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Model-Based Sensitivity Analysis and Experimental Investigation of Perlite Grain Expansion in a Vertical Electrical Furnace Panagiotis M. Angelopoulos, Dimitrios I. Gerogiorgis,* and Ioannis Paspaliaris Laboratory of Metallurgy, School of Mining and Metallurgical Engineering , National Technical University of Athens (NTUA), 9 Heroon Polytechneiou Street, , NTUA Zografou Campus GR 15780, Greece ABSTRACT: The new vertical electrical furnace which has been designed and operated at NTUA successfully produces expanded perlite of superior quality, unleashing its potential for high-performance thermal and acoustic insulation applications in the manufacturing and construction industries. A detailed sensitivity analysis has been performed on the basis of our dynamic model for perlite grain expansion, in order to quantitatively understand and systematically evaluate the effect and relative importance of feed quality and operating conditions on macroscopic (grain velocity and temperature evolution) and microscopic (steam bubble pressure, grain size) perlite particle state variables. Experimental campaign observations illustrate furnace efficiency and are in acceptable agreement with the model. Perlite feed quality (origin, chemical composition, effective water content, initial particle size distribution) is critical for adequate expansion and must be determined in advance of high-temperature processing. Process operating conditions (air feed flow rate and temperature, heating chamber wall temperature) are instrumental toward adequate expansion of a given perlite feed. Ambient air injection accomplishes sufficient expansion of the finer raw perlite fractions only, while preheated air injection achieves coarse fraction expansion but induces a risk of grain overheating and disintegration. Process efficiency increases dramatically when the furnace wall temperature is maintained within the 1100−1200 °C range.

1. INTRODUCTION The quest for high-performance thermal and acoustic insulation materials of low density and ultra-low toxicity which can be conveniently produced using local natural resources via economical and environmentally benign processes can spearhead sustained growth in the construction and manufacturing industries, enhance energy efficiency in new as well as old buildings, and enforce the principles of green engineering with evident economic incentives. Perlite is a naturally occurring volcanic siliceous rock which consists mainly of amorphous silica (70−76 wt % SiO2) and small amounts of other metal oxides (Al2O3, K2O, Na2O, Fe2O3), having the potential to expand between 4 and 20 times when heated beyond its softening point (700−1260 °C), due to the presence of 2−6% chemically bound water in its structure.1 During expansion, perlite acquires outstanding physical properties (low density, extremely low thermal conductivity, high sound reduction index) that render it exceptionally suitable for numerous production applications in various commodity industries.1−3 Conventionally expanded granular perlite is widely used in the construction and manufacturing industries (these uses of perlite account for more than 70% of global perlite consumption), in the chemical industry, and for certain agricultural applications. Novel perlite products which have been developed in the past few years (such as perlite mortars and plasterboards) successfully address new, demanding construction applications. Perlite is used in these novel materials in order to achieve a higher fire resistance, superior insulating properties, and easier handling due to its significantly lower density. These new applications have created unprecedented requirements for expanded perlite properties and quality specifications, especially with respect to particle size distribution and morphological characteristics of the perlite: very small perlite particles with high mechanical stability and well© 2013 American Chemical Society

controlled size distributions are essential for these novel demanding applications. For the most delicate applications, small single-bubble hollow spherical particles are required most, since they are mechanically resistant, easy to apply and excellent insulators.4 Evidently, expanded perlite particle characteristics strongly depend on furnace temperature spatiotemporal distribution, residence time, and heating rate: even the slightest variation of these crucial parameters has a dramatic impact on expanded product properties, as documented by previous experimental research studies.2 The precise control of process conditions is quintessential in producing expanded perlite for specific engineering applications. The currently prevalent perlite expansion process is the only globally reliable production method; although it has been in continuous use for more than 50 years, it remains a largely empirical industrial process, despite the rapid increase and proliferation of expanded perlite uses and applications over the last decades. Disadvantages identified with respect to both product quality as well as process economy render the review and improvement of the process necessary, in order to ensure that the perlite industry will remain competitive and successfully address the ever-increasing globalized new market demands. Traditionally, perlite grain expansion is accomplished in vertical or horizontal furnaces, where the significant amount of thermal energy required is provided by oil or gas open flame burners of adequate capacity (Figure 1). The conventional perlite expansion method is achieved by feeding presized ground Received: Revised: Accepted: Published: 17953

April 10, 2013 October 20, 2013 October 29, 2013 October 29, 2013 dx.doi.org/10.1021/ie401144r | Ind. Eng. Chem. Res. 2013, 52, 17953−17975

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic representation of the conventional expansion installation (left) and an industrial furnace of a perlite expansion plant (right).

perlite ore into a vertical furnace heated by direct gas flame at its bottom end, which thus creates upward forced air convection. Perlite ore particles are introduced directly into the hottest region of the expansion chamber, at or near the open flame, at a temperature of 1450 °C. After heating and expansion, particles have a much larger volume and lower density and are entrained upward by the hot ascending gas.5 The expansion process in conventional furnaces suffers the following serious disadvantages:3 • Perlite grain expansion occurs immediately and violently when raw perlite particles are introduced into the furnace, due to the extremely high heating rate and the enormous thermal energy which is rapidly and unevenly absorbed predominantly by the grains in the close flame vicinity. • The open flame and the hot off-gas stream adversely affect the macroscopic dynamic stability of the process system and hinder the efficient control of grain residence time and internal temperature evolution, both experimentally known as pivotal in determining expanded perlite quality. • Coarse perlite grain expansion is insufficient due to the gravitational effect: as their initial density is high, they tend to escape unexpanded from the furnace bottom because of the inability of the hot off-gas stream to hold them in suspension until their temperature is increased and their density is decreased. • Fine perlite grain expansion is insufficient due to upward entrainment upon entry: their premature acceleration due to momentum transfer from the hot off-gas stream results in short residence times, quick discharge, and incomplete expansion, due to a detrimental heat-momentum balance interplay.

• The hot off-gas stream absorbs a significant amount of thermal energy, thereby increasing the energy consumption of the process system and remarkably decreasing overall process efficiency. These conventional perlite expansion characteristics hamper product quality and process cost, which is appreciably increased due to a failure to achieve expansion of the finer and coarser fractions and the inevitably dramatic thermal energy losses suffered due to the high-enthalpy effluent gas stream. Limited fine fraction expansion induces more problems: as efficient cyclone separation of unexpanded fines from the hot effluent stream is problematic, bag filters for exhaust gas treatment become essential due to strict environmental regulations. Consequently, fixed and total process costs grow even higher. The foremost contribution of the present study is the construction of a novel vertical electrical furnace and the development of a more advantageous perlite expansion process which are demonstrated to achieve superior product quality, uniformity and reliability by means of multiparametric sensitivity analysis as well as experimental validation, for a wide range of feed quality and operating conditions. Numerous definite experimental findings indicate that the novel furnace and the proposed method positively improve perlite expansion efficiency as well as expanded perlite product properties. The main differences between these expansion processes merit a detailed discussion: in conventional expansion, perlite grains are introduced directly into the high-temperature region of the furnace, which often reaches 1450 °C and causes an extremely rapid increase of perlite grain temperature.5 Moreover, gas velocity exceeds 10 m·s−1 and particle residence time in the heating chamber is less than 3 s, while perlite grain expansion is completed within a second after the injection of raw perlite ore 17954

dx.doi.org/10.1021/ie401144r | Ind. Eng. Chem. Res. 2013, 52, 17953−17975


Article

Figure 2. Open view of the novel vertical electrical furnace for perlite expansion.

particles in the furnace.6 Particle residence time for finer fractions is extremely short and in most cases less than a second.7 In the present, milder expansion method, perlite grains are introduced into the top lower temperature furnace region and meet areas of gradually higher temperature while moving downward, until reaching the maximum temperature (less than 1200 °C) at the bottom of the furnace. The vertical geometry of the novel furnace design has a strong potential to significantly improve process operability and efficiency simultaneously, as its independently controlled resistance pairs allow for milder heating and rapid wall temperature profile adjustment to variable feed quality.

