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Modeling the Release of Nitrogen from Controlled-Release Fertilizer with Imperfect Coating in Soils and Water Thanh H. Trinh,*,†,‡ KuZilati KuShaari,*,† and Abdul Basit† †

Department of Chemical Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia Faculty of Chemical Engineering, HCMC University of Technology, Ho Chi Minh, Vietnam

‡

S Supporting Information *

ABSTRACT: Urea is vulnerable to losses from volatilization or leaching when applied to soils. This study proposes a porous model that couples the interfacial area ratio (IAR) equation for the diffusion of nitrogen with mass transport equation in porous medium (soil). The model presents the release of a single granule with an imperfect coating thickness in different environments. The model is validated with experiments in water and soil environments. In addition, it is compared to our previous model and shows an enhancement in its predictive ability because the imperfection of the coating layer has been integrated in the model. On the basis of the proposed model, the influence of coating variation and soil types also are investigated. In general, simulation results suggest that the coating layer imperfection leads to earlier and faster nitrogen release than an ideal one. Also, nitrogen release in soil depends on soil characteristics such as surface area, particle size, and density. The comparison with experimental observations taken from the literature has validated the model’s prediction of nitrogen release in different soil types. Finally, the model has an advantage that it can model the nitrogen release either in water or soil environments. By using the input from the experimental data for the release in water, the release in soil is extrapolated based on the specific soil properties, which can be obtained from experiments or the literature.

1. INTRODUCTION In addition to carbon, hydrogen, and water, plants require 14 additional nutrients for their development and growth.1 These additional nutrients are supplemented in appropriate amounts by fertilizers to eliminate the deficiencies to plants.2 Nitrogen (N) is essential to the protein production that promotes plant growth and enhances crop quality.3 Urea plays a role as an important supplementary source of nitrogen because of its high nitrogen content (47%) and good storage properties.4 However, its nutrient use efficiency (NUE) is only about 50−60%.5 Thus, several approaches on controlled-release fertilizer (CRF) have been developed to enhance NUE. Effect of nitrification and urease inhibitors on NUE have been reported by McCarty,6 Edmeades,7 Watson,8 and Lupwayi.9 Others have investigated condensation products of ureaaldehydes (slow-release fertilizers).5 Another approach is the investigation of novel material and their effect on NUE using a variety of coating materials like rosin coating,10 carboxymethylcellulose/hydroxyethylcellulose,11 polystyrene foam,12 super absorbent formula,13 and polydopamin.14 Understanding factors that induce the release of nutrients from fertilizers and affect nutrient uptake by plants as well as appropriate approaches to control the response mechanisms of materials in the soil environment are essential when selecting new material to enhance NUE.2 Hence, numerous researchers have explored the field. In 1989, Salman et al.15 studied the release behavior of polyethylene-coated urea at different temperatures (25, 35, 45 °C) in different media including water, sandy soil, and wetland rice soil. They concluded that coating quality was the controlling factor, and that pinholes and imperfections in the coating film led to higher urea release. Cahill et al.16 found no difference in the percentage of nitrogen © 2015 American Chemical Society

release of coated fertilizer treated in soil samples collected from Candor or Cecil, North Carolina. Medina17 used an incubation soil column to characterize the release of CRF in different soil types and temperatures. The percentage of N released/day to the soils typically increased as the textural class changed from sandy to loamy. Nevertheless, these studies ignored release kinetics related to soil type and did not establish a model to describe such effects on nitrogen release in soil. This research gap might be due to the complex nature of soil texture and microbial activities. Moreover, the release in soil not only concerns the movement of nutrients with soil water but also within the soil matrix. Nutrients occasionally react among themselves as well as with the soil matrix.18 Hence, the release behavior in soil is very important,14 and several studies attempted to explore that behavior. Kochba et al.19 proposed a first order kinetic for the release of nitrate fertilizer into soil and demonstrated that water vapor penetration was the controlling factor in the process. Gandeza20 applied a quadratic regression model to the effect of temperature on the cumulative release of polyolefin-coated urea in the field. Brar21 analyzed the release of potassium (K) fertilizer by fitting experimental data with several kinetic expressions including zero order, first order, parabolic diffusion, and power laws as well as Elovich equations. Furthermore, Xiaoyu22 compared nitrogen release data with exponent and double-exponent equations representing Fickian diffusion and dissolving−eroding diffusion mechanism. Most of their efforts Received: Revised: Accepted: Published: 6724

