BAHRAM TORKASHVAND ANALYSIS OF HEAT AND MOISTURE … No2_p171... · 2019-07-06 · the urea prilling process, the urea melt is dispersed by numbers of showers or rotating perforated

Chemical Industry & Chemical Engineering Quarterly

Available on line at Association of the Chemical Engineers of Serbia AChE www.ache.org.rs/CICEQ

Chem. Ind. Chem. Eng. Q. 25 (2) 171−182 (2019) CI&CEQ

171

BAHRAM TORKASHVAND1

SINA GILASSI2

REZA MOGHADAM3

1Department of Production Eng-ineering, National Petrochemical

Company (NPC), Tehran, Iran; [email protected]

2Department of Chemical Eng-ineering, Université Laval, Québec,

Canada 3Department of Applied Science

and Technology, Politecnico di Torino, Torino, Italy;

[email protected]

SCIENTIFIC PAPER

UDC 631.84:66.047.4/.6

ANALYSIS OF HEAT AND MOISTURE TRANSFER DURING DRYING OF UREA PARTICLES

Article Highlights • Developed a numerical model for drying of urea particles • Showed the effect of shrinkage coefficient on the size variation of particles • Investigated the effect of convection heat transfer mechanisms on the particle tem-

perature Abstract

Urea is an inexpensive form of nitrogen fertilizer which is widely used in the agricultural industry. Urea as granule is produced through a drying process by which moisture content decreases to avoid operational issues. In this study, a numerical model is proposed for the drying of urea particles in the prilling process. The model is developed based on mass, heat, and hydrodynamic transfer equations for the urea particles and cooling air. The moisture and tem-perature variations of particles and cooling air at different heights of the prilling tower are calculated under different operating conditions. The shrinkage of particles due to the moisture loss during the drying process at different heights of the tower is considered. The model is validated with the real data obtained from a urea drying plant operated under steady-state condition. The result highlights that the model can be used to manipulate the operating parameters to improve product quality and to minimize urea temperature to prevent lamps and caking formation in the tower.

Keywords: moving boundary condition, mixed convection, particle dry-ing, shrinkage, urea modeling.

Statistical data shows that the world population has been continuously growing since the end of the Great Famine of 1315–17 and the Black Death in 1350, when it was near 370 million, resulting in the growth of agricultural productions that supply a large part of food resources for people. The use of fertil-izers which contain three primary nutrients, nitrogen (N2), phosphate (P2O5) and potash (K2O), is a com-mon way to increase the agricultural yield in many countries. Solid urea is one of the nitrogen fertilizers which can be produced in the forms of granules and prills. It has the highest nitrogen content (46%)

Correspondence: S. Gilassi, Department of Chemical Eng-ineering, Université Laval, Québec, QC G1V 0A6, Canada. E-mail: [email protected]; [email protected] Paper received: 27 August, 2018 Paper revised: 13 October, 2018 Paper accepted: 30 October, 2018

https://doi.org/10.2298/CICEQ180827030T

amongst all solid nitrogenous fertilizers and is cur-rently considered to be a critical factor in the agri-cultural productivity growth in different countries. In 2014, it was reported that the world fertilizer nutrient consumption with a growth of 2 percent reached 186.9 Mt [1]. Since then there have been plans to build 60 new urea production lines by 2019. Twenty urea plants would be constructed in China, which will increase the global urea capacity to 211 Mt in 2019 [2]. By the same strategy, the global urea supply will be estimated at 208 Mt in 2020. Moreover, the global demand for urea production is forecasted to increase by 2% per year compared to 2015, 192 Mt in 2020 [3]. All statistics on the production and markets report a steady growth of global demand for urea production and also emphasize the importance of this strategic product for supplying food resources in the future.

Granulation is a key processing unit in forming or crystallizing solid particles and is commonly used

B. TORKASHVAND et al.: ANALYSIS OF HEAT AND MOISTURE TRANSFER… Chem. Ind. Chem. Eng. Q. 25 (2) 171−182 (2019)

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in different industries such as petroleum, food, and pharmaceutical. Urea prilling is a type of granulation process in which the urea melt as feed is solidified by transferring heat to the cooling air stream [4]. The urea melt can be sprayed by a pressure nozzle, a rot-ating perforated bucket, and two fluid nozzles [5]. In the urea prilling process, the urea melt is dispersed by numbers of showers or rotating perforated buckets with different nozzle sizes. In this process, at first, the sprayed spherical urea particles at a temperature above the urea melting point (132 °C) with moisture content of less than 5% fall through a cooling medium such as air with a temperature of 20 to 40 °C (dep-ending on the plant location), then both heat and moisture of the melting particles are steadily trans-ferred into the moist air. As the surface temperature of particles reaches the melting point temperature, the solidification process begins. In this state, the par-ticles have a thin boundary layer between the liquid and solid phases which gradually moves towards the center by changing the temperature. More details about the free and moving boundary condition are available in reference [6]. Finally, the fully solidified particles continue to transfer the heat and moisture to the moist air until settling on the floor of the prilling tower.

