Energy Fuels 2009, 23, 6131–6145 Published on Web 10/30/2009
: DOI:10.1021/ef900668f
Experimental Studies of Freezing Fouling of Model Food Fat Solutions Using a Novel Spinning Disc Apparatus R. Y. Nigo,† Y. M. J. Chew,*,† N. E. Houghton,‡ W. R. Paterson,† and D. I. Wilson† †
Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA, United Kingdom, and ‡Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, United Kingdom Received June 30, 2009. Revised Manuscript Received October 7, 2009
The freezing fouling behavior of a model food fat solution consisting of tripalmitin (PPP) in paraffin oil on 316 stainless-steel surfaces was studied using a novel spinning disc apparatus (SDA). The SDA features an internally cooled, vertical rotating cylinder, which is immersed in the warm test solution. Insulation ensures that deposition occurs only on the base. Computational fluid dynamics (CFD) simulations of the laminar flow field yielded heat-transfer predictions in good agreement with experimental measurements. The shear stress acting on the deposit and its surface temperature could therefore be estimated reliably. Studies of freezing fouling at surface temperatures of 2-30 K below the cloud point of solutions of 2-10 wt % PPP showed that the fouling behavior is sensitive to composition, surface temperature, and fluid flow. The deposit consisted of gels of PPP platelets, with solid concentrations much greater than that in the bulk solution. The composition of the deposit varied strongly with formation conditions, particularly flow velocity, indicating that deposition was strongly influenced by factors influencing gelation rather than by heat or mass transfer alone.
is indeed exploited in the manufacture of lubricants. Summaries of recent work in wax fouling include those by Akbarzadeh and Zougari4 and Parthasarathi and Mehrotra.5 Significant advances in the understanding of the kinetics of wax formation and aging have been achieved, and models have been developed for scaling up experimental results and predicting operating scenarios. Fouling phenomena analogous to wax deposition are experienced in the food sector, where liquid and semi-crystallized mixtures of fats are used in large quantities in baking and biscuit manufacture. Large quantities of fat mixtures are prepared in a central facility and transported to the points of use in the factory, such as mixers. Food fats are mixtures of triglycerides and smaller quantities of diglycerides and, similar to waxes, can cause freezing fouling when subjected to temperatures below their cloud point, Tc, so that deposits can build up on pipe walls. This “coring” occurs via crystallization and yields a viscous gel, which, over time, can harden to give a solid deposit. The impact of coring includes the extra costs for energy and cleaning, as well as the difficulty imposed in maintaining the quality (composition and state of crystallization) of the fat mixture, because its temperatureshear-time history is altered by the insulating layers on the equipment wall. Relatively little work has been reported on food fat fouling: Fernandez-Torres et al.6 reported a modeling approach, including a fouling regime map, using concepts taken from wax deposition in crude oil pipelines.
Introduction Fouling of heat transfer and other process equipment surfaces is a problem in many industries and can be particularly severe in the food sector, where the materials being processed contain components such as proteins, fats, and mineral salts that are precursors for the buildup of fouling layers. Such deposits reduce the efficiency of process units but also incur costs via extra cleaning to avoid contamination when lines are switched to other products or to maintain hygiene and microbial security. Epstein1 classified fouling according to the mechanisms of deposit formation and identified two variants of crystallization fouling, determined by the solubility behavior: (i) scaling, associated with inverse solubility salts, such as calcium carbonate and phosphate, in heated aqueous systems, and (ii) freezing fouling, where cooling the fluid induces solidification. In this context, freezing fouling is used to describe crystallization of solutes or minor components of the mixture, as opposed to solidification of the solvent as arises in ice growth.2,3 Most of the work on freezing fouling in heat-transfer systems to date has concentrated on petroleum blends, where cooling induces solidification of wax components in the mixture and
*To whom correspondence should be addressed. Telephone: þ44-(0)1223-334777. E-mail:
[email protected]. (1) Epstein, N. Thinking about heat transfer fouling: A 5 5 matrix. Heat Transfer Eng. 1983, 4 (1), 43–56. (2) Keary, A. C.; Bowen, R. J. Analytical study of the effect of natural convection on cryogenic pipe freezing. Int. J. Heat Mass Transfer 1998, 41 (10), 1129–1138. (3) Worster, M. G. Convection in mushy layers. Ann. Rev. Fluid Mech. 1997, 29, 91–122. (4) Akbarzadeh, K.; Zougari, M. Introduction to a novel approach for modeling wax deposition in fluid flows. 1. Taylor-Coutte system. Ind. Eng. Chem. Res. 2008, 47, 953–963. r 2009 American Chemical Society
(5) Parthasarathi, P.; Mehrotra, A. K. Solids deposition from multicomponent wax-solvent mixtures in a benchscale flow-loop apparatus with heat transfer. Energy Fuels 2005, 19, 1387–1398. (6) Fernandez-Torres, J. M.; Fitzgerald, A. M.; Paterson, W. R.; Wilson, D. I. A theoretical study of freeze fouling: Limiting behavior based on a heat and mass transfer analysis. Chem. Eng. Process. 2001, 40, 335–344.
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Fitzgerald et al. studied fouling from a model fat solution using a flat plate heat exchanger. Their model solution consisted of a single crystallizing component, tripalmitin (PPP), in a noncrystallizing paraffin solvent. PPP is often used as a model fat because it arises in many vegetable and food fat blends, and the melting point of pure PPP, at approximately 63 C, means that deposition can be studied with coolants operating near ambient temperature. They reported the formation of soft, porous deposits, which could detach, giving rise to occasional sawtooth behavior in fouling resistancetime plots. Similarities with the deposition of waxes were evident, particularly the importance of deposit gel strength. This paper extends the experimental investigations of Fitzgerald et al.7 using similar model solutions but using a novel test configuration, the spinning disc apparatus (SDA). The two most common techniques reported in the literature for studying the fouling behavior of waxes in crude oil are the flow cell loop8,9 and the coldfinger.10 In the former, warm oil (above its cloud point) flows along a long duct, often a pipe, with cooled walls, so that the wax solidifies on the wall. This configuration provides direct representation of a pipeline and a well-defined flow geometry. The volumes of fluid and size of the apparatus often prove too large for routine use in an assessment method. The coldfinger test employs smaller volumes and is simple in operation. Its basic principle is that warm oil (with a bulk temperature above its Tc) flows over a vertical cylinder, whose surface is held below Tc. The deposit forms on the surface of the finger and is collected and analyzed. The finger can be either stationary (the “coldfinger”) or rotating (termed a “rotating cylinder”). Finger systems are used routinely to gauge the performance of oils and effectiveness of additives. Their principal shortcoming lies in the complexity of the flow field and thereby difficulty in extrapolation of the results to operating systems, although computational fluid dynamics (CFD) simulations of this geometry have been reported.10 Spinning disc devices offer well-defined flow conditions,11 which have prompted their use in mass-transfer studies (e.g., dissolution12) and cleaning.13,14 Heated spinning discs have been used in fouling studies,15 where heat is supplied by either circulating hot oil or electrical heating via slip-ring connections. Chilled spinning discs are, to the authors’ knowledge,
