Interparticle Interactions in Highly Concentrated Coal–Water Slurries

May 18, 2015 - Energy Fuels , 2015, 29 (6), pp 3675–3683 ... Citation data is made available by participants in Crossref's Cited-by Linking service...
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Interparticle Interactions in Highly Concentrated Coal−Water Slurries and Their Effect on Slurry Viscosity Amrita Mukherjee and Sarma V. Pisupati* John and Willie Leone Department of Energy and Mineral Engineering and Earth and Mineral Sciences (EMS) Energy Institute, The Pennsylvania State University, 110 Hosler Building, University Park, Pennsylvania 16802, United States ABSTRACT: Coal/petcoke−water slurry viscosity is affected by interparticle interactions of the solids in water, which, in turn, is governed by the surface chemistry of the solids. To determine interparticle interactions of these carbonaceous solids in water, interfacial energies were determined on the basis of surface chemistries characterized by contact angle and ζ potential measurements. Hydrophobic/hydrophilic interaction energies, observed to be 2−3 orders of magnitude higher than the electrostatic interaction energies and the van der Waals interaction energies, were clearly the dominant interaction energies for such a system. Hydrophobic interactions lead to the formation of aggregation networks of solids in the suspensions with entrapped water, whereas hydrophilic interactions result in the formation of hydration layers around the carbonaceous solid particles, causing loss of free water from the slurry. This results in an increase in the effective solid volume fraction, leading to an increase in viscosity. The increase in the effective solid volume fraction was observed to be a function of surface chemistry of the solid. A relationship between the effective solid volume fraction and the oxygen/carbon ratio of the carbonaceous solid was developed using both experimental measurements and the Krieger−Dougherty (K−D) equation. This modification improved the predictive capabilities of the K−D equation. Therefore, to accurately predict slurry viscosity of any carbonaceous solid, the increased effective solid volume fraction predicted on the basis of its oxygen/carbon ratio should be used in the K−D equation to account for its surface chemistry. This modified model was validated using three concentrated carbonaceous solid−water slurries and was observed to accurately predict viscosity.

1. INTRODUCTION Coal−water slurries are highly concentrated suspensions of coal particles in water and used as gasifier feedstock. Carbonaceous solids, petcoke, and bitumen, which are byproducts of the oil industry, are also made into slurries and used for gasification.1,2 These slurries have high solids loading in the range of 60−75% (by weight).3 For easier handling and pumping of these highly loaded mixtures, slurry viscosity should be low. Higher viscosity of the slurries increases pumping energy requirement. Predicting viscosities of such slurries can be very useful for process control and design. Dependent upon the rank of the coal, surface properties of the coals vary. Low-rank coals have higher oxygen and moisture contents compared to high-rank coals, petcoke, and bitumen. Different carbonaceous solid−water slurries have widely varying viscosity for the same particle size distribution and same solids loading, owing to the differences in surface chemistry.4 Therefore, to explain the effect of surface chemistry on slurry viscosity and to incorporate surface chemistry for viscosity prediction, a thorough understanding of the solid−solid and solid−water interactions leading to different slurry viscosities is required. Viscosity of coal−water suspension is a complex function of the particle volume fraction φ, particle shape, particle size distribution, and interparticle interactions.5 On the basis of the solid volume fraction, a suspension may behave as a dilute, moderately concentrated, highly concentrated, or solid suspension.6 In the dilute suspensions, owing to a lower solid volume fraction, the interparticle distance is large compared to the range of interaction forces (hydrodynamic and surface forces). As the solid volume fraction increases, because of © 2015 American Chemical Society

