Journal of Industrial and Engineering Chemistry 17 (2011) 6270
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Journal of Industrial and Engineering Chemistry
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Rheological characteristics of coalwater slurry using microwave pretreatment A statistical approach
B.K. Sahoo a,b, S. De a, M. Carsky c, B.C. Meikap a,c,*
Department of Chemical Engineering, Indian Institute of Technology (IIT), Kharagpur, P.O. Kharagpur Technology, West Bengal 721302, India Research & Development Centre for Iron & Steel, Steel Authority of India Limited, Ranchi, Jharkhand 34002, India c School of Chemical Engineering, Faculty of Engineering, Howard College, University of Kwazulu-Natal(UKZN), King George V. Avenue, Durban 4041, South Africa

A R T I C L E I N F O

A B S T R A C T
Article history: Received 14 January 2010 Accepted 10 February 2010 Available online 8 October 2010 Keywords: Microwave pretreatment Coalwater slurry Rheology Modeling Optimization
The present study addresses the treatment of microwave energy for rheological characteristics of coal water slurries (CWS) performed in an online Bohlin viscometer. Detailed experimental investigations were carried out for high ash Indian coal (Jamadoba washery, 38% ash). Experiments were conducted at high power level (900 W) for all the test samples in microwave oven. The exposure times were xed at 30, 60, 90 and 120 s. Before and after treatment, the test samples were ground and sieved into different fractions for chemical and physical analysis. Central composite design (CCD) was applied to study the inuence of particle diameter, solid concentration, microwave (MW) exposure time and shear rate on apparent viscosity for rheology characteristics of coalwater slurry. A quadratic model was developed for apparent viscosity using Design-Expert software. The model was used to calculate the optimum operating conditions for minimization of apparent viscosity. The apparent viscosity (22.83 mPa s) produced at these operating conditions showed an excellent agreement with the amounts predicted by the models. 2010 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
1. Introduction In recent years, there has been a growing interest and acceptance of microwave heating of coal and minerals. However, it is well established that the impact of mining and subsequent processing operations must be reduced to meet future sustainability requirements. One such area is the use of microwave heating technologies to improve the efciency of various mineral processing unit operations including: leaching, refractory gold ore treatment, grindability and liberation and coal grinding. Microwave energy is perceived to provide a means for rapid, even heating, improved processing efciencies, and unobtainable materials properties. Even for materials and processes where microwave heating is technically an option, additional technical and economic considerations must be evaluated, on a case-by-case basis, to determine whether it is the best alternative. Microwave energy has found general, commercial application in very few areas. These include food processing, analytical chemistry, heating and vulcanization of rubber. Food processing and rubber manu-
* Corresponding author at: School of Chemical Engineering, Faculty of Engineering, Howard College, University of Kwazulu-Natal (UKZN), King George V. Avenue, Durban 4041, South Africa. Tel.: +27 (0) 3802. E-mail address: meikap@ukzn.ac.za (B.C. Meikap).
facture involve relatively high-volume, continuous processing. Despite the considerable effort that has been expended in microwave process development, there has been little industrial application to date, with most of the effort still in the laboratory stage. Some of the more signicant problems that have inhibited industrial application of microwave processing include: the cost of equipment; limited applicability, variation in dielectric properties with temperature and the inherent inefciency of electric power. Microwave energy is a non-ionizing electromagnetic radiation with frequencies in the range of 300 MHz300 GHz. Microwave frequencies include three bands: the ultra high frequency (UHF: 300 MHz3 GHz), the super high frequency (SHF: 3 GHz30 GHz) and the extremely high frequency (EHF: 30 GHz300 GHz). Above 300 GHz, the absorption of electromagnetic radiation by Earths atmosphere is so great that it is effectively opaque, until the atmosphere becomes transparent again in the so-called infrared and optical window frequency ranges. Microwaves have extensive application in the eld of communication; however, the Federal Communication Commission (FCC) has allocated certain frequencies for Industrial, Scientic, Medical and Instrumentations (ISMI) applications. Currently, 2450 MHz is the most commonly utilized frequency for the home microwave oven, which was invented by Percy L. Spencer almost 60 years ago [1,2]. Microwaves can pass through materials like glass, paper, plastic and ceramic, and be absorbed by foods and water; but they are reected by metals.