rarely used, principally owing to the challenges involved in supplying coolant to the rotating assembly. The advantages of spinning discs over conventional flow cell loops and coldfingers are that they simultaneously (i) use smaller volumes of solution, (ii) are simple to operate, (iii) allow for the fouling surface to be recovered for analysis, and (iv) feature welldefined flow conditions. Modeling of the turbulent flows arising in flow cell loops or coldfingers is time-consuming and requires extensive computing power because the fluid contains numerous mutually interacting, continuously changing eddies and vortices that move with the stream. CFD simulation in the SDA, however, is feasible and reliable because the device is operated in the laminar flow regime. Other rotating geometries have been employed: Akbarzadeh and Zougari4 reported the development of a system based on a Couette cell, where the fluid flow pattern in the laminar regime is similarly well-understood. The design and operation of an SDA featuring cooled, removable heat-transfer surfaces is reported here. The surface temperature and heat-transfer (cooling) rates are often key parameters in freezing fouling; therefore, these have been investigated experimentally and by CFD simulations. The SDA device is also employed in a study of freezing fouling for a model fat solution similar to that employed by Fitzgerald et al.,7 augmenting the results obtained therein with a larger flow loop system. Experimental Section Deposition Cell. The central feature of the SDA is a vertical cylinder or “can”, the lower part of which rotates in a warm solution, as shown in Figure 1. The apparatus includes a jacketed vessel holding the warm bulk solution, the rotating can, and a magnetic stirrer to aid mixing and maintain temperature uniformity in the bulk solution. Deposition occurs only on the cold, exposed surface at the base of the rotating cylinder, because the wall of the cylinder is insulated. The bulk reservoir is a 3 L borosilicate glass vessel (Lenz, The Netherlands) insulated with rubber foams (RS, U.K.). The jacket is connected to a recirculating water bath (Haake, Germany), and temperatures are measured by T-type thermocouples connected to a datalogging PC. The bulk liquid is mixed by a 5 cm long polytetrafluoroethylene (PTFE)-coated magnetic bar stirrer, which rotated at 2 rad/s in all studies reported here. The rotating can is insulated on its sides by water- and greaseproof rubber foams (RS, U.K.), and rotation is provided by a 35 W DC stepper motor (Premotec, The Netherlands). Coolant, here a water/glycol mixture, is supplied by a second recirculating water bath through a pair of coaxial tubes. The incoming coolant is sent through the central tube to impinge on the base of the can and leaves via the 3 mm annular gap between the inner and outer tubes. The coaxial tubes are stationary and constitute the shaft about which the can rotates. The inner tube extends to within a few millimeters of the base of the can. This arrangement affords the fresh coolant rapid contact with the test plate. Figure 2 shows schematics of the different can base arrangements employed in heat-transfer tests and fouling studies. The former was constructed later in this study and, therefore, was not available for the majority of fouling experiments. In this configuration, the detachable 4 mm thick and 80 mm diameter 316 stainless-steel (SS) discs were separated from the coolant by a brass block, in which a microfoil heat flux sensor (Rhopoint, U.K., type 27160) was mounted. The heat flux sensor has a nominal sensitivity of 0.82 μV/(W/m2), with the maximum measurable heat flux of 95 kW/m2. The sensor housing was lined with a heat-sink gel (RS, Corby, U.K.), and the components were screwed together carefully and tightly to exclude air and to minimize other contact resistances. The deposition
(7) Fitzgerald, A. M.; Barnes, J.; Smart, I.; Wilson, D. I. A model experimental study of coring by palm oil fats in distribution lines. Food Bioprod. Process. 2004, 82, 207–212. (8) Ghedamu, M.; Watkinson, A. P.; Epstein, N. Mitigation of wax oil build-up on cooled surfaces. In Fouling Mitigation of Industrial Heat Exchange Equipment; Panchal, C. B., Ed.; Begell House: New York, 1997; pp 473-489. (9) Toma, P.; Ivory, J.; Korpany, G.; de Rocco, M.; Holloway, L.; Goss, C.; Ibrahim, J.; Omar, I. A two-layer paraffin deposition structure observed and used to explain the removal and aging of paraffin deposits in wells and pipelines. J. Energy Resour. Technol. 2006, 128, 49–61. (10) Jennings, D. W.; Weispfennig, K. Effects of shear and temperature on wax deposition: Coldfinger investigation with a Gulf of Mexico crude oil. Energy Fuels 2005, 19, 1376–1386. (11) Gregory, D. P.; Riddiford, A. C. Transport to the surface of a rotating disc. J. Chem. Soc. 1956, 1956, 3756–3764. (12) Garside, A.; Mersmann, A.; Nyvlt, J. Measurement of Crystal Growth and Nucleation Rates, 2nd ed.; Institute of Chemical Engineers: London, U.K., 2002. (13) Grant, C. S.; Perka, A. T.; Thomas, W. D.; Caton, R. Cleaning of behenic acid residues from stainless steel. AIChE J. 1996, 42, 1465–1476. (14) Morison, K. R.; Larsen, S. Spinning disc measurement of twostage cleaning of heat transfer fouling deposits of milk. Food Bioprod. Process. 2005, 80 (C4), 319–325. (15) Rosmaninho, R.; Melo, L. F. The effect of citrate on calcium phosphate deposition from simulated milk ultrafiltrate (SMUF) solution. J. Food Eng. 2006, 73 (4), 379–387.
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Figure 2. Construction of the rotating can base for (a) heat transfer and (b) fouling experiments. Dimensions are in millimeters (not to scale). Table 1. Thermal Properties of Components in Heat-Transfer Calculations Figure 1. SDA cell. (a) Schematic of the unit. Dimensions are in millimeters (not to scale). (b) Photograph of the cell before connection and insulation. A, coolant inlet; B, coolant outlet; C, rotating can; D, jacketed vessel; E, metal support.
configuration (Figure 2b) omitted the brass block with the heat flux sensor. Temperatures were measured using T-type thermocouples at the locations marked in Figure 1a, where Tcw1 (inside the can, in contact with the surface of 316 SS discs), Tcw2 (inlet coolant), and Tcw3 (outlet coolant) are coolant temperatures, while Tb1 (approximately 5 cm below the base of the disc) and Tb2 (approximately 5 cm above the base of the reservoir) are bulk temperatures. All temperatures except Tcw1 were connected to a multichannel temperature data logger (Pico-USBTC-08, Pico Tech Ltd., U.K.). Tcw1 was monitored using a T-type thermocouple connected to a battery-powered stand-alone single-channel data logger (Therma Tag, Digitron, U.K.) located on the can roof. A similar device was used to record the heat flux sensor signal, eliminating the need for slip rings. Tcw1 was found to be similar to Tcw2 and Tcw3, i.e., ∼ (0.5 K; therefore, the coolant temperature, Tcw, was taken to be Tcw1. The values of Tb1 and Tb2 were also similar, i.e., ∼ (0.5 K, and the arithmetic mean of Tb1 and Tb2 was used as the bulk temperature, Tb. The temperature measurement locations are shown schematically in Figure 2. The warm solution is held at a bulk temperature, Tb, above its cloud point and is in contact with the initially clean cool outer wall surface of the disc at temperature Tss,out < Tc. The solution at the wall will become locally saturated and forms crystals; deposition generates an insulating fouling layer, with a solid-liquid interface temperature, Ts,
material
λ (W m-1 K-1)
δ (m)
R (m2 K W-1)
brass stainless steel heat flux sensor coolant PPP deposit/bulk paraffin
109 16.3 n/a 0.58-0.64 0.15
0.009 0.004 negligible
0.83 10-4 2.45 10-4 5.00 10-4 g50.0 10-4 varies
varies