furnace body consists of the heating chamber, the temperature control system, and the insulating shell. The heating chamber is 2.7 m long, has a diameter of 0.134 m and has been fabricated using Kanthal APM FeCrAl alloy.8 The chamber is heated by 6 pairs of electrical resistances located along the tube, defining six heating zones (Figure 2). Each pair consists of two semicylindrical resistances which have been placed against each other around the chamber. Each resistance is made of Kanthal alloy8 and provides a total heating capacity of 24 kW (2 kW for each resistance). A small air gap has been established between the outer wall of the expansion chamber and the inner surface of the heat source in order to prevent displacements in the electrical heat elements and to ensure heat transfer by radiation from the heating elements to the expansion chamber walls. The chamber and resistances are encased in a cylindrical aluminosilicate insulation case which has a thickness of 0.165 m. Temperature control in each thermal zone is achieved by a ceramic sheathed K-type thermocouple (NiCr/NiAl) placed at the center of the zone (Figure 3). Air temperature at the inlet is measured by another thermocouple before the furnace head. The furnace preheater and zone temperature profiles are established ad hoc by specifying desirable set points on a MIMO controller. The novel vertical electrical furnace is illustrated in Figure 2; a detailed schematic of its anatomy is depicted in Figure 3. The most important expanded perlite quality characteristics are the loose bulk density (LBD), the compression strength (CS), and the inner and surface pore distributions (IPD, SPD). The key parameters affecting the value and variation of these quality metrics are the temperature and grain residence time distributions in the heating chamber: Even the slightest variation of these operating conditions has a dramatic impact on product

2. EXPERIMENTAL STUDY The new furnace for perlite expansion has been constructed in the Laboratory of Metallurgy, at the School of Mining and Metallurgical Engineering of the National Technical University of Athens (NTUA), Greece. The vertical electrical furnace consists of the air preheater, the perlite feeding system, the heating chamber, and the temperature control system. Atmospheric air is introduced into the system by means of an air compressor and the volumetric flow rate is measured and controlled by a dedicated system of flowmeters and valves. The air is injected at the top of the furnace through six (6) 0.009 m diameter holes located symmetrically around the perlite inlet hole and at a distance of 0.044 m from the center. The air stream can be heated by an air preheater which has a total heat capacity of 2 kW and can raise the air temperature at up to 450 °C. The perlite is fed at the desirable feeding rate at the top of the furnace through a 0.08 m diameter central hole by a rotary air-lock feeder. The rotary air-lock feeder prevents the flow of hot air updrafts but also that of the perlite particles out of the furnace. The 17955



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Figure 3. Schematic of the prototypic experimental installation of the vertical electric furnace for perlite expansion: (a) electrical furnace cross section, (b) simplified geometry and the six electrical heating zones, (c) furnace head layout.

quality and performance. Roulia et al. proposed the term optimal time to obtain the maximum expansion ratio at each temperature.2 They also concluded that (a) grain overheating (when

heating exceeds the optimal time) results in observable shrinking, (b) the final expansion ratio strongly depends on origin (chemical composition) and raw perlite granulometry. 17956



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Figure 4. SEM micrographs of expanded perlite grains processed in a conventional (left) and in the novel vertical electrical furnace (right).

A thorough experimental campaign has been conducted as part of this study in order to evaluate the performance properties of expanded perlite products which have been produced in different furnaces. Two identical raw perlite ore feed samples have been processed in a conventional furnace and in the new vertical electrical furnace, resulting in the same LBD value (80 kg·m−3) but demonstrating significant differences in grain shape, form and texture after expansion, confirmed by the scanning electronic microscope (SEM) micrographs presented in Figure 4. Conventionally expanded perlite grains have irregular shapes and an extended network of open pores which are evident on their cracked facets and adversely impact their end-use performance characteristics. Conversely, expanded perlite grains produced in a vertical electrical furnace have a smooth external surface, without open surface pores, and approximate the shape of hollow spheres: this is a very desirable and extremely advantageous morphology because of its low liquid absorptivity, high mechanical stability as well as superior thermal and acoustic insulation properties. Compression strength tests have also been conducted using two perlite samples which have been expanded from the same perlite ore feed, both conventionally and in the novel vertical electrical furnace. Compession strength measurements are based on calculating the pressure on the surface of the sample after the sample height has been reduced by 3 cm by a hydraulic ram, according to S&B industrial standards.9 Experimental results for both expanded perlite grades are depicted in Figure 5. The clear conclusion is that expanded perlite produced in the vertical electrical furnace has a significantly higher mechanical stress resistance and is therefore more suitable for highperformance products used in construction industry applications. The compression strength achieved is a function of the shape, cohesion and structure of each individual perlite grain; the results clearly indicate that there is a spectacular improvement in compression strength and mechanical stress performance between the two different expanded perlite grades, a fact which corroborates the conclusion that superior expanded perlite quality characteristics can be achieved by implementing and optimizing the transition from a conventional (open-flame) to a novel vertical electrical expansion furnace. Milder perlite grain heating is therefore deemed capable of slower, thorough evolution and completion of the expansion process in the vertical electrical furnace: this clearly results in improved surface

Figure 5. Compression strength (CS) of samples expanded in a conventional vs a vertical electrical expansion furnace as a function of sample loose bulk density (LBD).

and inner structure, higher mechanical strength, durability and longevity of expanded perlite products. Obviously, the conventional expansion process must be reconsidered. A more flexible process must be developed in order to acquire in-depth knowledge and identify the optimal conditions under which successful expansion occurs, but also in order to efficiently vary and control these operating conditions toward the production of new expanded perlite grades for demanding engineering applications. Cost reduction is also required: this can be achieved by reducing heat losses and increasing expansion efficiency for the entire range of feed composition, water content, and grain size. The new vertical electrical furnace for perlite expansion enhances operability by allowing precise control of air temperature as well as grain residence time in the heating chamber. The temperature of the furnace in isothermal or vertical gradient operation mode undoubtedly affects the LBD of expanded perlite products. Another significant parameter of the process system is the volumetric air flow rate. For example, raw perlite feed samples treated at 1075 °C without any air feed achieved an LBD of 60 kg· m−3, while identical raw perlite feed samples treated at the same temperature but with simultaneous air injection (with an air flow rate of 100 L·min−1) achieved a quite higher LBD (93 kg·m−3), indicating that air injection as well as volumetric air flow rate are 17957



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Air dynamic viscosity varies significantly as a function of temperature and is pivotal in calculating the particle Reynolds number (eq 23) and the Nusselt number (eq 29); here, it is calculated as a function of temperature along the heating chamber by a nonlinear algebraic equation:

two extremely important operating parameters in order to achieve high process efficiency and product quality. Experimental measurements which can provide crucial information for the conditions prevailing in the heating chamber of the new vertical electrical furnace are difficult to obtain. This is attributed to the limited accessibility, because of the inevitable presence of the insulating material and the extremely high temperature in the furnace heating chamber. As a result, accurate air velocity and temperature measurements are extremely arduous. Most commercial velocimetry sensors which can provide accurate air velocity measurements have a working temperature that does not exceed 400 °C, while thermocouplebased air temperature measurements suffer from the significant error induced by the hostile radiative environment of the heating chamber.3,10 The knowledge of all time-dependent particle state variables (temperature, velocity, size) can clarify the evolution of grain expansion within the vertical heating chamber; nevertheless, such experiments are extremely laborious and expensive.

⎛ T ⎞nref μair = μair,ref ⎜⎜ air ⎟⎟ ⎝ Tair,ref ⎠

The necessary reference parameters are taken as: μair,ref = 1.72 × 10−5 Pa·s, Tair,ref = 273 K and nref = 0.7. The constant-pressure air heat capacity is also a strong function of temperature and is another key thermophysical parameter required in calculating the air temperature via the air Prandtl number (eq 5) and the differential heat balance (eq 25). The air heat capacity along the heating chamber is calculated as a function of temperature by a polynomial algebraic equation:11 CP ,air = αCP ,1Tair 3 + αCP ,2Tair 2 + αCP ,3Tair + αCP ,4

3. MATERIAL PROPERTIES 3.1. Air Thermophysical Properties. The calculation of the temperature of the air which is in contact with the particle is of great importance toward the accurate study of the convective heat transfer mechanism. An energy balance is applied for the air in the chamber and the inner surface of the chamber walls. The increase of air temperature affects all air thermophysical and transport properties (density, dynamic viscosity, thermal conductivity, heat capacity). Air can be injected into the heating chamber at a temperature of 25 °C and can be heated up to 1200 °C; thus, air property variations are expected to be dramatic, and their incorrect estimation induces significant error in air and perlite energy balances and heating chamber process modeling. This section presents all algebraic equations which are explicitly included in the dynamic model to account for temperatureinduced air property variations along the heating chamber. The air density variation directly affects the volumetric air flow rate air along the vertical heating chamber, inducing an increase of superficial air velocity; moreover, it affects the forces (buoyancy and drag) acting on the perlite particle as well as the convective heat transfer rate to the particle. In the present mathematical model, air density is considered implicitly, and its variation along the vertical heating chamber is calculated by the ideal gas law constitutive equation: P ρair = R gTair

(2)

(3)

Air thermal conductivity is a key transport parameter required in calculating the air heat transfer coefficient and the Prandtl number; here, it is calculated as a function of temperature by a similar polynomial algebraic equation:11 kair = αk ,1Tair 3 + αk ,2Tair 2 + αk ,3Tair + αk ,4