April 5, 2015 June 14, 2015 June 15, 2015 June 15, 2015 DOI: 10.1021/acs.iecr.5b01281 Ind. Eng. Chem. Res. 2015, 54, 6724−6733

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Industrial & Engineering Chemistry Research were based on regression models, whereas very few studies looked into the mathematical (mechanistic) modeling approach. A detailed program was written by Jarrell and Boersma23 that combined diffusion through holes in sulfurcoated urea granules with a regression model for the percentage of open granules. This model accounted for effects from microbial activity, temperature, and soil water but did not describe effect of nutrient release from different soil types. Shavit24 studied the release of KNO3 and urea from a tubular delivery device and coupled solute transport equations with the transport equation of vapor moisture within the device. However, they also did not study the effect from soil environments on nutrient release. In contrast to the release in soil, there have been numerous achievements in the mathematical modeling approach for the nitrogen release in water environment including, for example, models by Lu and Lee,25 Al-Zahrani,26 Shaviv,27 Du,28 and Lu.29 Recently, on the basis of a finite element method (FEM), the present authors30 proposed a multi-diffusion model that integrated diffusion through multi-layer and concentrationdependent diffusivity to solve a problem presented by the complexity in geometry and phenomena. The model has proved its robustness and reliability through a wide range of granule size and release period in prediction of the N release in water. Most recent research works on novel coating materials applied for CRF have focused on the nutrient release behaviors in water as well as soil11,13,16 because the release in soil is more important and reflects actual behavior under field conditions. Hence, a mathematical model that can predict nitrogen release patterns in soil would substantially support current researches. Besides, CRF coating imperfection is another significant factor that affects the release of nutrients.31 Consequently, the objective of the present work is to establish a release model in soil that accounts for the effect of coating imperfection and soil characteristics (i.e., porosity, particle size, and surface area).

Figure 1. (a) CRFs applied in soil. (b) Geometry and mesh generation of urea granule (core and coating layer) and environment in 2Dcoordinate, where R0(r, z) and Rl(r, z) are radii of urea core and urea granule, respectively.

2. METHODOLOGY 2.1. Mathematical Model. CRFs applied to a field are surrounded by a soil medium as shown in Figure 1a. It is generally assumed that a urea granule is symmetrical across its horizontal and vertical axes (from its core) so that the model can be described by a quarter of urea granule. A 2D-model of urea granules in soil is shown in Figure 1b. When fertilizers contact with water or soil environments, they are wetted for a period called lag time (t0). At this moment, the coating layer is saturated with water, and the release of nitrogen, in form of urea, begins. Water within the core will dissolve solid urea and nitrogen diffuse through the coating into environment. In this model, nitrogen transport through a coating layer can be described by mass transport equation for porous medium. The transient transport is represented by eq 1.29 ⎡ ∂ 2C(r , t ) ∂C(r , t ) 2 ∂C(r , t ) ⎤ De⎢ + ⎥=ε 2 r ∂t ∂r ⎦ ⎣ ∂r

where (ci) denotes the concentration of species i in the liquid (mole m−3); (θ) is liquid volume fraction; (De) is effective diffusivity (m2 s−1); (τF) is the dimensionless tortuosity factor and will be discussed in section 2.2; (Ri) is the reaction rate expression that accounts for reactions in the liquid, solid, or gas phase; and (Si) is an arbitrary source term (e.g., fluid flow source or sink). It is assumed that mass transfer of nitrogen in the soil surrounding the fertilizer is by diffusion, and there is no source/ sink or reaction occurred. Hence, this equation becomes ∂ci ∂ε + ci + ∇(ciu) = ∇·[(θτF , iDF , i)∇ci] (3) ∂t ∂t This model is based on the following assumptions: (i) The release of nitrogen (in the form of urea) is by means of diffusion, and there is no movement of soil water within the domain (stagnant condition). (ii) Temperature remains constant during release time. (iii) There is no reaction or loss of nitrogen in the soil environment. This condition occurs in laboratory setting in the absence of leaching and where the soil is sterilized prior to release experiments. Therefore, urea transformation by urease is minimized. Under field conditions, urea transforms to ammonium in the presence of urease. For purposes of this study, simulations of different soil types were ε

