In this paper, extensive experimental investigations of an impact oscillator with a onesided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the secondary spring. The most typical recorded scenario is when a non-impacting periodic orbit bifurcates into an impacting one via grazing mechanism. The resulting orbit can be stable, but in many cases it loses stability through grazing. Following such an event, the evolution of the attractor is governed by a complex interplay between smooth and nonsmooth bifurcations. In some cases, the occurrence of coexisting attractors is manifested through discontinuous transition from one orbit to another through boundary crisis. The stability of non-impacting and impacting period-1 orbits is then studied using a newly proposed experimental procedure. The results are compared with the predictions obtained from standard theoretical stability analysis and a good correspondence between them is shown for different stiffness ratios. A mathematical model of a damped impact oscillator with one-sided elastic constraint is used in the theoretical studies.
Low volumetric sweep efficiency, early breakthrough of injected fluid, and high risk of gas leakage from the reservoir are the major technical challenges associated with direct gas and water injection into oil reservoirs. Injection of carbonated water (CW) into oil reservoirs is a carbon dioxide-augmented water injection technique, which results in improved oil recovery and possible CO 2 storage in the reservoir. In this paper, the potential of carbonated water injection (CWI) into an Iranian carbonate reservoir for the purpose of improving oil recovery was investigated. In addition, the interfacial tension (IFT) of crude oil and two different carbonated brines (carbonated formation brine and carbonated seawater) as well as CO 2 solubility in these two carbonated brines was determined. Experimental results showed that CO 2 solubility in both brines increases with pressure and decreases with temperature. However, CO 2 solubility was more promising in seawater compared to formation brine because of the lower salinity. The IFT results showed that increasing the temperature from 40 to 100°C and increasing the pressure from 1000 to 2500 psi had a positive impact on reducing the IFT between carbonated brines and oil. In addition, core flooding experiments showed that oil recovery increased with CWI as compared to conventional water flooding (WF). However, secondary carbonated water injection (SCWI) resulted in higher oil recovery compared to tertiary carbonated water injection (TCWI). A maximum oil recovery of 21.75%, 61.63%, and 52.58% was achieved with conventional WF, SCWI, and TCWI, respectively.
In this work the strange behavior of an impact oscillator with a one-sided elastic constraint discovered experimentally is compared with the predictions obtained using its mathematical model. Extensive experimental investigations undertaken on the rig developed at the Aberdeen University reveal different bifurcation scenarios under varying excitation frequency near grazing which were recorded for a number of values of the excitation amplitude. In the paper, particular attention is paid to the chaotic oscillations recorded near grazing frequency when a nonimpacting orbit becomes an impacting one under increasing excitation frequency. It was found that the evolution of the attractor is governed by a complex interplay between smooth and nonsmooth bifurcations, and the interactions between a number of coexisting orbits. The occurrence of coexisting attractors is manifested in the experimental results through discontinuous transitions from one orbit to another via boundary crisis. In some cases, the basins of attraction have a fractal structure. Detailed numerical exploration also revealed coexisting unstable periodic orbits. These stable and unstable coexisting orbits are often born far from the parameter values at which they influence the system dynamics. The very rich dynamics of the bilinear oscillator close to grazing is demonstrated and typical mechanisms of the attractors' appearance and disappearance are explained using stability analysis.
We discovered a narrow band of chaos close to the grazing condition for a simple soft impact oscillator. The phenomenon was observed experimentally for a range of system parameters. Through numerical stability analysis, we argue that this abrupt onset to chaos is caused by a dangerous bifurcation in which two unstable period-3 orbits, created at "invisible" grazings, take part.
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