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This dissertation aims to propose a new and practical method to obtain equivalent fracture network permeability (EFNP), which represents and replaces all the existing fractures located in each grid block for the reservoir simulation of naturally fractured reservoirs. To achieve this, first the relationship between different geometrical properties of fracture networks and their EFNP was studied. A MATLAB program was written to generate many different realizations of 2-D fracture networks by changing fracture length, density and also orientation. Next, twelve different 2-D fractal-statistical properties of the generated fracture networks were measured to quantify different characteristics. In addition to the 2-D fractal-statistical properties, readily available 1-D and 3-D data were also measured for the models showing variations of fracture properties in the Z-direction. The actual EFNP of each fracture network was then measured using commercial software called FRACA. The relationship between the 1-, 2- and 3-D data and EFNP was analyzed using multivariable regression analysis and based on these analyses, correlations with different number of variables were proposed to estimate EFNP. To improve the accuracy of the predicted EFNP values, an artificial neural network with the back-propagation algorithm was also developed. Then, using the experimental design technique, the impact of each fracture network parameter including fracture length, density, orientation and conductivity on EFNP was investigated. On the basis of the results and the analyses, the conditions to obtain EFNP for practical applications based on the available data (1-D well, 2-D outcrop, and 3-D welltest) were presented. This methodology was repeated for natural fracture patterns obtained mostly from the outcrops of different geothermal reservoirs. The validity of the equations was also tested against the real welltest data obtained from the fields. Finally, the concept of the percolation theory was used to determine whether each fracture network in the domain is percolating (permeable) and to quantify the fracture connectivity, which controls the EFNP. For each randomly generated fracture network, the relationship between the combined fractal-percolation properties and the EFNP values was investigated and correlations for predicting the EFNP were proposed. As before, the results were validated with a new set of fracture networks. / Petroleum Engineering

Polymer matrix composites reinforced by metal fibers are observed to present an onset of the insulator-to-conductor transition through previous experimental studies. Analytical studies revealed that the percolation threshold occurs when fiber volume fraction reaches the critical value. The numerical study based on Monte Carlo simulations are performed to investigate such a relation. In this work, the conductive fillers are modeled as a three dimensional (3D) network of identical units randomly distributed in the polymer matrix. For the simplest case, straight fibers are used in the simulation. The effects of the aspect ratio and fiber length on the critical volume fraction are also studied. Linearization is made to the logarithm of simulation results. Next, in order to study the effects of emulsion particles and the emulsion particle sizes on the percolation behavior, cubic particles are aligned in the sample model. The gap width to particle size ratio is fixed at 1/10. The calculated critical volume fraction is used in the power-law function to predict the electrical conductivity of the polymer composites. Due to the insensitivity of the thermal conductivity to the percolation threshold, a combination of two empirical equations is used to predict the range of overall thermal conductivity.

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The cyber-physical systems (CPS), such as smart grid and intelligent transportation system, permeate into our modern societies recently. The infrastructures in such systems are closely interconnected and related, e.g., the intelligent transportation system is based on the reliable communication system, which requires the stable electricity provided by power grid for the proper function. We call such mutually related systems interdependent networks. This thesis addresses the cascading failure issue in interdependent cyber physical system. We consider CPS as a system that consists of physical-resource and computational-resource networks. The failure in physical-resource network might cause the failures in computational-resource network, and vice versa. This failure may recursively occur and cause a sequence of failures in both networks. In this thesis, we propose two novel interdependence models that better capture the interdependent networks. Then, we study the effect of cascading failures using percolation theory and present the detailed mathematical analysis on failure propagation in the system. By calculating the size of functioning parts in both networks, we analyze the robustness of our models against the random attacks and failures. The cascading failures in smart grid is also investigated, where two types of cascading failures are mixed. We estimate how the node tolerance parameter T (ratio of capacity to initial workload) affect the system performance. This thesis also explores the small clusters. We give insightful views on small cluster in interdependent networks, under different interdependence models and network topologies.

The foreseen massive deployment of the internet of things (IoT) is expected to suffer from high security risks. This mainly results from the difficulty to monitor and cure the IoT devices in such large-scale deployment. In this thesis, we propose a spatial random deployment of special nodes (firewalls) which can detect and cure infected nodes within certain radius. An important concern is to add sufficient number of firewalls to make an epidemics finite and, hence, prevent malware outbreak over the whole network. The problem will be analyzed using percolation theory. Namely, we derive an upperbound for the critical intensity of spatial firewalls which guarantees prevention of large-scale network epidemics, regardless of the intensity of regular nodes. Using tools from percolation theory, we analyze the proposed solution and show the conditions required to ensure its efficiency.

