Fluidization mass balance

Design and operation of recirculation systems can be compHcated. Problems are avoided by using a sludge-blanket clarifier, in which feed enters below a blanket of accumulated and flocculated soflds which become fluidized in the zone-settling regime by the upflowing feed. Feed soflds are trapped in the blanket. The soflds content of the blanket continuously increases and part must be bled off in order to maintain the mass balance. 

Owing to the high computational load, it is tempting to assume rotational symmetry to reduce to 2D simulations. However, the symmetrical axis is a wall in the simulations that allows slip but no transport across it. The flow in bubble columns or bubbling fluidized beds is never steady, but instead oscillates everywhere, including across the center of the reactor. Consequently, a 2D rotational symmetry representation is never accurate for these reactors. A second problem with axis symmetry is that the bubbles formed in a bubbling fluidized bed are simulated as toroids and the mass balance for the bubble will be problematic when the bubble moves in a radial direction. It is also problematic to calculate the void fraction with these models. 

The catalytic reactor is an example where reaction occurs only at the boundary with a solid phase, but, as long as the solid remains in the reactor and does not change, we did not need to write separate mass balances for the soHd phase because its residence time Tj is infinite. In a moving bed catalytic reactor or in a slurry or fluidized bed catalytic reactor... 

If we consider a total mass balance of the solids, assuming that no solids are entrained and carried out of the bed in the case of fluidization, the total mass of the solids in the fixed bed is constant and given by... 

The pressure drops in Eq. (10.16) can be obtained by assuming that the particles in the downcomer are in the incipient fluidization state. Neglecting the solids holdup in the connecting tube between the riser and the cyclone and in the cyclone, the mass balance of solid particles in the CFB loop can be expressed as... 

Under fairly low gas velocity conditions where U is close to t/mf or the bed is in particulate fluidization, the plug flow assumption for the gas phase can be reasonably made [Wen and Fane, 1982]. Considering the sublimation of species A from the solid phase to the gas phase, the mass balance on the concentration for species A in the gas phase, Ca, over the incremental height AH can be expressed as... 

This balance computes the adjusting mass transfer surface. The suspension loading depends on the liquid in the bed and the evaporation of this liquid from the particles. Moreover, mass of the suspension on the fluidized-bed particles depends on the solid mass in the suspension and of the solid leaving the suspension by accumulation at the fluidized-bed material. Under stationary conditions, the evaporated mass will correspond to the sprayed solid mass at the fluidized-bed particles. For simplicity, the suspension consists only of water, undissolved calcium hydroxide (Ca(OH)2) and product (CaSC>3 x ij2 H2O). The mass balance has the following form... 

The temporal change of the molar quantity of the element sulfur in the film on a fluidized-bed particle is caused by inflow and outflow of the material. This mass balance is needed only once, since the fluidized-bed particles and, thus, the liquid films on the particles are regarded as ideally mixed. The condition of the ideal mixing leads to the fact that with the mass and energy balance of the film, the average variables of state of the gas in the respective driving force approximations find the following form... 

A physical explanation of the process where the injection rate is changed can be described with help from the mass balance of the liquid within the fluidized bed. For simplicity, the suspension is regarded as a pure liquid. The particle movement follows the model of the ideal mixing, and the liquid on the particles is a thin film of constant thickness. Under these stationary conditions, the degree of wetting can be formulated from the moisture balance around the entire apparatus... 

Similar to the situation in bubbling fluidized beds the two phases exchange gas with each other and are modeled by separate equations which are obtained from mass balances for each component in each phase. 

The reactor was simulated for both steady and transient behaviour. The steady-state model is straightforward and will not be discussed in detail. The unsteady-steady state simulation took advantage of the fact that the rate of reaction is much faster than the thermal response rate. The concentration transient response can thus be modelled as pseudo-steady state in the actual fluidized bed this pseudo-steady state then follows the slowly changing temperature profile. A mass balance on the species, j, for each region (see Figure 2) is written as ... 