(4)

The polynomial equation coefficients for both the air heat capacity and air thermal conductivity correlations via eqs 3 and 4 are presented in Table 1.11 Table 1. Coefficients for the Calculation of Air Heat Capacity (eq 3) and Air Thermal Conductivity (eq 4) as Explicit Polynomial Functions of Temperature i

αCp,i

αk,i

1 2 3 4

−8.01440 × 10−8 2.10788 × 10−4 2.06329 × 10−2 9.83672 × 102

1.5207 × 10−11 −4.8574 × 10−8 1.0184 × 10−4 -3.9333 × 10−4 ̀

The air Prandtl number is thus calculated by definition, using all foregoing thermophysical properties: Prair =

CP ,airμair kair

(5)

3.2. Perlite Melt Thermophysical Properties. 3.2.1. Perlite Melt Chemical Composition. Perlite melt chemical composition largely coincides with the raw material perlite ore composition and has a pivotal role in the entire expansion process. Perlites originating from different mines with even the slightest measurable compositional differences, albeit processed and expanded under identical operating conditions, yield products with remarkably varying quality characteristics. Perlite expansion experiments in our vertical electrical furnace have shown that perlite samples having the same grain size distribution (GSD) but originating from the two different, Trachilas (TR) and Tsigrado (CH), mines of the island of Milos in Greece expand to different final expansion ratios and yield materials with different LBD, when treated under identical process operating conditions (identical air flow field and temperature distribution in the heating chamber). Table 2 summarizes our experimental observations for both sample origins in a variety of process operating conditions which closely

(1)

Even at the extreme case of the maximum air feed flow rate (150 L·min−1), the air velocity in the heating chamber does not exceed 1 m·s−1.3 The effect of the discrete phase (perlite particles) on the continuous phase (air) can be considered negligible, because the solid volume fraction in the vertical heating chamber is 0.46% even at the maximum perlite feed flow rate (0.004 kg·s−1). Klipfel et al. have made the same assumption by considering a very dilute gas−solid particle flow.6 Moreover, the surface area of the vertical electrical furnace open bottom end is 140 cm2, 2 orders of magnitude larger than the total surface area of all 6 air inlet holes (5.72 cm2); thus, it can be assumed that the gas phase flows unhindered toward the exit of the furnace. Accordingly, one can plausibly assume that the air pressure in the entire vertical heating chamber remains atmospheric (P = 1 atm) with no appreciable variation. 17958



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Table 2. Comparison of the LBD of Expanded Perlite Samples Originating from Trachilas (TR) and Tsigrado (CH) Mines and Processed under Identical Furnace Operating Conditions operating conditions heating zone temperatures (air volumetric flow rate) −1

950/1000/1050/1100/1150/1200 °C (Qair,in = 0 L·min ) 700/800/900/1000/1100/1200 °C (Qair,in = 15 L·min−1) 700/800/900/1000/1100/1200 °C (Qair,in = 100 L·min−1)

Table 3. Chemical Composition of Perlitic Ore Samples Trachilas (TR)

Tsigrado (CH)

SiO2 Al2O3 K2O Na2O Fe2O3 CaO MgO TiO2 lost on ignition (LOI) total

73.02 12.71 5.39 3.43 0.91 0.84 0.30 0.08 3.32 100.00

72.51 13.73 3.67 3.98 1.28 1.39 0.37 0.15 2.92 100.00

loose bulk density (LBD) (kg·m−3)

TR CH TR CH TR CH

57.3 75 70 98.5 87 146

ization and expansion, Shackley focused on the study of residual water in commercially expanded perlite, analyzing the amount of water contained in expanded perlite particles.14 Conducting loss on ignition (LOI) tests on expanded perlite samples, he calculated that only a percentage between 20 and 60% of the water initially contained in unexpanded perlite remains in the perlite structure after the completion of the expansion process. Consequently, it can be concluded that only part of the water initially contained in the perlite ore crystal structure participates in the expansion process by recombining, evaporating, and forming steam departing the solid phase. The presence of residual water in expanded perlite grains has been confirmed via LOI tests we have conducted on both raw and expanded TR and CH perlite samples, the latter expanded to the same LBD (85 kg·m−3): these LOI test results for expanded TR and CH samples are compared in Figure 6.

correspond to widely known industrial operation standards for given technical specifications. The chemical analysis of perlite samples has been conducted by means of a XEPOS energy dispersive X-ray fluoresence (EDXRF) instrument (SPECTRO A.I. GmbH). The samples have been dried (at 105 °C), milled, and 32 mm-diameter pellets have been formed by pressing 4 g of perlite sample and 1 g of wax powder (Fluxana, HoechstWax). The Al2O3 content has been determined by dissolving 0.2 g of the samples in a mixture of acids (HF−HClO4−HNO3−HCl) and subsequently measuring the concentration in a Perkin-Elmer 2100 atomic absorption spectrometry (AAS) instrument. Oxide concentration results for all ore samples are presented in Table 3.

perlitic ore oxides

sample origin

3.2.2. Perlite Water Content. Perlite expansion results in a final particle volume which is between 4 and 20 times larger than the original volume of the unexpanded material, due to the presence of 2−6% chemically bound water in its structure. The expansion happens as soon as the solid feed is heated at a temperature which is close to its softening point, in the range of 700−1260 °C.1 During the expansion and while temperature increases, the perlite grain starts softening superficially. At the pyroclastic stage, the water trapped inside the grain starts to evaporate and pushes its way out, resulting in the gradual expansion of the grain. Water plays the most important role in the expansion process not only by expanding the grain during evaporation but also by reducing the viscosity of the softened grain.12 The types of water contained in raw perlite have been the subject of several previous studies; researchers classify these water types depending on the temperature release profile as well as on water chemical form and bonding.2,7,13,14 King et al. conducted the first experimental study to establish how much of the water contained in raw perlite is responsible for its potential to expand on heating.15 Their conclusions are that (a) perlite water above 1.2% is loosely bound and therefore evaporates very quickly, (b) only the water content below 1.2% (perhaps considerably so) is effective during perlite heating and expansion. During his more recent research on perlite character-

Figure 6. Expanded perlite water portions as percentages of original water content.

Evidently, only about half of the original perlite water content evaporates and is removed from the grain during the expansion process. For the purpose of our mathematical modeling study, the water contained in the perlitic matrix is classified in two: the portion of the water whose evaporation induces perlite expansion (ef fective water) and the portion of water which remains dissolved in the perlitic matrix and is not affected by the expansion process (residual water). The effective water is considered entirely concentrated in the initial bubble nucleus and expands continuously, exerting pressure on the bubble-melt interface due to the increasing perlite grain temperature: in fact, the 17959



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Table 4. Coefficients for Calculation of VFT Parameters X and Y (J = −4.55 ± 0.21a) from Melt Compositions Expressed as %mol Oxides coefficient symbol

oxides

values

coefficient symbol

oxides

values

b1 b2 b3 b4 b5 b6 b7 b11 b12 b13

SiO2 + TiO2 Al2O3 FeO(T) + MnO+P2O5 MgO CaO Na2O + Vb V + ln(1 + H2O) (SiO2 + TiO2)*(FM) (SiO2+TA+P2O5)*(NK+H2O) (Al2O3)*(NK)

159.6 (7) −173.3 (22) 72.1 (14) 75.7 (13) −39.0 (9) −84.1 (13) 141.5 (19) −2.43 (0.3) −0.91 (0.3) 17.6 (1.8)

c1 c2 c3 c4 c5 c6 c11

SiO2 TAc FMd CaO NKe ln(1+V) (Al2O3+FM +CaO-P2O5)*(NK+V)

2.75 (0.4) 15.7 (1.6) 8.3 (0.5) 10.2 (0.7) −12.3 (1.3) −99.5 (4) 0.30 (0.04)

a Numbers in brackets indicate 95% confidence limits on values of model coefficients. bSum of H2O + F2O−1. cSum of TiO2 + Al2O3. dSum of FeO(T) + MnO + MgO. eSum of Na2O + K2O.