initially close to Tss,out but gradually increasing and approaching Tb as the deposit builds up. If Ts reaches Tc, the solution at the interface will be too warm for crystallization. The solid-liquid interface temperature Ts can be calculated from measurements of the heat flux and heat-transfer coefficients (shown later in eq 14). The heat flux through the rotating disc at any point, q, is given by Newton’s law of cooling q ¼ UðTb - Tcw Þ ¼ hb ðTb - Ts Þ ð1Þ where hb is the film heat-transfer coefficient on the solution side and U is the overall heat-transfer coefficient, calculated from 1 δf 1 δf 1 ¼ Rcw þ Rw þ þ ¼ Relse þ þ ð2Þ U hb hb λf λf Here, δf and λf are the thickness and thermal conductivity of the deposit, respectively, and Rcw and Rw are the resistance to heat transfer on the coolant side and through the base plate, respectively. Both of the latter terms are expected to remain constant during a fouling experiment, while Rcw is expected to be weakly related (compared to 1/hb) to rotational speed, owing to the strong influence of the impinging jet on the flow pattern within the can. Table 1 summarizes the thermal resistance of the fixed components in the heat-transfer configuration. Rw (i.e., the total 6133
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thermal resistance of the brass block, stainless steel, and heat flux sensor) is approximately 8.3 10-4 m2 K W-1 and is smaller than the resistance associated with a noticeable paraffin deposit. For example, a 130 μm thick paraffin layer would give a thermal resistance greater than the combined resistances of the base plates; Rw is not, therefore, expected to be a controlling factor in heat transfer. Model Solutions. Heat-transfer experiments used the same liquid paraffin (BDH Chemicals, U.K.; density at 20 C, 855 kg/m3) as was used as the solvent in the model solutions in the fouling experiments. The liquid paraffin is a n-alkane (CnH2nþ2) mixture, in which GC analysis (Perkin Elmer Clarus 500 GC) was shown to have a roughly Gaussian distribution of components ranging from C14 to C34, centred at C23. PPP was obtained as 90% pure from Sigma Chemicals, U.K., and dissolved in paraffin to give solutions of 2, 5, and 10 wt % composition. The apparent viscosity of the solutions was measured using a Bohlin CV120 controlled stress rheometer with 50 mm parallel plates and found to be independent of the PPP concentration (for PPP concentrations between 2 and 10 wt %) above the cloud point, following a temperature dependency of the form μb ¼ 375:74 expð-0:031TÞ ð3Þ
Figure 3. Effect of the PPP concentration on the melting point (O, from DSC) and cloud point (4, visual inspection). Locus shows the solid-liquid equilibrium relationship for an ideal solution and pure solid given by Atkins.18
formed by crystallization of the solutions at temperatures similar to those experienced on the clean test surface; therefore, a gap width of 1 mm was used. The sample was first heated to 65 C and held at this temperature for 10 min to allow for complete melting. The temperature was then reduced to the desired value at a cooling rate of ∼10 K/min and held at this temperature for 2 min before testing. Preshear is often applied to suspensions before testing19 but was not applied here because the impact of shearing on the formation of the suspension was uncertain. Samples were studied (i) in shear mode, with shear stress ramped up from 0.01 to 1000 Pa, held at 1000 Pa for 5 min, and then returned to 0.01 Pa, and (ii) in oscillatory mode, at an intermediate frequency of 1.59 Hz, with shear stress being ramped from 0.01 to 1000 Pa. Heat-Transfer Tests. The reservoir is charged with 2 L of the test solution, which is heated to the desired bulk temperature by circulating hot water through the heating jacket and mixed by the magnetic bar stirrer. The cooled can is initially isolated from the reservoir and brought to the required temperature by circulation of the coolant. A support frame was constructed to hold the can and motor assembly horizontal before and after immersion. The remote data loggers were activated, and temperature stabilization was monitored. Once temperatures had equilibrated, all condensate was removed from the can assembly and the disc was cleaned with hexane and dried. The can was then immersed in the solution, and rotation was started. It was important at this point to inspect the disc surface visually for air bubbles, because these can affect heat transfer and deposition. Air bubbles were displaced by increasing the rotation speed. Heat-transfer performance was studied using liquid paraffin over the range of conditions used in the fouling studies, with temperature driving forces, ΔT = Tb - Tcw, ranging from 17 to 52 K and ωd ranging from 3 to 60 rpm. Heat flux and temperatures were recorded over 30 min to ensure that any short-term transients had been eliminated. The effect of ΔT was investigated with Tb held constant, at 60 C, while Tcw was varied between 8 and 43 C at a can rotation speed of 60 rpm. The effect of ωd was studied at ΔT = 28 K, with Tb = 50 C and Tcw = 22 C. Fouling Tests. Fouling tests were performed at conditions of constant ΔT and ωd. A bulk temperature of 50 C was used in all tests. The coolant temperatures used were 2 C, (Tc - 5) K, and (Tc - 15) K, where Tc is the cloud point temperature of the solution. The lowest value, 2 C, reflects winter conditions in the U.K. and can be readily generated in a laboratory chiller over extended periods, while the latter values vary with the PPP concentration. The experimental conditions used in the fouling
where μb is the apparent viscosity of the bulk solution and T is the temperature in Kelvin. The freezing point of the PPP (90 wt %) was measured using a Pyris 1 differential scanning calorimeter (DSC, Perkin-Elmer, U.K.) fitted with a refrigeration intercooler, which yielded a value of 61.8 C. This compares favorably to the values reported for 95 wt % PPP16 of 63.0 C and 99 wt % PPP17 of 65 C and follows the expected trend. PPP exists in three polymorphic forms, R, β, and β0 , with the highest freezing point corresponding to the β0 form. The solidification behavior of the PPP solutions was studied using a Perkin-Elmer Pyris 1 DSC and a visual cloud point test. The latter employed a test apparatus similar to that reported by the European Oleochemicals and Allied Products Group, which is often used for food applications and confirmed the appearance of small crystals (size comparable to the wavelength of light). Samples were placed in a flat-bottomed test tube (3 cm in diameter and 12 cm in height) with a magnetic stirrer. The sample tube was located in a water bath and heated to 65 C to melt any PPP solids completely. The temperatures of the water bath and sample were measured by independent T-type thermocouples. The bath temperature was reduced at 1 K/min, and the temperature at which the sample began to cloud was recorded as the cloud point, Tc. The cloud point is known to be influenced by kinetic effects, particularly the cooling rate, and therefore, the Tc values reported here are taken as indicators of the onset of solidification. The visual test proved to be more reproducible than DSC estimation of Tc. The Tc results are presented in Figure 3 alongside the melting points measured by a DSC and the solid-liquid equilibrium locus for an ideal solution and pure solid given by Atkins.18 The melting points show reasonable agreement with ideal mixture behavior. The cloud points show approximately 12 K of supercooling over the concentration range studied. The Tc values for the solutions used in fouling tests were 28 C (2 wt %), 32 C (5 wt %), and 37 C (10 wt %). The rheology of the model solutions at temperatures below their cloud point was studied using a Bohlin CV120 controlled stress device fitted with roughened parallel plates to avoid slip. The aim of this work was to investigate the nature of the gels (16) Fitzgerald, A. M. Crystallisation and deposit behaviour of palm oil fractions. Ph.D. Thesis, University of Cambridge, Cambridge, U.K., 2002. (17) Kellens, M.; Meeussen, W.; Reynaers, H. Crystallization and phase transition studies of tripalmitin. Chem. Phys. Lipids 1990, 55, 163– 178. (18) Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford, U.K., 1997.
(19) Coussot, P. Rheometry of Pastes, Suspensions, and Granular Materials; Wiley Interscience: New York, 2005.
