Dynamic Simulation and Optimization of a Urea Granulation Circuit

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Ind. Eng. Chem. Res. 2010, 49, 6630–6640

Dynamic Simulation and Optimization of a Urea Granulation Circuit Ivana M. Cotabarren,*,† Diego Bertıń,† Jose´ Romagnoli,‡ Verońica Bucala´,† and Juliana Pinã† Department of Chemical Engineering, PLAPIQUI, UniVersidad Nacional del Sur, CONICET Camino La Carrindanga Km. 7, (8000) Bahıá Blanca, Argentina, and Chemical Engineering, Louisiana State UniVersity, Cain Department of Chemical Engineering South Stadium Road, Baton Rouge, Louisiana 70803

A dynamic model for a complete urea granulation circuit is presented in this work. The flowsheet includes a fluidized bed granulator, a cooling unit, a vibrating double-deck screen, and a double-roll crusher. This contribution is based on mathematical models for all the equipments, some of them previous validated against industrial data. All the units are modeled by means of the population balance equation (PBE). In addition, the granulator energy and mass balances for urea and air (used as a cooling medium and fluidization agent) are solved simultaneously with the PBE to properly represent the unit dynamics. Furthermore, mass, energy, and population balances are developed for the cooler. The individual units are successfully integrated under the gPROMS Model Builder Environment, which allows one to have a powerful tool for the circuit simulation and optimization. A sensitivity analysis is performed by running several dynamic and steady-state gPROMS simulations in order to evaluate the influence of different operating variables on the particle size distributions and mass flow rates of the circuit streams, as well as the mass holdup and thermal conditions in the granulator and cooler. The results indicate that both screen deck apertures, together with the crusher lower gap, are the variables that most affect the circuit performance. The circuit stability is also analyzed. Finally, different optimization scenarios are carried out to determine the values of the selected manipulated variables that maximize production on specification, minimize the recycle fraction, and allow a plant revamping. The urea granulation process simulator (including mass, energy, and population balances) constitutes a powerful tool to study the circuit responses under different disturbances, determine the optimal combination of operating and design variables in order to meet the production requirements and explore new process flow diagrams. 1. Introduction Granulation is a key particle size enlargement process, widely used in the pharmaceutical, food, mining, and fertilizer industries.1,2 This operation converts fine particles and/or atomizable liquids (suspensions, solutions, or melts) into granular material with desired properties. The granulation process is considered as one of the most significant advances in the fertilizers industry, providing products with higher resistance and lower tendency for caking and lump formation. Particularly, urea granulation is a complex operation that cannot be carried out in a single unit; rather, it is achieved by a combination of process units with specific functions constituting the granulation circuit (Figure 1). The main unit is the granulator, where small urea particles known as seeds (generally product out of specification) are continuously introduced and sprayed with a concentrated solution of the fertilizer. The seeds grow through deposition of the fertilizer solution droplets onto the solids surface followed by water evaporation and urea solidification.3 The granules that leave the size enlargement unit are cooled down and subsequently discharged into a conveyor that transfers them to be classified in double-deck screens into product, oversize, and undersize streams. The product is transported to storage facilities, while the oversize fraction is fed to crushers for size reduction. The crushed oversize particles are then combined with the undersize granules and returned to the granulator as seeds.4 Generally, in fertilizer granulation plants only a relatively small fraction of the material leaving the granulator is in the * To whom correspondence should be addressed. Tel: 54-291-4861700, ext. 269. Fax: 54-291-486-1600. E-mail: icotabarren@ plapiqui.edu.ar. † Universidad Nacional del Sur. ‡ Louisiana State University.

specified product size range; therefore, high recycle ratios are common. The characteristics of the recycle, which are the consequence of what happened previously in the granulator, influence what will happen later on in that unit. Thus, cycling surging and drifting of particles might take place. In extreme cases, these periodical oscillations coupled with large dead times can result in plant shut down or permanent variations in the plant capacity as well as product quality. To minimize these problems, it is necessary to have a fundamental understanding of the effects of the recycling material on the behavior of the granulation circuit.1,5 In view of this and the relatively high current installed world urea capacity and its forecasted expansion (a net growth of 46.8 Mt between 2008 and 2013, to reach 210.3 Mt in 2013), the dynamic modeling and simulation to optimize the urea granulation circuits operation will play an important role in this fertilizer economy.6 Even though there are publications in the field of granulation circuits and its dynamics, none of the reported studies covers completely the scope of this work. Wildeboer,7 Adetayo,8 Adetayo et al.,1 Zhang et al.,9 Balliu10 and Balliu and Cameron11 studied the dynamics and stability of drum wet granulation circuits, by solving the mass, energy, and population balances. Due to the wet nature of these processes and the type of granulators within these circuits, the results of the sensitivity analysis carried out by these authors are not valid for the urea melt granulation that takes place in multichamber fluidized bed units. Although Heinrich et al.,12 Heinrich et al.,5 Drechsler et al.,13 and Radichkov et al.14 studied circuits including fluidized bed granulators, all these continuous units are constituted by just one chamber where wet granulation processes occur. In addition, either these authors assumed constant mass holdup