effective water portion evaporates, thereby gradually expanding the softened inorganic material. The residual water is the portion of water which remains bound within the expanded grains and does not participate in the expansion phenomenon, but it is nevertheless released during the LOI tests performed on expanded perlite samples. Thus, it must be considered as a separate component in the perlite grain chemical composition and explicitly included in the dynamic expansion model. The 40% of the sample water content is considered as residual water and has been taken into account in perlitic melt thermophysical and transport property calculation, while the remainder (60%) is considered as effective water and has been taken into account in steam bubble growth which directly affects perlite expansion. 3.2.3. Melt Density. The density value of the unexpanded perlite particles has been measured in our laboratory by means of a volumetric cylinder and, after subtracting the empty space between the spherical grains occupied by the air, has been found equal to 2290 kg·m−3. Zähringer et al. assumed a constant perlite melt density value of 2350 kg·m−3 in their study,4 while Murase and McBirney observed that the density of obsidian melt changes very slightly between 800 and 1250 °C and is about 2200 kg· m−3.16 Kucuk developed a model for the glassy melt density calculation at 1400 °C while researching the structure and physicochemical properties of glasses and glass melts.17 By applying this model for the melt density estimation of both TR and CH samples at 1400 °C, similar values have been derived (2.294 and 2.322 kg·m−3, respectively): a constant melt density of 2300 kg·m−3 has thus been assumed in this study. 3.2.4. Melt Viscosity. Perlite expansion evolution is highly affected by molten grain shell viscosity, which varies significantly during the process and is a strong function of temperature. Extensive, uniform grain softening is a prerequisite for grain expansion and the evolution of the grain viscosity in terms of temperature is of high importance for accurate estimation of expansion evolution. Giordano et al. have investigated the effect of melt temperature as well as melt chemical composition on magmatic liquid viscosity, and developed a multiparametric algebraic model which calculates melt viscosity as a function of both chemical composition and absolute temperature, based on more than 1770 viscosity measurements on multicomponent anhydrous as well as volatile-rich silicate melts.18 The nonArrhenius temperature dependence of viscosity is accounted for by the Vogel−Fulcher−Tammann (VFT) equation, proposed by Vogel19 and Fulcher,20 according to Giordano et al.:18

log μ = J +

X Tm − Y

(6)

Here, J, X, and Y are adjustable parameters which are defined as the pre-exponential factor, the pseudoactivation energy, and the VFT temperature, respectively. The parameter J is the value of log μ (Pa·s) at infinite T, representing the high-temperature silicate melt viscosity limit: it is set at J = −4.55. Compositional effects are ascribed to parameters X and Y by assuming that both parameters can be expressed as a linear ensemble of combinations of oxide components and a subordinate number of multiplicative oxide cross-terms:18 7

X=

3

∑ (biMi) + ∑ [b1j(M11j M 21j)] i=1

j=1

(7)

6

Y=

∑ (ciNi) + [c11(N111N 211)] i=1

(8)

Parameters M and N refer to individual or summed %mol oxide concentrations, as per the corresponding oxides columns of Table 4. The 17 prescribed coefficients (bi, b1j, ci, c11) of Table 4 are thus sufficient for computing X and Y values of any given melt composition, via eqs 7 and 8.18 Considering a typical perlitic chemical composition, melt viscosity decreases by about six (6) orders of magnitude, within a limited temperature range (700−1200 °C), according to Giordano model results presented in Figure 7. The residual

Figure 7. Melt viscosity variation as a function of temperature for two different melt chemical compositions (TR and CH) and four different water content values (0.5, 1, 2, 3%) as calculated according to a literature model (Giordano et al., 2008). 17960



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with respect to temperature is described by the following linear algebraic equation:4

water content of the melt does not affect perlite expansion but influences molten grain shell viscosity, which is expected to decrease with increasing residual water content. For perlite, each percentage unit (1%) increase in residual water content generally induces a molten grain shell viscosity decrease of 1 order of magnitude.4,12,21 This approximate rule of thumb reported in the literature has also been confirmed by the melt viscosity model of Giordano et al.,18 which has been exclusively implemented in this dynamic model of the novel perlite expansion process. Table 5 presents the value of J, X, and Y constants for TR and CH samples, for the entire water content range of interest (0.5, 1, 2, 3%).

σ = 1.971·10−4Tm + 0.09317

3.2.6. Particle Heat Capacity. Particle heat capacity is of great importance in the dynamic model, due to its impact on particle temperature evolution. King et al. have proposed a nonlinear equation for anhydrous perlite heat capacity estimation as a function of temperature; this model is suitable for TR and CH ores:15 CP(0%H2O) = 41.868· (24.25 + 4.66· 10−3·T − 6.62·105·T −2)

Table 5. Numerical Values of J, X, and Y Constants Calculated by eqs 7 and 8 for Two Different (TR and CH) Ore Samples and the Entire Range of Perlitic Water Content perlitic ore origin

perlitic meltwater content (% wt)

J

X

Y

TR

0.5 1 2 3 0.5 1 2 3

−4.55 −4.55 −4.55 −4.55 −4.55 −4.55 −4.55 −4.55

11563.5 11383.4 11004.1 10642.5 11251.8 11078.4 10711.7 10361.7

202.1 153.2 97.0 61.9 229.4 180.8 125.1 90.3

CH

CP,H2O = 0.6417·T + 1646.9

CP ,p = wH2O,eff ·CP ,H2O + (1 − wH2O,eff ) ·CP ,(0%H2O)

(16)

4. MATHEMATICAL MODELING The mathematical modeling of perlite expansion processes has been the subject of several publications. Papanastassiou presented a simplified mathematical analysis of perlite expansion in a conventional vertical industrial furnace and studied theoretically perlite grain kinematics and energetics in the furnace heating chamber under the assumption of constant grain density.5 Klipfel et al. developed a computational code in order to simultaneously model combustion, nonisothermal gas flow, and perlite particle expansion in a conventional vertical expansion furnace.6 More recently, Zähringer et al. published a numerical study of perlite expansion4 using a model of Proussevitch et al. for simulation of magmatic foams during volcanic eruption.22 Therein, expansion is approximated by assuming diffusive steam bubble growth within a softened perlitic melt shell while both unexpanded and expanded perlite physical properties are calculated by detailed temperature-dependent models. Additionally, perlite particle expansion in a conventional furnace has been simulated under the assumption of a prescribed particle temperature evolution profile. In a recent publication, a Computational Fluid Dynamics (CFD) model has been employed to investigate air velocity and temperature profiles in the vertical furnace heating chamber as a function of key operating conditions (air feed flow rate, furnace wall temperature).3 The thorough investigation of perlite expansion in the vertical electrical furnace requires precise knowledge of heating chamber and particle state variables, a quest hampered by the considerable difficulties during experimental process investigation. Therefore, dynamic mathematical modeling of the perlite expansion process is a promising approach. The dynamic model for perlite expansion in the novel electrical furnace aims to provide detailed quantitative information about the thermal behavior of the system by (a) simulating the microscopic expansion of perlite grains as well as (b) studying the influence of all key operating parameters and geometric characteristics of the furnace heating

(9)

The Y constant for TR samples in terms of melt water content is calculated by a quadratic equation: (11)

The corresponding Y constant for CH samples is also calculated by a similar quadratic equation: YCH = 15.381(wH2O)2 − 108.33wH2O + 277.64

(15)

The effective particle heat capacity must be calculated as a function of both particle perlite and particle water mass fractions, at variable temperature. By considering a linear combination approximation, the particle heat capacity is calculated as a function of both temperature and effective water mass fraction:

The corresponding X constant for CH samples is also calculated by a similar linear equation: XCH = −357.44wH2O + 11432 (10)

YTR = 15.472(wH2O)2 − 109.09wH2O + 250.71

(14)

The steam heat capacity as a function of temperature is calculated by means of a linear correlation:23,24

Numerical values of X and Y constants vary with perlitic melt chemical composition and water content. The X constant for TR samples with respect to melt water content is calculated by a linear equation: X TR = −369.79wH2O + 11749

(13)

(12)

Equations 9−12 have been obtained via statistical regression of X and Y results computed for both TR and CH compositions in the entire water content range of interest (0.5−3%); they are used in the dynamic model of the process to calculate both X and Y constants in terms of perlitic ore chemical composition and water content, while the J constant is set as its default value (−4.55). Finally, perlitic melt viscosity temperature variation is explicitly considered by including eq 6 in the dynamic furnace model. 3.2.5. Melt Surface Tension. The surface tension which is exerted on the shell-bubble interface counteracts bubble expansion and its value is also a function of temperature. Murase and McBirney investigated and determined the surface tension of obsidian (0.5% water content) in the temperature range of 1000−1400 °C.16 Proussevitch et al. assumed a constant value of 0.32 N·m−1 in their study of bubble growth in rhyolitic magmas.22 The proposed linear dependence of surface tension 17961