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Table 2. Experimental Conditions in Fouling Experiments heat-transfer tests coolant temperature, Tcw (C)
19-52
bulk temperature, Tb (C)
50 (effect of ωd) 60 (effect of ΔT)
PPP concentration, (wt %) rotational speed of can, ωd (rpm) 3-60
fouling runs 2, (Tc - 5), and (Tc - 15) 50 2, 5, and 10 3, 33, and 60
tests are summarized in Table 2. The PPP concentrations are those employed by Fitzgerald et al.,7 who studied deposition in a flow cell fouling rig, where the test plate was one surface of a rectangular duct. The can rotational speeds correspond to rotational Reynolds number, Rer, values of 11-215. Temperatures were monitored over a fouling test. At the end of the test, the rotation was stopped and the can assembly was lifted off the main unit, placed on the support frame, and left standing for about 2 min to allow for excess solution to drip off the test plate. The gel formed on the test plate, including residual solution held by surface tension, was then carefully scraped off using a plastic spatula, weighed, and stored for analysis. The amount of residual solution could be significant; therefore, a blank run was performed after each fouling test to determine how much liquid remains on the fouling cell plate as a result of surface tension. The test plate was cleaned thoroughly, and the can was lowered into the reservoir and rotated at the experimental conditions for 1 min before withdrawing it and resting it on the support frame for 1-2 min. Liquid adhering to the test plate was removed and weighed. This amount was subtracted from the measured fouled plate mass to give the true deposit mass. Fouling tests could run for 24 h or longer. A few tests were repeated to gauge the reproducibility of the approach. These displayed good agreement, i.e. within 5%; therefore, tests were thereafter repeated only when the results were inconsistent with observed trends. Deposit Analysis. The solids content of the deposit was determined by filtration. About 2 g of deposit was placed on a 0.2 μm nylon membrane (Whatman International, U.K.) and washed with cold analytical-grade hexane under vacuum at ambient temperature. The filtered crystals were washed with laboratory-grade acetone and dried before weighing. This protocol was calibrated using known concentrations of PPP powder in paraffin, and solids recovery of >98% was achieved. The particle size distribution of the primary crystals formed (which are subsequently incorporated into agglomerates or gel networks) was estimated using laser diffraction on a Coulter LS230 device fitted with a small volume module. About 5 mg of particles was suspended in 6 mL of propan-2-ol and sonicated for 7 min to disperse the sample fully. The particle size and shape were studied using scanning electron microscopy (FEG SEM, Hillsboro, OR). Samples taken from filtered material were goldspluttered and imaged at 5 kV. Crystal morphology was probed by wide-angle X-ray spectroscopy (WAXS) using a Siemens Kristalloflex 760 source (45 kV, 45 mA) and Siemens HI-Start detector system. Data were collected across 5 < 2γ < 30 and analyzed using Bruker GADDS System software v3.325. The rheology of deposit gels formed from 10 wt % PPP solutions was characterized by oscillatory shear stress measurements on the Bohlin CV120 controlled stress device (1.59 Hz, shear stress ramped from 1 to 105 Pa), as described above, in a similar manner to that reported by Tinsley et al.20 The structure of the deposit gels will, admittedly, have been disturbed by the
Figure 4. FEM mesh of the simulation domain showing boundary labels (A-H). Only half of the system is considered, exploiting symmetry. The darkness of the areas in the figure indicates the density of the mesh.
process of transferring the sample to the rheometer, despite taking care to minimize shear of the material. These measurements are therefore subject to systematic error, but the results do, nevertheless, show significant differences in deposit structure compared to the “fresh” gels.
Numerical Simulation The surface temperature and shear stress acting on the surface are key parameters in freezing fouling. The SDA is operated in the laminar regime; therefore, CFD simulations can be performed with reasonable accuracy. The commercial finite element method (FEM) software COMSOL Multiphysics (version 3.5, chemical engineering module) was used for simulating the flow and heat-transfer behavior of pure paraffin liquid in the SDA, i.e., simulating the heat-transfer experiments; the predicted heat fluxes were compared to experimental measurements. Simulations of fouling experiments, as reported for water scaling by Brahim et al.,21 were not attempted. FEM simulations are based on the division of the flow domain into small (finite) unstructured elements. An example of the triangular elements generated using the software’s builtin mesh generator is shown in Figure 4. The flow field is simulated by solving the continuity equation and the axisymmetric, incompressible, steady-state Navier-Stokes equation for a Newtonian liquid. continuity : rv ¼ 0 ð4Þ Navier-Stokes : Fb ðvrvÞ ¼ -rp þ μb r2 v þ Fb g ð5Þ where v is the velocity vector, p is the pressure, Fb is the bulk density, μb is the bulk apparent viscosity, and g is the acceleration due to gravity, set to 0 in this case for computational convenience.22 This also assumes that natural convection is unimportant. All flows are laminar. The steady-state energy equation can be written as ð6Þ energy : Fb Cp, b ðvrTÞ ¼ rðλb rTÞ
(21) Brahim, F.; Augustin, W.; Bohnet, M. Numerical simulation of the fouling process. Int. J. Therm. Sci. 2003, 42 (3), 323–334. (22) Tritton, D. J. Physical Fluid Dynamics, 2nd ed.; Oxford University Press: Oxford, U.K., 1988.
(20) Tinsley, J. F.; Jahnke, J. P.; Dettman, H. D.; Prud’homme, R. K. Waxy gels with asphaltenes 1: Characterisation of precipitation, gelation, yield stress, and morphology. Energy Fuels 2009, 23, 2056–2064.
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where ωmag and rmag are the rotational speed and radius of the magnetic stirrer, respectively. E and F. Wall of the Heated Jacket. The inner wall temperature is specified to equal Tb, the temperature of the solution. The boundary is impermeable, and there is no slip at the wall. G. Liquid-Free Surface. There is little heat loss from the liquid surface, and therefore, it is treated as adiabatic. This free surface is also modeled with slip conditions. ð10Þ slip : vz ¼ 0 and vθ ¼ 0
Table 3. Summary of Parameters Used in the CFD Simulations parameter radius of disc, rd (m) bulk temperature, Tb (C) coolant temperature, Tcw (C) rotational speed of can, ωd (rpm) apparent viscosity of bulk, μb (kg m-1 s-1) density of bulk, Fb (kg/m3) thermal conductivity of bulk, λb (W m-1 K-1) specific heat capacity of bulk, Cp,b (J kg-1 K-1) rotational speed of magnetic stirrer, ωmag (rad/s)
value 0.04 50 22 3-60 (2 C): 0.040 (50 C): 0.016 855 0.15 2107 -2.0
where vz is the velocity component in the axial direction. Any vortex motion is therefore not modeled, which is consistent with other gravity effects, such as natural convection, being omitted from the analysis. H. Vertical Surface of Can. The wall is insulated and, therefore, is treated as adiabatic, with rotational speed given by eq 8.
