Table 1 Kinetics models for P release from classical fertilizers (control) and NEF in water and soil

First order

Ln (q₀–q_t) = a − (K_d * T)

q₀ = amount of P released at equilibrium mg·g⁻¹, q or q_t = amount of P released at time

t (h) mg·g⁻¹, K_d = Solubility rate (h⁻¹)

a = constant (mg.g⁻¹)

K_d

a

R²

SE

0.012

5.835

0.927

0.214

0.012

5.291

0.925

0.215

0.013

6.442

0.942

0.206

0.007

2.835

0.953

0.171

0.006

2.569

0.940

0.191

0.007

3.738

0.967

0.151

Elovich

q_t = (1/β)ln(αβ) + (1/β)lnt

α = initial desorption rate of P (mg/g·h)

β = constant related to P release (mg.g⁻¹)

α

β

R²

SE

20.58

0.020

0.742

56.36

11.44

0.034

0.739

32.89

60.59

0.010

0.789

94.78

0.187

0.196

0.961

2.608

1E-01

0.261

0.942

2.417

4E-01

0.080

0.973

1.581

Parabolic diffusion

q = a + k_dt ^1/2

a = constant (mg.g⁻¹)

K_d = apparent diffusion rate coefficient (mg/g.h^1/2.)

K_d

a

R²

SE

22.44

43.88

0.948

25.27

12.99

26.66

0.946

14.95

42.20

36.07

0.969

36.03

0.840

2.201

0.994

1.009

0.634

2.268

0.989

1.029

2.051

7.405

0.998

1.489

Power function^a

logq = logk_dC_ο + 1/m logt

K_d = apparent desorption rate coefficient(h⁻¹)

1/m = constant

Co = initial P concentration

K_d

1/m

R²

SE

6.380

0.705

0.978

0.087

2.764

0.765

0.978

0.096

38.17

0.492

0.964

0.078

0.316

0.643

0.993

0.018

0.164

0.696

0.995

0.016

0.410

0.743

0.993

0.021

Second order

qt = k_dq_e²t /1 + k_dq_et

k_d = apparent desorption rate coefficient (h⁻¹)

K_d

q_e

R²

SE

0.127

500

0.508

0.149

0.077

344.8

0.451

0.248

0.372

714.3

0.784

0.084

0.017

24.88

0.956

1.094

0.011

20.75

0.912

1.902

0.019

69.93

0.983

0.239