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chamber on perlite expansion evolution and efficiency. Differential equations which describe both momentum and energy balances determine air temperature distribution in the heating chamber as well as particle characteristics (particle size, velocity, and temperature along a trajectory), respectively. The validated dynamic mathematical model of the novel perlite expansion process which has been published in a previous study25 has been further developed in order to conduct a multiparametric sensitivity analysis of key furnace performance indicators with respect to perlite ore feed quality (origin, initial particle diameter, effective water content) as well as process operating conditions (air feed flow rate, air feed temperature, and furnace wall heating profile), in order to derive technical recommendations for efficient and profitable process operation. The more elaborate dynamic model concentrates on the momentum and energy balance description of single-grain expansion in the vertical electrical furnace, both at a microscopic and a macroscopic level. Microscopic mathematical analysis here refers to the investigation of internal particle temperature and steam bubble pressure evolution, as the interplay and rates of both these phenomena govern perlite grain expansion. Macroscopic mathematical analysis refers to particle motion and air temperature distribution. These transport phenomena are analyzed via a nonlinear system of algebraic and ordinary differential equations. The fundamental assumptions considered are important toward understanding the scope and accuracy of the model as well as the limits of its applicability: • Air is introduced via the entire cylindric chamber upper face, with no pressure drop (P = 1 atm). • Air temperature and velocity have negligible radial variation and are studied via axial models. • The entire internal chamber wall surface is smooth. • The effect of air components which are not transparent to thermal radiation (CO2, N2, H2O) is negligible and does not affect air heating. • Each perlite grain is perfectly spherical throughout the expansion process, and has a uniform temperature which varies during expansion only due to heating and evaporation phenomena. • Diffusion or mass transfer across the bubble-shell and the shell-air interface is negligible. • The entire effective water content of each grain is concentrated at the steam bubble nucleus. • Steam obeys the ideal gas law in the entire process. The enthalpy of water evaporation inside grains is explicitly considered, while mechanical work for bubble expansion is negligible. • Particle melting is explicitly modeled via the temperature dependence of perlite melt viscosity. Breaking of the expanded spherical perlite particles takes place when the internal bubble pressure exceeds the sum of molten shell surface tension and ambient pressure: albeit outside our scope here, breaking can be computationally predicted as the model tracks bubble pressure continuously. 4.1. Perlite Particle Motion along the Vertical Heating Chamber. The forces exerted on the falling particle are the gravitational force (FG) which accelerates the particle, and the drag (FD) and buoyancy (FB) forces which decelerate the perlite grain vertical fall: FG = mpg

1 ρ CDA proj(Uair − Up)2 2 air

FD =

FB = ρair gVp

(18) (19)

The momentum balance on the falling perlite particle follows Newton’s second law of mechanics: considering all forces exerted on the particle, its velocity is given by an ordinary differential equation:26

∑ F = mp =

dUp

⇒

dt ρp − ρair ρp

dUp dt

g−

2 3 ρair CD(Uair − Up) 4 Dpρp

(20)

The particle position is by definition linked with velocity and time by an ordinary differential equation:

dz dt

Up =

(21)

The drag force coefficient (CD) is calculated using a particle Reynolds number (Rep) correlation:27,28 CD =

24 (1 + 0.15·Rep0.687) Rep

(22)

The particle Reynolds number (Rep) is calculated via the relative velocity by the following equation:29 Rep =

ρair Dp|Up − Uair| μair

(23)

The volumetric air flow rate variation due to increase of air temperature and decrease of air density along the grain trajectory in the heating chamber is taken into account toward air velocity calculation:

Uair =

Q air,inTair A tubeTair,in

(24)

4.2. Air Heat Balance in the Vertical Heating Chamber. The problem of air temperature calculation in the heating chamber is solved as follows: air is injected into a vertical tube and flows at mean velocity, within the heated furnace walls of constant temperature. Thermal energy is transferred to air by convection, thus increasing air temperature: the latter is calculated via an adiabatic energy balance, using a simple initial condition: Tair (z = 0) = Tair,in. ⎛ πD h ⎞ dTair t ⎟⎟(Tw − Tair) = ⎜⎜ dz ̇ P ,air ⎠ ⎝ mC

(25)

The convective heat transfer coefficient (h) therein is calculated by definition via the next equation: h=

kair Nuair Dt

(26)

The length of the hydrodynamically developing flow region (Lhyd) is determined by the next correlation:30 L hyd = 0.05·Re·Dt

(27)

The length of the thermally developing flow region (Lth) is similarly determined by another correlation:30

(17) 17962



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Figure 8. Architecture of the dynamic mathematical model for the novel perlite expansion process.

L th = 0.05·Re·Pr ·Dt

(28)

dTp dt

The Nusselt number along the heating chamber is calculated by the Sieder−Tate equation for either hydrodynamically or thermally developing flow (z < Lhyd or z < Lth), but assumes its constant value of Nuair = 3.656 under fully developed flow conditions (z > Lhyd and z > Lth).30

Nuair

⎧ 1/3⎛ ⎞0.14 ⎪1.86⎛⎜ Re ·Pr·Dt ⎞⎟ ⎜ μair ⎟ , ⎪ ⎝ ⎠ ⎜⎝ μ ⎟⎠ z ⎪ w =⎨ < < if 0 z L or 0 < z < L th ⎪ hyd ⎪ ⎪ 3.656, if z > L hyd and z > L th ⎩

= εp·

A ss(Tw 4 − Tp 4) ρp VpCP ,p

+

A shc(Tair − Tp)

⎛ P ⎞⎛ 4πR 3 ⎞ b ⎟ − ΔHevap⎜⎜ b ⎟⎟⎜ ⎝ R gTp ⎠⎝ 3 ⎠

ρp VpCP ,p

(30)

Here, εp is the perlite particle emissivity, As is the perlite particle surface area, s is the Stefan−Boltzmann constant, and ΔHevap is the molar enthalpy of water evaporation (40.68 kJ·mol‑1). The emissivity of unexpanded and expanded perlite powder has been determined to be 0.7 and 0.55, respectively, according to our measurements which have been conducted with an AE1 emissometer (Devices and Services Company, USA); the model εp value is changed as soon as expansion begins (E > 1). 4.4. Steam Bubble Growth within the Perlite Grain. In the present mathematical modeling study, perlite expansion is approximated by a detailed single-grain model. The model particle consists of a spherical steam nucleus and a solid shell surrounding the steam bubble: steam is treated as an ideal gas, with no mass transfer across the steam−shell or the shell− environment interface permitted. During particle heating, the perlite grain temperature increase has a dual effect: first, steam enthalpy increases, thereby increasing the pressure exerted on the bubble-shell interface; concurrently, molten shell viscosity and cohesion decrease, thus facilitating bubble expansion and increasing steam bubble radius and perlite grain size. The pressure factors acting on the bubble−shell interface are the surface tension (σ), the steam pressure (Pb), and the ambient pressure (Pa): steam pressure acts toward expanding the bubble, while both surface tension and ambient pressure act against steam bubble growth. The steam bubble only contains the entire effective water amount, as the residual water amount is uniformly dispersed in the molten shell without affecting expansion. The initial steam bubble radius (Rb,i) is thus calculated as

(29)

4.3. Perlite Grain Energy Balance in the Vertical Heating Chamber. The falling perlite grain is assumed to have a uniformly varying temperature, as internal gradients are negligible. The validity of this assumption is confirmed by a Biot number (Bi) calculation for a compact unexpanded particle: for the thermophysical properties and conditions considered, its value does not exceed Bi = 0.047, even in the most unfavorable case of maximum resistance to conductive heating. As this maximum is much lower than the limit value for which the total radial temperature variation cannot exceed 5% (Bicr = 0.1), the uniform temperature assumption is valid.30 The solid particle absorbs energy by radiation and convection: both contribute to heating and expansion and are equally important heat transfer mechanisms in understanding furnace and process efficiency. The grain temperature evolution due to radiative heating is calculated on the basis of the Stefan−Maxwell law which accounts for thermal energy emitted by furnace walls and absorbed by the moving grain. Furthermore, the solid particle exchanges thermal energy with air by convective heating. This is an interesting phenomenon, as a sign reversal can be identified along the perlite grain trajectory: the cold particles are heated at entry by an upward air current, but are warmer than air toward the exit. Moreover, the latent heat of water vaporization must be considered. Consequently, perlite grain temperature evolution is governed by the combination of radiative and convective heat transfer mechanisms and phase transformation; the dynamic heat balance is an ordinary differential equation:

R b,i =

3

R p,i 3 −

3 mm 4π ρm

(31)

The molten shell mass (mm) is calculated on the basis of the perlite grain water mass fraction (wH2O) mm = (1 − wH2O)mp

(32)

The steam in the core of the grain is treated as an ideal gas: its instantaneous pressure is calculated by explicitly considering the bubble radius evolution and implementing the ideal gas constitutive equation: 17963



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Figure 9. Temporal evolution of TR particle state variables as a function of heating chamber wall temperature, for both air feed temperature extrema. Constant parameters: Qair,in = 50 L·m−1, Dp,i = 350 μm, wH2O,eff = 2.00%. 17964



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Figure 10. Temporal evolution of CH particle state variables as a function of heating chamber wall temperature, for both air feed temperature extrema. Constant parameters: Qair,in = 50 L·m−1, Dp,i = 350 μm, wH2O,eff = 1.75%. 17965



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Figure 11. Final perlite particle expansion ratios achieved as a function of furnace wall temperature and particle effective water content, for the entire grain size range. Air feed parameter: Qair,in = 50 L·min−1.

