Dynamics of an Industrial Fluidized-Bed Granulator for Urea Production

Ind. Eng. Chem. Res. 2010, 49, 317–326

317

Dynamics of an Industrial Fluidized-Bed Granulator for Urea Production Diego E. Bertıń,* Juliana Pinã, and Verońica Bucala´ Department of Chemical Engineering, UniVersidad Nacional del Sur, PLAPIQUI, CONICET, Camino La Carrindanga Km. 7, (8000) Bahıá Blanca, Argentina

Granulation is one of the fundamental operations in particulate processing; however, there is still need to provide insight into the complex dynamic state behavior of these units. The unsteady state of an industrial multichamber fluidized-bed granulator for urea production, with variable mass holdup, is studied under different imposed step changes in key operating variables. For the assayed disturbances, the unit dynamics is considerably slow. In fact, many important state variables (e.g., bed height, pressure drop, solid mass flow, etc.) required more than 1 h to achieve the new steady state. The observed nonsteady behavior indicates the need of an efficient control to return the system rapidly to the desired operational point. The discharge area, fluidization air flow rate, and temperature were determined to be the more appropriate manipulative variables, for granulator stability control purposes. Introduction Different size enlargement processes are used in industry, depending on the granular product requirements.1,2 Particularly, granulation includes several processes that purposely convert, by a sequence of events, small particles into large permanent masses in which the initial primary units are still identifiable. Several technologies are used for particle growth with different aims, such as improving handling and flowability, obtaining a certain size, enhancing the product appearance, controlling the particle moisture content, reducing dusting or material losses, producing structural useful forms, etc.3 In the agrochemical industry, after the fertilizer is synthesized, it is usually converted into particulate material, either through granulation or prilling. Because granules possess better attributes than prills, granulation becomes the preferred route for solid fertilizer production.4 After several years of extraordinary growth, the world economy is entering a depressed period. Although the situation deteriorated quickly during the third quarter of 2008, the nitrogenous fertilizers demand should not be greatly affected. In 2008, the global urea capacity was estimated at 163 Mt. In 2009, the global urea capacity is projected to increase by 11 Mt, to 174 Mt.5 There are many urea granulation plants in operation around the world and some under construction. However, the current tight market conditions for fertilizers may lead to the closure of uncompetitive plants. In this context, knowledge improvements to operate more efficiently urea granulation plants will be extremely worthy. The granulator is a key unit in the urea production process; in fact, this stage is essential to control several properties of the granules, to avoid potential problems that are associated with the granulation circuit stability, urea storage, transportation, and supply to the soil.6,7 Urea can be produced using different types of granulators; however, the fluidized-bed units are commonly being utilized.2 In continuous fluidized granulators, very small urea particles (usually called seeds, which come in a recycle stream constituted by product out of specification) are constantly incorporated to the bed while a concentrated urea solution (∼96%)8 is sprayed from the bottom of the unit. The high heat- and mass-transfer rates, provided by the fluidization, facilitate a fast water * To whom correspondence should be addressed. Tel.: +54-2914861700, ext. 268. E-mail: [email protected].

evaporation and urea solidification of the tiny atomized drops deposited onto the solid particles, leading to the growing phenomenon known as accretion.8 Industrial granulators often have several growth chambers, which allow the particle residence time distribution to be moved toward that of plug flow. Consequently, narrower particle size distributions are obtained.9,10 The growing particles realize an undercurrent flow in horizontal direction through the channel defined by the vertical wiers.11,12 Usually, cooling chamberss where no urea solution is supplied and, thus, no growth occurssare subsequently added.8 The purpose of these last chambers is to cool the solids to temperatures lower than those reached in the growth chambers, which are somewhat higher than 100 °C.8 An understanding of the urea fluidized-bed granulator dynamics is of great importance to produce granules with the desired attributes and to achieve stable operations of the granulation circuit.13,14 Generally, in fertilizer granulation circuits, only a relatively small fraction of the material leaving the granulator is in the specified product size range. Therefore, high recycle ratios are common. The characteristics of the recycle, which are a consequence of what happened previously in the granulator, screens, and crushers, influence what will happen a posteriori in the size enlargement equipment. Thus, cycling surging and drifting of particles might occur. In extreme cases, these periodical oscillations, coupled with large dead times, can result in plant shutdown or permanent variations in the plant capacity, as well as product quality.7,13 To minimize these problems and thoroughly analyze the narrow ranges of the variables that determine good operability of the industrial unit, accurate dynamic granulator models are required.15 In addition, the model solution should be low consumption, with regard to computational time, to be integrated with the peripheral units of the granulation circuit for its numerical simulation. Therefore, the objective of the present paper is to first study the open-loop dynamics of a continuous industrial fluidizedbed granulator for urea production and then propose some guidelines to select manipulative variables to control the main state variables. With this purpose, three growth and three cooling chambers with variable mass holdup are simulated in series.8 The mathematical model for each chamber is based on nonsteady-state mass and energy balances. To evaluate the granula-