smaller interparticle distances, interaction forces gain importance. Both hydrodynamic interaction and surface forces start playing dominant roles in determining the spatial structure of the system as well as its flow properties. For concentrated suspensions, the interparticle distance is of the order of the particle size, which allows the particles to diffuse, whereas for solid suspensions, the interparticle distance is smaller than the particle size. Several studies have been reported in the literature concerning the analysis of rheological behavior of suspensions of synthetic solids with controlled surface properties and shapes.7−9 Models developed in the past for predicting viscosities of suspensions are mainly semi-empirical equations combining apparent viscosity, solid volume fraction, and maximum packing fraction.10−13 Whereas maximum packing fraction takes into account the particle size distribution of the particles, the semi-empirical models fail to account for the surface chemistry of the solids. Therefore, the suite of semiempirical models, originally developed for spherical noninteracting spheres, are incapable of predicting viscosity of such complex slurries. Among these semi-empirical equations, the Krieger−Dougherty (K−D) equation was proven to be the most effective semi-empirical model.5,6,13,14 Dooher et al. developed a phenomenological model for viscosity prediction.15 Surface properties were taken into account but through statistical correlations. Their work only involved bituminous and sub-bituminous coal and did not include the entire range of Received: March 23, 2015 Revised: May 18, 2015 Published: May 18, 2015 3675

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Energy & Fuels carbonaceous solids. Moreover, the correlation developed by Dooher is proprietary. Usui proposed a thixotropic viscosity model, which can take into account the agglomerative nature of the hydrophobic carbonaceous solids but is not applicable for low-rank hydrophilic coal−water slurries, where slurry viscosity is affected because of adsorption or absorption of free water.16,17 Therefore, clearly, there is need for a viscosity model that can take into account surface chemistries of the entire range of carbonaceous solids, along with particle size distribution, to predict viscosity accurately. This study characterizes surface chemistry of five carbonaceous solids mainly by contact angle and ζ potential measurements. Surface free energy components and interparticle interaction energies are calculated using these measurements and established mathematical equations. These results provide the key to understanding the mechanism of interparticle interactions of these solid particles in water. On the basis of the understanding of the interparticle interaction mechanism, the semi-empirical K−D equation is modified to account for the surface chemistry of the carbonaceous solid. The modified equation is validated using three other carbonaceous solid−water slurry samples.

k=

(1 + cos θ )γ3 = 2( γ1LWγ3LW +

where H is the distance between particles and A131 is the effective Hamaker constant of the solids in the presence of a third medium. The Hamaker constants of the solid particles in vacuum were calculated using eq 3

A33 )2

γL (mJ/m2)

γLW (mJ/m2)

γ+ (mJ/m2)

γ− (mJ/m2)

water glycerol diiodomethane

72.80 64.00 50.80

21.80 34.00 50.80

25.50 4.92 0.00

25.50 57.40 0.00

−

γ1+ γ3− −

γ3LW )2 − 4( γ1+ γ1− + γ3+ γ1− )

⎛H − H⎞ ⎟ VH = πRλV H0 exp⎜ 0 ⎝ λ ⎠

(3)

γ3+ γ3− (8)

(9)

VH is the polar surface interaction energy between two spherical particles, V0H is the interface polar interaction energy constant, H is the distance between two particles, R is the radius of the particle, λ is the decay length (1 nm20) (this corresponds to the radius of gyration of the average size of water clusters having 4−5 water molecules per cluster, at room temperature), and H0 is the minimum equilibrium distance (0.157 nm20). The carbonaceous solid surfaces used in this work were characterized, and the interfacial forces were calculated. These results are reported and discussed in the Results and Discussion of the paper (section 4).

(4)

2.2. Electrostatic Interaction Energy. The electrostatic interaction energy between two spherical particles of radius R, in a dispersion media, is given by eq 5.19 Debye length (k−1) can be calculated using eq 6 VE = 2πεaRζ 2 ln[1 + exp( −kH )]

(7)

material

V H0 = −2( γ1LW −

where A11 is the Hamaker constant of the solid in vacuum and γLW 1 is the apolar component of surface tension. Calculations of γ1LW for the carbonaceous solids were performed on the basis of contact angle values and are explained in detail in section 2.3. The Hamaker constants (A131) of the solid particles, 1, in medium 3, can be calculated using eq 4. A131 = ( A11 −

γ1−γ3+ )

where θ is the contact angle of liquid on the solid surface, γ1 is the surface tension of the carbonaceous solid, and γ3 is the surface tension of the liquids. Surface energy parameters were then used in eq 8 to calculate the interface polar interaction energy constant (V0H), which, in turn, was used in eq 9 to calculate hydrophobic/hydrophilic interaction energy