10.1021/ie901885x  2010 American Chemical Society Published on Web 06/16/2010

Ind. Eng. Chem. Res., Vol. 49, No. 14, 2010

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Figure 1. Typical urea granulation circuit.

for the granulator and/or hypothetical particle size distributions for the outlet crusher stream (i.e., the crusher operation is not modeled). There are many plants of urea granulation spread around the world, which are generally operated by trial and error. On the basis of the urea world installed capacity and the forecasted growth of the urea market, there is a particular need to focus the research on urea granulation circuits to improve the efficiency of the plants in order to increase their competitiveness. Simulation tools, as the one developed in this work, can be very useful to explore new concepts of the urea granulation circuits. As aforementioned, the studies about circuit dynamics available in the literature cannot be extended to industrial urea granulation straightforwardly. A tool that takes into account the nature of the urea process (i.e., melt granulation, multichamber fluidized bed granulator with variable mass hold-up, the cooling stage, and validated models to represent the crusher and screens) has not been previously reported. In this paper, following our previous work,4,15-17 an integrated dynamic environment is implemented to evaluate and optimize the urea granulation circuit within a process of urea granules production. In this way the earlier developed models for the screen and crusher are integrated with the cooler and granulator model (which assumes accretion as the main growth mechanism in the multichamber fluidized bed granulation unit) into a dynamic circuit flowsheet. In our approach, all the units are modeled by means of the population balance equation (PBE). In addition, the cooler and granulator energy and mass balances for urea and air (used as cooling and fluidization medium) are solved simultaneously with the PBE to properly describe the size enlargement unit dynamics. The complete circuit dynamic model is then used to carry out sensitivity analyses by studying

the effect of different operating variables on the particle size distributions (PSDs) and mass flow rates of the product and recycle streams. Once the critical variables are identified, optimization studies are carried out aiming to maximize the plant production while the marketable product granulometry is maintained, together with other optimization scenarios. The modeling work was carried out using gPROMS modeling language, which provides a complete environment for modeling, analysis, and optimization of complex systems such as the one described in this work. Each of the components (see Figure 1) of the overall granulation circuit model is discussed briefly below. 2. Crushers, Screens, Granulator, and Cooler Mathematical Models Bearing in mind the importance of the simulation tools to predict the granulation circuit performance, which cannot be done intuitively, reliable models for all the circuit units are required.1,7,13,14 The double-roll type of crusher is commonly used as the size reduction unit in urea granulation circuits. This device is constituted of two pairs of rolls that rotate in opposite directions at a certain speed. The rolls can be smooth, corrugated, or toothed and the distance between them (GAP) is a key variable that strongly affects the crushed material’s PSD. In the breakage of urea, the double-roll crusher is preferred over other comminuting equipments because narrow size distributions, low dust, and limited noise generation are expected.18 The crusher model was presented in a previous contribution4 and is based on the one developed by Austin et al.19 for the mineral processing industry. It was validated using industrial data from a large-