where T is the temperature, Cp,b is the specific heat capacity, and λb is the bulk thermal conductivity. Physical properties, such as density, thermal conductivity, and specific heat capacity, do not change significantly with the temperature and are assumed uniform throughout. The temperature dependence of the kinematic viscosity is incorporated using eq 3. The physical and thermal properties used in the simulations are summarized in Table 3. The physical configuration is cylindrically symmetric; the geometry of the model is illustrated in Figure 4. Axisymmetry implies that only half of the system need be modeled. The mesh contains approximately 5000 triangular elements, with a higher concentration of elements at the boundary between the disc and the liquid (approximately 5 times greater than at the other boundaries). The number of elements was optimized by performing a series of simulations with different mesh sizes, starting from a coarse mesh and refining it until the results were mesh-independent. A converged solution took approximately 15 min on a desktop PC with a 3.16 GHz dual core processor and 3.33 GB RAM. Convergence was assessed by comparing the values of velocity and temperature from successive iterations; tolerances were set at 10-5 m/s (versus a lowest mean tangential velocity of the cooling can of 1.3 10-2 m/s) and 10-5 K (versus a lowest coolant temperature of -2 C) for the velocity and temperature, respectively. The tolerance dictates the error in each integration step. The quantitative information specified for each simulation is the rotational speeds of the can, ωd, and the magnetic stirrer, ωmag, as well as the temperatures of the coolant and the bulk warm solution. The outputs of the CFD calculation are the velocity field and temperature profile. The latter allows the heat flux across the region of the rotating disc beneath the heat flux sensor in the experimental apparatus (Figure 2a) to be compared to experimental data. The boundaries are labeled A-H in Figure 4 and are subject to the following conditions. A. Base of Disc. Uniform temperature: the surface temperature, Tss,out, is assumed to be uniform and equal the coolant temperature, Tcw. The boundary is impermeable, and the rotational speed is specified via impermeable : nv ¼ 0 ð7Þ rotation : vθ ¼ ωd r 0 e r e rd
Results and Discussion Rheology of Model Solutions. Although the liquid paraffin is a Newtonian liquid, dilute suspensions of PPP crystals in paraffin are likely to exhibit non-Newtonian behavior. The β form of PPP crystallizes as platelets23 (see SEM images later in Figure 17a), which give rise to non-Newtonian behavior at lower volume concentrations than do spherical particles, owing to rotation- and shear-dependent structuring.24 This was confirmed by rheological investigations of suspensions generated by holding solutions at various target temperatures below Tc for 2 min. The suspensions formed by this protocol differ from those generated at the SDA surface because they were generated under quiescent conditions, at constant temperature, and over shorter periods than in the fouling tests. The effect of the holding time, preshear, etc. was not pursued here because the aim of this study was to establish the behavior of simple suspensions for comparison to the gels formed in freezing fouling experiments. Figure 5a shows an example of a flow curve obtained for a 10 wt % solution at 32 C (=Tc - 5 C); similar profiles were obtained for all of the other suspensions tested. All exhibited shear thinning behavior, with a transition between a low shear and a high shear plateau. The apparent viscosity increased with the extent of supercooling, which is consistent with a higher solids content. These results indicate the existence of a shear-dependent microstructure in the suspensions, as described by the Carreau model.25 μlow - μhigh μapp ¼ μhigh þ ð11Þ :2 ð1 þ K γ Þn where μlow is the low shear viscosity, μhigh is the high shear viscosity, γ_ is the shear rate, and K and n are the consistency and flow index, respectively. The plots in the figure show that the data sets could be described by either the Carreau or the closely related Cross model, with somewhat better agreement for the former. Both of these models have been used to characterize data sets obtained for crude oil waxes26 and
ð8Þ
where vθ is the velocity component in the azimuthal direction and n is the normal vector of the boundary plane. B. Axis of Symmetry. There is no fluid or heat flow across the axis of symmetry. C and D. Magnetic Stirrer. The stirrer region is modeled as a second spinning can, with adiabatic and impermeable boundaries. The rotational speed is specified, viz. ð9Þ rotation : vθ ¼ -ωmag r 0 e r e rmag
(23) Persson, M. Alpha stable fats. Lipid Technol. 2008, 20 (1), 13–16. (24) Macosko, C. W. Rheology: Principles, Measurements and Applications; John Wiley and Sons: New York, 1994. (25) Carreau, P. J. Ph.D. Thesis, University of Wisconsin, Madison, WI, 1968. (26) Garcia-Morales, M.; Partal, P.; Navarro, F. J.; Martinez-Boza, F.; Gallegos, C.; Gonzalez, O.; Munoz, E. M. Viscous properties and microstructure of recycled Eva modified bitumen. Fuel 2003, 83, 31–38.
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Figure 6. Effect of the temperature driving force (ΔT = Tb - Tcw) on the measured heat flux. Conditions: liquid paraffin at 50 C, and ωd = 5.2 rad/s (50 rpm). Locus shows the regressed line of proportionality. The symbol size reflects experimental uncertainty.
Figure 5. Rheology of “fresh” 10 wt % PPP gels formed by cooling in rheometer. (a) Apparent (steady shear) viscosity as a function of the applied shear rate for 10 wt % at 32 C (=Tc - 5). Loci show the best fit lines for the Carreau and Cross models. (b) Oscillatory testing at 1.59 Hz, Tc - 15.
food-grade oils.27 Similar behavior was observed with 2 and 5 wt % solutions, with μlow and μhigh decreasing with solids content, as expected. These results indicate that the PPP solutions form pseudoplastic suspensions upon cooling and are likely to exhibit a solid-liquid transition at a critical shear stress, τy.19 Some workers refer to this transition as a yield stress, with the terminology the subject of an ongoing discussion.28 The critical stress of the PPP suspension structures, which we will term gels, was determined at the end of the linear viscoelastic region in oscillatory stress tests. This technique is often used to determine gelation and gel strength29 and has also been used to determine the critical stress of suspensions (e.g., peanut butter30 and chocolate31). Figure 5b shows an example for 10 wt % solution at 32 C (Tc - 15), where τy marks the crossover between the elastic and viscous regimes
Figure 7. Effect of the Reynolds number, Rer, on the heat flux. Conditions: liquid paraffin, Tcw = 22 C, and Tb = 50 C. Locus shows the line of best fit for a simple power law model. The symbol size reflects experimental uncertainty.
(storage modulus, G0 , > loss modulus, G00 ), at 5 Pa. There is some scatter in the data, which is expected because the concentration of solids is relatively small and the gels are fresh. This value is 2-3 orders of magnitude smaller than the values for aged waxy gels (related to crude oil) reported by Tinsley et al.20 and Venkatesan et al.32 Heat Transfer. Figure 6 shows an example of experimental data from the heat-transfer experiments. The heat flux is linearly proportional to the temperature driving force (ΔT = Tb - Tcw), as expected, and the overall heat-transfer coefficient, Uexp, can be extracted from the regression line. The effect of dimensionless disc speed, Rer, on heat flux at fixed ΔT (and therefore U) is presented in Figure 7. The fitted trend line clearly indicates that the heat flux varies with Rer0.51, indicating that the overall heat-transfer coefficient, Uexp, is roughly proportional to ωd1/2. A similar relationship
(27) Wan Nik, B. W.; Ani, F. N.; Masjuki, H. H.; Eng Giap, G. S. Rheology of bio-edible oils according to several rheological models and its potential as hydraulic fluid. Ind. Crops Prod. 2005, 22, 249–255. (28) Barnes, H. A. The yield stress;a review or ‘πRντR Fει’;everything flows? J. Non-Newtonian Fluid Mech. 1999, 81 (1-2), 133–178. (29) Steffe, J. F. Rheological Methods in Food Process Engineering; Freeman Press: East Lansing, MI, 1996. (30) Citerne, G. P.; Carreau, P. J.; Moan, M. Rheological properties of peanut butter. Rheol. Acta 2001, 40, 86. (31) Taylor, J. E.; Van Damme, I.; Johns, M. L.; Routh, A. F.; Wilson, D. I. Shear rheology of molten crumb chocolate. J. Food Sci. 2009, 74 (2), 55–61.
(32) Venkatesan, R.; Nagarajan, N. R.; Paso, K.; Yi, Y.-B.; Sastry, A. M.; Fogler, H. S. The strength of paraffin gels formed under static and flow conditions. Chem. Eng. Sci. 2005, 60, 3587–3598.
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Figure 8. Flow patterns and temperature profiles in the SDA for can rotational speeds of (a) 3 rpm, (b) 10 rpm, (c) 33 rpm, and (d) 60 rpm. Black arrows are velocity vectors. Color indicates temperature, with 50 C = dark red and 22 C = dark blue.
was obtained by Sparrow and Gregg33 in their investigations of the heat-transfer characteristics of rotating discs located in a large pool of quiescent liquid. The relationship expected for the film heat-transfer coefficient is hb 1/2Rer1/2, which
suggests that the other heat-transfer resistances in the system are small. These results indicate that the SDA is operating in the laminar regime and that the conditions employed in the experiments did not exceed the sensor sensitivity. CFD Simulation. The CFD simulation predicts the velocity and temperature distributions in the liquid in the heattransfer experiments. Mass transfer, e.g., associated with
(33) Sparrow, E. M.; Gregg, J. L. Heat transfer from a rotating disk to fluids of any Prandtl number. J. Heat Transfer 1959, 81, 249–251.
