SUMMARYThe finite element method is used for the computation of the variational modes of the system composed of an elastic tank partially filled with a compressible liquid. We propose, on the one hand, a direct approach based on a three field mixed variational formulation, and, on the other hand, a variational modal interaction scheme allowing the use of the acoustic eigenmodes of the liquid in a rigid motionless enclosure and the hydroelastic modes of the enclosure. Numerical results show the advantage of the second procedure.
Fossil fuel consumption is a primary source of CO2, a major greenhouse gas. Geologic methods, such as injection and sequestration of CO2 in coals may offer viable methods of reducing CO2 atmospheric emissions, while providing the added benefit of enhanced coalbed methane recovery. The potential for CO2 sequestration in low-rank coals is unknown, and it differs significantly from bituminous coals. To evaluate the feasibility and the environmental, technical, and economic impacts of CO2 sequestration in Texas low-rank coal beds, we are conducting a 2-year study to characterize the coals located near major electrical power plants. We have identified potential of CO2 sequestration sites in coals near 3 Texas power plants. These 3 power plants discharge 34,068,751 short tons of CO2 annually, accounting for 14.6 % of Texas' point-source emissions. On the basis of preliminary modeling of one site, using assumed permeability, CO2 storage and methane content values, we conclude that 360 wells on 80-acre spacing could sequester CO2 emissions for the Gibbons Creek plant for 11 years, while producing 90 Bcf of coalbed methane. However, reservoir properties are poorly known and, thus, the volumes of CO2 that may be sequestered and the amount of methane that may be produced are speculative at present. Future study will focus on better reservoir characterization and additional modeling. Introduction Texas, with 7% of the population of the United States, ranks first in the nation in consumption of petroleum, natural gas, coal, and electricity. Texas is also the biggest producer of electricity in the country.1 In 2000, 46% of electricity in Texas came from natural gas-fired plants, 41% from coal- and lignite-fired plants, and 13% from nuclear plants.2 We estimate that approximately 425,000,000 short tons of CO2 are emitted in Texas each year. This is based on an average CO2 emission rate of 20.57 metric tons per year per capita.3 In Texas, 274 power plants of various types produced 233,075,220 short tons of CO2 in 2001.4 This suggests that power plant emissions account for more than half of the total CO2 emissions in Texas. Sequestration of CO2 from power plants could have a direct and significant effect on Texas CO2 emissions. Approximately 54% of the total CO2 emitted by power plants is emitted by the 15 largest (major) power plants, and nearly 33% comes from the top 5 plants (Table 1 and Fig. 1). Martin Lake Plant, which is the largest lignite-fired generating plant in the world, produces 8% of total emissions from Texas power plants. Thus, sequestering CO2 from a few very large power plants could significantly impact CO2 emissions in Texas. Lignite and coal are the fuels used by the largest Texas CO2 emitters (Fig. 2). Major Texas power plants are concentrated in the most heavily populated eastern and southeastern parts of the state (Fig. 3). CO2 Sequestration in Coals A primary man-made source of greenhouse gas is CO2 from energy consumption. Viable methods of reducing CO2 emissions are greatly needed. Recently, researchers have suggested sequestering CO2 in coals. CO2 injected in coal beds may have the dual benefits of CO2 abatement and enhanced coalbed methane recovery by displacement.5 Primary recovery efficiencies of coalbed methane range from 20 to 60% of original gas in place. CO2 injection can improve methane recovery and help maintain reservoir pressure, thus offsetting operational costs by reducing the amount of gas compression required.