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scale urea plant. In order to predict the performance of the crusher (i.e., the outlet product PSD), the particle size distribution of the feed (screens oversize fraction) and the gap settings are the only required inputs. The fertilizer industry requires, as above-mentioned, a classification step that is usually performed by double-deck vibrating screens. Vibrating screens have been extensively studied by numerous authors also in the context of the mining processing industry.20-24 Models in the literature can be classified as phenomenological, empirical, and numerical, being based on theory of the screening process, empirical data, and computer solutions of Newtonian mechanics, respectively.25 The screen model used in this contribution was developed in a previous work.15 It is founded on the one proposed by Karra20 that represents a nonideal classification operation, like the actual screening process, by determining the oversize partition coefficients for each size interval. The screen mathematical model reported by Karra20 (usually recommended for predicting the performance of industrial vibrating screens26) was found, after thorough discrimination of several empirical, probabilistic, and kinetic models, as the most suitable one to reproduce available industrial data. Pseudo-steady-state models were used for the screen and crusher as the dynamics of these processes are much faster than those of the granulator and cooler and therefore do not have a significant influence on the whole circuit dynamics.7 The urea fluidized-bed granulator is basically a bed of solids fluidized by air, fed continuously with small urea particles (seeds) and a urea concentrated liquid solution (about 96 wt %) that is sprayed from the bottom of the unit. The bubbling nature of the fluidized bed, which is responsible for the strong solids mixing, promotes the repeatedly circulation of the granules through the spraying zone. The granules grow through the deposition of tiny liquid droplets on the seed material, followed by cooling and evaporation of the water content of the droplets, which cause the solidification of the urea present in the solution. To increase the residence time of the granules and narrow the outlet product PSD, the industrial units possess several growth chambers (where the urea concentrated solution is sprayed) connected in series. Subsequently, fluidized bed dedusting/cooling compartments are arranged to meet specific requirements for further processing of the granules.3 In this work, the granulator model developed by Bertin et al.16 was implemented. The granulation unit was represented by three growth and three cooling chambers in series. Dynamic mass and energy balances were solved for all the fluidized beds together with the population balance equation. The dynamic urea mass balance for a chamber k was given by the authors16,17 as dmkT )m ˙ kin + m ˙ kmelt(1 - xkmelt) - m ˙ kout dt

mkT(0) ) mkT0

(1)

k where mTk, m ˙ ink and m ˙ out are the solid mass holdup, inlet, and outlet particles mass flow rates, respectively. Due to the series k-1 configuration, m ˙ ink ) m ˙ out for k from 2 to 6. m ˙ 1in represents the k seeds mass flow rate to the first growth chamber, while m ˙ melt k and xmelt are the urea solution mass flow rate atomized into chamber k and its water mass fraction, respectively. Considering that the granulator has three growth chambers and three cooling k compartments, m ˙ melt ) 0 for chambers 4-6. The particles flow between chambers is proportional to the square root of the pressure drop through the under-current passage area. The outlet solids mass flow rates were obtained by applying the Bernoulli equation:

k+1 m ˙ kout ) CDAko√2gFkbed(FkbedHk - Fk+1 ) bed H

k ) 1-5 (2)

m ˙ 6out ) CDA60F6bed√2gH6

(3)

where A0k and Hk are the passage area and fluidized bed height of chamber k, respectively. CD is the discharge coefficient. According to Massimilla,27 CD takes values around 0.5 for k particles much smaller than the passage or discharge areas. Fbed is the bed density, defined as Fkbed ) Fp(1 - εk) + Fkaεk

(4)

Fp, Fak, and εk being the particle density, the fluidization air density, and bed porosity in chamber k, respectively. To complete the set of equations to be solved in order to determine the mass dynamics, the fluidized bed height within each chamber was computed as Hk )

mkT FpAkT(1 - εk)

(5)

ATk being the cross-sectional area of chamber k. The following dynamic energy balance given by Bertin et al.,16,17 which assumes complete evaporation of the small water fraction present in the urea solution (≈4 wt %),3 was considered to compute the temperature Tk in each chamber. mkTCpu(Tk)

k dTk )m ˙ kin Tk-1 T Cpu dT + m ˙ kmelt(1 - xkmelt) × dt k Tk Cpu dT + m ˙ kmeltxkmelt Tk T Cpw dT Tk

∫

∫

∫

melt

melt

m ˙ kmeltxkmelt∆HEV(Tk) + m ˙ kmelt(1 - xkmelt)∆HDIS(Tkmelt) + Tk Tk ˙ kaYk Tk Cpv dT Tk(0) ) Tk0 m ˙ ka Tk Cpa dT + m

∫

a

∫

(6)

a

k where Tmelt , Tak, and Tk-1 are the temperatures of the melt, fluidization air, and solids entering chamber k, respectively. Tk is the chamber temperature, and according to previous studies3 it can be accurately considered equal to the outlet solid and air temperatures. ∆HDIS and ∆HEV are the latent heats associated to the urea melt dissolution and water evaporation. Cpu, Cpw, Cpa, and Cpv are the mass heat capacities of the solid urea, liquid water, air, and water vapor, respectively. Bertin et al.16 developed the population balance model for the urea fluidized bed granulator assuming that only growth by accretion occurs (elutriation, agglomeration, breakage, attrition, and nucleation were supposedly negligible). Therefore, the dynamic PBE for a well-mixed granulation chamber results

∂nk ∂(Gknk) + ) n˙kin - n˙kout ∂t ∂Dp

(7)

where Gk is the growth rate, Dp is the particle’s diameter, and k n˙ink and n˙out are the number density function of flows in and out of the chamber k, respectively. The PBE discretization technique developed by Hounslow and Marshall28 and adopted by Bertin et al.16 was implemented to solve the discretized form of eq 7 together with the initial condition nk(Dp,0) ) n0k. Assuming that particles belonging to different size intervals grow proportionally to their fractional surface area, Gk is defined as16