(2)

A11 = 1.86 (± 0.0065) × 10−21γ1LW

γ1+γ3− +

Table 1. Surface Energy Components of the Three Chemicals (Liquids)

The net interactive force (VT) is repulsive for VT > 0 and attractive for VT < 0. 2.1. van der Waals Interaction Energy. van der Waals attractive energy between two identical spherical particles, 1, of radius R in a medium 3 is given by eq 218

A131 R 12H

(6)

where εa is the absolute dielectric constant of the dispersion media, ζ is the surface charge approximated as the ζ potential, k−1 is the debye length, H is the interparticle distance, e is the electric charge (1.602 × 10−19 C), NA is the Avogadro constant, I is the ionic strength, K is the Boltzmann constant, and T is the absolute temperature. 2.3. Hydrophobic/Hydrophilic Interaction Energy. Surface tension of a material, 1, has two components, apolar (nonpolar) and polar. The former is represented by the Lifshitz−van der Waals interaction parameter (γLW 1 ), and the latter includes Lewis acid (γ+1 ) and base (γ−1 ) parameters. For the carbonaceous solid particles, these parameters were determined using the Young−Dupre equation given by eq 7.18,19 To determine the three surface energy parameters (γLW 1 , γ+1 , and γ−1 ) for a particular carbonaceous solid, using a single eq 7, contact angles of water, glycerol, and diiodomethane on the carbonaceous solid surface were measured and eq 7 was simultaneously solved. The surface energy parameters of the liquids, obtained from published work, are given in Table 118

2. INTERACTION ENERGY CALCULATION Interaction energies between two macroscopic bodies suspended in a medium comprise van der Waals attractive energy (VW), electrical double-layer repulsive energy (VE), and hydrophobic/hydrophilic (VH) interaction energy, which can be both attractive and repulsive. The total interaction energy is given by eq 1.18 VT = VW + VE + VH (1)

VW = −

4e 2NAI εakT

3. EXPERIMENTAL SECTION 3.1. Materials. Experiments were carried out with Pust coal (lignite), Dietz coal (sub-bituminous), Illinois no. 6 coal (bituminous),

(5) 3676

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Energy & Fuels Orchard coal (anthracite), and petcoke suspensions in water. A laboratory-sized ball mill was used to grind these solids. The particles were then screened and separated into the following size ranges: −250 + 212, −212 + 180, −180 + 150, −150 + 125, −125 + 106, −106 + 90, −90 + 53, −53 + 44, −44 + 20, and −20 μm. Particle size distribution, as shown in Figure 1a was used for all of the experiments, except the

samples used for model validation are shown in Figure 1b. Proximate and ultimate analyses of all of the samples are presented in Table 2. 3.2. Preparation of the Carbonaceous Solid−Water Slurry. The calculated amount of carbonaceous solids (calculated on the basis of the targeted slurry concentration) was added to the weighed amount of distilled water. The mixture was then stirred by a propeller agitator for 10 min, and viscosity was measured.21 Solids loadings of carbonaceous solid−water slurries were calculated and reported on an as-received basis. 3.3. Viscosity. Viscosities were measured using a Bohlin 88 viscometer (a product of Malvern Instruments, Ltd., U.K.), which comprises a constant speed motor with a torque detecting system. For all of the experiments conducted in this work, measuring system no. 8 (i.e., the system designated as “wide gap” with the inner cylinder diameter of 25 mm and the outer cylinder diameter of 33 mm) was used. This measuring system was designed to be used for the range of viscosity values from 0.01 to 5.00 Pa s. The shear rate used for all of the measurements was 100 s−1 in keeping with the shear rate used in industry. All viscosity measurements were performed in the temperature range of 23−26 °C (ambient temperature). 3.4. Contact Angle. Contact angles were measured using a goniometer (ramé-hart model 295). Coal particles were made into pellets with a pressure of 2000 psi (without using resin).22 Contact angles of water, glycerol, and diiodomethane on the carbonaceous solid surfaces were measured using the sessile drop technique. Each experiment was repeated 6 times, and the average was used for calculations. 3.5. ζ Potential. ζ potential of the carbonaceous solid samples was measured using Malvern Zetasizer ZS, which uses an electrophoretic light scattering technique. Each experiment was repeated 6 times, and the average was used for calculations. 3.6. Inductively Coupled Plasma−Atomic Emission Spectrometry (ICP−AES). PerkinElmer Optima 5300DV ICP−AES was used to detect and measure the concentration of cations in the carbonaceous solid−water slurries. 3.7. Ionic Chromatography. A Thermo Scientific Dionex ion chromatography (IC) system was used for detecting and measuring the concentration of the anions in the carbonaceous solid−water slurries. 3.8. Uncertainty Analysis. To measure repeatability, each experiment was repeated 5 times. Important factors that might lead to errors in viscosity measurement include variation in the particle shape, sieve analysis limitations, weighing balance tolerance, and measurement error. Using a standard manufacturer-recommended procedure, the viscometer was calibrated prior to each experiment. Relative standard deviations (representing combined error as a result of all of these factors) of around 10% in lower viscosity values and around 5% in higher viscosity values were observed. The slight variation in the relative standard deviation from lower to higher viscosity measurements can be mainly attributed to measurement errors caused as a result of wall slip conditions and agglomerate formation in concentrated suspensions.23