10.1021/ie901155a CCC: $40.75  2010 American Chemical Society Published on Web 11/23/2009

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Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010

Figure 1. Schematic representation of an industrial fluidized-bed granulator for urea production.

tor open-loop behavior, with future control purposes, different step disturbances are assayed. Mathematical Model Fluidized-bed granulators have been modeled with different degrees of complexity. Regarding the bed hydrodynamics, the reported mathematical representations can be classified into two categories: the continuum models, which describe all the phases as interpenetrating continua, and the discrete models, which consider the particles as individual elements.16 The two-fluid (solid and gas phases) continuum models have been extensively used to represent fluidized-bed granulators.17-21 These models require constitutive relations, which are mainly empirical, to describe the granulation process within a continuum framework. On the other hand, the discrete element models (i.e., Lagrangian approach) have not often been used to represent fluidized-bed spray granulation, because of their higher complexity and computational cost. Moreover, the discrete models are limited by the total number of particles that can be handled, making their application to industrial-scale fluidized beds in the near future difficult.22,23 Different continuum models are usually applied to simulate fluidized-bed granulators. The simplest unit approximation consists in a black box where the particles and fluidization air are assumed to be perfectly mixed. On the other extreme, the granulator can be considered as a series of perfectly mixed zones in which coating and noncoating control volumes can also be distinguished.20,21,24 The multiple zones models are particularly useful and necessary for binder jets with a limited penetration length in the bed. Until now, the modeling of continuous granulators has received little attention. However, there are many continuous granulations in industry that operate far from optimal points. Most of the continuous operation and dynamic models reported in the literature are focused on the mathematical representation of single-chamber units;17,18,25,26 moreover, usually constant granulator mass holdup is assumed. In this work, a continuum perfectly mixed nonsteady state model is proposed to simulate the dynamics of an engineeringscale continuous multichamber fluidized granulator for urea production. The industrial granulator is constituted by six fluidized beds in series, divided by weirs arranged in a vertical direction.2,8 The first three fluidized beds are growth chambers, while the remaining ones are used for product cooling. Figure 1 presents a simplified schematic representation of the granulator. Small urea solid particles are continuously fed to the first chamber of the granulator. In addition, a highly concentrated urea solution (usually called the urea melt) is sprayed from the bottom of the growth chambers, using atomization air. The urea melt is injected at a temperature above its melting point (∼132 °C).8

Figure 2. Simplified representation of a single granulation chamber.