Gk )

2m ˙ kmelt(1

-

FpAkpT

xkmelt)

(8)

k where ApT denotes the total particles superficial area within chamber k. This equation states that all the particles, independent of their sizes, grow at the same rate. The numerical solution of eqs 7 and 8, together with the corresponding initial conditions, gives the dynamic evolution of the PSD within each granulator chamber. To avoid the particles caking and for better handling of the product, the granules that leave the granulator at relatively high temperature are further cooled down in a fluidized bed by using ambient air. The cooler was represented as a continuous stirred tank analogous to one of the cooling granulator chambers. Therefore, the dynamic mass, energy, and population balance equations solved for this unit are the same as those previously described for the last granulator chamber.

3. Implementation Environment gPROMS is a multipurpose tool mainly used to build and validate process models, for steady-state and dynamic simulations and optimizations.29 The models of the circuit units (dynamic multichamber granulator and fluidized bed cooler, stationary screen, and crusher) were integrated in the gPROMS Model Builder Environment in order to perform dynamic simulations and optimizations. The mass flow rate and PSD of the recycle stream (constituted by the crusher product and the screen undersize fraction) were successfully calculated, achieving convergence. Once all the units were integrated and the recycle was properly solved, a sensitivity analysis was performed in order to explore the circuit performance under changes in different operating conditions. The optimization tools presented in the gPROMS Model Builder Environment were also used. In the case under study, the optimization was specified to be a constrained point optimization in order to satisfy the bounds imposed on the variables during the steady-state operation by manipulating a set of decision variables.29 4. Results and Discussion 4.1. Open Loop Dynamics and Sensitivity Analysis. This study was performed by running different dynamic and steadystate gPROMS simulations of the entire granulation circuit. The standard mathematical solver for the solution of mixed sets of differential and algebraic equations in gPROMS, namely DASOLV, implements variable time step/variable order backward differentiation formulas (BDF).29 The aim was to determine the influence of different operating variables on the circuit performance. The manipulated variables chosen for the sensitivity k analysis were the urea melt flow rate (m ˙ melt ), top and bottom decks screen apertures (hT and hB), upper and lower crusher gaps (GAPU and GAPL), and the granulator fluidization air flow rate (m ˙ ak); each of them were disturbed (10% around the initial steady state values. All the dynamic simulations were started at t ) 0 in the initial steady state and the imposed disturbances were introduced 1000 s afterward. The circuit performance was monitored by tracking different variables, particularly the plant capacity (product flow rate), product and recycle quality, recycle fraction, granulation chamber heights, and temperatures. The quality of the solids streams was followed by the product and recycle SGN (size guide number) and the product fraction on specification. The SGN represents the particle size in millimeters for which 50% by weight of the product is coarser and 50% is

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finer, multiplied by 100. For the special case of granulated urea production, values of SGN between 300 and 320 are suggested.30 Furthermore, the product size is preferred to be within the range 2-4 mm.31 For this reason, in addition to the SGN, the cumulative mass fractions (W) under 2 mm and greater than 4 mm were also studied as a measurement of quality of the solids streams. In order to understand the effect of the disturbed variables on the granulator operation, the chambers’ heights and temperatures were also tracked. The chambers’ heights have a direct influence on the pressure drop, solid mass holdup, and degree of drops net deposition on the granules surface. These bed heights should be within certain values to guarantee stable operations and avoid the undesired attrition and agglomeration mechanisms. In addition, these heights should not exceed the chamber weir height, which would cause solids overflow or bypass. The growth bed temperatures have to remain high (not lower than 100 °C) to avoid the melt solidification in the spray nozzles and ensure complete water evaporation. However, too high temperatures (i.e., close to the urea melting point) would lead to partial or total quenching of the bed.17 As an example, the open loop dynamic analysis is shown through Figures 2a-f for a +10% step disturbance in the screen bottom deck. When the bottom deck aperture is increased, immediately bigger and more particles per unit time are allowed to pass through it to the undersize stream (7 and 38% initial increments in the undersize SGN and mass flow rate, Figures 2a,b). Consequently, coarser and less particles per unit time remain in the product stream (P), which at first lowers its mass flow rate 20% and augments its SGN 3%. The oversize stream remains unchanged at this first moment and until the disturbance reaches it after cycling through the whole circuit. The recycle stream is constituted by both the undersize (U) and oversize (O) streams from the screens, the oversize later being reduced to fines in the crusher. However, the undersize mass flow rate is 1 order of magnitude bigger than the crusher one. Therefore, the recycle behavior is almost a replicate of the trend exhibited by the undersize stream. As soon as the bottom deck aperture increases, the seeds flow coming into the granulator is higher and the particles are considerably bigger (initially changes of +35% and +7% for the seeds mass flow rate and SGN, respectively) as a consequence of the increments in the undersize stream SGN and mass flow rate. When the recycle particles enter the granulator immediately after the disturbance in the bottom deck aperture, the particles number in the growth chambers starts to raise, except for the first chamber, whose particles number initially shows a slight decrease (Figure 2c). The general increment in the particles number leads to greater solids superficial area and therefore to lower growth rate in all the chambers (Figure 2c), as can be inferred from eq 8. Consequently, after a complete cycle, the granulator product SGN decreases but its mass flow rate increases, because more particles per unit time are recycled to the size enlargement unit (Figures 2a,b). Thus, transitorily the stream that goes back to the top deck has a lower mass median and higher mass flow rate. As a result of the lower coarse fraction, the mass flow rate and SGN of the oversize diminish after the first cycle. For the screen product and undersize, reductions in the SGNs and increments in their flow rate are observed. The cycles take place until all the effects are compensated and the new steady state is reached. The behavior of the circuit can not be predicted without its simulation; in fact, both the quality and the mass flow of each solid stream have to be accounted for. Therefore, the tool here presented is essential to study the dynamics of the circuit.

