AnÃlise de sensibilidade do modelo fluidodinÃmico de um Riser atravÃs do formalismo diferencial perturbativo / Sensitivity analysis for a fluid-dynamic model of a riser via the differential pertubation method

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

In an oil refinery, the crude oil is pre-heated in order to promote the cracking of the large hydrocarbon chains, transforming the heavy oil into lighter components. These lighter and vaporized oil (gas oil) is now submitted to a fluid catalyst cracking inside a long column denominated riser, where an ascending mixture of gas oil and solid catalyst are simultaneously flowing. A set of four differential equations is sufficient to describe the fluid-dynamic behavior of the riser in an experimental model placed at room temperature, such behavior being evaluated by means of the velocity and volumetric fraction profiles of the gas and the solid catalyst phases along the riser. The sensitivity analysis for the mean concentration of the solid catalyst along the riser was carried out in relation to 7 parameters, namely: solid catalyst density, gas density, riser diameter, solid catalyst flow, gas flow, riser length and dynamic viscosity of the gas. In this analysis, the differential perturbation method and the response surface (direct) method were used. In the perturbation method, the derivative and adjoint operators were calculated, the bi-linear concomitant was determined and the adjoint system was established and numerically solved. Starting from the obtained adjoint functions, the contributions to the sensitivity coefficient for each parameter were calculated. The same coefficients were also calculated using the direct method. Finally, the sensitivities of the solid catalyst volumetric fraction in relation to each parameter were determined for both methods. When these results are compared, a good agreement is verified, showing a percentual deviation of less than 1% for most of the parameters. The riser diameter showed the highest value of absolute sensitivity, indicating its major influence on the solid catalyst volumetric fraction, whereas the dynamic viscosity of the gas had a minor influence on the same variable. It can be concluded that the differential perturbation method is well suited to sensitivity calculations in relation to the parameters of a fluid-dynamic gas-solid system, having the important advantage of eliminating the exhaustive repetitions in the computations, which are necessary in the direct method, especially if a great number of parameters is to be considered

ASSUNTO(S)

perturbation methods anÃlise de sensibilidade sensitivity analysis adjoint system gas-solid fluid-dynamic systems sistema adjunto fisica nuclear mÃtodo direto fluidodinÃmica de sistema gÃs-sÃlido mÃtodo perturbativo diferencial

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