Journal of Minerals & Materials Characterization & Engineering, Vol. 10, No.13, pp.1233-1241, 2011
jmmce.org Printed in the USA. All rights reserved
1233
Model for Per iodic Analysis of the Quantity of Water Evaporated during
Thermo-processing of Clay Designated for Pr od uc ti on of Oven R ef ractory
C. I. Nwoye1*, B. C. Chukwudi2, P. C. Agu3 and C. C. Ugwuegbu3
1*Department of Met allurgic al and Materials Engineering,
Nnamdi Azikiwe University, Awka, Nigeria
2Department of Mechanical Engineering, Imo State University, Owerri, Nigeria.
3Department of Materials and Metallurgical Engineering,
Federal University of Technology, Owerri, Nigeria.
*Corresponding Author: chikeyn@yahoo.com
Abstract
A model has been derived for periodic analysis of the quantity of water evaporated during
thermo -processing of clay designated for production of oven refractory. The model;
γ = exp lnt 1.3
2.9206
shows that the quantity of evaporated water during the drying process is dependent on the
drying time, with the evaporating surface being constant . It was found that the validity of the
model is rooted on the expression lnγ = (lnt/Logβ)N where both sides of the equation are
correspondingly almost equal. The maximum deviation of the model-predicted quantity of
evaporated water from the corresponding experimental value is less than 19% which is quite
within the acceptable deviation range of experimental results. Water evaporation rate as
obtained from experiment and derived model were evaluated to be 0.0536 and 0.0337g mins-1
respectively.
Keywords: Model, Water Evaporation, Thermo -processing, Clay, Oven Refractory.
1. INTRODUCTION
It is commonly believed that clay deposits exist in several locations all over the world.
However, the few products of clay used today have shown that clays are under utilized.
Clays are composed basically of minerals such as kaolinite, montmorillonite, and illite in
addition to varying amounts of quartz sand, micas, feldspars, gypsum, iron compounds and
organic materials [1].
1234 C. I. Nwoye, B. C. Chukwudi Vol.10, No.13
It has b een shown [2] that clays of alumino-silicat e minerals have ex celle nt high t emperatur e
volume stability, mechanical strength, thermal shock resistance and creep resistance.
Refractories and kiln linings made from these alumino-silicate materials have found
application in industrial fields, such as metallurgical and building materials industries [2].
Report [1] has indicated that clay minerals are activated when subjected to high temperature
as result of physical and chemical changes which alter their properties. A study [3] on the
drying of wet clay indicates three stages of drying: increasing rate, constant and decreasing
rate and also revealed that at constant rate, the evaporation rate and evaporation surface are
constant.
A model [4] has been derived for predicting the quantity of water evaporated during the
primary-stage processing of a bioceramic material sourced from kaolin. The model;
E = Exp[0.3424(LogT)2.439] (1)
shows that the quantity of evaporated water during the drying process is dependent on the
drying temperature, the evaporating surface being constant. It was found that the validity of
the model is rooted on the expression (Logβ x lnE)N = LogT where both sides of the
expression are correspondingly approximately equal to 2. The respective deviation of the
model-predicted quantity of evaporated water from the corresponding experimental value
was found to be less than 19% which is quite within the acceptable deviation range of
experimental results, hence depicting the usefulness of the model.
Model for calculating the quantity of water lost by evaporation during ove n drying of clay at
900C has been derived [5]. The model;
γ = exp[(lnt)1.0638 - 2.9206] (2)
indicated that the quantity of evaporated water, γ during the drying process is dependent on
the drying time t, the evaporating surface being constant. The validity of the model was found
to be rooted in the expression (Logβ + lnγ)N = lnt.
Derivation of a model [6] for predicting the quantity of water evaporated during drying of
clay at a temperature range 80-1100C has been carried out. The model;
E= exp[0.3424(LogT)2.3529] (3)
indicates that the quantity of evaporated water during the drying process is dependent on the
drying temperature, the evaporating surface being constant. The validity of the model is
rooted in the expression (lnE x Log β)N = Log T since both sides of the expression are
correspondingly approximately equal to 2. The respective deviation of the model-predicted
quantity of evaporated water from the corresponding experimental value is less than 20%
which is quite within the acceptable deviation range of experimental results, hence depicting
the usefulness of the model. Water evaporation per unit rise in the drying temperature
evaluated from experimental and model-predicted results are 0.078 and 0.0502g/0C
respectively, indicating proximate agreement.