1226-086X/$ see front matter 2010 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2010.10.010
B.K. Sahoo et al. / Journal of Industrial and Engineering Chemistry 17 (2011) 6270
Microwave energy is derived from electrical energy with a conversion efciency of approximately 50% for 2450 MHz and 85% for 915 MHz [3,4]. Microwaves have longer wave lengths and lower available energy quanta than other forms of electromagnetic energy such as visible, ultraviolet or infrared light. Microwaves processing of materials are a new, powerful and signicantly different technology to process materials that may not be amenable to convectional means of processing or to improve the performance characteristics of existing materials. However due to complexity of microwave interactions with materials, simply placing them in a microwave oven and expecting it to heat efciently will seldom lead to success [1]. Recently, continuously increasing demands for energy have led scientists to seek for ways of nding new energy sources. Thus, researchers have directed their attention towards various methods of burning coalwater slurries (CWS) for energy generation. Transportation of coal in the form of slurry through a pipeline is gaining importance. Microwave pretreatment of coal has been found to selectively heat the mineral matter based on differences in dielectric properties, thereby causing the pyrite to decompose magnetically susceptible pyrrhotite. Also, it resulted in weakening of the coalmineral matrix, thereby altering the angularity and surface properties of the ground particles. The rheological behavior of solidliquid suspensions has a great bearing on the power requirements for pumping of solidliquid suspensions. These rheological properties of suspensions are very much inuenced by the nature of the suspending medium, particle size, shape, surface characteristics, and size distribution [5]. The surface characteristics of microwave-treated coals and that microwave treatment on few Indian high-ash coals resulted in smoothing of surface and conversion of a-silica to b-silica. It was found that microwave-treated coal slurry facilitates enhanced ow characteristics and abates the erosion problem in pipeline transport as well as in coalslurry injection furnaces. It was found that as a result of microwave pre-treatment, the rate of breakage increases with increase in particle size and the grinding resistance was reduced with microwave pretreatment without altering the fundamental property of the coal [56]. The rheological properties of coaloilwater suspension containing solids of different sizes, the effect of coal particle size distributions on rheology of coal water slurries (CWS) was studied [78] and some previous work with respect to slurry rheology in ultrane grinding was reviewed [9]. Different chemicals were used as dispersing agent and stabilizer and have signicant effect on the stability and viscosity of coalwater slurries [10]. The properties, settling rates, and the rheology of coalwater mixtures (CWM) made up from different coals were investigated [11]. The two-parameter power-law, Bingham plastic and Casson empirical rheological models, and the three-parameter HerschelBulkley and Sisko models are used to t the shear stress/shear rate data. The rheological behavior of low-rank coalwater slurry from Lochiel, South Australia was reported as a function of solids concentration, particle size and size distribution [12]. The slurry behavior as well as rheology properties of various solutions have been reported in the literature [13] A new technique for the characterization of the rheology of mineral slurries into Newtonian and non-Newtonian ows was investigated [14]. A semi-empirical model was developed to predict slurry rheology from easily-measured slurry properties. The model demonstrates the complex inuence of these properties on rheology and also permits rheological information to be predicted in cases where it cannot be measured [15]. A new procedure was found for obtaining a full shear rateshear stress ow curve for unstable slurries using the single bobbin Debex online viscometer, which is based on the use of a calibration algorithm which incorporates a correction for turbulent ow in the