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Figure 11. Shear stress on the disc surface at the radial location r = 0.035 m, extracted from CFD simulations for various temperatures and can rotational speeds.
Figure 9. Effect of the can rotational speed on heat-transfer coefficients. (O) Experimental overall heat-transfer coefficients, Uexp. (b) Simulated film heat-transfer coefficient, hb,sim. Conditions: liquid paraffin, Tb = 50 C, Tcw = 22 C (experimental), and Ts = 22 C (simulation).
speeds, indicating that the dominant resistance to heat transfer is on the solution side. Relse varies from 0.02 to 0.006 m2 K W-1, which is noticeably greater than the estimated value of Rw, of 0.000 82 m2 K W-1 (Table 1), suggesting that the coolant side resistance, Rcw, is significant. This also implies that wall resistances play a minor part and the assumption that the wall is at uniform temperature is reasonable. Moreover, Rw will be smaller in the fouling experiments as the mounting (Figure 2b) involves less material. Rotation has a larger effect on Rb than Rcw, which is expected because the coolant flow is also determined by the internal circulation in the can. The flow field within the can was not simulated because initial estimates of Reynolds numbers indicated that the flow lay in the turbulent regime, requiring extensive further computational effort. The surface temperature of the disc in contact with the warm solution in fouling experiments (before fouling occurs) will be near, but not at, Tcw. Figure 10 suggests that a working estimate of surface temperatures could be made using Rcw ∼ 1/2Rb and assuming Rw being negligible, giving ðTss, out - Tcw Þ ðTb - Tcw Þ q ¼ ¼ ð12Þ ðRcw þ Rb Þ Rcw
Figure 10. Thermal resistances Rb (=1/hb, black circles), Rw (solid line), and Rcw (=Relse - Rw, gray circles) in the SDA apparatus in the heat-transfer testing configuration (Figure 2a).
\Tss, out ¼ Tcw þ
fouling, is not considered. Figure 8 shows the temperature profiles (colored map) and flow patterns (contour lines) for a set of simulations at can rotational speeds employed in the experiments reported in Figure 7. Two vortices are evident in the bulk liquid: an upper one driven by the rotation of the can and a lower one induced by the magnetic stirrer acting in the opposite direction. Because the magnetic stirrer speed is kept constant, increasing the can speed increases the size of the upper recirculation zone, as expected. It is also evident that the rotational speed has an effect on the flow patterns and, thus, the temperature profiles. At high can speeds, i.e., > 10 rpm, the temperature of the bulk liquid is more uniform. The film heat-transfer coefficient, hb,sim, can be extracted from the temperature profiles, and these are compared to the overall heat-transfer coefficient, Uexp, obtained from experiments in Figure 9. The hb,sim values are consistently larger than the Uexp values, which is expected because the latter includes the resistances across the can and coolant. The latter resistance, Relse (=Rcw þ Rw), can be estimated from (1/Uexp - 1/hb,sim), according to eq 1, and the results are plotted in Figure 10. Both resistances decrease with increasing Rer: Rb is consistently larger than Relse at all rotational
1 2 Rb 1 R 2 b þ Rb
2 1 ¼ Tcw þ Tb 3 3
ðTb - Tcw Þ ð13Þ
The shear rate and shear stress imposed on the surface disc can also be calculated from the simulation velocity field. The shear stress distributions show that the maximum shear stress is found at the outer edge of the disc. The same trend was observed for shear rates and for all other temperature and rotational speeds investigated. Figure 11 shows the shear stress values at r = 0.035 m (the radius of the disc rd is 0.040 m). It is also evident that the effect of the rotational speed on the magnitude of shear stress is greater than the effect of the surface temperature. The shear stresses, τ, imposed on the surface in the SDA device can be compared to those imposed by an oil in turbulent flow in a pipe. For a turbulent pipe flow, τ = 0.5 CfFbu2, where Cf is the Fanning friction factor and Fb is the density of the oil. For an oil of density 800 kg/m3 and a Fanning friction factor around 0.005, a wall shear stress of 2 Pa corresponds to a bulk velocity, u, of ∼1 m/s. This 6139
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increase, which can be estimated from the following rearrangement of eqs 1 and 2: q Ts ¼ Tb hb 0 1 ðTb - Tcw Þ B ¼ Tb -@ Rcw þ Rw þ πrmd 2f F λ1f þ f
C1 A 1 hb
ð14Þ
hb
where mf is the mass of the fouling deposits formed and Ff is the density of the fouling deposit, estimated from composition measurements. The reader is reminded that the bulk film heat-transfer coefficient, hb, in eq 14 was calculated from CFD simulations. Estimates of Ts for the profiles in Figure 12 confirmed that Ts approached Tc at the end of the test. The difference in initial behavior between the high and low rotational speeds is elucidated by the heat-transfer profiles in panels a-c of Figure 13, which were obtained under similar conditions. The fouling resistance, Rf, shown in Figure 13b, is calculated from 1 1 ð15Þ Rf ¼ U Uo
Figure 12. Reproducibility of fouling runs. Conditions: 10 wt % PPP, Tc = 37 C, Tcw = 2 C, and Tb = 50 C. Filled black and gray symbols represent the mass of foulant recovered, and crosses and asterisks are estimates of the surface temperatures calculated using eq 14. Circles and crosses, 3 rpm; triangles and asterisks, 60 rpm.
estimate suggests that the magnitude of the surface shear stresses that can be obtained at the bench scale using the SDA and relatively simple measurements can be related to the conditions employed in industrial operation. Care must be taken in transferring SDA results to commercial applications because the shear stress values obtainable in the current version of the SDA are substantially lower than those associated with high flow rate oil production lines and the SDA flow field does not replicate features of pipeline flow, such as near-wall turbulence. It should be noted that the surface shear stresses imposed on the disc [max o(2 Pa)] at the higher rotational speeds were comparable to the yield stress, τy, reported above for “fresh” gels (∼5 Pa; Figure 5b) generated in the rheometer over 2 min. The shear stresses imposed at low velocity, 3 rpm, are considerably lower and suggest that the gels deposited on the disc surface during crystallization at low velocities may be strong enough to withstand the shearing effect. Fouling Experiments. The majority of fouling studies were conducted using the setup shown in Figure 2b with suspensions of 2, 5, and 10 wt % PPP in paraffin. Results presented are primarily the mass of deposit formed, deposit composition (PPP solids, from filtration), extent of fouling (visual observation), and deposit analysis (WAXS and rheology of gels formed from 10 wt % PPP tests). A limited number were performed with the heat flux sensor system, which became available later in the study, which also yielded transient heattransfer behavior. Reproducibility. The reproducibility of fouling tests was confirmed by repeated tests with 10 wt % PPP solutions at Tcw = 2 C and ωd = 3 and 60 rpm (Rer = 11 and 215, respectively). The data in Figure 12 show agreement for each Rer value within the bounds of experimental error, as well as noticeably different deposit mass-time profiles for different Rer values. At higher ωd, there is a short induction period followed by rapid growth up to 4 h, after which deposition is slow. At the lower speed, no induction period is observed, with 6 g of deposit formed after 1 h; deposit growth thereafter is slow, reaching a slightly larger final value than at 60 rpm after 24 h. The asymptotic or falling rate fouling behavior observed is expected as the tests are performed under conditions of constant overall temperature driving force; as deposit accumulates, the deposit-solution interface temperature will
where Uo is the initial, clean, overall heat-transfer coefficient. This is most readily estimated by extrapolating the q-t data back to t = 0, because the early values contain transients associated with the start of rotation. The heat fluxes obtained at the lower speed, i.e., 3 rpm, are 3-4 times smaller than those obtained at higher rotational speeds and, therefore, contain more measurement scatter, but the data clearly show a sharp initial increase in Rf, mirroring that seen in the mass deposition measurements in Figure 12. This can be attributed to the formation of a weak gel on the surface, because of the low temperature in the liquid, which is able to resist removal because the shear induced by the rotation is low. This is not observed at higher rotational speeds, where the shear stresses are an order of magnitude higher; the gel, when formed, will need to be stronger, which is borne out by the composition results presented later. The deposit thickness profiles in Figure 13c were estimated using ð16Þ δf ¼ Rf λf where the deposit thermal conductivity, λf, was taken to be 0.15 W m-1 K-1, because the thermal conductivity of solid PPP is conveniently close to that of paraffin. The final thickness values at 3 rpm of 2-3 mm were consistent with visual observations. The mass deposition profiles in Figure 12 are not consistent with the thermal resistance-time profiles in Figure 13b. There is considerable uncertainty in estimating Uo at 3 rpm, which may explain part of the mismatch. The total mass measurement is also relatively coarse (particularly when correcting for associated solvent), and the induction period apparent in Figure 12 is not evident in Figure 13b. These uncertainties meant that the deposited mass data were not used to calculate deposition rates, and the study focuses on the final amount and composition of the deposit formed. The heat flux sensor system affords data for monitoring deposition rates more reliably; this is the subject of ongoing work. Effect of the Surface Temperature. No deposition was observed at surface temperatures at or above Tc. The amount of precipitative subcooling (ΔTp = Tc - Ts) had a marked effect on the rate of deposition for all concentrations studied, 6140
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Figure 14. Effect of surface temperature on the total mass of gel deposited: (a) 2 wt % PPP solution, (b) 5 wt % PPP solution, and (c) 10 wt % PPP solution. Conditions: Tb = 50 C and ωd = 6.28 rad/s (60 rpm). (Black circles) Tcw = 2 C, (gray circles) Tcw = (Tc - 15) K, and (white circles) Tcw = (Tc - 5) K.