So far, few modeling studies about the urea pril-ling process have been reported. Schweizer et al. [7] formulated the solidification concept of urea particle using the momentum and phase change equation with respect to the temperature variation of particles. Hassanien and El Safty [8] also proposed another simple model without considering the temperature change in the cooling air along the tower. Alamdari et al. [9] suggested a mathematical model on the basis of hydrodynamic, mass, and energy transfer equat-ions for the urea prilling process. The temperature variation of cooling air in this model was also not taken into account. The computational method was not consistent as the proposed numerical solution of a system of partial differential equations (PDE) con-sisted of both analytical and numerical methods for the moisture and heat transfer equations, respect-ively. Mehrez et al. [10] introduced a model to prevent the formations of lump and cake in hot and humid conditions. The heat transfer equation of particles was defined for three steps, including the cooling and solidification processes. The heat transfer term relat-ing to the evaporation enthalpy was not defined in the equation of boundary condition for the particles and cooling air. They used the enthalpy method to calcul-ate the temperature change of particles during the solidification step. Inconsistency was seen in the modeling results, such as the average temperature of

particles. This issue was attributed to the use of two separate explicit schemes for the discretization of the particle and air equations. Rahmanian et al. [11] dev-eloped a numerical model for a local industrial urea prilling tower with a rectangular cross-sectional area. The model was validated by the real data plant and a good agreement was seen in particle temperature at different sizes. The modeling result also showed that increasing the amount of cooling air could reduce the risk of caking tendency during the operation. Ricardo et al. [12] introduced a mathematical model for the solidification of urea particle in the prilling process. In the model assumption, the mass transfer between the particles and the cooling air was ignored, and the air temperature during the solidification was also kept constant. In terms of formulation strategies, the heat transfer equation of the particle was only derived on the basis of the convection heat transfer between the air and particles. They also presented results con-cerning a shrinking unsolidified core model [13] without considering moisture transfer to show the formation of the solid phase in the solidification zone. In terms of other industrial applications, Ali et al. [14] developed a model to predict the temperature and moisture profiles of one-phase particles in a drying process. Their model cannot be applicable to the urea drying process as the heat and moisture transfer equations are defined without considering the phase change of particles during the drying along the tower.

Under the steady-state conditions, a urea plant might have serious operating problems. The main issue relates to the breakage of urea particles along the prilling tower due to non-uniform heat and mass transfer between the melt urea and cooling air. This issue directly affects the quality of urea product so that the particles might contain a significant amount of moisture. On one hand, the incomplete drying con-sequently causes to form the large sticky blocks in the packing equipment and bags. On the other hand, the size variation of urea particles along the prilling tower needs to be precisely controlled to avoid forming dust and cake formations. In this case, a dusty flow causes to form large urea masses on the tower wall and gradually decay the stability of the drying process. Under steady-state conditions, these masses fall and settle in the bottom of the column resulting in a pro-cess shutdown. In this study, a comprehensive math-ematical model is developed for the urea particles fall-ing along the prilling tower. This model consists of mass, heat, and hydrodynamic transfer equations for the urea particles and cooling air. The particle shrink-age due to the moisture transfer to the cooling air, and free (natural) and mixed convection heat transfer


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mechanisms are investigated to demonstrate the particle size change under different operating condit-ions and parameters. In order to simulate a counter-current process, appropriate boundary conditions and numerical scheme are chosen to simultaneously solve the moisture and heat transfer equations along the prilling tower.

MODEL DEVELOPMENT

The drying process of melting particles involves the moisture and heat exchanges with the cooling air along the height of the tower (Figure 1). The heat is transferred from the surface of urea particles to the cooling air by the convection mechanism. Simult-aneously the heat is also transferred from the particle core to the surface by the conduction mechanism and consequently, the core temperature gradually dec-reases. This theory can also be applied to interpret the moisture transfer from the particle core to the surface and then cooling air. The moisture content of humid air as absolute humidity is calculated by the given data for relative humidity and air temperature. Hence, the solution approach is to simultaneously solve all the transfer equations of urea particles and cooling air. The modeling performance can later be analyzed to determine the more accurate ranges of values for the variation of particles and air tempera-ture, and moisture under different operating con-ditions. Some assumptions are chosen to simplify the model formulation as follows:

1. The drying process is steady state and urea melt with biuret content, as an impurity, of less than

1% is continuously dispersed by a rotary bucket. 2. The pressure drop in the prilling tower can be

calculated by the modified Bernoulli equation [11]. 3. Radiation heat transfer from the melt

particles to the wall is neglected. 4. An adiabatic process is expected due to the

large thickness and low thermal conductivity of the prilling tower wall.

