Browsing by Subject "Pattern formation"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item The effect of temperature and terrace geometry on carbonate precipitation rate in an experimental setting(2012-08) Reid, Ellen Elizabeth; Kim, WonsuckThrough flume experiments we demonstrate the calcite precipitation process seen at geothermal hot springs in the lab setting. A series of four experiments were run, varying temperature and terrace ridge height while all other experimental parameters, including initial substrate slope, spring water discharge, and CO₂ input were kept constant. The goal of the experiments was to measure the temperature and terrace height control quantitatively in terms of the amount of overall travertine aggradation, aggradation rate changes in time and downstream direction, as well as to observe the effect of these parameters on processes occurring during precipitation. Using the final deposit thickness measured manually at the end of each experiment and elevation data obtained from a laser topographic profiler, I conclude that high temperature and small terrace heights favor increased precipitation of travertine. However, the amount of precipitation also depends on location within a terrace pond. Flow velocity increases as it approaches a terrace lip, resulting in enhanced precipitation and greater thicknesses in the downstream direction through increased CO₂ degassing, a process called downstream coarsening.Item Flowers in three dimensions and beyond(2007-12) Thompson, Rebecca Caroline; Marder, Michael P., 1960-Pattern formation in buckled membranes was studied along with the morphology of flowers formed at the tip of silicon nanowires and ripples formed in suspended graphene sheets. Nash's perturbation method was tested for a simple case where initial and final metrics embed smoothly and there is a smooth path from one surface to another and was found to work successfully. The method was tested in more realistic conditions where a smooth path was not known and the method failed. Cylindrical flower-like membranes with a metric of negative Gaussian curvature were simulated in three and four dimensions. These four dimensional flowers had 2 orders of magnitude less energy than their three dimensional counterparts. Simulations were used to show that the addition of a fourth spatial dimension did not relieve all bending energy from the cylindrical membranes. Patterns formed at the tip of silicon nanowires were studied and found to be of the Dense Branching Morphology type. The rate of branching is dependent on the curvature of the gold bubble on which they are grown. Graphene was simulated using the modified embedded atom method potential and buckles were found to form if the carbon bonds were stretched. An energy functional was found for the energy of a sheet with a metric different from that of flat space.Item A rule based model of creating complex networks of connected fractures(2014-12) Eftekhari, Behzad; Patzek, Tadeusz W.The recent success in economical production of US shales and other low permeability reservoirs is primarily due to advances in hydraulic fracturing. In this well stimulation technique, a fracturing fluid is injected into the reservoir at pressures high enough to break down the reservoir rock and form fractures. The fractures drain the hydrocarbons in the rock matrix and provide connected pathways for the transport of hydrocarbons to the wellbore. Given the low permeability of the matrix, recent studies of shale gas production suggest that nearly all of the production has to come from a ramified, well-connected network of fractures. A recent study has shown, however, that for reasons yet unknown, the production history of more than 8000 wells in the Barnett Shale can be fit with reasonable accuracy with a linear flow model based on parallel planar hydraulic fractures perpendicular to the wellbore and spaced 1-2 meters apart. The current study is carried out to provide insights into the formation and production properties of complex hydraulic fracture networks. The end goal here is optimization of hydraulic fracture treatments: creating better-connected, more productive fracture networks that can drain the reservoir more quickly. The study provides a mechanistic model of how complexity can emerge in the pattern of hydraulic fracture networks, and describes production from such networks. Invasion percolation has been used in this study to model how the pattern of hydraulic fracture networks develop. The algorithm was chosen because it allows quick testing of different “what if” scenarios while avoiding the high computation cost associated with numerical methods such as the finite element method. The rules that govern the invasion are based on a proposed geo-mechanical model of hydraulic fracture-natural fracture interactions. In the geo-mechanical model, development of fracture networks is modeled as a sequence of basic geo-mechanical events that take place as hydraulic fractures grow and interact with natural fractures. Analytical estimates are provided to predict the occurrence of each event. A complex network of connected fractures is the output of the invasion percolation algorithm and the geo-mechanical model. To predict gas production from the network, this study uses a random walk algorithm. The random walk algorithm was chosen over other numerical methods because of its advantage in handling the complex boundary conditions present in the problem, simplicity, accuracy and speed.