Figure 13. Fouling of 10 wt % PPP solution: (a) heat flux, (b) fouling resistance, and (c) estimated deposit thickness. Conditions: Tcw = 22 C, Tb = 50 C, and ωmag = -2.0 rad/s.
strong enough to resist the shear forces imposed on it by the flow. The shear stress is, to a first approximation, determined by the rotational speed and the viscosity of the bulk liquid, whereas the rheology of the gel is determined by the proportion of solids, their packing, and the viscosity of the liquid trapped in the gel (and is therefore related to the surface temperature). The experiments in Figure 14 all featured the same bulk temperature and rotational speed, and the deposition composition profiles in Figure 15 show a marked influence of Ts. The proportion of solid PPP in the deposit is universally greater than the concentration in the original solution, by up to a factor of 10, indicating that the deposits differ from the “fresh” gels formed in near-quiescent conditions in the rheometers above. The solids content of the deposits is, furthermore, uniformly greater for a given concentration at higher surface temperatures (less subcooling); this is consistent with the description above of the deposit
as shown by the deposit mass-time profiles for ωd = 60 rpm in Figure 14. All of the profiles show the deposit mass increasing with time, and in several cases, an asymptotic level of deposition is reached. The instantaneous formation of a substantial initial gel reported for 10 wt % solutions at ωd = 3 rpm above was not observed at this rotational speed. The rate of deposition generally increased with ΔTp at all concentrations, which was expected because the driving force for crystallization is larger. It should be noted that a surface temperature of 2 C represents a different ΔTp value for each concentration. Asymptotic behavior is most obvious for cases with ΔTp = 5 K, and separate estimates of the solution-deposit interface temperature (via eq 14) indicated that Ts had reached Tc. The surface temperature also affects the composition of the fouling layer, because a gel will be removed if it is not 6141
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measurement interrupted the process and was time-consuming. One of the benefits of the heat flux sensor system is the capacity to monitor deposition non-invasively, and this will be exploited in future work; it only became available toward the end of the study reported here. The difference in deposition rates between 2 and 10 wt % in Figure 14 does, however, indicate that fouling was not heat-transfer-controlled because these tests were performed under almost identical heattransfer conditions. This is supported by the data sets collected for each concentration, where the amount and rate of deposition is not related consistently to the temperature driving force for heat transfer. A simple estimate of the heattransfer-limited fouling rate can be made from the data in Figure 13, which shows heat fluxes of ∼1500 W/m2 at 33 rpm for a 10 wt % PPP solution with Tcw = 22 C. This corresponds to a solidification rate of 10 g of PPP m-2 s-1; for the disc radius of 4 cm, this corresponds to an initial deposition rate of 3 g/min, which is much larger than that observed. Heat transfer alone is therefore not limiting the rate of freezing fouling. Rather, these observations confirm that deposition is a complex process involving coupled phenomena: heat and mass transfer, solution thermodynamics, and the kinetics of gel formation (which are, in turn, shear-dependent). Other Operating Variables. The effect of the bulk solution concentration on the deposition was studied at 33 and 3 rpm, and the observed behavior was similar to that at 60 rpm (Figures 14 and 15). For a given temperature driving force, both the mass of deposit and deposit solids content increased with the bulk PPP concentration. The effect of the can rotation speed was studied using 10 wt % solutions at the three different temperature driving forces. The results for Tc - 5 shown in Figure 16 are representative of those obtained at Tcw = 2 C and Tc - 15. The deposition-time profiles show a small effect of the rotational speed over the 20 range, which is unexpected if shear-driven removal is controlling deposition. The heat flux monitoring results in Figure 13b show similar behavior. The composition data in Figure 16b show a strong effect of the rotational speed, however, with a systematic increase in solids content with increasing ωd (and initial surface temperatures). Visual observations of the deposits after fouling runs confirmed these values; those formed at higher rotational speeds were firmer. The markedly low solids content at 3 rpm (30 cf. 62 wt % for 60 rpm) was also observed at other temperatures, viz. 19 wt % at Tc - 15 and 6 wt % at 2 C (Tc - 35). Deposition therefore appears to be driven by gel formation at the temperature and shear conditions acting at the surface/interface; at 3 rpm, the shear stress is considerably smaller, so that a relatively weak gel can resist removal. The nature of the gel has a relatively small influence on the temperature on deposit growth because the thermal conductivity of the PPP crystals is similar to the solvent; the surface temperature is therefore relatively insensitive to the composition of the existing gel. Similar observations have been reported for crude oil wax deposition.5,10,34-36 Singh et al.36 conducted a detailed
Figure 15. Effect of the surface temperature on the wt % PPP solids in the gel deposited on the disc surface for the results presented in Figure 14: (a) 2 wt % PPP solution, (b) 5 wt % PPP solution, and (c) 10 wt % PPP solution. Conditions: Tb = 50 C and ωd = 6.28 rad/s (60 rpm). (Black circles) Tcw = 2 C, (gray circles) Tcw = (Tc - 15) K, and (white circles) Tcw = (Tc - 5) K.
properties responding to the shear conditions present at the point of formation. The composition-time profiles show a small increase in solids content with time as deposition continues. This is consistent with the above observation, because the depositinterface temperature will increase as the deposit is formed, and the solids content of freshly formed gel will increase to match the shear conditions. There is little change after the asymptotic level of deposition is reached, indicating that little aging occurs in the gels over the time scale of the experiments. The time taken to reach the asymptotic composition took approximately 12 h for all PPP concentrations studied. Meaningful comparisons of fouling rates were not readily accessible from these deposit mass studies, because each
(34) Bott, R. T.; Gudmundsson, J. S. Deposition of paraffin wax from kerosene in cooled heat exchanger tubes. Can. J. Chem. Eng. 1977, 55, 381–385. (35) Singh, P.; Venkatesan, R.; Fogler, H. S. Formation and aging of incipient thin film wax-oil gels. AIChE J. 2000, 46 (5), 1059–1073. (36) Singh, P.; Venkatesan, R.; Fogler, H. S. Morphological evaluation of thick wax Deposits during aging. AIChE J. 2001, 47 (1), 1–18.