(1)

As the surrounding environment is soil, nutrient release in saturated porous medium can be described by eq 2 ε

∂ci ∂ε + ci + ∇(ciu) = ∇·[(θτF , iDF , i)∇ci] + R i + Si ∂t ∂t (2) 6725

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Industrial & Engineering Chemistry Research conducted, and the diffusion coefficient in soil is implemented according to section 2.2. 2.2. Urea Diffusion Coefficient in Soil Environment. The diffusion coefficient in soils (Ds) is slightly less than that in pure water (Df), mostly due to the tortuous flow paths in soils. This difference is represented as a dimensionless tortuosity factor (τF).18 Saripalli32 proposed a model (interfacial area ratio, IAR) to calculate the diffusivity of one solute in soil (Ds) based on the diffusivity of that solute in water (Df). The tortuosity factor in soil for the present study was therefore determined by interfacial areas ratio (IAR) model as follows: τF =

3.3ε Srp

(4)

where (S) is specific surface of porous medium (m2 m−3), (rp) is the particle radius of the porous medium (m), (ε) is porosity, and (τF) is dimensionless tortuosity factor. In addition, the diffusion of urea in water (Df) is concentration dependent and can be determined by eq 5:33 Df (r , t ) = (1.380 − 0.0782C(r , t ) + 0.00464C(r , t )2 )10−5 cm 2 s−1

(5)

2.3. Implementing Coating Thickness Distribution to the Model. Most existing models have been based on the assumption that fertilizer granules have a perfect coating and spherical shape. However, fertilizer granules are neither spherical nor are their coatings uniformly perfect. Furthermore, both parameters play significant roles in actual nutrient release.31 We accepted the assumption of spherical shape of urea core for this study but allowed for variance in the coating layer due to the coating process. The latter imperfection is illustrated in Figure 2a. Variability in coating observed in nature can be approximately by normal distribution as described in eq 6.34 f (x ; μ , σ ) =

⎛ (x − μ)2 ⎞ 1 exp⎜ − ⎟ σ 2π 2σ 2 ⎠ ⎝

Figure 2. (a) Structure of coating thickness via SEM. (b) Coating thickness distribution in coated fertilizer that is represented by normal distribution.

(6)

where [f(x; μ, σ)] is the probability density function, (μ) is median of coating thickness distribution, and (σ) is the standad deviation (STD) of the distribution (σ > 0). Figure 2b presents coating variation by normal distribution, and (l_distribution) is the cumulative (integral) form of coating distribution. When coating thickness varied from minimum to maximum thickness, the cumulative distribution (l_distribution) varied from 0 to 1, and the angle (θ) of parametric curve varied from 0 to π/2. To present this distribution for the model’s geometry, the granule radius [Rl(r, z)] can be specified as a parametric curve expressed as follows: ⎛π ⎞ r = (s + R 0) × cos⎜ × l _distribution(s)⎟ ⎝2 ⎠

(7)

⎛π ⎞ z = (s + R 0) × sin⎜ × l _distribution(s)⎟ ⎝2 ⎠

(8)

Figure 3. Presentation on converting coating distribution (l_distribution) to 2D geometry of granule fertilizer. Variable s presents the minimum to maximum thickness range of distribution, and R0 is urea core radius. Coating layer geometry was simulated via parametric curve (following eqs 7 and 8), which presents its distribution. In this figure, average coating thickness (μ) is 64 μm, standard deviation (σ) is 10 μm, and variable s varies from 38 to 90 μm.

where (l_distribution) is integral form of normal distribution function, and (s) is a variable representing the minimum to maximum thickness range of distribution. The geometry of the coating layer matching thickness distribution is demonstrated in Figure 3. Statistical distribution of coating thickness was determined by the standard deviation of coating thickness (σ). In this study, effect from variations in 6726