A model has been derived by Nwoye et al [7] for quantifying the extent and magnitude of water
evaporated during time dependent drying of clay. The model;
Vol.10, No.13 Model for Perio dic Analysis of t he Quantit y 1235
γ = exp((lnt/2.9206)1.4) (4)
indicates that the quantity of evaporated water γ during the drying process (at 900C) is
dependent on the drying time, t, with the evaporating surface being constant. It was
found that
the validity of the m odel is rooted in the expression
lnγ = (lnt/Logβ)N
where both sides of
the expre ssi on a re
correspondingly almost equal.
Nwoye et al. [8] derived a model for predictive analysis of the quantity of water evaporated
during the primary-
stage processing of a bioceramic material sourced from kaolin. The model;
α = e(lnt/2.199 2) (5)
shows that the quantity of water α, evaporated at 1100C, during the drying process is also
dependent on the drying time t, where the evaporating surface is constant. It was found that
the validity of the model is rooted on the expression (lnt/lnα)N = Logβ where both sides of the
expression are correspondingly approximately equal to 3. The respective deviation of the
model-predicted quantity of evaporated water from the corresponding experimental value was
found to be less than 22% which is quite within the acceptable deviation range of
experimental results.
The present work is to derive a model for periodic analysis of the quantity of water
evaporated during thermo-processi ng of clay (from Olokoro (Nigeria)) designated for
production of oven refractory.
2. MATERIALS AND METHODS
The clay sample was crushed to particle size of 425µm and homogenized separately; mixing
thoroughly with 10g bentonite (binder) and 6% water (of total weight). It was, moulded and
dried at a temperature of 900C in an electric oven to enhance loss of water by evaporation
through a drying time range; 50-130mins. A mould of surface area 833mm2 was used to make
a rectan gular sh ape of th e clay product. The initi al and fi nal masses of the cla y sampl es were
obtained before and after drying respectively to evaluate the mass of water removed from the
material.
2. 1 Model Formulation
Experimental data (Table 1) obtained from the research work carried out were used for the
model formulation.
Computational analysis of the experimental data shown in Table 1, gave rise to Table 2
which indicate that;
lnγ = lnt N (approximately) (6)
Log β
γ = exp lnt N (7)
Log β
1236 C. I. Nwoye, B. C. Chukwudi Vol.10, No.13
Introducing the values of β and N into equation (7)
γ = exp lnt 1.3 (8)
2.9206
Where
(γ) = Weight of water lost by evaporation during the drying process (g)
(β) = Area of evaporating surface (mm2)
N = 1.3; (Collapsibility coefficient of binder-clay particle boundary at the
drying temperature of 900C) calculated using a soft ware: C-NIKBRAN [9]
t = Drying time (mins.).
γM = γ values predicted by model.
Table 1: Variation of quantity of evaporated water with drying time
3. BOUNDARY AND INITIAL CONDITIONS
Consider a rectangular shaped clay product of evaporating surface area:833mm2, exposed to
dryi ng in the oven while it was in wet condition. Initially, atmospheric levels of oxygen are
assumed. Atmospheric pressure was assumed to be acting on the clay samples during the
drying process (since the furnace is not air-tight). The grain size of clay particles used is
425µm, weight of clay and binder (bentonite) used (for each rectangular product); 100g and
10g respectively, quantity of water used for mixing; 6% (of total weight), dr ying temperature
used; 900C, and range of drying time used; (50-130 mins.).
The boundary conditions are: Atmospheric levels of oxygen at the top and bottom of the clay
samples since they are dried under the atmospheric condition. No external force due to
compression or tension was applied to the drying clays. The sides of the particles and the
rectangular shaped clay products are taken to be symmetries.