measurement vessel [16]. An increase in the viscosity of suspensions with decreased in particle size for same solid concentration was reported. The effects of coal content, coal particle size and size distribution, and temperature on the slurry rheology are investigated [17]. Papachristodoulou and Trass studied the rheological properties of coaloil mixture of a bituminous coal in four types of oil, grade 2, grade 4, light grade 6 and heavy grade 6. The viscosity of a concentrated suspension of solid spheres was investigated by many authors [18,19]. A detailed study of coalwater slurry rheology has been carried out using 20 coals of different origins having ash content 2.6 37.8% by weight. They have generalized the ow behavior into three categories based on carbon content of coal [20]. Both rheological and hindered-settling characteristics of small particle size suspensions of 1050 mm with particles of thorium oxide in water, methanol in titian kaolin, and alumina and graphite in water was studied [21]. Literature review reveals that the viscosity of a suspension depends on the nature of the solid particles, shape, particle size distribution, nature of suspending medium, solid concentration, additives, pressure, and temperature. The rheology of coal slurries has been studied mostly with low-ash coals. Since Indian coals are high in ash content and moreover the nature of low-ash coal is completely different from at of those found elsewhere, it is very much essential to measure rheological characteristics. In addition, after microwave treatment, the rheological behavior of pretreated coal should show different behavior from that of untreated coal. As far as known to the authors, optimization studies of rheological characteristics of microwave-treated coalwater suspensions using the response surface methodology (RSM) approach are very limited. In the present investigation, therefore an attempt has been made to investigate the properties of microwave untreated and treated Indian high ash coal for rheological characterization. The goal of this study was to nd the optimum conditions to minimize viscosity of coalwater slurry by simultaneously considering the particle size, microwave exposure time, shear rate and solid concentration. 2. Experimental 2.1. Microwave treatment of coal The schematic diagram of experimental setup is shown in Fig. 1. Microwave treatment was carried out with a 900 W experimental prototype microwave oven with variable power at 2.45 GHz. The experimental setup mainly consists of a microwave oven, which was used for microwave pretreatment of coal and was a LG MC-808WAR model. The oven was a 530 mm (W) 500 mm (D) 322 mm (H) capacity with specications frequency 50 Hz, power level 900 W at high level, output frequency 2.45 GHz, usable volume 27 L, weight of 26 kg. Microwave oven has ve microwave power settings (i.e. 180 W, 360 W, 540 W, 720 W and 900 W). High power is automatically selected but repeated presses of the MICRO key will select a different power levels. The microwave oven consists of a door handle (incorporating an automatic door lath mechanism), microwave radiationproof oven cooker window (to visualize the sample during treatment), stirrer fan cover (plastic shield to cover the stirrer fan, which operates whenever the oven is used and provides uniform distribution of microwave energy throughout the cavity, revolving tray (rotates during operation and ensures uniform distribution of microwaves), control panel (consists of several soft-touch programmable panels, through which any desired values of power consumption, duration of heating, and start and stop operation are chosen) and oven cavity light. Nitrogen gas at a controlled ow rate was maintained within the oven as an inert

[()TD$FIG]

Fig. 1. Schematic of experimental setup for microwave treatment of coal sample.
atmosphere. Hot air, steam, and vapors were generated within the oven cavity during cooking in the microwave oven. Air vent was provided to expel these vapors and other gases during operation. For this work, the coal sample was collected from Jamadoba washery (TISCO, India) refereed as coal-X (38% ash content). Original coal sample of 15 kg was crushed in a jaw crusher, which gives 3/400 + 1/200 mesh sieves. The coal samples of 3/ 400 + 1/200 (19.0512.7 mm) fractions were taken in a glass container of around 0.5 kg capacity such that the height of the coal bed was approximately equal to the diameter of the container. The container containing the coal samples was placed on the oor of the oven in the revolving tray. Then nitrogen gas was purged at controlled rate through a rotameter in order to create an inert atmosphere for about 5 min, and then the door was closed carefully. Then the oven was set at a power level of 900 W and programmable time of 30, 60, 90, 120 s respectively. The temperature of the coal in the actual experiment was measured by a digital thermometer (range is 0 8C200 8C, type is Pt-100). Then the microwave treated coal samples were collected for different sized fractions by ball mill. The microwave treated coal of 3/400 + 1/200 (19.0512.7 mm) fractions was then grinded in a ball mill for 20 min. After every 5 min the sample was taken out and sieved with the help of a sieve shaker for 5 min to get the ve cut fractions (253 mm, 182 mm, 127 mm, 90 mm, 60 mm). Each of the fractions was collected and weighed. The oversize material (>295 mm) was returned to the mill for further grinding in successive intervals of 5 min for a total time of 20 min.
2.2. Rheology measurement of coalwater slurry The viscometer is the Bohlin Visco 88 BV, a portable, easily handled viscometer for laboratory, plant and eld use. The viscometer, which is widely used for industrials, including coating, foods and pharmaceuticals, directly measures the rotational speed of a rotor (a rotating inner cylinder), V (rpm) and the shear stress related torque, M (mNm), shear rate g (1/s), shear stress, t (Pa) and apparent viscosity m (Pas) are calculated by following formula, t = C1*M: shear stress [Pa], g = C2*V: shear rate [s1], m = t/g: viscosity [Pa s], where C1, C2 are constants related to a measuring system. The Bohlin Visco 88 BV employs a concentric cylindrical geometry with a rotating inner cylinder and stationary outer cylinder. The spindle is driven by a synchronous motor through a calibrated spring and the deection of the spring is displayed by the viscometer. It uses the idea that the torque required to turn an object in a uid, can indicate the viscosity of that uid. The exact volume of sample was placed in the annular space between the spindle and the cup, and measurements were taken at different rotational speeds of the spindle. The concentric cylinder can be congured in to 8 different measurement systems (3 DIN, 2 wide gap, 3 innite sea), corresponding to knob 18 on the instrument and its design allows the measurement of samples in situ (e.g. in a container) as well as on the laboratory bench. Any inner cylinder has 8 rotation speeds, which is from 20 to 1000 rpm (in agreement with a SPEED setting value 18 on the instrument); correspond to a shear rate range 121200 s1. The torque developed on the inner cylinder due to a sample is directly related to the sample viscosity and should be in a range of 0.59.5 mNm for the accurateness of