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Experimental results obtained from Ni et al.11 and simulation parameters are in Table S2 (Supporting Information). Third simulation compared nitrogen release in water and soil environment. Fertilizer parameters are mentioned in Table S1 of the Supporting Information, and soil characteristics are summarized in Table S332 of the Supporting Information. 2.5. Effect of Coating Thickness Distribution on Nitrogen Release. The simulations assumed granules of the same average thickness (64 μm) but with different distributions and standard deviations (σ) of 1, 2, 3, 5, and 10 μm. Simulation results were used to understand the effect of coating variation on nitrogen release and were compared with experimental data to choose the best matched distribution. 2.6. Effect of Soil Types on Nitrogen Release. We investigated effects of soil types on nitrogen release for several soils. The soils properties were obtained from the literature11,18,35 and are noted Table S4 of the Supporting Information. The utilized granule is described in Table S1 of the Supporting Information except for the coating’s standard deviation of 10 μm for this simulation. Mass transport within the soil domain was calculated as per eqs 3−5.

coating thickness was investigated by means of this standard deviation. 2.4. Model Simulation and Validation. The model was implemented with a 2D symmetrical coordinate solved by eqs 1, 3, 4, and 5. The urea model’s complexity is due to coating layer imperfection. Hence, the finite element method (FEM) was selected to investigate nitrogen release due to geometric irregularity and complex set of equations. Mesh generation created approximately 45,685 elements of average quality of 0.9801 and the implicit differential-algebraic (IDA) solver solved the set of equations with backward differentiation formulas (BDF). Error between iterations ranged from 10−19 to 10−16 during the calculation process, and the accuracy of simulation through mesh convergence analysis was 0.00125%. The maximum time step was 0.1 day. The simulation comprised two stages: constant and decay release. Hence, initial values and boundary conditions, as specified for the model, depended on each stage as described elsewhere.30 A summary of these conditions is as follows: Boundary conditions for constant release stage: C(R 0 , t ) = Csaturated(t 0 ≤ t ≤ t1)

C(R1 , t ) = 0(t0 ≤ t ≤ t1)

3. RESULTS AND DISCUSSION 3.1. Modeling Results and Validation. The proposed model was applied to the case that the surrounding environment is water, and results were compared and validated with multi-diffusion model reported by Trinh et al.30 Figure 4

(9) (10)

Boundary conditions for decay release stage: D∇C(R1 , t ) = 0(t ≥ t1)

(11)

The total amount of nitrogen release at any time t is calculated as Nrelease(t ) =

m urea released (t ) × 100% mtotal urea

(12)

where t0 is lag time, day; and t1 is “constant release” time, day. After this time, the release changes from constant release to decay release stage: Nrelease (t) is percent of nitrogen released from fertilizer at time t, wt %; murea released (t) is cumulative urea released from fertilizer at time t, g; and mtotal urea is total urea in fertilizer at the beginning, g. Three simulations were run to validate the model. The first simulation was run by assuming water as the release environment. The result was compared with the Trinh et al. model,30 and our real experimental data in water.30 In the experiments, release tests were conducted in a 250 mL beaker, and nitrogen concentration was measured with a UV−vis spectrometer for every 2−5 day. The simulation for nitrogen release in water was based on the porous model that was described in sections 2.1, 2.2, and 2.3. Because the surrounding environment is water, porosity and tortuosity approach unity as per eqs 13 and 14.

ε=1

(13)

τF = 1

(14)

Figure 4. Comparison between the proposed (porous) model with the model and experimental data in Trinh et al.30 on nitrogen release profile in water (*data adapted from Trinh30).

shows that the both models produced almost similar results. The porous (proposed) model also corresponded with experimental results. The standard errors of estimate (SEE) were 0.0296 and 0.0298 for the porous model and multidiffusion models, respectively. These results also indicated that the predictions of these models are almost similar; however, the prediction of the proposed model was enhanced for an aqueous environment, which was likely due to the inclusion effect from coating imperfections in predicted results, which will be discuss later. The next simulation focused on the release of nitrogen in soil, and diffusivity of urea in the soil domain was calculated following the IAR formula proposed by Saripalli.32 Simulation results corresponded with experimental results as shown in

Both parameters were used to validate the model along with geometry and other parameters as shown in Table S1 of the Supporting Information. A second simulation was conducted for the release of urea in silt loam with an environmentally friendly coating composed of attapulgite clay matrix and ethylcellulose film (APT/EC). 6727