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Figure 2. Open loop dynamic analysis for a +10% disturbance in the bottom deck aperture.

It is interesting to note that allowing more mass flow rate into the granulator by increasing the screen bottom deck aperture highly augments the solids mass holdup and therefore the fluidized bed heights in each chamber (Figure 2d). Together with this effect, the temperature of each chamber gets lower (Figure 2e). During the cycles, as the bed heights decrease, the temperatures increase and vice versa. As the mass holdup

increases, the inlet enthalpy provided by a constant melt flow rate becomes relatively lower per unit of bed mass, and as a result, the bed temperatures of the growth chambers have to decrease. Regarding the product quality, at the instant of the disturbance, there is an increase in the fraction of particles bigger than 4 mm and a decrease in the fraction of the particles smaller than 2 mm with a net increment in the stream SGN (Figure


Figure 3. PSD (number density) evolution with time for the last granulator chamber and a +10% disturbance in the bottom deck aperture.

2a). Nevertheless, both effects compensate and the fraction of product on specification remains almost unchanged during all times (Figure 2f). Even though this mass fraction is kept approximately constant, the marketable product stream evolves to a final steady state with higher SGN than the one corresponding to the initial steady state (Figure 2a). Even though, for a +10% disturbance in the bottom screen deck aperture, the system achieves a final steady state without any control action and the product SGN exhibits relatively low changes (as maximum 2% with respect to the initial steady state), the granulation beds show important deviations. The circuit has certain capability of self-control; however, the bed mass holdups should be kept under control to ensure the desired growth mechanism. Figure 3 shows the dynamic behavior of the particle size distribution (number density function) for the last granulator chamber and the +10% disturbance in the bottom deck aperture. As it is appreciated, the PSD exhibits oscillations during time. The time evolution of the PSD is in agreement with the effect described in Figure 2c (i.e., as the bottom deck aperture is increased more particles per unit time are allowed to enter the granulation unit, and consequently, the number of particles within the chambers increases, too). Figures 4-7 present the final steady-state response of some relevant granulation circuit variables when different disturbances are applied to the system. According to the steady-state simulation results, the screen top and bottom deck apertures are the variables that most influence the circuit performance. Figures 4a and 5b show that the product and recycle SGN increase as the top deck aperture increases because bigger particles are allowed to pass into the product stream. The presence of bigger particles in the feed to the bottom deck increases the probability of big particles passing through it to the undersize stream, which together with the crusher fines constitutes the recycle. In addition, the proportion of bigger particles in the oversize stream augments, although its total mass flow rate decreases. Accompanying this effect, the fraction of material in the product bigger than 4 mm increases while the fraction smaller than 2 mm decreases (Figure 4, parts c and b, respectively). Because the fraction of bigger particles increases in a higher proportion than the fraction of smaller particles diminishes, the fraction on specification in the product stream decreases (Figure 4d). Figure 6a,b illustrates that both the