Pb(t ) =

The Navier−Stokes equation for spherical creeping flow is combined with the melt radial velocity equation and the bubble surface stress balance, to yield an ordinary differential equation for bubble radius evolution:31−33

3NR gTp 3

4πR b (t )

(33)

17966



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Figure 12. Final perlite particle expansion ratios achieved as a function of furnace wall temperature and initial particle diameter, for the entire particle effective water content range. Air feed parameter: Qair, in = 50 L·min−1.

dR b R ⎛ 2σ ⎞ = b ⎜Pb(t ) − Pa − ⎟ dt 4μm ⎝ Rb ⎠

The initial condition is the miniscule steam bubble radius assumed at particle injection: Rb (t = 0) = Rb,i. The mathematical model presented does not use any arbitrary or tunable phenomenological parameter for triggering expansion: the latter

(34)

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the residence time of expanded particles is considerably longer. Preheated air injection in the heating chamber is crucial for adequate expansion: while in both cases (TR and CH grains) no significant expansion occurs under ambient air injection, preheated air injection (400 °C) causes rapid particle expansion, especially when furnace wall temperature exceeds 1000 °C. Dynamic model results confirm our experimental observations (Table 2): when particles are treated under the same operating conditions, TR particles attain higher expansion ratios than those achieved for CH particles. Thus, melt viscosity is recognized as a key expansion parameter. The strong impact of both particle water content and chemical composition on molten shell viscosity induces a widely varying particle expansion ratio (E). For ambient air injection and a furnace wall temperature of Tw = 1100 °C, E ranges between 4 (CH particles) and 5 (TR particles). Furthermore, the dynamic model results enlighten the dramatic impact of furnace wall temperature on expansion within the 1100−1200 °C range.25 Therein, high expansion ratios are achieved: E ranges between 5 and 7 for TR particles and between 4 and 6.5 for CH particles, depending on particle initial diameter. 5.2. Effect of Particle Physical Properties on Final Expansion Ratio. The effect of raw feed quality on perlite expansion is studied by means of the particle final expansion ratios achieved: initial particle diameter and effective water content effects are thus presented as a function of furnace wall temperature over the entire operating range (900−1200 °C), for both ambient and preheated air injection, for a TR grain chemical composition. 5.2.1. Effect of Particle Effective Water Content (wH2O,eff). Figure 11 presents the effect of particle effective water content on the final particle expansion ratio. Effective water content is critical for expansion evolution, as it increases bubble pressure and decreases molten shell viscosity: hence, the higher the initial effective water content is, the more efficiently perlite grains expand. The upper expansion ratio limit approximates Emax = 7 (particle diameter can increase up to seven times). When ambient air is injected at Tw = 1000 °C, even particles with the minimum effective water content (wH2O,eff = 1.50%) expand 100% (E = 2); particles with maximum effective water content (wH2O,eff = 2.25%) however, attain a final expansion ratio which is more than twice higher (E = 4.5). Thus, a modest increase of 0.75% in effective water content results in a striking increase of process efficiency by 125%. Generally, preheated air injection facilitates particle expansion, as it induces a global increase in air temperature and facilitates grain heating and expansion. 5.2.2. Effect of Particle Initial Diameter (Dp,i). The effect of initial particle diameter on the particle expansion ratio has been studied for a wide range of operating conditions. Figure 12 presents the final particle expansion ratio achieved as a function of initial particle diameter, for a range of furnace wall temperature and particle effective water content values. Particle initial diameter is a critical expansion parameter: finer grains achieve higher expansion ratios than coarser ones when treated under identical operating conditions. Furthermore, fine particles (Dp,i < 250 μm) expand even when furnace wall temperature is at a minimum (Tw = 900 °C) under preheated air injection; when the particle initial diameter exceeds Dp,i = 350 μm, expansion is evidently insufficient or even not observable. Generally, particle heating and expansion efficiency increase for decreasing size, provided that the minimum residence time condition is met.

occurs as soon as radiative heating has increased particle temperature so that melt viscosity is decreased sufficiently to allow for bubble pressure to cause molten shell deformation and gradual particle swelling and expansion. Perlite expansion thus emerges via the numerical interplay of both phenomena (bubble pressure increase and molten shell viscosity decrease).

5. RESULTS AND DISCUSSION The dynamic operation of the novel furnace is modeled using the Berkeley Madonna ODE modeling platform (version 8.3.18) while calculations have been performed on a dual-core Intel Pentium T3200 (2 GHz) with 3 GB of RAM in 32-bit Windows Vista OS. The nonlinear system of algebraic and ordinary differential equations is solved using a fourth-order Runge− Kutta numerical integration method with a solution time step of Δts = 0.01 s; the temporal evolution of state variables is monitored using a time step of Δtm = 0.05 s. The algorithmic architecture in terms of input and output variables is illustrated in Figure 8. Temperature-dependent air thermophysical property values are calculated in terms of the heating chamber air temperature, while particle viscosity and melt surface tension are calculated at the instantaneous particle temperature. Particle state variable time trajectories are illustrated until the perlite particle has traveled the entire chamber height (z = 2.70 m). Temporal values of particle position z(t), velocity Up(t), and temperature Tp(t) are presented and discussed. The variation of critical melt thermophysical properties enables detailed monitoring of particle size evolution, while key bubble state variable evolution provides insight into microscopic phenomena and perlite expansion potential. 5.1. Temporal Evolution of Particle State Variables. The temporal evolution of particle state variables as a function of perlite origin as well as furnace wall and air feed temperature is presented in Figures 9 and 10, respectively. Temperature variation of melt viscosity has been computed via eq 6 for both raw perlite compositions: constants X and Y have been determined by eqs 9 and 11 for TR ore particles, and by eqs 10 and 12 for CH ore particles. The effective water content (available for evaporation) is 2% and 1.75% for TR and CH particles, respectively. Figure 9 presents the temporal evolution of all key particle state variables for eight furnace wall and two air feed temperatures (25 and 400 °C). Particle composition and effective water content matches TR samples (wH2O,eff = 2.00%). Full circles mark the particle exit from the furnace bottom (residence time). Figure 10 presents the temporal evolution of particle state variables for the same furnace wall and air feed temperatures. Particle composition and effective water content matches CH samples (wH2O,eff = 1.75%). Full circles again mark particle exit from the furnace bottom (residence time). Remarkable quantitative observations and technical conclusions can be derived by comparing model results depicted in Figures 9 and 10. In both cases, particle pressure increases due to the increase of grain temperature: a relief is observed at 700 ± 15 °C, when shell viscosity and cohesion decrease and Rb(t) indicates that the bubble starts expanding. Both phenomena occurring within the perlite grain (molten shell softening and bubble expansion) clearly precede particle expansion. Particle temperature strongly depends on furnace wall temperature as well as on particle residence time in the heating chamber. Particles decelerate rapidly at expansion onset, due to the strong impact of particle radius on drag and buoyancy forces: as a result, 17968



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Figure 13. Perlite particle exit temperature achieved as a function of furnace wall temperature and particle initial diameter, for the entire particle effective water content range. Air feed parameter: Qair, in = 50 L·min−1.

5.3. Particle Heating and Motion. Particle residence time and furnace temperature have been recognized as fundamental

parameters with a critical effect on product quality. Perlite particle maximum as well as exit temperature have thus been 17969



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Figure 14. Maximum and final particle velocity as a function of particle initial diameter, effective water content and furnace wall temperature, for both air feed temperature extrema; upper and lower bar values represent the maximum and final (exit) particle velocity, respectively. Air feed parameter: Qair, in = 50 L·min−1.