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At the end of the release process (95−98% nitrogen released), the release rate in water became slower than that in soil, and the controlling factor slowly changed from coating layer to soil because of the low concentration gradient in the environment domain at this stage. Hence, the driving force within the environment became smaller than that in the coating layer and began dominating the release process. Analogous urea release profiles in different soil types and water have been reported in Salman’s experiments.15 This information is very useful for researchers who develop new coating materials because experiments in water have adequately represented for the release pattern of fertilizer in soil. Although the release patterns were similar in water and soil, there was a big difference in nitrogen concentration distribution in those environments. Figure 7 demonstrates concentration profiles of nitrogen in both water and soil media. Concentrations surrounding the granules were 4.5 and 26.0 mol m−3 from water and soil, respectively, being much lower in water than in soil. The difference likely was caused by lower resistance in the water domain, thus permitting nitrogen to move outward easily and reduce intraparticle concentration. These data are significant because nitrogen concentration was the determining factor to the loss of nitrogen through reaction and leaching of nutrients, actions that also affect nitrogen absorption by plant roots. As a rule of thumb, the difference in concentration also is applied for different soil types, which will be discussed later. This difference further explains effects of different soil types on the plant growth for which similar fertilizer applications were applied. 3.2. Effect of Coating Thickness Distribution on Nitrogen Release. Table 1 shows that SEE variance depended on coating distribution (σ), and that a coating deviation of 2 μm best matched the experimental data. Our simulation results demonstrated a trend toward an increasing release rate as coating imperfection in thickness increased (represented by σ: standard deviation). Therefore, the time for 90% nitrogen released (t2) decreased from 63.62 days to 58.76 days as σ

Figure 5, and the SEE values were acceptable (0.0746). The model thus proved reliable and robust for the prediction in water or soil environments.

Figure 5. Comparison between simulation and experiment on nitrogen release profile from APT/EC-coated fertilizer in soil. Simulation parameters are summarized in Table S2 (Supporting Information), and predicted results were based on the porous model. Experimental data is obtained from Ni et al.11

The third simulation compared nitrogen release profiles in sand (soil) and water environments. As shown in Figure 6, the release in sand was slower than in water, clearly indicating that environmental properties contribute to the restriction of nitrogen release. However, the difference of urea release in sand and water is very minute. This infers that the main controlling factor for nitrogen release is the coating layer itself and not the external environment that surrounds the coated fertilizer, be it water or sand.

Figure 6. Comparison between the release profiles of nitrogen in water and sand environments. Sand characteristic: porosity is 0.3, surface area is 450 cm2 cm−3, and particle radius of the porous medium is 100 μm. 6728

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Figure 7. 2D contour plots compare nitrogen concentration distribution between the release in (a) water and (b) soil medium after 3.9 day. White contours and color legend present nitrogen concentrations in mol m−3.

Table 1. Effect of Coating Distribution (σ) on Time (t2) and Standard Error of Estimate (SEE) σ (μm)a

t2 (days)b

SEEc

1 2 3 5 10

63.6 63.0 62.3 61.8 58.8

0.0296 0.0295 0.0295 0.0304 0.0377

Standard deviation of coating thickness is represented by σ. bt2 is the time for 90% nitrogen released. cSEE is the standard error of estimate between simulation and experimental data.

a

increased from 1 to 10. The release of nitrogen also is affected, therefore, by imperfections and decomposition of the coating.31 It had been posited that coating imperfections affect resistance to nitrogen transport. Where the coating is thinner, resistance is lower and permits easier nitrogen transport outward. This trend also was found in the release model of rosin-coated fertilizer.10 The soonest release occurred at the early stage in the case of highest variance in coating weight where the release rate was also higher than other distributions. However, the release slowed and was also slower than the other distribution in their study10 in contradiction to the present work in which release rate increased as imperfections in the coating layer increased, even toward the final stage (Figure 8). This contradiction is explained on the basis that our model demonstrated the release from a single granule instead of population of granules as stated in the literature.10 In the case of a population, if the granules have the same urea core diameter and different coating thickness, granules with thin coatings release first and those with thick coatings release later. Similarly, if the granules have the same coating thickness and different urea core diameter, the large granules release faster (at the beginning) and longer than the smaller ones.36 Hence, the cumulative urea is high at the early stage. These tendencies direct the researchers10 to the total release profile which was higher at the early on and lower toward the final stage as discussed earlier. For the simulation results of this work, during the release from a single granule, the ratio of nitrogen flowing through the thinner part of the coating

