Environmental Management: Modelling Plants Nutrients Values
During the Composting Process
NADIA RAMDANI1, MOKHTAR BOUNAZEF2
1Energies and Process Engineering department
Djillali Liabes University
Postal box 89, Faculty of Technology, Sidi bel abbes,
ALGERIA
2Mechanical Engineering Department
Djillali Liabes University
Postal box 89, Faculty of Technology, Sidi bel abbes
ALGERIA
Abstract: - Composting of domestic wastes is one of the natural methods of eliminating foods wastes without
damaging the environment. This process provides plants nutrients in the form of hygienic products, similar to
mineral-rich soil called agricultural compost. The content of these formed components depends on several
factors in the process, such as the humidity, the rejects quantities, their ratios to each other, the type of waste,
the composting temperature and the elements interactions during the physico-chemical transformations. The
innovation in this study, which remains the essential aim of this work, is to show how the formed essential
plants nutrients, such as potassium, nitrogen, and phosphorus, depend not only on the humidity of the
environment, the aeration by oxygen and the composition of the domestic wastes, but also on the interaction
between them combined with the transformation time. Mathematical modelling using the design of experiments
method, revealing that the presence of one element of three in the compost is a function of the two others in
time, shows this. The mathematical model showing the variation of composting time as function of the minerals
presence in the compost by graphs, contours and response surfaces; they simultaneously interprets the results of
this process.
One of the final objectives is to estimate by prediction the values of composting days without new experiments.
Key Words: - Domestic wastes, composting, Chimico-physical transformation, Fermentation, Natural fertiliser,
Mathematical modelling
Received: May 9, 2021. Revised: March 25, 2022. Accepted: April 27, 2022. Published: May 23, 2022.
1 Introduction
In the following, one shows that some of the mineral
elements necessary for plant nutrition that conserve
during the degradation and fermentation of food and
plant wastes vary with time. They depend, not only
on the quantities of the various wastes, the humidity,
the oxygen rate and the alteration time [1][2][3] but
also, they depend of the conserved elements
quantities and their interactions during the processes
in the compost as potassium, nitrogen, phosphorus
etc. One interests here in the three components
because their rate in the compost is significant, and
their nutritive role is important. The obtained
product, is a very useful fertiliser for agriculture and
gardening since it nourishes the plants and develops
them [4][5][6]. Each element acts on the other in
their formation, according to the time of
degradation; the mathematical model, which takes
into account the percent of each of them, shows this,
as one sees later in the text. The modelling of this
chimico-physical behaviour is done by the design of
experiments method using the Modde 6.0 software.
This mathematical model has several advantages
over other models. In addition to being
based on experiments: a- It is simple and
polynomial form. b- It does not include any difficult
trigonometric or logarithmic functions. c- It has the
ability to be descriptive and predictive at the same
time in the experimental field. d- It has an
interactive correlation between the factors and
finally, e- It does not require a high number of
experiments. This is here, where the innovative
aspect of this paper resides in other complicated
models, more involving difficult and complicated
mathematical functions are used in many sciences,
but describe only the process without any
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prediction. The used polynomial model has this
faculty with the ability to introduce interactions
between the factors and choose the estimated level
coefficient in our work at 95% to get closer to the
truth and real behaviour. All this cannot be done
with other modelling. However, before this stage,
experiments and measurements must be carried out
and the process of natural composting must be
successfully started, passing through the oxidative
phase where the temperature reaches 70 °C, then
through the maturation phase where it drops to 30
°C with a stabilised pH between 7.3 and 7.8. Sixteen
different parameters are measured every 30 days,
but the study focuses on three of them, which enter
into the composition of the KNOP compound used
by biologists. These are the quantities of potassium,
nitrogen and phosphorus, whose variation should
not be too pronounced because they tend to fall with
time [7][8][9][10][11]. The composting time is
analysed and optimised according to the variation of
these three elements. This analysis is possible using
the cited software, which allows to find the
behavioural model, but also to predict results not
known experimentally.
2 Preparation of the Experimental
Environment and Measurements
Biodegradable wastes are collected in a container
(composter) with side holes for aeration and a cover
to protect the residues from the weather conditions.