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Figure 16. Effect of the can rotational speed on the fouling behavior of 10 wt % PPP solutions: (a) mass of deposit and (b) solids content of PPP in the gel deposit. Conditions: Tcw = (Tc - 5) K and Tb = 50 C. (Black squares) 3 rpm, (gray squares) 33 rpm, and (white squares) 60 rpm.
Figure 17. Analysis of deposits recovered from disc after fouling 10 wt % PPP at 60 rpm and Ts = Tc -15: (a) SEM and (b) WAXS spectrum.
shows major peaks at 2γ ∼19, 22.5, and 23.2, indicative of the β polymorph.37 Persson23 reported this polymorph to be triclinic (i.e., platelet) and highly ordered, able to pack tightly in the crystal structure. Many of the deposits formed at 3 rpm were noticeably less firm, and this was confirmed by oscillatory rheometry. Figure 18 presents the results from testing many of the deposits generated using 10 wt % solutions alongside those obtained for “fresh” gels obtained by cooling model solutions for 2 min. Individual stress sweeps for deposit gels were similar to Figure 5b, except for the gels formed at 3 rpm and 2 C and Tc - 15, where the viscous modulus, G00 , was noticeably smaller than G0 across the range of shear stresses. These gels also featured lower solids content and lower G0 values than other gels formed at the same temperature and higher rotational speeds. Figure 18a shows the increase in G0 and τy, with increasing solids content expected for suspensions and reported for wax gels by Jennings and Weispfenning.10 The 33 and 60 rpm data lie together (along with the 3 rpm/(Tc - 5) data); within this group, a deposit formed at higher ωd and similar temperatures exhibited greater stiffness/strength. The 3 rpm and 2 C and Tc - 15 gels lie outside this cluster, owing to their lower solids content, but it is possible that they follow the same trend. The τy values obtained for the deposits are similar (and even larger) than those reported by Venkatesan et al.32 They observed that the shear strength depended upon both the shear stress applied during formation and the cooling rate, often with a maximum at an intermediate value of shear stress. These aspects were not explored further here, but our results confirm that the nature of the fouling deposit in this model system is sensitive to these factors.
investigation of the effects of the temperature and flow rate on model wax fouling using an annular flow loop system. Although there was a general decrease in the mass of deposit in their annular heat exchanger system, there was a general increase in wax content with the flow rate. Similar trends were observed by Fitzgerald et al.;7 fluid velocity had a noticeably smaller effect than the temperature and concentration. Sawtooth behavior, which they reported, was not observed in these tests. Extending this study to higher or periodic shear stress conditions would help to elucidate the onset of such behavior. Deposit Nature. Scanning electron microscopy of deposits, such as Figure 17a, showed that the PPP was crystallizing in the form of platelets and forming a porous open matrix, as reported by Fitzgerald et al.7 Particle size analysis of diluted samples by laser scattering regularly indicated a trimodal distribution in volume distribution, with peaks at 8, 20, and 35 μm, which was not consistent with the SEM images. This discrepancy reflects the inability of laser scattering, as an inverse method, to describe the platelet shape adequately. Both results confirm that the fat crystals were non-spherical, and their rheology is therefore expected to be non-Newtonian at lower concentrations than would be expected for suspensions of spherical particles. X-ray analysis did not show any variation in the PPP polymorph across the range of experimental tests. The WAXS spectrum in Figure 17b is a typical example and (37) Gwie, C. G.; Griffiths, R. J.; Cooney, D. T.; Johns, M. L.; Wilson, D. I. Microstructures formed by spray freezing of food fats. J. Am. Oil Chem. Soc. 2006, 83, 1053–1062.
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in a noncrystallizing solvent. The results obtained were mostly consistent with those obtained for the model solution by Fitzgerald et al.,7 although sawtooth behavior was not observed in this work. Fouling behavior, as measured by the rate or amount accumulated over time, was dominated by surface temperature and solution composition (via the degree of precipitative subcooling). The disc rotation speed had a marked influence on the composition and structure of the gel formed, as indicated by its composition and rheology. The results confirm the importance of the temperature and shear conditions on gelation in these systems, consistent with observations in related studies of wax deposition from crude oils. Acknowledgment. A studentship from the Association of Commonwealth Universities (U.K.), additional financial support from the Papua New Guinea University of Technology, and funding for Y.M.J.C. from the Royal Academy of Engineering are gratefully acknowledged. Construction of the SDA was supported by a Food Processing Faraday Fast Track grant and performed by Andrew Hubbard. We also thank Dr. Cesar Berrueco (Imperial College, London, U.K.) for his assistance with the GC results.
Nomenclature Cp = specific heat capacity (J kg-1 K-1) Cf = Fanning friction factor g = gravitational constant (m/s2) G0 = storage modulus (Pa) G00 = loss modulus (Pa) h = heat-transfer coefficient (W m-2 K-1) K = consistency index (s2) mf = mass of deposit (kg) n = flow index p = pressure (Pa) q = heat flux (W/m2) r = radial coordinate R = thermal resistance (m2 K W-1) Rer = Reynolds number based on the radius of the rotating disc t = time (s) T = temperature (C or K) ΔT = temperature difference / driving force (K) u = mean velocity (m/s) U, Uo = overall heat-transfer coefficient, initial value (W m-2 K-1) v = velocity vector (m/s) z = axial coordinate
Figure 18. Oscillatory rheometry of recovered deposits alongside gels formed from solution (labeled “static”): (a) storage modulus (open symbols) and yield stress (filled symbols) versus gel composition and (b) correlation between the storage modulus and critical stress.
Fouling deposits obtained from tests on 5 and 2 wt % solutions were not tested; this will be explored in future work. The G0 -τy correlation plot in Figure 18b also suggests that the 3 rpm gels belong to the same family, albeit with a much weaker structure. In all cases, however, the deposit gels exhibit larger G0 and τy values than the “fresh” gels, which is consistent with the lack of shear ordering and aging in the latter samples.
Greek Symbols δ = thickness (m) γ = angle of incidence in X-ray microscopy (deg) γ_ = shear rate (s-1) λ = thermal conductivity (W m-1 K-1) μ = dynamic viscosity (kg m-1 s-1) θ = azimuthal coordinate F = density (kg/m3) τ = shear stress (Pa) ω = rotational speed (rad/s)
Conclusions A novel SDA has been developed for studying freezing fouling behavior. The device operated reliably over experimental time scales and, particularly with the addition of heat flux monitoring, offers a useful variety of data. CFD simulations of heat transfer in the laminar regime showed good agreement with experimental data, allowing the conditions on the surface to be estimated with some confidence. Application of the SDA to freezing fouling on 316 SS surfaces was demonstrated with model solutions of PPP
Subscripts app = apparent b = bulk 6144
Energy Fuels 2009, 23, 6131–6145
: DOI:10.1021/ef900668f
Nigo et al.
c = cloud point cw = coolant d = disc else = everything else apart from bulk exp = experiment high = high low = low m = melting point mag = magnet p = precipitative subcooling s = surface
sim = simulation ss,out = outer surface of stainless-steel disc w = combined setup of brass, heat flux sensor, and stainless steel y = critical yield stress Acronyms CFD = computational fluid dynamics FEM = finite element method SDA = spinning disc apparatus PPP = Tripalmitin
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