5. The shrinkage occurs because of the mois-ture removal from the spherical particles along the tower height.

Hydrodynamics

The melting spherical particles are dispersed by a perforated rotary bucket which is installed at the top and center of the prilling tower. Under normal con-ditions, an emerged particle falls down the cooling air with an initial velocity that is dependent on the rot-ation speed and diameter size of the rotary bucket, and initial urea temperature and viscosity. More det-ails about CFD analysis of the performance of the perforated rotary bucket are also available in refer-ence [15]. Three different forces exerted on urea par-ticles can be defined during the drying process. The particle is pulled down due to the force of gravity, and at the same time, buoyancy and drag forces tend to suspend it upwards. Later, the particle reaches its terminal velocity (highest velocity attainable by falling through cooling air) with zero acceleration when the sum of vectors of the three different forces exerted on the particle equals zero. Based on Newton’s law of motion, the hydrodynamic transfer equation can be expressed as follows:

ρ

= −

− − −1( )

2

upzup up

D a up upz az upz az

dVm m g

dt

C A V V V V (1)

ρ= − − −1( )

2upr

up D a up upr ar upr ardV

m C A V V V Vdt

(2)

where mup, Aup, Vup, Vaz and ρa denote the mass (kg), surface area (m2), and velocity of the particle (m/s), and velocity and density of the cooling air (kg/m3), respectively. CD stands for the drag coefficient that can be calculated based on the Reynolds number at different heights of the prilling tower as follows:

= ∀ <<24Re 1

ReDC (3)

= + ∀ < <0.68724(1 0.15Re ) 0.1 Re 1000

ReDC (4)

= ∀ < <0.44 1000 Re 200000DC (5)

Figure 1. Schematic flow diagram of a urea drying plant.


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Moisture transfer

The moisture transfer equation for the urea particle is given by the following relation [16]:

ρρ

∂ ∂∂=∂ ∂ ∂

22

( ) 1( )up up up

upX X

r Dt r rr

(6)

where ρup, X, and D are the density of dry solid urea (kg/m3), moisture content (kg water/kg dry urea particle), and diffusivity coefficient (m2/s), respectively.

The initial and boundary conditions are also defined as follows:

= ≤ ≤ =0, 0 : (0, ) initialup up upt r R X r X (7)

∂> =

∂0 : 0upX

tr

(8)

ρ

ψ ψ

∂> = = − =

∂= −

0, :

( )

upsurfaceup M up

surface airm M M

Xt r R J D

rh

(9)

where Xupinitial and JM

surface are the initial moisture content of urea particle and moisture flux, respect-ively. ψM

surface and ψMair also represent the moisture

concentration at the particle surface and in the air, respectively. hm is defined as the convective mass transfer coefficient between the particle surface and cooling air. Mixed-convection heat transfer exists during the drying of urea particles when the buoyant motion is in the same direction as the forced motion. The combined forced and free (natural) convection heat transfer can be defined as follows [17]:

= ± 0.333 3( ) ( )total free forced

m m mNu Nu Nu (10)

= ++

0.25

0.56 0.440.589

2(1 (0.46 / Pr) )

freem

RaNu (11)

= + 0.5 0.332.0 0.6Re PrforcedmNu (12)

where Nu, Ra, Re, and Pr are dimensionless Nusselt, Rayleigh, Reynolds and Prandtl numbers, respect-ively.

The moisture transfer equation for the cooling air can also be defined as:

ρϕ

∂ = −∂

( )up surfaceaa a m up a

element

AXV h C Cz

(13)

where ρa, Xa, and Va present the density, moisture content, and velocity of cooling air, respectively. Aup and ϕelement are the surface area of urea particles and discretized volume of prilling tower, respectively. Cup

surface and Ca stand for the moisture concentration

at the particle surface and in the cooling air, respect-ively.