The inlet seeds grow through deposition of the concentrated urea drops onto the solid surfaces. Because the droplets are much smaller than the particles, size enlargement occurs, mainly by accretion.27 The rapid urea solidification is a result of two simultaneous processes: the cooling of tiny drops and water evaporation. Bertín et al.28 demonstrated that evaporation is almost instantaneous and complete when high urea concentrated solutions are used. For the model formulation, the following assumptions are considered: (1) All the phases are interpenetrating continua. The number of particles present in each chamber is >109, which, for this reason, makes the application of discrete models extremely difficult.29 (2) The wet and dry particles are perfectly mixed. This flow pattern can be supported on three grounds: relatively big particles, high melt discharge pressures, and important fluidization air velocities.17,30-32 (3) The gaseous and liquid phases operate at pseudo-steady state. The mass and energy accumulations of air and liquid within the fluidized chambers are neglected.33-36 (4) The coalescence and breakage phenomena are negligible in the urea industrial fluidized bed; the visual observation of the product samples does not indicate the presence of either agglomerates or granules fragments due to breakage. Indeed, the particles in the granulator discharge stream have a spherical shape. Because the inlet and outlet number flow of particles in the industrial urea granulator are within the same order of magnitude, the number change due to nucleation, attrition, and elutriation mechanisms is not significant. Consequently, the only growth process taken into account is accretion. (5) The seed and product particles are characterized by number-volume mean diameters. (6) The seeds are virtually dry. (7) The urea granules have constant density and are free of additives such as formaldehyde. (8) The water content of the urea melt drops is instantaneously and completely evaporated.28 Thus, there is no need to solve the gas mass balance (i.e., the gas mass balance is uncoupled from the urea one). (9) The temperature of each chamber is homogeneous, because of assumptions 2 and 8.37,38 (10) The chambers operate adiabatically.28 The main variables of a generic chamber j are shown in Figure 2. Under the above-mentioned assumptions, the nonsteady state urea mass balance for a chamber j becomes


dmSj dt

)m ˙ Sj-1 + m ˙ jL(1 - xjL) - m ˙ Sj

(for j ) 1 - 6)

(1)

where mjS, m ˙ j-1 ˙ jS are the bed mass, inlet, and outlet particle S , and m mass flow rates, respectively. The terms m ˙ Lj and xLj correspond to the urea solution mass flow sprayed into chamber j and its water mass fraction, respectively. The undercurrent movement of granules in the horizontal direction, from the first chamber to the last chamber, is driven by the pressure difference between chambers.39,40 Therefore, and by analogy with the principle of communicating vessels, the solids flows for the first five chambers are described by the Bernoulli equation as follows:41 j+1 m ˙ Sj ) CDAj0√2gFjbed(FjbedLj - Fj+1 ) bed L

(for j ) 1 - 5) (2)

j where CD is the discharge coefficient, A0j the passage area, Fbed the bed density, and Lj the fluidized bed height. Similarly, the discharge of particles through the granulator outlet is expressed by the following equation:

m ˙ S6 ) CDA06Fbed6√2gL6

(3)

where A06 is the discharge area. As suggested by Davidson,42 for particles much smaller than the passage or discharge areas, the value of the coefficient CD is set at 0.5. The fluidized-bed density for chamber j is calculated as follows: Fbed ) Fp(1 - ε ) + Fa ε j

j j

j

ε ) j

( )

εmfj

uj umfj

Kε

(5)

where εmfj is the porosity at minimum fluidization (assumed to be constant and equal to 0.4114), uj and umfj are the operating and minimum superficial fluidization air velocities for chamber j respectively, and Kε is defined as follows: Kε )

ln 1/εmfj ln utj /umfj

( (

) )

j

where AT is the chamber cross-sectional area.

dN j ) N˙ j-1 - N˙ j dt

(for j ) 1 - 6)

(8)

where N j is the number of particles and N˙ j is the solids outlet number flow rate for chamber j. Assuming that the particle population can be characterized by the number-volume mean diameter, the solids mass balance for each chamber (eq 1) can be rewritten as a function of the particles size and number: Fp

( π6 ) dtd [N (D ) ] ) m˙ j

j 3 p

+m ˙ Lj(1 - xLj) - m ˙ Sj

j-1 S

(for j ) 1 - 6)

(9)

where Dpj represents the number-volume mean diameter of the population inside chamber j. According to the assumption of a perfectly mixed solid phase, the number of particles and the outlet number flow rate for chamber j can be calculated by means of the following relationships: Nj )

N˙j )

mSj Fp(π/6)(Dpj)3 m ˙ Sj Fp(π/6)(Dpj)3

(for j ) 1 - 6)

(10)

(for j ) 1 - 6)

(11)