It also has a drain hole at the bottom to drain off the
nutrient-rich liquid from the process. Compost
material consists mainly of a mixture of kitchen
waste such as peelings and fruit and vegetable
residues, cellulose products such as paper, wet
plants and garden wastes, nutshells, and small
amounts of eggshells and coffee marc. To get the
process started quickly, already formed compost,
soil earthworms are added. Finally, it is important to
note that no fish, meat and plastics should be added,
because they prevent or slow down the degradation
of the other components [12][13]. Sewage sludge is
also added because it contains microorganisms that
accelerate the process. The humidity level must be
strictly controlled at each
stage by the wrist test, because too much humidity
causes rotting, and too less humidity causes drying
out; in both cases composting is not successful. This
conditions permit to the compost to be formed under
good circumstances in a quasi-neutral or slightly
acidic environment, and a humidity rate favouring
the proliferation of the bacteria, the fermentation
and the fertilisation of the environment. This
method eliminates between 30% and 50% of the
waste contents, as a function of its composition.
2.1 Measurements Results
The 127 experiments below in Table 1 are
developed under the surveillance of 2 essential
parameters which are the humidity rate with an
average of 37.9, and the pH with an average of 7.5.
These two values permit to the compost to be
formed under good conditions in a quasi-neutral or
slightly acidic environment, and a humidity rate
favouring the proliferation of the bacteria, the
fermentation and the fertilization of the
environment. Table 1 shows the cited values; they
are taken every 30 days from the composting
beginning to 210 days. In this table, one notes that
the K, N and P decrease at 210 days.
Table 1. Masses of mineral components and parameters rates of the compost during 210 days
Parameters
0 day
30 days
90 days
120 days
150 days
210 days
Humidity (%)
53.8
42.2
36.7
35.2
33.1
31.1
pH (-)
7.4
7.3
7.6
7.4
7.8
7.7
E.C (mS cm-1)
2.2
1.8
1.8
1.7
1.8
1.8
TOC %
35.5
36.6
42
35.2
29.3
29
TKN %
1.3
1.4
1.9
1.9
1.9
1.9
MO %
52.2
52.1 0
50.5
48.9
46.4
40.
Ash (g kg-1)
32.8
34.3
42.4
46.2
50.5
52.5
C/N
27.3
26.1
22.7
18.7
15.4
15
Dec % (1)
-
6.5
33.6
43.6
62.1
61.1
N-NH+ (mg g-1)
2.5
2.3
1.9
1.3
1.2
1.1
N-NO-3 (mg g-1)
2.7
2.5
1.6
0.9
0.6
0.6
Mg total (g kg-1)
2.5
2.6
2.8
3.1
3.5
3.3
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One notes that k, N and P decrease respectively of
33.08%, 48.07% and 4.34% of their initial values.
Our aim is to keep them high while forming this
natural fertilizer. This requires an optimisation
between the composting time and the elements
percentage in fertiliser.
3 Modelling of the Composting
Process
The chosen model differs from the others [8] [10]
by its polynomial form, which describes the
composting time as a function of the variation of the
three minerals K, N and P. It consists of a sum of 7
monomials in which the 3 elements xi (the factors)
are coded values multiplied by coefficients ai that
must be determined, while the time y (the response)
is represented in its real value, [14] [15][16][17]
(formula 1).
2 2 2
0 1 1 2 2 3 3 11 1 22 2 33 3
y a a x a x a x a x a x a x
However, the mentioned factors (xi) are
expressed with various units, and with a values
range very different from each other; they cannot be
represented by their real values in the model
because it is a sum of monoms. In order to satisfy
the model equation (1), there is a need for
normalisation for obtain the factors without unit and
situated between two extreme values ''-1'' and ''+1'',
using the following coding relation (coded values)
[17]:
max min
max min
2
2
i
i
uu
u
xuu






Where: xi is the coded parameters value, ui is the
real parameter value, umax is the maximal real value
of all parameters, and umin is the minimal real value
of all parameters. The coded values of the
parameters are given in Table 2 from 0 day to 210
days.