Heat transfer

In terms of the single phase (liquid or solid) heat analysis, the heat transfer equation for the urea particle can be defined by the following relation [16]:

ρ∂ ∂∂=∂ ∂ ∂

, ,2

2

( ) 1( )

s l s lup p up upC T T

r kt r rr

(14)

where Tups,l stands for the urea particle temperature.

This equation is valid for the time that the solid or liquid urea particle (single phase) is dried by the cooling air. ρup, Cp, and k are the density, specific heat at constant pressure, and thermal conductivity of urea particle, respectively.

In terms of two-phase heat analysis, numerous numerical methods were proposed for the solidific-ation case when the boundary condition moves from the solid to the liquid phase [18-21]. Because of the coupled moisture and heat transfer equations, the Apparent Heat Capacity method (AHCM) is chosen to reformulate the heat transfer equation of urea particle as follows:

ρ∂ ∂∂=∂ ∂ ∂

22

( ) 1( )

o oup app up upC T T

r kt r rr

(15)

where Tupo and Cp-app are the urea particle tempe-

rature of two phases and apparent heat capacity, respectively.

The boundary conditions between the solid and liquid phases are defined as follows [6,22]:

ρ∂ ∂ ∂= > − =∂ ∂ ∂

( )( ), 0 : s l

s lT T s tx s t t k k Lr r t

(16)

= = =( ) : ( , ) ( , )s l ms s t T x t T x t T (17)

where ks, kl, and, L are the thermal conductivity of solid and liquid phases, and the latent heat, respect-ively. s(t) and Tm stand for the location and tempe-rature of the solid-liquid interface which is expected to change over time (drying at different heights of the prilling tower).

The heat transfer equation for cooling air can also be expressed as:

ρϕ

∂ = −∂

( )upaa pa a t up a

element

ATC V h T Tz

(18)

where ht, Cpa, and Ta are the convection heat transfer coefficient, specific heat at constant pressure, and air temperature, respectively.


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Particle shrinkage

The total volume of a urea particle which is the sum of the volume of urea and moisture, can be expressed as follows:

ν ν ν= +Tup up m (19)

where νupT, νup, and νm are the volume of the urea

particle, dry urea particle, and moisture, respectively. In this study, the model of particle shrinkage which exists because of the moisture removal from the urea particles can be formulated based on a mass transfer analysis between the material and moisture content [23]. Based on the model proposed by Coumans [24], the volume of the urea particle due to shrinkage can be defined by a linear function of the average moisture content as follows:

ρν ν τ

ρ= +(1 )upT

up up upm

X (20)

ρ ν ρ ν=Ts up s up (21)

ρρ τ ρ

=+

1(1/ ) ( / )s

up up mX (22)

ππ

= 23

0

34 ( )

4

upR

up upup

X r X r drR

(23)

where ρ and τ are the density of urea particle and moisture, and shrinkage coefficient (0<τ<1), respectively. The diameter of the urea particle can also be expressed as a function of the shrinkage coefficient and moisture content as follows [25]:

ρ τρρ τρ

+=

+0 0.5

0( )m s upup up

m s up

XR R

X (24)

where Rup and Rup0 are the varied and initial diameter

of the urea particle, respectively.

Numerical solution

The developed model based on the mass, heat and hydrodynamic transfer of urea particle and cool-ing air forms a system of differential equations along with coupled boundary conditions. As all systems of partial and ordinary differential equations (PDEs and ODEs) needs to be solved simultaneously, the method of lines (MOL) is chosen to solve the dev-eloped heat and moisture equations. This technique uses the finite difference to approximate all derivat-ives with respect to all independent variables in order to make a system of ODEs over a domain [26]. In the previous modeling work, the Crank-Nicholson method and an analytical method were used to solve the

moisture and heat transfer equations and conse-quently the modeling results were seen as incon-sistent at the lowest part of the prilling tower [9]. The enthalpy method was also proposed for the heat ana-lysis in the solidification zone in the prilling process [10]. But this technique decreases the accuracy of the numerical solution as other transfer equations except the particle heat transfer equations are solved indi-vidually.

In order to validate the model, the modeling result was compared with real data of a urea plant (limited to inlet and outlet conditions) and a good agreement was seen for the outlet temperature of average size particles (Rp = 0.85 mm) based on the inlet and outlet temperature of cooling air.

Moreover, the air temperature along the pilling tower at different points was measured while the plant operated under the steady state condition. Then, these values were compared with the modeling values of the air temperature as reported in Table 1. The model was run to show the temperature and moisture profiles inside the urea particles of different sizes under a realistic operation condition. The amount of moisture flux releasing from the particle surface to cooling air was also investigated to mea-sure the particle shrinkage along different heights of the prilling tower. The real operational condition of the urea plant (Table 1), Khorasan Petroleum Company, which is located in Bojnord (Iran), is used to show the model performance under realistic operating conditions. Table 2 also shows the properties of urea melt used in this modeling.