Applying Leibniz’s law to eq 9 and considering eqs 8, 10, and 11, the expression defined as eq 9 can be rewritten as

{ [ ( )]

Dpj Dpj dDpj j-1 ) m ˙ 1 S dt 3mSj Dpj-1

3

+m ˙ Lj(1 - xLj)

}

(for j ) 1 - 6)

(12)

The total pressure drop in each chamber is constituted by two terms that take into account the weight of the fluidized bed and the air distributor pressure drop: ∆PTj ) ∆Pbedj + ∆Pdistj ) FbedjgLj + KpFaj(uj)2 (for j ) 1 - 6)

(13)

(6)

where utj represents the terminal velocity. Equations 5 and 6 allow the fluidized-bed porosity to be estimated in a simple way. The calculated porosity values are similar to those predicted by other alternative correlations, such as those proposed by Kunni and Levenspiel30 and Gorosko et al.2,44 The mass flow rate of the particles is a direct function of the bed density, height, and passage or discharge area. Indirectly, the solids movement is dependent on the mean diameter of the particles, which varies along the granulator and affects the terminal and minimum fluidization velocities (see eqs 4-6). The mass of solids within chamber j is related to its fluidizedbed height by means of the following equation: mSj ) FpATj(1 - εj)Lj

Considering accretion as the only growth mechanism, the rate of change of the total number particles (population zero moment) within each continuous non-steady-state granulator chamber is given by eq 8:45

(4)

where εj is the porosity of the fluidized bed j and Fp and Fa are the particle and air densities, respectively. The fluidized-bed porosity in each chamber (εj) is calculated with the following correlation:2,43

319

(7)

where Kp is the flow coefficient of the air distributor, which is a function of the design and geometry of the perforated plate.2 For the industrial triangular array, the perforated plate Kp value is ∼200. Because of the hypothesis of complete evaporation,28 the evaporated water flow rate can be considered equal to the water liquid loading. m ˙ EV ) m ˙ LixLi

(14)

To estimate the temperature T j in each chamber, the following non-steady-state energy balance is considered: mSjcpu(T j) m ˙ LjxLj

∫

dT j )m ˙ Sj dt

Tj

TLj

∫

Tj c T j-1 pu

dT + m ˙ Lj(1 - xLj)

∫

Tj

TLj

cpu dT +

cpw dT - m ˙ LjxLj∆HEV(T j) + m ˙ Lj(1 - xLj)∆HDIS(TLj) + m ˙ aj

∫

Tj

TAj

cpa dT + m ˙ ajY j

∫

Tj

Taj

cpv dT ) 0

(15)

320


Table 1. Physical Properties parameter

equation/value

density of urea, Fp (kg/m ) 3

range

source

T ) 80-400 K

55

T ) 50-1500 K

55

T ) 273-533 K

55

T ) 273-647 K

55

1333.8

3012/T [ sinh(3012/T) ]

heat capacity of air, cp,a (J/(kg K))

heat capacity of water, cp,w (J/(kg K))

55

287.5 + 3.8633T + 1.3167 × 10-3T 2

heat capacity of solid urea, cp,u (J/(kg K))

1005.49 + 326.04

1484/T [ cosh(1484/T) ]

2

+ 263.19

2

15353.9 - 116.12T + 0.4514T 2 - 7.8422 × 10-4T 3 + 5.2056 × 10-7T 4 2610.5/T [ sinh(2610.5/T) ]

heat capacity of vapor, cp,v (J/(kg K))

1853.5 + 1488.33

heat of dissolution, ∆HDIS (J/kg)

2

1169/T [ cosh(1169/T) ]

2

+ 494.22

T ) 406 K

243000.0 2.892 × 106 (1 - 1.54 × 10-3 T)0.3199-3.28×10

heat of evaporation, ∆HEV (J/kg)