Analysis of the hydrodynamic properties and response of flexible risers in various configurations is paramount to understanding their operative performance. Buoyancy modules play an integral role in providing compliance to flexible riser systems in wave configuration. This study utilised both model testing and numerical simulations to quantify the impact of discretised and smeared buoyancy module sections on the performance of a flexible riser in shallow water steep wave configuration under steady current loading. Model testing was facilitated in the Australian Maritime College’s Circulating Water Channel by a 1:15 scale 8″ flexible riser constructed from silicon hose and foam. Variances in the model’s buoyancy module section and system offset were tested at different flow velocities to estimate the effect on in-line drag and top tension, and the change in curvature radius experienced by the riser. The tested systems were also modelled in dynamic analysis software for comparative purposes, where industry recommended practices were employed to specify drag coefficients. Numerical simulations exhibited an appreciably higher in-line drag compared to model testing results at higher flow velocities. Comparison of curvature radius results demonstrated close agreement at lower flow velocities, with numerical simulations exhibiting increased deformations due to the higher in-line drag estimated at higher flow velocities. This discrepancy might be partially attributed to an overestimation of drag coefficients defined within industry recommended practices. The findings from this study have shown the significance of utilising scale model testing to quantify the hydrodynamic responses of a flexible riser, and facilitate a basis for further work which might provide additional insight into the discrepancies between analytical modelling and scale model tests.
A general size reduction procedure of large modal models is set up by means of Ritz–Galerkin projection techniques based on a reduced set of hybrid modes defined in each frequency band by an appropriate linear combination of the eigenmode shapes of the modal reference model. This method applies in the case of ‘‘broadband excitation’’ such as transient or random forces and leads in this case to good estimates of the vibration energy and of response maxima. It appears that the present approach differs from the well-known SEA mainly by accounting for the specificity of the external (or coupling) loads−an appropriate space averaging of the MHM leading to equipartition of energy and therefore to the SEA results. In a first part, this method is introduced in the modal analysis of the response of a structure to external forces (resp. to a prescribed motion) imposed on its interaction surface. It is shown that the hybrid modes cumulate the modal excitabilities (resp. the effective modal masses) of the ‘‘component modes.’’ The second part is devoted to the coupled vibroacoustic problem viewed through the coupling of two sets of acoustic and structure oscillators. It is shown that the resonant coupling problem can be reduced−in each frequency band−to the coupling of N acoustic hybrid modes with N structure hybrid modes corresponding to the N predominant singular values of the (rectangular) coupling matrices (additional structure hybrid modes must be considered for accounting for the external loading). The explicit solution of this problem is given in the case of a frequency band in which a cluster of modes of one subsystem is coupled with a single mode or a pair of modes of the other subsystem.
Subsea chokes differ from the standard choke designs that can be found in for example the IEC 60534-8-3 standard, due to their geometry but also due to the environment. Contrary to topside chokes where monitoring for sound and vibration can be carried out in a relatively straightforward manner, noise and vibration monitoring is not easily executed subsea, which means that the estimate of the generated noise needs to be calculated, or extrapolated in some way from lab data. Computational methods to validate designs often provide an alternative method to physical validation testing when size or recreating particular environments are impractical. However, to be able to use computational analysis for this purpose, it is essential to ensure that a sound and benchmarked methodology is applied. This paper discusses an optimized methodology that combines Computational Aeroacoustics and IEC 60534-8-3 for the estimation of the internal sound pressure level (SPL) generated by choke valves. Three broad types of tools (all broadband models) are available to estimate hydrodynamic induced SPL, namely: 1) one-way coupled Computational Fluid Dynamics (CFD), 2) acoustic solvers, 3) two-way coupled CFD and acoustic solvers, also called Computational Aeroacoustics (CAA) solvers. Out of these three types, CAA accounts for both the geometry of the equipment generating the internal SPL, but also models the complex interaction between hydrodynamics and acoustics, including tones generated by cavities. While the advantage in terms of output is significant, CAA comes at a large computational cost due to the requirements in space and time discretization that must be satisfied to properly resolve the frequency range from 12.5 Hz to 20 kHz. The CAA methodology presented in this paper is validated against two sets of data obtained in laboratory conditions for Mach numbers ranging from 0.08 to 0.36. Then the same methodology is applied to the specific design of the choke valve. The obtained outputs in form of an acoustical efficiency and peak frequency are then used to tune the IEC 60534-8-3 method, this allows accurate estimation of internal SPL for the given geometry. The combination of the CAA and IEC enables efficient consideration of the actual geometry of the choke with regards to internal SPL prediction against a wider range of conditions without requiring a larger set CAA calculations. The methodology presented in this paper can be applied to similar problems ensuring faster and more accurate results compared to the other available industry practices like physical testing.
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