Figure 1. (a) Particle size distribution of the carbonaceous solid particles in their respective slurries. (b) Particle size distribution of the carbonaceous solid particles in their respective slurries in the model validation experiments.

experiments concerning model validation. Particle size distribution was maintained constant to highlight the effect of surface properties of the carbonaceous solids on slurry viscosity. The weighted mean size of 72 μm was used for all interaction energy calculations. Model validation was performed using petcoke, Pittsburgh no. 8 (bituminous coal), and Beulah (lignite coal) coal−water slurries. In model validation experiments, different particle size distributions and two different carbonaceous solid samples were used to observe the sensitivity of the model to different particle size distributions and different carbonaceous solids. Particle size distributions for the various

Table 2. Proximate and Ultimate Analysis Resultsa proximate analysis (wt %, as-received basis) petcoke Orchard coal Pittsburgh no. 8 coal Illinois no. 6 coal Dietz coal Pust coal Beulah coal

ultimate analysis (wt %, as-received basis)

M

VM

A

FC

C

H

N

S

O

0.32 1.59 0.31 3.31 8.46 11.12 18.88

10.96 9.27 35.70 38.46 41.69 41.17 39.19

0.17 10.79 9.80 12.53 3.87 8.55 5.19

88.55 78.35 54.19 45.70 45.99 39.16 36.74

89.08 80.80 76.68 67.50 70.70 60.77 54.94

3.64 3.52 4.93 4.75 4.91 4.08 3.87

1.47 1.91 1.39 1.45 0.58 1.28 1.32

5.43 1.14 1.46 5.72 0.39 0.60 0.60

0.20 0.24 5.42 5.67 11.8 13.60 15.20

M, VM, A, and FC stand for moisture, volatile matter, ash, and fixed carbon, respectively, and C, H, N, S, and O denote carbon, hydrogen, nitrogen, total sulfur, and oxygen, respectively. a

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Energy & Fuels Table 3. Hamaker Constants of Carbonaceous Solids carbonaceous solids

γLW 1

A33 (×1020, J)

A11 (×1020, J)

A131 (×1020, J)

petcoke Orchard coal Illinois no. 6 coal Dietz coal Pust coal

43.38 47.73 49.47 50.80 50.80

4.84 4.84 4.84 4.84 4.84

8.07 8.88 9.20 9.45 9.45

4.78 6.89 7.81 8.55 8.55

Table 4. Anionic and Cationic Concentrations of the Carbonaceous Solid−Water Slurries petcoke Orchard coal Illinois no. 6 coal Dietz coal Pust coal

Ca (ppm)

Mg (ppm)

Na (ppm)

K (ppm)

Si (ppm)

Cl− (ppm)

SO42− (ppm)