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undersize and oversize streams diminish as the top deck aperture increase. Therefore, the recycle fraction, which is defined as the ratio between the material out of specification and the product [(O + U)/P], also decreases (Figure 5a). The overall effect of increasing the top deck aperture is a decrease in the fines that circulate through the granulation circuit; however, this advantage (as it is discussed below) is counterbalanced by more unstable operations. Since both screen apertures become more spaced as the top deck aperture increases, more particles per unit time are allowed into the product stream but not necessarily within the commercial size range. As expected, due to the lower seeds mass flow rate that enters to the granulator (Figure 5a), the bed temperatures increase (Figure 7a, first chamber temperature) while the bed height diminishes in all the chambers (Figure 7b, second chamber height variations). The aperture of the bottom deck is also a variable that highly affects the recycle and product streams. The effects of disturbing this variable were discussed above (Figure 2a-f). Although the screen top and bottom deck apertures cannot be changed under operation, the study of their influence on the circuit performance can be useful to define the appropriate screen meshes or to predict the effect of the apertures blinding. Regarding the impact of the urea melt, Figures 4a and 5b show that the product and recycle SGN decrease as the melt increase. Even though both the screen oversize and undersize streams increase (Figure 6a,b), the recycle fraction decreases because the product flow rate increases by the same amount the urea melt does (Figures 5a). Contrary to the effect caused by the screen apertures, the fraction of fines in the final product increases and that of the coarse material decreases, leaving the specification fraction almost unchanged (Figure 4b-d). Except for the product and oversize flows, the melt flow rate does not greatly affect the granulometry and flows of the others solids streams. Due to the higher seeds mass flow rate, the bed heights in the granulation chambers increase. Nevertheless, the increase in the granulator mass holdup is not enough to fully compensate the increments in the chambers temperature caused by the higher melt flow rate (Figure 6a,b). The simulation results indicate that the circuit variables seem to be quite insensitive to changes in the crusher upper gap. Even though the PSD of the upper pair of rolls outlet stream varies, the gap of the lower pair of rolls (constant for this analysis) allows almost reestablishing the final granulometry of the crushed stream. On the other hand, the influence of the lower gap on the product and recycle variables is relatively more important than the effect caused by the upper gap. As the lower gap increases (Figures 4a and 5b), both the product and recycle SGN increase because the particles undergo less breakage (i.e., bigger particles are generated by the crusher). The increment in the coarse material flow through the circuit results in a decrease of the fines classified by the screen and an increase in the oversize flow (Figure 6) with, as shown in Figure 5a, a net decrease in the recycle fraction (the undersize flow is higher than the oversize one). Regarding the product quality, an increase in the material bigger than 4 mm and a decrease in the material less than 2 mm are observed (Figure 4c,b). Overall, the product on specification slightly decreases, as shown through Figure 4d. As a consequence of the decrease in the recycle mass flow, the bed heights become somewhat lower and the chambers’ temperatures become higher (Figures 7a,b). The fluidization air does not directly influence the circuit PSDs and mass flow rates but has significant effect on the chambers levels and to a less extent on the bed temperatures.

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Figure 4. Product quality variables.

Figure 5. Recycle variables.

As expected, increases in the fluidization air flow rate lead to higher bed heights and lower temperatures in the granulator chambers (Figure 7). As can be seen in Figure 7a,b, some disturbances in the top and bottom deck apertures generate responses that are beyond the imposed limits for the chambers temperatures and heights, respectively. Therefore, the operation needs to be controlled to not surpass those limits. 4.2. Circuit Stability. To analyze the circuit stability, the effects of different step disturbances on the variables that most

affect the oversize mass flow rate were studied. As was described by other authors, the granulation circuits become less stable as the flow rate of the crushed material gets lower.5,12-14 Figure 8a presents the dynamic evolutions of the product SGN caused by changes performed in the crusher lower gap. As previously discussed, smaller lower gaps lead to more fines in the circuit and consequently to less material classified in the screens as oversize. This considerably augments the circuit instability, as indicated by the product SGN oscillations. Regarding the screen top deck aperture, the same effect


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Figure 6. Classification screens variables.

Figure 7. Multichamber granulator variables.

