Direct numerical simulation is used to study the effect of crossflow on the dynamics, entrainment and mixing characteristics of vortex rings issuing from a circular nozzle. Three distinct regimes exist, depending on the velocity ratio (ratio of the average nozzle exit velocity to free-stream crossflow velocity) and stroke ratio (ratio of stroke length to nozzle exit diameter). Coherent vortex rings are not obtained at velocity ratios below approximately 2. At these low velocity ratios, the vorticity in the crossflow boundary layer inhibits roll-up of the nozzle boundary layer at the leading edge. As a result, a hairpin vortex forms instead of a vortex ring. For large stroke ratios and velocity ratio below 2, a series of hairpin vortices is shed downstream. The shedding is quite periodic for very low Reynolds numbers. For velocity ratios above 2, two regimes are obtained depending upon the stroke ratio. Lower stroke ratios yield a coherent asymmetric vortex ring, while higher stroke ratios yield an asymmetric vortex ring accompanied by a trailing column of vorticity. These two regimes are separated by a transition stroke ratio whose value decreases with decreasing velocity ratio. For very high values of the velocity ratio, the transition stroke ratio approaches the ‘formation number’. In the absence of trailing vorticity, the vortex ring tilts towards the upstream direction, while the presence of a trailing column causes it to tilt downstream. This behaviour is explained. In the absence of crossflow, the trailing column is not very effective at entrainment, and is best avoided for optimal mixing and entrainment. However, in the presence of crossflow, the trailing column is found to contribute significantly to the overall mixing and entrainment. The trailing column interacts with the crossflow to generate a region of high pressure downstream of the nozzle that drives crossflow fluid towards the vortex ring. There is an optimal length of the trailing column for maximum downstream entrainment. A classification map which categorizes the different regimes is developed.
Direct numerical simulation is used to study the mixing of a passive scalar by a vortex ring issuing from a nozzle into stationary fluid. The ‘formation number’ (Gharibet al. J. Fluid Mech.vol. 360, 1998, p. 121), is found to be 3.6. Simulations are performed for a range of stroke ratios (ratio of stroke length to nozzle exit diameter) encompassing the formation number, and the effect of stroke ratio on entrainment and mixing is examined. When the stroke ratio is greater than the formation number, the resulting vortex ring with trailing column of fluid is shown to be less effective at mixing and entrainment. As the ring forms, ambient fluid is entrained radially into the ring from the region outside the nozzle exit. This entrainment stops once the ring forms, and is absent in the trailing column. The rate of change of scalar-containing fluid is found to depend linearly on stroke ratio until the formation number is reached, and falls below the linear curve for stroke ratios greater than the formation number. This behaviour is explained by considering the entrainment to be a combination of that due to the leading vortex ring and that due to the trailing column. For stroke ratios less than the formation number, the trailing column is absent, and the size of the vortex ring increases with stroke ratio, resulting in increased mixing. For stroke ratios above the formation number, the leading vortex ring remains the same, and the length of the trailing column increases with stroke ratio. The overall entrainment decreases as a result.
Advancement in fluid diverter technology has enabled successful initial stimulation of long interval carbonates without mechanical isolation, in excess of 1000 ft. by using in-situ crosslinked polymer systems and viscoelastic surfactant systems. These fluids build viscosity upon reacting with the formation, enhancing diverter performance. However, heavily stimulated, i.e. wormholed, formations require a step-level change in diversion performance to effectively stimulation new intervals, or previously under-stimulated layers. This paper will present the qualification and optimization of degradable fibers for use in re-stimulation of carbonate formations.The key performance aspects desired and evaluated are: (1) ability to block existing wormholes near the wellbore, as opposed to needing to fill the entire wormhole structure, (2) permeability and diversion capability of resulting fiber bridge, and (3) confirmation of degradation and cleanup in a dry gas environment within a reasonable timeframe. New experimental methods were developed to address these requirements, including gas/fluid degradation testing, bridging tests with slots to represent wormholes and fractures, and bridging experiments with 3D synthetic models of a wormhole structure. To be able to run repeatable experiments, wormholed structures were printed with a 3D printer using high-resolution CT scans from an actual wormholed core plug.Testing results showed the ability of the fibers to bridge within the wormhole network and provided guidance in designing the fiber diverter stages for already-stimulated wells. Addition of degradable particulates was shown to further improve wormhole bridging and diversion performance. Modeling the wormhole diversion process within advanced stimulation software identified additional optimizations, such as increased stage size and increased fiber concentrations to achieve desired diversion. A related presentation will discuss the successful re-stimulation of three high-rate gas wells (B. Clancey 2015).