4. MODEL VALIDATION
The model was validated by comparison of the model-predicted γ values and those from the
experiment for equality. Comparison between these γ values reveals deviations of model-
predicted γ from those of the experimental values. This is believed to be due to the fact that
the surface properties of the clay and the physiochemical interactions between the clay and
binder, which were found to have played vital role during the evaporation process were not
(t)
A
(γ)
50
60
70
90
95
110
130
833
833
833
833
833
833
833
4.40
5.02
5.60
6.60
6.91
7.70
8.60
Vol.10, No.13 Model for Perio dic Analysis of t he Quantit y 1237
considered during the model formulation. This necessitated the introduction of correction
factor, to bring the model-predicted γ value to that of the corresponding experimental value.
Deviation (De) (%) of model-predicted γ values from the experimental γ values is given by
De = Pw – Ew x 100 (9)
Ew
Correction factor (Cr) is the negative of the deviation i.e
Cr = -De (10)
Therefore
Cr = -100 Pw – Ew (11)
Ew
Where
De = Deviation (%)
Pw = Quantity of evaporated water as predicted by model (g)
Ew = Quantity of evaporated water as obtained from experiment (g)
Cr = Correction factor (%)
Introduction of the value of Cf from equation (11) into the model gives exactly the
corresponding experimental value of evaporated water.
The model was also validated by comparing the values of the standard deviation evaluated
from experimental and model-predicted data.
5. RESULTS AND DISCUSSION
The derived model is equation (8). Computational analysis of data in Table 1 gave rise to
Table 2.
Table 2: Variation of lnγ with (lnt/Log β)N
Int
Logβ
lnγ
(lnt/Logβ)N
3.9120
4.0943
4.2485
4.4998
4.5539
4.7005
4.8675
2.9206
2.9206
2.9206
2.9206
2.9206
2.9206
2.9206
1.4816
1.6134
1.7228
1.8871
1.9330
2.0412
2.1518
1.4622
1.5514
1.6278
1.7540
1.7815
1.8564
1.9426
5.1 Evaporation Rate
Water evaporation rate resulting from drying of the clay within a range of drying time 50-
130 mins. was determined following comparison of the evaporation rate obtained by
calculations involving experimental results, and model-predicted results obtained directly
from the model.
Evaporation rate, Er (g min-1) was calculated from the equation;
Er = E/t (12)
1238 C. I. Nwoye, B. C. Chukwudi Vol.10, No.13
R
2
= 0.998
2
3
4
5
6
7
8
9
10
3080130 180
Drying Time (mins.)
Quantity of water removed
(g)
Fig.1: Variation of the quantity of water evaporated with
drying time (as obtained from experi ment)
Therefore, a plot of mass of water evaporated E against dry ing t ime t , as in F ig. 1 using e xperimenta l
resu lts in Ta ble 1 , gives a slope , S a t points (5.02, 60) and (7.7, 110) f ollowing their substitution into the
mathematical expression;
S = ΔE/Δt (13)
Equation (14) is detailed as
S = E2 - E1/ t2 - t1 (14)
Where
ΔE = Change in the quantities of water evaporated E2, E1 at two dryin g t ime s values t2, t1. Considering
the points (5.02, 60) and (7.7, 110) for (E1, t 1) an d (E2, t2) respectively, and su bstituting th em
into equatio n (14), gives the slope as 0.0536g min-1 which is the water evaporation rate during the
actual experimental drying process.
R2 = 0.9965
2
3
4
5
6
7
8
3080130 180
Drying Time (mins.)
Quantity of water removed
(g)
Fig. 2: Variation of the quantity of water evaporated with
drying time (as predicted by derived model)
Also sim i la r plot ( a s in F ig . 2) using model-predicted results gives a slope. Considering points
(4.7181, 60) and (6.4007, 110) for (E1, t1) and (E2, t2) respectively and substituting them into
equation (14) gives the va lue of s lope , S as 0. 0337g min -1. This is the model-predicted water
evapo ra tion ra te du r ing the dry ing of the c l ay . A co mpar ison of the se two quan titi e s of wate r
evapo ra tion ra te s hows p roxi mat e agr eeme nt. Th is i ndica te s a ve ry high degre e o f va l idity for the
model as a reliable tool for predicting the water evaporation rate during drying of the clay within a
drying time range 50-130 mins..