Figure 8. Different step disturbances in the crusher lower gap and the screen top deck aperture.

described for decreases in the lower crusher gap was observed when increasing this deck aperture (Figure 8b). Nevertheless, the circuit seems to be considerably more unstable for the top deck aperture, basically because the effects of hT on the oversize flow rate are instantaneous while those of GAPL are delayed by the dynamics of the granulator and cooler, which act as buffer stages. 4.3. Process Optimizations. Different circuit optimizations were performed by means of the optimization tools presented in the gPROMS Model Builder Environment. In the case under study and to establish the optimal design circuit variables, the optimizations were specified to be point optimizations, i.e.,

optimal steady-state operations. For this reason, end-point constraints were imposed. From the two available standard mathematical solvers, namely CVP_SS and CVP_MS, the first one solves steady-state and dynamic optimization problems while the second one is just for dynamic optimizations. Therefore, the CVP_SS is used in this case, which employs by default the DASOLV code for the solution of the underlying DAE problem. Detailed description on this optimization solver can be found elsewhere.29 The first optimization was performed with the aim of maximizing the fraction of product on specification (within the range 2-4 mm), by manipulating the lower crusher gap and

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Table 1. Optimization Results base case optimization 1 optimization 2 optimization 3

0.5Hweir e Hk e Hweir for k ) 1-6

Objective Function fraction on 86.39 specification (%) recycle fraction R product mass P flow rate

94.73 -

-

-

0.71R -

1.15P

Optimization Variables GAPL hT hB urea melt flow rate

GAPL hT hB m ˙ melt

product SGN (mm ×100) height chamber 1 height chamber 2 height chamber 3 height chamber 4 height chamber 5 height chamber 6 temperature chamber 1 temperature chamber 2 temperature chamber 3 fraction on specification (%)

317.68

1.29GAPL 0.87hT 0.98hB m ˙ melt

100 °C e Tk e 120 °C for k ) 1-3 W2-4mm g 90% As indicated by the results (Table 1, optimization 2), the control variables were changed in the same direction as in optimization 1. However, the overall effect causes a diminution in the recycle fraction, which implies less mass in the granulator, as reflected by the lower heights and higher temperatures. Therefore, there is a compromise between having more product on specification and less recycle to the granulator. Another interesting optimization analysis includes a plant revamping, the objective function of which can be formulated as maximizing the product mass flow rate by manipulating only the urea melt (hT, hB, and GAPL remain constant) but satisfying the constraints imposed in the optimization 1 (Table 1, optimization 3):

1.21GAPL 0.92hT 0.87hB m ˙ melt

GAPL hT hB 1.15 m ˙ melt

300a

300a

315.74

0.74Hweir 0.80Hweir 0.77Hweir 0.78Hweir 0.72Hweir 0.67Hweir T1

0.92Hweir Hweira 0.96Hweir 0.98Hweir 0.91Hweir 0.84Hweir 0.96T1

0.60Hweir 0.65Hweir 0.61Hweir 0.63Hweir 0.57Hweir 0.53Hweir 1.06T1

0.92Hweir Hweira 0.95Hweir 0.97Hweir 0.90Hweir 0.84Hweir 1.04T1

T2

0.98T2

1.03T2

1.04T2

maxmmelt(P) 300 e SGNproduct e 320

T3

0.98T3

1.02T3

1.04T3

0.5Hweir e Hk e Hweir for k ) 1-6

-

90.00a

Other Variables 94.73

90.00

86.42

0.71R P

0.90R 1.15P

Constraints

86.39

fraction on 86.39 specification (%) recycle fraction R product mass P flow rate a

maxhT,hB,GAPL(R) 300 e SGNproduct e 320

1.24R P

-

Active constraint.

both screen decks apertures. This optimization was accomplished by considering the following constraints: the product SGN must be within the 300-320 range, the granulator bed heights within the weir and minimum operating limits and the growth chambers temperatures (chambers 1, 2 and 3) within 100-120 °C. Mathematically, the first optimization problem can be formulated as maxhT,hB,GAPL(W2-4mm) 300 e SGNproduct e 320 0.5Hweir e Hk e Hweir for k ) 1-6 100 °C e Tk e 120 °C for k ) 1-3 The values of all the granulator variables for the base case and this optimization (optimization 1) are shown in Table 1. The crusher lower gap was shifted toward less fines production, making the circuit performance more stable. Both deck apertures were modified in order to have a narrower product size range, increasing the proportion of granules on specification. The objective is achieved by lowering the product SGN, increasing the recycle and the bed heights, and diminishing the temperatures in the granulator chambers. Even though optimization 1 leads to an increase of 10% in the product mass fraction on specification with respect to the base case, the recycle stream is forced to increase significantly. Because of this, another optimization was designed. The objective was to minimize the recycle but keep the production on specification greater than or equal to 90%:

100 °C e Tk e 120 °C for k ) 1-3 According to the results, the plant capacity can be increased up to 15% with a decrease of about 10% in the recycle and the fraction of product on specification will be kept almost unchanged with respect to the base case. For product flow rates higher than 15% with respect to the steady state, the height in the second chamber surpasses the specified weir height. 5. Conclusions A detailed mathematical model to represent the steady and dynamic operation of a urea granulation plant was developed. The open loop behavior was analyzed by disturbing different operating variables in order to determine their impact on the circuit performance. Even though the assayed disturbances affect the system variables, the sensitivity analysis indicated that the circuit has a certain capacity of self-control. The present study revealed that the effect of the variables on the circuit operation verifies the following order of importance: hT > hB > GAPL > k m ˙ melt >m ˙ ak > GAPU. This result indicates that the screen apertures blinding over time may affect the product quality significantly, being particularly important for the bottom deck that handles a lot of fines. It was also demonstrated that, for the urea granulation circuit here presented, the circuit stability also strongly depends on the oversize flow rate, as mentioned by other authors. In this work, the effect of the top deck aperture on the oversize flow rate (i.e., circuit stability) was found to be stronger than that caused by the lower crusher gap. Another application of the circuit model is the optimization of urea granulation plants. Through three different scenarios it was possible to determine the combinations of the operating variables with more impact that allows one to maximize the fraction of product on specification, to minimize the recycle fraction to the granulator, and to revamp the plant production without losing product quality and keeping the granulator heights and temperatures within the operating limits. This work illustrates that the developed granulation circuit simulator, besides providing the PSD of all the circuit solid streams, is a valuable tool to select the appropriate variable values to meet the desired production requirements that can vary over time according to the market


rules. Also the presented flowsheet can be combined with control loops of the granulator heights and temperatures, a bypass to manipulate the recycle stream, etc.; these flowsheet refinements together with dynamic optimizations will be the subject of future papers. Acknowledgment The authors express their gratitude for the financial support by the Consejo de Investigaciones Cientı´ficas y Tećnicas (CONICET), Agencia Nacional de Promocioń Cientı´fica y Tecnolo´gica (ANPCyT), and Universidad Nacional del Sur (UNS) of Argentina. Notation k ApT ) total particle superficial area within chamber k (m2) k A0 ) passage or discharge area (m2) ATk ) chamber k cross-sectional area (m2) CD ) discharge coefficient Cpa ) mass heat capacity of air (J/kg K) Cpu ) mass heat capacity of solid urea (J/kg K) Cpv ) mass heat capacity of water vapor (J/kg K) Cpw ) mass heat capacity of liquid water (J/kg K) g ) gravity acceleration (m/s2) Dp ) particle diameter (m) Gk ) growth rate for chamber k (m/s) GAP ) distance between rolls in the crusher (mm) GAPL ) crusher lower gap (mm) GAPU ) crusher upper gap (mm) Hk ) height of chamber k, k ) 1-6 (m) hB ) bottom deck aperture (mm) hT ) top deck aperture (mm) Hweir ) weir height (m) m ˙ ak ) fluidization air mass flow rate in granulator chamber k, dry basis (kg/s) m ˙ ink ) particle mass flow rate entering granulator chamber k (kg/s) k m ˙ melt ) urea melt mass flow rate in granulator chamber k (kg/s) k m ˙ out ) particle mass flow rate coming out granulator chamber k (kg/s) mTk ) solid mass holdup in granulator chamber k (kg) mTk0 ) initial solid mass holdup in granulator chamber k (kg) nk ) number density function in chamber k (no./m) n˙ink ) number density function flowing in chamber k (no./m s) k n˙out ) number density function flowing out chamber k (no./m s) O ) screen oversize mass flow rate (kg/s) P ) screen product mass flow rate (kg/s) PBE ) population balance equation PSD ) particle size distribution R ) recycle fraction SGN ) size guide number, particle size corresponding to the 50% of the mass cumulative size distribution (mm × 100) t ) time (s) Tk ) temperature in chamber k, k ) 1-6 (K) T0k ) initial temperature in chamber k, k ) 1-6 (K) Tak ) temperature of the fluidization air in chamber k (K) k Tmelt ) temperature of the melt entering to chamber k (K) U ) screen undersize mass flow rate (kg/s) W ) product cuts, mass fraction (wt %) Yk ) mass air humidity in chamber k, dry basis (kgwater/kgdry air) k xmelt ) fraction of water in the melt stream of chamber k

Greek Symbols ∆HEV ) latent heat capacity of water evaporation (J/kg) ∆HDIS ) latent heat capacity of urea melt dissolution (J/kg)

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ε ) bed porosity of chamber k Fak ) air density in chamber k (kg/m3) k Fbed ) fluidized bed density in chamber k (kg/m3) Fp ) particle density (kg/m3) k

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ReceiVed for reView November 30, 2009 ReVised manuscript receiVed May 4, 2010 Accepted May 25, 2010 IE901885X

Dynamic Simulation and Optimization of a Urea Granulation Circuit

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