Simulation of an industrial rotary calciner with trona ore decomposition

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Znd. E n g . C h e m . Res. 1988,27, 1194-1198

1194

Simulation of an Industrial Rotary Calciner with Trona Ore Decomposition Nam K. Kim* and Rajeev Srivastava Michigan Technological University, Houghton, Michigan 49931

Jay Lyon FMC Wyoming Corporation, Green River, Wyoming 82935

Calciners are one of the most critical energy-intensive units often employed in chemical ore refining and manufacturing processes. They affect subsequent unit operations and eventually influence the final product's quality. The calciner is equipped with lifting flights to enhance the contact efficiency of solids with the hot gas stream. Mass, component, and energy balances for endothermic decomposition of natural trona ore (sodium sesquicarbonate) into soda ash result in a set of intercoupled, nonlinear differential equations and an algebraic equation. Steady-state simulations of the hot gas stream temperature, solid temperature, shell temperature, and product quality show a good agreement with the plant operating data and confirm the shell overheating problems previously experienced. Some useful suggestions are also made t o enhance the calciner operations. Calcination is a widely used unit operation in the chemical processing industries. When employed in a manufacturing process, it is usually one of the critically important stages and thus has a pronounced effect on the quality of final product. Despite extensive use, rotary calciners have remained a difficult system to analyze. Their design and performance have been simply covered by empirical procedures with relatively superficial insight into the theory of operation. This paper describes a steady-state mathematical model of an industrial calciner used in the production of soda ash from trona ore. It is a part of continuing research aimed a t developing a more effective, adaptive control scheme for the calciner than is possible using empirical techniques.

Calciner Description A calciner under study basically consists of a cylindrical shell, which is rotated about a slightly inclined, horizontal axis. Also calcining gases and trona ore pass cocurrently in direct contact with each other in the shell. Fourteen sections of closely spaced lifters (lifting fights) are installed inside the calciner to shower the solids through the gas stream and imprqve contacting efficiency. Heat is provied by burning natural gas, using a single center-line burner. In order to minimize showering of solids through the flame, the f i s t section of lifters starts 6.0 m from the burner. The lifters continue for 18 m, followed by 3.0 m of bare section to allow for dust disengagement from the flue gas. Dimensions of the calciner are shown in Figure 1. Distribution of Material in a Cross Section Bare Sections. In the feed and discharge end of the calciner, material essentially rolls or slides onto the inside surface of the lower shell and is distributed in a crescent-like section with fixed ends, as shown in Figure 2a. The heat-transfer area in these sections is small. Material distribution can be approximated by a circular segment. L1,L2, L,,and L, can be readily calculated given the material flow rate and calciner dimensions (Green, 1984). Flight-Fitted Section. In this section of the calciner, particles of solids are continuously spilled from the flights from the time they leave the rolling bed until they are empty. Heat transfer takes place as the particles fall through the hot gas stream and the exposed area drastically increases. Critical loading conditions are assumed, which imply that the material flow rate is just sufficient 0888-5885/88/2627-1194$01.50/0

to fill up the flights completely as they leave the bed. Distribution is shown in Figure 2b.

Mass-Transfer Equations Drying. Drying of solids in a rotary calciner occurs in two phases, a constant rate stage and a falling rate stage. When the moisture content of solids is greater than critical, moisture movement within the solids is rapid enough to maintain a saturated condition at the surface, and the rate of drying is controlled by the rate of heat transfer to the evaporating surface. The constant rate of vapor removal during this stage is given by (Coulson and Richardson, 1978)

-dQh - _-

htA(Tg - Tm)

dl

x

(1)

where Qh is the flow rate of moisture contained in the solids, is the latent heat of vaporization, h, is the total heat-transfer coefficient, and A is the exposed surface of the solids per unit length of the calciner. For the bare sections, A is simply equal to L2. For the lifter section, however, A is a function of flight design and material characteristics, as derived in the Appendix. Tgand T , are the calciner gas and material temperatures, respectively. When the moisture content of the solids is less than critical, the entire evaporating surface can no longer remain saturated. The rate of drying during this stage is controlled primarily by the mechanism of liquid flow inside the solid and is given by the relation dQh/dl = -KhQh (2) where Kh is a constant determined at the boundary between the two drying periods, which occurs when the moisture content of the solids equals the critical moisture content. Because of continuity, (1)and (2) can be equated at this point. Since we know the critical moisture content of the solids, Kh can be calculated. Reaction Kinetics. The function of the calciner is to decompose trona into crude soda ash according to the following reaction: 2(Na2CO3-NaHCO3*2H20) = 3NazCO3+ C 0 2 + 5H20 The activation energy, E , is 33.8 kcal/mol between 73 to 95 "C. High values of activation energy suggest that the chemical reaction is the rate-limiting step in this temperature range. A t temperatures higher than 95 "C, the 0 1988 American Chemical Society

Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 1195 1

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Figure 1. Calciner configuration.

