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International Society for Industrial Process Tomography

8th World Congress on Industrial Process Tomography

A Differential Equation Model Smoothly Approaches Solid Flow Distribution from Gamma Ray CT Measurements in a Circulating Fluidized Bed Pilot Unit

E. A. O. Lima1, W. F. de Souza Netto2, S. B. Melo2, C. C. Dantas2, A. O. de Santana2, E. S. Barbosa3, J. M. F. da Silva2,

1Escola Politécnica de Pernambuco Universidade de Pernambuco – UPE Rua Benfica 455, Madalena

50750-470 - Recife, PE – Brasil

2,Departamento de Energia Nuclear Centro de Tecnologia e Geociências

Universidade Federal de Pernambuco – UFPE 50740-540 Recife, PE


The axial and radial solid flow distribution from gamma transmission measurements was modeled and a good agreement between calculated and experimental data is obtained. For modeling the solid flow in riser of a cold FCC – Fluidized Catalytic Cracking type unit a smooth numerical technique is proposed. Air and FCC catalyst circulating under steady state operational conditions as it is required by fluid dynamic models hypothesis. Experimental setup for measuring gamma intensity is an 241Am isotopic gamma source and Na(Tl) scintillation detector. Three test sections are installed along riser to monitoring and evaluating operational conditions by the pressure and gamma transmission measurements. From online collected data, axial and radial solid distributions are calculated by means of the well known density equation, in a vertical riser of 6.700 m high and of 0.092 m in diameter. Circulating flow goes through a return column connected by the separation vase on the top. By considering a diffusive process with solid concentration as function of spatial and temporal variables the numerical computation according to finite difference method was carried out. A discretization squema ADI – Alternating Direction Implicit improves equation stability solution along with Thomas algorithm reducing computation time significantly. A smooth approach was applied across riser that goes into separation vase by a right angle according to FCC geometry. Therefore, solid distribution modeling was strongly perturbed due to end tube effect. To solve the geometry interface effect was used a level set approach that is interface will be indentified as zero level set of a smooth function. Algorithm computation was developed in Matlab. Criterion for comparison of experimental and calculated solid distribution was carried.

Keywords: Differential equation, process modeling, gamma transmission, solid transport, smooth approach

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