-4T+6.16×10-7T2

56 55

T ) 273-647 K

Table 2. Dimensionless Steady-State Simulation Results j

j

j

j

j

chamber

1 Lee/Lee

1 Dpee/Dpee

1 εee/εee

1 Tee/Tee

∆PTj ee/∆PT1 ee

m ˙ Sjee/m ˙ S1ee

1 j /Fbed Fbed ee ee

j 1 uee /uee

j 1 Fbed L /Fbed L1 ee ee ee ee

1 2 3 4 5 6

1.000 1.080 1.030 1.056 0.973 0.905

1.000 1.099 1.183 1.183 1.183 1.183

1.000 1.044 1.022 1.040 1.028 1.022

1.000 1.050 1.040 0.912 0.808 0.730

1.000 1.092 1.086 1.112 1.052 1.002

1.000 1.329 1.658 1.658 1.658 1.658

1.000 0.923 0.962 0.929 0.950 0.961

1.000 1.192 1.188 1.226 1.178 1.151

1.000 0.997 0.991 0.981 0.924 0.870

where TLj, Taj, and T j-1 are the temperatures of the melt, fluidization air, and solids entering into chamber j, respectively. The terms ∆HDIS and ∆HEV are the latent heats that are associated with the urea melt dissolution and water evaporation. The terms cpu, cpw, cpa, and cpv are the mass heat capacities of the solid urea, water solution content, fluidization air, and vapor, respectively. The only time-independent variables of the proposed model are CD, A0j, Fp, εmf, ATj, and Kp. All the other variables can be considered to be either independent of time or time-dependent. The physical properties used in the simulations are reported in Table 1. The presented dynamic model results in a set of 18 firstorder differential equations (eqs 1, 12, and 15 for the six granulator chambers), the complementary algebraic equations previously described, and the following initial conditions: mSj(t0) ) mS,0j

(16a)

Dpj(t0) ) Dp,0j

(16b)

T j(t0) ) T0j

(16c)

The model code is implemented in FORTRAN programming language. Because the six chambers are interacting, through the undercurrent solids flow, their respective mass and energy balances are solved simultaneously. At each time interval, the set of algebraic equations that allows prediction of the thermodynamic properties and fluidized-bed hydrodynamics is computed. Subsequently, and by means of a Gear subroutine, the set of ordinary differential equations (ODEs) is integrated to estimate the solid mass, bed temperature, and particle numbervolume mean diameter for each granulator chamber. Simulation Results Steady-State Operation. A given set of operating conditions is specified to define a base case, and the corresponding variables are chosen from typical industrial values.8 Table 2 summarizes, for this base case, the steady-state simulation results, expressed

as dimensionless variables, with respect to the values of the first chamber. Table 2 indicates that the product FbedL decreases from the first chamber to the last chamber; this trend along the granulator guarantees the solid flow toward the unit outlet (see eq 2). Consequently, and according to eq 13, the bed pressure drop follows the same tendency. However, the steady-state results shown in Table 1 indicate that the total pressure drop (which takes into account the bed and grid pressure drops) presents, along the chambers, the trend imposed by the superficial air velocity profile. In fact, for the base case, the pressure drop at the distributor considerably affects the total pressure drop. The superficial air velocity profile is a consequence of the air mass flow rates and chambers cross-sectional areas selected for this study. The bed porosity is strongly dependent on the fluidization air superficial velocity (eq 5); therefore, it behaves as the total pressure drop. As expected, the bed density behaves opposite to the bed porosity (see eq 4). As it can be seen in Table 2, the solids mass flows that leave chambers 3, 4, 5, and 6 are equal because no melt is fed in the last three fluidized beds. The solids flow increases evenly through chambers 1-3, as a result of the uniform melt distribution imposed in the simulations. Growth only occurs in the first three compartments; therefore, the particle numbervolume mean diameter increases from chamber 1 to chamber 3 and then remains constant up to the granulator outlet. The steady-state results indicate that the first chamber has a bed temperature lower than that of the next one, basically because the recycled seeds enter the granulator at a much lower temperature. Downstream from this compartment, the temperature increases, as a consequence of the melt addition that is sprayed at relatively high temperature (∼132 °C).8 Because the last three chambers are reserved for cooling purposes, the bed temperature decreases continuously from the third fluidized bed toward the granulator outlet. Dynamic State Operation. The proposed model is used to analyze the responses of the state variables to +10% step changes (around the steady-state values of the base case) in the product discharge area and in six inlet variables (seeds and


