditions that favor the direction of gas flux towards the wellbore and decreases the
probability of gas escape into the overlying formation.
Two conceptual models that bypass the need for explicit fracture domains are utilized for
this study, the semi-explicit conceptual model and the fractured continuum model. Fracture complexity is accounted for by modeling induced secondary hydraulic fractures. A novel approach to modeling the secondary fractures, which utilizes asymmetrical fractal representations is also implemented, and the governing equations for flow in the system are solved numerically using COMSOL Multiphysics 4.4b, a finite-element analysis software package. A parametric study is conducted on the reservoir and fracture properties and an assessment of their impacts on the production and formation leak off rates examined.
The study results are presented and analyzed using a combination of transient pressure
surface maps, production rate data curves and transient velocity distribution maps. Optimization of gas production rates from the studied formation is shown to be achievable by the use of long lateral fractures placed orthogonal to the wellbore. There is a need for an accounting of the distinct fracture systems present in a fractured formation for the accurate prediction of production values and flow patterns arising in the formation. This work extends the understanding associated with shale gas reservoir modeling and demonstrates the applicability of the fractured continuum model
approach for the simulation of complex fractured shale formations
- …