Table 1 Kinetics Models for P release from NEF in water and soil.

First order

\({\text{Ln}}\left( {{\text{q}}_{0} - {\text{q}}_{{\text{t}}} } \right) = {\text{a}} - ({\text{K}}_{{\text{d}}} *{\text{T}})\)

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

0.011

0.013

0.003

0.007

a

4.393

6.442

1.026

3.738

R²

0.913

0.942

0.975

0.967

SE

0.199

0.206

0.038

0.151

Elovich

\({\text{q}}_{{\text{t}}} = \left( {{1}/\upbeta } \right){\text{ln}}\left( {\alpha \upbeta } \right) + \left( {{1}/\upbeta } \right){\text{lnt}}\)

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

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

α

4E+00

6E+01

2E−02

4E−01

β

0.089

0.01

0.931

0.080

R²

0.669

0.789

0.810

0.973

SE

14.95

94.78

0.395

1.581

Parabolic diffusion

\({\text{q}} = {\text{a}} + {\text{K}}_{{\text{d}}} {\text{t}}^{{{1}/{2}}}\)

a = constant (mg g⁻¹)

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

K_d

5.131

42.21

0.184

2.051

a

13.50

36.07

1.336

7.405

R²

0.905

0.969

0.908

0.998

SE

8.015

36.03

0.273

1.489

Power function

\({\text{logq}} = {\text{log K}}_{{\text{d}}} {\text{C}}_{o} + {1}/{\text{m logt}}\)

K_d = apparent desorption rate coefficient(h⁻¹)

1/m = constant

Co = initial P concentration

K_d

0.577

38.17

0.003

0.410

1/m

0.868

0.492

1.117

0.743

R²

0.978

0.964

0.983

0.993

SE

0.115

0.078

0.049

0.021