Table 2. The coded values of parameters
Experiments
Coded
value of K
Coded
value of N
Coded
value of P
1
1
1
0,333
2
-0,51
0,771
0
3
-1
0,371
1
4
-1
0,0286
-1
5
-0,592
-0,714
-1
6
-0,633
-0,943
-0,333
7
-0,714
-1
0
8
-0,837
-1
0
3.1 Determination of the Coefficients Values
aij
By replacing these coded values in model (1), 8
different equations are formed and expressed in
matrix form; the solution of this equations system is
given by expression (3) [17]:
1
tt
ij
a X X X Y
Where: X: Factors model matrix, Xt: Transpose of
the factor model matrix, (XtX)-1: Information
matrix, (Y) is response matrix. Thus, model (1)
takes the equation form (4) [14][15][16][17]:
1 2 3
2 2 2
1 2 3
208.736 125.149 0.162633 32.8015
78.359 259.387 62.1935
y x x x
x x x
3.2 Model Quality Analysis
Several indicator coefficients and quality tests show
the ability of the model to describe correctly the
composting process. The indicator of the descriptive
quality of the model R2 (0≤R2≤+1) is in our case
equal at 0.999, the indicator of the predictive quality
of the model Q2 (-∞<Q2≤+1) is 0.993; they are both
close to +1, which indicate the very good quality of
the model.
3.3 Evaluation Tests
3.3.1 Coefficients Significance
The Student test shows the significance of the
coefficients aij that compose the mathematical
model. The statistical calculation [15], which
consists of comparing the absolute values of the
model coefficients and the variance Si multiplied by
the Student number tcrit (tcrit*Si) taken from the
K total (g kg-1)
13.6
9.9
8.7
9.7
9.6
9.1
P total (g kg-1)
2.3
2.2
1.9
1.9
2.1
2.2
Mn total (mg kg-1)
48.6
50.6
78.8
79.8
60.3
55.1
Fe total (mg kg-1)
4875
4777
3703
4057
4464
4350
(2)
(1)
(3)
(4)
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Student table for each coefficient [16][17][18] gives
the following results:
Table 3. Significance of model factors
Coef
Values
tcrit*Si
Significance
a0
208,736
0,79635
Significant factor
a1
125,149
Significant factor
a2
0,162633
Non-significant factor
a3
32,8015
Significant factor
a11
78,359
Significant factor
a22
259,387
Significant factor
a33
62,1935
Significant factor
Table 3 shows that only the factor a2=0.162633
does not predominate in model (4), because it is
inferior to tcrit*Si, it means that its effect on the
response y (composting time) is negligible, its
action does not change so much the value of y. The
model is therefore well developed because there are
not many insignificant factors. All the 6 other
remained factors (Table 3) are significant in model
(4); when they have a negative sign it means that
they decrease the value of the number of
composting days in the expression and vice versa.
3.3.2 The Fisher-Snedecor Test
The Fisher-Snedecor test is a statistical hypothesis
test, which permits to compare 2 variances by doing
their ratio which must not exceed a certain
theoretical value [17][18][19][20]. It depends on the
differences between the observed measurements and
the predicted values.
The comparison between the observed Fisher
number and the one from the theoretical tables
explains the regression of the composting time of
the wastes y in xi (factors: quantities of minerals). In
our case Fobs=200472 and Fcrit=233.99 (Fobs>Fcrit).
This demonstrates that the proposed model is
globally significant with a 95% chance of being
realised.
4 Results, Analysing and Discussion
One sees from Figure 1 that the maximum deviation
of wastes composting time between measuring
values and theoretical value is 0.07% (for
experiment 7: 180 days), while the minimum is
0.009% (for experiment 2: 30 days), compared to
initial values. This is an insignificant deviations; the
proposed model (4) is perfectly adapted to the
measured values of wastes composting. The 6 other
values are therefore between these 2 values.
Fig. 1: Illustration of the deviations between observed and predicted model values
4.1 Response Surfaces and Contours of
Wastes Composting Process
The graphs below in Figure 2 in the form of
response surfaces and contours are graphic
illustrations of the mathematical model (4). They
show how the composting time is a function of the
relative masses of the mineral elements in the
compost (Potassium, Nitrogen and Phosphorus).
The analysis is based on the formation time of the
natural
fertilizer and its fermentation and fertilisation,
keeping the quantities of these mineral plant
nutrients acceptable because they tend to decrease
(Table 1). In these graphs, the values of 2 elements
K and N (in the ions form of NH+ and NO3-) are
0
50
100
150
200
-10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220
Observed
Predicted
Investigation: Comp RAM (MLR)
Composting days
N=8 R2=1,000 R2 Adj.=1,000
DF=1 Q2=0,994 RSD=0,1773
1
2
3
4
5
6
7
11
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introduced, while keeping the 3rd mineral P
invariable at its minimum, medium and maximum
values.