Figure 8. Comparison of nitrogen release profiles for granules with different distributions (σ = 1, 2, and 10 μm). These granules have the same average coating thickness (μ) of 64 μm.

is higher than other sections. As shown in Figure 9, a higher nitrogen flux moved toward the thin part of the coating. This trend is kept until end of the release process. Hence, the release to the environment was greater and sooner even at the final stage of the release compared to an ideally coated granule having the same average coating thickness. In other words, the coating imperfection of a single granule increased the nitrogen release rate as compared with a perfectly coated granule. 3.3. Effects of Soil Type on Nitrogen Release. Figure 10 compares simulation results for the nitrogen release from various soils types, that is, sand, silt, silt loam, and clay. From 0 to 10 days, the nitrogen releases in these soils were almost similar. The release to sand, silt, silt loam, and clay increased from 35.63%, 35.22%, 29.04%, and 28.51% after 20 days to 74.01%, 71.85%, 70.58%, and 67.47% after 40 days, respectively. The difference among the nitrogen releases in these soils also increased, and the maximum difference is 6.62% at 35 days between the release in clay and in sand. Even though the differences are small, they can show that soil type was a 6729

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Figure 11 showed nitrogen distributions in different soil media and demonstrates that distribution depended on soil type. Nitrogen concentrations surrounding granules were 64, 200, 210, and 270 mol × m−3 for sand, silt, silt loam, and clay, respectively, markedly higher for silt loam and clay soils than for sand and silt. With a small percent of clay content, the surface area increased enormously from 125,000 to 262,771 cm2 × g−1, allowing an increase in mass transfer resistance in the environment that resulted in higher nitrogen concentration surrounding the granule compared to silt. Under field conditions, the concentration distribution will be affected by other factors, such as water retention ability and irrigation condition, which were not accounted for in our model. In general, a higher concentration can also lead to higher N loss via NH3 volatilization as favored by high soil pH,37,38 or an increase soil acidity through nitrification.38,39 As nitrogen concentration is high, germs and young roots can be injured if the fertilizer is applied too near them.37 In addition, mass transfer resistance in soil prevents nutrient absorption by the plant root if the fertilizer is applied too far from the root. Because different fertilizers and soil types give different N release behaviors and concentration distributions, nitrogen distribution data are essential to fertilizer management with regard to nutrient utility and loss during applications. Medina et al. also studied the effect of different soil types on nutrient release. Their experiments used a soil incubation column technique at ambient temperature. They took soil samples from Florida, California, Pennsylvania, and Iowa to analyze the effect of those soils on the release from fertilizer and concluded that the nitrogen release rate increased as soil’s texture changed from sandy to loamy.17 However, in our previous discussion, the release rate of nitrogen decreased as textural class changed from sand to clay. Their results seem to contradict the results from the present work at first glance because the nitrogen release in sand was slower than in silt or clay. The contradiction is due to different soil composition in soils even with the same textural class. To get a better understanding of this matter, simulations were conducted using soil information from Medina17 as summarized in Table S5 of the Supporting Information, and other parameters were calculated based on Lal et al.18 The simulation results show that the time (t2) for 90% N release was 63.4, 63.9, 66.3, and 72.5 days for soil samples from Iowa, California, Pennsylvania, and Florida, respectively. As discussed earlier, clay content (concentration) in soil plays an important role in enhancing soil surface area and tortuosity. Sandy soil from Florida contained only 2.4% clay, but its surface area was 51,903 (cm2 g−1). Although not as high as in other soils, its tortuosity factor (τF) was the lowest (0.003051). Hence, release of nitrogen in Florida soil had the longest duration (72.5 days according to our model) compared to other soils samples. These simulation results were comparable to results found in the Medina’s experiments because the release rates among soils have a similar trend to their conclusion. On one hand, our proposed model matched experimental observations and bore no contradiction to previous findings. Nevertheless, nitrogen release behavior in soil not only depends on soil texture (textural class) but also on the specific soil composition that determines surface area, tortuosity, and water retention. This comparison further illustrates the advantage of the proposed model as required parameters are easily obtained by either experiment or literature.

Figure 9. Presentation on N release trend in a nonuniform coated granule in 2D-coordinate. Color legend is urea concentration (mol m−3), and N diffusive fluxes are represented by the arrows. The sizes of arrows represent the ratio between diffusive fluxes. Trend was preferential movement toward the thin part of the coating.