the measurement. The gap between the inner bob/vane and outer cylinder is thin so that there is almost a constant gradient of shear over it. To prepare 40% by wt., 40 g of coal weighted accurately by digital pan type balance and put 60 g of distilled water to it. After stirring for minutes the exact volume of sample then placed in the cylinder of the viscometer after placing the bob/vane properly with in the cylinder. Then with the help of programmable panel the online viscometer is started on. The all function of rheometer is controlled by software through computer. It can automatically nish system identication, gap setting options, temperature options. According to the instructions shown on the computer screen, all operations can be done for the setting up the various options relating to the rheometer, geometry, sample details and shear rate range. A whole viscosity measurement was spent about 120 s. Based on the computer program, when the recorded numerical values under different shear rates were input the computer, the apparent viscosity at 224.60 s1 shear rate would be obtained. All rheological measurements of the samples were done in a shear rate range s1. In all the tests the pH value of the slurry varied between 7.05 and 7.25 and the temperature was kept constant at 8C. Plots of shear rate and shear stress obtained directly. Same procedure was repeated for all the samples. In this study, all samples were measured by the use of C14 system (C14 DIN), which has a gap width of 0.7 mm between the inner and outer cylinders. About 10 ml of slurry sample is required for each measurement. 2.3. Multivariate experimental design Response surface methodology is a statistical method that uses quantitative data from appropriate experiments to determine regression model equations and operating conditions [22]. RSM is a collection of mathematical and statistical techniques for modeling and analysis of problems in which a response of interest is inuenced by several variables [23]. A standard RSM design called central composite design (CCD) was applied in this work to study the variables for minimize the apparent viscosity of coalwater slurry [2425]. The central composite design was widely used for tting a second order model. By using this method, modeling is possible and it requires only a minimum number of experiments. It is not necessary in the modeling procedure to know the detailed reaction mechanism since the mathematical model is empirical. Generally, the CCD consists of a 2n factorial runs with 2n axial runs and nc center runs (six replicates). These designs consist of a 2n factorial or fractional (coded to the usual 1 notation) augmented by 2n axial points (a, 0,.0, 0), (0, a, 0,., 0),., (0, 0,., a), and nc center points (0, 0, 0,.,0) [26]. Each variable is investigated at two levels. Meanwhile, as the number of factors, n, increases, the number of runs for a complete replicate of the design increases rapidly. In this case, main effects and interactions may be estimated by fractional factorial designs running only a minimum number of experiments. Individual second-order effects cannot be estimated separately by 2n factorial designs. The responses and the corresponding parameters are modeled and optimized using ANOVA, which was used to estimate the statistical parameters by means of response surface methods. Basically, this optimization process involves three major steps, which are, performing the statistically designed experiments, estimating the coefcients in a mathematical model, predicting the response, and checking the adequacy of the model. Y f X 1 ; X 2 ; X 3 ; X 4. X n (1)