5.3.1. Particle Final Temperature. Figure 13 presents the final particle temperature achieved for various furnace wall and air

studied for various feed physical properties and operating conditions. 17970



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Table 6. Feedstock Properties and Furnace Operating Conditions Used for Experimental Validation run no. (TR)

Dp,i (μm)

Qair,in (L·min−1)

Tair, in (°C)

Tw (°C)

LBDexptl (kg·m−3)

LBDsim (kg·m−3)

Eexptl

Esim

E error (%)

1 2 3 4 5 6

180 180 180 180 180 180

50 50 50 50 50 50

20 20 20 20 20 20

800 900 950 975 1000 1025

1204 268 176 134 85 72

1204 617 225 110 45 19

1.00 1.65 1.90 2.08 2.42 2.56

1.00 1.25 1.75 2.22 3.00 4.00

0.00 −24.24 −7.89 +6.73 +23.97 +56.25

of initial grain size. For identical system properties, expansion is faster and maximum velocity decreases as furnace wall temperature increases. 5.4. Model Validation. Dynamic model validation consists of comparing the final expansion ratio (E) model simulation results with the original experimental data obtained from the novel vertical electrical furnace constructed and operated at the Laboratory of Metallurgy (School of Mining and Metallurgical Engineering, NTUA). For the purpose of all validation experiments and simulations, the TR grain composition (Table 3) has been considered, as the higher effective water content (2%) is expected to induce higher discrepancies. Particle size distribution (PSD) of all samples has been controlled using 70 and 100 mesh sieves, achieving a TR granulometry between 149 and 210 μm: the median sample diameter of D50 = 180 μm for all validation experiments coincides with the value considered in corresponding runs (D = 180 μm). Ambient air injection (Qair,in = 50 L·min−1) and spatially uniform wall temperatures have been assumed (Table 6). The experimental particle expansion ratio (Eexptl) is the key validation metric, which is calculated as

feed temperatures, as a function of particle initial diameter and effective water content. Particle exit temperature increases as a function of furnace wall temperature, which affects both convective and radiative heat transfer (eq 30). Preheated air injection further contributes to grain heating and increases particle exit temperature in all cases. Moreover, particle heating is significantly affected by particle initial diameter; exit temperatures of all fine fractions (Dp,i < 250 μm) exceed 800 °C, while preheated air injection is indispensable in order for coarser particles (Dp,i > 350 μm) to exceed the same temperature (800 °C). Furthermore, the prolonged residence time due to expansion accentuates particle heating: not surprisingly, the exit temperature of expanded particles is always higher than that of unexpanded ones. 5.3.2. Particle Velocity. Figure 14 presents perlite particle maximum and final velocities for various furnace wall and air feed temperatures, as a function of initial particle diameter and effective water content. Particle velocity (Up) is a state variable with evidently high importance during perlite expansion, as it affects residence time and heat transfer potential in the heating chamber. Its dynamic nature is clear, even for nonexpanding, free falling grains, whose velocity increases until reaching its maximum (terminal) value. Expanding particle motion is more complex: unexpanded particle velocity increases due to acceleration but then decreases with time due to the density dependence of both drag and buoyancy effects (eqs 18 and 19). Because of the assumed particle mass conservation, the increase of particle diameter induces a decrease of particle density (ρp), which complicates particle size as well as velocity evolution, particularly under preheated air injection. For the entire initial diameter and effective water content ranges, higher furnace wall temperatures induce larger decelerations (larger bars), affecting particle motion substantially. The dynamic model results indicate that particle velocity strongly depends on initial size; the maximum velocity of coarser particles is always higher than that of finer ones, explaining the longer residence time and easier processing of fine particles. The maximum velocity of finer particles (Dp,i < 250 μm) is less than 1 m·sec−1, ensuring that the corresponding residence time in the heating chamber exceeds 3 s. Conversely, the maximum velocity of coarser particles is higher than 2.5 m·sec−1, implying a much shorter residence time. The onset of expansion induces rapid particle deceleration: particle residence time increases due to decreasing particle velocity; when maximum and exit velocity coincide, no substantial perlite grain expansion has occurred. Conversely, longer bars imply remarkable particle deceleration, indicating observable particle expansion. This velocity variation bar plot is useful in quantitative visualization of expansion potential and efficiency, in the entire range of feed quality and process operating conditions. Remarkably, the exit velocity of fully expanded particles tends to approach a limit value strongly depending on furnace temperature, but is virtually independent

Eexp =

ρunexpanded 3

ρexpanded

(35)

For a monodisperse sample of perfectly spherical particles, sample density is correlated to LBD by

ρ = 1.91 ·LBD

(36)

The slope of this correlation (6/π = 1.91) results by dividing the volume of a cube by the volume of a sphere whose diameter equals the cube edge length: accordingly, both density values in eq 35 can be determined via eq 36 using LBD values, easily measured by slowly pouring a weighted sample into a volumetric cylinder. The experimental final expansion ratio (Eexptl) is then calculated via eq 35. Figure 15 presents the comparison of final particle expansion ratios determined by experimental expansion campaigns against those obtained by dynamic process simulations, considering a wide range of furnace wall temperatures. Experimental data are in good agreement with model results for furnace wall temperatures below 1000 °C; error increases due to LBD at higher furnace wall temperatures. In the steam bubble model, the mass conservation which has been assumed for both shell and bubble phases forbids any steam release to the environment (this in fact does occur at high temperatures, particularly for water molecules within the outer grain layer). Consequently, the high final particle expansion ratio computed may be attributed to an overestimation of instantaneous particle effective water content. Moreover, the steam bubble model implicitly assumes that the spherical particle shape is retained even when the molten shell viscosity has decreased significantly and the grain has reached its softening point. In fact, the molten shell viscosity decrease can lead to 17971



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thermophysical properties, probing air as well as particle momentum and heat balances and their effect on perlite acceleration, heating, and expansion. The particle heat balance considers heat transfer by convection from/to air and by incident thermal radiation emitted by the chamber inner wall surface, which is heated via independent embedded electrical resistances. The two-phase perlite particle assumption considers an initially miniscule core bubble and an amorphous shell: the entire portion of water available for evaporation is concentrated in the core bubble (effective water content), while the rest is homogeneously dissolved in the melting shell surrounding the bubble (residual water content). The model computes the evolution of all key particle state variables (i.e., bubble pressure, particle temperature, particle velocity, particle position, particle radius, and expansion ratio) and the air temperature distribution in the furnace, allowing the detailed investigation of the perlite expansion method toward cost-effective optimization. The process operating condition (furnace wall temperature, air feeding rate, air feed temperature) and raw material physical property (particle water content, initial particle diameter) variations have been considered as dynamic model input parameters, in order to probe their technical significance and relative effect on expansion efficiency by quantitatively determining their individual effect on the particle expansion ratio (the key product quality metric). The major conclusion of this modeling study is that the novel vertical electrical furnace design can successfully accomplish perlite expansion up to final product quality standards, within an acceptably wide operating regime. The new vertical electrical furnace enables precise control of three process operating parameters (air feed flow rate, air feed temperature, furnace wall temperature) which must be adjusted simultaneously, with indepth, model-based (not experiential) process understanding in order to tune perlite expansion successfully. Both furnace operating conditions and feed thermophysical properties strongly impact expanded perlite quality, as shown by model results probing the operating parameter ranges of the entire system for two Milos mine ore feeds. Raw perlite feedstock thermophysical properties affect perlite expansion efficiency dramatically, indicating that vertical electrical furnace tuning has paramount importance to ensure expansion for variable feed grade quality. Figures 6 and 7 corroborate quantitative observations derived from novel furnace experimental campaigns: the expansion ratio is strongly dependent on initial particle diameter as well as ore origin and chemical composition. Dynamic modeling results imply feed monodispersity is an ideal prerequisite for high-quality perlite production; in practice, optimal operating parameters vary and should be a priori determined for varying perlite ore feeds, especially when production-scale units process batches of widely varying origin and particle size distribution. Technical efficiency and economic viability can be maximized by consistent ore feed testing and preprocessing. A key process parameter is the perlite ore feed quality, as it directly affects particle motion as well as heating. The feed particle size distribution (Dp,i) bears high importance and should ideally be narrow and monodisperse. Feeds consisting of various size fractions yield poor product quality, due to the wide variety of expansion ratios. Finer particles move slower than coarser ones, because their lower initial mass and radius favorably impact the interplay of weight, drag, and buoyancy forces toward inducing a lower terminal velocity in comparison to coarser grains. The shorter residence time of coarser grains in the furnace

Figure 15. Comparison of experimental and simulation expansion ratio results for various furnace wall temperatures. Constant parameters: Qair,in = 50 L·min−1, Dpi = 180 μm, wH2O,eff = 2.00% (TR sample).

mechanical deformation and loss of cohesion of solid particles, as they move beyond the plastic yield point. Softened particles colliding with the hot furnace wall are likely to stick on it, creating viscous aggregates. Experimental observations made during and after perlite processing (both in the conventional but considerably less so in the new vertical electrical furnace, and even more less with concurrent air feed) indicate that part of the raw perlite feed does indeed stick onto the heating chamber inner walls, developing a molten material layer which hinders efficient heat transfer and impedes the expansion process. This molten material layer must be regularly removed by means of highpressure air injection or hammering. Thus, despite the fact that the particle expansion ratio during processing can clearly exceed the industrial limit values (E = 3.9, LBD = 35 kg·m−3), furnace maintenance and recovery are hindered by collision and sticking phenomena on the inner wall surface of the heating chamber. Particle sticking onto the heating chamber wall is further facilitated by the high grain temperature which induces low melt viscosity; thus, particles experiencing intense heating and expansion have a higher tendency to form sticky agglomerates in the chamber.