Figure 10. Comparison of nitrogen release profiles from various soil types (sand, silt, silt loam, and clay) based on porous (proposed) model. Standard deviation of coating thickness is 10 μm. For soil properties, see Table S4 (Supporting Information).

contributing factor to the release of nitrogen, and the rate of nitrogen release decreased as the soil environment changed from sand to clay. The release pattern from clay soil was markedly different from water or sand and was likely due to a tremendous increase in specific area of clay causing greater tortuosity and resistance to nutrient diffusion. Our proposed model, which combined mass transport equation in porous medium with IAR formula, plainly helped to predict nitrogen release in soil when the soil properties can be obtained from either experiments or literature. As previously discussed in section 3.1, the release profile in soil was similar to the release profile in water. Hence, when investigating novel CRF coating materials, researchers can use the release pattern in water as a reference base for comparison because the experiments in water is easier and far more consistent than in soil. 6730

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Figure 11. Comparison of concentration distribution in different soil environments (sand, silt, silt loam, and clay) after 3.9 days. Color legends and white contours presented urea concentration in mol m−3.

model obviously reduces the time needed to investigate a novel CRF coating material and also helps researchers understand release behavior in different soil types. The proposed model also focuses on the behavior of a single granule with imperfect coating. The advantages of FEM and flexibility of the parametric curve has been utilized to demonstrate the variation within the coating layer. Therefore, the prediction accuracy of the model is enhanced. The flexibility of the proposed method can apply not only in the case of the imperfect coating layer but also in other nonuniform parameters such as granule size distribution. Nevertheless, the model is suitable in laboratory conditions when soil medium is stagnant and saturated and therefore requires further development for analytical approaches to unsaturated and irrigation conditions.

Therefore, the proposed model can be used to study the release patterns of nitrogen to water. Furthermore, it can also estimate the release in a soil medium under saturated and stagnant conditions. The information for coating can be validated by experiments, and soil properties can be derived from either the literature or experiments that are utilized as input to predict nitrogen release in soil. In other words, the model utilizes nitrogen release in water as an extension to estimate its release in various soil environments. Nonetheless, more development of the model is needed for unsaturated soils and irrigation conditions.

4. CONCLUSION By coupling IAR diffusivity in a porous medium with the mass transport equation for a porous medium, the model demonstrates a predictive advantage for CRF nitrogen release profiles in water and soil environments. Of interest here is that researchers need only to provide preliminary experiments for the first stage of release in water and then predict the whole release process. Afterward, they can estimate the nitrogen release for expected soil types of which the required parameters are easily obtained from the analysis of soil characteristic. This

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ASSOCIATED CONTENT

S Supporting Information *

Parameters were used to simulate and validate nitrogen release in water (first simulation) (Table S1) and to simulate the nitrogen release from attapulgite/ethylcellulose-coated fertilizer in soil (second simulation) (Table S2). Soil parameters were 6731

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Industrial & Engineering Chemistry Research

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used in the model to compare the nitrogen release in water and sandy soil environments (Table S3). Soil properties were used to study the effect of different soil types (Table S4). Soil texture and characteristics of soil types vs predicted release time (t2) at 90% of total nitrogen released (Table S5). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b01281.

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AUTHOR INFORMATION

Corresponding Authors

*(T.H.T.) E-mail: [email protected]; ththanh@hcmut. edu.vn. *(K.K.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors offer our profound gratitude to OneBAJA and Universiti Teknologi PETRONAS for providing a congenial work environment and state-of-the-art research facilities. The research grants extended to us by the Ministry of Education, Malaysia (MOE) (LRGS Fasa 1/2011) for ongoing research projects are most highly appreciated. The authors are also grateful to the anonymous reviewers for their valuable comments on this paper that helped us to improve its quality, both in terms of the technical content and the linguistic perspective. The linguistic expertise shared by Mr. Babar Azeem, Universiti Teknologi PETRONAS, Perak, Malaysia, is also highly acknowledged.

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REFERENCES

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DOI: 10.1021/acs.iecr.5b01281 Ind. Eng. Chem. Res. 2015, 54, 6724−6733

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DOI: 10.1021/acs.iecr.5b01281 Ind. Eng. Chem. Res. 2015, 54, 6724−6733