Table 1 Relationship between coded and actual value of the variables. Code a +1 +a Actual level of variable Xmin [(Xmax + Xmin)/2] [(Xmax Xmin)/2b] (Xmax + Xmin)/2 [(Xmax + Xmin)/2] + [(Xmax Xmin)/2b] Xmax
where Xmax and Xmin are maximum and minimum values of X, respectively; b is 2n/4
and controllable by experiments with negligible errors. It is required to nd a suitable approximation for the true functional relationship between independent variables and the response surface [27]. The experimental sequence was randomized in order to minimize the effects of the uncontrolled factors. The response was used to develop an empirical model that correlated the responses to minimize apparent viscosity of rheological characteristics of coalwater slurry process variables using a seconddegree polynomial equation as given by Eq. (2): Y b0
0 n n n n X X XX bi X i bii Xi2 bi j X i X j i1 i1 i1 j > 1 0
where, Y is the predicted response, b0 the constant coefcient, bi the linear coefcients, bij the interaction coefcients, bii the quadratic coefcients and xi, xj are the coded values of the minimization of apparent viscosity for characterization of coal water slurry variables. The number of tests required for the CCD includes the standard 2n factorial with its origin at the center, 2n points xed axially at a distance, say a from the center to generate the quadratic terms, and replicate tests at the center; where n is the number of variables. The axial points are chosen such that they allow rotatability [28], which ensures that the variance of the model prediction is constant at all points equidistant from the design center. Replicates of the test at the center are very important as they provide an independent estimate of the experimental error. For four variables, the recommended number of tests at the center is six [29]. Hence, the total number of tests (N) required for the four independent variables is: N 2n 2n nc 30 (3)
Once the desired ranges of values of the variables are dened, they are coded to lie at 1 for the factorial points, 0 for the center points and a for the axial points. The codes are calculated as functions of the range of interest of each factor as shown in Table 1 [30]. 2.4. Model tting and statistical analysis The statistical software package Design-Expert, Stat-Ease, Inc., Minneapolis, USA was used for regression analysis of experimental data to t the equation developed and also to plot response surface. ANOVA was used to estimate the statistical parameters. 3. Results and discussion 3.1. Characterization of coal sample 3.1.1. Proximate and ultimate analysis The proximate analysis of the microwave pretreated and untreated coal-X for different sizes are presented in Table 2. Table 3 shows the ultimate analysis of the microwave pretreated and

where, Y is the response of the system, and Xi is the variables of action called factors. The goal is to optimize the response variable (Y). It is assumed that the independent variables are continuous
66 Table 2 The proximate analysis of coal sample-X. Constituents (%) (adb) MW untreated coal Fixed carbon Volatile matter Moisture Ash Microwave treated coal Fixed carbon Volatile matter Moisture Ash Microwave treated coal Fixed carbon Volatile matter Moisture Ash Microwave treated coal Fixed carbon Volatile matter Moisture Ash Microwave treated coal Fixed carbon Volatile matter Moisture Ash 253 mm 38.86 20.6 2.04 38.50 [900 W, 30 s] 40.85 19.9 1.15 38.10 [900 W, 60 s] [900 W, 90 s] 39.25 21.9 1.15 37.7 [900 W, 120 s] 43.56 18.4 1.04 37
182 mm 42.1.1 38.20 42.59 18.3 1.3 37.81 41.1.5 37.23 41.55 20.3 1.25 36.9 41.5 21.36.4
127 mm 45.1.15 37.17 44.3 18.3 1.2 36.20 44.1.05 35.82 43.4 19.7 1.3 35.6 44.7 18.5 1.5 35.3
90 mm 43.75 16.4 2.45 37.40 42.1.2 36.9 43.1.43.75 19.6 1.05 35.6 44.45 19.4 1.45 34.7
untreated coal-X of 90 mm. It has carried out by standard method. The contents of C, H, N, and S of the coal samples were measured using a LECO CHNS 932 Elemental Analyzer. The oxygen contents of samples were calculated by difference. Results show that the ash content of microwave-treated coals is lower than that of original untreated samples. This lowering of ash content due to microwave treatment may be due to the partial removal of mineral matter ner than 90 mm by grinding and screening. Due to microwave treatment mineral matter is heated faster than coal; as a result the binding force in minerals is weakened and the form nes while being ground in a ball mill. Also, the ash content increases as the particle size increases. This is a feature of this coal, as ash tends to concentrate in large fractions with Indian coals. Clearly, there has been little change in the total moisture content. However, the moisture content of microwave-treated coals was found to be lower than that of untreated coal. The same trend has been observed for coals of different particle sizes. The volatile matter and xed carbon of microwave-treated coals are found to be more than those of untreated coals, which is quite obvious, as discussed earlier, due to partial removal of mineral matter. 3.1.2. Particle size analysis The particle size distributions of the samples were determined by MAL1017204 type Mastersizer 2000 E Ver. 5.20 produced by Malvern Instruments Ltd., Malvern, UK. Water was used as the dispersion medium. The automatic particle size analysis can be obtained in the measuring range 0.11000 mm in suspension. The results are calculated on the basis of the Fraunhofer theory. The