The response surfaces (3D graphs) and their
projection (contours) are graphical representations
illustrating according to the mathematical model (4)
how the composting time in days varies according to
the 3 parameters initially described.
The contour is a curvilinear line on which the
number of days of composting stays the same;
therefore, it is an iso-time in our case.
The negative values of the iso-lines are purely
theoretical, they have no real meaning. The ideal is
to have a very short composting time, i.e. to
approach the "zero" iso line by changing the values
of the 3 parameters, one of which remains stable and
the 2 other are variable factors.
All 3 response surfaces have the same shape and
aspect, they are convex downwards to the minimum
point of curvature which shows that a minimum
point of theoretically negative number of days of
composting without physical significance is
reached.
Fig. 2: Illustrative response surfaces and contours of model
It is evident that the representations given by the
mathematical model in figure (2) show negative
non-real values of the days number. These values
are purely theoretical and therefore to be rejected.
Therefore, the analysis of the composting process
focuses on the positive values, i.e. beyond the zero
contour.
4.1.1 For relative Masse of Phosphorus Equal at
Minimal Value of 1.9 g kg-1
In order to keep the potassium and nitrogen
quantities high (close to the initial values recorded
before composting), in the case where the relative
mass of phosphorus is 1.9 g kg-1 (Figure 2-a), the
number of days of fermentation must approach 99
days. Below and above this, the values of these 2
elements are lower than the desired maximum
values. In this case, these are some predicted values
by the model for the working field (Table 4).
Table 4. Predicted values of compost elements when phosphorus value is 1.9 g kg-1
N°
P-quantities
(g kg-1)
k-quantities
(g kg-1)
N-quantities
(mg g-1)
Composting days
-
1
9.0
2.0
235
2
2.5
130
3
3.0
74
4
3.5
57
5
4.0
83
a: P-relative mass=1.9 g Kg-1 b: P-relative mass=2.2 g Kg-1 c: P-relative mass=2.5 g Kg-1
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4.1.2 For Relative Masse of Phosphorus Equal at
Mean Value of 2.2 g kg-1
In this second case, where the relative mass of
phosphorus is 2.2 g kg-1 (Figure 2-b), one notices
that the elliptical contours have moved to the left
compared to the first case; this means that the zero
value contour delimits 2 small zones (contours
in yellow and red colours), one at the top left, the
other at the bottom left, where there is presence of
phosphorus, potassium and nitrogen in the compost.
The green and blue zones (Figure 2-b) are purely
theoretical and are to be rejected because the
number of days is negative. Table 5 shows the
values predicted by model (4), where one sees that
for the phosphorus relative mass of 2.2 g kg-1, and
from the relative potassium mass of 11 g kg-1, it is
impossible to predict the composting days giving
real values of
the 3 minerals.
Table 5. Predicted values of compost elements when phosphorus value is 2.2 g kg-1
N°
P-quantities
(g kg-1)
k-quantities
(g kg-1)
N-quantities
(mg g-1)
Composting days
-
1
2.2
9.0
2.0
140
2
2.5
38
3
4.25
16
4
4.5
55
5
5.0
163
6
10.0
2.0
42
7
4.75
13
8
5.0
75
4.1.3 For Relative Masse of Phosphorus Equal at
Maximal Value of 2.5 g kg-1
In this situation, when the relative mass of
phosphorus is maximum and equal to 2.5 g kg-1, the
contours (Figure 2-c) are in an intermediate position
compared to the 2 previous cases since the area of
composting days beyond the zero contour is lower
than the case of 1.9 g kg-1, but higher than 2.2 g kg-1.
In theoretical zone predicted by the mathematical
model (4) below the zero-contour is relatively large
and should be rejected because it is not a true
representation of reality. Table 6 shows some
predicted values of the number of composting days
as function to the relative masses of the 3 plant
nutrients in the natural fertiliser when the relative
mass of phosphorus is 2.5 g kg-1.