In fixed-bed catalytic cracking tests the proper decreasing delta coke response as catalyst-to-oil is increased is possible if a constant catalyst load and a constant feed injection rate are maintained. As CCR increases above 4 wt%, however, fixed-bed cracking methods are suspect because the mass balance drops significantly and the cracking performance can be measured better using other techniques (e.g.s., circulating pilot plants or fluidized-bed reactors). 

Conradson carbon coke deposits shortly after feed introduction. If high conradson carbon feed is processed in a MST unit, coke will deposit shortly after feed introduction. As the MST reactor consists of a fixed bed reactor, the feed will still meet clean catalyst after passing the first zone, where CCR coke deposits. Consequently the mechanism is different compared to commercial units. It can also be shown that material boiling above the MST reactor temperature does not leave the reactor, resulting in a low mass balance (9, 10). Therefore it is recommended to test high CCR feeds (CCR> 4-5%) in a fluidized bed system or in a riser unit. 

Table 17.5 Mass balance of the pyrolysis of mixed plastics (different fractions A and B see Table 17.4) in a fluidized bed with different feedstocks and plants using pyrolysis gas for fluidization...

Due to their complexity, the model equations will not be derived or presented here. Details can be found elsewhere [Adris, 1994 Abdalla and Elnashaie, 1995]. Basically mass and heat balances arc performed for the dense and bubble phases. It is noted that associated reaction terms need to be included in those equations for the dense phase but not for the bubble phase. Hydrogen permeation, the rate of which follows Equation (10-51b) with n=0.5, is accounted for in the mass balance for the dense phase. Hydrodynamic parameters important to the fluidized bed reactor operation include minimum fluidization velocity, bed porosity at minimum fluidization, average bubble diameter, bubble rising velocity and volume fraction of bubbles in the fluidized bed. The equations used for estimating these and other hydrodynamic parameters are taken from various established sources in the fluidized bed literature and have been given by Abdalla and Elnashaie [1995]. 

Fluidized-Bed Dryers In design mode, the required gas flow rate can be obtained from a heat and mass balance. Bed cross-sectional area is found from the scoping design calculation the required gas velocity should be found from fluidization tests, but for initial design puiposes, a typical value is 0.5 m/s. 

Saraiva et al [121] presented an extended model for a circulating atmospheric fluidized bed combustor (CAFBC) which included hydrodynamics for the fast section at the top of the bed as well a bubbling bed section at the bottom of the CAFBC. For the fast section of the bed, one dimensional momentum and energy balances were used to predict the temperature and velocity profiles for gas and particles throughout the reactor. The model contain species mass balances for five gas species including SO2, as well as a model of SO2 retention by limestone particles. A bubbling bed model was considered to simulate the chemical process at the bottom of the combustor. 

Chapter 10 contains a literature survey of the basic fluidized bed reactor designs, principles of operation and modeling. The classical two- and three phase fluidized bed models for bubbling beds are defined based on heat and species mass balances. The fluid dynamic models are based on kinetic theory of granular flow. A reactive flow simulation of a particular sorption enhanced steam reforming process is assessed. 

In a single-phase model, the fluidized bed is regarded essentially as a continuum (Figure 8.4). Heat and mass balances are applied over the fluidized bed. It is assumed that particles in the bed are perfectly mixed. Equations 8.22 and 8.23 are the equations of moisture balance and energy balance, respectively [34]. 

Zahed et al. [48] have presented mass and energy balance equations for the dense phase and the bubble phase for fluidized bed drying. Mass balance of liquid in the bubble phase gives the following equation ... 

Sizing of the bed is based on simple holdup mass balance. Cross-sectional area of the fluidized bed can be determined from the following equation after the solids flow rate (dry basis), F , bed density, and bed height, are specified and particle residence time, tg, is determined ... 

In the mass balances of the fluidized-bed countercurrent process the true movement of the solid has to be taken into account. Furthermore, the process is divided into diverse separation zones with different flow rates of the fluid phase due to different in- or outgoing streams. 

Results of the METSIM heat and mass balance provided the basis for sizing of the equipment. Based on the particle size distribution of the feed as well as particle and gas properties, a fluidization velocity of 0.7 m/s was selected to ensure complete fluidization in the bubbling regime, while minimizing solids elutriation to the cyclone. 

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