Fig. 2. Malvern particle size distribution of coal-X (60 mm) before MW treatment and after MW treatment [900 W, 1 min].
data recording/result presentations are obtained by MS Windows programme. A comparison of the particle size distribution and some size parameters of untreated and microwave treated coal of 60 mm particles are shown in Fig. 2. The particle size is corresponding to the accumulative mass percentage of particles that pass the size on the distribution curve. D10, D50 and D90 refer to the particle sizes that 10%, 50%, 90% of coal particles by weight can exactly pass, respectively. As seen from Fig. 2, microwave-treated coal sample contains signicant amount of ner particles than microwave untreated coal sample. Also it has found that the surface area of microwave treated coal is more than that of untreated coal. It has concluded that the particle size distribution of coal after microwave treatment is more depended on the coal grinding process than before microwave treatment. Almost the same trend of size distribution has been observed for other samples. 3.1.3. Density measurement Densities of different coal particles for both microwave-treated and untreated coals are presented in Table 4. It has been found that the density of microwave treated particles was found to be less than that of untreated particles for the same size. For coals, density gradually increases with increased particle diameter. It may be due
Table 3 The ultimate analysis of coal sample-X [90 mm]. Constituents (%) w/w, dry basis Carbon Hydrogen Nitrogen Sulphur Oxygen Untreated coal 59.54 3.86 2.60 0.52 33.48 Microwave treated coal [900 W, 1 min] 60.52 3.78 2.65 0.48 32.57 Microwave treated coal [900 W, 2 min] 57.25 3.59 2.56 0.43 36.17
B.K. Sahoo et al. / Journal of Industrial and Engineering Chemistry 17 (2011) 6270 Table 4 Density of MW treated [900 W] and untreated coal-X. Particle size (mm) 60 MW untreated (g/cm3) 1.750 1.733 1.625 1.610 1.600 MW treated [1 min] (g/cm3) 1.738 1.725 1.610 1.575 1.532
MW treated [2 min] (g/cm3) 1.740 1.710 1.600 1.515 1.480
to the effect of microwave treatment of mineral matter resulting in the decomposition of pyrite and mullite and possibly the conversion of a-silica to b-silica, which may reduce the erosion considerably. 3.2. Rheological characteristics of coalwater slurry The optimization of apparent viscosity for rheological characteristics of coalwater slurry have been studied by considering the effects of operating parameters in the range such as solid concentrations (wt%), particle diameter (60253 mm), microwave exposure time (0120 s), and shear rate (20.72 224.60 s1) using response surface methodology. 3.2.1. Development of regression model equation The CCD was used to develop correlation between the operating variables of coalwater slurry to the apparent viscosity. The complete experimental range and levels of independent variables are given in Table 5. Runs 2530 at the center point were used to determine the experimental error. According to the sequential model sum of squares, the models were selected based on the highest order polynomials where the additional terms were signicant and the models were not aliased. The quadratic model was selected as suggested by the software. Experiments were planned to obtain a quadratic model consisting of 24 trials plus a star conguration (a = 2) and there replicates at the center point. The design of this experiment and the experimental results is given in Table 6. The minimum apparent viscosity of coalwater slurry was found to be 25 mPa s. Regression analysis was performed to t the response function of apparent viscosity (mPa s). The model expressed by Eq. (2) (where the variables take their coded values) represents apparent viscosity (Y) as a function of particle diameter (X1), solid concentrations (X2), microwave (MW) exposure time (X3), and shear rate (X4). The nal empirical model in terms of coded factors for apparent viscosity (Y) is given in Eq. (4). Y 31 7:46X 1 4:04X 2 4:21X 3 11:04X 4 0:06X 1 X 2 0:69X 1 X 3 3:69X 1 X 4 0:19X 2 X 3 1:06X 2 X 4

1:31X 3 X 4 3:18X1 4:68X2 0:93X3 7:93X4
3.2.2. Statistical analysis The actual and the predicted apparent viscosity are shown in Fig. 3. Actual values are the measured response data for a particular run, and the predicted values are evaluated from the model and are generated by using the approximating functions. In Fig. 3, the values of R2 and R2 were found to be 0.954 and 0.912, respectively. adj The fair correlation coefcients might have resulted by the insignicant terms in Table 7, and most likely due to four different variables selected in wide ranges with a limited number of experiments as well as the non-linear inuence of the investigated parameters on process response. Eq. (4) has been used to visualize the effects of experimental factors on apparent viscosity response in Figs. 4(a) and (b), 7(a) and (b), 8(a) and (b). The model adequacy check is an important part of the data analysis procedure, as the approximating model would give poor or misleading results if it were an inadequate t. This is done by looking at the residual plots, which are examined for the approximating model [31]. The normal probability and studentized residuals plot is carried out for apparent viscosity for characterization of coalwater slurry. It has been found that residuals show how well the model satises the assumptions of the analysis of variance (ANOVA) whereas the studentized residuals
Table 6 Experimental design matrix and results for apparent viscosity for rheology characteristics of coalwater slurry. Run Coded level of variables X++++++++1 a +a X1 +1 +1 +1 +1 +1 +1 +1 +0 a +a X1 +1 +1 +1 +1 +1 +1 +1 +0 a +a X1 +1 +1 +1 +1 +1 +1 +1 +0 a +a Actual level of variables X1 (mm) X2 (wt.%) X3 (s) X4 (s1) Apparent viscosity, m (mPa s) 31 31
Positive sign in front of the terms indicates synergistic effect, whereas negative sign indicates antagonistic effect.
Table 5 Experimental range and levels of independent variables for apparent viscosity for rheology characteristics of coalwater slurry. Variables Particle diameter (mm) Solid concentration (wt.%) MW exposure time (s) Shear rate (s1) Symbol X1 X2 X3 X4 a 0 20.108.30 71.156.60 122.66 +1 204.90 173.63 +a 120 224.6
Apparent Viscosity (mPa-s)
23 200.00 45.00 40.00 175.00 150.00 35.00 125.00 30.00 100.00