Table 6. Predicted values of compost elements when phosphorus value is 2.5 g kg-1
N°
P-quantities
(g kg-1)
k-quantities
(g kg-1)
N-quantities
(mg g-1)
Composting days
-
1
2.5
9.0
2.0
170
2
2.5
68
3
3.0
8
4
4.0
16
5
4.5
85
6
5.0
199
7
10.0
2.0
76
6
1.9
4.5
150
7
5.0
264
8
10.0
2.0
141
9
2.5
39
10
4.5
60
11
5.0
170
12
11.0
2.0
69
13
2.25
13
14
4.75
41
15
5.0
99
16
12.0
2.0
29
17
5.0
54
18
13.0
2.0
23
19
5.0
44
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8
5.0
104
9
11.0
2.0
8
10
5
37
Comparing the 3 studied situations, it is easy to
see in case 3, that the relative masses of the mineral
elements in the compost are very close to the initial
state, since the values of 2.5 g kg-1, 11.0 g kg-1, and
5.0 mg g-1 respectively for phosphorus, potassium
and nitrogen are maintained for only 37 days of
composting (Table 6). This is considered as a results
optimisation because the drop in relative masses of
nutrient components is not very pronounced, and the
number of composting days is relatively low. This
time is already sufficient for the formation of
potting soil.
4.2 Predicted Values of Composting Days
with Particular Relative Masses of Plants
Nutrients
Another analysis can be done, it is to see how
composting days varies in relation to only one of the
3 factors in the model, while leaving the 2 other
factors unchanged at the maximal, mean and
minimal values.
Table 7. The 3 used parameters values for
analysis of composting days
Min value
Mean value
Max value
K
8.7
11.5
13.6
N
1.7
3.45
5.2
P
1.9
2.2
2.5
Table 7 shows the three used particular values
for the 3 minerals (factors) (K, N, and P) which
affect the days number of composting, i.e. the
minimal, the mean and the maximal.
4.2.1 Composting Days with the K-variation
Firstly, the black curves in Figure 3 indicate the true
change of the number of composting days described
by the polynomial expression; the blue and red ones
take into account the ±5% confidence interval.
When one introduces in the mathematical model (4)
the mean values (table 7) of K=11.5 g kg-1, N=3.45
mg g-1 and P= 2.2 g kg-1 (figure 3-b) expressed in
coded values, one notices that the days number of
composting is negative. This is not real and remains
purely theoretical values; this case is to be rejected.
Figures 3-a (for minimal values of N
and P) and 3-c (for maximal values of N and P)
show
that the relative mass of K remains high and equal to
13.6 g kg-1 at the beginning of the process. This is
around 33 days of composting for the maximum
values (Figure 3-c), and 99 days for the minimum
values (Figure 3-a). It is clear that the case in Figure
3-c optimises the process with a high relative mass
of potassium and a minimum days number of
composting.
4.2.2 Composting Days with the N-variation
The same approach is done when one analyses the
days number of wastes composting with the
nitrogen change when introducing in the model the
values of the 3 elements. Figure 4-a-b-c show how
the composting days vary with increasing nitrogen.
a:
b:
a
c:
y=78.359 x12-125.149 x1+145.48337
y=78.359 x12-125.149 x1-208.736
y=78.359 x12-125.149 x1+80.20563
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Fig. 3: Variation of composting days as a function of K-element under conditions of the 2 others (N and P)
For curves 4-b and 4-c, the theoretical values for
the number of negative days, are far from the
reality. Therefore, one analyses essentially the case
of the variation of the composting days number as a
function of nitrogen under the presence of the
minimum values of P and K (table 7) (Figure 4-a).
Fig. 4: Variation of composting days as a function of N-element under conditions of the 2 others (P and K)
When the minimum values of K = 8.7 g kg-1 and
P = 1.9 g kg-1 (Table 7) act on the days number of
composting as a function of the variation of
nitrogen, the minimal relative mass of 3.48 mg g-1 of
nitrogen is present when 90 days of composting is
reached. On the other hand, the maximum value of
5.18 mg g-1 of nitrogen is theoretically reached after
350 days. Relative masses of nitrogen of 5.18 mg g-1
at 51 days and 5.18 mg g-1 at 34 days are present in
the compost in the respective cases of mean (Figure
4-b) and maximal (Figure 4-c) values of potassium
and phosphorus.
4.2.3 Composting Days with the P-variation
Under the influence of nitrogen and potassium in
their minimum, mean and maximum values, the
days number of composting changes according to
the prediction of the mathematical model (4)
differently. In the case of Figure 5-b, it can be seen
again that the number of days is negative along the
length of the measurement domain of the potassium
quantity present in the compost. No real
interpretation can be given; this remains a purely
theoretical case. When the quantities of K and N
have their minimum value (Figure 5-a), 2.5 g kg-1 of
phosphorus is retained at 283 days of composting;
this is considered as a very high number of days.