Figure 3. Fluidized bed heights for a +10% step change in the seeds mass flow as a function of time. All the remaining inlet variables and the granulator discharge area were kept constant at their initial steady-state values.

fluidization air temperatures and mass flow rates, melt composition, and seeds number-volume mean diameter). The magnitude chosen for the imposed step changes is consistent with the common disturbances found in practice. Although the melt solution flow rate is also an inlet variable that can be manipulated, it is not modified from its steady-state value, because a constant granulation plant capacity is desired. All the dynamic simulations are started (t ) 0) at the initial steady state and the imposed disturbances are introduced 10 min afterward. Figure 3 shows, for all the chambers, the bed heights as a function of time when a +10% step change in the seeds mass flow is imposed. For a fixed discharge area, and as it can be inferred from eq 1, this disturbance causes mass accumulation within the granulator and, therefore, higher fluidized bed heights. In agreement with the first term of eq 13, the bed pressure drop transient profiles exhibit the same trend as the bed heights. However, the total pressure drop deviations (with respect to the steady-state values) are somewhat lower than those found for the bed heights, because of the grid pressure drop contribution, which is constant (i.e., not affected by the assayed disturbance) and not negligible. For the +10% step change in the seeds mass flow, the temperature of every bed monotonically decreases over time (data not shown). The temperature reduction is higher in the first chamber (because of the higher seeds flow rate, fed at a relatively low temperature) and diminishes toward the granulator outlet. Nevertheless, the temperature variation is almost negligible for the six chambers, indicating that the seeds mass flow (for the step change introduced) does not have a strong influence on the temperature profile along the granulator. In other words, the bed thermal inertia is very important, because of the high bed masses. A +10% step change in the seeds number-volume mean diameter causes the number-volume mean diameter of the particle population within each chamber to increase (see Figure 4). For all the compartments, the granule number-volume mean diameter at the new steady state is exactly 10% higher than its initial value. In fact, under steady-state conditions, the numbervolume mean diameter in each bed is directly proportional to the number-volume mean diameter of the solid stream entering the chamber (see eq 12, with the time derivative set to zero). This proportionality is satisfied for the assayed disturbance, because the melt and seeds mass flow rates are fixed at the

321

Figure 4. Granules mean diameter for a +10% step change in the seeds mean diameter as a function of time. All the remaining inlet variables and the granulator discharge area were kept constant at their initial steady-state values.

Figure 5. Fluidized bed porosities for a +10% step change in the seeds mean diameter as a function of time. All the remaining inlet variables and the granulator discharge area were kept constant at their initial steady-state values.

steady-state value of the base case and because the final steadystate values of the solids mass flow through all the chambers must return to their respective initial steady-state values to fulfill eq 1. For the +10% step change in the seeds number-volume mean diameter, Figure 5 shows the bed porosity transient profiles for all the compartments. The bed porosity decreases over time, basically because of the influence of the population numbervolume mean diameter on the air velocity at minimum fluidization and terminal conditions (see eqs 5 and 6). In contrast, given that Fp . Faj, the bed density in every chamber increases with time (see eq 4). The bed heights show decreasing profiles as a function of time (data not shown). The diminution in these heights is a consequence of the increase observed in the bed density and the identical solids mass flow values found for the initial and final steady states (see eqs 1 and 3). The solids mass holdup and bed pressure drop within each chamber present the same dynamic evolution as the bed height, because the diminution in this variable is more significant than the increase in the bed compactness or density (see eqs 7 and 13). When a +10% step disturbance is introduced in the total fluidization air mass flow entering into each compartment, the

322


Figure 6. Fluidized bed heights for a +10% step change in the fluidization air mass flowrate as a function of time. All the remaining inlet variables and the granulator discharge area were kept constant at their initial steadystate values.

fluidization air superficial velocities increase immediately. However, the changes in these air velocities between the initial and final steady states are

Dynamics of an Industrial Fluidized-Bed Granulator for Urea Production

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