Predicted

Solid Concentration (%)

Particle Diameter (m)

25.00 42.50 60.00 77.50 95.00
56 50.25 44.5 38.60.00 52.00 44.00 150.00 36.00 125.00 28.00 100.00 200.00 175.00

Actual

Fig. 3. Actual and predicted plot of apparent viscosity.
measure the number of standard deviations separating the actual and predicted values. It shows that neither response transformation was needed nor there was any apparent problem with normality. The studentized residuals versus predicted apparent viscosity have been also measured. The general impression is that it is a random scatter, suggesting the variance of original observations is constant for all values of the response. If the variance of the response depends on the mean level of Y, then this plot often exhibits a funnel-shaped pattern. This is also an indication that there was no need for transformation of the response variable. 3.2.3. Apparent viscosity To investigate the effects of the four factors on the apparent viscosity for rheological characteristics of coalwater slurry, the response surface methodology was used, and three-dimensional plots were drawn. Based on the ANOVA results obtained, solid concentrations, particle diameter, microwave exposure time, and shear rate were found to have signicant effects on the apparent

MW Exposure Time (s)

Fig. 4. (a) Combined effect of solid concentration and particle diameter on apparent viscosity at MW exposure time 60 s and shear rate 110 s1, (b) combined effect of MW exposure time and particle diameter on apparent viscosity at solid concentration 50% and shear rate 110 s1.
viscosity of coalwater slurry, with shear rate imposing the greatest effect on apparent viscosity of coalwater slurry. Solid concentration on the other hand imposed the least effect on the response. The quadratic effects of microwave exposure time and particle diameter as well as the interaction effects between X1X2, X1X3, X1X4, X2X3, X2X4, and X3X4 were considered moderate. The apparent viscosity response surface graphs are shown in Figs. 4(a) and (b), 7(a) and (b), 8(a) and (b).
Table 7 Analysis of variance (ANOVA) for response surface quadratic model for apparent viscosity for rheology characteristics of coalwater slurry. Source Model X1 X2 X3 X4 X1 X2 X1 X3 X1 X4 X2 X3 X2 X4 X3X4 X12 X22 X32 X42 Residual Lack of t Pure error Correlation total Sum of squares 7517.55 1335.042 392.042 425.042 2926.042 0.063 7.563 217.563 0.563 18.063 27.563 276.860 600.003 23.575 1723.574 359.417 359.417 0.001 7876.967 Degree of freedom 29 Mean square 536.968 1335.042 392.042 425.042 2926.042 0.063 7.563 217.563 0.563 18.063 27.563 276.860 600.003 23.575 1723.574 23.961 35.942 0.001 F value 22.409 55.717 16.362 17.739 122.116 0.003 0.316 9.080 0.024 0.754 1.150 11.555 25.041 0.984 71.932 1259.004 Prob > F < 0.0001 < 0.0001 0.0011 0.0008 < 0.0001 0.9599 0.5826 0.0087 0.8803 0.3989 0.3004 0.0040 0.0002 0.3370 <0.0001 < 0.0001 Remarks Signicant Signicant Signicant Signicant Signicant

Signicant

Signicant Signicant Signicant Signicant
69 59.40.150.00 130.00 110.00
200.00 175.00 150.00 90.00 125.00 70.00 100.00
150.00 130.00 110.00 40.00 90.00 70.00 30.00 35.00 45.00

Shear Rate (1/s)

