# Effect of Adding Surfactants to a Solution of Fertilizer on the Granulation Process

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup and Procedure

- TI—temperature sensors (TI 1—temperature of the fluidized bed; TI 2—temperature of the inlet air; TI 3—temperature of the exhaust air),
- PI—pressure measurement or the measurement of pressure drop,
- FI—process air flow sensor (FI 6) or liquid flow sensor (FI 1–5).

^{3}/h (±100 m

^{3}/h). The density of the fertilizer solution ${\rho}_{L}$ = 1270 kg/m

^{3}, and DM = 0.35. At the appropriate time of the test, a solution with the addition of polyglucoside surfactants (Agnique PG8105, Basf) and betains (C12-14-alkyldimethyl) at a total amount not exceeding 3.5% (V/V) of the final solution was prepared.

#### 2.2. Population Balance Modeling

_{sl}is the moisture fraction in the slurry and Φ is the effective spray inflow volumetric rate, which is defined as the ratio of the fresh fertilizer spray rate ${\dot{m}}_{sl}$ and the material density of the solid particles ${\rho}_{S}$.

_{p}.

^{th}interval due to their growth is as follows:

_{i}is the number of particles in the ith interval, r is the ratio of the upper bound L

_{i}

_{+1}and lower bound L

_{i}of this interval, and the parameter r is defined as follows [34]:

_{0}(t) is the aggregation rate constant and β*(L

_{x},L

_{y}) is the particle-size dependent part. The success of using population balances to model granulation processes depends on the proper choice of kernel. Many different kernel dependencies with regards to time and particle size have been proposed and analyzed [38]. They can be divided into empirical and physic-based kernels.

_{0}(t) is affected by the aggregation efficiency and the collision rate. The collision rate depends on the particle velocity, granulation temperature, and particle concentration distribution in the granulation zone. Therefore, a theoretical description of its time dependency is difficult. Typically, it is assumed that the aggregation rate constant is time-independent and averaged over the entire bed [37]. However, sometime dependent expressions for β

_{0}are reported in the literature. Adetayo and co-authors [20] proposed a sequential kernel, according to which the granulation process can be divided into stages, with different kernel values being applied for each stage. When the aggregation rate constant is a continuous function of time, it typically has the linear form [40,41]:

_{A}and β

_{B}are parameters that are estimated by fitting techniques.

_{0}(t) was assumed to be constant in time. Therefore, given the mathematical form of the kernels adopted, as well as the fact that the values of the parameters present in the expression for the growth constant are known, only the aggregation rate constant β

_{0}had to be estimated from the experimental data. The parameter estimation was performed in Matlab software by minimizing the sum of square residuals between the simulated and experimental data. The fitting procedure was implemented with the use of fminsearch (with an embedded ode15s solver), which was implemented for the resolution of in order to solve the DPB equation at each iteration of the optimization function.

## 3. Results and Discussion

_{p}

_{50}shown in Figure 4 reveals significant differences in the evolution of the granule size distribution. The strong influence of the surfactant additive is particularly evident in the early stage of the batch granulation process, i.e., up to t = 10 min, where the rate of growth in median diameter is much higher for the test performed with the additive.

_{0}, which is a measure of the frequency of successful “sticking” after two granules collide. The EKE kernel (Figure 5) was taken as the baseline because it is generally accepted as the most suitable for fluid bed granulation. For comparison purposes, calculations were also performed using the simplest size-independent random kernel and the Brownian kernel.

_{3}calculated with the best fitted β

_{0}values, namely β

_{0}= 1.890 × 10

^{−12}for the test performed without the addition of the surfactant (Figure 6a) and β

_{0}= 2.497 × 10

^{−12}(Figure 6b) for the test performed with the addition of the surfactant. The results obtained indicate much better efficiency (also in terms of the aggregation rate) of the granulation process, in which the solution of fertilizer was enriched with surfactant (~32% higher value of β

_{0}).