RESULT AND DISCUSSION

The analysis of heat and moisture transfer in the drying process is dependent on the trajectories of urea particles along the height of the prilling tower. The rotation rate and nozzle radius of the perforated bucket also affect the velocity of urea particles until reaching the terminal velocity where the particles tend to fall vertically at constant axial velocity. The cooling air velocity is another parameter that directly influ-ences the final temperature of the product. It is exp-ected that the Reynolds number which changes with the cooling air velocity and viscosity, and particle dia-meter, directly affects the heat and moisture transfer mechanisms by altering Nusselt and Sherwood num-bers. The shrinkage of urea particle which occurs due to the particle moisture loss along the height of prilling tower can slightly decline the Reynolds number. Any change in the Reynolds number directly affects the drying efficiency, as the heat transfer coefficient


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between cooling air and urea particles is also pro-portional to the Nusselt number. The particles with three different sizes (0.85, 1.2, and 1.5 mm) are chosen to investigate the effect of air temperature on the variation of temperature and moisture content, and size of urea particles.

Table 2. Properties of urea

Variable Value

Urea melt density (kg/m3) 1220

Melting point (°C) 132.7

Thermal conductivity (kW/(m K)) 2.651x10-5

Specific heat capacity (kJ/)kg K)) 1.334

Melting heat (kJ/kg) 224

Moisture diffusivity (m2/s) 2.74x10-9

Figure 2 demonstrates the temperature change inside the particles at the different heights of prilling tower. In the first zone, the particles with initial tem-perature (140 °C) lose their heat and reach the solid-ification temperature (132 °C). Then, the temperature of two-phase particles reduces until settling at the bottom of the prilling tower. The modeling results show that the variation of core and surface tempe-rature is increased by increasing the radius size even for such particle scale size. The solidification process is fully completed for the finer particle, its temperature profile is uniform whereas the coarser particles (1.2 and 1.5 mm) experience a sharper temperature pro-file. It is expected that the coarser particles fall faster

than the finer particles and consequently have lower time for the heat exchanging process with the cooling air along the height of the prilling tower. Decreasing the inlet temperature of cooling air may enhance the temperature of coarser particles. It is worth noting that the final core temperature of the coarser particles may remain above the solidification temperature (132 °C). As a result, the particles with a higher tempera-ture at the bottom of the prilling tower give rise to some operational issues for the packing section. In some cases, it is required to install cooling equipment to control and reduce the high temperature of the final product.

Figure 3 demonstrates the variation of particle moisture content (kg water/m3 dry solid) at the differ-ent heights of prilling tower. Similarly, the moisture content of the particles at the bottom of the prilling tower is increased by increasing the radius size. The modeling results show that the finer particle incurs more moisture loss than the coarser particles. Much more moisture is removed during the solidification process (zone 1) as the mass transfer resistance is lower for the liquid phase compared to the solid phase. When the first layer of solid appears at the outer surface of urea particles, the heat exchange rate coming from the core to the surface gradually decreases. Increasing the thickness of solid-phase layer directly influences the moisture content remain-ing inside the particles as the moisture transfer mech-anism changes for the two phases due to different

Table 1. Real operational parameters of a urea process plant

Variable Value

Error, % Inlet Observed Calculated

Tower height (m) 79.9

Tower diameter (m) 17

Conic angle of perforated rotary bucket (degree) 25

Rotation speed of perforated rotary bucket (rpm) 219

Particle average size (mm) 0.85

Moisture content of urea feed (wt.% (dry base)) 0.3

Temperature of urea feed (°C) 140

Moisture content of cooling air (wt.%) 3.7

Temperature of cooling air (°C) 35

Flow rate of urea feed (ton/hr) 75

Flow rate of cooling air (ton/hr) 775

Temperature of urea product (°C) 60 64.5 7.50

Temperature of hot air (°C) 65 69.4 6.76

Temperature of hot air along tower (°C)

Point A (20 m from bottom) 42 46.1 9.76

Point B (40 m from bottom) 55 58.3 6.00

Point C (60 m from bottom) 61 63.2 3.60


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Figure 2. Variation of particle temperature a) r = 0.00085 m, b) r = 0.0012 m, c) r = 0.0015 m.