Comets, remnants of the solar system's formation, exhibits partially unexplained outbursts that are closely tied to the physical structure of the nucleus. To investigate outbursts, we employed pore network modeling techniques, such as the Bower-Watson algorithm and Voronoi diagrams, to better represent the nucleus' complex porous structure and simulate gas transfer processes. We examined heat diffusion in the comet's subsurface and its influence on crystallization. The extra heat generated by crystallization can shift the crystalline front deeper into the nucleus, accelerating subsurface evaporation rates. This process results in the formation of a thicker ice mantle with reduced porosity on the surface, trapping evaporated gas in the underlying layers. As gas pressure accumulates over time, the mantle eventually succumbs to the buildup. By applying percolation theory, we identified the critical point at which trapped gas breaks through the surface, ultimately leading to a better understanding of comet outburst formation.

This work describes a model of the piezoresistive behavior in nanocomposite sensors. These sensors are also called flexible sensors because the polymer matrix allows for large deformations without failure. The sensors have conductive nanoparticles dispersed through an insulative polymer matrix. The insulative polymer gaps between nanoparticles are assumed to be possible locations for electron tunneling. When the distance between two nanoparticles is small enough, electrons can tunnel from one nanoparticle to the next and ultimately through the entire sensor. The evolution of this gap distance with strain is important to understand the overall conductivity of the strain sensor. The gap evolution was modeled in two ways: (1) applying Poisson's contraction to the sensor as a homogenous material, referred to as Simple Poisson's Contraction (SPC) and (2) modeling the nanoparticle-polymer system with Finite Element Analysis (FEA). These two gap evolution models were tested in a random resistor network model where each polymer gap was treated as a single resistor in the network. The overall resistance was calculated by solving the resistor network system. The SPC approach, although much simpler, was sufficient for cases where various orientations of nanoparticles were used in the same sensor. The SPC model differed significantly from the FEA, however, in cases where nanoparticles had specific alignment, e.g. all nanoparticles parallel to the tensile axis. It was also found that the distribution used to determine initial gap sizes for the polymer gaps as well as the mean of that distribution significantly impacted the overall resistivity of the sensor.Another key part of this work was to determine if the piezoresistivity in the sensors follows a percolation type behavior under strain. The conductance versus strain curve showed the characteristic s-curve behavior of a percolative system. The conductance-strain curve was also compared to the effective medium and generalized effective medium equations and the latter (which includes percolation theory) fit the random resistor network much more closely. Percolation theory is, therefore, an accurate way to describe this polymer-nanoparticle piezoresistive system.Finally, the FEA and SPC models were compared against experimental data to verify their accuracy. There are also two design problems addressed: one to find the sensor with the largest gauge factor and another to determine how to remove the characteristic initial spike in resistivity seen in nanocomposite sensors.

No description available.

Reliable signal transmission among cells is important for long-range coordination. While higher organisms have designated structures for signal transmission, such as axons, it remains unclear how simpler communities of cells are organized to relay signals. Furthermore, many biological systems exhibit spatial heterogeneity, which can interrupt signal propagation. In this thesis, we investigate this problem by modeling the spatial organization and dynamics of electrochemical signaling, and we compare our results to experiments from our collaborators on Bacillus subtilis bacterial biofilms. The experiments show that only a fraction of cells participates in signal propagation and that these cells are spatially clustered with a size distribution that follows a power-law decay. These observations suggest that the fraction of participating cells is just at the tipping point between a disconnected and a fully connected conduit for signal transmission. We utilize percolation theory and a minimal FitzHugh-Nagumo-type excitable dynamics model to test this hypothesis, and genetically modified biofilms with altered structure and dynamics to validate our modeling. Our results suggest that the biofilm is organized near the critical percolation point in order to negotiate the benefit and cost of long-range signal transmission. Then, more detailed experiments show that the participation probability is correlated from cell to cell and varies in space. We use these observations to develop an enhanced percolation model, and show using simulations and a renormalization argument that the main conclusions are unaffected by these features. Finally, we use our dynamic model to investigate the effects of heterogeneity beyond the radial wave regime and into the spiral wave regime. We find that spatial correlations in the heterogeneity promote or suppress spiraling depending on the parameters, a surprising feature that we explain by demonstrating that these spirals form by distinct mechanisms. We characterize the dependence of the spiral period on the heterogeneity using techniques from percolation theory. Taken together, our results reveal that the spatial structure of cell-to-cell heterogeneity can have important consequences for signal propagation in cellular communities.<br>