Vol.10, No.13 Model for Perio dic Analysis of t he Quantit y 1239
An ideal compari son of the water evapo ration r ate as obtai ned from experim ent and as predicted by the
model for the purpose of testing the validity of the model is achieved by considerin g the R2 values.
The values of the correlation coefficient, R calculated from the equation;
R = √R2 (15)
using the r-squared values (coefficient of determination) from Figs. 1 and 2 show close
correlation (0.9982) between model-predicted water evaporation rate and that obtained from
experiment (0.9990). This suggests proximate agreement between model-predicted water
evaporation and that of the experiment.
0
1
2
3
4
5
6
7
8
9
10
4090 140
Drying Time (mins.)
Quantity of water removed
(g)
ExD
MoD
Fig. 3: Comparison of the water evaporation rates
(as obtained from experiment and derived model)
Fig. 3 shows very close alignment of the curves from model-predicted values of the quantity
of evaporated water (MoD) and that from the corresponding experimental values (ExD). The
degree of alignment of these curves is indicative of the proximate agreement between both
experimental and model-predicted quantity of evaporated water.
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
3 57 9
Quantity of water removed (g)
Deviation (%)
Fig. 4: Variation of model-predicted quantity of water removed
with its associated deviation from experimental result
It is also shown in Fig. 4 that the maximum deviation of values of the model-predicted
quantity of water removed (from those of the experiment) is less than 19% which is quite
within the acceptable deviation limit of experimental results. The deviation (of the model-
predicted quantity of water removed) from the actual experimental values show highest and
least values at -18.87 and -1.92% respectively (Fig.4).
1240 C. I. Nwoye, B. C. Chukwudi Vol.10, No.13
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
050100 150
Drying Time (g)
Deviation (%)
Fig. 5: Variation of deviation of model-predicted quantity
of water removed (from experimental result with drying time
Fig. 4 also shows that these deviation values correspond to model-predicted quantity of
removed water:6.9769 and 4.3154g respectively. Comparison of Figs. 4 and 5 shows that
these marked deviation values in association with the respective quantities of water removed
corresponds to drying times: 130 and 50 mins. respectively.
0
2
4
6
8
10
12
14
16
18
20
3 57 9
Quantity of water removed (g)
Correction factor (%)
Fig. 6: Variation of model-predicted quantity of water removed
with its associated correction factor
Correction factor to the model-predicted quantity of water removed (shown in Fig. 6) gives
highest and least values; +18.87 and +1.92% respectively (negative) to the deviations in Figs.
4 and 5. Furthermore, the orientation of this curve is opposite that of the deviation of model-
predicted quantity of water removed in Figs. 4 and 5. This is because correction factor is the
negative of the deviation as shown in equations (10) and (11). It is believed that the
correction factor takes care of the effects of the surface properties of the clay and the
physiochemical interaction between the clay and the binder which (affected experimental
results) were not considered during the model formulation.
It was found that the validity of the model is rooted on the expression lnγ = (lnt/Logβ)N where
both sides of the equation are correspondingly almost equal. Table 2 also agrees wi t h
equation (6) following the values of lnγ and (lnt/Logβ)N evaluated as a result of statistical and
computational analysis carried out on the experimental results in Table1.
Vol.10, No.13 Model for Perio dic Analysis of t he Quantit y 1241
6. CONCLUSION
The model gives a periodic analysis of the quantity of water evaporated during thermo-
processing of Olokoro clay (designated for production of refractory) at 900C within a drying
time range of 50-130 mins.. It was found that the validity of the model is rooted in expression
lnγ = (lnt/Logβ)N where both sides of the expression are correspondingly almost equal. The
maximum deviation of the model-predicted water evaporation rate from the corresponding
experimental value is less than 19% which is quite within the acceptable deviation range of
experi mental resul ts. Water evaporation rate as obtained from experiment and derived model
were evaluated to be 0.0536 and 0.0337g min-1 respectively.
Further works should incorporate more process parameters into the model with the aim of
reducing the deviations of the model-predicted γ values from those of the experimental.
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