NO3− (ppm)

ionic strength (mol/m3)

0.87 5.22 9.76 2.53 4.01

0.31 0.6 0.81 1.70 2.50

0.33 0.19 2.56 2.32 2.23

0.08 0.10 0.22 0.20 0.20

0.00 0.04 0.23 0.13 0.31

1.16 0.50 5.54 1.97 1.74

0.37 1.62 8.54 2.00 2.32

0.39 0.20 0.17 0.00 0.00

0.21 0.72 1.75 0.79 1.08

4. RESULTS AND DISCUSSION 4.1. Interaction Energy Calculations and Analyses. 4.1.1. van der Waals Interaction Energy Calculation. Hamaker constants for the five carbonaceous solids in vacuum (A11) and water (A131) were calculated using eqs 3 and 4, respectively, and are reported in Table 3. The apolar component of surface tensions (γLW i ) was determined using contact angle measurements of water, glycerol, and diiodomethane on the carbonaceous solid surfaces. The contact angle values are given in Table 6. The Hamaker constant of water (A33) was taken as 4.84 × 10−20 J. It can be observed from the table that the Hamaker constants of all of the carbonaceous solids are almost identical. The values of the Hamaker constant of carbonaceous solids agree well with published work.24 The Hamaker constants of the carbonaceous solids in water (A131) were used in eq 2 to calculate van der Waals interaction energies. 4.1.2. Electrostatic Interaction Energy Calculation. Ionic strengths were calculated on the basis of measured ionic concentrations. Ionic concentrations and ionic strengths of carbonaceous solid−water slurries are given in Table 4. ζ potentials of the carbonaceous solids and their Debye lengths in water (calculated using eq 6) are reported in Table 5.

Table 6. Contact Angles of Liquids on the Surfaces of Carbonaceous Solids water petcoke Orchard coal Illinois no. 6 coal Dietz coal Pust coal

ζ potential (mV)

Debye length (nm)

−31 −28 −36 −39 −43

8.47 4.57 2.93 4.37 3.73

± ± ± ± ±

glycerol 1.9 2.0 1.9 2.8 6.6

98.4 ± 78.3 ± 62.2 ± 22 ± 0.0

2.2 3.5 3.1 3.5

diiodomethane 32.6 ± 4.5 20.2 ± 5.2 13.1 ± 5.6 0.0 0.0

Table 7. Surface Energy Parameters material

γLW (mJ/m2)

γ+ (mJ/m2)

γ− (mJ/m2)

petcoke Orchard coal Illinois no. 6 coal Dietz coal Pust coal

43.38 47.73 49.47 50.80 50.80

0.82 0.06 0.71 2.03 1.63

3.91 3.26 8.40 20.45 41.44

It can be observed from Table 5 that, as already pointed out by Good, the apolar component and the Lewis acid component of surface free energy remain almost constant for all of the carbonaceous solids, whereas the Lewis base component of surface free energy increases with an increase in the oxygen content of the carbonaceous solid, such as in the case of lowrank Dietz coal and Pust coal.20 A higher Lewis base component of surface energy indicates greater tendency of the carbonaceous solids to form hydrogen bonds with the polar medium (water in this case). Therefore, it can be said that, in this case, hydration layers around Pust coal particles would be thicker than those hydration layers around other carbonaceous solids. Hydration layers would also exist around Dietz and Illinois no. 6 coal particles. Petcoke and anthracite particles would have a very thin layer of water surrounding them, with the water directly adjacent to the particle surface having an interrupted hydrogen bond network. Components of surface free energy were used in eq 5 to determine interparticle hydrophobic/hydrophilic interaction energies. 4.2. Comparison of Interparticle Interaction Energies. Panels a−e of Figure 2 compare interaction energies of the five carbonaceous solid−water slurries. It is apparent from panels a−e of Figure 2 that hydrophobic/ hydrophilic interaction energy (polar interaction energy) is 2−3 orders of magnitude greater than van der Waals or electrostatic interaction energy for an interparticle distance less than 4 nm, in all of the cases. Therefore, it can be said that polar