mass transfer resistances. As shown, the moisture content variation exactly corresponds to the tempe-rature variation inside the dried particles at the bottom of the prilling tower. The particle with a radius of 0.00085 m has a more uniform profile of moisture content whereas the coarser particles have no sig-nificant variation. For instance, the moisture content of a particle with a radius of 0.0015 m remains at the initial value of around 0.36 kg water/m3 dry solid even at the bottom of prilling tower. In this case, the high amount of particle moisture content in the product stream may cause lump formation. Furthermore, the humidity of cooling air also influences the final mois-ture content of particles as the moisture inside the particles tends to be in equilibrium with the air mois-ture content. Hence, it is expected that when the cool-ing air with higher humidity enters the prilling tower to reduce the temperature of urea particles, the moisture boundary layer at the particle surface equals the same value of the air moisture content and, conse-quently, a lower amount of moisture can be trans-ferred between the moist air and the particles.

The average temperature and moisture content along the height of the prilling tower are shown in Figure 4. The finer particle loses its heat more quickly than the coarser particle, particularly in the first zone until reaching the solidification point. An evident dif-ference in the particle average temperature can be seen at the different heights of prilling tower. The ave-rage temperature of the fine particle (0.00085 m) dec-reases significantly until the height of 400 cm and then tends to level off until the bottom of the prilling tower. The linear part of the temperature curve also indicates the uniform temperature profile of solid par-ticles. The average temperature curve of the coarser particles slightly reduces and its slope corresponds to the higher temperature variation inside the particles. Similarly, it is seen that the average moisture content curve of the finer particles reduces more quickly than the coarser particles. As mentioned, they have a more uniform temperature profile and lower surface temperature; these directly affect the equilibrium moisture concentration and vapour saturation pres-sure at the interface between the solid and gas phase. As shown, the higher amount of moisture is


178

Figure 3. Variation of particle moisture content a) r = 0.00085 m, b) r = 0.0012 m, c) r = 0.0015 m.

Figure 4. a) Average temperature and b) average moisture

content of particles along the prilling tower.

removed in the first 10 m of the prilling tower where the layer thickness of the solid phase is still thin. The average moisture content curves slowly go down for the coarser particles. This is because the residence time of particles in the prilling tower is relatively short. In this case, the layer thickness of the solid-phase is still thin due to the non-uniform variation of the temperature inside the particles. It is expected that selection of optimal values of the urea feed flow rate and temperature, cooling air flow rate and tempe-rature have significant effects on the temperature and moisture profile inside urea particles.

Figure 5 illustrates the average temperature curve of the particle size of 0.00085 m (reported as particle average size) with the forced and mixed-con-vection heat transfer mechanisms as well as changes of the heat transfer coefficient along the height of pril-ling tower. In the drying process, the temperature and velocity of cooling air are considered as the vital oper-ating parameters which directly affect the drying effi-ciency. It is expected that the heat is exchanged between the cooling air and urea particles based on the forced convection transfer mechanism. When the temperature difference between the feed and product


179

streams is high, the mixed-convection transfer mech-anism can also be taken into account. The free (nat-ural) convection heat transfer mechanism occurs while the cooling air temperature gradually drops throughout the prilling tower. It is expected that the cooling air stream with higher temperature tends to go up to the top of the prilling tower. As discussed, the Nusselt number of each segment is calculated based on both free and forced-convection. As shown, the effect of free convection on the average temperature is low due to the high volume of cooling air compared to the urea feed flow rate.

Figure 5. Effect of forced and mixed-convection heat transfer

mechanisms on the average temperature of particles, as well as changes of heat transfer coefficient along the height of

prilling tower.

It is expected that the heat transfer coefficient for all particle sizes increases due to the increase in the Nusselt number and the coarser particles will have a higher Nusselt number than the finer particles. As the heat transfer coefficient is proportional to the Nusselt number, air thermal conductivity, and particle diameter, increasing the Nusselt number and particle diameter increases the heat transfer coefficient even for the particles with small sizes ranging from 0.85 to 1.5 mm. However, the net growth of the heat transfer coefficient along the tower decreases due to increasing of the particle size (0.85, 1.2 and 1.5 mm) with respect to the relation between conductive and convective heat transfer (Nu = htDp/k). In other words,

the heat transfer coefficient of the finer particles is lower than the coarser particles due to the significant effect of particle size. As the particle shrinkage begins from the initial to full solidification steps due to the moisture loss along the prilling tower, the heat trans-fer coefficient curve tends to increase and/or level off depending on the shrinkage rate at the different heights of the prilling tower. As shown, the curve of the finer particle (0.50 mm) levels off while the shrink-age mechanism stops along the prilling tower (h = 35 m). It is also expected that the transfer of moisture loss greatly reduces in the middle of the prilling tower for fine particles. Referring to Figure 3, the coarser particles (1.2 mm) which contain a higher amount of moisture, undergo the lower size reduction along the prilling tower. This relates to the lower moisture trans-fer from the center to the surface of these particles compared to the fine particles (0.50 mm). As shown, the curve of heat transfer coefficient along the tower steadily rises and then immediately levels off due to the smaller shrinkage. Furthermore, the Nusselt num-ber calculated by the free convection transfer mech-anism changes significantly for the coarser particles as the buoyancy force depends on the particle size whereas the viscous force changes with the air vis-cosity.