6. CONCLUSIONS AND TECHNICAL RECOMMENDATIONS A detailed sensitivity analysis with respect to raw feed properties and process operating conditions has been performed on the basis of a novel mathematical model which has been developed for perlite grain expansion within a novel vertical electrical furnace. In the novel process illustrated here, the need for separation of expanded from unexpanded particles is eliminated, because the entire raw perlite feed is processed into microspherical particles: experimental evidence indicates that the quality of the entire expanded product in our NTUA experiments (without any separation) is clearly superior to the final expanded product of the conventional process (after cyclone separation), as seen in Figure 5. The dynamic model consists of ordinary differential equations for both air and particle heat and momentum balances, as well as nonlinear algebraic equations for air and perlite melt 17972



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intense heat transfer throughout flight, without deteriorating side-effects. Air feed flow rate must be adjusted to ensure the optimal residence time but without reducing the heating chamber air temperature. Consequently, air feed flow rate is a key dynamic optimization variable and its adjustment is required toward addressing raw perlite grade variation. Preheated air injection is crucial in achieving adequate perlite heating and commercially acceptable expansion, especially when coarse raw material is fed in the heating chamber, by providing a more uniform driving force for particle heating and thereby enhancing process controllability. Air feed temperature (Tair,in) affects the heating chamber temperature profile and particle temperature evolution. In all cases of large initial mean particle diameter (Dp,i > 400 μm) and/or polydispersity of perlite ore feed, and when furnace wall temperature does not exceed 1000 °C, ambient air use is a very poor processing choice: it results either in no expansion or in unacceptably low product quality, even for particles with the highest effective water content considered. Furnace wall temperature (Tw) affects grain expansion evolution dramatically. In cases where ambient air is fed into the heating chamber, particle expansion is almost never observed when the furnace operates at low wall temperature (Tw = 900 °C). High-temperature operation (Tw > 1000 °C) is thus essential toward observable expansion and higher expansion ratios (Tw > 1100 °C). The impact of furnace wall temperature on the particle expansion ratio is evident in the 1100−1200 °C range, motivating a focused investigation of furnace operation at a higher resolution (20 °C increments) therein. Model results indicate process efficiency increases greatly at high power input; for certain feeds, the final expansion ratio increases up to 5 times when the furnace wall temperature increases only by 100 °C; it is thus an effective yet costly manipulation variable. A critical process design consideration is the heating chamber (and the entire furnace) height. When particle heating is inefficient, increasing the total particle trajectory length increases residence time and exit temperature: increased furnace height enables successful processing of even coarser (Dp,i > 450 μm) feed fractions, as a longer flight path guarantees the required residence time, thereby adequate heating and expansion. Excessive overdesign must be avoided, to elude the risk of finer fraction overheating and disintegration, and ensure flexibility.

implies that heating rates may be inadequate, so expansion may not commence or conclude due to the unfavorable interplay of gravity, drag, and air injection. Moreover, a higher particle mass implies a higher heat amount required to increase its enthalpy and temperature. The total (inlet-to-outlet) particle temperature increase may thus be insufficient, causing a low expansion ratio. Residence time is crucial for coarser particles, whose terminal velocity is higher than that of finer ones: as the former travel quicker containing more water, adequate heating, softening, and expansion may not occur. This definite difficulty in expanding coarser particles has also been observed experimentally. However, it can be effectively overcome by decreasing air feed flow rate and/or increasing the temperature: both control manipulations increase particle residence time and air temperature in the heating chamber. Optimal operating conditions strongly depend on perlite ore, so quality control and preprocessing is advisable. Common industrial practice avoids feed screening, since narrowing the feed particle size distribution inevitably raises process cost; mixing feeds from different ore mines is also very rare due to the increased uncertainty. Currently, when the feed is characterized by a wide size distribution, a mean particle diameter is determined and the feed is processed under the optimal conditions corresponding to the mean particle diameter and composition. The existence of unexpanded and shattered particles in the expanded perlite product is thus inevitable; however, postprocess quality control ensures the commercial product meets the desired expanded perlite specifications. Effective water content (wH2O,eff) is another feed physical property affecting perlite expansion and final grain size. The important distinction made in our model between residual and effective water in each perlite grain has been motivated by mass balance results from LOI tests conducted for both raw and expanded perlite grains. Particle water content is distinguished as an effective (bubble) portion and a residual (melt) portion, affecting bubble dynamics as well as shell viscosity, which is the pivotal melt thermophysical property. Particles with more water tend to expand to higher ratios, even under mild heating (lower furnace temperatures). A higher shell water content induces quicker melt viscosity reduction, facilitating rapid grain expansion. Increasing grain water content also implies a larger bubble mass and increased steam pressure exerted on the bubble−shell interface, thus increasing the driving force for grain expansion and improving process potential. Low-water content perlite ore feeds can be processed for a longer residence time, by means of decreasing the air feed flow rate and/or increasing the furnace wall temperature and heating intensity. The maximum final particle expansion ratio achieved for adequately high effective water content (wH2O,eff > 2%) is almost independent of initial perlite grain diameter and dynamic model simulations indicate it does not exceed Emax = 7. Air feed flow rate (Qair,in) has a confirmed high impact and control potential, both on the particle momentum and on the air heat balance. Air injection reduces residence time and can be used for restricting (ambient) or enhancing (hot) heat transfer. Finer ore feeds (Dp,i ≤ 250 μm) expand sufficiently and independently of air feed rate, as long as furnace wall temperature exceeds 1100 °C throughout the heating chamber: here air injection is not necessary, but can be quite useful against overheating and ultrafine particle disintegration. Coarser ore feeds (Dp,i > 350 μm) must be treated at low ambient air feed flows (Qair,in < 50 L·min−1) in order to promote particle acceleration and expansion: here, air injection is essential toward

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +30 210772177. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

This research work has been financed by the European Union Seventh Framework Programme under Grant Agreement Number CP-IP 228697-2 (“Efficient exploitation of EU perlite resources for the development of a new generation of innovative and high added value micro-perlite based materials for the chemical, construction and manufacturing industry”, EXPERL). Dr. Panagiotis M. Angelopoulos would also like to hereby gratefully acknowledge the financial support of the Greek State Scholarships Foundation (IKY). 17973



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NOMENCLATURE

Latin Letters

a = air thermophysical property polynomial equation coefficient, dimensionless A = surface, m2 Bi = Biot number, dimensionless CD = drag force coefficient Cp = constant-pressure specific heat capacity, J·kg−1·K−1 D = diameter, m E = expansion ratio, dimensionless F = force, N g = gravitational acceleration, 9.81 m·s−2 h = heat transfer coefficient, W·m−2·K−1 H = molar enthalpy, kJ·mol−1 J = VFT equation pre-exponential factor, Pa·s k = thermal conductivity, W·m−1·K−1 K = Morsi−Alexander equation coefficient, dimensionless L = length, m ṁ = mass flow rate, kg·s−1 M = molar mass, kg·mol−1 Ms = VFT model molar oxide fractions’ combination coefficient, dimensionless n = viscosity equation exponent, dimensionless N = bubble steam molar mass, mol Ns = VFT model molar oxide fractions’ combination coefficient, dimensionless Nu = Nusselt number, dimensionless P = pressure, Pa Q = volumetric flow rate, m3·s−1 R = radius, m Rg = gas constant, 8.3144 J·mol−1·K−1 Re = Reynolds number, dimensionless s = Stefan−Boltzmann constant, 5.6703 × 10−8 W·m−2·K−4 T = temperature, K U = velocity, m·s−1 V = volume, m3 w = mass fraction, dimensionless X = VFT equation pseudoactivation energy, dimensionless Y = VFT temperature, K z = vertical position coordinate, m

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p = particle proj = projected area ref = reference value r = radiative heat transfer s = surface sim = simulated t = tube th = thermal w = wall value

REFERENCES

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Greek Letters

γ = acceleration, m·s−2 ε = emissivity, dimensionless μ = dynamic viscosity, Pa·s ρ = density, kg·m−3 σ = surface tension, N·m−1

Indices

a = ambient b = bubble B = buoyancy c = convective heat transfer cr = critical D = drag ev = evaporation exptl = experimental G = gravitational hyd = hydrodynamic i = initial value in = inlet m = melt max = maximum out = outlet 17974



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