Table 5. ζ Potential and Debye Length of the Carbonaceous Solids in Suspension with Water petcoke Orchard coal Illinois no. 6 coal Dietz coal Pust coal

124.1 109.4 72.8 42.1 14.1

As observed from Table 5, ζ potentials increase slightly for low-rank coals, owing to the greater oxygen functional group content and higher mineral matter content.25 Ionic strength and Debye length do not vary much for the different carbonaceous solid−water slurry samples. The ζ potential and Debye lengths were used in eq 5 to determine electrostatic interaction energies. 4.1.3. Hydrophobic/Hydrophilic Interaction Energy Calculation. The contact angles and surface energy parameters of the carbonaceous solids are listed in Tables 6 and 7, respectively. 3678

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the polar interaction energies decay approximately at a distance of 4 nm is in agreement with existing work.26 Interparticle polar interaction energies are hydrophobic for petcoke, Orchard coal, Illinois no. 6 coal, and Dietz coal, and its magnitude decreases from petcoke to Dietz coal. Even though Illinois no. 6 coal and Dietz coal have a higher Lewis base component of surface free energy compared to petcoke and Orchard coal, the interparticle interaction is still hydrophobic, implying that these carbonaceous solids are weakly hydrophobic with hydrophilic characteristics. Interparticle repulsive hydrophilic interaction exists in the case of the Pust coal−water slurry. To summarize, (1) high contact angles (>100°) of water droplets on petcoke and Orchard coal surfaces imply that these carbonaceous solids are highly hydrophobic, and water can only coalesce on the surface of these solids. A negligible oxygen content of these solids (as evident from Table 2) contributes to their apolar nature. The hydrophobic interparticle interaction energy causes them to form aggregation networks in water, entrapping coalescing water droplets in the voids.27 (2) Water contact angles on Illinois no. 6 coal and Dietz coal are 73° and 42°, respectively. These indicate that an energetically stable layer of water can exist around these particles. Therefore, these particles in suspension with water would have hydration layers.18 The oxygen functional groups present on the surfaces would form hydrogen bonds with the neighboring water molecules. The hydration layer would be thicker in the case of Dietz coal compared to Illinois no. 6 coal because of the higher basic component of surface free energy. These coal particles would also form aggregation networks because of the interparticle hydrophobic interaction energy. (3) In the case of Pust coal, a very high basic component of surface free energy contributes to the high wettability of this carbonaceous solid. This is also evident from its low water contact angle. Therefore, Pust coal in water would form thick hydration layers. Moreover, because the interparticle interaction energy is predominantly hydrophilic repulsive in this case, these particles would not form aggregation networks or flocs in suspension. (4) It can be observed that, in all of these cases discussed above, free water is lost from the bulk of the slurry, either in the form of coalescing droplets entrapped in the aggregation networks of the hydrophobic petcoke and Orchard coal or as hydration layers in the other coals. The volume of loss of free water is different for different carbonaceous solids. It equals the volume of the entrapped water or the volume of the hydration layer and is, therefore, a function of the surface chemistry of the carbonaceous solid. Panels a−c of Figure 3 provide schematics of the proposed interparticle interactions of the different carbonaceous solid particles in water. Because petcoke and Orchard coal demonstrate similar behavior in water, these are represented by a single schematic (Figure 3a). Illinois no. 6 coal and Dietz coal also having a similar behavior in water are represented by Figure 3b. 4.3. Viscosity Prediction of Carbonaceous Solid− Water Slurries. As discussed in the previous section, interparticle interactions of the carbonaceous solids led to the loss of free water from the bulk of the slurry, which, in turn, resulted in the increase in the effective solid volume fraction.28 This loss of water depends upon the type of carbonaceous solid and, hence, is characteristic of the carbonaceous solid. To determine the change in the solid volume fraction, viscosities of the five carbonaceous solid−water slurries were

Figure 2. Variation of the interparticle interaction energy with interparticle distance.

interaction energies play the key role in determining slurry rheology of highly concentrated slurries, where particles are closely packed with very small interparticle distance. To control the viscosity, these interaction energies should be modified accordingly, using appropriate additives. The observation that 3679