Figure 6 also shows the changes of the Grashof number at the different heights of prilling tower, as well as the effect of cooling air temperature on the particle average temperature. The Grashof number as the ratio between the buoyancy forces to the viscous forces is defined to show the effects of the particle temperature and size on the heat transfer mechanism along the tower. As shown, a sharp drop is seen while the particles move down to h ≈ 5 m (the formation of the solid surface). This highlights the impact of the natural convection on the heat transfer between air and particles when the temperature difference between the melt particles and the air is at maximum. It is expected that the solid layer immediately forms at the particle surface and the moisture loss results in the size reduction of particles. As shown, the variation of the Grashof number of the coarser particles is much higher than the finer particles along the prilling tower. This is because the Grashof number is pro-portional to the air and surface temperatures, and to the third power of the particle size. When the moisture loss decreases along the tower due to the solid-ification, the effect of natural convection on the heat transfer mechanism disappears quickly. Referring to Figure 2 which shows the profiles of particle tempera-ture, the difference in the final surface temperature between the fine and coarse particles is about 5-10


180

°C along the tower. In this case, the effect of surface temperature becomes negligible for all particles. As discussed, the moisture loss of particles changes their sizes, particularly in the solidification zone. Hence, it is expected that the particle size variation along the tower is a dominant parameter in the change of the Grashof number compared to the sur-face temperature along the tower height. However, the value of Grashof number along the tower dras-tically decreases for all particles which indicates the lower moisture transfer and the high impact of forced convection on the heat transfer mechanism between urea particles and cooling air. Decreasing the cooling air temperature results in the reduction of the average temperature of the final product. This change directly impacts the particle surface temperature along the tower and consequently improves the heat transfer from the core to the surface of the particles. More-over, a higher amount of moisture can be transferred to the cooling air. It is expected that the optimal values of air temperature and flow rate may result in the lower average temperature and moisture content in the final product.

Figure 7 shows the effect of mean shrinkage coefficient on the particle size variation at different heights of the prilling tower. As discussed, the shrink-age coefficient is a dynamic variable and can vary

from 0.1 to 1. As shown, the radius of fine particles decreases much more than the coarser particles because the shrinkage rate is higher and also a higher amount of moisture is removed during the dry-ing process throughout the prilling tower. Three dif-ferent particles with sizes of 0.0005, 0.00085 and 0.0012 m are chosen to investigate the effect of shrinkage coefficient value on the particle size. Refer to the previous modeling result, it is expected that the finest particle (0.0005 m) loses all its moisture during the drying process. The curve of particle size variation suddenly decreases until the first 20 meters of the tower and then levels off until the bottom of the tower as no moisture is transferred to the cooling air any-more. On the contrary, the curves of coarser particles steadily decrease until the bottom of the prilling tower. In fact, the reduction rate of particle size decreases as the lower moisture is removed during the drying process.

Figure 7. Effect of mean shrinkage coefficient (τ = 0.5) on

particle size.

Figure 8 shows the effect of minimum and max-imum shrinkage coefficient for the particles of 0.00085 and 0.0012 m. The change in particle size (%) between the initial and final diameter is given in Table 3. The shrinkage rate is highly dependent on the shrinkage coefficient as the particle diameter reduces sharply for the maximum value. Based on the shrinkage model, the variation of particle size corres-ponds to the moisture loss at three different drying zones. The particle volume is also a function of the average moisture content during the shrinkage. As a result, the change of particle size can directly affect the drying performances such as the profiles of mois-ture and temperature variations inside the particles. All of the operating parameters such as Nu, Re, Gr, and h change due to the change in particle size. The

Figure 6. Grashof number of particles at different heights of

tower as well as effect of cooling air temperature on the particle average temperature (r = 0.00085 m).