_{0}fitted to the DPB combined with different kernels are shown in Table 2. In all cases, the values of the aggregation rate obtained for the case with tenside additive are about ~32–33% higher than the values obtained when the additive was not added to the fertilizer solution. It has to be underlined that the different order of magnitude of the optimal value of β

_{0}found for each model is due to their different mathematical forms. In any case, the predictions obtained with all the adopted models, shown in Figure 7 and Figure 8, respectively, for the tests performed without and with additive, are very similar, with the EKE kernel performing slightly better, especially after some time from the start of the process, i.e., at t = 20 min (Figure 7c and Figure 8c). This finding is consistent with previous studies of Honslow [40], which indicate that the EKE kernel is most suitable for fluidized bed granulation. Furthermore, as also indicated in the above cited work, the results presented in Table 2 confirm that despite its rather simple nature, PBE allows for the extraction of physical information about the granulation rate.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Experimental mass-based histograms of particle size distribution: (

**a**) initial particle size distribution for the test without surfactant addition; (

**b**) particle size distribution after t = 20 min for the test without surfactant addition; (

**c**) initial particle size distribution for the test with surfactant addition; (

**d**) particle size distribution after t = 20 min for the test with surfactant addition.

**Figure 5.**3D representation of the particle size dependent part β*(d

_{p}

_{1}, d

_{p}

_{2}) of the equipartition kinetic energy (EKE) kernel.

**Figure 6.**Mass density distribution q

_{3}simulated with the EKE kernel: (

**a**) test without tenside; (

**b**) test with tenside.

**Figure 7.**Measured and simulated mass density distribution q

_{3}for the test without tenside: (

**a**) t = 0 min; (

**b**) t = 10 min; (

**c**) t = 20 min.

**Figure 8.**Measured and simulated mass density distribution q

_{3}for the test with tenside: (

**a**) t = 0 min; (

**b**) t = 10 min; (

**c**) t = 20 min.

Sample ^{1,2} | Granule Density [kg/m^{3}] | Bulk Density [kg/m^{3}] | Tapped Bulk Density [kg/m^{3}] |
---|---|---|---|

A1 | 1779 | 1000 | 1140 |

A2 | 1772 | 890 | 950 |

B1 | 1510 | 730 | 800 |

B2 | 1571 | 680 | 780 |

^{1}Samples A1 and A2 are the mixtures of granules without additives, which were taken at the beginning and at the end of the experiment.

^{2}Samples B1 and B2 are the mixtures of granules with the addition of a surfactant, which were taken at the beginning and at the end of the experiment.

Test | Random | EKE | Brownian |
---|---|---|---|

Without tenside | 2.656 × 10^{−13} | 1.890 × 10^{−12} | 6.103 × 10^{−14} |

With tenside | 3.446 × 10^{−13} | 2.497 × 10^{−12} | 8.136 × 10^{−14} |

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**MDPI and ACS Style**

Michałek, B.; Ochowiak, M.; Bizon, K.; Włodarczak, S.; Krupińska, A.; Matuszak, M.; Boroń, D.; Gierczyk, B.; Olszewski, R. Effect of Adding Surfactants to a Solution of Fertilizer on the Granulation Process. *Energies* **2021**, *14*, 7557.
https://doi.org/10.3390/en14227557

**AMA Style**

Michałek B, Ochowiak M, Bizon K, Włodarczak S, Krupińska A, Matuszak M, Boroń D, Gierczyk B, Olszewski R. Effect of Adding Surfactants to a Solution of Fertilizer on the Granulation Process. *Energies*. 2021; 14(22):7557.
https://doi.org/10.3390/en14227557

**Chicago/Turabian Style**

Michałek, Bernard, Marek Ochowiak, Katarzyna Bizon, Sylwia Włodarczak, Andżelika Krupińska, Magdalena Matuszak, Dominika Boroń, Błażej Gierczyk, and Radosław Olszewski. 2021. "Effect of Adding Surfactants to a Solution of Fertilizer on the Granulation Process" *Energies* 14, no. 22: 7557.
https://doi.org/10.3390/en14227557