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entrapped water than to release the stable thicker layer of water. This explains why VFCF increases with decreasing hydrophobicity and increasing hydrophilicity. VFCF of a carbonaceous solid can be calculated as a function of the polar interaction energy. Polar interaction energies, in turn, primarily depend upon the oxygen and carbon contents of the solid.28 It varies with the oxygen/carbon ratio, as shown in Figure 5. As observed from Figure 5, polar interaction energies vary linearly with oxygen/carbon ratios of the carbonaceous solid. Therefore, VFCF can be directly calculated as a function of the more fundamental oxygen/carbon ratio of the carbonaceous solid. This would also simplify the calculation of VFCF. Variation of the mean VFCFs of the carbonaceous solids in water with the oxygen/carbon ratio has been plotted in Figure 6. As evident from Figure 6, VFCF of a carbonaceous solid correlates very well with the oxygen/carbon ratio of the solid. Therefore, VFCF of a carbonaceous solid can be calculated using eq 12, and viscosity of carbonaceous solid−water slurries can be determined using the modified K−D equation given by eq 13

Figure 3. Schematics of interparticle interactions of (a) petcoke and Orchard coal, (b) Illinois no. 6 coal and Dietz coal, and (c) Pust coal in water.

VFCF = 2.04

measured as a function of the initial solid volume fraction. On the basis of the particle size distribution (which was kept constant for all five carbonaceous solid samples), the maximum volume fraction (φm) was calculated using the Veytsman model and was 0.74 in all cases. The measured viscosities were used in the K−D equation to determine the final solid volume fraction and then the volume fraction correction factor (VFCF) in the following manner: −[η]ϕm ⎛ ϕf ⎞ ⎟⎟ measured viscosity = ηr = ⎜⎜1 − ϕm ⎠ ⎝

VFCF =

(12)

−[η]ϕm O ⎡ 2.04 C + 1.29 ϕ ⎤⎥ ⎢ ηr = ⎢1 − ⎥ ϕm ⎣ ⎦

(

)

(13)

where O is the oxygen content of the carbonaceous solid on a dry basis, C is the carbon content of the carbonaceous solid on a dry basis, φ is the initial solids loading, and φm is the maximum volume fraction/maximum solids loading. Other terms in the equation have already been defined in the previous sections. 4.4. Validation of the Modified Model. The modified model was validated using petcoke, Pittsburgh no. 8 coal (bituminous coal), and Beulah coal (lignite coal) samples. Maximum packing efficiencies of these samples were determined on the basis of their particle size distributions using Veytsman’s model.29 Oxygen/carbon ratios as obtained from ultimate analyses of the samples were used in eq 2 to obtain the VFCFs of the corresponding carbonaceous solids in water. Maximum packing efficiencies (φm) and VFCFs, inputs to the modified K−D equation, are reported in Table 9. Experimentally measured viscosities of these slurries were then compared to predictions of both the K−D equation and the modified K−D equation, as shown in panels a−c of Figure 7. Viscosities of these concentrated slurries were measured and reported until the point where the slurry viscosity was infinite and could not be measured. It can be observed from the graphs that the modified K−D equation predictions match experimental results much more accurately than the original K−D equation, especially at higher initial solids loadings. Slight deviations of the predicted results from the experimental measurements toward higher volume loading can be attributed to a slight decrease in the VFCF value of a particular sample with the increase in the solid volume fraction (as discussed in section 4.4). The maximum deviation of the predicted result from the experimental measurement can be observed for Beulah coal at a solid volume fraction of 0.46. This is probably because low-rank coals, such as Beulah, have thicker hydration layers at medium solids loadings, and with a

(10)