We use direct numerical simulation to study the mixing behaviour of pulsed jets in crossflow. The pulse is a square wave and the simulations consider several jet velocity ratios and pulse conditions. Our objective is to study the effects of pulsing and to explain the wide range of optimal pulsing conditions found in experimental studies of the problem. The central theme is that pulsing generates vortex rings; the effect of pulsing on transverse jets can therefore be explained by the behaviour of vortex rings in crossflow. Sau & Mahesh (J. Fluid Mech., vol. 604, 2008, pp. 389–409) show that vortex rings in crossflow exhibit three distinct flow regimes depending on stroke and ring velocity ratios. The simulations of pulsed transverse jets in this paper show that at high velocity ratios, optimal pulse conditions correspond to the transition of the vortex rings produced by pulsing between the different regimes. At low velocity ratios, optimal pulsing conditions are related to the natural time scale on which hairpin vortices form. An optimal curve in the space of stroke and velocity ratios is presented. Data from various experiments are interpreted in terms of the properties of the equivalent vortex rings and shown to collapse on the optimal curve. The proposed regime map allows the effects of experimental parameters such as pulse frequency, duty cycle, modulation and pulse energy all to be predicted by determining their effect on the equivalent stroke and velocity ratios.
In this paper, a new carbonate stimulation methodology and its impact to the planning of very long, open hole completions will be presented. While the key objective of stimulation is to connect the well to the reservoir, completion equipment design and related well performance have become more important factors. Traditional methods of stimulation modeling and fluid placement are no longer sufficient for these types of wells. This paper introduces how completion design becomes more complex for more aggressive stimulations. For example, completions with pre-drilled or slotted liners for stimulation with coil tubing acid wash are less sophisticated than ball drop liners for high-volume acidizing or fracturing. In long horizontal completions, computer modeling of stimulation needs to address the flow conditions caused by liners, swell packers and inflow control devices (ICDs). Recent well planning for a long horizontal pilot well (Pilot Well 5) has included the use of new carbonate matrix stimulation software to design a fit-for-purpose completion liner that will accommodate bullhead treatment of a long completion interval. Various completion designs were considered based on objectives from reservoir engineering and geology. Being part of a pilot well program, the strategy is to test fit-for-purpose liners that would balance completion cost with long term productivity and recovery. The well design required more than 100 runs of the new carbonate matrix acidization software to finalize a liner design that employs over 200 holes distributed along the length of the lateral. The final design was developed to accommodate uncertainties in the reservoir properties and allow for safe and reliable rig operations. The resulting design could serve as a lower-cost alternative to ball drop stimulation liners for long openhole completions.
An unequal diameter (1 : 3), two roll thin strip cessing, are some of the expected benefits of the procedure. casting machine has been designed and fabricatedThe history of thin strip casting dates back to the 1850s.1 for investigation of the direct casting of thin strip Highly precise control of process parameters is required on a laboratory scale. The system consists of a for successful operation on an industrial scale. A large preheatable shallow tundish with online heating number of research organisations have been working on facility, water cooled rotating rolls (chill and the development of the technology and a number of reviews auxiliary) for solidification of the liquid metal, and have been published.2 a stripper assembly. The machine has a variable The Research and Development Centre for Iron and Steel, speed. Roll gap setting and roll pressure Steel Authority of India Ltd (SAIL) embarked upon a proadjustment are two important features of the gramme of study of thin strip casting in 1988. The studies machine. It is also possible to vary the placement were first conducted using a single roll caster, which was angle of the auxiliary roll with respect to the chill subsequently converted to a two roll, unequal diameter horiroll. A heat transfer model was developed, based zontal caster. The objective was to develop design and process on experimental casting results. Experiments were parameters for a laboratory scale caster through physicalconducted using AISI 304 grade stainless steel. Up mathematical modelling and experimental investigation using to 100 kg of steel was cast without interruption into AISI 304 stainless steel. strips of widths 100 and 200 mm and thickness varying between 1 and 2 mm. Some of the process parameters affecting the quality of the strip were DESIGN FEATURES identified. I&S/1460The experimental cast shown in Fig. 1 has been designed for the following parameters:
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