Fig. 5: Variation of composting days as a function of P-element under conditions of the 2 others (N and K)
a:
b:
c:
y=259.387x22+0.16263x2+89.767
y=259.387x22+0.16263x2-208.736
y=259.387x22+0.16263x2-226.134
y=62.1935x32-32.8015x3+253.99637
y=62.1935x32-32.8015x3-208.736
y=62.1935x32-32.8015x3+4.0236
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However, when they reach their maximum value
K=13.6 g kg-1, N=5.2 mg g-1 (Figure 5-c), the
quantity of phosphorus remains at 2.50 g kg-1 at
only 34 days of composting; this is considered as a
good result. Depending on the number of days of
composting of the household waste, which degrades
and then turns into a natural fertilizer only after 30
days of fertilisation, and depending on the action of
each level of values of the elements K, N and P, the
graphs predicted by the model in Figures 3, 4 and 5
are resumed in table 8 below:
Table 8. Summary of the predicted compost elements values according to 3 categories
Values of
components
Value of K and
composting days
Value of N and
composting days
Value of P and
Composting days
Kmin – Nmin - Pmin
13.6 g kg-1 - 99 days
5.18 mg g-1 - 350 days
2.5 g kg-1 - 283 days
Kmoy – Nmoy - Pmoy
-
5.18 mg g-1 - 51 days
-
Kmax – Nmax - Pmax
13.6 g kg-1 - 33 days
5.18 mg g-1 - 34 days
2.5 g kg-1 - 34 days
Table 8 can be expanded and replenished
indefinitely with values of K, N and P taken from
the experimental design domain in a haphazard and
disordered manner because the software is user-
friendly and can predict an infinite number of
composting days based on the mathematical model
(4) . However, our choice is made on simultaneous
minimum, average and maximum values taken for
the 3 elements K, N and P to show how the number
of predicted days varies when the experiment has
not been done with these values.
4.2.4 Comparative Study
Comparing the 3 cases in Figure 2, where a change
in phosphorus mass from 1.9 g Kg-1 to 2.5 g Kg-1, it
can be seen that case (a) where P-relative mass=1.9
g Kg-1 is more descriptive than the other 2 and is
close to the actual values for 2 essential reasons:
The first is that the area of positive composting days
between 0 and 240 days is larger than the other two
cases, which improves the prediction of the values
not obtained by experimentation. The second is that
the extreme values of negative composting days that
are rejected as not reflecting reality is only -160
days in case (a) while the other two are respectively
-240 days and - 220 days, which enlarges the
theoretical zone that does not describe composting.
5 Conclusion
The study carried out through the different analyses
illustrated by graphs and tables has sought to keep
the relative masses of the compost nutrients initially
existing before decomposition and fertilisation of
the wastes in their maximum values. In addition to
the interaction between the formations of these
elements, they tend to decrease with the days
number in the process. However, it is also necessary
to allow the formation of potting soil after the waste
has decomposed without rotting by controlling
humidity and temperature. These 2 parameters are
inversely proportional, the number of days activates
the formation of fertilizer, but decreases the relative
masses of these minerals. There is therefore a choice
to do and a consensus to reach on the values to
chosen according to the importance of each element
in the plant nutrition. There remains the composting
time, the duration of which must take into account.
It is obvious that it is greater, the risk that the
components values decrease. Then the compost
availability takes
a longer time. However, modern methods can
achieve retention of K, N and P losses and eliminate
the odours of NH3 and N2O by introducing physical,
chemical and microbial additives. This is a separate
study to be carried out. This study using non-
conventional experimental design modelling is used
for the first time in this field of composting and
gives very satisfactory results; the fact of predicting
a composting time without any additional costly and
time-consuming experiments makes this work
different from the results of other works and
differentiates it from other models.
Acknowledgements:
I would like address thanks to the staff of the
Charles Coulomb Laboratory, France, for their
warm welcome and valuable scientific assistance,
and to the laboratory of Aix-Marseille, University of
Marseille 1 France.
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WSEAS TRANSACTIONS on ENVIRONMENT and DEVELOPMENT
DOI: 10.37394/232015.2022.18.54
Nadia Ramdani, Mokhtar Bounazef
E-ISSN: 2224-3496
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Volume 18, 2022