ϕf ϕi

O + 1.29 C

(11)

where φf is the final solids loading (dry basis), determined using eq 10, and φi is the initial solids loading (dry basis), already known. Panels a−e of Figure 4 show the viscosity variation of the carbonaceous solids water slurry (CSWS) with initial solid volume fractions. The determined VFCFs are tabulated in Table 8. For each of these carbonaceous solid− water slurries, initial solids volume fractions were varied until a point until the slurry ceased to flow (i.e., point where the slurry had infinite viscosity). As observed from Table 8, the VFCF values of a particular carbonaceous solid vary slightly for different solid volume fractions (as indicated by the small standard deviation). Therefore, a mean VFCF was calculated for each of the carbonaceous solid. The small variation can be attributed to the fact that the increase in initial solid volume fraction leads to more and more crowding of the solid particles in the water, leaving less space for the entrapped water or the hydration layer. The VFCF increases with the increase in the oxygen/ carbon ratio. For a hydrophobic carbonaceous solid, the coalescing droplets of water entrapped in the aggregation network between particles are weak because of the small adhesion energy of water and the solid. The hydration layer thickness and stability of water on the surface of particles increases with the Lewis base component of free energy. At a particular shear rate, it is easier to release the unstable 3680

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Figure 4. Variation of viscosity with initial solids volume fraction for the (a) petcoke−water slurry, (b) Orchard coal−water slurry, (c) Illinois no. 6 coal−water slurry, (d) Dietz coal−water slurry, and (e) Pust coal−water slurry.

Table 8. VFCF Values of the Different Carbonaceous Solids carbonaceous solids water slurries initial solids volume fraction

petcoke

Orchard coal

Illinois no. 6 coal

Dietz coal

Pust coal

0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58

N/A N/A N/A N/A N/A N/A N/A N/A 1.32 1.31 1.27 1.24 1.28 .03

N/A N/A N/A N/A N/A N/A 1.36 1.35 1.33 1.3 1.27 infinite viscosity 1.31 .04

N/A N/A N/A N/A 1.54 1.52 1.47 1.42 infinite viscosity

N/A N/A 1.7 1.65 1.59 1.54 1.48 infinite viscosity

1.85 1.82 1.77 1.74 1.67 infinite viscosity

1.49 .053

1.59 .07

1.77 .07

mean standard deviation

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Figure 5. Variation of the polar interaction energy with the oxygen/ carbon ratio.

Figure 6. Variation of VFCF with the oxygen/carbon ratio.

Table 9. Input Parameters to the Modified K−D Equation petcoke Pittsburgh no. 8 coal Beulah coal

maximum packing efficiency

VFCF

0.78 0.76 0.86

1.28 1.43 1.86

Figure 7. Comparison of experimentally measured viscosities with model-predicted viscosities as a function of the initial solid volume fraction.

further increase in solids loading, hydration layers cannot increase proportionally because of excessive crowding of solids.

oxygen/carbon ratio of the carbonaceous solid because of the hydration layer being thicker and more stable for surfaces with a higher oxygen content. (5) VFCF when used with the K−D equation can predict viscosity accurately. The modified model was validated using petcoke−water slurry, Pittsburgh no. 8 coal−water slurry, and Beulah coal−water slurry. The modified model predictions were observed to match experimental results more closely compared to the original K−D equation predictions.

5. CONCLUSION Through this study, the following conclusions can be drawn: (1) The surface energy components of the carbonaceous solids determine its interparticle behavior and affinity toward water. A higher Lewis base component of surface free energy of a carbonaceous solid leads to a higher tendency of hydrogen bond formation with the surrounding water. (2) Interaction energy calculation performed in this study showed that hydrophobic/hydrophilic interaction energies are 2−3 orders of magnitude greater than the van der Waals interaction energies and the electrostatic interaction energies of the carbonaceous solids in water. These strong interaction energies decay at an interparticle distance of 4−5 nm. (3) On the basis of the surface chemistry, carbonaceous solids when in water either form aggregation networks and entrap water in those networks or adsorb/absorb water on their surface. This loss of water leads to an increase in the solid volume fraction of the slurry. The increase in the solid volume fraction given by VFCF was determined for five carbonaceous solids with varying oxygen/carbon ratio. (4) VFCF was found to increase with the

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AUTHOR INFORMATION

Corresponding Author

*Telephone: 814-865-0874. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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DOI: 10.1021/acs.energyfuels.5b00616 Energy Fuels 2015, 29, 3675−3683