Figure 3. Heat fluxes.

gas to wall; and Hm, from inner wall to material) can be expressed as follows (Dumont and Belanger, 1978; Manitius et al., 1974): bare sections

+ ~L3t,t,(T,4 - Tw4)

(8)

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(9)

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= hJ,(Tw

flight-fitted section

Hgm= UA(T g- T,) Figure 2. (a, top) Calciner cross section: material distribution in bare section. (b, bottom) Material distribution in lifter section.

reaction exhibits an activation energy level of less than 12 kcal/mol. This indicated that another resistance, diffusion of reaction products out of the particles, becomes increasingly important at higher temperatures. The reaction is first order; thus, it is directly proportional to sesquicarbonate content of the solids. The rate of decomposition is given by dSq/dt = -KrSqe-E/(RTm)

(3)

where K, is the frequency factor. By use of 1 = V,t, where V, is the velocity of solids inside the calciner, (4)

Material and Gas Flow Rates. Drying of solids and evolution of carbon dioxide and water vapors due to decomposition of trona results in an increase in the gas flow rate, Qg,and a decrease in the material flow rate, Qm,down the length of the calciner. Considering the stoichiometry of the reaction,

Heat-Transfer Equations Radically different material distribution in the bare sections and the flight-fitted section of the calciner makes it necessary to evaluate the various heat-transfer coefficients and fluxes separately for each of these sections. To simplify the heat-transfer equations, three assumptions were made: (1)all parameters in a cross section of the calciner are assumed to be constant, (2) conduction is important only in the radial direction, and (3) axial heat transfer due to conduction and radiation (except radiation from the flame) is negligible. Heat fluxes considered in the development of the mathematical model are shown in Figure 3. Heat fluxes (Hp, from gas to material, Hgw,from

Hgw= h&3/(Tg - T,) Hwm

+ uL3'twtg(T; - Tw4)

= h&L,'(Tw - T m )

(10) (11) (12)

Loss of heat from the outside surface of the calciner wall to the surrounding air is represented by

Hwo= uwo~D(T, - To) (13) Heat-transfer coefficients h,, h,, U , and Uwoand emissivities e,, em,and t, are given in the Appendix. T , and

Toare the temperatures of the calciner wall and its surroundings, respectively. Drying of solids causes the following heat fluxes: Hgv, from the gas to the water vapor produced by drying, and He,, consumed by evaporation. Mathematically they are expressed as

where C, is the vapor specific heat. HP is computed assuming that the vapor temperature rises instantaneously from 373 K to the gas temperature. Endothermic decomposition of trona results in cooling of material inside the calciner. H,, the heat flux consumed by reaction, is directly proportional to the rate of reaction and is given by

where AH is the heat of reaction. Heat transfer from the flame is incorporated by considering Hfm,the flux from flame to material; H,, the flux from flame to inner wall; and Hfg,the flux from flame to calciner gas. These are expressed as

1196 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988

Ff, and Ff, are geometric shape factors, Sf is the lateral surface area, and Tf is the temperature of the flame. Considering the above-mentioned fluxes, the heat balance equations can be written as

0 = Hf,+ Hgw- H,

-

H,,

""i

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(22)

C, and C, are the specific heat of the calciner gas and the solid material. Retention Time Bare Sections. Retention time of solids in a rotating cylindrical shell is controlled by parameters such as diameter, length, slope, rate of revolution of the shell, and physical characteristics of the solid material. The following relation is used for the bare sections of the calciner: retention time (min) = C(square root of the angle of repose)(lb in ft)/(slope in in./ft)(rpm)(D in ft) (23) where Lb is the length of the bare section and D is the diameter of the calciner. C is a constant which has been concealed for confidentiality purposes. This equation has been experimentally verified for the calciner under study and has been proven to be in close agreement with the actual plant measurements. Flight-Fitted Section. The retention time model for this section is mostly dependent upon the dynamics of the particle movement in a gas stream, although it is also influenced by the geometry of the flights and the slope and revolution of the calciner. Relative motion of the gas imposes a longitudinal drag on the particles as they fall from the flights. Retention time is calculated by solving the equation of motion of the particles retention time (min) = Lf (24) Yavgsin (Y + -KV2t2 1 2 where Yavgis the weighted mean length of fall of particles and 6 is the ratio of the circumference to the distance an average particle travels on the periphery before it falls from the flight. Both Yavgand 6 are complex functions of flight dimensions and the material characteristics. Lf is the length of the flight-fitted section, K is a function of particle Reynolds number, and V is the velocity of calciner gas. In (241, t is the average time of fall, given by

( &) +

Detailed analysis can be obtained elsewhere (Schofield and Glikin, 1962).

Algorithm Computation of the state of the calciner requires solution of six nonlinear, intercoupled, differential equations, ( l ) , (4), (5), (6), (201, and (21), and an algebraic equation, (22). This is an initial value problem where conditions a t the inlet and exit end of the calciner are known. The algorithm can be summarized as follows: (1)Sq, T , Tf, T,, Qh, and Q, are known a t the hot (1 = 0) end. dsing Tg, Tf, and T,, calculate T, from (22) by using the Newton-Raphson technique.

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