35.5 30.60.00 52.00 44.00 40.00 36.00 35.00 28.00 30.00 50.00 45.00

67 58.25 49.5 40.75 32

150.00 130.00 110.00 44.00 90.00 70.00 28.00 36.00 52.00
Fig. 5. (a) Combined effect of shear rate and particle diameter on apparent viscosity at solid concentration 50% and MW exposure time 60 s, (b) combined effect of MW exposure time and solid concentration on apparent viscosity at particle diameter 150 mm and shear rate 110 s1.
Fig. 4(a) shows the three dimensional response surfaces, the combined effect of solid concentration and particle diameter on apparent viscosity at MW exposure time 60 s and shear rate 110 s1. A minimum apparent viscosity 26 mPa s was determined at MW exposure time 60 s and shear rate 110 s1. The combined effect of MW exposure time and particle diameter on apparent viscosity at solid concentration 50% and shear rate 110 s1 is shown in Fig. 4(b), the three dimensional
Fig. 6. (a) Combined effect of shear rate and solid concentration on apparent viscosity at particle diameter 150 mm and MW exposure time 60 s, (b) combined effect of shear rate and MW exposure time on apparent viscosity at particle diameter 150 mm and solid concentration 50%.
response surfaces. A minimum apparent viscosity 40 mPa s was determined at solid concentration 50% and shear rate 110 s1. Fig. 5(a) shows the three dimensional response surfaces which were constructed to show the most important two variables (shear rate and particle diameter) on apparent viscosity at solid
Fig. 7. The optimum region on the solid concentration and particle diameter for minimization of apparent viscosity for characteristics of coalwater slurry.
concentration 50% and MW exposure time 60 s. A minimum apparent viscosity 38 mPa s was determined at solid concentration 50% and MW exposure time 60 s. The three dimensional response surfaces of the combined effect of MW exposure time and solid concentration on apparent viscosity at particle diameter 150 mm and shear rate 110 s1 is shown in Fig. 5 (b). A minimum apparent viscosity 28 mPa s was determined at particle diameter 150 mm and shear rate 110 s1. Fig. 6 (a) shows the combined effect of shear rate and solid concentration on apparent viscosity at particle diameter 150 mm and MW exposure time 60 s. It can be seen that the minimum apparent viscosity 29 mPa s was determined at particle diameter 150 mm and MW exposure time 60 s. It can be clear from the Fig. 6(b) that the combined effect of shear rate and MW exposure time on apparent viscosity at particle diameter 150 mm and solid concentration 50%. It can be seen that the minimum apparent viscosity 38 mPa s was determined at particle diameter 150 mm and solid concentration 50%. 3.2.4. Optimization by response surface modeling The main aim of this study was to nd out the optimum process parameters in order to minimize the apparent viscosity for rheology characteristics of coalwater slurry from the mathematical model equations developed by RSM. The quadratic model equation was optimized using quadratic programming (QP) to minimize the apparent viscosity within the experimental range studied. The optimum processing conditions (Fig. 7) determined were particle diameter 194.33 mm, solid concentration 38.05%, microwave exposure time 56.14 s and shear rate 131.97 s1 have been determined as optimum levels of the process parameters to achieve the minimum apparent viscosity of 22.83 mPa s, compared to 25 mPa s that was minimum apparent viscosity in the tests conducted. 4. Conclusions In this study, the response surface methodology, central composite design, and quadratic programming were used to model and optimize the inuence of four process parameters on apparent viscosity for rheology characteristics of coalwater slurry. These four process parameters were particle diameter, solid concentration, microwave (MW) exposure time and shear rate. Mathematical model equations were derived for apparent viscosity by using sets of experimental data and ANOVA. The major ndings are: 3D response surface plots, which are simulations from the models, were presented to describe the effect of the process variables on the apparent viscosity for rheology characteristics of coalwater slurry.

Predicted values obtained using the model equations were in very good agreement with the observed values. By the help of quadratic programming, 194.33 mm particle diameter, 38.05% solid concentration, 56.14 s microwave (MW) exposure time and 131.97 s1 shear rate have been determined as optimum levels of the process parameters to achieve the minimum apparent viscosity 22.83 mPa s compared to 25 mPa s that was minimum apparent viscosity in the tests conducted. Acknowledgments The authors thankfully acknowledge the reviewers for suggesting valuable technical comments of this paper. The author is very much thankful to the sponsor CSIR (Council of Scientic and Industrial Research), New Delhi for their nancial grant to carry out the present research work. References
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