181

presented model can predict the change in the par-ticle size during the drying process by the difference in the initial and final moisture contents even for the fine particles. It may be difficult to determine the pre-cise value of the shrinkage coefficient without an accurate measurement of particle radius under a steady state condition. As shown, the finer particles experience more changes in size due to the higher moisture loss. It can be estimated that the size of coarser particles may be reduced up to 50 percent when the shrinkage coefficient equals unity (max-imum value).

CONCLUSION

A numerical model was developed based on the hydrodynamic, heat, and mass transfer equations between the urea particles and cooling air to show the

effects of operating parameters on the drying per-formance. For validation, the modeling result was compared with the data of a urea plant operated under steady state condition. The model performance was appropriate for the various range of small particle sizes. The finer particles had the lower average tem-perature and moisture content, whereas the moisture content of coarser particles did not change much after the solidification period. The result revealed that dec-reasing the air temperature had a significant effect on the particle temperature. However, this plan may not be applied as the cooling process of the air increases energy consumption and product cost. The change in particle size along the height of the tower was also modeled based on the shrinkage coefficient and moisture loss. The result showed that the particle size continuously changed depending on the drying zone due to the transfer of moisture to the cooling air. Finally, this model can be used for optimization of energy and drying cost and to prevent caking and lump formations inside the tower due to the income-plete drying.

Acknowledgment

The authors would like to thank Khorasan Pet-roleum Company and Mr. Alireza Karimi for technical support.

Nomenclature

Aup Urea surface area (m2) CD Drag coefficient D Diffusivity coefficient (m2/s) Dp Particle diameter (m) Cp Specific heat capacity (J/kg.K) Gr Grashof number hm Convective mass transfer coefficient (m/s) ht Convective heat transfer coefficient (W/m.K) k Thermal conductivity (W/m2.K) m Mass of urea particle (kg) Nu Nusselt number Pr Prantdl number Re Reynolds number i Rayleigh number Sc Schmidt number Sh Sherwood number t Time (s) T Temperature (K) V Velocity (m/s) X Moisture content (kg water/kg dry urea)

Superscripts r Radial direction up Urea particles z Axial direction

Figure 8. Effect of minimum and maximum shrinkage coefficient (τ) on the particle size a) d=0.0017 m, b) d=0.0024 m.

Table 3. Percentage of particle size variation for the different shrinkage coefficients

Dp (m) Shrinkage coefficient

0.1 0.2 0.5 0.7 1

0.0017 13.32 27.99 35.21 41.79 46.64

0.0024 8.9 17.35 21.46 23.94 26.24


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Greek letters ρ Density (kg/m3) ϕ Element volume (m3) τ Shrinkage coefficient ν Volume (m3) ψ Moisture concentration (kg/m3)

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BAHRAM TORKASHVAND1

SINA GILASSI2

REZA MOGHADAM3

1Department of Production Engineer-ing, National Petrochemical Company

(NPC), Tehran, Iran 2Department of Chemical Engineering,

Université Laval, Québec, Canada 3Department of Applied Science and

Technology, Politecnico di Torino, Torino, Italy

NAUČNI RAD

ANALIZA PRENOSA TOPLOTE I VLAGE TOKOM SUŠENJA ČESTICA UREE

Urea je jeftin oblik azotnog đubriva koji se široko koristi u poljoprivrednoj industriji. Urea u obliku granula proizvodi se procesom sušenja, pri čemu se sadržaj vlage smanjuje kako bi se izbjegli problemi u radu. U ovom radu predložen je numerički model za su-šenje čestica uree u procesu granuliranja. Model je razvijen na osnovu masenih, top-lotnih i hidrodinamičkih jednačina prenos za čestice uree i rashladnog vazduha. Varij-acije vlage i temperature čestica i rashladnog vazduha na različitim visinama tornja za granuliranje izračunavaju se pod različitim radnim uslovima. Razmatra se skupljanje čestica zbog gubitka vlage tokom procesa sušenja na različitim visinama tornja. Model je validiran realnim podacima dobijenim iz postrojenja za sušenje ureje koje radi u sta-bilnom stanju. Dobijeni rezultat naglašava da se model može koristiti za manipulaciju radnim parametrima kako bi se poboljšao kvalitet proizvoda i kako bi se smanjila tempe-ratura ureje da bi se sprečilo stvaranje grudvica u tornju.

Ključne reči: pokretni granični uslov, mešana konvekcija, sušenje čestica, sku-pljanje, modelovanje granuliranja uree.

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BAHRAM TORKASHVAND ANALYSIS OF HEAT AND MOISTURE … No2_p171... · 2019-07-06 · the urea prilling process, the urea melt is dispersed by numbers of showers or rotating perforated